A stochastic approach to chemical evolution

International Nuclear Information System (INIS)

Copi, C.J.

1997-01-01

Observations of elemental abundances in the Galaxy have repeatedly shown an intrinsic scatter as a function of time and metallicity. The standard approach to chemical evolution does not attempt to address this scatter in abundances since only the mean evolution is followed. In this work, the scatter is addressed via a stochastic approach to solving chemical evolution models. Three simple chemical evolution scenarios are studied using this stochastic approach: a closed box model, an infall model, and an outflow model. These models are solved for the solar neighborhood in a Monte Carlo fashion. The evolutionary history of one particular region is determined randomly based on the star formation rate and the initial mass function. Following the evolution in an ensemble of such regions leads to the predicted spread in abundances expected, based solely on different evolutionary histories of otherwise identical regions. In this work, 13 isotopes are followed, including the light elements, the CNO elements, a few α-elements, and iron. It is found that the predicted spread in abundances for a 10 5 M circle-dot region is in good agreement with observations for the α-elements. For CN, the agreement is not as good, perhaps indicating the need for more physics input for low-mass stellar evolution. Similarly for the light elements, the predicted scatter is quite small, which is in contradiction to the observations of 3 He in HII regions. The models are tuned for the solar neighborhood so that good agreement with HII regions is not expected. This has important implications for low-mass stellar evolution and on using chemical evolution to determine the primordial light-element abundances in order to test big bang nucleosynthesis. copyright 1997 The American Astronomical Society

Left passage probability of Schramm-Loewner Evolution

Science.gov (United States)

Najafi, M. N.

2013-06-01

SLE(κ,ρ⃗) is a variant of Schramm-Loewner Evolution (SLE) which describes the curves which are not conformal invariant, but are self-similar due to the presence of some other preferred points on the boundary. In this paper we study the left passage probability (LPP) of SLE(κ,ρ⃗) through field theoretical framework and find the differential equation governing this probability. This equation is numerically solved for the special case κ=2 and hρ=0 in which hρ is the conformal weight of the boundary changing (bcc) operator. It may be referred to loop erased random walk (LERW) and Abelian sandpile model (ASM) with a sink on its boundary. For the curve which starts from ξ0 and conditioned by a change of boundary conditions at x0, we find that this probability depends significantly on the factor x0-ξ0. We also present the perturbative general solution for large x0. As a prototype, we apply this formalism to SLE(κ,κ-6) which governs the curves that start from and end on the real axis.

Stochastic quantization and gauge invariance

International Nuclear Information System (INIS)

Viana, R.L.

1987-01-01

A survey of the fundamental ideas about Parisi-Wu's Stochastic Quantization Method, with applications to Scalar, Gauge and Fermionic theories, is done. In particular, the Analytic Stochastic Regularization Scheme is used to calculate the polarization tensor for Quantum Electrodynamics with Dirac bosons or Fermions. The regularization influence is studied for both theories and an extension of this method for some supersymmetrical models is suggested. (author)

Almost Periodic Solutions for Impulsive Fractional Stochastic Evolution Equations

Directory of Open Access Journals (Sweden)

Toufik Guendouzi

2014-08-01

Full Text Available In this paper, we consider the existence of square-mean piecewise almost periodic solutions for impulsive fractional stochastic evolution equations involving Caputo fractional derivative. The main results are obtained by means of the theory of operators semi-group, fractional calculus, fixed point technique and stochastic analysis theory and methods adopted directly from deterministic fractional equations. Some known results are improved and generalized.

Evolution and mass extinctions as lognormal stochastic processes

Science.gov (United States)

Maccone, Claudio

2014-10-01

In a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely called Evo-SETI. The relevant mathematical tools are: (1) Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black-Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing or, more rarely, decreasing exponential function of the time. (2) The probability distributions known as b-lognormals, i.e. lognormals starting at a certain positive instant b>0 rather than at the origin. These b-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (Peak-Locus theorem). In the framework of Darwinian Evolution, the resulting mathematical construction was shown to be what evolutionary biologists call Cladistics. (3) The (Shannon) entropy of such b-lognormals is then seen to represent the `degree of progress' reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, human history may then be cast into the language of b-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller `chaos'), and have their peaks on the increasing GBM exponential. This exponential is thus the `trend of progress' in human history. (4) All these results also match with SETI in that the statistical Drake equation (generalization of the ordinary Drake equation to encompass statistics) leads just to the lognormal distribution as the probability distribution for the number of extra

Invariant submanifold flows

Energy Technology Data Exchange (ETDEWEB)

Olver, Peter J [School of Mathematics, University of Minnesota, Minneapolis, MN 55455 (United States)], E-mail: olver@math.umn.edu

2008-08-29

Given a Lie group acting on a manifold, our aim is to analyze the evolution of differential invariants under invariant submanifold flows. The constructions are based on the equivariant method of moving frames and the induced invariant variational bicomplex. Applications to integrable soliton dynamics, and to the evolution of differential invariant signatures, used in equivalence problems and object recognition and symmetry detection in images, are discussed.

Stochastic quantization and gauge theories

International Nuclear Information System (INIS)

Kolck, U. van.

1987-01-01

Stochastic quantization is presented taking the Flutuation-Dissipation Theorem as a guide. It is shown that the original approach of Parisi and Wu to gauge theories fails to give the right results to gauge invariant quantities when dimensional regularization is used. Although there is a simple solution in an abelian theory, in the non-abelian case it is probably necessary to start from a BRST invariant action instead of a gauge invariant one. Stochastic regularizations are also discussed. (author) [pt

Stochastic geometry of critical curves, Schramm-Loewner evolutions and conformal field theory

International Nuclear Information System (INIS)

Gruzberg, Ilya A

2006-01-01

Conformally invariant curves that appear at critical points in two-dimensional statistical mechanics systems and their fractal geometry have received a lot of attention in recent years. On the one hand, Schramm (2000 Israel J. Math. 118 221 (Preprint math.PR/9904022)) has invented a new rigorous as well as practical calculational approach to critical curves, based on a beautiful unification of conformal maps and stochastic processes, and by now known as Schramm-Loewner evolution (SLE). On the other hand, Duplantier (2000 Phys. Rev. Lett. 84 1363; Fractal Geometry and Applications: A Jubilee of Benot Mandelbrot: Part 2 (Proc. Symp. Pure Math. vol 72) (Providence, RI: American Mathematical Society) p 365 (Preprint math-ph/0303034)) has applied boundary quantum gravity methods to calculate exact multifractal exponents associated with critical curves. In the first part of this paper, I provide a pedagogical introduction to SLE. I present mathematical facts from the theory of conformal maps and stochastic processes related to SLE. Then I review basic properties of SLE and provide practical derivation of various interesting quantities related to critical curves, including fractal dimensions and crossing probabilities. The second part of the paper is devoted to a way of describing critical curves using boundary conformal field theory (CFT) in the so-called Coulomb gas formalism. This description provides an alternative (to quantum gravity) way of obtaining the multifractal spectrum of critical curves using only traditional methods of CFT based on free bosonic fields

Identification of invariant measures of interacting systems

International Nuclear Information System (INIS)

Chen Jinwen

2004-01-01

In this paper we provide an approach for identifying certain mixture representations of some invariant measures of interacting stochastic systems. This is related to the problem of ergodicity of certain extremal invariant measures that are translation invariant. Corresponding to these, results concerning the existence of invariant measures and certain weak convergence of the systems are also provided

Weak Galilean invariance as a selection principle for coarse-grained diffusive models.

Science.gov (United States)

Cairoli, Andrea; Klages, Rainer; Baule, Adrian

2018-05-29

How does the mathematical description of a system change in different reference frames? Galilei first addressed this fundamental question by formulating the famous principle of Galilean invariance. It prescribes that the equations of motion of closed systems remain the same in different inertial frames related by Galilean transformations, thus imposing strong constraints on the dynamical rules. However, real world systems are often described by coarse-grained models integrating complex internal and external interactions indistinguishably as friction and stochastic forces. Since Galilean invariance is then violated, there is seemingly no alternative principle to assess a priori the physical consistency of a given stochastic model in different inertial frames. Here, starting from the Kac-Zwanzig Hamiltonian model generating Brownian motion, we show how Galilean invariance is broken during the coarse-graining procedure when deriving stochastic equations. Our analysis leads to a set of rules characterizing systems in different inertial frames that have to be satisfied by general stochastic models, which we call "weak Galilean invariance." Several well-known stochastic processes are invariant in these terms, except the continuous-time random walk for which we derive the correct invariant description. Our results are particularly relevant for the modeling of biological systems, as they provide a theoretical principle to select physically consistent stochastic models before a validation against experimental data.

Time evolution of one-dimensional gapless models from a domain wall initial state: stochastic Loewner evolution continued?

International Nuclear Information System (INIS)

Calabrese, Pasquale; Hagendorf, Christian; Doussal, Pierre Le

2008-01-01

We study the time evolution of quantum one-dimensional gapless systems evolving from initial states with a domain wall. We generalize the path integral imaginary time approach that together with boundary conformal field theory allows us to derive the time and space dependence of general correlation functions. The latter are explicitly obtained for the Ising universality class, and the typical behavior of one- and two-point functions is derived for the general case. Possible connections with the stochastic Loewner evolution are discussed and explicit results for one-point time dependent averages are obtained for generic κ for boundary conditions corresponding to stochastic Loewner evolution. We use this set of results to predict the time evolution of the entanglement entropy and obtain the universal constant shift due to the presence of a domain wall in the initial state

On the boundary behavior of left-invariant Hitchin and hypo flows

DEFF Research Database (Denmark)

Belgun, Florin; Cortés, Vicente; Freibert, Marco

2015-01-01

We investigate left-invariant Hitchin and hypo flows on 5-, 6- and 7-dimensional Lie groups. They provide Riemannian cohomogeneity-one manifolds of one dimension higher with holonomy contained in SU(3), G2 and Spin(7), respectively, which are in general geodesically incomplete. Generalizing results...... of Conti, we prove that for large classes of solvable Lie groups G these manifolds cannot be completed: a complete Riemannian manifold with parallel SU(3)-, G2- or Spin(7)-structure which is of cohomogeneity one with respect to G is flat, and has no singular orbits. We furthermore classify, on the non...

The Pathwise Numerical Approximation of Stationary Solutions of Semilinear Stochastic Evolution Equations

International Nuclear Information System (INIS)

Caraballo, T.; Kloeden, P.E.

2006-01-01

Under a one-sided dissipative Lipschitz condition on its drift, a stochastic evolution equation with additive noise of the reaction-diffusion type is shown to have a unique stochastic stationary solution which pathwise attracts all other solutions. A similar situation holds for each Galerkin approximation and each implicit Euler scheme applied to these Galerkin approximations. Moreover, the stationary solution of the Euler scheme converges pathwise to that of the Galerkin system as the stepsize tends to zero and the stationary solutions of the Galerkin systems converge pathwise to that of the evolution equation as the dimension increases. The analysis is carried out on random partial and ordinary differential equations obtained from their stochastic counterparts by subtraction of appropriate Ornstein-Uhlenbeck stationary solutions

Discrete changes of current statistics in periodically driven stochastic systems

International Nuclear Information System (INIS)

Chernyak, Vladimir Y; Sinitsyn, N A

2010-01-01

We demonstrate that the counting statistics of currents in periodically driven ergodic stochastic systems can show sharp changes of some of its properties in response to continuous changes of the driving protocol. To describe this effect, we introduce a new topological phase factor in the evolution of the moment generating function which is akin to the topological geometric phase in the evolution of a periodically driven quantum mechanical system with time-reversal symmetry. This phase leads to the prediction of a sign change for the difference of the probabilities to find even and odd numbers of particles transferred in a stochastic system in response to cyclic evolution of control parameters. The driving protocols that lead to this sign change should enclose specific degeneracy points in the space of control parameters. The relation between the topology of the paths in the control parameter space and the sign changes can be described in terms of the first Stiefel–Whitney class of topological invariants. (letter)

A stochastic version of the Price equation reveals the interplay of deterministic and stochastic processes in evolution

Directory of Open Access Journals (Sweden)

Rice Sean H

2008-09-01

Full Text Available Abstract Background Evolution involves both deterministic and random processes, both of which are known to contribute to directional evolutionary change. A number of studies have shown that when fitness is treated as a random variable, meaning that each individual has a distribution of possible fitness values, then both the mean and variance of individual fitness distributions contribute to directional evolution. Unfortunately the most general mathematical description of evolution that we have, the Price equation, is derived under the assumption that both fitness and offspring phenotype are fixed values that are known exactly. The Price equation is thus poorly equipped to study an important class of evolutionary processes. Results I present a general equation for directional evolutionary change that incorporates both deterministic and stochastic processes and applies to any evolving system. This is essentially a stochastic version of the Price equation, but it is derived independently and contains terms with no analog in Price's formulation. This equation shows that the effects of selection are actually amplified by random variation in fitness. It also generalizes the known tendency of populations to be pulled towards phenotypes with minimum variance in fitness, and shows that this is matched by a tendency to be pulled towards phenotypes with maximum positive asymmetry in fitness. This equation also contains a term, having no analog in the Price equation, that captures cases in which the fitness of parents has a direct effect on the phenotype of their offspring. Conclusion Directional evolution is influenced by the entire distribution of individual fitness, not just the mean and variance. Though all moments of individuals' fitness distributions contribute to evolutionary change, the ways that they do so follow some general rules. These rules are invisible to the Price equation because it describes evolution retrospectively. An equally general

Stochastic evolutions and hadronization of highly excited hadronic matter

International Nuclear Information System (INIS)

Carruthers, P.

1984-01-01

Stochastic ingredients of high energy hadronic collisions are analyzed, with emphasis on multiplicity distributions. The conceptual simplicity of the k-cell negative binomial distribution is related to the evolution of probability distributions via the Fokker-Planck and related equations. The connection to underlying field theory ideas is sketched. 17 references

On Continuous Selection Sets of Non-Lipschitzian Quantum Stochastic Evolution Inclusions

Directory of Open Access Journals (Sweden)

Sheila Bishop

2015-01-01

Full Text Available We establish existence of a continuous selection of multifunctions associated with quantum stochastic evolution inclusions under a general Lipschitz condition. The coefficients here are multifunctions but not necessarily Lipschitz.

Time-reversal invariance in multiple collisions between coupled masses

International Nuclear Information System (INIS)

Crawford, F.S.

1989-01-01

The time evolution of two mechanical oscillators coupled by a spring can (but need not) exhibit an instant t = 2t' when the initial conditions at t = 0 have been exactly restored. When that is the case, then at t = t' energy and momentum have been exchanged exactly as in an elastic collision between two free particles, and the evolution of the system from t = t' to 2t' is related to that from 0 to t' by time-reversal invariance. A similar ''simulation of elastic scattering'' at t = t' can occur for two free particles coupled via collisions with an intermediary mass that bounces back and forth between the two particles provided the intermediary is left at rest at t = t'. Examined here is the time evolution of the exchange of momentum and energy for these two examples, determining the values of the coupling spring constant (or mass value) of the intermediating spring (or mass) needed to simulate single elastic scattering between free particles, and looking at the manifestation of time-reversal invariance

Stochastic evolution of the Universe: A possible dynamical process ...

Indian Academy of Sciences (India)

C Sivakumar

2017-12-11

Dec 11, 2017 ... https://doi.org/10.1007/s12043-017-1491-z. Stochastic evolution of the Universe: A possible dynamical process leading to fractal structures. C SIVAKUMAR. Department of Physics, Maharaja's College, Ernakulam 682 011, India. E-mail: thrisivc@yahoo.com. MS received 6 July 2016; revised 26 June 2017; ...

The Dynamical Invariant of Open Quantum System

OpenAIRE

Wu, S. L.; Zhang, X. Y.; Yi, X. X.

2015-01-01

The dynamical invariant, whose expectation value is constant, is generalized to open quantum system. The evolution equation of dynamical invariant (the dynamical invariant condition) is presented for Markovian dynamics. Different with the dynamical invariant for the closed quantum system, the evolution of the dynamical invariant for the open quantum system is no longer unitary, and the eigenvalues of it are time-dependent. Since any hermitian operator fulfilling dynamical invariant condition ...

Calibration of a stochastic health evolution model using NHIS data

Science.gov (United States)

Gupta, Aparna; Li, Zhisheng

2011-10-01

This paper presents and calibrates an individual's stochastic health evolution model. In this health evolution model, the uncertainty of health incidents is described by a stochastic process with a finite number of possible outcomes. We construct a comprehensive health status index (HSI) to describe an individual's health status, as well as a health risk factor system (RFS) to classify individuals into different risk groups. Based on the maximum likelihood estimation (MLE) method and the method of nonlinear least squares fitting, model calibration is formulated in terms of two mixed-integer nonlinear optimization problems. Using the National Health Interview Survey (NHIS) data, the model is calibrated for specific risk groups. Longitudinal data from the Health and Retirement Study (HRS) is used to validate the calibrated model, which displays good validation properties. The end goal of this paper is to provide a model and methodology, whose output can serve as a crucial component of decision support for strategic planning of health related financing and risk management.

Coordinate invariance in stochastic singular optics

CSIR Research Space (South Africa)

Roux, FS

2013-11-01

Full Text Available The study of optical vortices in stochastic optical fields involves various quantities, including the vortex density and topological charge density, that are defined in terms of local expectation values of the distributions of optical vortices...

Stochastic star formation and the evolution of galaxies

International Nuclear Information System (INIS)

Seiden, P.E.; Schulman, L.S.; Gerola, H.

1979-01-01

The mechanism of stochastic self-propagating star formation has previously been invoked to explain the origin of spiral arms in galaxies. In this paper we extend the application of this mechanism to account for the diversity of morphological types and the evolution of galaxies. The new property that arises from consideration of this mechanism is that the rate of star formation exhibits the critical behavior of a phase transition. This is a general property of the system and is not strongly dependent on the details of the star--interstellar gas interaction. Examination of the properties of this phase transition provides a general scenario for the evolution of galaxies and the origin of the various morphological types

Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves

DEFF Research Database (Denmark)

Eldeberky, Y.; Madsen, Per A.

1999-01-01

and stochastic formulations are solved numerically for the case of cross shore motion of unidirectional waves and the results are verified against laboratory data for wave propagation over submerged bars and over a plane slope. Outside the surf zone the two model predictions are generally in good agreement......This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary...... is significantly underestimated for larger wave numbers. In the present work we correct this inconsistency. In addition to the improved deterministic formulation, we present improved stochastic evolution equations in terms of the energy spectrum and the bispectrum for multidirectional waves. The deterministic...

Stochasticity and transport in Hamiltonian systems

International Nuclear Information System (INIS)

MacKay, R.S.; Meiss, J.D.; Percival, I.C.

1983-08-01

The theory of transport in nonlinear dynamics is developed in terms of leaky barriers which remain when invariant tori are destroyed. We describe the organization of stochastic motion by these barriers and give an explanation of long-time correlations in the stochastic regime

Exact many-body dynamics with stochastic one-body density matrix evolution

International Nuclear Information System (INIS)

Lacroix, D.

2004-05-01

In this article, we discuss some properties of the exact treatment of the many-body problem with stochastic Schroedinger equation (SSE). Starting from the SSE theory, an equivalent reformulation is proposed in terms of quantum jumps in the density matrix space. The technical details of the derivation a stochastic version of the Liouville von Neumann equation are given. It is shown that the exact Many-Body problem could be replaced by an ensemble of one-body density evolution, where each density matrix evolves according to its own mean-field augmented by a one-body noise. (author)

Environmental Noise Could Promote Stochastic Local Stability of Behavioral Diversity Evolution

Science.gov (United States)

Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi

2018-05-01

In this Letter, we investigate stochastic stability in a two-phenotype evolutionary game model for an infinite, well-mixed population undergoing discrete, nonoverlapping generations. We assume that the fitness of a phenotype is an exponential function of its expected payoff following random pairwise interactions whose outcomes randomly fluctuate with time. We show that the stochastic local stability of a constant interior equilibrium can be promoted by the random environmental noise even if the system may display a complicated nonlinear dynamics. This result provides a new perspective for a better understanding of how environmental fluctuations may contribute to the evolution of behavioral diversity.

Quantum dynamical time evolutions as stochastic flows on phase space

International Nuclear Information System (INIS)

Combe, P.; Rodriguez, R.; Guerra, F.; Sirigue, M.; Sirigue-Collin, M.

1984-01-01

We are mainly interested in describing the time development of the Wigner functions by means of stochastic processes. In the second section we recall the main properties of the Wigner functions as well as those of their Fourier transform. In the next one we derive the evolution equation of these functions for a class of Hamiltonians and we give a probabilistic expression for the solution of these equations by means of a stochastic flow in phase space which reminds of the classical flows. In the last section we remark that the previously defined flow can be extended to the bounded continuous functions on phase space and that this flow conserves the cone generated by the Wigner functions. (orig./HSI)

Possible description of domain walls in two-dimensional spin glasses by stochastic Loewner evolutions

International Nuclear Information System (INIS)

Bernard, Denis; Le Doussal, Pierre; Middleton, A. Alan

2007-01-01

Domain walls for spin glasses are believed to be scale invariant; a stronger symmetry, conformal invariance, has the potential to hold. The statistics of zero-temperature Ising spin glass domain walls in two dimensions are used to test the hypothesis that these domain walls are described by a Schramm-Loewner evolution SLE κ . Multiple tests are consistent with SLE κ , where κ=2.32±0.08. Both conformal invariance and the domain Markov property are tested. The latter does not hold in small systems, but detailed numerical evidence suggests that it holds in the continuum limit

Left Right Patterning, Evolution and Cardiac Development

Science.gov (United States)

Dykes, Iain M.

2018-01-01

Many aspects of heart development are determined by the left right axis and as a result several congenital diseases have their origins in aberrant left-right patterning. Establishment of this axis occurs early in embryogenesis before formation of the linear heart tube yet impacts upon much later morphogenetic events. In this review I discuss the differing mechanisms by which left-right polarity is achieved in the mouse and chick embryos and comment on the evolution of this system. I then discus three major classes of cardiovascular defect associated with aberrant left-right patterning seen in mouse mutants and human disease. I describe phenotypes associated with the determination of atrial identity and venous connections, looping morphogenesis of the heart tube and finally the asymmetric remodelling of the embryonic branchial arch arterial system to form the leftward looped arch of aorta and associated great arteries. Where appropriate, I consider left right patterning defects from an evolutionary perspective, demonstrating how developmental processes have been modified in species over time and illustrating how comparative embryology can aide in our understanding of congenital heart disease. PMID:29755990

Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation

International Nuclear Information System (INIS)

Caraballo, Tomas; Kloeden, Peter E.; Schmalfuss, Bjoern

2004-01-01

We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of anon-trivial stationary solution which is exponentially stable, where the stationary solution is generated by the composition of a random variable and the Wiener shift. We also construct stationary solutions with the stronger property of attracting bounded sets uniformly. The existence of these stationary solutions follows from the theory of random dynamical systems and their attractors. In addition, we prove some perturbation results and formulate conditions for the existence of stationary solutions for semilinear stochastic partial differential equations with Lipschitz continuous non-linearities

Continuum modeling of ion-beam eroded surfaces under normal incidence: Impact of stochastic fluctuations

International Nuclear Information System (INIS)

Dreimann, Karsten; Linz, Stefan J.

2010-01-01

Graphical abstract: Deterministic surface pattern (left) and its stochastic counterpart (right) arising in a stochastic damped Kuramoto-Sivashinsky equation that serves as a model equation for ion-beam eroded surfaces and is systematically investigated. - Abstract: Using a recently proposed field equation for the surface evolution of ion-beam eroded semiconductor target materials under normal incidence, we systematically explore the impact of additive stochastic fluctuations that are permanently present during the erosion process. Specifically, we investigate the dependence of the surface roughness, the underlying pattern forming properties and the bifurcation behavior on the strength of the fluctuations.

Stochastic transformation of points in polygons according to the Voronoi tessellation: microstructural description.

Science.gov (United States)

Di Vito, Alessia; Fanfoni, Massimo; Tomellini, Massimo

2010-12-01

Starting from a stochastic two-dimensional process we studied the transformation of points in disks and squares following a protocol according to which at any step the island size increases proportionally to the corresponding Voronoi tessera. Two interaction mechanisms among islands have been dealt with: coalescence and impingement. We studied the evolution of the island density and of the island size distribution functions, in dependence on island collision mechanisms for both Poissonian and correlated spatial distributions of points. The island size distribution functions have been found to be invariant with the fraction of transformed phase for a given stochastic process. The n(Θ) curve describing the island decay has been found to be independent of the shape (apart from high correlation degrees) and interaction mechanism.

Superfield formulation of stochastic quantization for gauge theories

International Nuclear Information System (INIS)

Egoryan, Ed.Sh.; Manvelian, R.P.

1990-01-01

Using gauge symmetry localization relative to superspace coordinates an extended stochastic action for the Yang-Mills field possessing supergauge invariance is obtained. This allows to formulate correctly a mechanism of stochastic reduction for gauge theories beyond the framework of perturbation theory. 12 refs

Analytic stochastic regularization in QCD and its supersymmetric extension

International Nuclear Information System (INIS)

Abdalla, E.; Vianna, R.L.

1987-08-01

We outline some features of stochastic quantization and regularization of fermionic fields with applications to spinor QCD, showing the appearence of a non-gauge invariant counterterm. We also show that non-invariant terms cancel in supersymmetric multiplets. (Author) [pt

Analytic stochastic regularization: gauge and supersymmetry theories

International Nuclear Information System (INIS)

Abdalla, M.C.B.

1988-01-01

Analytic stochastic regularization for gauge and supersymmetric theories is considered. Gauge invariance in spinor and scalar QCD is verified to brak fown by an explicit one loop computation of the two, theree and four point vertex function of the gluon field. As a result, non gauge invariant counterterms must be added. However, in the supersymmetric multiplets there is a cancellation rendering the counterterms gauge invariant. The calculation is considered at one loop order. (author) [pt

Constructing conditionally integrable evolution systems in (1+1) dimensions: a generalization of invariant modules approach

International Nuclear Information System (INIS)

Sergyeyev, A.

2002-01-01

Given a generalized (Lie-Baecklund) vector field satisfying certain nondegeneracy assumptions, we explicitly describe all (1+1)-dimensional evolution systems that admit this vector field as a generalized conditional symmetry. The connection with the theory of symmetries of systems of ODEs and with the theory of invariant modules is discussed. (author)

Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime

Directory of Open Access Journals (Sweden)

Gianluca Calcagni

2017-10-01

Full Text Available We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.

Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime

International Nuclear Information System (INIS)

Calcagni, Gianluca; Ronco, Michele

2017-01-01

We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow) and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales) and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.

Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime

Science.gov (United States)

Calcagni, Gianluca; Ronco, Michele

2017-10-01

We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow) and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales) and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.

Stochastic quantization of field theories on the lattice and supersymmetrical models

International Nuclear Information System (INIS)

Aldazabal, Gerardo.

1984-01-01

Several aspects of the stochastic quantization method are considered. Specifically, field theories on the lattice and supersymmetrical models are studied. A non-linear sigma model is studied firstly, and it is shown that it is possible to obtain evolution equations written directly for invariant quantities. These ideas are generalized to obtain Langevin equations for the Wilson loops of non-abelian lattice gauge theories U (N) and SU (N). In order to write these equations, some different ways of introducing the constraints which the fields must satisfy are discussed. It is natural to have a strong coupling expansion in these equations. The correspondence with quantum field theory is established, and it is noticed that at all orders in the perturbation theory, Langevin equations reduce to Schwinger-Dyson equations. From another point of view, stochastic quantization is applied to large N matrix models on the lattice. As a result, a simple and systematic way of building reduced models is found. Referring to stochastic quantization in supersymmetric theories, a simple supersymmetric model is studied. It is shown that it is possible to write an evolution equation for the superfield wich leads to quantum field theory results in equilibrium. As the Langevin equation preserves supersymmetry, the property of dimensional reduction known for the quantum model is shown to be valid at all times. (M.E.L.) [es

Stochastic Optimal Prediction with Application to Averaged Euler Equations

Energy Technology Data Exchange (ETDEWEB)

Bell, John [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Chorin, Alexandre J. [Univ. of California, Berkeley, CA (United States); Crutchfield, William [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

2017-04-24

Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is approximated by its conditional expectation with respect to the invariant measure. In higher-order OP, unresolved information is approximated by a stochastic estimator, leading to a system of random or stochastic differential equations. We explain the ideas through a simple example, and then apply them to the solution of Averaged Euler equations in two space dimensions.

Propagator of stochastic electrodynamics

International Nuclear Information System (INIS)

Cavalleri, G.

1981-01-01

The ''elementary propagator'' for the position of a free charged particle subject to the zero-point electromagnetic field with Lorentz-invariant spectral density proportionalω 3 is obtained. The nonstationary process for the position is solved by the stationary process for the acceleration. The dispersion of the position elementary propagator is compared with that of quantum electrodynamics. Finally, the evolution of the probability density is obtained starting from an initial distribution confined in a small volume and with a Gaussian distribution in the velocities. The resulting probability density for the position turns out to be equal, to within radiative corrections, to psipsi* where psi is the Kennard wave packet. If the radiative corrections are retained, the present result is new since the corresponding expression in quantum electrodynamics has not yet been found. Besides preceding quantum electrodynamics for this problem, no renormalization is required in stochastic electrodynamics

Analytic stochastic regularization and gauge theories

International Nuclear Information System (INIS)

Abdalla, E.; Gomes, M.; Lima-Santos, A.

1987-04-01

We prove that analytic stochatic regularization braks gauge invariance. This is done by an explicit one loop calculation of the two three and four point vertex functions of the gluon field in scalar chromodynamics, which turns out not to be geuge invariant. We analyse the counter term structure, Langevin equations and the construction of composite operators in the general framework of stochastic quantization. (author) [pt

Dynamics of the stochastic Lorenz chaotic system with long memory effects

Energy Technology Data Exchange (ETDEWEB)

Zeng, Caibin, E-mail: zeng.cb@mail.scut.edu.cn; Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Mathematics, South China University of Technology, Guangzhou 510640 (China)

2015-12-15

Little seems to be known about the ergodic dynamics of stochastic systems with fractional noise. This paper is devoted to discern such long time dynamics through the stochastic Lorenz chaotic system (SLCS) with long memory effects. By a truncation technique, the SLCS is proved to generate a continuous stochastic dynamical system Λ. Based on the Krylov-Bogoliubov criterion, the required Lyapunov function is further established to ensure the existence of the invariant measure of Λ. Meanwhile, the uniqueness of the invariant measure of Λ is proved by examining the strong Feller property, together with an irreducibility argument. Therefore, the SLCS has exactly one adapted stationary solution.

Analysis of stochastic effects in Kaldor-type business cycle discrete model

Science.gov (United States)

Bashkirtseva, Irina; Ryashko, Lev; Sysolyatina, Anna

2016-07-01

We study nonlinear stochastic phenomena in the discrete Kaldor model of business cycles. A numerical parametric analysis of stochastically forced attractors (equilibria, closed invariant curves, discrete cycles) of this model is performed using the stochastic sensitivity functions technique. A spatial arrangement of random states in stochastic attractors is modeled by confidence domains. The phenomenon of noise-induced transitions ;chaos-order; is discussed.

Stochastic Evolution Dynamic of the Rock-Scissors-Paper Game Based on a Quasi Birth and Death Process.

Science.gov (United States)

Yu, Qian; Fang, Debin; Zhang, Xiaoling; Jin, Chen; Ren, Qiyu

2016-06-27

Stochasticity plays an important role in the evolutionary dynamic of cyclic dominance within a finite population. To investigate the stochastic evolution process of the behaviour of bounded rational individuals, we model the Rock-Scissors-Paper (RSP) game as a finite, state dependent Quasi Birth and Death (QBD) process. We assume that bounded rational players can adjust their strategies by imitating the successful strategy according to the payoffs of the last round of the game, and then analyse the limiting distribution of the QBD process for the game stochastic evolutionary dynamic. The numerical experiments results are exhibited as pseudo colour ternary heat maps. Comparisons of these diagrams shows that the convergence property of long run equilibrium of the RSP game in populations depends on population size and the parameter of the payoff matrix and noise factor. The long run equilibrium is asymptotically stable, neutrally stable and unstable respectively according to the normalised parameters in the payoff matrix. Moreover, the results show that the distribution probability becomes more concentrated with a larger population size. This indicates that increasing the population size also increases the convergence speed of the stochastic evolution process while simultaneously reducing the influence of the noise factor.

Deterministic and stochastic analysis of size effects and damage evolution in quasi-brittle materials

NARCIS (Netherlands)

Gutiérrez, M.A.; Borst, R. de

1999-01-01

This study presents some recent results on damage evolution in quasi-brittle materials including stochastic imperfections. The material strength is described as a random field and coupled to the response. The most probable configurations of imperfections leading to failure are sought by means of an

Change of adiabatic invariant near the separatrix

International Nuclear Information System (INIS)

Bulanov, S.V.

1995-10-01

The properties of particle motion in the vicinity of the separatrix in a phase plane are investigated. The change of adiabatic invariant value due to the separatrix crossing is evaluated as a function of a perturbation parameter magnitude and a phase of a particle for time dependent Hamiltonians. It is demonstrated that the change of adiabatic invariant value near the separatrix birth is much larger than that in the case of the separatrix crossing near the saddle point in a phase plane. The conditions of a stochastic regime to appear around the separatrix are found. The results are applied to study the longitudinal invariant behaviour of charged particles near singular lines of the magnetic field. (author). 22 refs, 9 figs

Stochastic evolution of refractory interstellar dust during the chemical evolution of a two-phase interstellar medium

International Nuclear Information System (INIS)

Liffman, K.; Clayton, D.D.

1989-01-01

The evolution course of refractory interstellar dust during the chemical evolution of a two-phase interstellar medium (ISM) is studied using a simple model of the chemical evolution of ISM. It is assumed that, in this medium, the stars are born in molecular clouds, but new nucleosynthesis products and stellar return are entered into a complementary diffuse medium; the well-mixed matter of each interstellar phase is repeatedly cycled stochastically through the complementary phase and back. The dust is studied on a particle-by-particle bases as it is sputtered by shock waves in the diffuse medium, accretes an amorphous mantle of gaseous refractory atoms while its local medium joins the molecular cloud medium, and encounters the possibility of astration within molecular clouds. Results are presented relevant to the size spectrum of accreted mantles, its age spectrum and the distinction among its several lifetimes, depletion factors of refractory atoms in the diffuse gas, and isotopic anomalies. 26 refs

The propagator of stochastic electrodynamics

Science.gov (United States)

Cavalleri, G.

1981-01-01

The "elementary propagator" for the position of a free charged particle subject to the zero-point electromagnetic field with Lorentz-invariant spectral density ~ω3 is obtained. The nonstationary process for the position is solved by the stationary process for the acceleration. The dispersion of the position elementary propagator is compared with that of quantum electrodynamics. Finally, the evolution of the probability density is obtained starting from an initial distribution confined in a small volume and with a Gaussian distribution in the velocities. The resulting probability density for the position turns out to be equal, to within radiative corrections, to ψψ* where ψ is the Kennard wave packet. If the radiative corrections are retained, the present result is new since the corresponding expression in quantum electrodynamics has not yet been found. Besides preceding quantum electrodynamics for this problem, no renormalization is required in stochastic electrodynamics.

Homogenization of the evolution Stokes equation in a perforated domain with a stochastic Fourier boundary condition

KAUST Repository

Bessaih, Hakima; Efendiev, Yalchin; Maris, Florin

2015-01-01

The evolution Stokes equation in a domain containing periodically distributed obstacles subject to Fourier boundary condition on the boundaries is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior

Asymmetrical Damage Partitioning in Bacteria: A Model for the Evolution of Stochasticity, Determinism, and Genetic Assimilation.

Science.gov (United States)

Chao, Lin; Rang, Camilla Ulla; Proenca, Audrey Menegaz; Chao, Jasper Ubirajara

2016-01-01

Non-genetic phenotypic variation is common in biological organisms. The variation is potentially beneficial if the environment is changing. If the benefit is large, selection can favor the evolution of genetic assimilation, the process by which the expression of a trait is transferred from environmental to genetic control. Genetic assimilation is an important evolutionary transition, but it is poorly understood because the fitness costs and benefits of variation are often unknown. Here we show that the partitioning of damage by a mother bacterium to its two daughters can evolve through genetic assimilation. Bacterial phenotypes are also highly variable. Because gene-regulating elements can have low copy numbers, the variation is attributed to stochastic sampling. Extant Escherichia coli partition asymmetrically and deterministically more damage to the old daughter, the one receiving the mother's old pole. By modeling in silico damage partitioning in a population, we show that deterministic asymmetry is advantageous because it increases fitness variance and hence the efficiency of natural selection. However, we find that symmetrical but stochastic partitioning can be similarly beneficial. To examine why bacteria evolved deterministic asymmetry, we modeled the effect of damage anchored to the mother's old pole. While anchored damage strengthens selection for asymmetry by creating additional fitness variance, it has the opposite effect on symmetry. The difference results because anchored damage reinforces the polarization of partitioning in asymmetric bacteria. In symmetric bacteria, it dilutes the polarization. Thus, stochasticity alone may have protected early bacteria from damage, but deterministic asymmetry has evolved to be equally important in extant bacteria. We estimate that 47% of damage partitioning is deterministic in E. coli. We suggest that the evolution of deterministic asymmetry from stochasticity offers an example of Waddington's genetic assimilation

Asymmetrical Damage Partitioning in Bacteria: A Model for the Evolution of Stochasticity, Determinism, and Genetic Assimilation.

Directory of Open Access Journals (Sweden)

Lin Chao

2016-01-01

Full Text Available Non-genetic phenotypic variation is common in biological organisms. The variation is potentially beneficial if the environment is changing. If the benefit is large, selection can favor the evolution of genetic assimilation, the process by which the expression of a trait is transferred from environmental to genetic control. Genetic assimilation is an important evolutionary transition, but it is poorly understood because the fitness costs and benefits of variation are often unknown. Here we show that the partitioning of damage by a mother bacterium to its two daughters can evolve through genetic assimilation. Bacterial phenotypes are also highly variable. Because gene-regulating elements can have low copy numbers, the variation is attributed to stochastic sampling. Extant Escherichia coli partition asymmetrically and deterministically more damage to the old daughter, the one receiving the mother's old pole. By modeling in silico damage partitioning in a population, we show that deterministic asymmetry is advantageous because it increases fitness variance and hence the efficiency of natural selection. However, we find that symmetrical but stochastic partitioning can be similarly beneficial. To examine why bacteria evolved deterministic asymmetry, we modeled the effect of damage anchored to the mother's old pole. While anchored damage strengthens selection for asymmetry by creating additional fitness variance, it has the opposite effect on symmetry. The difference results because anchored damage reinforces the polarization of partitioning in asymmetric bacteria. In symmetric bacteria, it dilutes the polarization. Thus, stochasticity alone may have protected early bacteria from damage, but deterministic asymmetry has evolved to be equally important in extant bacteria. We estimate that 47% of damage partitioning is deterministic in E. coli. We suggest that the evolution of deterministic asymmetry from stochasticity offers an example of Waddington

Phenomenological and ratio bifurcations of a class of discrete time stochastic processes

NARCIS (Netherlands)

Diks, C.G.H.; Wagener, F.O.O.

2011-01-01

Zeeman proposed a classification of stochastic dynamical systems based on the Morse classification of their invariant probability densities; the associated bifurcations are the ‘phenomenological bifurcations’ of L. Arnold. The classification is however not invariant under diffeomorphisms of the

Quantum Ito's formula and stochastic evolutions

International Nuclear Information System (INIS)

Hudson, R.L.; Parthasarathy, K.R.

1984-01-01

Using only the Boson canonical commutation relations and the Riemann-Lebesgue integral we construct a simple theory of stochastic integrals and differentials with respect to the basic field operator processes. This leads to a noncommutative Ito product formula, a realisation of the classical Poisson process in Fock space which gives a noncommutative central limit theorem, the construction of solutions of certain noncommutative stochastic differential equations, and finally to the integration of certain irreversible equations of motion governed by semigroups of completely positive maps. The classical Ito product formula for stochastic differentials with respect to Brownian motion and the Poisson process is a special case. (orig.)

Inviscid limit of stochastic damped 2D Navier–Stokes equations

International Nuclear Information System (INIS)

Bessaih, Hakima; Ferrario, Benedetta

2014-01-01

We consider the inviscid limit of the stochastic damped 2D Navier–Stokes equations. We prove that, when the viscosity vanishes, the stationary solution of the stochastic damped Navier–Stokes equations converges to a stationary solution of the stochastic damped Euler equation and that the rate of dissipation of enstrophy converges to zero. In particular, this limit obeys an enstrophy balance. The rates are computed with respect to a limit measure of the unique invariant measure of the stochastic damped Navier–Stokes equations. (paper)

Stochastic Stabilityfor Contracting Lorenz Maps and Flows

Science.gov (United States)

Metzger, R. J.

In a previous work [M], we proved the existence of absolutely continuous invariant measures for contracting Lorenz-like maps, and constructed Sinai-Ruelle-Bowen measures f or the flows that generate them. Here, we prove stochastic stability for such one-dimensional maps and use this result to prove that the corresponding flows generating these maps are stochastically stable under small diffusion-type perturbations, even though, as shown by Rovella [Ro], they are persistent only in a measure theoretical sense in a parameter space. For the one-dimensional maps we also prove strong stochastic stability in the sense of Baladi and Viana[BV].

Emergence of fractal scale-free networks from stochastic evolution on the Cayley tree

Energy Technology Data Exchange (ETDEWEB)

Chełminiak, Przemysław, E-mail: geronimo@amu.edu.pl

2013-11-29

An unexpected recognition of fractal topology in some real-world scale-free networks has evoked again an interest in the mechanisms stimulating their evolution. To explain this phenomenon a few models of a deterministic construction as well as a probabilistic growth controlled by a tunable parameter have been proposed so far. A quite different approach based on the fully stochastic evolution of the fractal scale-free networks presented in this Letter counterpoises these former ideas. It is argued that the diffusive evolution of the network on the Cayley tree shapes its fractality, self-similarity and the branching number criticality without any control parameter. The last attribute of the scale-free network is an intrinsic property of the skeleton, a special type of spanning tree which determines its fractality.

Renormalization of an abelian gauge theory in stochastic quantization

International Nuclear Information System (INIS)

Chaturvedi, S.; Kapoor, A.K.; Srinivasan, V.

1987-01-01

The renormalization of an abelian gauge field coupled to a complex scalar field is discussed in the stochastic quantization method. The super space formulation of the stochastic quantization method is used to derive the Ward Takahashi identities associated with supersymmetry. These Ward Takahashi identities together with previously derived Ward Takahashi identities associated with gauge invariance are shown to be sufficient to fix all the renormalization constants in terms of scaling of the fields and of the parameters appearing in the stochastic theory. (orig.)

Transport near the onset of stochasticity

Energy Technology Data Exchange (ETDEWEB)

Meiss, J D

1986-01-01

For two-degree-of-freedom Hamiltonians (e.g., a particle in a 2-D potential or the flow of magnetic-field lines), an invariant torus in phase space acts as an absolute barrier for trajectories. When an invariant torus is destroyed by perturbation, a remnant remains with gaps. This 'cantorus' forms a formidable barrier even well into the stochastic regime. We show that correlation functions decay algebraically, invalidating the common assumptions of chaos. The decay rate is given by a universal exponent, obtained from self-similar scaling.

Second-order gauge-invariant perturbations during inflation

International Nuclear Information System (INIS)

Finelli, F.; Marozzi, G.; Vacca, G. P.; Venturi, G.

2006-01-01

The evolution of gauge invariant second-order scalar perturbations in a general single field inflationary scenario are presented. Different second-order gauge-invariant expressions for the curvature are considered. We evaluate perturbatively one of these second order curvature fluctuations and a second-order gauge-invariant scalar field fluctuation during the slow-roll stage of a massive chaotic inflationary scenario, taking into account the deviation from a pure de Sitter evolution and considering only the contribution of super-Hubble perturbations in mode-mode coupling. The spectra resulting from their contribution to the second order quantum correlation function are nearly scale-invariant, with additional logarithmic corrections with respect to the first order spectrum. For all scales of interest the amplitude of these spectra depends on the total number of e-folds. We find, on comparing first and second order perturbation results, an upper limit to the total number of e-folds beyond which the two orders are comparable

Transport near the onset of stochasticity

International Nuclear Information System (INIS)

Meiss, J.D.

1985-05-01

For two-degree-of-freedom Hamiltonians, (e.g., a particle in a 2-D potential or the flow of magnetic field lines) an invariant torus in phase space acts as an absolute barrier for trajectories. When an invariant torus is destroyed by a perturbation, a remnant remains with gaps. This ''cantorus'' forms a formidable barrier even well into the stochastic regime. We show that correlation functions decay algebraically invalidating the common assumptions of chaos. The decay rate is given by a universal exponent, obtained from self-similar scaling

Complexity, rate of energy exchanges and stochasticity

International Nuclear Information System (INIS)

Casartelli, M.; Sello, S.

1987-01-01

The complexity of trajectories in the phase of anharmonic crystal (mostly a Lennard-Jones chain) is analysed by the variance of microcanonical density and by new parameters P and chi defined, respectively, as the mean value of the time averages and the relative variance of the absolute exchange rate of energies among the normal modes. Evidence is given to the trapping action of residual invariant surfaces in low stochastic regime of motion. The parameter chi, moreover, proves efficient in exploring the border of stochasticity. A simple power law for P vs. the specific energy is obtained and proved to be independent of stochasticity and of the type of anharmonic potential

Convergence and Consistency Analysis for A 3D Invariant-EKF SLAM

OpenAIRE

Zhang, Teng; Wu, Kanzhi; Song, Jingwei; Huang, Shoudong; Dissanayake, Gamini

2017-01-01

In this paper, we investigate the convergence and consistency properties of an Invariant-Extended Kalman Filter (RI-EKF) based Simultaneous Localization and Mapping (SLAM) algorithm. Basic convergence properties of this algorithm are proven. These proofs do not require the restrictive assumption that the Jacobians of the motion and observation models need to be evaluated at the ground truth. It is also shown that the output of RI-EKF is invariant under any stochastic rigid body transformation...

Stochastic processes

CERN Document Server

Borodin, Andrei N

2017-01-01

This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times. Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.

Stochastic quantization and gauge-fixing of the linearized gravitational field

International Nuclear Information System (INIS)

Hueffel, H.; Rumpf, H.

1984-01-01

Due to the indefiniteness of the Euclidean gravitational action the Parisi-Wu stochastic quantization scheme fails in the case of the gravitational field. Therefore we apply a recently proposed modification of stochastic quantization that works in Minkowski space and preserves all the advantages of the original Parisi-Wu method; in particular no gauge-fixing is required. Additionally stochastic gauge-fixing may be introduced and is also studied in detail. The graviton propagators obtained with and without stochastic gauge-fixing all exhibit a noncausal contribution, but apart from this effect the gauge-invariant quantities are the same as those of standard quantization. (Author)

Stochastic catastrophe theory and instabilities in plasma turbulence

International Nuclear Information System (INIS)

Rajkovic, Milan; Skoric, Milos

2009-01-01

Full text: A Langevin equation (LE) describing evolution of turbulence amplitude in plasma is analyzed from the aspect of stochastic catastrophe theory (SCT) so that turbulent plasma is considered as a stochastic gradient system. According to SCT the dynamics of the system is completely determined by the stochastic potential function and the maximum likelihood estimates of stable and unstable equilibria are associated with the modes and anti-modes, respectively, of the system's stationary probability density function. First order phase transitions occur at degenerate equilibrium points and the potential function at these points may be represented in a generic way. Since the diffusion function of plasma LE is not constant the probability density function (pdf) is not a reliable estimator of the number of stable states. We show that the generalized pdf represented as the product of the stationary pdf and the diffusion function is a reliable estimator of the stable states and that it can be evaluated from the zero mean crossing analysis of plasma turbulence signal. Stochastic bifurcations, and particularly the sudden (catastrophic) ones, are recognized from the pdf's obtained by the zero crossing analysis and we illustrate the applications of SCT in plasma turbulence on data obtained from the MAST (Mega Ampere Spherical Tokamak) for low (L), high (H) and unstable dithering (L/H) confinement regimes. The relationship of the transformation invariant zero-crossing function and SCT is shown to provide important information about the nature of edge localized modes (ELMs) and L-H transition. Finally we show that ELMs occur as a result of catastrophic (hard) bifurcations ruling out the self-organized criticality scenario for their origin. (author)

Space-time-modulated stochastic processes

Science.gov (United States)

Giona, Massimiliano

2017-10-01

Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.

Random function representation of stationary stochastic vector processes for probability density evolution analysis of wind-induced structures

Science.gov (United States)

Liu, Zhangjun; Liu, Zenghui

2018-06-01

This paper develops a hybrid approach of spectral representation and random function for simulating stationary stochastic vector processes. In the proposed approach, the high-dimensional random variables, included in the original spectral representation (OSR) formula, could be effectively reduced to only two elementary random variables by introducing the random functions that serve as random constraints. Based on this, a satisfactory simulation accuracy can be guaranteed by selecting a small representative point set of the elementary random variables. The probability information of the stochastic excitations can be fully emerged through just several hundred of sample functions generated by the proposed approach. Therefore, combined with the probability density evolution method (PDEM), it could be able to implement dynamic response analysis and reliability assessment of engineering structures. For illustrative purposes, a stochastic turbulence wind velocity field acting on a frame-shear-wall structure is simulated by constructing three types of random functions to demonstrate the accuracy and efficiency of the proposed approach. Careful and in-depth studies concerning the probability density evolution analysis of the wind-induced structure have been conducted so as to better illustrate the application prospects of the proposed approach. Numerical examples also show that the proposed approach possesses a good robustness.

Fast stochastic algorithm for simulating evolutionary population dynamics

Science.gov (United States)

Tsimring, Lev; Hasty, Jeff; Mather, William

2012-02-01

Evolution and co-evolution of ecological communities are stochastic processes often characterized by vastly different rates of reproduction and mutation and a coexistence of very large and very small sub-populations of co-evolving species. This creates serious difficulties for accurate statistical modeling of evolutionary dynamics. In this talk, we introduce a new exact algorithm for fast fully stochastic simulations of birth/death/mutation processes. It produces a significant speedup compared to the direct stochastic simulation algorithm in a typical case when the total population size is large and the mutation rates are much smaller than birth/death rates. We illustrate the performance of the algorithm on several representative examples: evolution on a smooth fitness landscape, NK model, and stochastic predator-prey system.

Conformally invariant processes in the plane

International Nuclear Information System (INIS)

Lawler, G.F.

2004-01-01

These lectures will focus on recent rigorous work on continuum limits of planar lattice models from statistical physics at criticality. For an introduction, I would like to discuss the general problem of critical exponents and scaling limits for lattice models in equilibrium statistical mechanics. There are a number of models, [e.g., self-avoiding walk (polymers), percolation, loop-erased random walk (uniform spanning trees, domino tilings), Ising model, Potts model, nonintersecting simple random walks] that fall under this general framework. These lectures will consider the case d = 2. Mathematicians are now starting to understand rigorously the scaling limit of two-dimensional systems. For most of these models, the general strategy can be described as: Construct possible continuum limits for these models. Show that there are only a limited number of such limits that are conformally invariant. Prove that the lattice model approaches the continuum limit. We should think of the first step as being similar for all of these models. We will spend the next couple of lectures discussing the continuum limits. One example you should already know - the scaling limit of simple random walk is Brownian motion (which in two dimensions is conformally invariant). The important new ideas are restriction measures and stochastic Loewner evolution (SLE). The later lectures will discuss rigorous results about lattice models approaching the continuum limit - we will discuss nonintersecting random walks (which can be shown to be equivalent to problems about exceptional sets of Brownian paths), percolation on the triangular lattice, and the loop-erased random walk. As a rule, the methods used for the second step are particular to each model

EXPONENTIAL ERGODICITY FOR STOCHASTIC BURGERS AND 2D NAVIER-STOKES EQUATIONS

CERN Document Server

Goldys, B

2004-01-01

It is shown that transition measures of the stochastic Navier-Stokes equation in dimension 2 converge exponentially fast to the corresponding invariant measures in the distance of total variation. As a corollary we obtain the existence of spectral gap for a related semigroup obtained by a sort of ground state trasformation. Analogous results are proved for the stochastic Burgers equation.

Homogenization of the evolution Stokes equation in a perforated domain with a stochastic Fourier boundary condition

KAUST Repository

Bessaih, Hakima

2015-04-01

The evolution Stokes equation in a domain containing periodically distributed obstacles subject to Fourier boundary condition on the boundaries is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the obstacles. We represent the solid obstacles by holes in the fluid domain. The macroscopic (homogenized) equation is derived as another stochastic partial differential equation, defined in the whole non perforated domain. Here, the initial stochastic perturbation on the boundary becomes part of the homogenized equation as another stochastic force. We use the twoscale convergence method after extending the solution with 0 in the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. In order to pass to the limit on the boundary integrals, we rewrite them in terms of integrals in the whole domain. In particular, for the stochastic integral on the boundary, we combine the previous idea of rewriting it on the whole domain with the assumption that the Brownian motion is of trace class. Due to the particular boundary condition dealt with, we get that the solution of the stochastic homogenized equation is not divergence free. However, it is coupled with the cell problem that has a divergence free solution. This paper represents an extension of the results of Duan and Wang (Comm. Math. Phys. 275:1508-1527, 2007), where a reaction diffusion equation with a dynamical boundary condition with a noise source term on both the interior of the domain and on the boundary was studied, and through a tightness argument and a pointwise two scale convergence method the homogenized equation was derived. © American Institute of Mathematical Sciences.

Stationary stochastic processes theory and applications

CERN Document Server

Lindgren, Georg

2012-01-01

Some Probability and Process BackgroundSample space, sample function, and observablesRandom variables and stochastic processesStationary processes and fieldsGaussian processesFour historical landmarksSample Function PropertiesQuadratic mean propertiesSample function continuityDerivatives, tangents, and other characteristicsStochastic integrationAn ergodic resultExercisesSpectral RepresentationsComplex-valued stochastic processesBochner's theorem and the spectral distributionSpectral representation of a stationary processGaussian processesStationary counting processesExercisesLinear Filters - General PropertiesLinear time invariant filtersLinear filters and differential equationsWhite noise in linear systemsLong range dependence, non-integrable spectra, and unstable systemsThe ARMA-familyLinear Filters - Special TopicsThe Hilbert transform and the envelopeThe sampling theoremKarhunen-Loève expansionClassical Ergodic Theory and MixingThe basic ergodic theorem in L2Stationarity and transformationsThe ergodic th...

Hamiltonian evolutions of twisted polygons in RPn

International Nuclear Information System (INIS)

Beffa, Gloria Marì; Wang, Jing Ping

2013-01-01

In this paper we find a discrete moving frame and their associated invariants along projective polygons in RP n , and we use them to describe invariant evolutions of projective N-gons. We then apply a reduction process to obtain a natural Hamiltonian structure on the space of projective invariants for polygons, establishing a close relationship between the projective N-gon invariant evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that any Hamiltonian evolution is induced on invariants by an invariant evolution of N-gons—what we call a projective realization—and both evolutions are connected explicitly in a very simple way. Finally, we provide a completely integrable evolution (the Boussinesq lattice related to the lattice W 3 -algebra), its projective realization in RP 2 and its Hamiltonian pencil. We generalize both structures to n-dimensions and we prove that they are Poisson, defining explicitly the n-dimensional generalization of the planar evolution (a discretization of the W n -algebra). We prove that the generalization is completely integrable, and we also give its projective realization, which turns out to be very simple. (paper)

Stochastic space-time and quantum theory

International Nuclear Information System (INIS)

Frederick, C.

1976-01-01

Much of quantum mechanics may be derived if one adopts a very strong form of Mach's principle such that in the absence of mass, space-time becomes not flat, but stochastic. This is manifested in the metric tensor which is considered to be a collection of stochastic variables. The stochastic-metric assumption is sufficient to generate the spread of the wave packet in empty space. If one further notes that all observations of dynamical variables in the laboratory frame are contravariant components of tensors, and if one assumes that a Lagrangian can be constructed, then one can obtain an explanation of conjugate variables and also a derivation of the uncertainty principle. Finally the superposition of stochastic metrics and the identification of root -g in the four-dimensional invariant volume element root -g dV as the indicator of relative probability yields the phenomenon of interference as will be described for the two-slit experiment

The first Donaldson invariant as the winding number of a Nicolai map

International Nuclear Information System (INIS)

Mansfield, P.

1988-01-01

The authors show that the first Donaldson invariant expressed by Witten as the partition function of a relativistic quantum field theory can be interpreted as the winding number of the stochastic map introduced by Nicolai in the context of supersymmetric Yang-Mills theories

Adaptive grid based multi-objective Cauchy differential evolution for stochastic dynamic economic emission dispatch with wind power uncertainty.

Science.gov (United States)

Zhang, Huifeng; Lei, Xiaohui; Wang, Chao; Yue, Dong; Xie, Xiangpeng

2017-01-01

Since wind power is integrated into the thermal power operation system, dynamic economic emission dispatch (DEED) has become a new challenge due to its uncertain characteristics. This paper proposes an adaptive grid based multi-objective Cauchy differential evolution (AGB-MOCDE) for solving stochastic DEED with wind power uncertainty. To properly deal with wind power uncertainty, some scenarios are generated to simulate those possible situations by dividing the uncertainty domain into different intervals, the probability of each interval can be calculated using the cumulative distribution function, and a stochastic DEED model can be formulated under different scenarios. For enhancing the optimization efficiency, Cauchy mutation operation is utilized to improve differential evolution by adjusting the population diversity during the population evolution process, and an adaptive grid is constructed for retaining diversity distribution of Pareto front. With consideration of large number of generated scenarios, the reduction mechanism is carried out to decrease the scenarios number with covariance relationships, which can greatly decrease the computational complexity. Moreover, the constraint-handling technique is also utilized to deal with the system load balance while considering transmission loss among thermal units and wind farms, all the constraint limits can be satisfied under the permitted accuracy. After the proposed method is simulated on three test systems, the obtained results reveal that in comparison with other alternatives, the proposed AGB-MOCDE can optimize the DEED problem while handling all constraint limits, and the optimal scheme of stochastic DEED can decrease the conservation of interval optimization, which can provide a more valuable optimal scheme for real-world applications.

BRS symmetry in stochastic quantization of the gravitational field

International Nuclear Information System (INIS)

Nakazawa, Naohito.

1989-12-01

We study stochastic quantization of gravity in terms of a BRS invariant canonical operator formalism. By introducing artificially canonical momentum variables for the original field variables, a canonical formulation of stochastic quantization is proposed in a sense that the Fokker-Planck hamiltonian is the generator of the fictitious time translation. Then we show that there exists a nilpotent BRS symmetry in an enlarged phase space for gravity (in general, for the first-class constrained systems). The stochastic action of gravity includes explicitly an unique De Witt's type superspace metric which leads to a geometrical interpretation of quantum gravity analogous to nonlinear σ-models. (author)

Stochastic thermodynamics of quantum maps with and without equilibrium.

Science.gov (United States)

Barra, Felipe; Lledó, Cristóbal

2017-11-01

We study stochastic thermodynamics for a quantum system of interest whose dynamics is described by a completely positive trace-preserving (CPTP) map as a result of its interaction with a thermal bath. We define CPTP maps with equilibrium as CPTP maps with an invariant state such that the entropy production due to the action of the map on the invariant state vanishes. Thermal maps are a subgroup of CPTP maps with equilibrium. In general, for CPTP maps, the thermodynamic quantities, such as the entropy production or work performed on the system, depend on the combined state of the system plus its environment. We show that these quantities can be written in terms of system properties for maps with equilibrium. The relations that we obtain are valid for arbitrary coupling strengths between the system and the thermal bath. The fluctuations of thermodynamic quantities are considered in the framework of a two-point measurement scheme. We derive the entropy production fluctuation theorem for general maps and a fluctuation relation for the stochastic work on a system that starts in the Gibbs state. Some simplifications for the probability distributions in the case of maps with equilibrium are presented. We illustrate our results by considering spin 1/2 systems under thermal maps, nonthermal maps with equilibrium, maps with nonequilibrium steady states, and concatenations of them. Finally, and as an important application, we consider a particular limit in which the concatenation of maps generates a continuous time evolution in Lindblad form for the system of interest, and we show that the concept of maps with and without equilibrium translates into Lindblad equations with and without quantum detailed balance, respectively. The consequences for the thermodynamic quantities in this limit are discussed.

MAIT, MR1, microbes and riboflavin: a paradigm for the co-evolution of invariant TCRs and restricting MHCI-like molecules?

Science.gov (United States)

Mondot, Stanislas; Boudinot, Pierre; Lantz, Olivier

2016-08-01

MAIT cells express an invariant TCR that recognizes non-peptidic microbial antigens presented by the non-polymorphic MHCI-like molecule, MR1. We briefly describe how the antigens recognized by MAIT cells are generated from an unstable precursor of the riboflavin (Vitamin B2) biosynthesis pathway, as well as the main features of MAIT cells in comparison with other related T cell subsets. In silico analysis of bacterial genomes shows that the riboflavin biosynthesis pathway is highly prevalent in all groups of Prokaryotes with, however, notable exceptions. We discuss the putative functions and the evolution of the MAIT/MR1 couple: it appeared in the ancestors of mammals and is highly conserved across this group, but was independently lost in three orders. We describe the four instances of known invariant TCR and MHC-I-like molecules encountered in Vertebrates. Both T cells bearing semi-invariant TCR and the associated, evolutionarily conserved MHC-I related molecules have been found in mammals or in amphibians, which suggests that other MHC1-like/invariant TCR couples might be present in other classes of Vertebrates to detect generic microbial compounds. This allows us to discuss how the recognition of riboflavin precursor derivatives by the MAIT TCR may be a way to detect invasive microbes in specific organs, and may epitomize other invariant T cell systems across vertebrates.

Size Evolution and Stochastic Models: Explaining Ostracod Size through Probabilistic Distributions

Science.gov (United States)

Krawczyk, M.; Decker, S.; Heim, N. A.; Payne, J.

2014-12-01

The biovolume of animals has functioned as an important benchmark for measuring evolution throughout geologic time. In our project, we examined the observed average body size of ostracods over time in order to understand the mechanism of size evolution in these marine organisms. The body size of ostracods has varied since the beginning of the Ordovician, where the first true ostracods appeared. We created a stochastic branching model to create possible evolutionary trees of ostracod size. Using stratigraphic ranges for ostracods compiled from over 750 genera in the Treatise on Invertebrate Paleontology, we calculated overall speciation and extinction rates for our model. At each timestep in our model, new lineages can evolve or existing lineages can become extinct. Newly evolved lineages are assigned sizes based on their parent genera. We parameterized our model to generate neutral and directional changes in ostracod size to compare with the observed data. New sizes were chosen via a normal distribution, and the neutral model selected new sizes differentials centered on zero, allowing for an equal chance of larger or smaller ostracods at each speciation. Conversely, the directional model centered the distribution on a negative value, giving a larger chance of smaller ostracods. Our data strongly suggests that the overall direction of ostracod evolution has been following a model that directionally pushes mean ostracod size down, shying away from a neutral model. Our model was able to match the magnitude of size decrease. Our models had a constant linear decrease while the actual data had a much more rapid initial rate followed by a constant size. The nuance of the observed trends ultimately suggests a more complex method of size evolution. In conclusion, probabilistic methods can provide valuable insight into possible evolutionary mechanisms determining size evolution in ostracods.

Mean Square Synchronization of Stochastic Nonlinear Delayed Coupled Complex Networks

Directory of Open Access Journals (Sweden)

Chengrong Xie

2013-01-01

Full Text Available We investigate the problem of adaptive mean square synchronization for nonlinear delayed coupled complex networks with stochastic perturbation. Based on the LaSalle invariance principle and the properties of the Weiner process, the controller and adaptive laws are designed to ensure achieving stochastic synchronization and topology identification of complex networks. Sufficient conditions are given to ensure the complex networks to be mean square synchronization. Furthermore, numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.

Field transformations, collective coordinates and BRST invariance

International Nuclear Information System (INIS)

Alfaro, J.; Damgaard, P.H.

1989-12-01

A very large class of general field transformations can be viewed as a field theory generalization of the method of collective coordinates. The introduction of new variables induces a gauge invariance in the transformed theory, and the freedom left in gauge fixing this new invariance can be used to find equivalent formulations of the same theory. First the Batalin-Fradkin-Vilkovisky formalism is applied to the Hamiltonian formulation of physical systems that can be described in terms of collective coordinates. We then show how this type of collective coordinate scheme can be generalized to field transformations, and discuss the War Identities of the associated BRST invariance. For Yang-Mills theory a connection to topological field theory and the background field method is explained in detail. In general the resulting BRST invariance we find hidden in any quantum field theory can be viewed as a consequence of our freedom in choosing a basis of coordinates φ(χ) in the action S[φ]. (orig.)

Hybrid Semantics of Stochastic Programs with Dynamic Reconfiguration

Directory of Open Access Journals (Sweden)

Alberto Policriti

2009-10-01

Full Text Available We begin by reviewing a technique to approximate the dynamics of stochastic programs --written in a stochastic process algebra-- by a hybrid system, suitable to capture a mixed discrete/continuous evolution. In a nutshell, the discrete dynamics is kept stochastic while the continuous evolution is given in terms of ODEs, and the overall technique, therefore, naturally associates a Piecewise Deterministic Markov Process with a stochastic program. The specific contribution in this work consists in an increase of the flexibility of the translation scheme, obtained by allowing a dynamic reconfiguration of the degree of discreteness/continuity of the semantics. We also discuss the relationships of this approach with other hybrid simulation strategies for biochemical systems.

Perturbation theory for continuous stochastic equations

International Nuclear Information System (INIS)

Chechetkin, V.R.; Lutovinov, V.S.

1987-01-01

The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probability distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes, stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion-controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and non-equilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered. (author)

Yang-Mills theory on a momentum lattice: Gauge invariance, chiral invariance, and no fermion doubling

International Nuclear Information System (INIS)

Berube, D.; Kroeger, H.; Lafrance, R.; Marleau, L.

1991-01-01

We discuss properties of a noncompact formulation of gauge theories with fermions on a momentum (k) lattice. (a) This formulation is suitable to build in Fourier acceleration in a direct way. (b) The numerical effort to compute the action (by fast Fourier transform) goes essentially like logV with the lattice volume V. (c) For the Yang-Mills theory we find that the action conserves gauge symmetry and chiral symmetry in a weak sense: On a finite lattice the action is invariant under infinitesimal transformations with compact support. Under finite transformations these symmetries are approximately conserved and they are restored on an infinite lattice and in the continuum limit. Moreover, these symmetries also hold on a finite lattice under finite transformations, if the classical fields, instead of being c-number valued, take values from a finite Galois field. (d) There is no fermion doubling. (e) For the φ 4 model we investigate the transition towards the continuum limit in lattice perturbation theory up to second order. We compute the two- and four-point functions and find local and Lorentz-invariant results. (f) In QED we compute a one-loop vacuum polarization and find in the continuum limit the standard result. (g) As a numerical application, we compute the propagator left-angle φ(k)φ(k')right-angle in the φ 4 model, investigate Euclidean invariance, and extract m R as well as Z R . Moreover we compute left-angle F μν (k)F μν (k')right-angle in the SU(2) model

On the physical realizability of quantum stochastic walks

Science.gov (United States)

Taketani, Bruno; Govia, Luke; Schuhmacher, Peter; Wilhelm, Frank

Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The recently developed quantum stochastic walk combines the concepts of a quantum walk and a classical random walk through open system evolution of a quantum system, and have been shown to have applications in as far reaching fields as artificial intelligence. However, nature puts significant constraints on the kind of open system evolutions that can be realized in a physical experiment. In this work, we discuss the restrictions on the allowed open system evolution, and the physical assumptions underpinning them. We then introduce a way to circumvent some of these restrictions, and simulate a more general quantum stochastic walk on a quantum computer, using a technique we call quantum trajectories on a quantum computer. We finally describe a circuit QED approach to implement discrete time quantum stochastic walks.

HOMOCLINIC TANGLE BIFURCATIONS AND EDGE STOCHASTICITY IN DIVERTED TOKAMAKS

International Nuclear Information System (INIS)

EVANS, T.E.; ROEDER, R.K.W.; CARTER, J.A.; RAPOPORT, B.I.

2003-01-01

OAK-B135 The boundary and pedestal region of a poloidally diverted tokamak is particularly susceptible to the onset of vacuum magnetic field stochasticity due to small non-axisymmetric resonant perturbations. Recent calculations of the separatrix topology in diverted tokamaks, when subjected to small magnetic perturbations, show the existence of complex invariant manifold structures known as homoclinic tangles. These structures appear above a relatively low perturbation threshold that depends on certain equilibrium shape parameters. Homoclinic tangles represent a splitting of the unperturbed separatrix into stable and unstable invariant manifolds associated with each X-point (hyperbolic point). The manifolds that make up homoclinic tangles set the boundaries that prescribe how stochastic field line trajectories are organized i.e., how field lines from the inner domain of the unperturbed separatrix mix and are transported to plasma facing surfaces such as divertor target plates and protruding baffle structures. Thus, the topology of these tangles determines which plasma facing components are most likely to interact with escaping magnetic field lines and the parallel heat and particle flux they carry

On left (θ,ϕ-derivations in BCI-algebras

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G. Muhiuddin

2014-07-01

Full Text Available The notion of (regular left (θ,ϕ-derivations of a BCI-algebra is introduced, some useful examples are discussed, and related properties are investigated. Conditions for a left (θ,ϕ-derivation to be regular are provided. The concepts of a d(θ,ϕ-invariant left (θ,ϕ-derivation and θ-ideal are introduced, and their relations are discussed. Furthermore, some more interesting results are established.

On the Stochastic Wave Equation with Nonlinear Damping

International Nuclear Information System (INIS)

Kim, Jong Uhn

2008-01-01

We discuss an initial boundary value problem for the stochastic wave equation with nonlinear damping. We establish the existence and uniqueness of a solution. Our method for the existence of pathwise solutions consists of regularization of the equation and data, the Galerkin approximation and an elementary measure-theoretic argument. We also prove the existence of an invariant measure when the equation has pure nonlinear damping

Do stochastic inhomogeneities affect dark-energy precision measurements?

Science.gov (United States)

Ben-Dayan, I; Gasperini, M; Marozzi, G; Nugier, F; Veneziano, G

2013-01-11

The effect of a stochastic background of cosmological perturbations on the luminosity-redshift relation is computed to second order through a recently proposed covariant and gauge-invariant light-cone averaging procedure. The resulting expressions are free from both ultraviolet and infrared divergences, implying that such perturbations cannot mimic a sizable fraction of dark energy. Different averages are estimated and depend on the particular function of the luminosity distance being averaged. The energy flux being minimally affected by perturbations at large z is proposed as the best choice for precision estimates of dark-energy parameters. Nonetheless, its irreducible (stochastic) variance induces statistical errors on Ω(Λ)(z) typically lying in the few-percent range.

Do stochastic inhomogeneities affect dark-energy precision measurements?

CERN Document Server

Ben-Dayan, Ido; Marozzi, Giovanni; Nugier, Fabien; Veneziano, Gabriele

2013-01-01

The effect of a stochastic background of cosmological perturbations on the luminosity-redshift relation is computed to second order through a recently proposed covariant and gauge-invariant light-cone averaging procedure. The resulting expressions are free from both ultraviolet and infrared divergences, implying that such perturbations cannot mimic a sizable fraction of dark energy. Different averages are estimated and depend on the particular function of the luminosity distance being averaged. The energy flux, being minimally affected by perturbations at large z, is proposed as the best choice for precision estimates of dark-energy parameters. Nonetheless, its irreducible (stochastic) variance induces statistical errors on \\Omega_{\\Lambda}(z) typically lying in the few-percent range.

The Apparent Lack of Lorentz Invariance in Zero-Point Fields with Truncated Spectra

Directory of Open Access Journals (Sweden)

Daywitt W. C.

2009-01-01

Full Text Available The integrals that describe the expectation values of the zero-point quantum-field-theoretic vacuum state are semi-infinite, as are the integrals for the stochastic electrodynamic vacuum. The unbounded upper limit to these integrals leads in turn to infinite energy densities and renormalization masses. A number of models have been put forward to truncate the integrals so that these densities and masses are finite. Unfortunately the truncation apparently destroys the Lorentz invariance of the integrals. This note argues that the integrals are naturally truncated by the graininess of the negative-energy Planck vacuum state from which the zero-point vacuum arises, and are thus automatically Lorentz invariant.

Stochastic model of Rayleigh-Taylor turbulent mixing

International Nuclear Information System (INIS)

Abarzhi, S.I.; Cadjan, M.; Fedotov, S.

2007-01-01

We propose a stochastic model to describe the random character of the dissipation process in Rayleigh-Taylor turbulent mixing. The parameter alpha, used conventionally to characterize the mixing growth-rate, is not a universal constant and is very sensitive to the statistical properties of the dissipation. The ratio between the rates of momentum loss and momentum gain is the statistic invariant and a robust parameter to diagnose with or without turbulent diffusion accounted for

Mutation, Witten index, and quiver invariant

Energy Technology Data Exchange (ETDEWEB)

Kim, Heeyeon [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, N2L 2Y5, Ontario (Canada); Lee, Seung-Joo [Department of Physics, Robeson Hall, Virginia Tech,Blacksburg, VA 24061 (United States); Yi, Piljin [School of Physics, Korea Institute for Advanced Study,Seoul 130-722 (Korea, Republic of)

2015-07-20

We explore Seiberg-like dualities, or mutations, for N=4 quiver quantum mechanics in the context of wall-crossing. In contrast to higher dimensions, the 1d Seiberg-duality must be performed with much care. With fixed Fayet-Iliopoulos constants, at most two nodes can be mutated, one left and the other right, mapping a chamber of a quiver into a chamber of a mutated quiver. We delineate this complex pattern for triangle quivers and show how the Witten indices are preserved under such finely chosen mutations. On the other hand, the quiver invariants, or wall-crossing-safe part of supersymmetric spectra, mutate more straightforwardly, whereby a quiver is mapped to a quiver. The mutation rule that preserves the quiver invariant is different from the usual one, however, which we explore and confirm numerically.

Mutation, Witten index, and quiver invariant

International Nuclear Information System (INIS)

Kim, Heeyeon; Lee, Seung-Joo; Yi, Piljin

2015-01-01

We explore Seiberg-like dualities, or mutations, for N=4 quiver quantum mechanics in the context of wall-crossing. In contrast to higher dimensions, the 1d Seiberg-duality must be performed with much care. With fixed Fayet-Iliopoulos constants, at most two nodes can be mutated, one left and the other right, mapping a chamber of a quiver into a chamber of a mutated quiver. We delineate this complex pattern for triangle quivers and show how the Witten indices are preserved under such finely chosen mutations. On the other hand, the quiver invariants, or wall-crossing-safe part of supersymmetric spectra, mutate more straightforwardly, whereby a quiver is mapped to a quiver. The mutation rule that preserves the quiver invariant is different from the usual one, however, which we explore and confirm numerically.

Stochastic Eulerian Lagrangian methods for fluid-structure interactions with thermal fluctuations

International Nuclear Information System (INIS)

Atzberger, Paul J.

2011-01-01

We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for operators coupling these descriptions. Stochastic driving fields for the formalism are derived using principles from statistical mechanics. The stochastic differential equations of the formalism are found to exhibit significant stiffness in some physical regimes. To cope with this issue, we derive reduced stochastic differential equations for several physical regimes. We also present stochastic numerical methods for each regime to approximate the fluid-structure dynamics and to generate efficiently the required stochastic driving fields. To validate the methodology in each regime, we perform analysis of the invariant probability distribution of the stochastic dynamics of the fluid-structure formalism. We compare this analysis with results from statistical mechanics. To further demonstrate the applicability of the methodology, we perform computational studies for spherical particles having translational and rotational degrees of freedom. We compare these studies with results from fluid mechanics. The presented approach provides for fluid-structure systems a set of rather general computational methods for treating consistently structure mechanics, hydrodynamic coupling, and thermal fluctuations.

Interpretation of scrape-off layer profile evolution and first-wall ion flux statistics on JET using a stochastic framework based on fillamentary motion

Science.gov (United States)

Walkden, N. R.; Wynn, A.; Militello, F.; Lipschultz, B.; Matthews, G.; Guillemaut, C.; Harrison, J.; Moulton, D.; Contributors, JET

2017-08-01

This paper presents the use of a novel modelling technique based around intermittent transport due to filament motion, to interpret experimental profile and fluctuation data in the scrape-off layer (SOL) of JET during the onset and evolution of a density profile shoulder. A baseline case is established, prior to shoulder formation, and the stochastic model is shown to be capable of simultaneously matching the time averaged profile measurement as well as the PDF shape and autocorrelation function from the ion-saturation current time series at the outer wall. Aspects of the stochastic model are then varied with the aim of producing a profile shoulder with statistical measurements consistent with experiment. This is achieved through a strong localised reduction in the density sink acting on the filaments within the model. The required reduction of the density sink occurs over a highly localised region with the timescale of the density sink increased by a factor of 25. This alone is found to be insufficient to model the expansion and flattening of the shoulder region as the density increases, which requires additional changes within the stochastic model. An example is found which includes both a reduction in the density sink and filament acceleration and provides a consistent match to the experimental data as the shoulder expands, though the uniqueness of this solution can not be guaranteed. Within the context of the stochastic model, this implies that the localised reduction in the density sink can trigger shoulder formation, but additional physics is required to explain the subsequent evolution of the profile.

Stochasticity and the m = 1 mode in tokamaks

International Nuclear Information System (INIS)

Izzo, R.; Monticello, D.A.; Stodiek, W.; Park, W.

1986-05-01

It has recently been proposed that stochasticity resulting from toroidal coupling could lead to a saturation of the m = 1 internal mode in tokamaks. We present results from the nonlinear evolution of the m = 1 mode with toroidal coupling that show that stochasticity is not enough to cause saturation of the m = 1 mode

Hidden invariance of the free classical particle

International Nuclear Information System (INIS)

Garcia, S.

1994-01-01

A formalism describing the dynamics of classical and quantum systems from a group theoretical point of view is presented. We apply it to the simple example of the classical free particle. The Galileo group G is the symmetry group of the free equations of motion. Consideration of the free particle Lagrangian semi-invariance under G leads to a larger symmetry group, which is a central extension of the Galileo group by the real numbers. We study the dynamics associated with this group, and characterize quantities like Noether invariants and evolution equations in terms of group geometric objects. An extension of the Galileo group by U(1) leads to quantum mechanics

Global solvability of the differential operators non-invariants on semi-simple Lie groups

International Nuclear Information System (INIS)

El Hussein, K.

1991-09-01

Let G be a connected semi-simple Lie group with finite centre and let G=KAN be the Iwasawa decomposition of G. Let P be a differential operator on G, which is right invariant by the sub-group AN and left invariant by the sub-group K. In this paper, we give a necessary and sufficient condition for the global solvability of P on G. (author). 5 refs

Viability, invariance and applications

CERN Document Server

Carja, Ovidiu; Vrabie, Ioan I

2007-01-01

The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time.The book includes the most important necessary and sufficient conditions for viability starting with Nagumo's Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In th...

Stochastic simulations for the time evolution of systems which obey generalized statistics: fractional exclusion statistics and Gentile's statistics

International Nuclear Information System (INIS)

Nemnes, G A; Anghel, D V

2010-01-01

We present a stochastic method for the simulation of the time evolution in systems which obey generalized statistics, namely fractional exclusion statistics and Gentile's statistics. The transition rates are derived in the framework of canonical ensembles. This approach introduces a tool for describing interacting fermionic and bosonic systems in non-equilibrium as ideal FES systems, in a computationally efficient manner. The two types of statistics are analyzed comparatively, indicating their intrinsic thermodynamic differences and revealing key aspects related to the species size

Levy-Student processes for a stochastic model of beam halos

Energy Technology Data Exchange (ETDEWEB)

Petroni, N. Cufaro [Department of Mathematics, University of Bari, and INFN Sezione di Bari, via E. Orabona 4, 70125 Bari (Italy)]. E-mail: cufaro@ba.infn.it; De Martino, S. [Department of Physics, University of Salerno, and INFN Sezione di Napoli (gruppo di Salerno), Via S. Allende, I-84081 Baronissi (SA) (Italy); De Siena, S. [Department of Physics, University of Salerno, and INFN Sezione di Napoli (gruppo di Salerno), Via S. Allende, I-84081 Baronissi (SA) (Italy); Illuminati, F. [Department of Physics, University of Salerno, and INFN Sezione di Napoli (gruppo di Salerno), Via S. Allende, I-84081 Baronissi (SA) (Italy)

2006-06-01

We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the stochastic mechanics which produces time reversal invariant diffusion processes. In this paper we analyze the consequences of introducing the generalized Student laws, namely non-Gaussian, Levy infinitely divisible (but not stable) distributions. We will analyze this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) stochastic model is a Student distribution; (b) by supposing that our model is based on a (non-Gaussian) Levy process whose increments are Student distributed. In the case (a) the longer tails of the power decay of the Student laws, and in the case (b) the discontinuities of the Levy-Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams.

Levy-Student processes for a stochastic model of beam halos

International Nuclear Information System (INIS)

Petroni, N. Cufaro; De Martino, S.; De Siena, S.; Illuminati, F.

2006-01-01

We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the stochastic mechanics which produces time reversal invariant diffusion processes. In this paper we analyze the consequences of introducing the generalized Student laws, namely non-Gaussian, Levy infinitely divisible (but not stable) distributions. We will analyze this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) stochastic model is a Student distribution; (b) by supposing that our model is based on a (non-Gaussian) Levy process whose increments are Student distributed. In the case (a) the longer tails of the power decay of the Student laws, and in the case (b) the discontinuities of the Levy-Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams

Stochastic modelling in design of mechanical properties of nanometals

International Nuclear Information System (INIS)

Tengen, T.B.; Wejrzanowski, T.; Iwankiewicz, R.; Kurzydlowski, K.J.

2010-01-01

Polycrystalline nanometals are being fabricated through different processing routes and conditions. The consequence is that nanometals having the same mean grain size may have different grain size dispersion and, hence, may have different material properties. This has often led to conflicting reports from both theoretical and experimental findings about the evolutions of the mechanical properties of nanomaterials. The present paper employs stochastic model to study the impact of microstructure evolution during grain growth on the mechanical properties of polycrystalline nanometals. The stochastic model for grain growth and the stochastic model for changes in mechanical properties of nanomaterials are proposed. The model for the mechanical properties developed is tested on aluminium samples.Many salient features of the mechanical properties of the aluminium samples are revealed. The results show that the different mechanisms of grain growth impart different nature of response to the material mechanical properties. The conventional, homologous and anomalous temperature dependences of the yield stress have also been revealed to be due to different nature of interactions of the microstructures during evolution.

Parameter-free resolution of the superposition of stochastic signals

Energy Technology Data Exchange (ETDEWEB)

Scholz, Teresa, E-mail: tascholz@fc.ul.pt [Center for Theoretical and Computational Physics, University of Lisbon (Portugal); Raischel, Frank [Center for Geophysics, IDL, University of Lisbon (Portugal); Closer Consulting, Av. Eng. Duarte Pacheco Torre 1 15" 0, 1070-101 Lisboa (Portugal); Lopes, Vitor V. [DEIO-CIO, University of Lisbon (Portugal); UTEC–Universidad de Ingeniería y Tecnología, Lima (Peru); Lehle, Bernd; Wächter, Matthias; Peinke, Joachim [Institute of Physics and ForWind, Carl-von-Ossietzky University of Oldenburg, Oldenburg (Germany); Lind, Pedro G. [Institute of Physics and ForWind, Carl-von-Ossietzky University of Oldenburg, Oldenburg (Germany); Institute of Physics, University of Osnabrück, Osnabrück (Germany)

2017-01-30

This paper presents a direct method to obtain the deterministic and stochastic contribution of the sum of two independent stochastic processes, one of which is an Ornstein–Uhlenbeck process and the other a general (non-linear) Langevin process. The method is able to distinguish between the stochastic processes, retrieving their corresponding stochastic evolution equations. This framework is based on a recent approach for the analysis of multidimensional Langevin-type stochastic processes in the presence of strong measurement (or observational) noise, which is here extended to impose neither constraints nor parameters and extract all coefficients directly from the empirical data sets. Using synthetic data, it is shown that the method yields satisfactory results.

Treatment of constraints in the stochastic quantization method and covariantized Langevin equation

International Nuclear Information System (INIS)

Ikegami, Kenji; Kimura, Tadahiko; Mochizuki, Riuji

1993-01-01

We study the treatment of the constraints in the stochastic quantization method. We improve the treatment of the stochastic consistency condition proposed by Namiki et al. by suitably taking into account the Ito calculus. Then we obtain an improved Langevin equation and the Fokker-Planck equation which naturally leads to the correct path integral quantization of the constrained system as the stochastic equilibrium state. This treatment is applied to an O(N) non-linear σ model and it is shown that singular terms appearing in the improved Langevin equation cancel out the δ n (0) divergences in one loop order. We also ascertain that the above Langevin equation, rewritten in terms of independent variables, is actually equivalent to the one in the general-coordinate transformation covariant and vielbein-rotation invariant formalism. (orig.)

Stochastic clustering of material surface under high-heat plasma load

Science.gov (United States)

Budaev, Viacheslav P.

2017-11-01

The results of a study of a surface formed by high-temperature plasma loads on various materials such as tungsten, carbon and stainless steel are presented. High-temperature plasma irradiation leads to an inhomogeneous stochastic clustering of the surface with self-similar granularity - fractality on the scale from nanoscale to macroscales. Cauliflower-like structure of tungsten and carbon materials are formed under high heat plasma load in fusion devices. The statistical characteristics of hierarchical granularity and scale invariance are estimated. They differ qualitatively from the roughness of the ordinary Brownian surface, which is possibly due to the universal mechanisms of stochastic clustering of material surface under the influence of high-temperature plasma.

Effects of extrinsic mortality on the evolution of aging: a stochastic modeling approach.

Directory of Open Access Journals (Sweden)

Maxim Nikolaievich Shokhirev

Full Text Available The evolutionary theories of aging are useful for gaining insights into the complex mechanisms underlying senescence. Classical theories argue that high levels of extrinsic mortality should select for the evolution of shorter lifespans and earlier peak fertility. Non-classical theories, in contrast, posit that an increase in extrinsic mortality could select for the evolution of longer lifespans. Although numerous studies support the classical paradigm, recent data challenge classical predictions, finding that high extrinsic mortality can select for the evolution of longer lifespans. To further elucidate the role of extrinsic mortality in the evolution of aging, we implemented a stochastic, agent-based, computational model. We used a simulated annealing optimization approach to predict which model parameters predispose populations to evolve longer or shorter lifespans in response to increased levels of predation. We report that longer lifespans evolved in the presence of rising predation if the cost of mating is relatively high and if energy is available in excess. Conversely, we found that dramatically shorter lifespans evolved when mating costs were relatively low and food was relatively scarce. We also analyzed the effects of increased predation on various parameters related to density dependence and energy allocation. Longer and shorter lifespans were accompanied by increased and decreased investments of energy into somatic maintenance, respectively. Similarly, earlier and later maturation ages were accompanied by increased and decreased energetic investments into early fecundity, respectively. Higher predation significantly decreased the total population size, enlarged the shared resource pool, and redistributed energy reserves for mature individuals. These results both corroborate and refine classical predictions, demonstrating a population-level trade-off between longevity and fecundity and identifying conditions that produce both

Left ventricular assist device: exercise capacity evolution and rehabilitation added value.

Science.gov (United States)

Lamotte, Michel X; Chimenti, Sara; Deboeck, Gael; Gillet, Alexis; Kacelenenbogen, Raymond; Strapart, Jonathan; Vandeneynde, Frédéric; Van Nooten, Guido; Antoine, Martine

2018-06-01

With more than 15,000 implanted patients worldwide and a survival rate of 80% at 1-year and 59% at 5-years, left ventricular assist device (LVAD) implantation has become an interesting strategy in the management of heart failure patients who are resistant to other kinds of treatment. There are limited data in the literature on the change over time of exercise capacity in LVAD patients, as well as limited knowledge about the beneficial effects that rehabilitation might have on these patients. Therefore, the aim of our study was to evaluate the evolution of exercise capacity on a cohort of patients implanted with the same device (HeartWare © ) and to analyse the potential impact of rehabilitation. Sixty-two patients implanted with a LVAD between June 2011 and June 2015 were screened. Exercise capacity was evaluated by cardiopulmonary exercise testing at 6 weeks, 6 and 12 months after implantation. We have observed significant differences in the exercise capacity and evolution between the trained and non-trained patients. Some of the trained patients nearly normalised their exercise capacity at the end of the rehabilitation programme. Exercise capacity of patient implanted with a HeartWare © LVAD increased in the early period after implantation. Rehabilitation allowed implanted patients to have a significantly better evolution compared to non-rehabilitated patients.

Invariance Signatures: Characterizing contours by their departures from invariance

OpenAIRE

Squire, David; Caelli, Terry M.

1997-01-01

In this paper, a new invariant feature of two-dimensional contours is reported: the Invariance Signature. The Invariance Signature is a measure of the degree to which a contour is invariant under a variety of transformations, derived from the theory of Lie transformation groups. It is shown that the Invariance Signature is itself invariant under shift, rotation and scaling of the contour. Since it is derived from local properties of the contour, it is well-suited to a neural network implement...

Stochastic resonance and the evolution of Daphnia foraging strategy

International Nuclear Information System (INIS)

Dees, Nathan D; Bahar, Sonya; Moss, Frank

2008-01-01

Search strategies are currently of great interest, with reports on foraging ranging from albatrosses and spider monkeys to microzooplankton. Here, we investigate the role of noise in optimizing search strategies. We focus on the zooplankton Daphnia, which move in successive sequences consisting of a hop, a pause and a turn through an angle. Recent experiments have shown that their turning angle distributions (TADs) and underlying noise intensities are similar across species and age groups, suggesting an evolutionary origin of this internal noise. We explore this hypothesis further with a digital simulation (EVO) based solely on the three central Darwinian themes: inheritability, variability and survivability. Separate simulations utilizing stochastic resonance (SR) indicate that foraging success, and hence fitness, is maximized at an optimum TAD noise intensity, which is represented by the distribution's characteristic width, σ. In both the EVO and SR simulations, foraging success is the criterion, and the results are the predicted characteristic widths of the TADs that maximize success. Our results are twofold: (1) the evolving characteristic widths achieve stasis after many generations; (2) as a hop length parameter is changed, variations in the evolved widths generated by EVO parallel those predicted by SR. These findings provide support for the hypotheses that (1) σ is an evolved quantity and that (2) SR plays a role in evolution. (communication)

Scale-invariant curvature fluctuations from an extended semiclassical gravity

Energy Technology Data Exchange (ETDEWEB)

Pinamonti, Nicola, E-mail: pinamont@dima.unige.it, E-mail: siemssen@dima.unige.it [Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova (Italy); INFN Sezione di Genova, Via Dodecaneso 33, 16146 Genova (Italy); Siemssen, Daniel, E-mail: pinamont@dima.unige.it, E-mail: siemssen@dima.unige.it [Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova (Italy)

2015-02-15

We present an extension of the semiclassical Einstein equations which couple n-point correlation functions of a stochastic Einstein tensor to the n-point functions of the quantum stress-energy tensor. We apply this extension to calculate the quantum fluctuations during an inflationary period, where we take as a model a massive conformally coupled scalar field on a perturbed de Sitter space and describe how a renormalization independent, almost-scale-invariant power spectrum of the scalar metric perturbation is produced. Furthermore, we discuss how this model yields a natural basis for the calculation of non-Gaussianities of the considered metric fluctuations.

New insights into the stochastic ray production frontier

DEFF Research Database (Denmark)

Henningsen, Arne; Bělín, Matěj; Henningsen, Géraldine

The stochastic ray production frontier was developed as an alternative to the traditional output distance function to model production processes with multiple inputs and multiple outputs. Its main advantage over the traditional approach is that it can be used when some output quantities of some o...... important than the existing criticisms: taking logarithms of the polar coordinate angles, non-invariance to units of measurement, and ordering of the outputs. We also give some practical advice on how to address the newly raised issues....

New insights into the stochastic ray production frontier

DEFF Research Database (Denmark)

Henningsen, Arne; Bělín, Matěj; Henningsen, Geraldine

2017-01-01

The stochastic ray production frontier was developed as an alternative to the traditional output distance function to model production processes with multiple inputs and multiple outputs. Its main advantage over the traditional approach is that it can be used when some output quantities of some o...... important than the existing criticisms: taking logarithms of the polar coordinate angles, non-invariance to units of measurement, and ordering of the outputs. We also give some practical advice on how to address the newly raised issues....

Invariant-based inverse engineering for fluctuation transfer between membranes in an optomechanical cavity system

Science.gov (United States)

Chen, Ye-Hong; Shi, Zhi-Cheng; Song, Jie; Xia, Yan

2018-02-01

In this paper, by invariant-based inverse engineering, we design classical driving fields to transfer quantum fluctuations between two suspended membranes in an optomechanical cavity system. The transfer can be quickly attained through a nonadiabatic evolution path determined by a so-called dynamical invariant. Such an evolution path allows one to optimize the occupancies of the unstable "intermediate" states; thus, the influence of cavity decays can be suppressed. Numerical simulation demonstrates that a perfect fluctuation transfer between two membranes can be rapidly achieved in one step, and the transfer is robust to both the amplitude noises and cavity decays.

Perturbative QCD Lagrangian at large distances and stochastic dimensionality reduction. Pt. 2

International Nuclear Information System (INIS)

Shintani, M.

1986-11-01

Using the method of stochastic dimensional reduction, we derive a four-dimensional quantum effective Lagrangian for the classical Yang-Mills system coupled to the Gaussian white noise. It is found that the Lagrangian coincides with the perturbative QCD at large distances constructed in our previous paper. That formalism is based on the local covariant operator formalism which maintains the unitarity of the S-matrix. Furthermore, we show the non-perturbative equivalence between super-Lorentz invariant sectors of the effective Lagrangian and two dimensional QCD coupled to the adjoint pseudo-scalars. This implies that stochastic dimensionality reduction by two is approximately operative in QCD at large distances. (orig.)

Invariant strings and pattern-recognizing properties of one-dimensional cellular automata

International Nuclear Information System (INIS)

Jen, E.

1986-01-01

A cellular automaton is a discrete dynamical system whose evolution is governed by a deterministic rule involving local interactions. It is shown that given an arbitrary string of values and an arbitry neighborhood size (representing the range of interaction), a simple procedure can be used to find the fules of that neighborhood size under which the string is unvarian. The set of nearestneighbor rules for which invariant strings exist is completely specified, as is the set of strings invariant under each such rule. For any automaton rule, an associated ''filtering'' rule is defined for which the only attractors are spatial sequences consisting of concatenations of invariant strings. A result is provided defining the rule of minimum neighborhood size for which an arbitrrily chosen string is the unique invariant string. The applications of filtering rules to pttern recognition problems are discussed

Kinetic theory of age-structured stochastic birth-death processes

Science.gov (United States)

Greenman, Chris D.; Chou, Tom

2016-01-01

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.

Tsunamis: stochastic models of occurrence and generation mechanisms

Science.gov (United States)

Geist, Eric L.; Oglesby, David D.

2014-01-01

The devastating consequences of the 2004 Indian Ocean and 2011 Japan tsunamis have led to increased research into many different aspects of the tsunami phenomenon. In this entry, we review research related to the observed complexity and uncertainty associated with tsunami generation, propagation, and occurrence described and analyzed using a variety of stochastic methods. In each case, seismogenic tsunamis are primarily considered. Stochastic models are developed from the physical theories that govern tsunami evolution combined with empirical models fitted to seismic and tsunami observations, as well as tsunami catalogs. These stochastic methods are key to providing probabilistic forecasts and hazard assessments for tsunamis. The stochastic methods described here are similar to those described for earthquakes (Vere-Jones 2013) and volcanoes (Bebbington 2013) in this encyclopedia.

Analysis and reconstruction of stochastic coupled map lattice models

International Nuclear Information System (INIS)

Coca, Daniel; Billings, Stephen A.

2003-01-01

The Letter introduces a general stochastic coupled lattice map model together with an algorithm to estimate the nodal equations involved based only on a small set of observable variables and in the presence of stochastic perturbations. More general forms of the Frobenius-Perron and the transfer operators, which describe the evolution of densities under the action of the CML transformation, are derived

Stochastic Effects; Application in Nuclear Physics

International Nuclear Information System (INIS)

Mazonka, O.

2000-04-01

Stochastic effects in nuclear physics refer to the study of the dynamics of nuclear systems evolving under stochastic equations of motion. In this dissertation we restrict our attention to classical scattering models. We begin with introduction of the model of nuclear dynamics and deterministic equations of evolution. We apply a Langevin approach - an additional property of the model, which reflect the statistical nature of low energy nuclear behaviour. We than concentrate our attention on the problem of calculating tails of distribution functions, which actually is the problem of calculating probabilities of rare outcomes. Two general strategies are proposed. Result and discussion follow. Finally in the appendix we consider stochastic effects in nonequilibrium systems. A few exactly solvable models are presented. For one model we show explicitly that stochastic behaviour in a microscopic description can lead to ordered collective effects on the macroscopic scale. Two others are solved to confirm the predictions of the fluctuation theorem. (author)

Stochastic Cooling at the CERN Antiproton Decelerator

CERN Document Server

Carli, Christian

2000-01-01

When transforming the CERN Antiproton Collector (AC) into the Antiproton Decelerator (AD), the stochastic cooling systems were rebuilt to cope with the new requirements. Instead of using the original three frequency bands, (0.9-1.6 GHz, 1.6-2.45 GHz and 2.4-3.2 GHz) only the first of these was used due to lattice limitations and other constraints. The same pick-ups and kickers are in use at two different energies. As in the AC, simultaneous cooling in all three phase planes is required. Switching between two transmission paths (at 3.5 GeV/c and 2.0 GeV/c) became necessary, including separate notch filters and delay compensation for the kicker sections. The tanks has to be rendered bakeable (150 C) to make the vacuum properties (<10-10 Torr) compatible with deceleration to low energies. Further improvements included programmable, phase-invariant electronic attenuators and amplitude-invariant delays. Experience during commissioning showed that careful optimization (depth and periodicity) of the notch filters...

Stochastic volatility and stochastic leverage

DEFF Research Database (Denmark)

Veraart, Almut; Veraart, Luitgard A. M.

This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...

Green's function-stochastic methods framework for probing nonlinear evolution problems: Burger's equation, the nonlinear Schroedinger's equation, and hydrodynamic organization of near-molecular-scale vorticity

International Nuclear Information System (INIS)

Keanini, R.G.

2011-01-01

Research highlights: → Systematic approach for physically probing nonlinear and random evolution problems. → Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. → Organization of near-molecular scale vorticity mediated by hydrodynamic modes. → Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the

Stochastic dynamics of melt ponds and sea ice-albedo climate feedback

Science.gov (United States)

Sudakov, Ivan

Evolution of melt ponds on the Arctic sea surface is a complicated stochastic process. We suggest a low-order model with ice-albedo feedback which describes stochastic dynamics of melt ponds geometrical characteristics. The model is a stochastic dynamical system model of energy balance in the climate system. We describe the equilibria in this model. We conclude the transition in fractal dimension of melt ponds affects the shape of the sea ice albedo curve.

Stochastic Evolution Equations Driven by Fractional Noises

Science.gov (United States)

2016-11-28

paper is to establish the weak convergence, in the topology of the Skorohod space, of the ν-symmetric Riemann sums for functionals of the fractional...stochastic heat equation with fractional-colored noise: existence of the solution. ALEA Lat. Am. J. Probab. Math . Stat. 4 (2008), 57–87. [8] P. Carmona, Y...Hu: Strong disorder implies strong localization for directed polymers in a random environment. ALEA Lat. Am. J. Probab. Math . Stat. 2 (2006), 217

State vector reduction - 2: Elements of physical reality, nonlocality and stochasticity in relativistic dynamical reduction models

International Nuclear Information System (INIS)

Ghirardi, G.C.; Pearle, P.

1991-02-01

The problem of getting a relativistic generalization of the CSL dynamical reduction model, which has been presented in part I, is discussed. In so doing we have the opportunity to introduce the idea of a stochastically invariant theory. The theoretical model we present, that satisfies this kind of invariance requirement, offers us the possibility to reconsider, from a new point of view, some conceptually relevant issues such as nonlocality, the legitimacy of attributing elements of physical reality to physical systems and the problem of establishing causal relations between physical events. (author). Refs, 3 figs

Scale-invariance underlying the logistic equation and its social applications

Energy Technology Data Exchange (ETDEWEB)

Hernando, A., E-mail: alberto.hernando@irsamc.ups-tlse.fr [Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex 09 (France); Plastino, A., E-mail: plastino@fisica.unlp.edu.ar [National University La Plata, IFLP-CCT-CONICET, C.C. 727, 1900 La Plata (Argentina); Universitat de les Illes Balears and IFISC-CSIC, 07122 Palma de Mallorca (Spain)

2013-01-03

On the basis of dynamical principles we i) advance a derivation of the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and ii) demonstrate that scale-invariance and a mean-value constraint are sufficient and necessary conditions for obtaining it. We also generalize the LE to multi-component systems and show that the above dynamical mechanisms underlie a large number of scale-free processes. Examples are presented regarding city-populations, diffusion in complex networks, and popularity of technological products, all of them obeying the multi-component logistic equation in an either stochastic or deterministic way.

Scale-invariance underlying the logistic equation and its social applications

International Nuclear Information System (INIS)

Hernando, A.; Plastino, A.

2013-01-01

On the basis of dynamical principles we i) advance a derivation of the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and ii) demonstrate that scale-invariance and a mean-value constraint are sufficient and necessary conditions for obtaining it. We also generalize the LE to multi-component systems and show that the above dynamical mechanisms underlie a large number of scale-free processes. Examples are presented regarding city-populations, diffusion in complex networks, and popularity of technological products, all of them obeying the multi-component logistic equation in an either stochastic or deterministic way.

The response analysis of fractional-order stochastic system via generalized cell mapping method.

Science.gov (United States)

Wang, Liang; Xue, Lili; Sun, Chunyan; Yue, Xiaole; Xu, Wei

2018-01-01

This paper is concerned with the response of a fractional-order stochastic system. The short memory principle is introduced to ensure that the response of the system is a Markov process. The generalized cell mapping method is applied to display the global dynamics of the noise-free system, such as attractors, basins of attraction, basin boundary, saddle, and invariant manifolds. The stochastic generalized cell mapping method is employed to obtain the evolutionary process of probability density functions of the response. The fractional-order ϕ 6 oscillator and the fractional-order smooth and discontinuous oscillator are taken as examples to give the implementations of our strategies. Studies have shown that the evolutionary direction of the probability density function of the fractional-order stochastic system is consistent with the unstable manifold. The effectiveness of the method is confirmed using Monte Carlo results.

PC analysis of stochastic differential equations driven by Wiener noise

KAUST Repository

Le Maitre, Olivier

2015-03-01

A polynomial chaos (PC) analysis with stochastic expansion coefficients is proposed for stochastic differential equations driven by additive or multiplicative Wiener noise. It is shown that for this setting, a Galerkin formalism naturally leads to the definition of a hierarchy of stochastic differential equations governing the evolution of the PC modes. Under the mild assumption that the Wiener and uncertain parameters can be treated as independent random variables, it is also shown that the Galerkin formalism naturally separates parametric uncertainty and stochastic forcing dependences. This enables us to perform an orthogonal decomposition of the process variance, and consequently identify contributions arising from the uncertainty in parameters, the stochastic forcing, and a coupled term. Insight gained from this decomposition is illustrated in light of implementation to simplified linear and non-linear problems; the case of a stochastic bifurcation is also considered.

Fractional Stochastic Field Theory

Science.gov (United States)

Honkonen, Juha

2018-02-01

Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.

Invariant subspaces

CERN Document Server

Radjavi, Heydar

2003-01-01

This broad survey spans a wealth of studies on invariant subspaces, focusing on operators on separable Hilbert space. Largely self-contained, it requires only a working knowledge of measure theory, complex analysis, and elementary functional analysis. Subjects include normal operators, analytic functions of operators, shift operators, examples of invariant subspace lattices, compact operators, and the existence of invariant and hyperinvariant subspaces. Additional chapters cover certain results on von Neumann algebras, transitive operator algebras, algebras associated with invariant subspaces,

Measurement invariance versus selection invariance: Is fair selection possible?

NARCIS (Netherlands)

Borsboom, D.; Romeijn, J.W.; Wicherts, J.M.

2008-01-01

This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement

Measurement invariance versus selection invariance : Is fair selection possible?

NARCIS (Netherlands)

Borsboom, Denny; Romeijn, Jan-Willem; Wicherts, Jelte M.

This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement

Simple stochastic simulation.

Science.gov (United States)

Schilstra, Maria J; Martin, Stephen R

2009-01-01

Stochastic simulations may be used to describe changes with time of a reaction system in a way that explicitly accounts for the fact that molecules show a significant degree of randomness in their dynamic behavior. The stochastic approach is almost invariably used when small numbers of molecules or molecular assemblies are involved because this randomness leads to significant deviations from the predictions of the conventional deterministic (or continuous) approach to the simulation of biochemical kinetics. Advances in computational methods over the three decades that have elapsed since the publication of Daniel Gillespie's seminal paper in 1977 (J. Phys. Chem. 81, 2340-2361) have allowed researchers to produce highly sophisticated models of complex biological systems. However, these models are frequently highly specific for the particular application and their description often involves mathematical treatments inaccessible to the nonspecialist. For anyone completely new to the field to apply such techniques in their own work might seem at first sight to be a rather intimidating prospect. However, the fundamental principles underlying the approach are in essence rather simple, and the aim of this article is to provide an entry point to the field for a newcomer. It focuses mainly on these general principles, both kinetic and computational, which tend to be not particularly well covered in specialist literature, and shows that interesting information may even be obtained using very simple operations in a conventional spreadsheet.

The Asymptotic Behaviour of a Stochastic 3D LANS-α Model

International Nuclear Information System (INIS)

Caraballo, Tomas; Marquez-Duran, Antonio M.; Real, Jose

2006-01-01

The long-time behaviour of a stochastic 3D LANS-α model on a bounded domain is analysed. First, we reformulate the model as an abstract problem. Next, we establish sufficient conditions ensuring the existence of stationary (steady state) solutions of this abstract nonlinear stochastic evolution equation, and study the stability properties of the model. Finally, we analyse the effects produced by stochastic perturbations in the deterministic version of the system (persistence of exponential stability as well as possible stabilisation effects produced by the noise). The general results are applied to our stochastic LANS-α system throughout the paper

On orthogonality preserving quadratic stochastic operators

Energy Technology Data Exchange (ETDEWEB)

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)

2015-05-15

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

On orthogonality preserving quadratic stochastic operators

International Nuclear Information System (INIS)

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

2015-01-01

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too

An upper limit on the stochastic gravitational-wave background of cosmological origin.

Science.gov (United States)

Abbott, B P; Abbott, R; Acernese, F; Adhikari, R; Ajith, P; Allen, B; Allen, G; Alshourbagy, M; Amin, R S; Anderson, S B; Anderson, W G; Antonucci, F; Aoudia, S; Arain, M A; Araya, M; Armandula, H; Armor, P; Arun, K G; Aso, Y; Aston, S; Astone, P; Aufmuth, P; Aulbert, C; Babak, S; Baker, P; Ballardin, G; Ballmer, S; Barker, C; Barker, D; Barone, F; Barr, B; Barriga, P; Barsotti, L; Barsuglia, M; Barton, M A; Bartos, I; Bassiri, R; Bastarrika, M; Bauer, Th S; Behnke, B; Beker, M; Benacquista, M; Betzwieser, J; Beyersdorf, P T; Bigotta, S; Bilenko, I A; Billingsley, G; Birindelli, S; Biswas, R; Bizouard, M A; Black, E; Blackburn, J K; Blackburn, L; Blair, D; Bland, B; Boccara, C; Bodiya, T P; Bogue, L; Bondu, F; Bonelli, L; Bork, R; Boschi, V; Bose, S; Bosi, L; Braccini, S; Bradaschia, C; Brady, P R; Braginsky, V B; Brand, J F J van den; Brau, J E; Bridges, D O; Brillet, A; Brinkmann, M; Brisson, V; Van Den Broeck, C; Brooks, A F; Brown, D A; Brummit, A; Brunet, G; Bullington, A; Bulten, H J; Buonanno, A; Burmeister, O; Buskulic, D; Byer, R L; Cadonati, L; Cagnoli, G; Calloni, E; Camp, J B; Campagna, E; Cannizzo, J; Cannon, K C; Canuel, B; Cao, J; Carbognani, F; Cardenas, L; Caride, S; Castaldi, G; Caudill, S; Cavaglià, M; Cavalier, F; Cavalieri, R; Cella, G; Cepeda, C; Cesarini, E; Chalermsongsak, T; Chalkley, E; Charlton, P; Chassande-Mottin, E; Chatterji, S; Chelkowski, S; Chen, Y; Christensen, N; Chung, C T Y; Clark, D; Clark, J; Clayton, J H; Cleva, F; Coccia, E; Cokelaer, T; Colacino, C N; Colas, J; Colla, A; Colombini, M; Conte, R; Cook, D; Corbitt, T R C; Corda, C; Cornish, N; Corsi, A; Coulon, J-P; Coward, D; Coyne, D C; Creighton, J D E; Creighton, T D; Cruise, A M; Culter, R M; Cumming, A; Cunningham, L; Cuoco, E; Danilishin, S L; D'Antonio, S; Danzmann, K; Dari, A; Dattilo, V; Daudert, B; Davier, M; Davies, G; Daw, E J; Day, R; De Rosa, R; Debra, D; Degallaix, J; Del Prete, M; Dergachev, V; Desai, S; Desalvo, R; Dhurandhar, S; Di Fiore, L; Di Lieto, A; Di Paolo Emilio, M; Di Virgilio, A; Díaz, M; Dietz, A; Donovan, F; Dooley, K L; Doomes, E E; Drago, M; Drever, R W P; Dueck, J; Duke, I; Dumas, J-C; Dwyer, J G; Echols, C; Edgar, M; Effler, A; Ehrens, P; Ely, G; Espinoza, E; Etzel, T; Evans, M; Evans, T; Fafone, V; Fairhurst, S; Faltas, Y; Fan, Y; Fazi, D; Fehrmann, H; Ferrante, I; Fidecaro, F; Finn, L S; Fiori, I; Flaminio, R; Flasch, K; Foley, S; Forrest, C; Fotopoulos, N; Fournier, J-D; Franc, J; Franzen, A; Frasca, S; Frasconi, F; Frede, M; Frei, M; Frei, Z; Freise, A; Frey, R; Fricke, T; Fritschel, P; Frolov, V V; Fyffe, M; Galdi, V; Gammaitoni, L; Garofoli, J A; Garufi, F; Genin, E; Gennai, A; Gholami, I; Giaime, J A; Giampanis, S; Giardina, K D; Giazotto, A; Goda, K; Goetz, E; Goggin, L M; González, G; Gorodetsky, M L; Gobler, S; Gouaty, R; Granata, M; Granata, V; Grant, A; Gras, S; Gray, C; Gray, M; Greenhalgh, R J S; Gretarsson, A M; Greverie, C; Grimaldi, F; Grosso, R; Grote, H; Grunewald, S; Guenther, M; Guidi, G; Gustafson, E K; Gustafson, R; Hage, B; Hallam, J M; Hammer, D; Hammond, G D; Hanna, C; Hanson, J; Harms, J; Harry, G M; Harry, I W; Harstad, E D; Haughian, K; Hayama, K; Heefner, J; Heitmann, H; Hello, P; Heng, I S; Heptonstall, A; Hewitson, M; Hild, S; Hirose, E; Hoak, D; Hodge, K A; Holt, K; Hosken, D J; Hough, J; Hoyland, D; Huet, D; Hughey, B; Huttner, S H; Ingram, D R; Isogai, T; Ito, M; Ivanov, A; Johnson, B; Johnson, W W; Jones, D I; Jones, G; Jones, R; Sancho de la Jordana, L; Ju, L; Kalmus, P; Kalogera, V; Kandhasamy, S; Kanner, J; Kasprzyk, D; Katsavounidis, E; Kawabe, K; Kawamura, S; Kawazoe, F; Kells, W; Keppel, D G; Khalaidovski, A; Khalili, F Y; Khan, R; Khazanov, E; King, P; Kissel, J S; Klimenko, S; Kokeyama, K; Kondrashov, V; Kopparapu, R; Koranda, S; Kozak, D; Krishnan, B; Kumar, R; Kwee, P; La Penna, P; Lam, P K; Landry, M; Lantz, B; Laval, M; Lazzarini, A; Lei, H; Lei, M; Leindecker, N; Leonor, I; Leroy, N; Letendre, N; Li, C; Lin, H; Lindquist, P E; Littenberg, T B; Lockerbie, N A; Lodhia, D; Longo, M; Lorenzini, M; Loriette, V; Lormand, M; Losurdo, G; Lu, P; Lubinski, M; Lucianetti, A; Lück, H; Machenschalk, B; Macinnis, M; Mackowski, J-M; Mageswaran, M; Mailand, K; Majorana, E; Man, N; Mandel, I; Mandic, V; Mantovani, M; Marchesoni, F; Marion, F; Márka, S; Márka, Z; Markosyan, A; Markowitz, J; Maros, E; Marque, J; Martelli, F; Martin, I W; Martin, R M; Marx, J N; Mason, K; Masserot, A; Matichard, F; Matone, L; Matzner, R A; Mavalvala, N; McCarthy, R; McClelland, D E; McGuire, S C; McHugh, M; McIntyre, G; McKechan, D J A; McKenzie, K; Mehmet, M; Melatos, A; Melissinos, A C; Mendell, G; Menéndez, D F; Menzinger, F; Mercer, R A; Meshkov, S; Messenger, C; Meyer, M S; Michel, C; Milano, L; Miller, J; Minelli, J; Minenkov, Y; Mino, Y; Mitrofanov, V P; Mitselmakher, G; Mittleman, R; Miyakawa, O; Moe, B; Mohan, M; Mohanty, S D; Mohapatra, S R P; Moreau, J; Moreno, G; Morgado, N; Morgia, A; Morioka, T; Mors, K; Mosca, S; Mossavi, K; Mours, B; Mowlowry, C; Mueller, G; Muhammad, D; Mühlen, H Zur; Mukherjee, S; Mukhopadhyay, H; Mullavey, A; Müller-Ebhardt, H; Munch, J; Murray, P G; Myers, E; Myers, J; Nash, T; Nelson, J; Neri, I; Newton, G; Nishizawa, A; Nocera, F; Numata, K; Ochsner, E; O'Dell, J; Ogin, G H; O'Reilly, B; O'Shaughnessy, R; Ottaway, D J; Ottens, R S; Overmier, H; Owen, B J; Pagliaroli, G; Palomba, C; Pan, Y; Pankow, C; Paoletti, F; Papa, M A; Parameshwaraiah, V; Pardi, S; Pasqualetti, A; Passaquieti, R; Passuello, D; Patel, P; Pedraza, M; Penn, S; Perreca, A; Persichetti, G; Pichot, M; Piergiovanni, F; Pierro, V; Pinard, L; Pinto, I M; Pitkin, M; Pletsch, H J; Plissi, M V; Poggiani, R; Postiglione, F; Principe, M; Prix, R; Prodi, G A; Prokhorov, L; Punken, O; Punturo, M; Puppo, P; Putten, S van der; Quetschke, V; Raab, F J; Rabaste, O; Rabeling, D S; Radkins, H; Raffai, P; Raics, Z; Rainer, N; Rakhmanov, M; Rapagnani, P; Raymond, V; Re, V; Reed, C M; Reed, T; Regimbau, T; Rehbein, H; Reid, S; Reitze, D H; Ricci, F; Riesen, R; Riles, K; Rivera, B; Roberts, P; Robertson, N A; Robinet, F; Robinson, C; Robinson, E L; Rocchi, A; Roddy, S; Rolland, L; Rollins, J; Romano, J D; Romano, R; Romie, J H; Röver, C; Rowan, S; Rüdiger, A; Ruggi, P; Russell, P; Ryan, K; Sakata, S; Salemi, F; Sandberg, V; Sannibale, V; Santamaría, L; Saraf, S; Sarin, P; Sassolas, B; Sathyaprakash, B S; Sato, S; Satterthwaite, M; Saulson, P R; Savage, R; Savov, P; Scanlan, M; Schilling, R; Schnabel, R; Schofield, R; Schulz, B; Schutz, B F; Schwinberg, P; Scott, J; Scott, S M; Searle, A C; Sears, B; Seifert, F; Sellers, D; Sengupta, A S; Sentenac, D; Sergeev, A; Shapiro, B; Shawhan, P; Shoemaker, D H; Sibley, A; Siemens, X; Sigg, D; Sinha, S; Sintes, A M; Slagmolen, B J J; Slutsky, J; van der Sluys, M V; Smith, J R; Smith, M R; Smith, N D; Somiya, K; Sorazu, B; Stein, A; Stein, L C; Steplewski, S; Stochino, A; Stone, R; Strain, K A; Strigin, S; Stroeer, A; Sturani, R; Stuver, A L; Summerscales, T Z; Sun, K-X; Sung, M; Sutton, P J; Swinkels, B L; Szokoly, G P; Talukder, D; Tang, L; Tanner, D B; Tarabrin, S P; Taylor, J R; Taylor, R; Terenzi, R; Thacker, J; Thorne, K A; Thorne, K S; Thüring, A; Tokmakov, K V; Toncelli, A; Tonelli, M; Torres, C; Torrie, C; Tournefier, E; Travasso, F; Traylor, G; Trias, M; Trummer, J; Ugolini, D; Ulmen, J; Urbanek, K; Vahlbruch, H; Vajente, G; Vallisneri, M; Vass, S; Vaulin, R; Vavoulidis, M; Vecchio, A; Vedovato, G; van Veggel, A A; Veitch, J; Veitch, P; Veltkamp, C; Verkindt, D; Vetrano, F; Viceré, A; Villar, A; Vinet, J-Y; Vocca, H; Vorvick, C; Vyachanin, S P; Waldman, S J; Wallace, L; Ward, H; Ward, R L; Was, M; Weidner, A; Weinert, M; Weinstein, A J; Weiss, R; Wen, L; Wen, S; Wette, K; Whelan, J T; Whitcomb, S E; Whiting, B F; Wilkinson, C; Willems, P A; Williams, H R; Williams, L; Willke, B; Wilmut, I; Winkelmann, L; Winkler, W; Wipf, C C; Wiseman, A G; Woan, G; Wooley, R; Worden, J; Wu, W; Yakushin, I; Yamamoto, H; Yan, Z; Yoshida, S; Yvert, M; Zanolin, M; Zhang, J; Zhang, L; Zhao, C; Zotov, N; Zucker, M E; Zweizig, J

2009-08-20

A stochastic background of gravitational waves is expected to arise from a superposition of a large number of unresolved gravitational-wave sources of astrophysical and cosmological origin. It should carry unique signatures from the earliest epochs in the evolution of the Universe, inaccessible to standard astrophysical observations. Direct measurements of the amplitude of this background are therefore of fundamental importance for understanding the evolution of the Universe when it was younger than one minute. Here we report limits on the amplitude of the stochastic gravitational-wave background using the data from a two-year science run of the Laser Interferometer Gravitational-wave Observatory (LIGO). Our result constrains the energy density of the stochastic gravitational-wave background normalized by the critical energy density of the Universe, in the frequency band around 100 Hz, to be theory models. This search for the stochastic background improves on the indirect limits from Big Bang nucleosynthesis and cosmic microwave background at 100 Hz.

Born's reciprocity principle in stochastic phase space

International Nuclear Information System (INIS)

Prugovecki, E.

1981-01-01

It is shown that the application of Born's reciprocity principle to relativistic quantum mechanics in stochastic phase space (by the requirement that the proper wave functions of extended particles satisfy the Born-Lande as well as the Klein-Gordon equation) leads to the unique determination of these functions for any given value of their rms radius. The resulting particle propagators display not only Lorentz but also reciprocal invariance. This feature remains true even in the case of mass-zero particles, such as photons, when their localization is achieved by means of extended test particles whose proper wave functions obey the reciprocity principle. (author)

A stochastic Friedman Universe with dissipation

International Nuclear Information System (INIS)

Gruszczak, J.

1985-01-01

A probabilistic measure is constructed for the radiation-filled Friedman Universe with bulk viscosity and the equation of state perturbed by a ''white noise''. The corresponding Fokker-Planck equation is solved. In the stochastic evolution singularities turn out to be irrelevant. 3 refs., 1 fig. (author)

Semi-blind identification of wideband MIMO channels via stochastic sampling

OpenAIRE

Andrieu, Christophe; Piechocki, Robert J.; McGeehan, Joe P.; Armour, Simon M.

2003-01-01

In this paper we address the problem of wide-band multiple-input multiple-output (MIMO) channel (multidimensional time invariant FIR filter) identification using Markov chains Monte Carlo methods. Towards this end we develop a novel stochastic sampling technique that produces a sequence of multidimensional channel samples. The method is semi-blind in the sense that it uses a very short training sequence. In such a framework the problem is no longer analytically tractable; hence we resort to s...

Time-invariant PT product and phase locking in PT -symmetric lattice models

Science.gov (United States)

Joglekar, Yogesh N.; Onanga, Franck Assogba; Harter, Andrew K.

2018-01-01

Over the past decade, non-Hermitian, PT -symmetric Hamiltonians have been investigated as candidates for both a fundamental, unitary, quantum theory and open systems with a nonunitary time evolution. In this paper, we investigate the implications of the former approach in the context of the latter. Motivated by the invariance of the PT (inner) product under time evolution, we discuss the dynamics of wave-function phases in a wide range of PT -symmetric lattice models. In particular, we numerically show that, starting with a random initial state, a universal, gain-site location dependent locking between wave-function phases at adjacent sites occurs in the PT -symmetry-broken region. Our results pave the way towards understanding the physically observable implications of time invariants in the nonunitary dynamics produced by PT -symmetric Hamiltonians.

Stochastic Jeux

Directory of Open Access Journals (Sweden)

Romanu Ekaterini

2006-01-01

Full Text Available This article shows the similarities between Claude Debussy’s and Iannis Xenakis’ philosophy of music and work, in particular the formers Jeux and the latter’s Metastasis and the stochastic works succeeding it, which seem to proceed parallel (with no personal contact to what is perceived as the evolution of 20th century Western music. Those two composers observed the dominant (German tradition as outsiders, and negated some of its elements considered as constant or natural by "traditional" innovators (i.e. serialists: the linearity of musical texture, its form and rhythm.

Relative Error Model Reduction via Time-Weighted Balanced Stochastic Singular Perturbation

DEFF Research Database (Denmark)

Tahavori, Maryamsadat; Shaker, Hamid Reza

2012-01-01

A new mixed method for relative error model reduction of linear time invariant (LTI) systems is proposed in this paper. This order reduction technique is mainly based upon time-weighted balanced stochastic model reduction method and singular perturbation model reduction technique. Compared...... by using the concept and properties of the reciprocal systems. The results are further illustrated by two practical numerical examples: a model of CD player and a model of the atmospheric storm track....

Critical dynamics in the evolution of stochastic strategies for the iterated prisoner's dilemma.

Directory of Open Access Journals (Sweden)

Dimitris Iliopoulos

2010-10-01

Full Text Available The observed cooperation on the level of genes, cells, tissues, and individuals has been the object of intense study by evolutionary biologists, mainly because cooperation often flourishes in biological systems in apparent contradiction to the selfish goal of survival inherent in Darwinian evolution. In order to resolve this paradox, evolutionary game theory has focused on the Prisoner's Dilemma (PD, which incorporates the essence of this conflict. Here, we encode strategies for the iterated Prisoner's Dilemma (IPD in terms of conditional probabilities that represent the response of decision pathways given previous plays. We find that if these stochastic strategies are encoded as genes that undergo Darwinian evolution, the environmental conditions that the strategies are adapting to determine the fixed point of the evolutionary trajectory, which could be either cooperation or defection. A transition between cooperative and defective attractors occurs as a function of different parameters such as mutation rate, replacement rate, and memory, all of which affect a player's ability to predict an opponent's behavior. These results imply that in populations of players that can use previous decisions to plan future ones, cooperation depends critically on whether the players can rely on facing the same strategies that they have adapted to. Defection, on the other hand, is the optimal adaptive response in environments that change so quickly that the information gathered from previous plays cannot usefully be integrated for a response.

Evolutionary stability concepts in a stochastic environment

Science.gov (United States)

Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi

2017-09-01

Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in economics and social sciences. Nonetheless, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this study, we investigate conditions for stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model with random payoffs following pairwise interactions. Based on this model, we develop the concepts of stochastic evolutionary stability (SES) and stochastic convergence stability (SCS). We show that the condition for a pure strategy to be SES and SCS is more stringent than in a constant environment, while the condition for a constant mixed strategy to be SES is less stringent than the condition to be SCS, which is less stringent than the condition in a constant environment.

Stochastic heating in the cyclotron resonance of electrons

International Nuclear Information System (INIS)

Gutierrez T, C.; Hernandez A, O.

1999-01-01

The study of the different schemes of plasma heating by radiofrequency waves is a very actual problem related with the plasma heating in different machines and the particle acceleration mechanisms. In this work, it is obtained the expression for the temporal evolution of the energy absorbed in the cyclotron resonance of electrons where it is showed the stochastic character of the energy absorption. It is obtained the stochastic criteria in a magnetic configuration of an Ecr type plasma source. (Author)

Climate and weather across scales: singularities and stochastic Levy-Clifford algebra

Science.gov (United States)

Schertzer, Daniel; Tchiguirinskaia, Ioulia

2016-04-01

There have been several attempts to understand and simulate the fluctuations of weather and climate across scales. Beyond mono/uni-scaling approaches (e.g. using spectral analysis), this was done with the help of multifractal techniques that aim to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations of these equations (Royer et al., 2008, Lovejoy and Schertzer, 2013). However, these techniques were limited to deal with scalar fields, instead of dealing directly with a system of complex interactions and non trivial symmetries. The latter is unfortunately indispensable to answer to the challenging question of being able to assess the climatology of (exo-) planets based on first principles (Pierrehumbert, 2013) or to fully address the question of the relevance of quasi-geostrophic turbulence and to define an effective, fractal dimension of the atmospheric motions (Schertzer et al., 2012). In this talk, we present a plausible candidate based on the combination of Lévy stable processes and Clifford algebra. Together they combine stochastic and structural properties that are strongly universal. They therefore define with the help of a few physically meaningful parameters a wide class of stochastic symmetries, as well as high dimensional vector- or manifold-valued fields respecting these symmetries (Schertzer and Tchiguirinskaia, 2015). Lovejoy, S. & Schertzer, D., 2013. The Weather and Climate: Emergent Laws and Multifractal Cascades. Cambridge U.K. Cambridge Univeristy Press. Pierrehumbert, R.T., 2013. Strange news from other stars. Nature Geoscience, 6(2), pp.81-83. Royer, J.F. et al., 2008. Multifractal analysis of the evolution of simulated precipitation over France in a climate scenario. C.R. Geoscience, 340(431-440). Schertzer, D. et al., 2012. Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply. Atmos. Chem. Phys., 12, pp.327-336. Schertzer, D

Bond-based linear indices of the non-stochastic and stochastic edge-adjacency matrix. 1. Theory and modeling of ChemPhys properties of organic molecules.

Science.gov (United States)

Marrero-Ponce, Yovani; Martínez-Albelo, Eugenio R; Casañola-Martín, Gerardo M; Castillo-Garit, Juan A; Echevería-Díaz, Yunaimy; Zaldivar, Vicente Romero; Tygat, Jan; Borges, José E Rodriguez; García-Domenech, Ramón; Torrens, Francisco; Pérez-Giménez, Facundo

2010-11-01

Novel bond-level molecular descriptors are proposed, based on linear maps similar to the ones defined in algebra theory. The kth edge-adjacency matrix (E(k)) denotes the matrix of bond linear indices (non-stochastic) with regard to canonical basis set. The kth stochastic edge-adjacency matrix, ES(k), is here proposed as a new molecular representation easily calculated from E(k). Then, the kth stochastic bond linear indices are calculated using ES(k) as operators of linear transformations. In both cases, the bond-type formalism is developed. The kth non-stochastic and stochastic total linear indices are calculated by adding the kth non-stochastic and stochastic bond linear indices, respectively, of all bonds in molecule. First, the new bond-based molecular descriptors (MDs) are tested for suitability, for the QSPRs, by analyzing regressions of novel indices for selected physicochemical properties of octane isomers (first round). General performance of the new descriptors in this QSPR studies is evaluated with regard to the well-known sets of 2D/3D MDs. From the analysis, we can conclude that the non-stochastic and stochastic bond-based linear indices have an overall good modeling capability proving their usefulness in QSPR studies. Later, the novel bond-level MDs are also used for the description and prediction of the boiling point of 28 alkyl-alcohols (second round), and to the modeling of the specific rate constant (log k), partition coefficient (log P), as well as the antibacterial activity of 34 derivatives of 2-furylethylenes (third round). The comparison with other approaches (edge- and vertices-based connectivity indices, total and local spectral moments, and quantum chemical descriptors as well as E-state/biomolecular encounter parameters) exposes a good behavior of our method in this QSPR studies. Finally, the approach described in this study appears to be a very promising structural invariant, useful not only for QSPR studies but also for similarity

Stochastic modeling of the hypothalamic pulse generator activity.

Science.gov (United States)

Camproux, A C; Thalabard, J C; Thomas, G

1994-11-01

Luteinizing hormone (LH) is released by the pituitary in discrete pulses. In the monkey, the appearance of LH pulses in the plasma is invariably associated with sharp increases (i.e, volleys) in the frequency of the hypothalamic pulse generator electrical activity, so that continuous monitoring of this activity by telemetry provides a unique means to study the temporal structure of the mechanism generating the pulses. To assess whether the times of occurrence and durations of previous volleys exert significant influence on the timing of the next volley, we used a class of periodic counting process models that specify the stochastic intensity of the process as the product of two factors: 1) a periodic baseline intensity and 2) a stochastic regression function with covariates representing the influence of the past. This approach allows the characterization of circadian modulation and memory range of the process underlying hypothalamic pulse generator activity, as illustrated by fitting the model to experimental data from two ovariectomized rhesus monkeys.

Existence and density theorems for stochastic maps on commutative C*-algebras

International Nuclear Information System (INIS)

Alberti, P.M.; Uhlmann, A.

1979-06-01

Theorems are presented on the structure of stochastic and normalized positive linear maps over commutative C*-algebras. It is shown how strongly the solution of the n-tupel problem for stochastic maps relates to the fact that stochastic maps of finite rank are weakly dense within stochastic maps in case of a commutative C*-algebra. A new proof of the density theorem is given and (besides the solution of the n-tupel problem) results are derived concerning the extremal maps of certain convex subsets which are weakly dense. All stated facts suggest application in statistical physics (algebraic approach), especially concerning questions around evolution of classical systems. (author)

Space-time evolution of Gaussian wave packets through superlattices containing left-handed layers

Energy Technology Data Exchange (ETDEWEB)

Pereyra, P; Romero-Serrano, M [Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana-Azcapotzalco, Mexico DF (Mexico); Robledo-Martinez, A, E-mail: ppereyra@correo.azc.uam.m, E-mail: a.robledo@mailaps.or [Departamento de EnergIa, Universidad Autonoma Metropolitana-Azcapotzalco, Mexico DF (Mexico)

2009-05-01

We study the space-time evolution of Gaussian electromagnetic wave packets moving through (L/R){sup n} superlattices, containing alternating layers of left and right-handed materials. We show that the time spent by the wave packet moving through arbitrary (L/R){sup n} superlattices are well described by the phase time. We show that in the particular case where the thicknesses d{sub L,R} and indices n{sub l,r} of the layers satisfy the condition d{sub L}|n{sub L}| = d{sub R}n{sub R}, the usual band structure becomes a sequence of isolated and equidistant peaks with negative phase times.

Robust stability for stochastic bidirectional associative memory neural networks with time delays

Science.gov (United States)

Shu, H. S.; Lv, Z. W.; Wei, G. L.

2008-02-01

In this paper, the asymptotic stability is considered for a class of uncertain stochastic bidirectional associative memory neural networks with time delays and parameter uncertainties. The delays are time-invariant and the uncertainties are norm-bounded that enter into all network parameters. The aim of this paper is to establish easily verifiable conditions under which the delayed neural network is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. By employing a Lyapunov-Krasovskii functional and conducting the stochastic analysis, a linear matrix inequality matrix inequality (LMI) approach is developed to derive the stability criteria. The proposed criteria can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed criteria.

Adaptive optimal stochastic state feedback control of resistive wall modes in tokamaks

International Nuclear Information System (INIS)

Sun, Z.; Sen, A.K.; Longman, R.W.

2006-01-01

An adaptive optimal stochastic state feedback control is developed to stabilize the resistive wall mode (RWM) instability in tokamaks. The extended least-square method with exponential forgetting factor and covariance resetting is used to identify (experimentally determine) the time-varying stochastic system model. A Kalman filter is used to estimate the system states. The estimated system states are passed on to an optimal state feedback controller to construct control inputs. The Kalman filter and the optimal state feedback controller are periodically redesigned online based on the identified system model. This adaptive controller can stabilize the time-dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of roughly four times the inverse of the growth rate for the time-invariant model used

Nonlinear stochastic interacting dynamics and complexity of financial gasket fractal-like lattice percolation

Science.gov (United States)

Zhang, Wei; Wang, Jun

2018-05-01

A novel nonlinear stochastic interacting price dynamics is proposed and investigated by the bond percolation on Sierpinski gasket fractal-like lattice, aim to make a new approach to reproduce and study the complexity dynamics of real security markets. Fractal-like lattices correspond to finite graphs with vertices and edges, which are similar to fractals, and Sierpinski gasket is a well-known example of fractals. Fractional ordinal array entropy and fractional ordinal array complexity are introduced to analyze the complexity behaviors of financial signals. To deeper comprehend the fluctuation characteristics of the stochastic price evolution, the complexity analysis of random logarithmic returns and volatility are preformed, including power-law distribution, fractional sample entropy and fractional ordinal array complexity. For further verifying the rationality and validity of the developed stochastic price evolution, the actual security market dataset are also studied with the same statistical methods for comparison. The empirical results show that this stochastic price dynamics can reconstruct complexity behaviors of the actual security markets to some extent.

Computational stochastic model of ions implantation

Energy Technology Data Exchange (ETDEWEB)

Zmievskaya, Galina I., E-mail: zmi@gmail.ru; Bondareva, Anna L., E-mail: bal310775@yandex.ru [M.V. Keldysh Institute of Applied Mathematics RAS, 4,Miusskaya sq., 125047 Moscow (Russian Federation); Levchenko, Tatiana V., E-mail: tatlevchenko@mail.ru [VNII Geosystem Russian Federal Center, Varshavskoye roadway, 8, Moscow (Russian Federation); Maino, Giuseppe, E-mail: giuseppe.maino@enea.it [Scuola di Lettere e BeniCulturali, University di Bologna, sede di Ravenna, via Mariani 5, 48100 Ravenna (Italy)

2015-03-10

Implantation flux ions into crystal leads to phase transition /PT/ 1-st kind. Damaging lattice is associated with processes clustering vacancies and gaseous bubbles as well their brownian motion. System of stochastic differential equations /SDEs/ Ito for evolution stochastic dynamical variables corresponds to the superposition Wiener processes. The kinetic equations in partial derivatives /KE/, Kolmogorov-Feller and Einstein-Smolukhovskii, were formulated for nucleation into lattice of weakly soluble gases. According theory, coefficients of stochastic and kinetic equations uniquely related. Radiation stimulated phase transition are characterized by kinetic distribution functions /DFs/ of implanted clusters versus their sizes and depth of gas penetration into lattice. Macroscopic parameters of kinetics such as the porosity and stress calculated in thin layers metal/dielectric due to Xe{sup ++} irradiation are attracted as example. Predictions of porosity, important for validation accumulation stresses in surfaces, can be applied at restoring of objects the cultural heritage.

Astrophysical disks Collective and Stochastic Phenomena

CERN Document Server

Fridman, Alexei M; Kovalenko, Ilya G

2006-01-01

The book deals with collective and stochastic processes in astrophysical discs involving theory, observations, and the results of modelling. Among others, it examines the spiral-vortex structure in galactic and accretion disks , stochastic and ordered structures in the developed turbulence. It also describes sources of turbulence in the accretion disks, internal structure of disk in the vicinity of a black hole, numerical modelling of Be envelopes in binaries, gaseous disks in spiral galaxies with shock waves formation, observation of accretion disks in a binary system and mass distribution of luminous matter in disk galaxies. The editors adaptly brought together collective and stochastic phenomena in the modern field of astrophysical discs, their formation, structure, and evolution involving the methodology to deal with, the results of observation and modelling, thereby advancing the study in this important branch of astrophysics and benefiting Professional Researchers, Lecturers, and Graduate Students.

Stochastic frontier model approach for measuring stock market efficiency with different distributions.

Science.gov (United States)

Hasan, Md Zobaer; Kamil, Anton Abdulbasah; Mustafa, Adli; Baten, Md Azizul

2012-01-01

The stock market is considered essential for economic growth and expected to contribute to improved productivity. An efficient pricing mechanism of the stock market can be a driving force for channeling savings into profitable investments and thus facilitating optimal allocation of capital. This study investigated the technical efficiency of selected groups of companies of Bangladesh Stock Market that is the Dhaka Stock Exchange (DSE) market, using the stochastic frontier production function approach. For this, the authors considered the Cobb-Douglas Stochastic frontier in which the technical inefficiency effects are defined by a model with two distributional assumptions. Truncated normal and half-normal distributions were used in the model and both time-variant and time-invariant inefficiency effects were estimated. The results reveal that technical efficiency decreased gradually over the reference period and that truncated normal distribution is preferable to half-normal distribution for technical inefficiency effects. The value of technical efficiency was high for the investment group and low for the bank group, as compared with other groups in the DSE market for both distributions in time-varying environment whereas it was high for the investment group but low for the ceramic group as compared with other groups in the DSE market for both distributions in time-invariant situation.

Stochastic frontier model approach for measuring stock market efficiency with different distributions.

Directory of Open Access Journals (Sweden)

Md Zobaer Hasan

Full Text Available The stock market is considered essential for economic growth and expected to contribute to improved productivity. An efficient pricing mechanism of the stock market can be a driving force for channeling savings into profitable investments and thus facilitating optimal allocation of capital. This study investigated the technical efficiency of selected groups of companies of Bangladesh Stock Market that is the Dhaka Stock Exchange (DSE market, using the stochastic frontier production function approach. For this, the authors considered the Cobb-Douglas Stochastic frontier in which the technical inefficiency effects are defined by a model with two distributional assumptions. Truncated normal and half-normal distributions were used in the model and both time-variant and time-invariant inefficiency effects were estimated. The results reveal that technical efficiency decreased gradually over the reference period and that truncated normal distribution is preferable to half-normal distribution for technical inefficiency effects. The value of technical efficiency was high for the investment group and low for the bank group, as compared with other groups in the DSE market for both distributions in time-varying environment whereas it was high for the investment group but low for the ceramic group as compared with other groups in the DSE market for both distributions in time-invariant situation.

AA, stochastic precooling pickup

CERN Multimedia

CERN PhotoLab

1980-01-01

The freshly injected antiprotons were subjected to fast stochastic "precooling". In this picture of a precooling pickup, the injection orbit is to the left, the stack orbit to the far right. After several seconds of precooling with the system's kickers (in momentum and in the vertical plane), the precooled antiprotons were transferred, by means of RF, to the stack tail, where they were subjected to further stochastic cooling in momentum and in both transverse planes, until they ended up, deeply cooled, in the stack core. During precooling, a shutter near the central orbit shielded the pickups from the signals emanating from the stack-core, whilst the stack-core was shielded from the violent action of the precooling kickers by a shutter on these. All shutters were opened briefly during transfer of the precooled antiprotons to the stack tail. Here, the shutter is not yet mounted. Precooling pickups and kickers had the same design, except that the kickers had cooling circuits and the pickups had none. Peering th...

Analytical Assessment for Transient Stability Under Stochastic Continuous Disturbances

Energy Technology Data Exchange (ETDEWEB)

Ju, Ping [Hohai Univ., Nanjing (China); Li, Hongyu [Hohai Univ., Nanjing (China); Gan, Chun [The Univ. of Tennessee, Knoxville, TN (United States); Liu, Yong [The Univ. of Tennessee, Knoxville, TN (United States); Yu, Yiping [Hohai Univ., Nanjing (China); Liu, Yilu [Univ. of Tennessee, Knoxville, TN (United States)

2017-06-28

Here, with the growing integration of renewable power generation, plug-in electric vehicles, and other sources of uncertainty, increasing stochastic continuous disturbances are brought to power systems. The impact of stochastic continuous disturbances on power system transient stability attracts significant attention. To address this problem, this paper proposes an analytical assessment method for transient stability of multi-machine power systems under stochastic continuous disturbances. In the proposed method, a probability measure of transient stability is presented and analytically solved by stochastic averaging. Compared with the conventional method (Monte Carlo simulation), the proposed method is many orders of magnitude faster, which makes it very attractive in practice when many plans for transient stability must be compared or when transient stability must be analyzed quickly. Also, it is found that the evolution of system energy over time is almost a simple diffusion process by the proposed method, which explains the impact mechanism of stochastic continuous disturbances on transient stability in theory.

Gas contract portfolio management: a stochastic programming approach

International Nuclear Information System (INIS)

Haurie, A.; Smeers, Y.; Zaccour, G.

1991-01-01

This paper deals with a stochastic programming model which complements long range market simulation models generating scenarios concerning the evolution of demand and prices for gas in different market segments. Agas company has to negociate contracts with lengths going from one to twenty years. This stochastic model is designed to assess the risk associated with committing the gas production capacity of the company to these market segments. Different approaches are presented to overcome the difficulties associated with the very large size of the resulting optimization problem

Computational invariant theory

CERN Document Server

Derksen, Harm

2015-01-01

This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be ...

Simulation of the stochastic wave loads using a physical modeling approach

DEFF Research Database (Denmark)

Liu, W.F.; Sichani, Mahdi Teimouri; Nielsen, Søren R.K.

2013-01-01

In analyzing stochastic dynamic systems, analysis of the system uncertainty due to randomness in the loads plays a crucial role. Typically time series of the stochastic loads are simulated using traditional random phase method. This approach combined with fast Fourier transform algorithm makes...... reliability or its uncertainty. Moreover applicability of the probability density evolution method on engineering problems faces critical difficulties when the system embeds too many random variables. Hence it is useful to devise a method which can make realization of the stochastic load processes with low...

Stochastic bosonization for a d ≥ 3 Fermi system

International Nuclear Information System (INIS)

Accardi, L.; Lu, Y.G.; Mastropietro, V.

1997-01-01

We consider a system of fermions interacting via an external field and we prove, in d ≥ 3, that a suitable collective operator, bilinear in the fermionic fields, in the stochastic limit becomes a boson quantum brownian motion. The evolution operator after the limit satisfies a quantum stochastic differential equation, in which the imaginary part of the Ito correction is the ground state shift while its real part is the lifetime of the ground state. (orig.)

Stochastic dynamics of complex systems: from glasses to evolution (series on complexity science)

CERN Document Server

Sibani, Paolo

2013-01-01

Dynamical evolution over long time scales is a prominent feature of all the systems we intuitively think of as complex - for example, ecosystems, the brain or the economy. In physics, the term ageing is used for this type of slow change, occurring over time scales much longer than the patience, or indeed the lifetime, of the observer. The main focus of this book is on the stochastic processes which cause ageing, and the surprising fact that the ageing dynamics of systems which are very different at the microscopic level can be treated in similar ways. The first part of this book provides the necessary mathematical and computational tools and the second part describes the intuition needed to deal with these systems. Some of the first few chapters have been covered in several other books, but the emphasis and selection of the topics reflect both the authors' interests and the overall theme of the book. The second part contains an introduction to the scientific literature and deals in some detail with the desc...

Stochastic spin evolution of neutron stars

OpenAIRE

Popov, S. B.; Prokhorov, M. E.; Khoperskov, A. V.; Lipunov, V. M.

2001-01-01

In this paper we present calculations of period distribution for old accreting isolated neutron stars (INSs). At the age about a few billions years low velocity INSs come to the stage of accretion. At that stage their period evolution is governed by magnetic breaking and accreted angular momentum. Due to turbulence of the interstellar medium (ISM) accreted momentum can both accelerate and decelerate rotation of an INS and spin evolution has chaotic character. Calculations show that for consta...

Effects of stochastic noise on dynamical decoupling procedures

Energy Technology Data Exchange (ETDEWEB)

Bernad, Jozsef Zsolt; Frydrych, Holger; Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)

2013-07-01

Dynamical decoupling is a well-established technique to protect quantum systems from unwanted influences of their environment by exercising active control. It has been used experimentally to drastically increase the lifetime of qubit states in various implementations. The efficiency of different dynamical decoupling schemes defines the lifetime. However, errors in control operations always limit this efficiency. We propose a stochastic model as a possible description of imperfect control pulses and discuss the impact of this kind of error on different decoupling schemes. In the limit of continuous control, i.e. if the number of pulses N → ∞, we derive a stochastic differential equation for the evolution of the density operator of the controlled system and its environment. In the context of this modified time evolution we discuss possibilities of protecting qubit states against environmental noise.

Dynamics of stochastic systems

CERN Document Server

Klyatskin, Valery I

2005-01-01

Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''''oil slicks''''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of ...

Jump diffusion models and the evolution of financial prices

International Nuclear Information System (INIS)

Figueiredo, Annibal; Castro, Marcio T. de; Silva, Sergio da; Gleria, Iram

2011-01-01

We analyze a stochastic model to describe the evolution of financial prices. We consider the stochastic term as a sum of the Wiener noise and a jump process. We point to the effects of the jumps on the return time evolution, a central concern of the econophysics literature. The presence of jumps suggests that the process can be described by an infinitely divisible characteristic function belonging to the De Finetti class. We then extend the De Finetti functions to a generalized nonlinear model and show the model to be capable of explaining return behavior. -- Highlights: → We analyze a stochastic model to describe the evolution of financial prices. → The stochastic term is considered as a sum of the Wiener noise and a jump process. → The process can be described by an infinitely divisible characteristic function belonging to the De Finetti class. → We extend the De Finetti functions to a generalized nonlinear model.

Real-space mapping of topological invariants using artificial neural networks

Science.gov (United States)

Carvalho, D.; García-Martínez, N. A.; Lado, J. L.; Fernández-Rossier, J.

2018-03-01

Topological invariants allow one to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wave functions under twisted boundary conditions. However, those procedures do not allow one to calculate a topological invariant by evaluating the system locally, and thus require information about the wave functions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a one-dimensional topological superconductor and a two-dimensional quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the kernel polynomial method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.

Scale-invariant Green-Kubo relation for time-averaged diffusivity

Science.gov (United States)

Meyer, Philipp; Barkai, Eli; Kantz, Holger

2017-12-01

In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time- and ensemble-averaged mean-squared displacement are remarkably different. The ensemble-averaged diffusivity is obtained from a scaling Green-Kubo relation, which connects the scale-invariant nonstationary velocity correlation function with the transport coefficient. Here we obtain the relation between time-averaged diffusivity, usually recorded in single-particle tracking experiments, and the underlying scale-invariant velocity correlation function. The time-averaged mean-squared displacement is given by 〈δ2¯〉 ˜2 DνtβΔν -β , where t is the total measurement time and Δ is the lag time. Here ν is the anomalous diffusion exponent obtained from ensemble-averaged measurements 〈x2〉 ˜tν , while β ≥-1 marks the growth or decline of the kinetic energy 〈v2〉 ˜tβ . Thus, we establish a connection between exponents that can be read off the asymptotic properties of the velocity correlation function and similarly for the transport constant Dν. We demonstrate our results with nonstationary scale-invariant stochastic and deterministic models, thereby highlighting that systems with equivalent behavior in the ensemble average can differ strongly in their time average. If the averaged kinetic energy is finite, β =0 , the time scaling of 〈δ2¯〉 and 〈x2〉 are identical; however, the time-averaged transport coefficient Dν is not identical to the corresponding ensemble-averaged diffusion constant.

Stochastic methods for the description of multiparticle production

International Nuclear Information System (INIS)

Carruthers, P.

1984-01-01

Dynamical questions in the evolution of excited hadronic matter are reviewed, with emphasis on KNO scaling and its possible violation. It is suggested that the KNO distributions is described by a stochastic evolution of the Fokker-Planck type related to underlying field theory by coupled rate equations approximated by Langevin equations with noise. Refined correlation analysis of data, especially the use of intensity interferometry techniques, is recommended for data analysis. 26 references

Numerical simulation of effective mechanical properties of stochastic composites with consideration for structural evolution under intensive dynamic loading

Energy Technology Data Exchange (ETDEWEB)

Karakulov, Valerii V., E-mail: valery@ftf.tsu.ru [National Research Tomsk State University, Tomsk, 634050 (Russian Federation); Smolin, Igor Yu., E-mail: smolin@ispms.ru, E-mail: skrp@ftf.tsu.ru; Skripnyak, Vladimir A., E-mail: smolin@ispms.ru, E-mail: skrp@ftf.tsu.ru [National Research Tomsk State University, Tomsk, 634050, Russia and Institute of Strength Physics and Materials Science SB RAS, Tomsk, 634055 (Russian Federation)

2014-11-14

Mechanical behavior of stochastic metal-ceramic composites with the aluminum matrix under high-rate deformation at shock-wave loading is numerically simulated with consideration for structural evolution. Effective values of mechanical parameters of metal-ceramic composites AlB{sub 4}C, AlSiC, and AlAl{sub 2}O{sub 3} are evaluated depending on different concentration of ceramic inclusions.

Existence of weak solutions to stochastic evolution inclusions

OpenAIRE

Jakubowski , Adam; Kamenskii , Mikhail; Raynaud de Fitte , Paul

2005-01-01

International audience; We consider the Cauchy problem for a semilinear stochastic differential inclusion in a Hilbert space. The linear operator generates a strongly continuous semigroup and the nonlinear term is multivalued and satisfies a condition which is more heneral than the Lipschitz condition. We prove the existence of a mild solution to this problem. This solution is not "strong" in the probabilistic sense, that is, it is not defined on the underlying probability space, but on a lar...

Smoothing of Fault Slip Surfaces by Scale Invariant Wear

Science.gov (United States)

Dascher-Cousineau, K.; Kirkpatrick, J. D.

2017-12-01

multi-scale wear model to explain the evolution of faults with displacement. We suggest that together, asperity failure as a scale invariant process, and the stochastic strength of host rocks are consistent with qualitative and quantitative observational constraints made in this study.

Probability density function evolution of power systems subject to stochastic variation of renewable energy

Science.gov (United States)

Wei, J. Q.; Cong, Y. C.; Xiao, M. Q.

2018-05-01

As renewable energies are increasingly integrated into power systems, there is increasing interest in stochastic analysis of power systems.Better techniques should be developed to account for the uncertainty caused by penetration of renewables and consequently analyse its impacts on stochastic stability of power systems. In this paper, the Stochastic Differential Equations (SDEs) are used to represent the evolutionary behaviour of the power systems. The stationary Probability Density Function (PDF) solution to SDEs modelling power systems excited by Gaussian white noise is analysed. Subjected to such random excitation, the Joint Probability Density Function (JPDF) solution to the phase angle and angular velocity is governed by the generalized Fokker-Planck-Kolmogorov (FPK) equation. To solve this equation, the numerical method is adopted. Special measure is taken such that the generalized FPK equation is satisfied in the average sense of integration with the assumed PDF. Both weak and strong intensities of the stochastic excitations are considered in a single machine infinite bus power system. The numerical analysis has the same result as the one given by the Monte Carlo simulation. Potential studies on stochastic behaviour of multi-machine power systems with random excitations are discussed at the end.

A novel method for unsteady flow field segmentation based on stochastic similarity of direction

Science.gov (United States)

Omata, Noriyasu; Shirayama, Susumu

2018-04-01

Recent developments in fluid dynamics research have opened up the possibility for the detailed quantitative understanding of unsteady flow fields. However, the visualization techniques currently in use generally provide only qualitative insights. A method for dividing the flow field into physically relevant regions of interest can help researchers quantify unsteady fluid behaviors. Most methods at present compare the trajectories of virtual Lagrangian particles. The time-invariant features of an unsteady flow are also frequently of interest, but the Lagrangian specification only reveals time-variant features. To address these challenges, we propose a novel method for the time-invariant spatial segmentation of an unsteady flow field. This segmentation method does not require Lagrangian particle tracking but instead quantitatively compares the stochastic models of the direction of the flow at each observed point. The proposed method is validated with several clustering tests for 3D flows past a sphere. Results show that the proposed method reveals the time-invariant, physically relevant structures of an unsteady flow.

Language-invariant verb processing regions in Spanish-English bilinguals.

Science.gov (United States)

Willms, Joanna L; Shapiro, Kevin A; Peelen, Marius V; Pajtas, Petra E; Costa, Albert; Moo, Lauren R; Caramazza, Alfonso

2011-07-01

Nouns and verbs are fundamental grammatical building blocks of all languages. Studies of brain-damaged patients and healthy individuals have demonstrated that verb processing can be dissociated from noun processing at a neuroanatomical level. In cases where bilingual patients have a noun or verb deficit, the deficit has been observed in both languages. This suggests that the noun-verb distinction may be based on neural components that are common across languages. Here we investigated the cortical organization of grammatical categories in healthy, early Spanish-English bilinguals using functional magnetic resonance imaging (fMRI) in a morphophonological alternation task. Four regions showed greater activity for verbs than for nouns in both languages: left posterior middle temporal gyrus (LMTG), left middle frontal gyrus (LMFG), pre-supplementary motor area (pre-SMA), and right middle occipital gyrus (RMOG); no regions showed greater activation for nouns. Multi-voxel pattern analysis within verb-specific regions showed indistinguishable activity patterns for English and Spanish, indicating language-invariant bilingual processing. In LMTG and LMFG, patterns were more similar within than across grammatical category, both within and across languages, indicating language-invariant grammatical class information. These results suggest that the neural substrates underlying verb-specific processing are largely independent of language in bilinguals, both at the macroscopic neuroanatomical level and at the level of voxel activity patterns. Copyright © 2011 Elsevier Inc. All rights reserved.

Elementary amplitudes from full QCD and the stochastic vacuum model

International Nuclear Information System (INIS)

Martini, A.F.; Menon, M.J.

2002-01-01

In a previous work, making use of the gluon gauge-invariant two-point correlation function determined from lattice QCD in the quenched approximation and the stochastic vacuum model, we determined the elementary (parton-parton) scattering amplitude in the momentum transfer space. In this communication we compute the elementary amplitude from new lattice QCD calculations that include the effects of dynamical fermions (full QCD). The main conclusion is that the inclusion of dynamical fermions leads to a normalized elementary amplitude that decreases more quickly with the momentum transfer than that in the quenched approximation. (author)

Stochastic Averaging and Stochastic Extremum Seeking

CERN Document Server

Liu, Shu-Jun

2012-01-01

Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering  and analysis of bacterial  convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...

Stochastic ice stream dynamics.

Science.gov (United States)

Mantelli, Elisa; Bertagni, Matteo Bernard; Ridolfi, Luca

2016-08-09

Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution.

Aspects if stochastic models for short-term hydropower scheduling and bidding

Energy Technology Data Exchange (ETDEWEB)

Belsnes, Michael Martin [Sintef Energy, Trondheim (Norway); Follestad, Turid [Sintef Energy, Trondheim (Norway); Wolfgang, Ove [Sintef Energy, Trondheim (Norway); Fosso, Olav B. [Dep. of electric power engineering NTNU, Trondheim (Norway)

2012-07-01

This report discusses challenges met when turning from deterministic to stochastic decision support models for short-term hydropower scheduling and bidding. The report describes characteristics of the short-term scheduling and bidding problem, different market and bidding strategies, and how a stochastic optimization model can be formulated. A review of approaches for stochastic short-term modelling and stochastic modelling for the input variables inflow and market prices is given. The report discusses methods for approximating the predictive distribution of uncertain variables by scenario trees. Benefits of using a stochastic over a deterministic model are illustrated by a case study, where increased profit is obtained to a varying degree depending on the reservoir filling and price structure. Finally, an approach for assessing the effect of using a size restricted scenario tree to approximate the predictive distribution for stochastic input variables is described. The report is a summary of the findings of Work package 1 of the research project #Left Double Quotation Mark#Optimal short-term scheduling of wind and hydro resources#Right Double Quotation Mark#. The project aims at developing a prototype for an operational stochastic short-term scheduling model. Based on the investigations summarized in the report, it is concluded that using a deterministic equivalent formulation of the stochastic optimization problem is convenient and sufficient for obtaining a working prototype. (author)

Stochastic inflation: Quantum phase-space approach

International Nuclear Information System (INIS)

Habib, S.

1992-01-01

In this paper a quantum-mechanical phase-space picture is constructed for coarse-grained free quantum fields in an inflationary universe. The appropriate stochastic quantum Liouville equation is derived. Explicit solutions for the phase-space quantum distribution function are found for the cases of power-law and exponential expansions. The expectation values of dynamical variables with respect to these solutions are compared to the corresponding cutoff regularized field-theoretic results (we do not restrict ourselves only to left-angle Φ 2 right-angle). Fair agreement is found provided the coarse-graining scale is kept within certain limits. By focusing on the full phase-space distribution function rather than a reduced distribution it is shown that the thermodynamic interpretation of the stochastic formalism faces several difficulties (e.g., there is no fluctuation-dissipation theorem). The coarse graining does not guarantee an automatic classical limit as quantum correlations turn out to be crucial in order to get results consistent with standard quantum field theory. Therefore, the method does not by itself constitute an explanation of the quantum to classical transition in the early Universe. In particular, we argue that the stochastic equations do not lead to decoherence

Invariant and Absolute Invariant Means of Double Sequences

Directory of Open Access Journals (Sweden)

Abdullah Alotaibi

2012-01-01

Full Text Available We examine some properties of the invariant mean, define the concepts of strong σ-convergence and absolute σ-convergence for double sequences, and determine the associated sublinear functionals. We also define the absolute invariant mean through which the space of absolutely σ-convergent double sequences is characterized.

GillespieSSA: Implementing the Gillespie Stochastic Simulation Algorithm in R

Directory of Open Access Journals (Sweden)

Mario Pineda-Krch

2008-02-01

Full Text Available The deterministic dynamics of populations in continuous time are traditionally described using coupled, first-order ordinary differential equations. While this approach is accurate for large systems, it is often inadequate for small systems where key species may be present in small numbers or where key reactions occur at a low rate. The Gillespie stochastic simulation algorithm (SSA is a procedure for generating time-evolution trajectories of finite populations in continuous time and has become the standard algorithm for these types of stochastic models. This article presents a simple-to-use and flexible framework for implementing the SSA using the high-level statistical computing language R and the package GillespieSSA. Using three ecological models as examples (logistic growth, Rosenzweig-MacArthur predator-prey model, and Kermack-McKendrick SIRS metapopulation model, this paper shows how a deterministic model can be formulated as a finite-population stochastic model within the framework of SSA theory and how it can be implemented in R. Simulations of the stochastic models are performed using four different SSA Monte Carlo methods: one exact method (Gillespie's direct method; and three approximate methods (explicit, binomial, and optimized tau-leap methods. Comparison of simulation results confirms that while the time-evolution trajectories obtained from the different SSA methods are indistinguishable, the approximate methods are up to four orders of magnitude faster than the exact methods.

Stochastic volatility models and Kelvin waves

Science.gov (United States)

Lipton, Alex; Sepp, Artur

2008-08-01

We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics.

Stochastic volatility models and Kelvin waves

International Nuclear Information System (INIS)

Lipton, Alex; Sepp, Artur

2008-01-01

We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics

Stochastic volatility models and Kelvin waves

Energy Technology Data Exchange (ETDEWEB)

Lipton, Alex [Merrill Lynch, Mlfc Main, 2 King Edward Street, London EC1A 1HQ (United Kingdom); Sepp, Artur [Merrill Lynch, 4 World Financial Center, New York, NY 10080 (United States)], E-mail: Alex_Lipton@ml.com, E-mail: Artur_Sepp@ml.com

2008-08-29

We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics.

Evolution in fluctuating environments: decomposing selection into additive components of the Robertson-Price equation.

Science.gov (United States)

Engen, Steinar; Saether, Bernt-Erik

2014-03-01

We analyze the stochastic components of the Robertson-Price equation for the evolution of quantitative characters that enables decomposition of the selection differential into components due to demographic and environmental stochasticity. We show how these two types of stochasticity affect the evolution of multivariate quantitative characters by defining demographic and environmental variances as components of individual fitness. The exact covariance formula for selection is decomposed into three components, the deterministic mean value, as well as stochastic demographic and environmental components. We show that demographic and environmental stochasticity generate random genetic drift and fluctuating selection, respectively. This provides a common theoretical framework for linking ecological and evolutionary processes. Demographic stochasticity can cause random variation in selection differentials independent of fluctuating selection caused by environmental variation. We use this model of selection to illustrate that the effect on the expected selection differential of random variation in individual fitness is dependent on population size, and that the strength of fluctuating selection is affected by how environmental variation affects the covariance in Malthusian fitness between individuals with different phenotypes. Thus, our approach enables us to partition out the effects of fluctuating selection from the effects of selection due to random variation in individual fitness caused by demographic stochasticity. © 2013 The Author(s). Evolution © 2013 The Society for the Study of Evolution.

Continuous stochastic approach to birth and death processes and co-operative behaviour of systems far from equilibrium

Energy Technology Data Exchange (ETDEWEB)

Chechetkin, V.R.; Lutovinov, V.S.

1986-09-11

The continuous stochastic formalism for the description of systems with birth and death processes randomly distributed in space is developed with the use of local birth and death operators and local generalization of the corresponding Chapman-Kolmogorov equation. The functional stochastic equation for the evolution of the probability functional is derived and its modifications for evolution of the characteristic functional and the first passage time problem are given. The corresponding evolution equations for equal-time correlators are also derived. The results are generalized then on the exothermic and endothermic chemical reactions. As examples of the particular applications of the results the small fluctuations near stable equilibrium state and fluctuations in mono-molecular reactions, Lotka-Volterra model, Schloegl reaction and brusselator are considered. It is shown that the two-dimensional Lotka-Volterra model may exhibit synergetic phase transition analogous to the topological transition of the Kosterlitz-Thouless-Berezinskii type. At the end of the paper some general consequences from stochastic evolution of the birth and death processes are discussed and the arguments on their importance in evolution of populations, cellular dynamics and in applications to various chemical and biological problems are presented.

Limits for Stochastic Reaction Networks

DEFF Research Database (Denmark)

Cappelletti, Daniele

Reaction systems have been introduced in the 70s to model biochemical systems. Nowadays their range of applications has increased and they are fruitfully used in dierent elds. The concept is simple: some chemical species react, the set of chemical reactions form a graph and a rate function...... is associated with each reaction. Such functions describe the speed of the dierent reactions, or their propensities. Two modelling regimes are then available: the evolution of the dierent species concentrations can be deterministically modelled through a system of ODE, while the counts of the dierent species...... at a certain time are stochastically modelled by means of a continuous-time Markov chain. Our work concerns primarily stochastic reaction systems, and their asymptotic properties. In Paper I, we consider a reaction system with intermediate species, i.e. species that are produced and fast degraded along a path...

Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension

International Nuclear Information System (INIS)

Qu Gai-Zhu; Zhang Shun-Li; Li Yao-Long

2014-01-01

In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators. (general)

Invariant and semi-invariant probabilistic normed spaces

Energy Technology Data Exchange (ETDEWEB)

Ghaemi, M.B. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: mghaemi@iust.ac.ir; Lafuerza-Guillen, B. [Departamento de Estadistica y Matematica Aplicada, Universidad de Almeria, Almeria E-04120 (Spain)], E-mail: blafuerz@ual.es; Saiedinezhad, S. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: ssaiedinezhad@yahoo.com

2009-10-15

Probabilistic metric spaces were introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of probabilistic normed space based on the definition of Menger . We introduce the concept of semi-invariance among the PN spaces. In this paper we will find a sufficient condition for some PN spaces to be semi-invariant. We will show that PN spaces are normal spaces. Urysohn's lemma, and Tietze extension theorem for them are proved.

Stochastic Simulation of Biomolecular Reaction Networks Using the Biomolecular Network Simulator Software

National Research Council Canada - National Science Library

Frazier, John; Chusak, Yaroslav; Foy, Brent

2008-01-01

.... The software uses either exact or approximate stochastic simulation algorithms for generating Monte Carlo trajectories that describe the time evolution of the behavior of biomolecular reaction networks...

Invariant class operators in the decoherent histories analysis of timeless quantum theories

International Nuclear Information System (INIS)

Halliwell, J. J.; Wallden, P.

2006-01-01

The decoherent histories approach to quantum theory is applied to a class of reparametrization-invariant models whose state is an energy eigenstate. A key step in this approach is the construction of class operators characterizing the questions of physical interest, such as the probability of the system entering a given region of configuration space without regard to time. In nonrelativistic quantum mechanics these class operators are given by time-ordered products of projection operators. But in reparametrization-invariant models, where there is no time, the construction of the class operators is more complicated, the main difficulty being to find operators which commute with the Hamiltonian constraint (and so respect the invariance of the theory). Here, inspired by classical considerations, we put forward a proposal for the construction of such class operators for a class of reparametrization-invariant systems. They consist of continuous infinite temporal products of Heisenberg picture projection operators. We investigate the consequences of this proposal in a number of simple models and also compare with the evolving constants method. The formalism developed here is ultimately aimed at cosmological models described by a Wheeler-DeWitt equation, but the specific features of such models are left to future papers

Stochastic cooling for beginners

International Nuclear Information System (INIS)

Moehl, D.

1984-01-01

These two lectures have been prepared to give a simple introduction to the principles. In Part I we try to explain stochastic cooling using the time-domain picture which starts from the pulse response of the system. In Part II the discussion is repeated, looking more closely at the frequency-domain response. An attempt is made to familiarize the beginners with some of the elementary cooling equations, from the 'single particle case' up to equations which describe the evolution of the particle distribution. (orig.)

Integral relations for invariants constructed from three Riemann tensors and their applications in quantum gravity

International Nuclear Information System (INIS)

van Nieuwenhuizen, P.; Wu, C.C.

1977-01-01

The lowest order quantum corrections to pure gravitation are finite because there exists an integral relation between products of two Riemann tensors (the Gauss--Bonnet theorem). In this article several algebraic and integral relations are determined between products of three Riemann tensors in four- and six-dimensional spacetime. In both cases, one is left with only one invariant when R/sub μ//sub ν/=0, viz., ∫ (-g) 1 / 2 (R/sub b//sub β//sub μ//sub ν/R/sup μ//sup ν//sup rho//sup sigma/R/sub rho//sub sigma/ /sup α//sup β/).It is explicitly shown that this invariant does not vanish, even when R/sub μ//sub ν/=0. Consequently, the two-loop quantum corrections to pure gravitation will only be finite if, due to miraculous cancellation, the coefficient of this invariant vanishes

Aggregation patterns from nonlocal interactions: Discrete stochastic and continuum modeling

KAUST Repository

Hackett-Jones, Emily J.

2012-04-17

Conservation equations governed by a nonlocal interaction potential generate aggregates from an initial uniform distribution of particles. We address the evolution and formation of these aggregating steady states when the interaction potential has both attractive and repulsive singularities. Currently, no existence theory for such potentials is available. We develop and compare two complementary solution methods, a continuous pseudoinverse method and a discrete stochastic lattice approach, and formally show a connection between the two. Interesting aggregation patterns involving multiple peaks for a simple doubly singular attractive-repulsive potential are determined. For a swarming Morse potential, characteristic slow-fast dynamics in the scaled inverse energy is observed in the evolution to steady state in both the continuous and discrete approaches. The discrete approach is found to be remarkably robust to modifications in movement rules, related to the potential function. The comparable evolution dynamics and steady states of the discrete model with the continuum model suggest that the discrete stochastic approach is a promising way of probing aggregation patterns arising from two- and three-dimensional nonlocal interaction conservation equations. © 2012 American Physical Society.

Matrix models and stochastic growth in Donaldson-Thomas theory

Energy Technology Data Exchange (ETDEWEB)

Szabo, Richard J. [Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS, United Kingdom and Maxwell Institute for Mathematical Sciences, Edinburgh (United Kingdom); Tierz, Miguel [Grupo de Fisica Matematica, Complexo Interdisciplinar da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, PT-1649-003 Lisboa (Portugal); Departamento de Analisis Matematico, Facultad de Ciencias Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain)

2012-10-15

We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kaehler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.

Matrix models and stochastic growth in Donaldson-Thomas theory

International Nuclear Information System (INIS)

Szabo, Richard J.; Tierz, Miguel

2012-01-01

We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kähler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.

Spatially heterogeneous stochasticity and the adaptive diversification of dormancy.

Science.gov (United States)

Rajon, E; Venner, S; Menu, F

2009-10-01

Diversified bet-hedging, a strategy that leads several individuals with the same genotype to express distinct phenotypes in a given generation, is now well established as a common evolutionary response to environmental stochasticity. Life-history traits defined as diversified bet-hedging (e.g. germination or diapause strategies) display marked differences between populations in spatial proximity. In order to find out whether such differences can be explained by local adaptations to spatially heterogeneous environmental stochasticity, we explored the evolution of bet-hedging dormancy strategies in a metapopulation using a two-patch model with patch differences in stochastic juvenile survival. We found that spatial differences in the level of environmental stochasticity, restricted dispersal, increased fragmentation and intermediate survival during dormancy all favour the adaptive diversification of bet-hedging dormancy strategies. Density dependency also plays a major role in the diversification of dormancy strategies because: (i) it may interact locally with environmental stochasticity and amplify its effects; however, (ii) it can also generate chaotic population dynamics that may impede diversification. Our work proposes new hypotheses to explain the spatial patterns of bet-hedging strategies that we hope will encourage new empirical studies of this topic.

Stochastic solution of population balance equations for reactor networks

International Nuclear Information System (INIS)

Menz, William J.; Akroyd, Jethro; Kraft, Markus

2014-01-01

This work presents a sequential modular approach to solve a generic network of reactors with a population balance model using a stochastic numerical method. Full-coupling to the gas-phase is achieved through operator-splitting. The convergence of the stochastic particle algorithm in test networks is evaluated as a function of network size, recycle fraction and numerical parameters. These test cases are used to identify methods through which systematic and statistical error may be reduced, including by use of stochastic weighted algorithms. The optimal algorithm was subsequently used to solve a one-dimensional example of silicon nanoparticle synthesis using a multivariate particle model. This example demonstrated the power of stochastic methods in resolving particle structure by investigating the transient and spatial evolution of primary polydispersity, degree of sintering and TEM-style images. Highlights: •An algorithm is presented to solve reactor networks with a population balance model. •A stochastic method is used to solve the population balance equations. •The convergence and efficiency of the reported algorithms are evaluated. •The algorithm is applied to simulate silicon nanoparticle synthesis in a 1D reactor. •Particle structure is reported as a function of reactor length and time

A stochastic approach for automatic registration and fusion of left atrial electroanatomic maps with 3D CT anatomical images

International Nuclear Information System (INIS)

Cristoforetti, Alessandro; Mase, Michela; Faes, Luca; Centonze, Maurizio; Greco, Maurizio Del; Antolini, Renzo; Nollo, Giandomenico; Ravelli, Flavia

2007-01-01

The integration of electroanatomic maps with highly resolved computed tomography cardiac images plays an important role in the successful planning of the ablation procedure of arrhythmias. In this paper, we present and validate a fully-automated strategy for the registration and fusion of sparse, atrial endocardial electroanatomic maps (CARTO maps) with detailed left atrial (LA) anatomical reconstructions segmented from a pre-procedural MDCT scan. Registration is accomplished by a parameterized geometric transformation of the CARTO points and by a stochastic search of the best parameter set which minimizes the misalignment between transformed CARTO points and the LA surface. The subsequent fusion of electrophysiological information on the registered CT atrium is obtained through radial basis function interpolation. The algorithm is validated by simulation and by real data from 14 patients referred to CT imaging prior to the ablation procedure. Results are presented, which show the validity of the algorithmic scheme as well as the accuracy and reproducibility of the integration process. The obtained results encourage the application of the integration method in post-intervention ablation assessment and basic AF research and suggest the development for real-time applications in catheter guiding during ablation intervention

Rotationally invariant correlation filtering

International Nuclear Information System (INIS)

Schils, G.F.; Sweeney, D.W.

1985-01-01

A method is presented for analyzing and designing optical correlation filters that have tailored rotational invariance properties. The concept of a correlation of an image with a rotation of itself is introduced. A unified theory of rotation-invariant filtering is then formulated. The unified approach describes matched filters (with no rotation invariance) and circular-harmonic filters (with full rotation invariance) as special cases. The continuum of intermediate cases is described in terms of a cyclic convolution operation over angle. The angular filtering approach allows an exact choice for the continuous trade-off between loss of the correlation energy (or specificity regarding the image) and the amount of rotational invariance desired

Stochastic many-body problems in ecology, evolution, neuroscience, and systems biology

Science.gov (United States)

Butler, Thomas C.

-patterns exist over a much larger range of physically accessible parameters than the patterns predicted in mean field theory and therefore account for the apparent observations in ecology of patterns in regimes where Turing patterns do not occur. I further show that quasi-patterns have statistical properties that allow them to be distinguished empirically from mean field Turing patterns. I next analyze a model of visual cortex in the brain that has striking similarities to the activator-inhibitor model of ecosystem quasi-pattern formation. Through analysis of the resulting phase diagram, I show that the architecture of the neural network in the visual cortex is configured to make the visual cortex robust to unwanted internally generated spatial structure that interferes with normal visual function. I also predict that some geometric visual hallucinations are quasi-patterns and that the visual cortex supports a new phase of spatially scale invariant behavior present far from criticality. In the final chapter, I explore the effects of fluctuations on cycles in systems biology, specifically the pervasive phenomenon of circadian rhythms. By exploring the behavior of a generic stochastic model of circadian rhythms, I show that the circadian rhythm circuit exploits leaky mRNA production to safeguard the cycle from failure. I also show that this safeguard mechanism is highly robust to changes in the rate of leaky mRNA production. Finally, I explore the failure of the deterministic model in two different contexts, one where the deterministic model predicts cycles where they do not exist, and another context in which cycles are not predicted by the deterministic model.

Necessity of intermediate mass scales in grand unified theories with spontaneously broken CP invariance

International Nuclear Information System (INIS)

Senjanovic, G.

1982-07-01

It is demonstrated that the spontaneous breakdown of CP invariance in grand unified theories requires the presence of intermediate mass scales. The simplest realization is provided by weakly broken left-right symmetry in the context of SU(2)sub(L) x SU(2)sub(R) x U(1)sub(B-L) model embedded in grand unified theories. (author)

Structure and properties of Hughston's stochastic extension of the Schroedinger equation

International Nuclear Information System (INIS)

Adler, Stephen L.; Horwitz, Lawrence P.

2000-01-01

Hughston has recently proposed a stochastic extension of the Schroedinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a general proof that Hughston's equation leads to state vector collapse to energy eigenstates, with collapse probabilities given by the quantum mechanical probabilities computed from the initial state. We discuss the relation of Hughston's equation to earlier work on norm-preserving stochastic equations, and show that Hughston's equation can be written as a manifestly unitary stochastic evolution equation for the pure state density matrix. We discuss the behavior of systems constructed as direct products of independent subsystems, and briefly address the question of whether an energy-based approach, such as Hughston's, suffices to give an objective interpretation of the measurement process in quantum mechanics. (c) 2000 American Institute of Physics

Properties of invariant modelling and invariant glueing of vector fields

International Nuclear Information System (INIS)

Petukhov, V.R.

1987-01-01

Invariant modelling and invariant glueing of both continuous (rates and accelerations) and descrete vector fields, gradient and divergence cases are considered. The following appendices are discussed: vector fields in crystals, crystal disclinations, topological charges and their fields

Mean Field Games for Stochastic Growth with Relative Utility

Energy Technology Data Exchange (ETDEWEB)

Huang, Minyi, E-mail: mhuang@math.carleton.ca [Carleton University, School of Mathematics and Statistics (Canada); Nguyen, Son Luu, E-mail: sonluu.nguyen@upr.edu [University of Puerto Rico, Department of Mathematics (United States)

2016-12-15

This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.

Mean Field Games for Stochastic Growth with Relative Utility

International Nuclear Information System (INIS)

Huang, Minyi; Nguyen, Son Luu

2016-01-01

This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.

Provably unbounded memory advantage in stochastic simulation using quantum mechanics

Science.gov (United States)

Garner, Andrew J. P.; Liu, Qing; Thompson, Jayne; Vedral, Vlatko; Gu, mile

2017-10-01

Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the simulation is thus generally limited by the internal memory available to the simulator. Here, using tools from computational mechanics, we show that quantum processors with a fixed finite memory can simulate stochastic processes of real variables to arbitrarily high precision. This demonstrates a provable, unbounded memory advantage that a quantum simulator can exhibit over its best possible classical counterpart.

Stereo matching based on SIFT descriptor with illumination and camera invariance

Science.gov (United States)

Niu, Haitao; Zhao, Xunjie; Li, Chengjin; Peng, Xiang

2010-10-01

Stereo matching is the process of finding corresponding points in two or more images. The description of interest points is a critical aspect of point correspondence which is vital in stereo matching. SIFT descriptor has been proven to be better on the distinctiveness and robustness than other local descriptors. However, SIFT descriptor does not involve color information of feature point which provides powerfully distinguishable feature in matching tasks. Furthermore, in a real scene, image color are affected by various geometric and radiometric factors,such as gamma correction and exposure. These situations are very common in stereo images. For this reason, the color recorded by a camera is not a reliable cue, and the color consistency assumption is no longer valid between stereo images in real scenes. Hence the performance of other SIFT-based stereo matching algorithms can be severely degraded under the radiometric variations. In this paper, we present a new improved SIFT stereo matching algorithms that is invariant to various radiometric variations between left and right images. Unlike other improved SIFT stereo matching algorithms, we explicitly employ the color formation model with the parameters of lighting geometry, illuminant color and camera gamma in SIFT descriptor. Firstly, we transform the input color images to log-chromaticity color space, thus a linear relationship can be established. Then, we use a log-polar histogram to build three color invariance components for SIFT descriptor. So that our improved SIFT descriptor is invariant to lighting geometry, illuminant color and camera gamma changes between left and right images. Then we can match feature points between two images and use SIFT descriptor Euclidean distance as a geometric measure in our data sets to make it further accurate and robust. Experimental results show that our method is superior to other SIFT-based algorithms including conventional stereo matching algorithms under various

Family of probability distributions derived from maximal entropy principle with scale invariant restrictions.

Science.gov (United States)

Sonnino, Giorgio; Steinbrecher, György; Cardinali, Alessandro; Sonnino, Alberto; Tlidi, Mustapha

2013-01-01

Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing the minimum entropy production and the maximum entropy principle under the scale invariance restrictions. The obtained probability distribution presents a singularity that has immediate physical interpretation in terms of the intermittency models. The derived reference probability distribution function is interpreted as time and ensemble average of the real physical one. A generic family of stochastic processes describing noise-driven intermittency, where the stationary density distribution coincides exactly with the one resulted from entropy maximization, is presented.

Intermittent targeted therapies and stochastic evolution in patients affected by chronic myeloid leukemia

Science.gov (United States)

Pizzolato, N.; Persano Adorno, D.; Valenti, D.; Spagnolo, B.

2016-05-01

Front line therapy for the treatment of patients affected by chronic myeloid leukemia (CML) is based on the administration of tyrosine kinase inhibitors, namely imatinib or, more recently, axitinib. Although imatinib is highly effective and represents an example of a successful molecular targeted therapy, the appearance of resistance is observed in a proportion of patients, especially those in advanced stages. In this work, we investigate the appearance of resistance in patients affected by CML, by modeling the evolutionary dynamics of cancerous cell populations in a simulated patient treated by an intermittent targeted therapy. We simulate, with the Monte Carlo method, the stochastic evolution of initially healthy cells to leukemic clones, due to genetic mutations and changes in their reproductive behavior. We first present the model and its validation with experimental data by considering a continuous therapy. Then, we investigate how fluctuations in the number of leukemic cells affect patient response to the therapy when the drug is administered with an intermittent time scheduling. Here we show that an intermittent therapy (IT) represents a valid choice in patients with high risk of toxicity, despite an associated delay to the complete restoration of healthy cells. Moreover, a suitably tuned IT can reduce the probability of developing resistance.

Left-Handed W bosons at the LHC

International Nuclear Information System (INIS)

Dixon, Lance

2011-01-01

The production of W bosons in association with jets is an important background to new physics at the LHC. Events in which the W carries large transverse momentum and decays leptonically lead to large missing energy and are of particular importance. We show that the left-handed nature of the W coupling, combined with valence quark domination at a pp machine, leads to a large left-handed polarization for both W + and W - bosons at large transverse momenta. The polarization fractions are very stable with respect to QCD corrections. The leptonic decay of the W +- bosons translates the common left-handed polarization into a strong asymmetry in transverse momentum distributions between positrons and electrons, and between neutrinos and anti-neutrinos (missing transverse energy). Such asymmetries may provide an effective experimental handle on separating W +jets from top quark production, which exhibits very little asymmetry due to C invariance, and from various types of new physics.

Left-Handed W bosons at the LHC

Energy Technology Data Exchange (ETDEWEB)

Bern, Z.; /UCLA; Diana, G.; /Saclay, SPhT; Dixon, L.J.; /CERN /SLAC; Cordero, F.Febres; /Simon Bolivar U.; Forde, D.; /Simon Bolivar U. /NIKHEF, Amsterdam; Gleisberg, T.; Hoeche, S.; /SLAC; Ita, H.; /UCLA; Kosower, D.A.; /Saclay, SPhT; Maitre, D.; /CERN /Durham U.; Ozeren, K.; /UCLA

2011-05-20

The production of W bosons in association with jets is an important background to new physics at the LHC. Events in which the W carries large transverse momentum and decays leptonically lead to large missing energy and are of particular importance. We show that the left-handed nature of the W coupling, combined with valence quark domination at a pp machine, leads to a large left-handed polarization for both W{sup +} and W{sup -} bosons at large transverse momenta. The polarization fractions are very stable with respect to QCD corrections. The leptonic decay of the W{sup +-} bosons translates the common left-handed polarization into a strong asymmetry in transverse momentum distributions between positrons and electrons, and between neutrinos and anti-neutrinos (missing transverse energy). Such asymmetries may provide an effective experimental handle on separating W +jets from top quark production, which exhibits very little asymmetry due to C invariance, and from various types of new physics.

Extended Jacobi Elliptic Function Rational Expansion Method and Its Application to (2+1)-Dimensional Stochastic Dispersive Long Wave System

International Nuclear Information System (INIS)

Song Lina; Zhang Hongqing

2007-01-01

In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the (2+1)-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.

Left ventricular hypertrophy: virtuous intentions, malign consequences.

Science.gov (United States)

Pokharel, Saraswati; Sharma, Umesh C; Pinto, Yigal M

2003-06-01

Left ventricular hypertrophy (LVH) is currently the focus of intense cardiovascular research, with the resultant rapid evolution of novel concepts relating to its exceedingly complex pathophysiology. In addition to the alterations in signal transduction and disturbances in Ca(2+) homeostasis, there are structural changes in myofilaments, disorganization of the cytoskeletal framework and increased collagen synthesis. LVH is associated with progressive left ventricular remodeling that culminates to heart failure. The modern treatment of left ventricular hypertrophy is now largely based on the hypothesis that neuroendocrine activation is important in the progression of the disease and inhibition of neurohormones is likely to have long-term benefit with regard to morbidity and mortality. Drugs specifically designed to unload the left ventricle, such as diuretics and vasodilators, appears to be less effective in reducing LV mass and improving prognosis. Thus, the evolution of treatment for LVH itself has provided much enlightenment for our understanding of the fundamental biology of the disorder.

Remarks on the E-invariant and the Casson invariant

International Nuclear Information System (INIS)

Seade, J.

1991-08-01

In this work a framed manifold means a pair (M,F) consisting of a closed C ∞ , stably parallelizable manifold M, together with a trivialization F of its stable tangent bundle. The purpose of this work is to understand and determine in higher dimensions the invariant h(M,F) appearing in connection with the Adams e-invariants. 28 refs

Stochastic hyperfine interactions modeling library

Science.gov (United States)

Zacate, Matthew O.; Evenson, William E.

2011-04-01

The stochastic hyperfine interactions modeling library (SHIML) provides a set of routines to assist in the development and application of stochastic models of hyperfine interactions. The library provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized; however, there was a need to develop supplementary code to find an orthonormal set of (left and right) eigenvectors of complex, non-Hermitian matrices. In addition, example code is provided to illustrate the use of SHIML to generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than A can be neglected. Program summaryProgram title: SHIML Catalogue identifier: AEIF_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL 3 No. of lines in distributed program, including test data, etc.: 8224 No. of bytes in distributed program, including test data, etc.: 312 348 Distribution format: tar.gz Programming language: C Computer: Any Operating system: LINUX, OS X RAM: Varies Classification: 7.4 External routines: TAPP [1], BLAS [2], a C-interface to BLAS [3], and LAPACK [4] Nature of problem: In condensed matter systems, hyperfine methods such as nuclear magnetic resonance (NMR), Mössbauer effect (ME), muon spin rotation (μSR), and perturbed angular correlation spectroscopy (PAC) measure electronic and magnetic structure within Angstroms of nuclear probes through the hyperfine interaction. When

A stochastic differential equation framework for the turbulent velocity field

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler; Schmiegel, Jürgen

We discuss a stochastic differential equation, as a modelling framework for the turbulent velocity field, that is capable of capturing basic stylized facts of the statistics of velocity increments. In particular, we focus on the evolution of the probability density of velocity increments...

Cultural evolution as a nonstationary stochastic process

DEFF Research Database (Denmark)

Nicholson, Arwen; Sibani, Paolo

2016-01-01

We present an individual based model of cultural evolution, where interacting agents are coded by binary strings standing for strategies for action, blueprints for products or attitudes and beliefs. The model is patterned on an established model of biological evolution, the Tangled Nature Model...... (TNM), where a “tangle” of interactions between agents determines their reproductive success. In addition, our agents also have the ability to copy part of each other's strategy, a feature inspired by the Axelrod model of cultural diversity. Unlike the latter, but similarly to the TNM, the model...

Stochastic Coastal/Regional Uncertainty Modelling: a Copernicus marine research project in the framework of Service Evolution

Science.gov (United States)

Vervatis, Vassilios; De Mey, Pierre; Ayoub, Nadia; Kailas, Marios; Sofianos, Sarantis

2017-04-01

The project entitled Stochastic Coastal/Regional Uncertainty Modelling (SCRUM) aims at strengthening CMEMS in the areas of ocean uncertainty quantification, ensemble consistency verification and ensemble data assimilation. The project has been initiated by the University of Athens and LEGOS/CNRS research teams, in the framework of CMEMS Service Evolution. The work is based on stochastic modelling of ocean physics and biogeochemistry in the Bay of Biscay, on an identical sub-grid configuration of the IBI-MFC system in its latest CMEMS operational version V2. In a first step, we use a perturbed tendencies scheme to generate ensembles describing uncertainties in open ocean and on the shelf, focusing on upper ocean processes. In a second step, we introduce two methodologies (i.e. rank histograms and array modes) aimed at checking the consistency of the above ensembles with respect to TAC data and arrays. Preliminary results highlight that wind uncertainties dominate all other atmosphere-ocean sources of model errors. The ensemble spread in medium-range ensembles is approximately 0.01 m for SSH and 0.15 °C for SST, though these values vary depending on season and cross shelf regions. Ecosystem model uncertainties emerging from perturbations in physics appear to be moderately larger than those perturbing the concentration of the biogeochemical compartments, resulting in total chlorophyll spread at about 0.01 mg.m-3. First consistency results show that the model ensemble and the pseudo-ensemble of OSTIA (L4) observation SSTs appear to exhibit nonzero joint probabilities with each other since error vicinities overlap. Rank histograms show that the model ensemble is initially under-dispersive, though results improve in the context of seasonal-range ensembles.

Lateral diffusion of the topological charge density in stochastic optical fields

CSIR Research Space (South Africa)

Roux, FS

2010-01-01

Full Text Available Stochastic (i.e. random and quasi-random) optical fields may contain distributions of optical vortices that are represented by non-uniform topological charge densities. Numerical simulations are used to investigate the evolution under free...

Invariants of generalized Lie algebras

International Nuclear Information System (INIS)

Agrawala, V.K.

1981-01-01

Invariants and invariant multilinear forms are defined for generalized Lie algebras with arbitrary grading and commutation factor. Explicit constructions of invariants and vector operators are given by contracting invariant forms with basic elements of the generalized Lie algebra. The use of the matrix of a linear map between graded vector spaces is emphasized. With the help of this matrix, the concept of graded trace of a linear operator is introduced, which is a rich source of multilinear forms of degree zero. To illustrate the use of invariants, a characteristic identity similar to that of Green is derived and a few Racah coefficients are evaluated in terms of invariants

TIME-DEPENDENT STOCHASTIC ACCELERATION MODEL FOR FERMI BUBBLES

Energy Technology Data Exchange (ETDEWEB)

Sasaki, Kento; Asano, Katsuaki; Terasawa, Toshio, E-mail: kentos@icrr.u-tokyo.ac.jp, E-mail: asanok@icrr.u-tokyo.ac.jp, E-mail: terasawa@icrr.u-tokyo.ac.jp [Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8582 (Japan)

2015-12-01

We study stochastic acceleration models for the Fermi bubbles. Turbulence is excited just behind the shock front via Kelvin–Helmholtz, Rayleigh–Taylor, or Richtmyer–Meshkov instabilities, and plasma particles are continuously accelerated by the interaction with the turbulence. The turbulence gradually decays as it goes away from the shock fronts. Adopting a phenomenological model for the stochastic acceleration, we explicitly solve the temporal evolution of the particle energy distribution in the turbulence. Our results show that the spatial distribution of high-energy particles is different from those for a steady solution. We also show that the contribution of electrons that escaped from the acceleration regions significantly softens the photon spectrum. The photon spectrum and surface brightness profile are reproduced by our models. If the escape efficiency is very high, the radio flux from the escaped low-energy electrons can be comparable to that of the WMAP haze. We also demonstrate hadronic models with the stochastic acceleration, but they are unlikely in the viewpoint of the energy budget.

Diffusive processes in a stochastic magnetic field

International Nuclear Information System (INIS)

Wang, H.; Vlad, M.; Vanden Eijnden, E.; Spineanu, F.; Misguich, J.H.; Balescu, R.

1995-01-01

The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing, in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle's trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works

Stochasticity and superadiabaticity in radiofrequency plasma heating

International Nuclear Information System (INIS)

Stix, T.H.

1979-04-01

In a plasma subject to radiofrequency fields, it is only the resonant particles - comprising just a minor portion of the total velocity distribution - which are strongly affected. Under near-fusion conditions, thermalization by Coulomb collisions is slow, and noncollisional stochasticity can play an important role in reshaping f(v). It is found that the common rf interactions, including Landau, cyclotron and transit-time damping, can be fitted in a unified manner by a simple two-step one-parameter (epsilon) mapping which can display collision-free stochastic or adiabatic (also called superadiabatic) behavior, depending on the choice of epsilon. The effect on the evolution of the space averaged f (x,v,t) is reasonably well described by a pseudo-stochastic diffusion function, D/sub PS/(v,epsilon) which is the quasilinear diffusion coefficient but with appropriate widening of the delta-function spikes. Coulomb collisions, leading to D/sub Coul/(v) which may be added and directly compared to D/sub PS/(v,epsilon), are introduced by Langevin terms in the mapping equations

On density of the Vassiliev invariants

DEFF Research Database (Denmark)

Røgen, Peter

1999-01-01

The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots......The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots...

Stochastic cooling equipment at the ISR

CERN Multimedia

1983-01-01

The photo shows (centre) an experimental set-up for stochastic cooling of vertical betatron oscillations, used at the ISR in the years before the ICE ring was built. Cooling times of about 30 min were obtained in the low intensity range (~0.3 A). To be noted the four 50 Ohm brass input/output connections with cooling fins, and the baking-out sheet around the cylinder. On the left one sees a clearing electrode box allowing the electrode current to be measured, and the pressure seen by the beam to be evaluated.

Constraining Stochastic Parametrisation Schemes Using High-Resolution Model Simulations

Science.gov (United States)

Christensen, H. M.; Dawson, A.; Palmer, T.

2017-12-01

Stochastic parametrisations are used in weather and climate models as a physically motivated way to represent model error due to unresolved processes. Designing new stochastic schemes has been the target of much innovative research over the last decade. While a focus has been on developing physically motivated approaches, many successful stochastic parametrisation schemes are very simple, such as the European Centre for Medium-Range Weather Forecasts (ECMWF) multiplicative scheme `Stochastically Perturbed Parametrisation Tendencies' (SPPT). The SPPT scheme improves the skill of probabilistic weather and seasonal forecasts, and so is widely used. However, little work has focused on assessing the physical basis of the SPPT scheme. We address this matter by using high-resolution model simulations to explicitly measure the `error' in the parametrised tendency that SPPT seeks to represent. The high resolution simulations are first coarse-grained to the desired forecast model resolution before they are used to produce initial conditions and forcing data needed to drive the ECMWF Single Column Model (SCM). By comparing SCM forecast tendencies with the evolution of the high resolution model, we can measure the `error' in the forecast tendencies. In this way, we provide justification for the multiplicative nature of SPPT, and for the temporal and spatial scales of the stochastic perturbations. However, we also identify issues with the SPPT scheme. It is therefore hoped these measurements will improve both holistic and process based approaches to stochastic parametrisation. Figure caption: Instantaneous snapshot of the optimal SPPT stochastic perturbation, derived by comparing high-resolution simulations with a low resolution forecast model.

Stochastic problems in population genetics

CERN Document Server

Maruyama, Takeo

1977-01-01

These are" notes based on courses in Theoretical Population Genetics given at the University of Texas at Houston during the winter quarter, 1974, and at the University of Wisconsin during the fall semester, 1976. These notes explore problems of population genetics and evolution involving stochastic processes. Biological models and various mathematical techniques are discussed. Special emphasis is given to the diffusion method and an attempt is made to emphasize the underlying unity of various problems based on the Kolmogorov backward equation. A particular effort was made to make the subject accessible to biology students who are not familiar with stochastic processes. The references are not exhaustive but were chosen to provide a starting point for the reader interested in pursuing the subject further. Acknowledgement I would like to use this opportunity to express my thanks to Drs. J. F. Crow, M. Nei and W. J. Schull for their hospitality during my stays at their universities. I am indebted to Dr. M. Kimura...

Beam life-time with intrabeam scattering and stochastic cooling

International Nuclear Information System (INIS)

Wei, J.; Ruggiero, A.G.

1991-01-01

A transport equation has been derived in terms of the longitudinal action variable to describe the time evolution of the longitudinal density distribution of a bunched hadron beam in the presence of intrabeam scattering and stochastic cooling. A computer program has been developed to numerically solve this equation. Both beam loss and bunch-shape evolution have been investigated for the 197 Au 79+ beams during the 10-hour storage in the Relativistic Heavy Ion Collider currently under construction at the Brookhaven National Laboratory. 9 refs., 1 fig

Adiabatic invariants in stellar dynamics. 1: Basic concepts

Science.gov (United States)

Weinberg, Martin D.

1994-01-01

The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly varying perturbation is exponentially small. Recent mathematical results that precisely define the conditions for invariance show that this model does not apply in general. In particular, a slowly varying perturbation may cause significant evolution stellar dynamical systems even if its time scale is longer than any internal orbital time scale. This additional 'heating' may have serious implications for the evolution of star clusters and dwarf galaxies which are subject to long-term environmental forces. The mathematical developments leading to these results are reviewed, and the conditions for applicability to and further implications for stellar systems are discussed. Companion papers present a computational method for a general time-dependent disturbance and detailed example.

ENVIRONMENT: a computational platform to stochastically simulate reacting and self-reproducing lipid compartments

Science.gov (United States)

Mavelli, Fabio; Ruiz-Mirazo, Kepa

2010-09-01

'ENVIRONMENT' is a computational platform that has been developed in the last few years with the aim to simulate stochastically the dynamics and stability of chemically reacting protocellular systems. Here we present and describe some of its main features, showing how the stochastic kinetics approach can be applied to study the time evolution of reaction networks in heterogeneous conditions, particularly when supramolecular lipid structures (micelles, vesicles, etc) coexist with aqueous domains. These conditions are of special relevance to understand the origins of cellular, self-reproducing compartments, in the context of prebiotic chemistry and evolution. We contrast our simulation results with real lab experiments, with the aim to bring together theoretical and experimental research on protocell and minimal artificial cell systems.

Classical and spatial stochastic processes with applications to biology

CERN Document Server

Schinazi, Rinaldo B

2014-01-01

The revised and expanded edition of this textbook presents the concepts and applications of random processes with the same illuminating simplicity as its first edition, but with the notable addition of substantial modern material on biological modeling. While still treating many important problems in fields such as engineering and mathematical physics, the book also focuses on the highly relevant topics of cancerous mutations, influenza evolution, drug resistance, and immune response. The models used elegantly apply various classical stochastic models presented earlier in the text, and exercises are included throughout to reinforce essential concepts. The second edition of Classical and Spatial Stochastic Processes is suitable as a textbook for courses in stochastic processes at the advanced-undergraduate and graduate levels, or as a self-study resource for researchers and practitioners in mathematics, engineering, physics, and mathematical biology. Reviews of the first edition: An appetizing textbook for a f...

Cohomological invariants in Galois cohomology

CERN Document Server

Garibaldi, Skip; Serre, Jean Pierre

2003-01-01

This volume is concerned with algebraic invariants, such as the Stiefel-Whitney classes of quadratic forms (with values in Galois cohomology mod 2) and the trace form of �tale algebras (with values in the Witt ring). The invariants are analogues for Galois cohomology of the characteristic classes of topology. Historically, one of the first examples of cohomological invariants of the type considered here was the Hasse-Witt invariant of quadratic forms. The first part classifies such invariants in several cases. A principal tool is the notion of versal torsor, which is an analogue of the universal bundle in topology. The second part gives Rost's determination of the invariants of G-torsors with values in H^3(\\mathbb{Q}/\\mathbb{Z}(2)), when G is a semisimple, simply connected, linear group. This part gives detailed proofs of the existence and basic properties of the Rost invariant. This is the first time that most of this material appears in print.

Epigenetics and Evolution: Transposons and the Stochastic Epigenetic Modification Model

Directory of Open Access Journals (Sweden)

Sergio Branciamore

2015-04-01

Full Text Available In addition to genetic variation, epigenetic variation and transposons can greatly affect the evolutionary fitnesses landscape and gene expression. Previously we proposed a mathematical treatment of a general epigenetic variation model that we called Stochastic Epigenetic Modification (SEM model. In this study we follow up with a special case, the Transposon Silencing Model (TSM, with, once again, emphasis on quantitative treatment. We have investigated the evolutionary effects of epigenetic changes due to transposon (T insertions; in particular, we have considered a typical gene locus A and postulated that (i the expression level of gene A depends on the epigenetic state (active or inactive of a cis- located transposon element T, (ii stochastic variability in the epigenetic silencing of T occurs only in a short window of opportunity during development, (iii the epigenetic state is then stable during further development, and (iv the epigenetic memory is fully reset at each generation. We develop the model using two complementary approaches: a standard analytical population genetics framework (di usion equations and Monte-Carlo simulations. Both approaches led to similar estimates for the probability of fixation and time of fixation of locus TA with initial frequency P in a randomly mating diploid population of effective size Ne. We have ascertained the e ect that ρ, the probability of transposon Modification during the developmental window, has on the population (species. One of our principal conclusions is that as ρ increases, the pattern of fixation of the combined TA locus goes from "neutral" to "dominant" to "over-dominant". We observe that, under realistic values of ρ, epigenetic Modifications can provide an e cient mechanism for more rapid fixation of transposons and cis-located gene alleles. The results obtained suggest that epigenetic silencing, even if strictly transient (being reset at each generation, can still have signi cant

Provably unbounded memory advantage in stochastic simulation using quantum mechanics

International Nuclear Information System (INIS)

Garner, Andrew J P; Thompson, Jayne; Vedral, Vlatko; Gu, Mile; Liu, Qing

2017-01-01

Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the simulation is thus generally limited by the internal memory available to the simulator. Here, using tools from computational mechanics, we show that quantum processors with a fixed finite memory can simulate stochastic processes of real variables to arbitrarily high precision. This demonstrates a provable, unbounded memory advantage that a quantum simulator can exhibit over its best possible classical counterpart. (paper)

Stochastic mechanics of mixed states

International Nuclear Information System (INIS)

Jaekel, M.T.; Pignon, D.

1984-01-01

Nelson's stochastic interpretation of quantum mechanics is extended from the case of pure states to that of mixed states. It is shown that a pure probabilistic formalism, which applies the Newton-Nelson Law to the initial position and velocity distributions, does not reproduce the time evolution predicted by quantum mechanics. In order to recover the latter, a new notion must be introduced, that of pure quantum states, over which the mixture has to be decomposed, and which then satisfy the Newton-Nelson Law independently. (author)

Cosmological disformal invariance

Energy Technology Data Exchange (ETDEWEB)

Domènech, Guillem; Sasaki, Misao [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Naruko, Atsushi, E-mail: guillem.domenech@yukawa.kyoto-u.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: misao@yukawa.kyoto-u.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)

2015-10-01

The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open question. In this paper, it is shown that a pure disformal transformation without any conformal factor is equivalent to rescaling the time coordinate. Since this rescaling applies equally to all the physical quantities, physics must be invariant under a disformal transformation, that is, neither causal structure, propagation speed nor any other property of the fields are affected by a disformal transformation itself. This fact is presented at the action level for gravitational and matter fields and it is illustrated with some examples of observable quantities. We also find the physical invariance for cosmological perturbations at linear and high orders in perturbation, extending previous studies. Finally, a comparison with Horndeski and beyond Horndeski theories under a disformal transformation is made.

Donaldson invariants in algebraic geometry

International Nuclear Information System (INIS)

Goettsche, L.

2000-01-01

In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)

Chirality invariance and 'chiral' fields

International Nuclear Information System (INIS)

Ziino, G.

1978-01-01

The new field model derived in the present paper actually gives a definite answer to three fundamental questions concerning elementary-particle physics: 1) The phenomenological dualism between parity and chirality invariance: it would be only an apparent display of a general 'duality' principle underlying the intrinsic nature itself of (spin 1/2) fermions and expressed by the anticommutativity property between scalar and pseudoscalar charges. 2) The real physical meaning of V - A current structure: it would exclusively be connected to the one (just pointed out) of chiral fields themselves. 3) The unjustified apparent oddness shown by Nature in weak interactions, for the fact of picking out only one of the two (left- and right-handed) fermion 'chiral' projections: the key to such a 'mystery' would just be provided by the consequences of the dual and partial character of the two fermion-antifermion field bases. (Auth.)

Moment invariants for particle beams

International Nuclear Information System (INIS)

Lysenko, W.P.; Overley, M.S.

1988-01-01

The rms emittance is a certain function of second moments in 2-D phase space. It is preserved for linear uncoupled (1-D) motion. In this paper, the authors present new functions of moments that are invariants for coupled motion. These invariants were computed symbolically using a computer algebra system. Possible applications for these invariants are discussed. Also, approximate moment invariants for nonlinear motion are presented

Exotic fermions in the left-right symmetric model

International Nuclear Information System (INIS)

Choi, J.; Volkas, R.R.

1992-01-01

A systematic study is made of non-standard fermion multiplets in left-right symmetric models with gauge group SU(3) x SU(2) L x SU(2) R x U(1) BL . Constraints from gauge anomaly cancellation and invariance of Yukawa coupling terms are used to define interesting classes of exotic fermions. The standard quark lepton spectrum of left-right symmetric models was identified as the simplest member of an infinite class. Phenomenological implications of the next simplest member of this class are then studied. Classes of exotic fermions which may couple to the standard fermions through doublet Higgs bosons were also considered, then shown that some of these exotics may be used to induce a generalised universal see-saw mechanism. 12 refs., 1 tab

Stochastic Analysis 2010

CERN Document Server

Crisan, Dan

2011-01-01

"Stochastic Analysis" aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume "Stochastic Analysis 2010" provides a sa

Experiments and stochastic simulations of lignite coal during pyrolysis and gasification

International Nuclear Information System (INIS)

Ahmed, I.I.; Gupta, A.K.

2013-01-01

Highlights: ► Lignite pyrolysis and gasification has been conducted in a semi batch reactor. ► The objective is to understand mechanism of syngas evolution during pyrolysis. ► Stochastic simulations of lignite pyrolysis were conducted using Gillespie algorithm. ► First order, single step mechanism failed to fit cumulative yield of hydrogen. ► Evolution of hydrogen via pyrolysis of gaseous hydrocarbon following bridges scission. -- Abstract: Lignite pyrolysis and gasification has been conducted in a semi batch reactor at reactor temperatures of 800–950 °C in 50 °C intervals. CO 2 has been used as the gasifying agent for gasification experiments. The objective of this investigation is to understand the mechanism of syngas evolution during pyrolysis and to unravel the effect of CO 2 on pyrolysis mechanism. Stochastic simulations of lignite pyrolysis have been conducted using Gillespie algorithm. Two reaction mechanisms have been used in the simulations; first order, single step mechanism and the FLASHCHAIN mechanism. The first order single step mechanism was successful in fitting cumulative yield of CO 2 , CO, CH 4 and other hydrocarbons (C n H m ). The first order, single step failed to fit the cumulative yield of hydrogen, which suggests a more complex mechanism for hydrogen evolution. Evolution of CO 2 , CO, CH 4 , C n H m and H 2 flow rates has been monitored. The only effect of CO 2 on pyrolysis mechanism is promotion of reverse water gas shift reaction for the experiments described here. Methane evolution extended for slightly longer time than other hydrocarbons and hydrogen evolution extended for a slightly longer time than methane. This indicated the evolution of hydrogen via further pyrolysis of aliphatic hydrocarbon. It is also suggested that this step occurs in series after aliphatic hydrocarbons evolution by bridges scission.

Right retrograde brachial cerebral angiography with simultaneous compression of the left carotid artery

International Nuclear Information System (INIS)

Ericson, K.; Mosskin, M.

1981-01-01

Right retrograde brachial angiography with simultaneous compression of the left common carotid artery was performed in 12 patients, invariably resulting in filling of the right vertebral and the basilar artery. In all but one patient, the right carotid artery and its branches were also filled. Retrograde filling of the left internal carotid artery occurred in 8 patients. Furthermore, retrograde filling of the intracranial part of the left vertebral artery was obtained in 5 of 12 patients. A complete four-vessel cranial angiography was thus obtained in one third of the patients. The method may be considered as a safe and valuable adjunct to other angiographic techniques. (Auth.)

The effect of stochasticity on the lac operon: an evolutionary perspective.

Directory of Open Access Journals (Sweden)

Milan van Hoek

2007-06-01

Full Text Available The role of stochasticity on gene expression is widely discussed. Both potential advantages and disadvantages have been revealed. In some systems, noise in gene expression has been quantified, in among others the lac operon of Escherichia coli. Whether stochastic gene expression in this system is detrimental or beneficial for the cells is, however, still unclear. We are interested in the effects of stochasticity from an evolutionary point of view. We study this question in the lac operon, taking a computational approach: using a detailed, quantitative, spatial model, we evolve through a mutation-selection process the shape of the promoter function and therewith the effective amount of stochasticity. We find that noise values for lactose, the natural inducer, are much lower than for artificial, nonmetabolizable inducers, because these artificial inducers experience a stronger positive feedback. In the evolved promoter functions, noise due to stochasticity in gene expression, when induced by lactose, only plays a very minor role in short-term physiological adaptation, because other sources of population heterogeneity dominate. Finally, promoter functions evolved in the stochastic model evolve to higher repressed transcription rates than those evolved in a deterministic version of the model. This causes these promoter functions to experience less stochasticity in gene expression. We show that a high repression rate and hence high stochasticity increases the delay in lactose uptake in a variable environment. We conclude that the lac operon evolved such that the impact of stochastic gene expression is minor in its natural environment, but happens to respond with much stronger stochasticity when confronted with artificial inducers. In this particular system, we have shown that stochasticity is detrimental. Moreover, we demonstrate that in silico evolution in a quantitative model, by mutating the parameters of interest, is a promising way to unravel

Assessing and accounting for time heterogeneity in stochastic actor oriented models

NARCIS (Netherlands)

Lospinoso, Joshua A.; Schweinberger, Michael; Snijders, Tom A. B.; Ripley, Ruth M.

This paper explores time heterogeneity in stochastic actor oriented models (SAOM) proposed by Snijders (Sociological methodology. Blackwell, Boston, pp 361-395, 2001) which are meant to study the evolution of networks. SAOMs model social networks as directed graphs with nodes representing people,

Entropy Evolution and Uncertainty Estimation with Dynamical Systems

Directory of Open Access Journals (Sweden)

X. San Liang

2014-06-01

Full Text Available This paper presents a comprehensive introduction and systematic derivation of the evolutionary equations for absolute entropy H and relative entropy D, some of which exist sporadically in the literature in different forms under different subjects, within the framework of dynamical systems. In general, both H and D are dissipated, and the dissipation bears a form reminiscent of the Fisher information; in the absence of stochasticity, dH/dt is connected to the rate of phase space expansion, and D stays invariant, i.e., the separation of two probability density functions is always conserved. These formulas are validated with linear systems, and put to application with the Lorenz system and a large-dimensional stochastic quasi-geostrophic flow problem. In the Lorenz case, H falls at a constant rate with time, implying that H will eventually become negative, a situation beyond the capability of the commonly used computational technique like coarse-graining and bin counting. For the stochastic flow problem, it is first reduced to a computationally tractable low-dimensional system, using a reduced model approach, and then handled through ensemble prediction. Both the Lorenz system and the stochastic flow system are examples of self-organization in the light of uncertainty reduction. The latter particularly shows that, sometimes stochasticity may actually enhance the self-organization process.

On a possible origin of modular invariance

International Nuclear Information System (INIS)

Tahir Shah, K.

1991-06-01

We propose an information theoretic model of the space-time pre-geometry where the pre-geometry is considered as a ''coded state of matter and space-time'', distinctly different from the classical space-time or any known state of matter. Assuming that physical processes at Planck's dimensions are stochastic Markov processes and using information theoretic and algebro-geometric coding techniques, we show that modular invariance is a natural consequence of: 1. Shannon's channel capacity theorem. 2. Nature selects and uses only those error-correcting codes to transfer information between space-time entities which allow the value of propagation rate R reaching its critical value R C , the channel capacity. Next, using the strong converse theorem we show that a phase-transition occurs at (R C -R) 0. Furthermore, it is known that some symmetrically packed optimal codes lead to E 8 lattice while others to a 26-dimensional Lorentz lattice used in string theories. This suggests a precise connection between our model and string theories. (author). 26 refs

Feedback-Driven Dynamic Invariant Discovery

Science.gov (United States)

Zhang, Lingming; Yang, Guowei; Rungta, Neha S.; Person, Suzette; Khurshid, Sarfraz

2014-01-01

Program invariants can help software developers identify program properties that must be preserved as the software evolves, however, formulating correct invariants can be challenging. In this work, we introduce iDiscovery, a technique which leverages symbolic execution to improve the quality of dynamically discovered invariants computed by Daikon. Candidate invariants generated by Daikon are synthesized into assertions and instrumented onto the program. The instrumented code is executed symbolically to generate new test cases that are fed back to Daikon to help further re ne the set of candidate invariants. This feedback loop is executed until a x-point is reached. To mitigate the cost of symbolic execution, we present optimizations to prune the symbolic state space and to reduce the complexity of the generated path conditions. We also leverage recent advances in constraint solution reuse techniques to avoid computing results for the same constraints across iterations. Experimental results show that iDiscovery converges to a set of higher quality invariants compared to the initial set of candidate invariants in a small number of iterations.

Kinematic morphology of large-scale structure: evolution from potential to rotational flow

International Nuclear Information System (INIS)

Wang, Xin; Szalay, Alex; Aragón-Calvo, Miguel A.; Neyrinck, Mark C.; Eyink, Gregory L.

2014-01-01

As an alternative way to describe the cosmological velocity field, we discuss the evolution of rotational invariants constructed from the velocity gradient tensor. Compared with the traditional divergence-vorticity decomposition, these invariants, defined as coefficients of the characteristic equation of the velocity gradient tensor, enable a complete classification of all possible flow patterns in the dark-matter comoving frame, including both potential and vortical flows. We show that this tool, first introduced in turbulence two decades ago, is very useful for understanding the evolution of the cosmic web structure, and in classifying its morphology. Before shell crossing, different categories of potential flow are highly associated with the cosmic web structure because of the coherent evolution of density and velocity. This correspondence is even preserved at some level when vorticity is generated after shell crossing. The evolution from the potential to vortical flow can be traced continuously by these invariants. With the help of this tool, we show that the vorticity is generated in a particular way that is highly correlated with the large-scale structure. This includes a distinct spatial distribution and different types of alignment between the cosmic web and vorticity direction for various vortical flows. Incorporating shell crossing into closed dynamical systems is highly non-trivial, but we propose a possible statistical explanation for some of the phenomena relating to the internal structure of the three-dimensional invariant space.

Kinematic morphology of large-scale structure: evolution from potential to rotational flow

Energy Technology Data Exchange (ETDEWEB)

Wang, Xin; Szalay, Alex; Aragón-Calvo, Miguel A.; Neyrinck, Mark C.; Eyink, Gregory L. [Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218 (United States)

2014-09-20

As an alternative way to describe the cosmological velocity field, we discuss the evolution of rotational invariants constructed from the velocity gradient tensor. Compared with the traditional divergence-vorticity decomposition, these invariants, defined as coefficients of the characteristic equation of the velocity gradient tensor, enable a complete classification of all possible flow patterns in the dark-matter comoving frame, including both potential and vortical flows. We show that this tool, first introduced in turbulence two decades ago, is very useful for understanding the evolution of the cosmic web structure, and in classifying its morphology. Before shell crossing, different categories of potential flow are highly associated with the cosmic web structure because of the coherent evolution of density and velocity. This correspondence is even preserved at some level when vorticity is generated after shell crossing. The evolution from the potential to vortical flow can be traced continuously by these invariants. With the help of this tool, we show that the vorticity is generated in a particular way that is highly correlated with the large-scale structure. This includes a distinct spatial distribution and different types of alignment between the cosmic web and vorticity direction for various vortical flows. Incorporating shell crossing into closed dynamical systems is highly non-trivial, but we propose a possible statistical explanation for some of the phenomena relating to the internal structure of the three-dimensional invariant space.

Relating measurement invariance, cross-level invariance, and multilevel reliability

OpenAIRE

Jak, S.; Jorgensen, T.D.

2017-01-01

Data often have a nested, multilevel structure, for example when data are collected from children in classrooms. This kind of data complicate the evaluation of reliability and measurement invariance, because several properties can be evaluated at both the individual level and the cluster level, as well as across levels. For example, cross-level invariance implies equal factor loadings across levels, which is needed to give latent variables at the two levels a similar interpretation. Reliabili...

Stochastic beam dynamics in storage rings

International Nuclear Information System (INIS)

Pauluhn, A.

1993-12-01

In this thesis several approaches to stochastic dynamics in storage rings are investigated. In the first part the theory of stochastic differential equations and Fokker-Planck equations is used to describe the processes which have been assumed to be Markov processes. The mathematical theory of Markov processes is well known. Nevertheless, analytical solutions can be found only in special cases and numerical algorithms are required. Several numerical integration schemes for stochastic differential equations will therefore be tested in analytical solvable examples and then applied to examples from accelerator physics. In particular the stochastically perturbed synchrotron motion is treated. For the special case of a double rf system several perturbation theoretical methods for deriving the Fokker-Planck equation in the action variable are used and compared with numerical results. The second part is concerned with the dynamics of electron storage rings. Due to the synchrotron radiation the electron motion is influenced by damping and exciting forces. An algorithm for the computation of the density function in the phase space of such a dissipative stochastically excited system is introduced. The density function contains all information of a process, e.g. it determines the beam dimensions and the lifetime of a stored electron beam. The new algorithm consists in calculating a time propagator for the density function. By means of this propagator the time evolution of the density is modelled very computing time efficient. The method is applied to simple models of the beam-beam interaction (one-dimensional, round beams) and the results of the density calculations are compared with results obtained from multiparticle tracking. Furthermore some modifications of the algorithm are introduced to improve its efficiency concerning computing time and storage requirements. Finally, extensions to two-dimensional beam-beam models are described. (orig.)

Foliated vector fields, the Godbillon-Vey invariant and the invariant I(F)

International Nuclear Information System (INIS)

Banyaga, A.; Landa, Alain Musesa

2004-03-01

We prove that if the invariant I(F) constructed in 'An invariant of contact structures and transversally oriented foliations', Ann. Global Analysis and Geom. 14(1996) 427-441 (A. Banyaga), through the Lie algebra of infinitesimal automorphisms of transversally oriented foliations F is trivial, then the Godbillon-Vey invariant GV (F) of F is also trivial, but that the converse is not true. For codimension one foliations, the restrictions I τ , (F) of I(F) to the Lie subalgebra of vector fields tangent to the leaves is the Reeb class R(F) of F. We also prove that if there exists a foliated vector field which is everywhere transverse to a codimension one foliation, then the Reeb class R(F) is trivial, hence so is the GV(F) invariant. (author)

Excited states in stochastic electrodynamics

International Nuclear Information System (INIS)

Franca, H.M.; Marshall, T.W.

1987-12-01

It is shown that the set of Wigner functions associated with the excited states of the harmonic oscillator constitute a complete set of functions over the phase space. An arbitraty distribution can be expanded in terms of these Wigner functions. By studying the time evolution, according to Stochastic Electrodynamics, of the expansion coefficients, becomes feasible to separate explicity the contributionsof the radiative reaction and the vaccuum field to the Einsten. A coefficients for this system. A simple semiclassical explanation of the Weisskopf-Heitler phenomenon in resonance fluorescence is also supplied. (author) [pt

Enhanced activation of the left hemisphere promotes normative decision making.

Science.gov (United States)

Corser, Ryan; Jasper, John D

2014-01-01

Previous studies have reported that enhanced activation of the left cerebral hemisphere reduces risky-choice, attribute, and goal-framing effects relative to enhanced activation of the right cerebral hemisphere. The present study sought to extend these findings and show that enhanced activation of the left hemisphere also reduces violations of other normative principles, besides the invariance principle. Participants completed ratio bias (Experiment 1, N = 296) and base rate neglect problems (Experiment 2, N = 145) under normal (control) viewing or with the right or left hemisphere primarily activated by imposing a unidirectional gaze. In Experiment 1 we found that enhanced left hemispheric activation reduced the ratio bias relative to normal viewing and a group experiencing enhanced right hemispheric activation. In Experiment 2 enhanced left hemispheric activation resulted in using base rates more than normal viewing, but not significantly more than enhanced right hemispheric activation. Results suggest that hemispheric asymmetries can affect higher-order cognitive processes, such as decision-making biases. Possible theoretical accounts are discussed as well as implications for dual-process theories.

Gauge invariance rediscovered

International Nuclear Information System (INIS)

Moriyasu, K.

1978-01-01

A pedagogical approach to gauge invariance is presented which is based on the analogy between gauge transformations and relativity. By using the concept of an internal space, purely geometrical arguments are used to teach the physical ideas behind gauge invariance. Many of the results are applicable to general gauge theories

Link invariants from finite Coxeter racks

OpenAIRE

Nelson, Sam; Wieghard, Ryan

2008-01-01

We study Coxeter racks over $\\mathbb{Z}_n$ and the knot and link invariants they define. We exploit the module structure of these racks to enhance the rack counting invariants and give examples showing that these enhanced invariants are stronger than the unenhanced rack counting invariants.

Extinction in neutrally stable stochastic Lotka-Volterra models

Science.gov (United States)

Dobrinevski, Alexander; Frey, Erwin

2012-05-01

Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.

A non-linear dimension reduction methodology for generating data-driven stochastic input models

Science.gov (United States)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low

A non-linear dimension reduction methodology for generating data-driven stochastic input models

International Nuclear Information System (INIS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-01-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R n . An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R d (d<< n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology

Stochastic dynamic modeling of regular and slow earthquakes

Science.gov (United States)

Aso, N.; Ando, R.; Ide, S.

2017-12-01

Both regular and slow earthquakes are slip phenomena on plate boundaries and are simulated by a (quasi-)dynamic modeling [Liu and Rice, 2005]. In these numerical simulations, spatial heterogeneity is usually considered not only for explaining real physical properties but also for evaluating the stability of the calculations or the sensitivity of the results on the condition. However, even though we discretize the model space with small grids, heterogeneity at smaller scales than the grid size is not considered in the models with deterministic governing equations. To evaluate the effect of heterogeneity at the smaller scales we need to consider stochastic interactions between slip and stress in a dynamic modeling. Tidal stress is known to trigger or affect both regular and slow earthquakes [Yabe et al., 2015; Ide et al., 2016], and such an external force with fluctuation can also be considered as a stochastic external force. A healing process of faults may also be stochastic, so we introduce stochastic friction law. In the present study, we propose a stochastic dynamic model to explain both regular and slow earthquakes. We solve mode III problem, which corresponds to the rupture propagation along the strike direction. We use BIEM (boundary integral equation method) scheme to simulate slip evolution, but we add stochastic perturbations in the governing equations, which is usually written in a deterministic manner. As the simplest type of perturbations, we adopt Gaussian deviations in the formulation of the slip-stress kernel, external force, and friction. By increasing the amplitude of perturbations of the slip-stress kernel, we reproduce complicated rupture process of regular earthquakes including unilateral and bilateral ruptures. By perturbing external force, we reproduce slow rupture propagation at a scale of km/day. The slow propagation generated by a combination of fast interaction at S-wave velocity is analogous to the kinetic theory of gasses: thermal

Rotation Invariance Neural Network

OpenAIRE

Li, Shiyuan

2017-01-01

Rotation invariance and translation invariance have great values in image recognition tasks. In this paper, we bring a new architecture in convolutional neural network (CNN) named cyclic convolutional layer to achieve rotation invariance in 2-D symbol recognition. We can also get the position and orientation of the 2-D symbol by the network to achieve detection purpose for multiple non-overlap target. Last but not least, this architecture can achieve one-shot learning in some cases using thos...

Lorentz invariance with an invariant energy scale.

Science.gov (United States)

Magueijo, João; Smolin, Lee

2002-05-13

We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.

New evolution equations for the joint response-excitation probability density function of stochastic solutions to first-order nonlinear PDEs

Science.gov (United States)

Venturi, D.; Karniadakis, G. E.

2012-08-01

By using functional integral methods we determine new evolution equations satisfied by the joint response-excitation probability density function (PDF) associated with the stochastic solution to first-order nonlinear partial differential equations (PDEs). The theory is presented for both fully nonlinear and for quasilinear scalar PDEs subject to random boundary conditions, random initial conditions or random forcing terms. Particular applications are discussed for the classical linear and nonlinear advection equations and for the advection-reaction equation. By using a Fourier-Galerkin spectral method we obtain numerical solutions of the proposed response-excitation PDF equations. These numerical solutions are compared against those obtained by using more conventional statistical approaches such as probabilistic collocation and multi-element probabilistic collocation methods. It is found that the response-excitation approach yields accurate predictions of the statistical properties of the system. In addition, it allows to directly ascertain the tails of probabilistic distributions, thus facilitating the assessment of rare events and associated risks. The computational cost of the response-excitation method is order magnitudes smaller than the one of more conventional statistical approaches if the PDE is subject to high-dimensional random boundary or initial conditions. The question of high-dimensionality for evolution equations involving multidimensional joint response-excitation PDFs is also addressed.

Nonsingular cosmology with a scale-invariant spectrum of cosmological perturbations from Lee-Wick theory

International Nuclear Information System (INIS)

Cai Yifu; Qiu Taotao; Brandenberger, Robert; Zhang Xinmin

2009-01-01

We study the cosmology of a Lee-Wick type scalar field theory. First, we consider homogeneous and isotropic background solutions and find that they are nonsingular, leading to cosmological bounces. Next, we analyze the spectrum of cosmological perturbations which result from this model. Unless either the potential of the Lee-Wick theory or the initial conditions are finely tuned, it is impossible to obtain background solutions which have a sufficiently long period of inflation after the bounce. More interestingly, however, we find that in the generic noninflationary bouncing cosmology, perturbations created from quantum vacuum fluctuations in the contracting phase have the correct form to lead to a scale-invariant spectrum of metric inhomogeneities in the expanding phase. Since the background is nonsingular, the evolution of the fluctuations is defined unambiguously through the bounce. We also analyze the evolution of fluctuations which emerge from thermal initial conditions in the contracting phase. The spectrum of gravitational waves stemming from quantum vacuum fluctuations in the contracting phase is also scale-invariant, and the tensor to scalar ratio is not suppressed.

Stochasticity and stereotypy in the Ciona notochord.

Science.gov (United States)

Carlson, Maia; Reeves, Wendy; Veeman, Michael

2015-01-15

Fate mapping with single cell resolution has typically been confined to embryos with completely stereotyped development. The lineages giving rise to the 40 cells of the Ciona notochord are invariant, but the intercalation of those cells into a single-file column is not. Here we use genetic labeling methods to fate map the Ciona notochord with both high resolution and large sample sizes. We find that the ordering of notochord cells into a single column is not random, but instead shows a distinctive signature characteristic of mediolaterally-biased intercalation. We find that patterns of cell intercalation in the notochord are somewhat stochastic but far more stereotyped than previously believed. Cell behaviors vary by lineage, with the secondary notochord lineage being much more constrained than the primary lineage. Within the primary lineage, patterns of intercalation reflect the geometry of the intercalating tissue. We identify the latest point at which notochord morphogenesis is largely stereotyped, which is shortly before the onset of mediolateral intercalation and immediately after the final cell divisions in the primary lineage. These divisions are consistently oriented along the AP axis. Our results indicate that the interplay between stereotyped and stochastic cell behaviors in morphogenesis can only be assessed by fate mapping experiments that have both cellular resolution and large sample sizes. Copyright © 2014 Elsevier Inc. All rights reserved.

Topics in conformal invariance and generalized sigma models

International Nuclear Information System (INIS)

Bernardo, L.M.; Lawrence Berkeley National Lab., CA

1997-05-01

This thesis consists of two different parts, having in common the fact that in both, conformal invariance plays a central role. In the first part, the author derives conditions for conformal invariance, in the large N limit, and for the existence of an infinite number of commuting classical conserved quantities, in the Generalized Thirring Model. The treatment uses the bosonized version of the model. Two different approaches are used to derive conditions for conformal invariance: the background field method and the Hamiltonian method based on an operator algebra, and the agreement between them is established. The author constructs two infinite sets of non-local conserved charges, by specifying either periodic or open boundary conditions, and he finds the Poisson Bracket algebra satisfied by them. A free field representation of the algebra satisfied by the relevant dynamical variables of the model is also presented, and the structure of the stress tensor in terms of free fields (and free currents) is studied in detail. In the second part, the author proposes a new approach for deriving the string field equations from a general sigma model on the world sheet. This approach leads to an equation which combines some of the attractive features of both the renormalization group method and the covariant beta function treatment of the massless excitations. It has the advantage of being covariant under a very general set of both local and non-local transformations in the field space. The author applies it to the tachyon, massless and first massive level, and shows that the resulting field equations reproduce the correct spectrum of a left-right symmetric closed bosonic string

Large-scale stochasticity in Hamiltonian systems

International Nuclear Information System (INIS)

Escande, D.F.

1982-01-01

Large scale stochasticity (L.S.S.) in Hamiltonian systems is defined on the paradigm Hamiltonian H(v,x,t) =v 2 /2-M cos x-P cos k(x-t) which describes the motion of one particle in two electrostatic waves. A renormalization transformation Tsub(r) is described which acts as a microscope that focusses on a given KAM (Kolmogorov-Arnold-Moser) torus in phase space. Though approximate, Tsub(r) yields the threshold of L.S.S. in H with an error of 5-10%. The universal behaviour of KAM tori is predicted: for instance the scale invariance of KAM tori and the critical exponent of the Lyapunov exponent of Cantori. The Fourier expansion of KAM tori is computed and several conjectures by L. Kadanoff and S. Shenker are proved. Chirikov's standard mapping for stochastic layers is derived in a simpler way and the width of the layers is computed. A simpler renormalization scheme for these layers is defined. A Mathieu equation for describing the stability of a discrete family of cycles is derived. When combined with Tsub(r), it allows to prove the link between KAM tori and nearby cycles, conjectured by J. Greene and, in particular, to compute the mean residue of a torus. The fractal diagrams defined by G. Schmidt are computed. A sketch of a methodology for computing the L.S.S. threshold in any two-degree-of-freedom Hamiltonian system is given. (Auth.)

Stochastic and non-stochastic effects - a conceptual analysis

International Nuclear Information System (INIS)

Karhausen, L.R.

1980-01-01

The attempt to divide radiation effects into stochastic and non-stochastic effects is discussed. It is argued that radiation or toxicological effects are contingently related to radiation or chemical exposure. Biological effects in general can be described by general laws but these laws never represent a necessary connection. Actually stochastic effects express contingent, or empirical, connections while non-stochastic effects represent semantic and non-factual connections. These two expressions stem from two different levels of discourse. The consequence of this analysis for radiation biology and radiation protection is discussed. (author)

Stochastic control theory dynamic programming principle

CERN Document Server

Nisio, Makiko

2015-01-01

This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-ma...

Synthesizing Modular Invariants for Synchronous Code

Directory of Open Access Journals (Sweden)

Pierre-Loic Garoche

2014-12-01

Full Text Available In this paper, we explore different techniques to synthesize modular invariants for synchronous code encoded as Horn clauses. Modular invariants are a set of formulas that characterizes the validity of predicates. They are very useful for different aspects of analysis, synthesis, testing and program transformation. We describe two techniques to generate modular invariants for code written in the synchronous dataflow language Lustre. The first technique directly encodes the synchronous code in a modular fashion. While in the second technique, we synthesize modular invariants starting from a monolithic invariant. Both techniques, take advantage of analysis techniques based on property-directed reachability. We also describe a technique to minimize the synthesized invariants.

Gauge-invariant perturbations in hybrid quantum cosmology

Energy Technology Data Exchange (ETDEWEB)

Gomar, Laura Castelló; Marugán, Guillermo A. Mena [Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid (Spain); Martín-Benito, Mercedes, E-mail: laura.castello@iem.cfmac.csic.es, E-mail: m.martin@hef.ru.nl, E-mail: mena@iem.cfmac.csic.es [Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, Heyendaalseweg 135, NL-6525 AJ Nijmegen (Netherlands)

2015-06-01

We consider cosmological perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field and present a formulation which is designed to preserve covariance. We truncate the action at quadratic perturbative order and particularize our analysis to flat compact spatial sections and a field potential given by a mass term, although the formalism can be extended to other topologies and potentials. The perturbations are described in terms of Mukhanov-Sasaki gauge invariants, linear perturbative constraints, and variables canonically conjugate to them. This set is completed into a canonical one for the entire system, including the homogeneous degrees of freedom. We find the global Hamiltonian constraint of the model, in which the contribution of the homogeneous sector is corrected with a term quadratic in the perturbations, that can be identified as the Mukhanov-Sasaki Hamiltonian in our formulation. We then adopt a hybrid approach to quantize the model, combining a quantum representation of the homogeneous sector with a more standard field quantization of the perturbations. Covariance is guaranteed in this approach inasmuch as no gauge fixing is adopted. Next, we adopt a Born-Oppenheimer ansatz for physical states and show how to obtain a Schrödinger-like equation for the quantum evolution of the perturbations. This evolution is governed by the Mukhanov-Sasaki Hamiltonian, with the dependence on the homogeneous geometry evaluated at quantum expectation values, and with a time parameter defined also in terms of suitable expectation values on that geometry. Finally, we derive effective equations for the dynamics of the Mukhanov-Sasaki gauge invariants, that include quantum contributions, but have the same ultraviolet limit as the classical equations. They provide the master equation to extract predictions about the power spectrum of primordial scalar perturbations.

Gauge-invariant perturbations in hybrid quantum cosmology

International Nuclear Information System (INIS)

Gomar, Laura Castelló; Marugán, Guillermo A. Mena; Martín-Benito, Mercedes

2015-01-01

We consider cosmological perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field and present a formulation which is designed to preserve covariance. We truncate the action at quadratic perturbative order and particularize our analysis to flat compact spatial sections and a field potential given by a mass term, although the formalism can be extended to other topologies and potentials. The perturbations are described in terms of Mukhanov-Sasaki gauge invariants, linear perturbative constraints, and variables canonically conjugate to them. This set is completed into a canonical one for the entire system, including the homogeneous degrees of freedom. We find the global Hamiltonian constraint of the model, in which the contribution of the homogeneous sector is corrected with a term quadratic in the perturbations, that can be identified as the Mukhanov-Sasaki Hamiltonian in our formulation. We then adopt a hybrid approach to quantize the model, combining a quantum representation of the homogeneous sector with a more standard field quantization of the perturbations. Covariance is guaranteed in this approach inasmuch as no gauge fixing is adopted. Next, we adopt a Born-Oppenheimer ansatz for physical states and show how to obtain a Schrödinger-like equation for the quantum evolution of the perturbations. This evolution is governed by the Mukhanov-Sasaki Hamiltonian, with the dependence on the homogeneous geometry evaluated at quantum expectation values, and with a time parameter defined also in terms of suitable expectation values on that geometry. Finally, we derive effective equations for the dynamics of the Mukhanov-Sasaki gauge invariants, that include quantum contributions, but have the same ultraviolet limit as the classical equations. They provide the master equation to extract predictions about the power spectrum of primordial scalar perturbations

Hidden scale invariance of metals

DEFF Research Database (Denmark)

Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.

2015-01-01

Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between the thermal fluctuations of the virial and the potential energy in the isochoric ensemble. This demonstrates a general “hidden” scale invariance...... of metals making the condensed part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Grüneisen parameter, are in good agreement with experimental values for the 16 elements where reliable data were...... available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant...

Reducing Lookups for Invariant Checking

DEFF Research Database (Denmark)

Thomsen, Jakob Grauenkjær; Clausen, Christian; Andersen, Kristoffer Just

2013-01-01

This paper helps reduce the cost of invariant checking in cases where access to data is expensive. Assume that a set of variables satisfy a given invariant and a request is received to update a subset of them. We reduce the set of variables to inspect, in order to verify that the invariant is still...

Convergent and invariant object representations for sight, sound, and touch.

Science.gov (United States)

Man, Kingson; Damasio, Antonio; Meyer, Kaspar; Kaplan, Jonas T

2015-09-01

We continuously perceive objects in the world through multiple sensory channels. In this study, we investigated the convergence of information from different sensory streams within the cerebral cortex. We presented volunteers with three common objects via three different modalities-sight, sound, and touch-and used multivariate pattern analysis of functional magnetic resonance imaging data to map the cortical regions containing information about the identity of the objects. We could reliably predict which of the three stimuli a subject had seen, heard, or touched from the pattern of neural activity in the corresponding early sensory cortices. Intramodal classification was also successful in large portions of the cerebral cortex beyond the primary areas, with multiple regions showing convergence of information from two or all three modalities. Using crossmodal classification, we also searched for brain regions that would represent objects in a similar fashion across different modalities of presentation. We trained a classifier to distinguish objects presented in one modality and then tested it on the same objects presented in a different modality. We detected audiovisual invariance in the right temporo-occipital junction, audiotactile invariance in the left postcentral gyrus and parietal operculum, and visuotactile invariance in the right postcentral and supramarginal gyri. Our maps of multisensory convergence and crossmodal generalization reveal the underlying organization of the association cortices, and may be related to the neural basis for mental concepts. © 2015 Wiley Periodicals, Inc.

Lectures on Dynamics of Stochastic Systems

CERN Document Server

Klyatskin, Valery I

2010-01-01

Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. Models naturally render to statistical description, where random processes and fields express the input parameters and solutions. The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of the system and initial data. This book is a revised a

Accelerated Genetic Algorithm Solutions Of Some Parametric Families Of Stochastic Differential Equations

Directory of Open Access Journals (Sweden)

Eman Ali Hussain

2015-01-01

Full Text Available Absract In this project A new method for solving Stochastic Differential Equations SDEs deriving by Wiener process numerically will be construct and implement using Accelerated Genetic Algorithm AGA. An SDE is a differential equation in which one or more of the terms and hence the solutions itself is a stochastic process. Solving stochastic differential equations requires going away from the recognizable deterministic setting of ordinary and partial differential equations into a world where the evolution of a quantity has an inherent random component and where the expected behavior of this quantity can be described in terms of probability distributions. We applied our method on the Ito formula which is equivalent to the SDE to find approximation solution of the SDEs. Numerical experiments illustrate the behavior of the proposed method.

The invariance of second-order functionals revisited

International Nuclear Information System (INIS)

Battezzati, M.

1984-01-01

In this paper some invariance properties of certain homogeneous functional forms of perturbative second-order energies with respect to transformations on the arguments are briefly considered. It has been shown that, if this energy is regarded as an Hamiltonian governing the time evolution of the arguments, which are the components of the first-order perturbed functions, the x and y couples play naturally the role of canonically conjugated co-ordinates and momenta. A search has been made for those linear transformations on these functions which preserve the above duality or reciprocity relations. It has been found that certain canonical transformations are of this type. In particular, the spinorial covariant-contravariant transformations for rotations in four-dimensional space-time

Schrodinger Evolution for the Universe: Reparametrization

OpenAIRE

Gryb, Sean; Thebault, Karim

2015-01-01

Starting from a generalized Hamilton-Jacobi formalism, we develop a new framework for constructing observables and their evolution in theories invariant under global time reparametrizations. Our proposal relaxes the usual Dirac prescription for the observables of a totally constrained system (`perennials') and allows one to recover the influential partial and complete observables approach in a particular limit. Difficulties such as the non-unitary evolution of the complete observables in term...

SLUG-STOCHASTICALLY LIGHTING UP GALAXIES. I. METHODS AND VALIDATING TESTS

Energy Technology Data Exchange (ETDEWEB)

Da Silva, Robert L.; Fumagalli, Michele; Krumholz, Mark [Department of Astronomy and Astrophysics, UCO/Lick Observatory, University of California, 1156 High Street, Santa Cruz, CA 95064 (United States)

2012-02-01

The effects of stochasticity on the luminosities of stellar populations are an often neglected but crucial element for understanding populations in the low-mass or the low star formation rate regime. To address this issue, we present SLUG, a new code to 'Stochastically Light Up Galaxies'. SLUG synthesizes stellar populations using a Monte Carlo technique that properly treats stochastic sampling including the effects of clustering, the stellar initial mass function, star formation history, stellar evolution, and cluster disruption. This code produces many useful outputs, including (1) catalogs of star clusters and their properties such as their stellar initial mass distributions and their photometric properties in a variety of filters, (2) two dimensional histograms of color-magnitude diagrams of every star in the simulation, and (3) the photometric properties of field stars and the integrated photometry of the entire simulated galaxy. After presenting the SLUG algorithm in detail, we validate the code through comparisons with STARBURST99 in the well-sampled regime, and with observed photometry of Milky Way clusters. Finally, we demonstrate SLUG's capabilities by presenting outputs in the stochastic regime. SLUG is publicly distributed through the Web site http://sites.google.com/site/runslug/.

Stochastic processes, slaves and supersymmetry

International Nuclear Information System (INIS)

Drummond, I T; Horgan, R R

2012-01-01

We extend the work of Tănase-Nicola and Kurchan on the structure of diffusion processes and the associated supersymmetry algebra by examining the responses of a simple statistical system to external disturbances of various kinds. We consider both the stochastic differential equations (SDEs) for the process and the associated diffusion equation. The influence of the disturbances can be understood by augmenting the original SDE with an equation for slave variables. The evolution of the slave variables describes the behaviour of line elements carried along in the stochastic flow. These line elements, together with the associated surface and volume elements constructed from them, provide the basis of the supersymmetry properties of the theory. For ease of visualization, and in order to emphasize a helpful electromagnetic analogy, we work in three dimensions. The results are all generalizable to higher dimensions and can be specialized to one and two dimensions. The electromagnetic analogy is a useful starting point for calculating asymptotic results at low temperature that can be compared with direct numerical evaluations. We also examine the problems that arise in a direct numerical simulation of the stochastic equation together with the slave equations. We pay special attention to the dependence of the slave variable statistics on temperature. We identify in specific models the critical temperature below which the slave variable distribution ceases to have a variance and consider the effect on estimates of susceptibilities. (paper)

Algorithms in invariant theory

CERN Document Server

Sturmfels, Bernd

2008-01-01

J. Kung and G.-C. Rota, in their 1984 paper, write: "Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics". The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students will find the book an easy introduction to this "classical and new" area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to a wealth of research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems.

Absolute continuity under time shift of trajectories and related stochastic calculus

CERN Document Server

Löbus, Jörg-Uwe

2017-01-01

The text is concerned with a class of two-sided stochastic processes of the form X=W+A. Here W is a two-sided Brownian motion with random initial data at time zero and A\\equiv A(W) is a function of W. Elements of the related stochastic calculus are introduced. In particular, the calculus is adjusted to the case when A is a jump process. Absolute continuity of (X,P) under time shift of trajectories is investigated. For example under various conditions on the initial density with respect to the Lebesgue measure, m, and on A with A_0=0 we verify \\frac{P(dX_{\\cdot -t})}{P(dX_\\cdot)}=\\frac{m(X_{-t})}{m(X_0)}\\cdot \\prod_i\\left|\

A stochastic differential equation framework for the timewise dynamics of turbulent velocities

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler; Schmiegel, Jürgen

2008-01-01

We discuss a stochastic differential equation as a modeling framework for the timewise dynamics of turbulent velocities. The equation is capable of capturing basic stylized facts of the statistics of temporal velocity increments. In particular, we focus on the evolution of the probability density...

Linear algebra of the permutation invariant Crow-Kimura model of prebiotic evolution.

Science.gov (United States)

Bratus, Alexander S; Novozhilov, Artem S; Semenov, Yuri S

2014-10-01

A particular case of the famous quasispecies model - the Crow-Kimura model with a permutation invariant fitness landscape - is investigated. Using the fact that the mutation matrix in the case of a permutation invariant fitness landscape has a special tridiagonal form, a change of the basis is suggested such that in the new coordinates a number of analytical results can be obtained. In particular, using the eigenvectors of the mutation matrix as the new basis, we show that the quasispecies distribution approaches a binomial one and give simple estimates for the speed of convergence. Another consequence of the suggested approach is a parametric solution to the system of equations determining the quasispecies. Using this parametric solution we show that our approach leads to exact asymptotic results in some cases, which are not covered by the existing methods. In particular, we are able to present not only the limit behavior of the leading eigenvalue (mean population fitness), but also the exact formulas for the limit quasispecies eigenvector for special cases. For instance, this eigenvector has a geometric distribution in the case of the classical single peaked fitness landscape. On the biological side, we propose a mathematical definition, based on the closeness of the quasispecies to the binomial distribution, which can be used as an operational definition of the notorious error threshold. Using this definition, we suggest two approximate formulas to estimate the critical mutation rate after which the quasispecies delocalization occurs. Copyright © 2014 Elsevier Inc. All rights reserved.

Higher-order stochastic differential equations and the positive Wigner function

Science.gov (United States)

Drummond, P. D.

2017-12-01

General higher-order stochastic processes that correspond to any diffusion-type tensor of higher than second order are obtained. The relationship of multivariate higher-order stochastic differential equations with tensor decomposition theory and tensor rank is explained. Techniques for generating the requisite complex higher-order noise are proved to exist either using polar coordinates and γ distributions, or from products of Gaussian variates. This method is shown to allow the calculation of the dynamics of the Wigner function, after it is extended to a complex phase space. The results are illustrated physically through dynamical calculations of the positive Wigner distribution for three-mode parametric downconversion, widely used in quantum optics. The approach eliminates paradoxes arising from truncation of the higher derivative terms in Wigner function time evolution. Anomalous results of negative populations and vacuum scattering found in truncated Wigner quantum simulations in quantum optics and Bose-Einstein condensate dynamics are shown not to occur with this type of stochastic theory.

Stochastic heterogeneous interaction promotes cooperation in spatial prisoner's dilemma game.

Directory of Open Access Journals (Sweden)

Ping Zhu

Full Text Available Previous studies mostly investigate player's cooperative behavior as affected by game time-scale or individual diversity. In this paper, by involving both time-scale and diversity simultaneously, we explore the effect of stochastic heterogeneous interaction. In our model, the occurrence of game interaction between each pair of linked player obeys a random probability, which is further described by certain distributions. Simulations on a 4-neighbor square lattice show that the cooperation level is remarkably promoted when stochastic heterogeneous interaction is considered. The results are then explained by investigating the mean payoffs, the mean boundary payoffs and the transition probabilities between cooperators and defectors. We also show some typical snapshots and evolution time series of the system. Finally, the 8-neighbor square lattice and BA scale-free network results indicate that the stochastic heterogeneous interaction can be robust against different network topologies. Our work may sharpen the understanding of the joint effect of game time-scale and individual diversity on spatial games.

Evolution and non-equilibrium physics

DEFF Research Database (Denmark)

Becker, Nikolaj; Sibani, Paolo

2014-01-01

We argue that the stochastic dynamics of interacting agents which replicate, mutate and die constitutes a non-equilibrium physical process akin to aging in complex materials. Specifically, our study uses extensive computer simulations of the Tangled Nature Model (TNM) of biological evolution...

Physical Invariants of Intelligence

Science.gov (United States)

Zak, Michail

2010-01-01

A program of research is dedicated to development of a mathematical formalism that could provide, among other things, means by which living systems could be distinguished from non-living ones. A major issue that arises in this research is the following question: What invariants of mathematical models of the physics of systems are (1) characteristic of the behaviors of intelligent living systems and (2) do not depend on specific features of material compositions heretofore considered to be characteristic of life? This research at earlier stages has been reported, albeit from different perspectives, in numerous previous NASA Tech Briefs articles. To recapitulate: One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Mathematical models of motor dynamics are used to simulate the observable physical behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. At the time of reporting the information for this article, the focus of this research was upon the following aspects of the formalism: Intelligence is considered to be a means by which a living system preserves itself and improves its ability to survive and is further considered to manifest itself in feedback from the mental dynamics to the motor dynamics. Because of the feedback from the mental dynamics, the motor dynamics attains quantum-like properties: The trajectory of the physical aspect of the system in the space of dynamical variables splits into a family of different trajectories, and each of those trajectories can be chosen with a probability prescribed by the mental dynamics. From a slightly different perspective

Cartan invariants and event horizon detection

Science.gov (United States)

Brooks, D.; Chavy-Waddy, P. C.; Coley, A. A.; Forget, A.; Gregoris, D.; MacCallum, M. A. H.; McNutt, D. D.

2018-04-01

We show that it is possible to locate the event horizon of a black hole (in arbitrary dimensions) by the zeros of certain Cartan invariants. This approach accounts for the recent results on the detection of stationary horizons using scalar polynomial curvature invariants, and improves upon them since the proposed method is computationally less expensive. As an application, we produce Cartan invariants that locate the event horizons for various exact four-dimensional and five-dimensional stationary, asymptotically flat (or (anti) de Sitter), black hole solutions and compare the Cartan invariants with the corresponding scalar curvature invariants that detect the event horizon.

Metric fluctuations and their evolution during inflation

International Nuclear Information System (INIS)

Anabitarte, M.; Bellini, M.

2004-01-01

We discuss the evolution of the fluctuations in a symmetric φ c -exponential potential which provides a power-law expansion during inflation using both the gauge-invariant field Φ and the Sasaki-Mukhanov field. (orig.)

Improved stochastic approximation methods for discretized parabolic partial differential equations

Science.gov (United States)

Guiaş, Flavius

2016-12-01

We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).

Indirect Inference for Stochastic Differential Equations Based on Moment Expansions

KAUST Repository

Ballesio, Marco

2016-01-06

We provide an indirect inference method to estimate the parameters of timehomogeneous scalar diffusion and jump diffusion processes. We obtain a system of ODEs that approximate the time evolution of the first two moments of the process by the approximation of the stochastic model applying a second order Taylor expansion of the SDE s infinitesimal generator in the Dynkin s formula. This method allows a simple and efficient procedure to infer the parameters of such stochastic processes given the data by the maximization of the likelihood of an approximating Gaussian process described by the two moments equations. Finally, we perform numerical experiments for two datasets arising from organic and inorganic fouling deposition phenomena.

Mass generation within conformal invariant theories

International Nuclear Information System (INIS)

Flato, M.; Guenin, M.

1981-01-01

The massless Yang-Mills theory is strongly conformally invariant and renormalizable; however, when masses are introduced the theory becomes nonrenormalizable and weakly conformally invariant. Conditions which recover strong conformal invariance are discussed in the letter. (author)

Parametrization of open systems with effective quadratic hamiltonians plus stochastic force

International Nuclear Information System (INIS)

Hernandez, E.S.; Mizrahi, S.S.

1981-12-01

The evolution generated by general dissipative Hamiltonians is analyzed when a stochastic force is included. A mapping technique allows to easily write the equations of motion for the observables of interest. A general dissipativity condition is extracted, whose fullfilment guarantees that thermal equilibrium is reached as the final stage of the evolution. Several existing frictional Hamiltonians are examined and it is seen that the correlation of the fluctuating force is essential to the destruction of a constant of motion inherent to pure quantal behaviour. (Author) [pt

Classification of ξ(s)-Quadratic Stochastic Operators on 2D simplex

International Nuclear Information System (INIS)

Mukhamedov, Farrukh; Saburov, Mansoor; Qaralleh, Izzat

2013-01-01

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some QSO has been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for the quadratic stochastic operators. To study this problem it was investigated several classes of such QSO. In this paper we study ξ (s) -QSO class of operators. We study such kind of operators on 2D simplex. We first classify these ξ (s) -QSO into 20 classes. Further, we investigate the dynamics of one class of such operators.

A Thermodynamically-Consistent Non-Ideal Stochastic Hard-Sphere Fluid

Energy Technology Data Exchange (ETDEWEB)

Donev, A; Alder, B J; Garcia, A L

2009-08-03

A grid-free variant of the Direct Simulation Monte Carlo (DSMC) method is proposed, named the Isotropic DSMC (I-DSMC) method, that is suitable for simulating collision-dominated dense fluid flows. The I-DSMC algorithm eliminates all grid artifacts from the traditional DSMC algorithm and is Galilean invariant and microscopically isotropic. The stochastic collision rules in I-DSMC are modified to introduce a non-ideal structure factor that gives consistent compressibility, as first proposed in [Phys. Rev. Lett. 101:075902 (2008)]. The resulting Stochastic Hard Sphere Dynamics (SHSD) fluid is empirically shown to be thermodynamically identical to a deterministic Hamiltonian system of penetrable spheres interacting with a linear core pair potential, well-described by the hypernetted chain (HNC) approximation. We develop a kinetic theory for the SHSD fluid to obtain estimates for the transport coefficients that are in excellent agreement with particle simulations over a wide range of densities and collision rates. The fluctuating hydrodynamic behavior of the SHSD fluid is verified by comparing its dynamic structure factor against theory based on the Landau-Lifshitz Navier-Stokes equations. We also study the Brownian motion of a nano-particle suspended in an SHSD fluid and find a long-time power-law tail in its velocity autocorrelation function consistent with hydrodynamic theory and molecular dynamics calculations.

Coordinate-invariant regularization

International Nuclear Information System (INIS)

Halpern, M.B.

1987-01-01

A general phase-space framework for coordinate-invariant regularization is given. The development is geometric, with all regularization contained in regularized DeWitt Superstructures on field deformations. Parallel development of invariant coordinate-space regularization is obtained by regularized functional integration of the momenta. As representative examples of the general formulation, the regularized general non-linear sigma model and regularized quantum gravity are discussed. copyright 1987 Academic Press, Inc

Stochastic Dynamics through Hierarchically Embedded Markov Chains.

Science.gov (United States)

Vasconcelos, Vítor V; Santos, Fernando P; Santos, Francisco C; Pacheco, Jorge M

2017-02-03

Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects-such as mutations in evolutionary dynamics and a random exploration of choices in social systems-including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.

Invariant sets for Windows

CERN Document Server

Morozov, Albert D; Dragunov, Timothy N; Malysheva, Olga V

1999-01-01

This book deals with the visualization and exploration of invariant sets (fractals, strange attractors, resonance structures, patterns etc.) for various kinds of nonlinear dynamical systems. The authors have created a special Windows 95 application called WInSet, which allows one to visualize the invariant sets. A WInSet installation disk is enclosed with the book.The book consists of two parts. Part I contains a description of WInSet and a list of the built-in invariant sets which can be plotted using the program. This part is intended for a wide audience with interests ranging from dynamical

A biologically inspired neural network model to transformation invariant object recognition

Science.gov (United States)

Iftekharuddin, Khan M.; Li, Yaqin; Siddiqui, Faraz

2007-09-01

Transformation invariant image recognition has been an active research area due to its widespread applications in a variety of fields such as military operations, robotics, medical practices, geographic scene analysis, and many others. The primary goal for this research is detection of objects in the presence of image transformations such as changes in resolution, rotation, translation, scale and occlusion. We investigate a biologically-inspired neural network (NN) model for such transformation-invariant object recognition. In a classical training-testing setup for NN, the performance is largely dependent on the range of transformation or orientation involved in training. However, an even more serious dilemma is that there may not be enough training data available for successful learning or even no training data at all. To alleviate this problem, a biologically inspired reinforcement learning (RL) approach is proposed. In this paper, the RL approach is explored for object recognition with different types of transformations such as changes in scale, size, resolution and rotation. The RL is implemented in an adaptive critic design (ACD) framework, which approximates the neuro-dynamic programming of an action network and a critic network, respectively. Two ACD algorithms such as Heuristic Dynamic Programming (HDP) and Dual Heuristic dynamic Programming (DHP) are investigated to obtain transformation invariant object recognition. The two learning algorithms are evaluated statistically using simulated transformations in images as well as with a large-scale UMIST face database with pose variations. In the face database authentication case, the 90° out-of-plane rotation of faces from 20 different subjects in the UMIST database is used. Our simulations show promising results for both designs for transformation-invariant object recognition and authentication of faces. Comparing the two algorithms, DHP outperforms HDP in learning capability, as DHP takes fewer steps to

Time evolution of the quark-gluon plasma

International Nuclear Information System (INIS)

Cooper, F.; New Hampshire Univ., Durham, NH

1993-01-01

We review progress in our understanding the production and time evolution of the quark gluon plasma starting with boost invariant initial conditions in a filed theory model based on the Schwinger mechanism of particle production via tunneling

Stochastic inflation as a time-dependent random walk

International Nuclear Information System (INIS)

Kandrup, H.E.

1989-01-01

This paper exploits the ''stochastic inflation'' paradigm introduced by Starobinskii to study the evolution of long-wavelength modes for a free scalar field Phi in an inflationary Universe. By relaxing the assumption of a ''slow roll,'' it becomes obvious that the well-known late-time infrared divergence of the vacuum for a massless field in de Sitter space may be viewed as a consequence of the fluctuation-dissipation theorem. This stochastic model is also extended to allow for nonvacuum states and power-law inflation, situations where the fluctuation-dissipation theorem no longer holds. One recovers the correct late-time form for the expectation value 2 > in these cases as well, corroborating thereby the intuitive picture that, quite generally, the long-wavelength modes of the field evolve in a thermal ''bath'' provided by the shorter-wavelength modes

What's hampering measurement invariance : Detecting non-invariant items using clusterwise simultaneous component analysis

NARCIS (Netherlands)

De Roover, K.; Timmerman, Marieke; De Leersnyder, J.; Mesquita, B.; Ceulemans, Eva

2014-01-01

The issue of measurement invariance is ubiquitous in the behavioral sciences nowadays as more and more studies yield multivariate multigroup data. When measurement invariance cannot be established across groups, this is often due to different loadings on only a few items. Within the multigroup CFA

On an aggregation in birth-and-death stochastic dynamics

Science.gov (United States)

Finkelshtein, Dmitri; Kondratiev, Yuri; Kutoviy, Oleksandr; Zhizhina, Elena

2014-06-01

We consider birth-and-death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density-dependent decreasing death rate. The corresponding statistical dynamics is constructed. Using the Vlasov-type scaling we derive the limiting mesoscopic evolution and prove that this evolution propagates chaos. We study a nonlinear non-local kinetic equation for the first correlation function (density of population). The existence of uniformly bounded solutions as well as solutions growing inside of a bounded domain and expanding in the space are shown. These solutions describe two regimes in the mesoscopic system: regulation and aggregation.

On an aggregation in birth-and-death stochastic dynamics

International Nuclear Information System (INIS)

Finkelshtein, Dmitri; Kondratiev, Yuri; Kutoviy, Oleksandr; Zhizhina, Elena

2014-01-01

We consider birth-and-death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density-dependent decreasing death rate. The corresponding statistical dynamics is constructed. Using the Vlasov-type scaling we derive the limiting mesoscopic evolution and prove that this evolution propagates chaos. We study a nonlinear non-local kinetic equation for the first correlation function (density of population). The existence of uniformly bounded solutions as well as solutions growing inside of a bounded domain and expanding in the space are shown. These solutions describe two regimes in the mesoscopic system: regulation and aggregation. (paper)

Extraction and analysis of left ventricular contours in cardiac radionuclide angiographies

International Nuclear Information System (INIS)

Jouan, A.

1991-01-01

The analysis of cardiac scintigraphic sequences is commonly realized with the help of functional or parametric images. The decomposition of the original sequence into a linear combination of the main temporal behaviors yields, after orthogonalization, a set of parametric images representing the pure temporal behaviors present in the original data. The properties of these images are used to extract automatically the left ventricular boundary. The Fourier Descriptors method is then used to get a quantified analysis of the shape of the ventricle. Because of their property of invariance by change of scale, the Fourier descriptors method applied on a sequence of left ventricular contours yields a quantified assessment of the cardiac contraction

Noncausal stochastic calculus

CERN Document Server

Ogawa, Shigeyoshi

2017-01-01

This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but ...

Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance

KAUST Repository

Happola, Juho

2017-09-19

Stochastic Differential Equations (SDE) offer a rich framework to model the probabilistic evolution of the state of a system. Numerical approximation methods are typically needed in evaluating relevant Quantities of Interest arising from such models. In this dissertation, we present novel effective methods for evaluating Quantities of Interest relevant to computational finance when the state of the system is described by an SDE.

Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance

KAUST Repository

Happola, Juho

2017-01-01

Stochastic Differential Equations (SDE) offer a rich framework to model the probabilistic evolution of the state of a system. Numerical approximation methods are typically needed in evaluating relevant Quantities of Interest arising from such models. In this dissertation, we present novel effective methods for evaluating Quantities of Interest relevant to computational finance when the state of the system is described by an SDE.

Stochastic Resonance in a System of Coupled Chaotic Oscillators

International Nuclear Information System (INIS)

Krawiecki, A.

1999-01-01

Noise-free stochastic resonance is investigated numerically in a system of two coupled chaotic Roessler oscillators. Periodic signal is applied either additively or multiplicatively to the coupling term. When the coupling constant is varied the oscillators lose synchronization via attractor bubbling or on-off intermittency. Properly chosen signals are analyzed which reflect the sequence of synchronized (laminar) phases and non-synchronized bursts in the time evolution of the oscillators. Maximum of the signal-to-noise ratio as a function of the coupling constant is observed. Dependence of the signal-to-noise ratio on the frequency of the periodic signal and parameter mismatch between the oscillators is investigated. Possible applications of stochastic resonance in the recovery of signals in secure communication systems based on chaotic synchronization are briefly discussed. (author)

Environmental versus demographic variability in stochastic predator–prey models

International Nuclear Information System (INIS)

Dobramysl, U; Täuber, U C

2013-01-01

In contrast to the neutral population cycles of the deterministic mean-field Lotka–Volterra rate equations, including spatial structure and stochastic noise in models for predator–prey interactions yields complex spatio-temporal structures associated with long-lived erratic population oscillations. Environmental variability in the form of quenched spatial randomness in the predation rates results in more localized activity patches. Our previous study showed that population fluctuations in rare favorable regions in turn cause a remarkable increase in the asymptotic densities of both predators and prey. Very intriguing features are found when variable interaction rates are affixed to individual particles rather than lattice sites. Stochastic dynamics with demographic variability in conjunction with inheritable predation efficiencies generate non-trivial time evolution for the predation rate distributions, yet with overall essentially neutral optimization. (paper)

Improved upper limits on the stochastic gravitational-wave background from 2009-2010 LIGO and Virgo data.

Science.gov (United States)

Aasi, J; Abbott, B P; Abbott, R; Abbott, T; Abernathy, M R; Accadia, T; Acernese, F; Ackley, K; Adams, C; Adams, T; Addesso, P; Adhikari, R X; Affeldt, C; Agathos, M; Aggarwal, N; Aguiar, O D; Ain, A; Ajith, P; Alemic, A; Allen, B; Allocca, A; Amariutei, D; Andersen, M; Anderson, R; Anderson, S B; Anderson, W G; Arai, K; Araya, M C; Arceneaux, C; Areeda, J; Aston, S M; Astone, P; Aufmuth, P; Aulbert, C; Austin, L; Aylott, B E; Babak, S; Baker, P T; Ballardin, G; Ballmer, S W; Barayoga, J C; Barbet, M; Barish, B C; Barker, D; Barone, F; Barr, B; Barsotti, L; Barsuglia, M; Barton, M A; Bartos, I; Bassiri, R; Basti, A; Batch, J C; Bauchrowitz, J; Bauer, Th S; Behnke, B; Bejger, M; Beker, M G; Belczynski, C; Bell, A S; Bell, C; Bergmann, G; Bersanetti, D; Bertolini, A; Betzwieser, J; Beyersdorf, P T; Bilenko, I A; Billingsley, G; Birch, J; Biscans, S; Bitossi, M; Bizouard, M A; Black, E; Blackburn, J K; Blackburn, L; Blair, D; Bloemen, S; Blom, M; Bock, O; Bodiya, T P; Boer, M; Bogaert, G; Bogan, C; Bond, C; Bondu, F; Bonelli, L; Bonnand, R; Bork, R; Born, M; Boschi, V; Bose, Sukanta; Bosi, L; Bradaschia, C; Brady, P R; Braginsky, V B; Branchesi, M; Brau, J E; Briant, T; Bridges, D O; Brillet, A; Brinkmann, M; Brisson, V; Brooks, A F; Brown, D A; Brown, D D; Brückner, F; Buchman, S; Bulik, T; Bulten, H J; Buonanno, A; Burman, R; Buskulic, D; Buy, C; Cadonati, L; Cagnoli, G; Bustillo, J Calderón; Calloni, E; Camp, J B; Campsie, P; Cannon, K C; Canuel, B; Cao, J; Capano, C D; Carbognani, F; Carbone, L; Caride, S; Castiglia, A; Caudill, S; Cavaglià, M; Cavalier, F; Cavalieri, R; Celerier, C; Cella, G; Cepeda, C; Cesarini, E; Chakraborty, R; Chalermsongsak, T; Chamberlin, S J; Chao, S; Charlton, P; Chassande-Mottin, E; Chen, X; Chen, Y; Chincarini, A; Chiummo, A; Cho, H S; Chow, J; Christensen, N; Chu, Q; Chua, S S Y; Chung, S; Ciani, G; Clara, F; Clark, J A; Cleva, F; Coccia, E; Cohadon, P-F; Colla, A; Collette, C; Colombini, M; Cominsky, L; Constancio, M; Conte, A; Cook, D; Corbitt, T R; Cordier, M; Cornish, N; Corpuz, A; Corsi, A; Costa, C A; Coughlin, M W; Coughlin, S; Coulon, J-P; Countryman, S; Couvares, P; Coward, D M; Cowart, M; Coyne, D C; Coyne, R; Craig, K; Creighton, J D E; Crowder, S G; Cumming, A; Cunningham, L; Cuoco, E; Dahl, K; Canton, T Dal; Damjanic, M; Danilishin, S L; D'Antonio, S; Danzmann, K; Dattilo, V; Daveloza, H; Davier, M; Davies, G S; Daw, E J; Day, R; Dayanga, T; Debreczeni, G; Degallaix, J; Deléglise, S; Del Pozzo, W; Denker, T; Dent, T; Dereli, H; Dergachev, V; De Rosa, R; DeRosa, R T; DeSalvo, R; Dhurandhar, S; Díaz, M; Di Fiore, L; Di Lieto, A; Di Palma, I; Di Virgilio, A; Donath, A; Donovan, F; Dooley, K L; Doravari, S; Dossa, S; Douglas, R; Downes, T P; Drago, M; Drever, R W P; Driggers, J C; Du, Z; Dwyer, S; Eberle, T; Edo, T; Edwards, M; Effler, A; Eggenstein, H; Ehrens, P; Eichholz, J; Eikenberry, S S; Endrőczi, G; Essick, R; Etzel, T; Evans, M; Evans, T; Factourovich, M; Fafone, V; Fairhurst, S; Fang, Q; Farinon, S; Farr, B; Farr, W M; Favata, M; Fehrmann, H; Fejer, M M; Feldbaum, D; Feroz, F; Ferrante, I; Ferrini, F; Fidecaro, F; Finn, L S; Fiori, I; Fisher, R P; Flaminio, R; Fournier, J-D; Franco, S; Frasca, S; Frasconi, F; Frede, M; Frei, Z; Freise, A; Frey, R; Fricke, T T; Fritschel, P; Frolov, V V; Fulda, P; Fyffe, M; Gair, J; Gammaitoni, L; Gaonkar, S; Garufi, F; Gehrels, N; Gemme, G; Genin, E; Gennai, A; Ghosh, S; Giaime, J A; Giardina, K D; Giazotto, A; Gill, C; Gleason, J; Goetz, E; Goetz, R; Gondan, L; González, G; Gordon, N; Gorodetsky, M L; Gossan, S; Gossler, S; Gouaty, R; Gräf, C; Graff, P B; Granata, M; Grant, A; Gras, S; Gray, C; Greenhalgh, R J S; Gretarsson, A M; Groot, P; Grote, H; Grover, K; Grunewald, S; Guidi, G M; Guido, C; Gushwa, K; Gustafson, E K; Gustafson, R; Hammer, D; Hammond, G; Hanke, M; Hanks, J; Hanna, C; Hanson, J; Harms, J; Harry, G M; Harry, I W; Harstad, E D; Hart, M; Hartman, M T; Haster, C-J; Haughian, K; Heidmann, A; Heintze, M; Heitmann, H; Hello, P; Hemming, G; Hendry, M; Heng, I S; Heptonstall, A W; Heurs, M; Hewitson, M; Hild, S; Hoak, D; Hodge, K A; Holt, K; Hooper, S; Hopkins, P; Hosken, D J; Hough, J; Howell, E J; Hu, Y; Huerta, E; Hughey, B; Husa, S; Huttner, S H; Huynh, M; Huynh-Dinh, T; Ingram, D R; Inta, R; Isogai, T; Ivanov, A; Iyer, B R; Izumi, K; Jacobson, M; James, E; Jang, H; Jaranowski, P; Ji, Y; Jiménez-Forteza, F; Johnson, W W; Jones, D I; Jones, R; Jonker, R J G; Ju, L; K, Haris; Kalmus, P; Kalogera, V; Kandhasamy, S; Kang, G; Kanner, J B; Karlen, J; Kasprzack, M; Katsavounidis, E; Katzman, W; Kaufer, H; Kawabe, K; Kawazoe, F; Kéfélian, F; Keiser, G M; Keitel, D; Kelley, D B; Kells, W; Khalaidovski, A; Khalili, F Y; Khazanov, E A; Kim, C; Kim, K; Kim, N; Kim, N G; Kim, Y-M; King, E J; King, P J; Kinzel, D L; Kissel, J S; Klimenko, S; Kline, J; Koehlenbeck, S; Kokeyama, K; Kondrashov, V; Koranda, S; Korth, W Z; Kowalska, I; Kozak, D B; Kremin, A; Kringel, V; Królak, A; Kuehn, G; Kumar, A; Kumar, P; Kumar, R; Kuo, L; Kutynia, A; Kwee, P; Landry, M; Lantz, B; Larson, S; Lasky, P D; Lawrie, C; Lazzarini, A; Lazzaro, C; Leaci, P; Leavey, S; Lebigot, E O; Lee, C-H; Lee, H K; Lee, H M; Lee, J; Leonardi, M; Leong, J R; Le Roux, A; Leroy, N; Letendre, N; Levin, Y; Levine, B; Lewis, J; Li, T G F; Libbrecht, K; Libson, A; Lin, A C; Littenberg, T B; Litvine, V; Lockerbie, N A; Lockett, V; Lodhia, D; Loew, K; Logue, J; Lombardi, A L; Lorenzini, M; Loriette, V; Lormand, M; Losurdo, G; Lough, J; Lubinski, M J; Lück, H; Luijten, E; Lundgren, A P; Lynch, R; Ma, Y; Macarthur, J; Macdonald, E P; MacDonald, T; Machenschalk, B; MacInnis, M; Macleod, D M; Magana-Sandoval, F; Mageswaran, M; Maglione, C; Mailand, K; Majorana, E; Maksimovic, I; Malvezzi, V; Man, N; Manca, G M; Mandel, I; Mandic, V; Mangano, V; Mangini, N; Mantovani, M; Marchesoni, F; Marion, F; Márka, S; Márka, Z; Markosyan, A; Maros, E; Marque, J; Martelli, F; Martin, I W; Martin, R M; Martinelli, L; Martynov, D; Marx, J N; Mason, K; Masserot, A; Massinger, T J; Matichard, F; Matone, L; Matzner, R A; Mavalvala, N; Mazumder, N; Mazzolo, G; McCarthy, R; McClelland, D E; McGuire, S C; McIntyre, G; McIver, J; McLin, K; Meacher, D; Meadors, G D; Mehmet, M; Meidam, J; Meinders, M; Melatos, A; Mendell, G; Mercer, R A; Meshkov, S; Messenger, C; Meyers, P; Miao, H; Michel, C; Mikhailov, E E; Milano, L; Milde, S; Miller, J; Minenkov, Y; Mingarelli, C M F; Mishra, C; Mitra, S; Mitrofanov, V P; Mitselmakher, G; Mittleman, R; Moe, B; Moesta, P; Mohan, M; Mohapatra, S R P; Moraru, D; Moreno, G; Morgado, N; Morriss, S R; Mossavi, K; Mours, B; Mow-Lowry, C M; Mueller, C L; Mueller, G; Mukherjee, S; Mullavey, A; Munch, J; Murphy, D; Murray, P G; Mytidis, A; Nagy, M F; Kumar, D Nanda; Nardecchia, I; Naticchioni, L; Nayak, R K; Necula, V; Nelemans, G; Neri, I; Neri, M; Newton, G; Nguyen, T; Nitz, A; Nocera, F; Nolting, D; Normandin, M E N; Nuttall, L K; Ochsner, E; O'Dell, J; Oelker, E; Oh, J J; Oh, S H; Ohme, F; Oppermann, P; O'Reilly, B; O'Shaughnessy, R; Osthelder, C; Ottaway, D J; Ottens, R S; Overmier, H; Owen, B J; Padilla, C; Pai, A; Palashov, O; Palomba, C; Pan, H; Pan, Y; Pankow, C; Paoletti, F; Paoletti, R; Paris, H; Pasqualetti, A; Passaquieti, R; Passuello, D; Pedraza, M; Penn, S; Perreca, A; Phelps, M; Pichot, M; Pickenpack, M; Piergiovanni, F; Pierro, V; Pinard, L; Pinto, I M; Pitkin, M; Poeld, J; Poggiani, R; Poteomkin, A; Powell, J; Prasad, J; Premachandra, S; Prestegard, T; Price, L R; Prijatelj, M; Privitera, S; Prodi, G A; Prokhorov, L; Puncken, O; Punturo, M; Puppo, P; Qin, J; Quetschke, V; Quintero, E; Quiroga, G; Quitzow-James, R; Raab, F J; Rabeling, D S; Rácz, I; Radkins, H; Raffai, P; Raja, S; Rajalakshmi, G; Rakhmanov, M; Ramet, C; Ramirez, K; Rapagnani, P; Raymond, V; Re, V; Read, J; Reed, C M; Regimbau, T; Reid, S; Reitze, D H; Rhoades, E; Ricci, F; Riles, K; Robertson, N A; Robinet, F; Rocchi, A; Rodruck, M; Rolland, L; Rollins, J G; Romano, J D; Romano, R; Romanov, G; Romie, J H; Rosińska, D; Rowan, S; Rüdiger, A; Ruggi, P; Ryan, K; Salemi, F; Sammut, L; Sandberg, V; Sanders, J R; Sannibale, V; Santiago-Prieto, I; Saracco, E; Sassolas, B; Sathyaprakash, B S; Saulson, P R; Savage, R; Scheuer, J; Schilling, R; Schnabel, R; Schofield, R M S; Schreiber, E; Schuette, D; Schutz, B F; Scott, J; Scott, S M; Sellers, D; Sengupta, A S; Sentenac, D; Sequino, V; Sergeev, A; Shaddock, D; Shah, S; Shahriar, M S; Shaltev, M; Shapiro, B; Shawhan, P; Shoemaker, D H; Sidery, T L; Siellez, K; Siemens, X; Sigg, D; Simakov, D; Singer, A; Singer, L; Singh, R; Sintes, A M; Slagmolen, B J J; Slutsky, J; Smith, J R; Smith, M; Smith, R J E; Smith-Lefebvre, N D; Son, E J; Sorazu, B; Souradeep, T; Sperandio, L; Staley, A; Stebbins, J; Steinlechner, J; Steinlechner, S; Stephens, B C; Steplewski, S; Stevenson, S; Stone, R; Stops, D; Strain, K A; Straniero, N; Strigin, S; Sturani, R; Stuver, A L; Summerscales, T Z; Susmithan, S; Sutton, P J; Swinkels, B; Tacca, M; Talukder, D; Tanner, D B; Tarabrin, S P; Taylor, R; Ter Braack, A P M; Thirugnanasambandam, M P; Thomas, M; Thomas, P; Thorne, K A; Thorne, K S; Thrane, E; Tiwari, V; Tokmakov, K V; Tomlinson, C; Toncelli, A; Tonelli, M; Torre, O; Torres, C V; Torrie, C I; Travasso, F; Traylor, G; Tse, M; Ugolini, D; Unnikrishnan, C S; Urban, A L; Urbanek, K; Vahlbruch, H; Vajente, G; Valdes, G; Vallisneri, M; van den Brand, J F J; Van Den Broeck, C; van der Putten, S; van der Sluys, M V; van Heijningen, J; van Veggel, A A; Vass, S; Vasúth, M; Vaulin, R; Vecchio, A; Vedovato, G; Veitch, J; Veitch, P J; Venkateswara, K; Verkindt, D; Verma, S S; Vetrano, F; Viceré, A; Vincent-Finley, R; Vinet, J-Y; Vitale, S; Vo, T; Vocca, H; Vorvick, C; Vousden, W D; Vyachanin, S P; Wade, A; Wade, L; Wade, M; Walker, M; Wallace, L; Wang, M; Wang, X; Ward, R L; Was, M; Weaver, B; Wei, L-W; Weinert, M; Weinstein, A J; Weiss, R; Welborn, T; Wen, L; Wessels, P; West, M; Westphal, T; Wette, K; Whelan, J T; White, D J; Whiting, B F; Wiesner, K; Wilkinson, C; Williams, K; Williams, L; Williams, R; Williams, T; Williamson, A R; Willis, J L; Willke, B; Wimmer, M; Winkler, W; Wipf, C C; Wiseman, A G; Wittel, H; Woan, G; Worden, J; Yablon, J; Yakushin, I; Yamamoto, H; Yancey, C C; Yang, H; Yang, Z; Yoshida, S; Yvert, M; Zadrożny, A; Zanolin, M; Zendri, J-P; Zhang, Fan; Zhang, L; Zhao, C; Zhu, X J; Zucker, M E; Zuraw, S; Zweizig, J

2014-12-05

Gravitational waves from a variety of sources are predicted to superpose to create a stochastic background. This background is expected to contain unique information from throughout the history of the Universe that is unavailable through standard electromagnetic observations, making its study of fundamental importance to understanding the evolution of the Universe. We carry out a search for the stochastic background with the latest data from the LIGO and Virgo detectors. Consistent with predictions from most stochastic gravitational-wave background models, the data display no evidence of a stochastic gravitational-wave signal. Assuming a gravitational-wave spectrum of Ω_{GW}(f)=Ω_{α}(f/f_{ref})^{α}, we place 95% confidence level upper limits on the energy density of the background in each of four frequency bands spanning 41.5-1726 Hz. In the frequency band of 41.5-169.25 Hz for a spectral index of α=0, we constrain the energy density of the stochastic background to be Ω_{GW}(f)waves.

Quantum noise and stochastic reduction

International Nuclear Information System (INIS)

Brody, Dorje C; Hughston, Lane P

2006-01-01

In standard nonrelativistic quantum mechanics the expectation of the energy is a conserved quantity. It is possible to extend the dynamical law associated with the evolution of a quantum state consistently to include a nonlinear stochastic component, while respecting the conservation law. According to the dynamics thus obtained, referred to as the energy-based stochastic Schroedinger equation, an arbitrary initial state collapses spontaneously to one of the energy eigenstates, thus describing the phenomenon of quantum state reduction. In this paper, two such models are investigated: one that achieves state reduction in infinite time and the other in finite time. The properties of the associated energy expectation process and the energy variance process are worked out in detail. By use of a novel application of a nonlinear filtering method, closed-form solutions-algebraic in character and involving no integration-are obtained of both these models. In each case, the solution is expressed in terms of a random variable representing the terminal energy of the system and an independent noise process. With these solutions at hand it is possible to simulate explicitly the dynamics of the quantum states of complicated physical systems

A Multilevel Network Study of the Effects of Delinquent Behavior on Friendship Evolution

NARCIS (Netherlands)

Snijders, T.A.B.; Baerveldt, Chris

2003-01-01

A multilevel approach is proposed to the study of the evolution of multiple networks. In this approach, the basic evolution process is assumed to be the same, while parameter values may differ between different networks. For the network evolution process, stochastic actor-oriented models are used,

What’s hampering measurement invariance: Detecting non-invariant items using clusterwise simultaneous component analysis

Directory of Open Access Journals (Sweden)

Kim eDe Roover

2014-06-01

Full Text Available The issue of measurement invariance is ubiquitous in the behavioral sciences nowadays as more and more studies yield multivariate multigroup data. When measurement invariance cannot be established across groups, this is often due to different loadings on only a few items. Within the multigroup CFA framework, methods have been proposed to trace such non-invariant items, but these methods have some disadvantages in that they require researchers to run a multitude of analyses and in that they imply assumptions that are often questionable. In this paper, we propose an alternative strategy which builds on clusterwise simultaneous component analysis (SCA. Clusterwise SCA, being an exploratory technique, assigns the groups under study to a few clusters based on differences and similarities in the covariance matrices, and thus based on the component structure of the items. Non-invariant items can then be traced by comparing the cluster-specific component loadings via congruence coefficients, which is far more parsimonious than comparing the component structure of all separate groups. In this paper we present a heuristic for this procedure. Afterwards, one can return to the multigroup CFA framework and check whether removing the non-invariant items or removing some of the equality restrictions for these items, yields satisfactory invariance test results. An empirical application concerning cross-cultural emotion data is used to demonstrate that this novel approach is useful and can co-exist with the traditional CFA approaches.

Double complexes and cohomological hierarchy in a space of weakly invariant Lagrangians of mechanics

International Nuclear Information System (INIS)

Khudaverdyan, O.M.; Saakyan, D.A.

1998-01-01

For a given configuration space M and Lie algebra G acting on M the space ν 0.0 of weakly G-invariant Lagrangians, i.e., Lagrangians whose motion equations left-hand sides are G-invariant, is studied. The problem is reformulated in terms of the double complex of Lie algebra cochains with values in the complex of Lagrangians. Calculating the cohomology of this complex by the method of spectral sequences we arrive at the hierarchy in the space ν 0.0 . The double filtration {ν s.σ }, s = 0,1,2,3,4, σ = 0,1, and the homomorphisms on every space ν s,σ are constructed. These homomorphisms take values in the cohomologies of the algebra G and the configuration space M. On one hand, every space ν s,σ in the kernel of the corresponding homomorphism, while the space itself is defined by its physical properties

Stochasticity in economic losses increases the value of reputation in indirect reciprocity.

Science.gov (United States)

dos Santos, Miguel; Placì, Sarah; Wedekind, Claus

2015-12-14

Recent theory predicts harsh and stochastic conditions to generally promote the evolution of cooperation. Here, we test experimentally whether stochasticity in economic losses also affects the value of reputation in indirect reciprocity, a type of cooperation that is very typical for humans. We used a repeated helping game with observers. One subject (the "Unlucky") lost some money, another one (the "Passer-by") could reduce this loss by accepting a cost to herself, thereby building up a reputation that could be used by others in later interactions. The losses were either stable or stochastic, but the average loss over time and the average efficiency gains of helping were kept constant in both treatments. We found that players with a reputation of being generous were generally more likely to receive help by others, such that investing into a good reputation generated long-term benefits that compensated for the immediate costs of helping. Helping frequencies were similar in both treatments, but players with a reputation to be selfish lost more resources under stochastic conditions. Hence, returns on investment were steeper when losses varied than when they did not. We conclude that this type of stochasticity increases the value of reputation in indirect reciprocity.

A Simulation-Based Dynamic Stochastic Route Choice Model for Evacuation

Directory of Open Access Journals (Sweden)

Xing Zhao

2012-01-01

Full Text Available This paper establishes a dynamic stochastic route choice model for evacuation to simulate the propagation process of traffic flow and estimate the stochastic route choice under evacuation situations. The model contains a lane-group-based cell transmission model (CTM which sets different traffic capacities for links with different turning movements to flow out in an evacuation situation, an actual impedance model which is to obtain the impedance of each route in time units at each time interval and a stochastic route choice model according to the probit-based stochastic user equilibrium. In this model, vehicles loading at each origin at each time interval are assumed to choose an evacuation route under determinate road network, signal design, and OD demand. As a case study, the proposed model is validated on the network nearby Nanjing Olympic Center after the opening ceremony of the 10th National Games of the People's Republic of China. The traffic volumes and clearing time at five exit points of the evacuation zone are calculated by the model to compare with survey data. The results show that this model can appropriately simulate the dynamic route choice and evolution process of the traffic flow on the network in an evacuation situation.

A constrained approach to multiscale stochastic simulation of chemically reacting systems

KAUST Repository

Cotter, Simon L.

2011-01-01

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems. © 2011 American Institute of Physics.

On the maximal noise for stochastic and QCD travelling waves

International Nuclear Information System (INIS)

Peschanski, Robi

2008-01-01

Using the relation of a set of nonlinear Langevin equations to reaction-diffusion processes, we note the existence of a maximal strength of the noise for the stochastic travelling wave solutions of these equations. Its determination is obtained using the field-theoretical analysis of branching-annihilation random walks near the directed percolation transition. We study its consequence for the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation. For the related Langevin equation modeling the quantum chromodynamic nonlinear evolution of gluon density with rapidity, the physical maximal-noise limit may appear before the directed percolation transition, due to a shift in the travelling-wave speed. In this regime, an exact solution is known from a coalescence process. Universality and other open problems and applications are discussed in the outlook

Evolution of Isolated Neutron Stars

OpenAIRE

Popov, S. B.

2001-01-01

In this paper we briefly review our recent results on evolution and properties of isolated neutron stars (INSs) in the Galaxy. As the first step we discuss stochastic period evolution of INSs. We briefly discuss how an INS's spin period evolves under influence of interaction with turbulized interstellar medium. To investigate statistical properties of the INS population we calculate a {\\it census} of INSs in our Galaxy. Then we show that for exponential field decay the range of minimum value ...

Stochastic dynamics modeling solute transport in porous media modeling solute transport in porous media

CERN Document Server

Kulasiri, Don

2002-01-01

Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas ...

Gauge-invariant cosmological density perturbations

International Nuclear Information System (INIS)

Sasaki, Misao.

1986-06-01

Gauge-invariant formulation of cosmological density perturbation theory is reviewed with special emphasis on its geometrical aspects. Then the gauge-invariant measure of the magnitude of a given perturbation is presented. (author)

Translation invariant time-dependent solutions to massive gravity II

Science.gov (United States)

Mourad, J.; Steer, D. A.

2014-06-01

This paper is a sequel to JCAP 12 (2013) 004 and is also devoted to translation-invariant solutions of ghost-free massive gravity in its moving frame formulation. Here we consider a mass term which is linear in the vielbein (corresponding to a β3 term in the 4D metric formulation) in addition to the cosmological constant. We determine explicitly the constraints, and from the initial value formulation show that the time-dependent solutions can have singularities at a finite time. Although the constraints give, as in the β1 case, the correct number of degrees of freedom for a massive spin two field, we show that the lapse function can change sign at a finite time causing a singular time evolution. This is very different to the β1 case where time evolution is always well defined. We conclude that the β3 mass term can be pathological and should be treated with care.

Stochastic approach to pitting-corrosion-extreme modelling in low-carbon steel

Energy Technology Data Exchange (ETDEWEB)

Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado 10400, La Habana (Cuba); Caleyo, F. [Departamento de Ingenieria Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)], E-mail: fcaleyo@gmail.com; Rivas, D.; Hallen, J.M. [Departamento de Ingenieria Metalurgica, IPN-ESIQIE, UPALM Edif. 7, Zacatenco, Mexico DF 07738 (Mexico)

2010-03-15

A stochastic model previously developed by the authors using Markov chains has been improved in the light of new experimental evidence. The new model has been successfully applied to reproduce the time evolution of extreme pitting corrosion depths in low-carbon steel. The model is shown to provide a better physical understanding of the pitting process.

Stochastic approach to pitting-corrosion-extreme modelling in low-carbon steel

International Nuclear Information System (INIS)

Valor, A.; Caleyo, F.; Rivas, D.; Hallen, J.M.

2010-01-01

A stochastic model previously developed by the authors using Markov chains has been improved in the light of new experimental evidence. The new model has been successfully applied to reproduce the time evolution of extreme pitting corrosion depths in low-carbon steel. The model is shown to provide a better physical understanding of the pitting process.

Conformal invariance in hydrodynamic turbulence

International Nuclear Information System (INIS)

Falkovich, Gregory

2007-01-01

This short survey is written by a physicist. It contains neither theorems nor precise definitions. Its main content is a description of the results of numerical solution of the equations of fluid mechanics in the regime of developed turbulence. Due to limitations of computers, the results are not very precise. Despite being neither exact nor rigorous, the findings may nevertheless be of interest for mathematicians. The main result is that the isolines of some scalar fields (vorticity, temperature) in two-dimensional turbulence belong to the class of conformally invariant curves called SLE (Scramm-Loewner evolution) curves. First, this enables one to predict and find a plethora of quantitative relations going far beyond what was known previously about turbulence. Second, it suggests relations between phenomena that seemed unrelated, like the Euler equation and critical percolation. Third, it shows that one is able to get exact analytic results in statistical hydrodynamics. In short, physicists have found something unexpected and hope that mathematicians can help to explain it.

Conformally symmetric contributions to BFKL evolution at next to leading order

International Nuclear Information System (INIS)

Coriano, C.; White, A.R.

1995-01-01

Unitarity corrections to the BFKL evolution at next to leading order determine a new component of the evolution kernel which is shown to possess conformal invariance properties. Expressions for the complete spectrum of the new component and the correction to the intercept of the pomeron trajectory are presented

Revisiting measurement invariance in intelligence testing in aging research: Evidence for almost complete metric invariance across age groups.

Science.gov (United States)

Sprague, Briana N; Hyun, Jinshil; Molenaar, Peter C M

2017-01-01

Invariance of intelligence across age is often assumed but infrequently explicitly tested. Horn and McArdle (1992) tested measurement invariance of intelligence, providing adequate model fit but might not consider all relevant aspects such as sub-test differences. The goal of the current paper is to explore age-related invariance of the WAIS-R using an alternative model that allows direct tests of age on WAIS-R subtests. Cross-sectional data on 940 participants aged 16-75 from the WAIS-R normative values were used. Subtests examined were information, comprehension, similarities, vocabulary, picture completion, block design, picture arrangement, and object assembly. The two intelligence factors considered were fluid and crystallized intelligence. Self-reported ages were divided into young (16-22, n = 300), adult (29-39, n = 275), middle (40-60, n = 205), and older (61-75, n = 160) adult groups. Results suggested partial metric invariance holds. Although most of the subtests reflected fluid and crystalized intelligence similarly across different ages, invariance did not hold for block design on fluid intelligence and picture arrangement on crystallized intelligence for older adults. Additionally, there was evidence of a correlated residual between information and vocabulary for the young adults only. This partial metric invariance model yielded acceptable model fit compared to previously-proposed invariance models of Horn and McArdle (1992). Almost complete metric invariance holds for a two-factor model of intelligence. Most of the subtests were invariant across age groups, suggesting little evidence for age-related bias in the WAIS-R. However, we did find unique relationships between two subtests and intelligence. Future studies should examine age-related differences in subtests when testing measurement invariance in intelligence.

EFT Beyond the Horizon: Stochastic Inflation and How Primordial Quantum Fluctuations Go Classical

CERN Document Server

Burgess, C P; Tasinato, G; Williams, M

2015-01-01

We identify the effective theory describing inflationary super-Hubble scales and show it to be a special case of effective field theories appropriate to open systems. Open systems allow information to be exchanged between the degrees of freedom of interest and those that are integrated out, such as for particles moving through a fluid. Strictly speaking they cannot in general be described by an effective lagrangian; rather the appropriate `low-energy' limit is instead a Lindblad equation describing the evolution of the density matrix of the slow degrees of freedom. We derive the equation relevant to super-Hubble modes of quantum fields in near-de Sitter spacetimes and derive two implications. We show the evolution of the diagonal density-matrix elements quickly approaches the Fokker-Planck equation of Starobinsky's stochastic inflationary picture. This provides an alternative first-principles derivation of this picture's stochastic noise and drift, as well as its leading corrections. (An application computes ...

Constructing Invariant Fairness Measures for Surfaces

DEFF Research Database (Denmark)

Gravesen, Jens; Ungstrup, Michael

1998-01-01

of the size of this vector field is used as the fairness measure on the family.Six basic 3rd order invariants satisfying two quadratic equations are defined. They form a complete set in the sense that any invariant 3rd order function can be written as a function of the six basic invariants together...

On logarithmic extensions of local scale-invariance

International Nuclear Information System (INIS)

Henkel, Malte

2013-01-01

Ageing phenomena far from equilibrium naturally present dynamical scaling and in many situations this may be generalised to local scale-invariance. Generically, the absence of time-translation-invariance implies that each scaling operator is characterised by two independent scaling dimensions. Building on analogies with logarithmic conformal invariance and logarithmic Schrödinger-invariance, this work proposes a logarithmic extension of local scale-invariance, without time-translation-invariance. Carrying this out requires in general to replace both scaling dimensions of each scaling operator by Jordan cells. Co-variant two-point functions are derived for the most simple case of a two-dimensional logarithmic extension. Their form is compared to simulational data for autoresponse functions in several universality classes of non-equilibrium ageing phenomena

A One-Dimensional Wave Equation with White Noise Boundary Condition

International Nuclear Information System (INIS)

Kim, Jong Uhn

2006-01-01

We discuss the Cauchy problem for a one-dimensional wave equation with white noise boundary condition. We also establish the existence of an invariant measure when the noise is additive. Similar problems for parabolic equations were discussed by several authors. To our knowledge, there is only one work which investigated the initial-boundary value problem for a wave equation with random noise at the boundary. We handle a more general case by a different method. Our result on the existence of an invariant measure relies on the author's recent work on a certain class of stochastic evolution equations

Stochastic-hydrodynamic model of halo formation in charged particle beams

Directory of Open Access Journals (Sweden)

Nicola Cufaro Petroni

2003-03-01

Full Text Available The formation of the beam halo in charged particle accelerators is studied in the framework of a stochastic-hydrodynamic model for the collective motion of the particle beam. In such a stochastic-hydrodynamic theory the density and the phase of the charged beam obey a set of coupled nonlinear hydrodynamic equations with explicit time-reversal invariance. This leads to a linearized theory that describes the collective dynamics of the beam in terms of a classical Schrödinger equation. Taking into account space-charge effects, we derive a set of coupled nonlinear hydrodynamic equations. These equations define a collective dynamics of self-interacting systems much in the same spirit as in the Gross-Pitaevskii and Landau-Ginzburg theories of the collective dynamics for interacting quantum many-body systems. Self-consistent solutions of the dynamical equations lead to quasistationary beam configurations with enhanced transverse dispersion and transverse emittance growth. In the limit of a frozen space-charge core it is then possible to determine and study the properties of stationary, stable core-plus-halo beam distributions. In this scheme the possible reproduction of the halo after its elimination is a consequence of the stationarity of the transverse distribution which plays the role of an attractor for every other distribution.

Theoretical and Numerical Investigation of the Cavity Evolution in Gypsum Rock

Science.gov (United States)

Li, Wei; Einstein, Herbert H.

2017-11-01

When water flows through a preexisting cylindrical tube in gypsum rock, the nonuniform dissolution alters the tube into an enlarged tapered tube. A 2-D analytical model is developed to study the transport-controlled dissolution in an enlarged tapered tube, with explicit consideration of the tapered geometry and induced radial flow. The analytical model shows that the Graetz solution can be extended to model dissolution in the tapered tube. An alternative form of the governing equations is proposed to take advantage of the invariant quantities in the Graetz solution to facilitate modeling cavity evolution in gypsum rock. A 2-D finite volume model was developed to validate the extended Graetz solution. The time evolution of the transport-controlled and the reaction-controlled dissolution models for a single tube with time-invariant flow rate are compared. This comparison shows that for time-invariant flow rate, the reaction-controlled dissolution model produces a positive feedback between the tube enlargement and dissolution, while the transport-controlled dissolution does not.

Nonperturbative effects in B → Xsl+l- for large dilepton invariant mass

International Nuclear Information System (INIS)

Buchalla, G.

1998-01-01

The authors consider the calculation of O(Λ QCD 2 /m b 2 ) nonperturbative corrections to B → X s l + l - decay. The analysis confirms the results of Ali et al. for the dilepton invariant mass spectrum, which were in disagreement with an earlier publication, and for the lepton forward-backward asymmetry. The authors also give expressions for the O(Λ QCD 2 /m b 2 ) corrections to the left-right asymmetry. In addition the authors discuss the breakdown of the heavy quark expansion near the point of maximal dilepton invariant mass q 2 and consider a model independent approach to this region using heavy hadron chiral perturbation theory. The modes B → Kl + l - and B → Kπl + l - , which determine the endpoint region of the inclusive decay, are analysed within this framework. An interpolation is suggested between the region of moderately high q 2 , where the heavy quark expansion is still valid, and the vicinity of the endpoint described by chiral perturbation theory. The authors also comment on further nonperturbative effects in B → Kl + l -

Fuzzy stochastic damage mechanics (FSDM based on fuzzy auto-adaptive control theory

Directory of Open Access Journals (Sweden)

Ya-jun Wang

2012-06-01

Full Text Available In order to fully interpret and describe damage mechanics, the origin and development of fuzzy stochastic damage mechanics were introduced based on the analysis of the harmony of damage, probability, and fuzzy membership in the interval of [0,1]. In a complete normed linear space, it was proven that a generalized damage field can be simulated through β probability distribution. Three kinds of fuzzy behaviors of damage variables were formulated and explained through analysis of the generalized uncertainty of damage variables and the establishment of a fuzzy functional expression. Corresponding fuzzy mapping distributions, namely, the half-depressed distribution, swing distribution, and combined swing distribution, which can simulate varying fuzzy evolution in diverse stochastic damage situations, were set up. Furthermore, through demonstration of the generalized probabilistic characteristics of damage variables, the cumulative distribution function and probability density function of fuzzy stochastic damage variables, which show β probability distribution, were modified according to the expansion principle. The three-dimensional fuzzy stochastic damage mechanical behaviors of the Longtan rolled-concrete dam were examined with the self-developed fuzzy stochastic damage finite element program. The statistical correlation and non-normality of random field parameters were considered comprehensively in the fuzzy stochastic damage model described in this paper. The results show that an initial damage field based on the comprehensive statistical evaluation helps to avoid many difficulties in the establishment of experiments and numerical algorithms for damage mechanics analysis.

Invariant density analysis: modeling and analysis of the postural control system using Markov chains.

Science.gov (United States)

Hur, Pilwon; Shorter, K Alex; Mehta, Prashant G; Hsiao-Wecksler, Elizabeth T

2012-04-01

In this paper, a novel analysis technique, invariant density analysis (IDA), is introduced. IDA quantifies steady-state behavior of the postural control system using center of pressure (COP) data collected during quiet standing. IDA relies on the analysis of a reduced-order finite Markov model to characterize stochastic behavior observed during postural sway. Five IDA parameters characterize the model and offer physiological insight into the long-term dynamical behavior of the postural control system. Two studies were performed to demonstrate the efficacy of IDA. Study 1 showed that multiple short trials can be concatenated to create a dataset suitable for IDA. Study 2 demonstrated that IDA was effective at distinguishing age-related differences in postural control behavior between young, middle-aged, and older adults. These results suggest that the postural control system of young adults converges more quickly to their steady-state behavior while maintaining COP nearer an overall centroid than either the middle-aged or older adults. Additionally, larger entropy values for older adults indicate that their COP follows a more stochastic path, while smaller entropy values for young adults indicate a more deterministic path. These results illustrate the potential of IDA as a quantitative tool for the assessment of the quiet-standing postural control system.

Stochastic description of supersymmetric fields with values in a manifold

International Nuclear Information System (INIS)

Hoba, Z.

1986-01-01

This paper discusses the mathematical problem of the imaginary time quantum mechanics of a particle moving in Euclidean space as considered from the theory of diffusion processes. The diffusion process is defined by a stochastic equation; the equation describes the diffusion process as a time evolution of a Brownian particle in a force field. The paper considers a Brownian particle on a Riemannian manifold

Evolution of polarization in an atomic vapour with negative refractive index

International Nuclear Information System (INIS)

Zhuang Fei; Shen Jianqi

2006-01-01

A three-level Lambda-configuration atomic vapour may exhibit simultaneously negative permittivity and permeability in the optical frequency band, and an isotropic left-handed vapour medium could therefore be realized within the framework of quantum optics. One of the most remarkable features of the present scheme is that both the refractive index and the photon helicity reversal inside the vapour can be controllably manipulated by an external coupling light field. The phenomenological Hamiltonian that describes the process of helicity reversal is constructed and the time-dependent Schroedinger equation governing the time evolution of the polarization states of the lightwave is solved by means of the Lewis-Riesenfeld invariant theory. The transition between the polarization states (and hence the accompanied photon helicity reversal), which is exactly analogous to the transition operation between bits in digital circuit, may be valuable for the development of new techniques in quantum optics and would have potential applications in information technology

Nonlocal, yet translation invariant, constraints for rotationally invariant slave bosons

Science.gov (United States)

Ayral, Thomas; Kotliar, Gabriel

The rotationally-invariant slave boson (RISB) method is a lightweight framework allowing to study the low-energy properties of complex multiorbital problems currently out of the reach of more comprehensive, yet more computationally demanding methods such as dynamical mean field theory. In the original formulation of this formalism, the slave-boson constraints can be made nonlocal by enlarging the unit cell and viewing the quantum states enclosed in this new unit cell as molecular levels. In this work, we extend RISB to constraints which are nonlocal while preserving translation invariance. We apply this extension to the Hubbard model.

STOCHASTIC FLOWS OF MAPPINGS

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.

Anomalous transport regimes in a stochastic advection-diffusion model

International Nuclear Information System (INIS)

Dranikov, I.L.; Kondratenko, P.S.; Matveev, L.V.

2004-01-01

A general solution to the stochastic advection-diffusion problem is obtained for a fractal medium with long-range correlated spatial fluctuations. A particular transport regime is determined by two basic parameters: the exponent 2h of power-law decay of the two-point velocity correlation function and the mean advection velocity u. The values of these parameters corresponding to anomalous diffusion are determined, and anomalous behavior of the tracer distribution is analyzed for various combinations of u and h. The tracer concentration is shown to decrease exponentially at large distances, whereas power-law decay is predicted by fractional differential equations. Equations that describe the essential characteristics of the solution are written in terms of coupled space-time fractional differential operators. The analysis relies on a diagrammatic technique and makes use of scale-invariant properties of the medium

Analytic invariants of boundary links

OpenAIRE

Garoufalidis, Stavros; Levine, Jerome

2001-01-01

Using basic topology and linear algebra, we define a plethora of invariants of boundary links whose values are power series with noncommuting variables. These turn out to be useful and elementary reformulations of an invariant originally defined by M. Farber.

Status of time reversal invariance

International Nuclear Information System (INIS)

Henley, E.M.

1989-01-01

Time Reversal Invariance is introduced, and theories for its violation are reviewed. The present experimental and theoretical status of Time Reversal Invariance and tests thereof will be presented. Possible future tests will be discussed. 30 refs., 2 figs., 1 tab

Low temperature electroweak phase transition in the Standard Model with hidden scale invariance

Directory of Open Access Journals (Sweden)

Suntharan Arunasalam

2018-01-01

Full Text Available We discuss a cosmological phase transition within the Standard Model which incorporates spontaneously broken scale invariance as a low-energy theory. In addition to the Standard Model fields, the minimal model involves a light dilaton, which acquires a large vacuum expectation value (VEV through the mechanism of dimensional transmutation. Under the assumption of the cancellation of the vacuum energy, the dilaton develops a very small mass at 2-loop order. As a result, a flat direction is present in the classical dilaton-Higgs potential at zero temperature while the quantum potential admits two (almost degenerate local minima with unbroken and broken electroweak symmetry. We found that the cosmological electroweak phase transition in this model can only be triggered by a QCD chiral symmetry breaking phase transition at low temperatures, T≲132 MeV. Furthermore, unlike the standard case, the universe settles into the chiral symmetry breaking vacuum via a first-order phase transition which gives rise to a stochastic gravitational background with a peak frequency ∼10−8 Hz as well as triggers the production of approximately solar mass primordial black holes. The observation of these signatures of cosmological phase transitions together with the detection of a light dilaton would provide a strong hint of the fundamental role of scale invariance in particle physics.

Fundamental solution of bond pricing in the Ho-Lee stochastic interest rate model under the invariant criteria

Directory of Open Access Journals (Sweden)

Burhaneddin İzgi

2017-03-01

under the invariant criteria. We obtain transformations between Ho-Lee model with the corresponding linear (1 + 1 partial differential equation and the first Lie canonical form which is identical to the classical heat equation. These transformations help us to generate the fundamental solution for the Ho-Lee model with respect to the fundamental solution of the classical heat equation sense. Moreover, as a financial application of the Ho-Lee model, we choose the drift term from power functions and perform simulations via Milstein method. Furthermore, we obtain important results for the parameter calibration of the corresponding drift term by using the simulation results.

Stochastic Lorentz forces on a point charge moving near the conducting plate

International Nuclear Information System (INIS)

Hsiang, J.-T.; Wu, T.-H.; Lee, D.-S.

2008-01-01

The influence of quantized electromagnetic fields on a nonrelativistic charged particle moving near a conducting plate is studied. We give a field-theoretic derivation of the nonlinear, non-Markovian Langevin equation of the particle by the method of Feynman-Vernon influence functional. This stochastic approach incorporates not only the stochastic noise manifested from electromagnetic vacuum fluctuations, but also dissipation backreaction on a charge in the form of the retarded Lorentz forces. Since the imposition of the boundary is expected to anisotropically modify the effects of the fields on the evolution of the particle, we consider the motion of a charge undergoing small-amplitude oscillations in the direction either parallel or normal to the plane boundary. Under the dipole approximation for nonrelativistic motion, velocity fluctuations of the charge are found to grow linearly with time in the early stage of the evolution at the rather different rate, revealing strong anisotropic behavior. They are then asymptotically saturated as a result of the fluctuation-dissipation relation, and the same saturated value is found for the motion in both directions. The observational consequences are discussed

Summational invariants

International Nuclear Information System (INIS)

Mackrodt, C.; Reeh, H.

1997-01-01

General summational invariants, i.e., conservation laws acting additively on asymptotic particle states, are investigated within a classical framework for point particles with nontrivial scattering. copyright 1997 American Institute of Physics

Stochastic processes

CERN Document Server

Parzen, Emanuel

1962-01-01

Well-written and accessible, this classic introduction to stochastic processes and related mathematics is appropriate for advanced undergraduate students of mathematics with a knowledge of calculus and continuous probability theory. The treatment offers examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models, and it develops the methods of probability model-building.Chapter 1 presents precise definitions of the notions of a random variable and a stochastic process and introduces the Wiener and Poisson processes. Subsequent chapters examine

Link invariants for flows in higher dimensions

International Nuclear Information System (INIS)

Garcia-Compean, Hugo; Santos-Silva, Roberto

2010-01-01

Linking numbers in higher dimensions and their generalization including gauge fields are studied in the context of BF theories. The linking numbers associated with n-manifolds with smooth flows generated by divergence-free p-vector fields, endowed with an invariant flow measure, are computed in the context of quantum field theory. They constitute invariants of smooth dynamical systems (for nonsingular flows) and generalize previous proposals of invariants. In particular, they generalize Arnold's asymptotic Hopf invariant from three to higher dimensions. This invariant is generalized by coupling with a non-Abelian gauge flat connection with nontrivial holonomy. The computation of the asymptotic Jones-Witten invariants for flows is naturally extended to dimension n=2p+1. Finally, we give a possible interpretation and implementation of these issues in the context of 11-dimensional supergravity and string theory.

Spatiotemporal Diffusive Evolution and Fractal Structure of Ground Motion

Science.gov (United States)

Suwada, Tsuyoshi

2018-02-01

The spatiotemporal diffusive evolution and fractal structure of ground motion have been investigated at the in-ground tunnel of the KEK B-Factory (KEKB) injector linear accelerator (linac). The slow dynamic fluctuating displacements of the tunnel floor are measured in real time with a new remote-controllable sensing system based on a laser-based alignment system. Based on spatiotemporal analyses with linear-regression models, which were applied in both the time and frequency domains to time-series data recorded over a period of approximately 8 months, both coherent and stochastic components in the displacements of the tunnel floor were clearly observed along the entire length of the linac. In particular, it was clearly observed that the stochastic components exhibited characteristic spatiotemporal diffusive evolution with the fractal structure and fractional dimension. This report describes in detail the experimental techniques and analyses of the spatiotemporal diffusive evolution of ground motion observed at the in-ground tunnel of the injector linac using a real-time remote-controllable sensing system.

Dynamical topological invariant after a quantum quench

Science.gov (United States)

Yang, Chao; Li, Linhu; Chen, Shu

2018-02-01

We show how to define a dynamical topological invariant for one-dimensional two-band topological systems after a quantum quench. By analyzing general two-band models of topological insulators, we demonstrate that the reduced momentum-time manifold can be viewed as a series of submanifolds S2, and thus we are able to define a dynamical topological invariant on each of the spheres. We also unveil the intrinsic relation between the dynamical topological invariant and the difference in the topological invariant of the initial and final static Hamiltonian. By considering some concrete examples, we illustrate the calculation of the dynamical topological invariant and its geometrical meaning explicitly.

Left ventricular hypertrophy : virtuous intentions, malign consequences

NARCIS (Netherlands)

Pokharel, S; Sharma, UC; Pinto, YM

Left ventricular hypertrophy (LVH) is currently the focus of intense cardiovascular research, with the resultant rapid evolution of novel concepts relating to its exceedingly complex pathophysiology. In addition to the alterations in signal transduction and disturbances in Ca2+ homeostasis, there

Left ventricular hypertrophy: virtuous intentions, malign consequences

NARCIS (Netherlands)

Pokharel, Saraswati; Sharma, Umesh C.; Pinto, Yigal M.

2003-01-01

Left ventricular hypertrophy (LVH) is currently the focus of intense cardiovascular research, with the resultant rapid evolution of novel concepts relating to its exceedingly complex pathophysiology. In addition to the alterations in signal transduction and disturbances in Ca(2+) homeostasis, there

Phenomenology of local scale invariance: from conformal invariance to dynamical scaling

International Nuclear Information System (INIS)

Henkel, Malte

2002-01-01

Statistical systems displaying a strongly anisotropic or dynamical scaling behaviour are characterized by an anisotropy exponent θ or a dynamical exponent z. For a given value of θ (or z), we construct local scale transformations, which can be viewed as scale transformations with a space-time-dependent dilatation factor. Two distinct types of local scale transformations are found. The first type may describe strongly anisotropic scaling of static systems with a given value of θ, whereas the second type may describe dynamical scaling with a dynamical exponent z. Local scale transformations act as a dynamical symmetry group of certain non-local free-field theories. Known special cases of local scale invariance are conformal invariance for θ=1 and Schroedinger invariance for θ=2. The hypothesis of local scale invariance implies that two-point functions of quasi primary operators satisfy certain linear fractional differential equations, which are constructed from commuting fractional derivatives. The explicit solution of these yields exact expressions for two-point correlators at equilibrium and for two-point response functions out of equilibrium. A particularly simple and general form is found for the two-time auto response function. These predictions are explicitly confirmed at the uniaxial Lifshitz points in the ANNNI and ANNNS models and in the aging behaviour of simple ferromagnets such as the kinetic Glauber-Ising model and the kinetic spherical model with a non-conserved order parameter undergoing either phase-ordering kinetics or non-equilibrium critical dynamics

Quantifying Translation-Invariance in Convolutional Neural Networks

OpenAIRE

Kauderer-Abrams, Eric

2017-01-01

A fundamental problem in object recognition is the development of image representations that are invariant to common transformations such as translation, rotation, and small deformations. There are multiple hypotheses regarding the source of translation invariance in CNNs. One idea is that translation invariance is due to the increasing receptive field size of neurons in successive convolution layers. Another possibility is that invariance is due to the pooling operation. We develop a simple ...

Model reduction for slow–fast stochastic systems with metastable behaviour

International Nuclear Information System (INIS)

Bruna, Maria; Chapman, S. Jonathan; Smith, Matthew J.

2014-01-01

The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. The method is extended here to slow–fast systems in which the fast variables exhibit metastable behaviour. The key parameter that determines the form of the reduced model is the ratio of the timescale for the switching of the fast variables between metastable states to the timescale for the evolution of the slow variables. The method is illustrated with two examples: one from biochemistry (a fast-species-mediated chemical switch coupled to a slower varying species), and one from ecology (a predator–prey system). Numerical simulations of each model reduction are compared with those of the full system

Violation of CPT invariance in the early universe and leptogenesis/baryogenesis

CERN Document Server

Mavromatos, Nick E

2013-01-01

In this talk, I review some plausible scenarios entailing violation of CPT symmetry in the early Universe, due to space-time backgrounds which do not respect some of the assumptions for the validity of the CPT theorem (here considered will be Lorentz invariance and/or Unitarity). The key point in all these models is that the background induces different populations of fermions as compared to antifermions, and hence CPT Violation (CPTV), already in thermal equilibrium. Such populations may freeze out at various conditions depending on the details of the underlying microscopic model, thereby leading to leptogenesis and baryogenesis. Among the considered scenarios is a stringy one, in which the CPTV is associated with a cosmological background with torsion provided by the Kalb-Ramond antisymmetric tensor field (axion) of the string gravitational multiplet. We also discuss briefly (Lorentz Violating) CPTV models that go beyond the local effective lagrangian framework, such as a stochastic Finsler metric and D-par...

Invariant measures in brain dynamics

International Nuclear Information System (INIS)

Boyarsky, Abraham; Gora, Pawel

2006-01-01

This note concerns brain activity at the level of neural ensembles and uses ideas from ergodic dynamical systems to model and characterize chaotic patterns among these ensembles during conscious mental activity. Central to our model is the definition of a space of neural ensembles and the assumption of discrete time ensemble dynamics. We argue that continuous invariant measures draw the attention of deeper brain processes, engendering emergent properties such as consciousness. Invariant measures supported on a finite set of ensembles reflect periodic behavior, whereas the existence of continuous invariant measures reflect the dynamics of nonrepeating ensemble patterns that elicit the interest of deeper mental processes. We shall consider two different ways to achieve continuous invariant measures on the space of neural ensembles: (1) via quantum jitters, and (2) via sensory input accompanied by inner thought processes which engender a 'folding' property on the space of ensembles

A Stochastic Hybrid Systems framework for analysis of Markov reward models

International Nuclear Information System (INIS)

Dhople, S.V.; DeVille, L.; Domínguez-García, A.D.

2014-01-01

In this paper, we propose a framework to analyze Markov reward models, which are commonly used in system performability analysis. The framework builds on a set of analytical tools developed for a class of stochastic processes referred to as Stochastic Hybrid Systems (SHS). The state space of an SHS is comprised of: (i) a discrete state that describes the possible configurations/modes that a system can adopt, which includes the nominal (non-faulty) operational mode, but also those operational modes that arise due to component faults, and (ii) a continuous state that describes the reward. Discrete state transitions are stochastic, and governed by transition rates that are (in general) a function of time and the value of the continuous state. The evolution of the continuous state is described by a stochastic differential equation and reward measures are defined as functions of the continuous state. Additionally, each transition is associated with a reset map that defines the mapping between the pre- and post-transition values of the discrete and continuous states; these mappings enable the definition of impulses and losses in the reward. The proposed SHS-based framework unifies the analysis of a variety of previously studied reward models. We illustrate the application of the framework to performability analysis via analytical and numerical examples

Hill functions for stochastic gene regulatory networks from master equations with split nodes and time-scale separation

Science.gov (United States)

Lipan, Ovidiu; Ferwerda, Cameron

2018-02-01

The deterministic Hill function depends only on the average values of molecule numbers. To account for the fluctuations in the molecule numbers, the argument of the Hill function needs to contain the means, the standard deviations, and the correlations. Here we present a method that allows for stochastic Hill functions to be constructed from the dynamical evolution of stochastic biocircuits with specific topologies. These stochastic Hill functions are presented in a closed analytical form so that they can be easily incorporated in models for large genetic regulatory networks. Using a repressive biocircuit as an example, we show by Monte Carlo simulations that the traditional deterministic Hill function inaccurately predicts time of repression by an order of two magnitudes. However, the stochastic Hill function was able to capture the fluctuations and thus accurately predicted the time of repression.

Stochastic effects in hybrid inflation

Science.gov (United States)

Martin, Jérôme; Vennin, Vincent

2012-02-01

Hybrid inflation is a two-field model where inflation ends due to an instability. In the neighborhood of the instability point, the potential is very flat and the quantum fluctuations dominate over the classical motion of the inflaton and waterfall fields. In this article, we study this regime in the framework of stochastic inflation. We numerically solve the two coupled Langevin equations controlling the evolution of the fields and compute the probability distributions of the total number of e-folds and of the inflation exit point. Then, we discuss the physical consequences of our results, in particular, the question of how the quantum diffusion can affect the observable predictions of hybrid inflation.

STOCHASTIC OPTICS: A SCATTERING MITIGATION FRAMEWORK FOR RADIO INTERFEROMETRIC IMAGING

Energy Technology Data Exchange (ETDEWEB)

Johnson, Michael D., E-mail: mjohnson@cfa.harvard.edu [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)

2016-12-10

Just as turbulence in the Earth’s atmosphere can severely limit the angular resolution of optical telescopes, turbulence in the ionized interstellar medium fundamentally limits the resolution of radio telescopes. We present a scattering mitigation framework for radio imaging with very long baseline interferometry (VLBI) that partially overcomes this limitation. Our framework, “stochastic optics,” derives from a simplification of strong interstellar scattering to separate small-scale (“diffractive”) effects from large-scale (“refractive”) effects, thereby separating deterministic and random contributions to the scattering. Stochastic optics extends traditional synthesis imaging by simultaneously reconstructing an unscattered image and its refractive perturbations. Its advantages over direct imaging come from utilizing the many deterministic properties of the scattering—such as the time-averaged “blurring,” polarization independence, and the deterministic evolution in frequency and time—while still accounting for the stochastic image distortions on large scales. These distortions are identified in the image reconstructions through regularization by their time-averaged power spectrum. Using synthetic data, we show that this framework effectively removes the blurring from diffractive scattering while reducing the spurious image features from refractive scattering. Stochastic optics can provide significant improvements over existing scattering mitigation strategies and is especially promising for imaging the Galactic Center supermassive black hole, Sagittarius A*, with the Global mm-VLBI Array and with the Event Horizon Telescope.

STOCHASTIC OPTICS: A SCATTERING MITIGATION FRAMEWORK FOR RADIO INTERFEROMETRIC IMAGING

International Nuclear Information System (INIS)

Johnson, Michael D.

2016-01-01

Just as turbulence in the Earth’s atmosphere can severely limit the angular resolution of optical telescopes, turbulence in the ionized interstellar medium fundamentally limits the resolution of radio telescopes. We present a scattering mitigation framework for radio imaging with very long baseline interferometry (VLBI) that partially overcomes this limitation. Our framework, “stochastic optics,” derives from a simplification of strong interstellar scattering to separate small-scale (“diffractive”) effects from large-scale (“refractive”) effects, thereby separating deterministic and random contributions to the scattering. Stochastic optics extends traditional synthesis imaging by simultaneously reconstructing an unscattered image and its refractive perturbations. Its advantages over direct imaging come from utilizing the many deterministic properties of the scattering—such as the time-averaged “blurring,” polarization independence, and the deterministic evolution in frequency and time—while still accounting for the stochastic image distortions on large scales. These distortions are identified in the image reconstructions through regularization by their time-averaged power spectrum. Using synthetic data, we show that this framework effectively removes the blurring from diffractive scattering while reducing the spurious image features from refractive scattering. Stochastic optics can provide significant improvements over existing scattering mitigation strategies and is especially promising for imaging the Galactic Center supermassive black hole, Sagittarius A*, with the Global mm-VLBI Array and with the Event Horizon Telescope.

Stochastic backgrounds of relic gravitons: a theoretical appraisal

CERN Document Server

Giovannini, Massimo

2010-01-01

Stochastic backgrounds or relic gravitons, if ever detected, will constitute a prima facie evidence of physical processes taking place during the earliest stages of the evolution of the plasma. The essentials of the stochastic backgrounds of relic gravitons are hereby introduced and reviewed. The pivotal observables customarily employed to infer the properties of the relic gravitons are discussed both in the framework of the $\\Lambda$CDM paradigm as well as in neighboring contexts. The complementarity between experiments measuring the polarization of the Cosmic Microwave Background (such as, for instance, WMAP, Capmap, Quad, Cbi, just to mention a few) and wide band interferometers (e.g. Virgo, Ligo, Geo, Tama) is emphasized. While the analysis of the microwave sky strongly constrains the low-frequency tail of the relic graviton spectrum, wide-band detectors are sensitive to much higher frequencies where the spectral energy density depends chiefly upon the (poorly known) rate of post-inflationary expansion.

Stochastic modelling of avascular tumour growth and therapy

International Nuclear Information System (INIS)

Sahoo, S; Sahoo, A; Shearer, S F C

2011-01-01

In this paper, a generalized stochastic model for the growth of avascular tumours is presented. This model captures the dynamical evolution of avascular tumour cell subpopulations by incorporating Gaussian white noise into the growth rate of the mitotic function. This work generalizes the deterministic model proposed by Sherratt and Chaplain (2001 J. Math. Biol. 43 291) where they formulated a tumour model in an in vivo setting, in terms of continuum densities of proliferating, quiescent and necrotic cells. Detailed simulations of our model show that the inclusion of Gaussian noise in the original model of Sherratt and Chaplain substantially distorts the overall structure of the density profiles in addition to reducing the speed of tumour growth. Within this stochastic carcinogenesis framework the action of therapy is also investigated by replacing Gaussian white noise with a therapy term. We compare a constant therapy protocol with a logarithmic time-dependent protocol. Our results predict that a logarithmic therapy is more effective than the constant therapy protocol.

The non-equilibrium nature of culinary evolution

Science.gov (United States)

Kinouchi, Osame; Diez-Garcia, Rosa W.; Holanda, Adriano J.; Zambianchi, Pedro; Roque, Antonio C.

2008-07-01

Food is an essential part of civilization, with a scope that ranges from the biological to the economic and cultural levels. Here, we study the statistics of ingredients and recipes taken from Brazilian, British, French and Medieval cookery books. We find universal distributions with scale invariant behaviour. We propose a copy-mutate process to model culinary evolution that fits our empirical data very well. We find a cultural 'founder effect' produced by the non-equilibrium dynamics of the model. Both the invariant and idiosyncratic aspects of culture are accounted for by our model, which may have applications in other kinds of evolutionary processes.

Evaluation of scale invariance in physiological signals by means of balanced estimation of diffusion entropy

Science.gov (United States)

Zhang, Wenqing; Qiu, Lu; Xiao, Qin; Yang, Huijie; Zhang, Qingjun; Wang, Jianyong

2012-11-01

By means of the concept of the balanced estimation of diffusion entropy, we evaluate the reliable scale invariance embedded in different sleep stages and stride records. Segments corresponding to waking, light sleep, rapid eye movement (REM) sleep, and deep sleep stages are extracted from long-term electroencephalogram signals. For each stage the scaling exponent value is distributed over a considerably wide range, which tell us that the scaling behavior is subject and sleep cycle dependent. The average of the scaling exponent values for waking segments is almost the same as that for REM segments (˜0.8). The waking and REM stages have a significantly higher value of the average scaling exponent than that for light sleep stages (˜0.7). For the stride series, the original diffusion entropy (DE) and the balanced estimation of diffusion entropy (BEDE) give almost the same results for detrended series. The evolutions of local scaling invariance show that the physiological states change abruptly, although in the experiments great efforts have been made to keep conditions unchanged. The global behavior of a single physiological signal may lose rich information on physiological states. Methodologically, the BEDE can evaluate with considerable precision the scale invariance in very short time series (˜102), while the original DE method sometimes may underestimate scale-invariance exponents or even fail in detecting scale-invariant behavior. The BEDE method is sensitive to trends in time series. The existence of trends may lead to an unreasonably high value of the scaling exponent and consequent mistaken conclusions.

The usage of color invariance in SURF

Science.gov (United States)

Meng, Gang; Jiang, Zhiguo; Zhao, Danpei

2009-10-01

SURF (Scale Invariant Feature Transform) is a robust local invariant feature descriptor. However, SURF is mainly designed for gray images. In order to make use of the information provided by color (mainly RGB channels), this paper presents a novel colored local invariant feature descriptor, CISURF (Color Invariance based SURF). The proposed approach builds the descriptors in a color invariant space, which stems from Kubelka-Munk model and provides more valuable information than the gray space. Compared with the conventional SURF and SIFT descriptors, the experimental results show that descriptors created by CISURF is more robust to the circumstance changes such as the illumination direction, illumination intensity, and the viewpoints, and are more suitable for the deep space background objects.

Stochastic flow modeling : Quasi-Geostrophy, Taylor state and torsional wave excitation

DEFF Research Database (Denmark)

Gillet, Nicolas; Jault, D.; Finlay, Chris

We reconstruct the core flow evolution over the period 1840-2010 under the quasi-geostrophic assumption, from the stochastic magnetic field model COV-OBS and its full model error covariance matrix. We make use of a prior information on the flow temporal power spectrum compatible with that of obse......We reconstruct the core flow evolution over the period 1840-2010 under the quasi-geostrophic assumption, from the stochastic magnetic field model COV-OBS and its full model error covariance matrix. We make use of a prior information on the flow temporal power spectrum compatible....... Large length-scales flow features are naturally dominated by their equatorially symmetric component from about 1900 when the symmetry constraint is relaxed. Equipartition of the kinetic energy in both symmetries coincides with the poor prediction of decadal length-of-day changes in the XIXth century. We...... interpret this as an evidence for quasi-geostrophic rapid flow changes, and the consequence of a too loose data constraint during the oldest period. We manage to retrieve rapid flow changes over the past 60 yrs, and in particular modulated torsional waves predicting correctly interannual length-of day...

Stochastic heating in the cyclotron resonance of electrons; Calentamiento estocastico en la resonancia ciclotronica de los electrones

Energy Technology Data Exchange (ETDEWEB)

Gutierrez T, C.; Hernandez A, O. [Instituto Nacional de Investigaciones Nucleares, A.P. 18-1027, 11801 Mexico D.F. (Mexico)

1999-07-01

The study of the different schemes of plasma heating by radiofrequency waves is a very actual problem related with the plasma heating in different machines and the particle acceleration mechanisms. In this work, it is obtained the expression for the temporal evolution of the energy absorbed in the cyclotron resonance of electrons where it is showed the stochastic character of the energy absorption. It is obtained the stochastic criteria in a magnetic configuration of an Ecr type plasma source. (Author)

Anisotropic Weyl invariance

Energy Technology Data Exchange (ETDEWEB)

Perez-Nadal, Guillem [Universidad de Buenos Aires, Buenos Aires (Argentina)

2017-07-15

We consider a non-relativistic free scalar field theory with a type of anisotropic scale invariance in which the number of coordinates ''scaling like time'' is generically greater than one. We propose the Cartesian product of two curved spaces, the metric of each space being parameterized by the other space, as a notion of curved background to which the theory can be extended. We study this type of geometries, and find a family of extensions of the theory to curved backgrounds in which the anisotropic scale invariance is promoted to a local, Weyl-type symmetry. (orig.)

The invariant theory of matrices

CERN Document Server

Concini, Corrado De

2017-01-01

This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of m\\times m matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving the first fundamental theorem that describes a set of generators in the ring of invariants, and the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case...

Stochastic resonance induced by novel random transitions of motion of FitzHugh-Nagumo neuron model

International Nuclear Information System (INIS)

Zhang Guangjun; Xu Jianxue

2005-01-01

In contrast to the previous studies which have dealt with stochastic resonance induced by random transitions of system motion between two coexisting limit cycle attractors in the FitzHugh-Nagumo (FHN) neuron model after Hopf bifurcation and which have dealt with the phenomenon of stochastic resonance induced by external noise when the model with periodic input has only one attractor before Hopf bifurcation, in this paper we have focused our attention on stochastic resonance (SR) induced by a novel transition behavior, the transitions of motion of the model among one attractor on the left side of bifurcation point and two attractors on the right side of bifurcation point under the perturbation of noise. The results of research show: since one bifurcation of transition from one to two limit cycle attractors and the other bifurcation of transition from two to one limit cycle attractors occur in turn besides Hopf bifurcation, the novel transitions of motion of the model occur when bifurcation parameter is perturbed by weak internal noise; the bifurcation point of the model may stochastically slightly shift to the left or right when FHN neuron model is perturbed by external Gaussian distributed white noise, and then the novel transitions of system motion also occur under the perturbation of external noise; the novel transitions could induce SR alone, and when the novel transitions of motion of the model and the traditional transitions between two coexisting limit cycle attractors after bifurcation occur in the same process the SR also may occur with complicated behaviors types; the mechanism of SR induced by external noise when FHN neuron model with periodic input has only one attractor before Hopf bifurcation is related to this kind of novel transition mentioned above

Stochastic simulation of grain growth during continuous casting

International Nuclear Information System (INIS)

Ramirez, A.; Carrillo, F.; Gonzalez, J.L.; Lopez, S.

2006-01-01

The evolution of microstructure is a very important topic in material science engineering because the solidification conditions of steel billets during continuous casting process affect directly the properties of the final products. In this paper a mathematical model is described in order to simulate the dendritic growth using data of real casting operations; here a combination of deterministic and stochastic methods was used as a function of the solidification time of every node in order to create a reconstruction about the morphology of cast structures

Stochastic simulation of grain growth during continuous casting

Energy Technology Data Exchange (ETDEWEB)

Ramirez, A. [Department of Aerounatical Engineering, S.E.P.I., E.S.I.M.E., IPN, Instituto Politecnico Nacional (Unidad Profesional Ticoman), Av. Ticoman 600, Col. Ticoman, C.P.07340 (Mexico)]. E-mail: adalop123@mailbanamex.com; Carrillo, F. [Department of Processing Materials, CICATA-IPN Unidad Altamira Tamps (Mexico); Gonzalez, J.L. [Department of Metallurgy and Materials Engineering, E.S.I.Q.I.E.-IPN (Mexico); Lopez, S. [Department of Molecular Engineering of I.M.P., AP 14-805 (Mexico)

2006-04-15

The evolution of microstructure is a very important topic in material science engineering because the solidification conditions of steel billets during continuous casting process affect directly the properties of the final products. In this paper a mathematical model is described in order to simulate the dendritic growth using data of real casting operations; here a combination of deterministic and stochastic methods was used as a function of the solidification time of every node in order to create a reconstruction about the morphology of cast structures.

Non-Markovian stochastic Schroedinger equations: Generalization to real-valued noise using quantum-measurement theory

International Nuclear Information System (INIS)

Gambetta, Jay; Wiseman, H.M.

2002-01-01

Do stochastic Schroedinger equations, also known as unravelings, have a physical interpretation? In the Markovian limit, where the system on average obeys a master equation, the answer is yes. Markovian stochastic Schroedinger equations generate quantum trajectories for the system state conditioned on continuously monitoring the bath. For a given master equation, there are many different unravelings, corresponding to different sorts of measurement on the bath. In this paper we address the non-Markovian case, and in particular the sort of stochastic Schroedinger equation introduced by Strunz, Diosi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum-measurement theory approach, we rederive their unraveling that involves complex-valued Gaussian noise. We also derive an unraveling involving real-valued Gaussian noise. We show that in the Markovian limit, these two unravelings correspond to heterodyne and homodyne detection, respectively. Although we use quantum-measurement theory to define these unravelings, we conclude that the stochastic evolution of the system state is not a true quantum trajectory, as the identity of the state through time is a fiction

Research on neutron noise analysis stochastic simulation method for α calculation

International Nuclear Information System (INIS)

Zhong Bin; Shen Huayun; She Ruogu; Zhu Shengdong; Xiao Gang

2014-01-01

The prompt decay constant α has significant application on the physical design and safety analysis in nuclear facilities. To overcome the difficulty of a value calculation with Monte-Carlo method, and improve the precision, a new method based on the neutron noise analysis technology was presented. This method employs the stochastic simulation and the theory of neutron noise analysis technology. Firstly, the evolution of stochastic neutron was simulated by discrete-events Monte-Carlo method based on the theory of generalized Semi-Markov process, then the neutron noise in detectors was solved from neutron signal. Secondly, the neutron noise analysis methods such as Rossia method, Feynman-α method, zero-probability method, and cross-correlation method were used to calculate a value. All of the parameters used in neutron noise analysis method were calculated based on auto-adaptive arithmetic. The a value from these methods accords with each other, the largest relative deviation is 7.9%, which proves the feasibility of a calculation method based on neutron noise analysis stochastic simulation. (authors)

Scale invariant Volkov–Akulov supergravity

Energy Technology Data Exchange (ETDEWEB)

Ferrara, S., E-mail: sergio.ferrara@cern.ch [Th-Ph Department, CERN, CH-1211 Geneva 23 (Switzerland); INFN – Laboratori Nazionali di Frascati, Via Enrico Fermi 40, 00044 Frascati (Italy); Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1547 (United States); Porrati, M., E-mail: mp9@nyu.edu [Th-Ph Department, CERN, CH-1211 Geneva 23 (Switzerland); CCPP, Department of Physics, NYU, 4 Washington Pl., New York, NY 10003 (United States); Sagnotti, A., E-mail: sagnotti@sns.it [Th-Ph Department, CERN, CH-1211 Geneva 23 (Switzerland); Scuola Normale Superiore and INFN, Piazza dei Cavalieri 7, 56126 Pisa (Italy)

2015-10-07

A scale invariant goldstino theory coupled to supergravity is obtained as a standard supergravity dual of a rigidly scale-invariant higher-curvature supergravity with a nilpotent chiral scalar curvature. The bosonic part of this theory describes a massless scalaron and a massive axion in a de Sitter Universe.

On the invariance principle

Energy Technology Data Exchange (ETDEWEB)

Moller-Nielsen, Thomas [University of Oxford (United Kingdom)

2014-07-01

Physicists and philosophers have long claimed that the symmetries of our physical theories - roughly speaking, those transformations which map solutions of the theory into solutions - can provide us with genuine insight into what the world is really like. According to this 'Invariance Principle', only those quantities which are invariant under a theory's symmetries should be taken to be physically real, while those quantities which vary under its symmetries should not. Physicists and philosophers, however, are generally divided (or, indeed, silent) when it comes to explaining how such a principle is to be justified. In this paper, I spell out some of the problems inherent in other theorists' attempts to justify this principle, and sketch my own proposed general schema for explaining how - and when - the Invariance Principle can indeed be used as a legitimate tool of metaphysical inference.

Numerical resolution of N-dimensional Fokker-Plank stochastic equations

International Nuclear Information System (INIS)

Garcia-Olivares, A.; Muoz, A.

1992-01-01

This document describes the use of a library of programs able to solve stochastic Fokker-Planck equations in a N-dimensional space. the input data are essentially: (i) the initial distribution of the stochastic variable, (ii) the drift and fluctuation coefficients as a function of the state (which can be obtained from the transition probabilities between neighboring states) and (iii) some parameters controlling the run. A last version of the library accepts sources and sinks defined in the states space. The output is the temporal evolution of the probability distribution in the space defined by a N-dimensional grid. Some applications and readings in Synergetics, Self-Organization, transport phenomena, Ecology and other fields are suggested. If the probability distribution is interpreted as a distribution of particles then the codes can be used to solve the N-dimensional problem of advection-diffusion. (author) 21 fig. 16 ref

Numerical Resolution of N-dimensional Fokker-Planck stochastic equations

International Nuclear Information System (INIS)

Garcia-Olivares, R. A.; Munoz Roldan, A.

1992-01-01

This document describes the use of a library of programs able to solve stochastic Fokker-Planck equations in a N-dimensional space. The input data are essentially: (i) the initial distribution of the stochastic variable, (ii) the drift and fluctuation coefficients as a function of the state (which can be obtained from the transition probabilities between neighboring states) and (iii) some parameters controlling the run. A last version of the library accepts sources and sinks defined in the states space. The output is the temporal evolution of the probability distribution in the space defined by a N-dimensional grid. Some applications and readings in Synergetic, Self-Organization, transport phenomena, Ecology and other fields are suggested. If the probability distribution is interpreted as a distribution of particles then the codes can be used to solve the N-dimensional problem of advection-diffusion. (Author) 16 refs

A functional LMO invariant for Lagrangian cobordisms

DEFF Research Database (Denmark)

Cheptea, Dorin; Habiro, Kazuo; Massuyeau, Gwénaël

2008-01-01

Lagrangian cobordisms are three-dimensional compact oriented cobordisms between once-punctured surfaces, subject to some homological conditions. We extend the Le–Murakami–Ohtsuki invariant of homology three-spheres to a functor from the category of Lagrangian cobordisms to a certain category...... of Jacobi diagrams. We prove some properties of this functorial LMO invariant, including its universality among rational finite-type invariants of Lagrangian cobordisms. Finally, we apply the LMO functor to the study of homology cylinders from the point of view of their finite-type invariants....

Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility

NARCIS (Netherlands)

van Haastrecht, A.; Lord, R.; Pelsser, A.; Schrager, D.

2009-01-01

We consider the pricing of long-dated insurance contracts under stochastic interest rates and stochastic volatility. In particular, we focus on the valuation of insurance options with long-term equity or foreign exchange exposures. Our modeling framework extends the stochastic volatility model of

Continuous Integrated Invariant Inference, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — The proposed project will develop a new technique for invariant inference and embed this and other current invariant inference and checking techniques in an...

Test of charge conjugation invariance

International Nuclear Information System (INIS)

Nefkens, B.M.K.; Prakhov, S.; Gaardestig, A.; Clajus, M.; Marusic, A.; McDonald, S.; Phaisangittisakul, N.; Price, J.W.; Starostin, A.; Tippens, W.B.; Allgower, C.E.; Spinka, H.; Bekrenev, V.; Koulbardis, A.; Kozlenko, N.; Kruglov, S.; Lopatin, I.; Briscoe, W.J.; Shafi, A.; Comfort, J.R.

2005-01-01

We report on the first determination of upper limits on the branching ratio (BR) of η decay to π 0 π 0 γ and to π 0 π 0 π 0 γ. Both decay modes are strictly forbidden by charge conjugation (C) invariance. Using the Crystal Ball multiphoton detector, we obtained BR(η→π 0 π 0 γ) -4 at the 90% confidence level, in support of C invariance of isoscalar electromagnetic interactions of the light quarks. We have also measured BR(η→π 0 π 0 π 0 γ) -5 at the 90% confidence level, in support of C invariance of isovector electromagnetic interactions

Scale invariant Volkov–Akulov supergravity

Directory of Open Access Journals (Sweden)

S. Ferrara

2015-10-01

Full Text Available A scale invariant goldstino theory coupled to supergravity is obtained as a standard supergravity dual of a rigidly scale-invariant higher-curvature supergravity with a nilpotent chiral scalar curvature. The bosonic part of this theory describes a massless scalaron and a massive axion in a de Sitter Universe.

The interpolation method of stochastic functions and the stochastic variational principle

International Nuclear Information System (INIS)

Liu Xianbin; Chen Qiu

1993-01-01

Uncertainties have been attaching more importance to increasingly in modern engineering structural design. Viewed on an appropriate scale, the inherent physical attributes (material properties) of many structural systems always exhibit some patterns of random variation in space and time, generally the random variation shows a small parameter fluctuation. For a linear mechanical system, the random variation is modeled as a random one of a linear partial differential operator and, in stochastic finite element method, a random variation of a stiffness matrix. Besides the stochasticity of the structural physical properties, the influences of random loads which always represent themselves as the random boundary conditions bring about much more complexities in structural analysis. Now the stochastic finite element method or the probabilistic finite element method is used to study the structural systems with random physical parameters, whether or not the loads are random. Differing from the general finite element theory, the main difficulty which the stochastic finite element method faces is the inverse operation of stochastic operators and stochastic matrices, since the inverse operators and the inverse matrices are statistically correlated to the random parameters and random loads. So far, many efforts have been made to obtain the reasonably approximate expressions of the inverse operators and inverse matrices, such as Perturbation Method, Neumann Expansion Method, Galerkin Method (in appropriate Hilbert Spaces defined for random functions), Orthogonal Expansion Method. Among these methods, Perturbation Method appear to be the most available. The advantage of these methods is that the fairly accurate response statistics can be obtained under the condition of the finite information of the input. However, the second-order statistics obtained by use of Perturbation Method and Neumann Expansion Method are not always the appropriate ones, because the relevant second

Stochastic thermodynamics

Science.gov (United States)

Eichhorn, Ralf; Aurell, Erik

2014-04-01

'Stochastic thermodynamics as a conceptual framework combines the stochastic energetics approach introduced a decade ago by Sekimoto [1] with the idea that entropy can consistently be assigned to a single fluctuating trajectory [2]'. This quote, taken from Udo Seifert's [3] 2008 review, nicely summarizes the basic ideas behind stochastic thermodynamics: for small systems, driven by external forces and in contact with a heat bath at a well-defined temperature, stochastic energetics [4] defines the exchanged work and heat along a single fluctuating trajectory and connects them to changes in the internal (system) energy by an energy balance analogous to the first law of thermodynamics. Additionally, providing a consistent definition of trajectory-wise entropy production gives rise to second-law-like relations and forms the basis for a 'stochastic thermodynamics' along individual fluctuating trajectories. In order to construct meaningful concepts of work, heat and entropy production for single trajectories, their definitions are based on the stochastic equations of motion modeling the physical system of interest. Because of this, they are valid even for systems that are prevented from equilibrating with the thermal environment by external driving forces (or other sources of non-equilibrium). In that way, the central notions of equilibrium thermodynamics, such as heat, work and entropy, are consistently extended to the non-equilibrium realm. In the (non-equilibrium) ensemble, the trajectory-wise quantities acquire distributions. General statements derived within stochastic thermodynamics typically refer to properties of these distributions, and are valid in the non-equilibrium regime even beyond the linear response. The extension of statistical mechanics and of exact thermodynamic statements to the non-equilibrium realm has been discussed from the early days of statistical mechanics more than 100 years ago. This debate culminated in the development of linear response

A stochastic model of multiple scattering of charged particles: process, transport equation and solutions

International Nuclear Information System (INIS)

Papiez, L.; Moskvin, V.; Tulovsky, V.

2001-01-01

The process of angular-spatial evolution of multiple scattering of charged particles can be described by a special case of Boltzmann integro-differential equation called Lewis equation. The underlying stochastic process for this evolution is the compound Poisson process on the surface of the unit sphere. The significant portion of events that constitute compound Poisson process that describes multiple scattering have diffusional character. This property allows to analyze the process of angular-spatial evolution of multiple scattering of charged particles as combination of soft and hard collision processes and compute appropriately its transition densities. These computations provide a method of the approximate solution to the Lewis equation. (orig.)

Portfolio Optimization with Stochastic Dividends and Stochastic Volatility

Science.gov (United States)

Varga, Katherine Yvonne

2015-01-01

We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…

Stability in distribution of a stochastic hybrid competitive Lotka–Volterra model with Lévy jumps

International Nuclear Information System (INIS)

Zhao, Yu; Yuan, Sanling

2016-01-01

Stability in distribution, implying the existence of the invariant probability measure, is an important measure of stochastic hybrid system. However, the effect of Lévy jumps on the stability in distribution is still unclear. In this paper, we consider a n-species competitive Lotka–Volterra model with Lévy jumps under regime-switching. First, we prove the existence of the global positive solution, obtain the upper and lower boundedness. Then, asymptotic stability in distribution as the main result of our paper is derived under some sufficient conditions. Finally, numerical simulations are carried out to support our theoretical results and a brief discussion is given.

Stochastic optimal control as non-equilibrium statistical mechanics: calculus of variations over density and current

Science.gov (United States)

Chernyak, Vladimir Y.; Chertkov, Michael; Bierkens, Joris; Kappen, Hilbert J.

2014-01-01

In stochastic optimal control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive), for a system participating in forced and controlled Langevin dynamics. We extend the SOC problem by introducing an additional cost-of-dynamics, characterized by a vector potential. We propose derivation of the generalized gauge-invariant Hamilton-Jacobi-Bellman equation as a variation over density and current, suggest hydrodynamic interpretation and discuss examples, e.g., ergodic control of a particle-within-a-circle, illustrating non-equilibrium space-time complexity.

Long wavelength limit of evolution of nonlinear cosmological perturbations

International Nuclear Information System (INIS)

Hamazaki, Takashi

2008-01-01

In the general matter composition where the multiple scalar fields and the multiple perfect fluids coexist, in the leading order of the gradient expansion, we construct all of the solutions of the nonlinear evolutions of the locally homogeneous universe. From the momentum constraint, we derive the constraints which the solution constants of the locally homogeneous universe must satisfy. We construct the gauge invariant perturbation variables in the arbitrarily higher order nonlinear cosmological perturbation theory around the spatially flat Friedmann-Robertson-Walker universe. We construct the nonlinear long wavelength limit formula representing the long wavelength limit of the evolution of the nonlinear gauge invariant perturbation variables in terms of perturbations of the evolutions of the locally homogeneous universe. By using the long wavelength limit formula, we investigate the evolution of nonlinear cosmological perturbations in the universe dominated by the multiple slow rolling scalar fields with an arbitrary potential. The τ function and the N potential introduced in this paper make it possible to write the evolution of the multiple slow rolling scalar fields with an arbitrary interaction potential and the arbitrarily higher order nonlinear Bardeen parameter at the end of the slow rolling phase analytically. It is shown that the nonlinear parameters such as f NL and g NL are suppressed by the slow rolling expansion parameters.

Sequence Learning with Stochastic Feedback in a Cross-Cultural Sample of Boys in the Autistic Spectrum

Science.gov (United States)

Hentschel, Maren; Lange-Kuttner, Christiane; Averbeck, Bruno B.

2016-01-01

The study investigated sequence learning from stochastic feedback in boys with Autistic Spectrum Disorder (ASD) and typically developed (TD) boys. We asked boys with ASD from Nigeria and the UK as well as age- and gender-matched controls (also males only) to deduce a sequence of four left and right button presses, LLRR, RRLL, LRLR, RLRL, LRRL and…

Recent progress in invariant pattern recognition

Science.gov (United States)

Arsenault, Henri H.; Chang, S.; Gagne, Philippe; Gualdron Gonzalez, Oscar

1996-12-01

We present some recent results in invariant pattern recognition, including methods that are invariant under two or more distortions of position, orientation and scale. There are now a few methods that yield good results under changes of both rotation and scale. Some new methods are introduced. These include locally adaptive nonlinear matched filters, scale-adapted wavelet transforms and invariant filters for disjoint noise. Methods using neural networks will also be discussed, including an optical method that allows simultaneous classification of multiple targets.

Finite type invariants and fatgraphs

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Bene, Alex; Meilhan, Jean-Baptiste Odet Thierry

2010-01-01

–Murakami–Ohtsuki of the link invariant of Andersen–Mattes–Reshetikhin computed relative to choices determined by the fatgraph G; this provides a basic connection between 2d geometry and 3d quantum topology. For each fixed G, this invariant is shown to be universal for homology cylinders, i.e., G establishes an isomorphism...

Ermakov–Lewis invariants and Reid systems

Energy Technology Data Exchange (ETDEWEB)

Mancas, Stefan C., E-mail: stefan.mancas@erau.edu [Department of Mathematics, Embry-Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Camino a la presa San José 2055, Col. Lomas 4a Sección, 78216 San Luis Potosí, S.L.P. (Mexico)

2014-06-13

Reid's mth-order generalized Ermakov systems of nonlinear coupling constant α are equivalent to an integrable Emden–Fowler equation. The standard Ermakov–Lewis invariant is discussed from this perspective, and a closed formula for the invariant is obtained for the higher-order Reid systems (m≥3). We also discuss the parametric solutions of these systems of equations through the integration of the Emden–Fowler equation and present an example of a dynamical system for which the invariant is equivalent to the total energy. - Highlights: • Reid systems of order m are connected to Emden–Fowler equations. • General expressions for the Ermakov–Lewis invariants both for m=2 and m≥3 are obtained. • Parametric solutions of the Emden–Fowler equations related to Reid systems are obtained.

Critical spaces for quasilinear parabolic evolution equations and applications

Science.gov (United States)

Prüss, Jan; Simonett, Gieri; Wilke, Mathias

2018-02-01

We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal Lp-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given.

Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods

KAUST Repository

Loizou, Nicolas

2017-12-27

In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.

Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods

KAUST Repository

Loizou, Nicolas; Richtarik, Peter

2017-01-01

In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.

On the Radio-emitting Particles of the Crab Nebula: Stochastic Acceleration Model

Energy Technology Data Exchange (ETDEWEB)

Tanaka, Shuta J. [Department of Physics, Faculty of Science and Engineering, Konan University, 8-9-1 Okamoto, Kobe, Hyogo 658-8501 (Japan); Asano, Katsuaki, E-mail: sjtanaka@center.konan-u.ac.jp [Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa City, Chiba, 277-8582 (Japan)

2017-06-01

The broadband emission of pulsar wind nebulae (PWNe) is well described by non-thermal emissions from accelerated electrons and positrons. However, the standard shock acceleration model of PWNe does not account for the hard spectrum in radio wavelengths. The origin of the radio-emitting particles is also important to determine the pair production efficiency in the pulsar magnetosphere. Here, we propose a possible resolution for the particle energy distribution in PWNe; the radio-emitting particles are not accelerated at the pulsar wind termination shock but are stochastically accelerated by turbulence inside PWNe. We upgrade our past one-zone spectral evolution model to include the energy diffusion, i.e., the stochastic acceleration, and apply the model to the Crab Nebula. A fairly simple form of the energy diffusion coefficient is assumed for this demonstrative study. For a particle injection to the stochastic acceleration process, we consider the continuous injection from the supernova ejecta or the impulsive injection associated with supernova explosion. The observed broadband spectrum and the decay of the radio flux are reproduced by tuning the amount of the particle injected to the stochastic acceleration process. The acceleration timescale and the duration of the acceleration are required to be a few decades and a few hundred years, respectively. Our results imply that some unveiled mechanisms, such as back reaction to the turbulence, are required to make the energies of stochastically and shock-accelerated particles comparable.

Calculating Higher-Order Moments of Phylogenetic Stochastic Mapping Summaries in Linear Time

Science.gov (United States)

Dhar, Amrit

2017-01-01

Abstract Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the evolutionary process on the phylogeny and, unlike parsimony-based mapping, conditions on the observed data to randomly draw substitution mappings that do not necessarily require the minimum number of events on a tree. Most stochastic mapping applications simulate substitution mappings only to estimate the mean and/or variance of two commonly used mapping summaries: the number of particular types of substitutions (labeled substitution counts) and the time spent in a particular group of states (labeled dwelling times) on the tree. Fast, simulation-free algorithms for calculating the mean of stochastic mapping summaries exist. Importantly, these algorithms scale linearly in the number of tips/leaves of the phylogenetic tree. However, to our knowledge, no such algorithm exists for calculating higher-order moments of stochastic mapping summaries. We present one such simulation-free dynamic programming algorithm that calculates prior and posterior mapping variances and scales linearly in the number of phylogeny tips. Our procedure suggests a general framework that can be used to efficiently compute higher-order moments of stochastic mapping summaries without simulations. We demonstrate the usefulness of our algorithm by extending previously developed statistical tests for rate variation across sites and for detecting evolutionarily conserved regions in genomic sequences. PMID:28177780

Stochastic neuron models

CERN Document Server

Greenwood, Priscilla E

2016-01-01

This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain...

Conformal invariance in the long-range Ising model

Directory of Open Access Journals (Sweden)

Miguel F. Paulos

2016-01-01

Full Text Available We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.

Conformal Invariance in the Long-Range Ising Model

CERN Document Server

Paulos, Miguel F; van Rees, Balt C; Zan, Bernardo

2016-01-01

We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.

Conformal invariance in the long-range Ising model

Energy Technology Data Exchange (ETDEWEB)

Paulos, Miguel F. [CERN, Theory Group, Geneva (Switzerland); Rychkov, Slava, E-mail: slava.rychkov@lpt.ens.fr [CERN, Theory Group, Geneva (Switzerland); Laboratoire de Physique Théorique de l' École Normale Supérieure (LPTENS), Paris (France); Faculté de Physique, Université Pierre et Marie Curie (UPMC), Paris (France); Rees, Balt C. van [CERN, Theory Group, Geneva (Switzerland); Zan, Bernardo [Institute of Physics, Universiteit van Amsterdam, Amsterdam (Netherlands)

2016-01-15

We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.

Stochastic disk dynamo as a model of reversals of the Earth's magnetic field

International Nuclear Information System (INIS)

Ito, H.M.

1988-01-01

A stochastic model is given of a system composed of N similar disk dynamos interacting with one another. The time evolution of the system is governed by a master equation of the class introduced by van Kampen as relevant to stochastic macrosystems. In the model, reversals of the Earth's magnetic field are regarded as large deviations caused by a small random force of O(N/sup -1/2/) from one of the field polarities to the other. Reversal processes are studied by simulation, which shows that the model explains well the activities of the paleomagnetic field inclusive of statistical laws of the reversal sequence and the intensity distribution. Comparison are made between the model and dynamical disk dynamo models

BRDF invariant stereo using light transport constancy.

Science.gov (United States)

Wang, Liang; Yang, Ruigang; Davis, James E

2007-09-01

Nearly all existing methods for stereo reconstruction assume that scene reflectance is Lambertian and make use of brightness constancy as a matching invariant. We introduce a new invariant for stereo reconstruction called light transport constancy (LTC), which allows completely arbitrary scene reflectance (bidirectional reflectance distribution functions (BRDFs)). This invariant can be used to formulate a rank constraint on multiview stereo matching when the scene is observed by several lighting configurations in which only the lighting intensity varies. In addition, we show that this multiview constraint can be used with as few as two cameras and two lighting configurations. Unlike previous methods for BRDF invariant stereo, LTC does not require precisely configured or calibrated light sources or calibration objects in the scene. Importantly, the new constraint can be used to provide BRDF invariance to any existing stereo method whenever appropriate lighting variation is available.

A scale invariance criterion for LES parametrizations

Directory of Open Access Journals (Sweden)

Urs Schaefer-Rolffs

2015-01-01

Full Text Available Turbulent kinetic energy cascades in fluid dynamical systems are usually characterized by scale invariance. However, representations of subgrid scales in large eddy simulations do not necessarily fulfill this constraint. So far, scale invariance has been considered in the context of isotropic, incompressible, and three-dimensional turbulence. In the present paper, the theory is extended to compressible flows that obey the hydrostatic approximation, as well as to corresponding subgrid-scale parametrizations. A criterion is presented to check if the symmetries of the governing equations are correctly translated into the equations used in numerical models. By applying scaling transformations to the model equations, relations between the scaling factors are obtained by demanding that the mathematical structure of the equations does not change.The criterion is validated by recovering the breakdown of scale invariance in the classical Smagorinsky model and confirming scale invariance for the Dynamic Smagorinsky Model. The criterion also shows that the compressible continuity equation is intrinsically scale-invariant. The criterion also proves that a scale-invariant turbulent kinetic energy equation or a scale-invariant equation of motion for a passive tracer is obtained only with a dynamic mixing length. For large-scale atmospheric flows governed by the hydrostatic balance the energy cascade is due to horizontal advection and the vertical length scale exhibits a scaling behaviour that is different from that derived for horizontal length scales.

Numerical simulations of piecewise deterministic Markov processes with an application to the stochastic Hodgkin-Huxley model

Science.gov (United States)

Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan

2016-12-01

The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.

Stochastic tools in turbulence

CERN Document Server

Lumey, John L

2012-01-01

Stochastic Tools in Turbulence discusses the available mathematical tools to describe stochastic vector fields to solve problems related to these fields. The book deals with the needs of turbulence in relation to stochastic vector fields, particularly, on three-dimensional aspects, linear problems, and stochastic model building. The text describes probability distributions and densities, including Lebesgue integration, conditional probabilities, conditional expectations, statistical independence, lack of correlation. The book also explains the significance of the moments, the properties of the

Construction of time-dependent dynamical invariants: A new approach

International Nuclear Information System (INIS)

Bertin, M. C.; Pimentel, B. M.; Ramirez, J. A.

2012-01-01

We propose a new way to obtain polynomial dynamical invariants of the classical and quantum time-dependent harmonic oscillator from the equations of motion. We also establish relations between linear and quadratic invariants, and discuss how the quadratic invariant can be related to the Ermakov invariant.

Wavelet-based moment invariants for pattern recognition

Science.gov (United States)

Chen, Guangyi; Xie, Wenfang

2011-07-01

Moment invariants have received a lot of attention as features for identification and inspection of two-dimensional shapes. In this paper, two sets of novel moments are proposed by using the auto-correlation of wavelet functions and the dual-tree complex wavelet functions. It is well known that the wavelet transform lacks the property of shift invariance. A little shift in the input signal will cause very different output wavelet coefficients. The autocorrelation of wavelet functions and the dual-tree complex wavelet functions, on the other hand, are shift-invariant, which is very important in pattern recognition. Rotation invariance is the major concern in this paper, while translation invariance and scale invariance can be achieved by standard normalization techniques. The Gaussian white noise is added to the noise-free images and the noise levels vary with different signal-to-noise ratios. Experimental results conducted in this paper show that the proposed wavelet-based moments outperform Zernike's moments and the Fourier-wavelet descriptor for pattern recognition under different rotation angles and different noise levels. It can be seen that the proposed wavelet-based moments can do an excellent job even when the noise levels are very high.

Evolution of ocean wave statistics in shallow water : Refraction and diffraction over seafloor topography

NARCIS (Netherlands)

Janssen, T.T.; Herbers, T.H.C.; Battjes, J.A.

2008-01-01

We present a stochastic model for the evolution of random ocean surface waves in coastal waters with complex seafloor topography. First, we derive a deterministic coupled-mode model based on a forward scattering approximation of the nonlinear mild slope equation; this model describes the evolution

Stochastic processes in cell biology

CERN Document Server

Bressloff, Paul C

2014-01-01

This book develops the theory of continuous and discrete stochastic processes within the context of cell biology.  A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods.   This text is primarily...

Experimental study of the semi-active control of a nonlinear two-span bridge using stochastic optimal polynomial control

Science.gov (United States)

El-Khoury, O.; Kim, C.; Shafieezadeh, A.; Hur, J. E.; Heo, G. H.

2015-06-01

This study performs a series of numerical simulations and shake-table experiments to design and assess the performance of a nonlinear clipped feedback control algorithm based on optimal polynomial control (OPC) to mitigate the response of a two-span bridge equipped with a magnetorheological (MR) damper. As an extended conventional linear quadratic regulator, OPC provides more flexibility in the control design and further enhances system performance. The challenges encountered in this case are (1) the linearization of the nonlinear behavior of various components and (2) the selection of the weighting matrices in the objective function of OPC. The first challenge is addressed by using stochastic linearization which replaces the nonlinear portion of the system behavior with an equivalent linear time-invariant model considering the stochasticity in the excitation. Furthermore, a genetic algorithm is employed to find optimal weighting matrices for the control design. The input current to the MR damper installed between adjacent spans is determined using a clipped stochastic optimal polynomial control algorithm. The performance of the controlled system is assessed through a set of shake-table experiments for far-field and near-field ground motions. The proposed method showed considerable improvements over passive cases especially for the far-field ground motion.

Experimental study of the semi-active control of a nonlinear two-span bridge using stochastic optimal polynomial control

International Nuclear Information System (INIS)

El-Khoury, O; Shafieezadeh, A; Hur, J E; Kim, C; Heo, G H

2015-01-01

This study performs a series of numerical simulations and shake-table experiments to design and assess the performance of a nonlinear clipped feedback control algorithm based on optimal polynomial control (OPC) to mitigate the response of a two-span bridge equipped with a magnetorheological (MR) damper. As an extended conventional linear quadratic regulator, OPC provides more flexibility in the control design and further enhances system performance. The challenges encountered in this case are (1) the linearization of the nonlinear behavior of various components and (2) the selection of the weighting matrices in the objective function of OPC. The first challenge is addressed by using stochastic linearization which replaces the nonlinear portion of the system behavior with an equivalent linear time-invariant model considering the stochasticity in the excitation. Furthermore, a genetic algorithm is employed to find optimal weighting matrices for the control design. The input current to the MR damper installed between adjacent spans is determined using a clipped stochastic optimal polynomial control algorithm. The performance of the controlled system is assessed through a set of shake-table experiments for far-field and near-field ground motions. The proposed method showed considerable improvements over passive cases especially for the far-field ground motion. (paper)

Novel topological invariants and anomalies

International Nuclear Information System (INIS)

Hirayama, M.; Sugimasa, N.

1987-01-01

It is shown that novel topological invariants are associated with a class of Dirac operators. Trace formulas which are similar to but different from Callias's formula are derived. Implications of these topological invariants to anomalies in quantum field theory are discussed. A new class of anomalies are calculated for two models: one is two dimensional and the other four dimensional

Wilson loop invariants from WN conformal blocks

Directory of Open Access Journals (Sweden)

Oleg Alekseev

2015-12-01

Full Text Available Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern–Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate crossing and braiding matrices for WN conformal blocks with one component in the fundamental representation and another component in a rectangular representation of SU(N, which can be used to obtain HOMFLY knot and link invariants for these cases. We also discuss how our approach can be generalized to invariants in higher-representations of WN algebra.

Invariants of triangular Lie algebras

International Nuclear Information System (INIS)

Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman

2007-01-01

Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated

From stochastic phase space evolution to Brownian motion in collective space

International Nuclear Information System (INIS)

Benhassine, B.; Farine, M.; Hernandez, E.S.; Idier, D.; Remaud, B.; Sebille, F.

1993-01-01

Within the framework of stochastic transport equations in phase space, the dynamics of fluctuations on collective variables in homogeneous fermion systems is studied. The transport coefficients are formally deduced in the relaxation time approximation and a general method to compute dynamically the dispersions of collective observables is proposed as a set of coupled equations. Independently, the general covariance matrix of phase space fluctuations and the dispersion on collective variables at equilibrium are derived. Detailed numerical applications show that dynamics of fluctuations can be extracted from noisy numerical simulations and that the leading parameter for collective fluctuations is the excitation energy whatever is its degree of thermalization. (authors). 16 refs., 12 figs

Stochastic pump effect and geometric phases in dissipative and stochastic systems

Energy Technology Data Exchange (ETDEWEB)

Sinitsyn, Nikolai [Los Alamos National Laboratory

2008-01-01

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).

Stochastic evolutionary voluntary public goods game with punishment in a Quasi-birth-and-death process.

Science.gov (United States)

Quan, Ji; Liu, Wei; Chu, Yuqing; Wang, Xianjia

2017-11-23

Traditional replication dynamic model and the corresponding concept of evolutionary stable strategy (ESS) only takes into account whether the system can return to the equilibrium after being subjected to a small disturbance. In the real world, due to continuous noise, the ESS of the system may not be stochastically stable. In this paper, a model of voluntary public goods game with punishment is studied in a stochastic situation. Unlike the existing model, we describe the evolutionary process of strategies in the population as a generalized quasi-birth-and-death process. And we investigate the stochastic stable equilibrium (SSE) instead. By numerical experiments, we get all possible SSEs of the system for any combination of parameters, and investigate the influence of parameters on the probabilities of the system to select different equilibriums. It is found that in the stochastic situation, the introduction of the punishment and non-participation strategies can change the evolutionary dynamics of the system and equilibrium of the game. There is a large range of parameters that the system selects the cooperative states as its SSE with a high probability. This result provides us an insight and control method for the evolution of cooperation in the public goods game in stochastic situations.

Massless scalar field in de Sitter spacetime: unitary quantum time evolution

International Nuclear Information System (INIS)

Cortez, Jerónimo; Blas, Daniel Martín-de; Marugán, Guillermo A Mena; Velhinho, José M

2013-01-01

We prove that, under the standard conformal scaling, a free scalar field in de Sitter spacetime admits an O(4)-invariant Fock quantization such that time evolution is unitarily implemented. Since this applies in particular to the massless case, this result disproves previous claims in the literature. We discuss the relationship between this quantization with unitary dynamics and the family of O(4)-invariant Hadamard states given by Allen and Folacci, as well as with the Bunch–Davies vacuum. (paper)

Action priors for learning domain invariances

CSIR Research Space (South Africa)

Rosman, Benjamin S

2015-04-01

Full Text Available behavioural invariances in the domain, by identifying actions to be prioritised in local contexts, invariant to task details. This information has the effect of greatly increasing the speed of solving new problems. We formalise this notion as action priors...

Using stochastic cell division and death to probe minimal units of cellular replication

Science.gov (United States)

Chib, Savita; Das, Suman; Venkatesan, Soumya; Sai Narain Seshasayee, Aswin; Thattai, Mukund

2018-03-01

The invariant cell initiation mass measured in bacterial growth experiments has been interpreted as a minimal unit of cellular replication. Here we argue that the existence of such minimal units induces a coupling between the rates of stochastic cell division and death. To probe this coupling we tracked live and dead cells in Escherichia coli populations treated with a ribosome-targeting antibiotic. We find that the growth exponent from macroscopic cell growth or decay measurements can be represented as the difference of microscopic first-order cell division and death rates. The boundary between cell growth and decay, at which the number of live cells remains constant over time, occurs at the minimal inhibitory concentration (MIC) of the antibiotic. This state appears macroscopically static but is microscopically dynamic: division and death rates exactly cancel at MIC but each is remarkably high, reaching 60% of the antibiotic-free division rate. A stochastic model of cells as collections of minimal replicating units we term ‘widgets’ reproduces both steady-state and transient features of our experiments. Sub-cellular fluctuations of widget numbers stochastically drive each new daughter cell to one of two alternate fates, division or death. First-order division or death rates emerge as eigenvalues of a stationary Markov process, and can be expressed in terms of the widget’s molecular properties. High division and death rates at MIC arise due to low mean and high relative fluctuations of widget number. Isolating cells at the threshold of irreversible death might allow molecular characterization of this minimal replication unit.

Maxwell equations in conformal invariant electrodynamics

International Nuclear Information System (INIS)

Fradkin, E.S.; AN SSSR, Novosibirsk. Inst. Avtomatiki i Ehlektrometrii); Kozhevnikov, A.A.; Palchik, M.Ya.; Pomeransky, A.A.

1983-01-01

We consider a conformal invariant formulation of quantum electrodynamics. Conformal invariance is achieved with a specific mathematical construction based on the indecomposable representations of the conformal group associated with the electromagnetic potential and current. As a corolary of this construction modified expressions for the 3-point Green functions are obtained which both contain transverse parts. They make it possible to formulate a conformal invariant skeleton perturbation theory. It is also shown that the Euclidean Maxwell equations in conformal electrodynamics are manifestations of its kinematical structure: in the case of the 3-point Green functions these equations follow (up to constants) from the conformal invariance while in the case of higher Green functions they are equivalent to the equality of the kernels of the partial wave expansions. This is the manifestation of the mathematical fast of a (partial) equivalence of the representations associated with the potential, current and the field tensor. (orig.)

Embedded graph invariants in Chern-Simons theory

International Nuclear Information System (INIS)

Major, Seth A.

1999-01-01

Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines -- an embedded graph invariant. Using a generalization of the variational method, lowest-order results for invariants for graphs of arbitrary valence and general vertex tangent space structure are derived. Gauge invariant operators are introduced. Higher order results are found. The method used here provides a Vassiliev-type definition of graph invariants which depend on both the embedding of the graph and the group structure of the gauge theory. It is found that one need not frame individual vertices. However, without a global projection of the graph there is an ambiguity in the relation of the decomposition of distinct vertices. It is suggested that framing may be seen as arising from this ambiguity -- as a way of relating frames at distinct vertices

Relating measurement invariance, cross-level invariance, and multilevel reliability

NARCIS (Netherlands)

Jak, S.; Jorgensen, T.D.

2017-01-01

Data often have a nested, multilevel structure, for example when data are collected from children in classrooms. This kind of data complicate the evaluation of reliability and measurement invariance, because several properties can be evaluated at both the individual level and the cluster level, as

Stochastic population dynamics under resource constraints

Energy Technology Data Exchange (ETDEWEB)

Gavane, Ajinkya S., E-mail: ajinkyagavane@gmail.com; Nigam, Rahul, E-mail: rahul.nigam@hyderabad.bits-pilani.ac.in [BITS Pilani Hyderabad Campus, Shameerpet, Hyd - 500078 (India)

2016-06-02

This paper investigates the population growth of a certain species in which every generation reproduces thrice over a period of predefined time, under certain constraints of resources needed for survival of population. We study the survival period of a species by randomizing the reproduction probabilities within a window at same predefined ages and the resources are being produced by the working force of the population at a variable rate. This randomness in the reproduction rate makes the population growth stochastic in nature and one cannot predict the exact form of evolution. Hence we study the growth by running simulations for such a population and taking an ensemble averaged over 500 to 5000 such simulations as per the need. While the population reproduces in a stochastic manner, we have implemented a constraint on the amount of resources available for the population. This is important to make the simulations more realistic. The rate of resource production then is tuned to find the rate which suits the survival of the species. We also compute the mean life time of the species corresponding to different resource production rate. Study for these outcomes in the parameter space defined by the reproduction probabilities and rate of resource production is carried out.

Intimate Partner Violence: A Stochastic Model.

Science.gov (United States)

Guidi, Elisa; Meringolo, Patrizia; Guazzini, Andrea; Bagnoli, Franco

2017-01-01

Intimate partner violence (IPV) has been a well-studied problem in the past psychological literature, especially through its classical methodology such as qualitative, quantitative and mixed methods. This article introduces two basic stochastic models as an alternative approach to simulate the short and long-term dynamics of a couple at risk of IPV. In both models, the members of the couple may assume a finite number of states, updating them in a probabilistic way at discrete time steps. After defining the transition probabilities, we first analyze the evolution of the couple in isolation and then we consider the case in which the individuals modify their behavior depending on the perceived violence from other couples in their environment or based on the perceived informal social support. While high perceived violence in other couples may converge toward the own presence of IPV by means a gender-specific transmission, the gender differences fade-out in the case of received informal social support. Despite the simplicity of the two stochastic models, they generate results which compare well with past experimental studies about IPV and they give important practical implications for prevention intervention in this field. Copyright: © 2016 by Fabrizio Serra editore, Pisa · Roma.

Conformal invariance and two-dimensional physics

International Nuclear Information System (INIS)

Zuber, J.B.

1993-01-01

Actually, physicists and mathematicians are very interested in conformal invariance: geometric transformations which keep angles. This symmetry is very important for two-dimensional systems as phase transitions, string theory or node mathematics. In this article, the author presents the conformal invariance and explains its usefulness

Pattern recognition: invariants in 3D

International Nuclear Information System (INIS)

Proriol, J.

1992-01-01

In e + e - events, the jets have a spherical 3D symmetry. A set of invariants are defined for 3D objects with a spherical symmetry. These new invariants are used to tag the number of jets in e + e - events. (K.A.) 3 refs

A test for ordinal measurement invariance

NARCIS (Netherlands)

Ligtvoet, R.; Millsap, R.E.; Bolt, D.M.; van der Ark, L.A.; Wang, W.-C.

2015-01-01

One problem with the analysis of measurement invariance is the reliance of the analysis on having a parametric model that accurately describes the data. In this paper an ordinal version of the property of measurement invariance is proposed, which relies only on nonparametric restrictions. This

A scale invariant covariance structure on jet space

DEFF Research Database (Denmark)

Pedersen, Kim Steenstrup; Loog, Marco; Markussen, Bo

2005-01-01

This paper considers scale invariance of statistical image models. We study statistical scale invariance of the covariance structure of jet space under scale space blurring and derive the necessary structure and conditions of the jet covariance matrix in order for it to be scale invariant. As par...

Stochastic mean-field dynamics for fermions in the weak coupling limit

International Nuclear Information System (INIS)

Lacroix, D.

2005-09-01

Assuming that the effect of the residual interaction beyond mean-field is weak and can be treated as a statistical ensemble of two-body interactions, a Markovian quantum jump theory is developed for fermionic systems. In this theory, jumps occur between many-body densities formed of pairs of states D |Φ a > b | / b | |Φ a > where |Φ a > and |Φ b > are anti-symmetrized products of single-particle states. The underlying Stochastic Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a spherical 40 Ca nucleus under the influence of a statistical ensemble of two-body contact interactions. In this example, the mean-field evolution of one-body observables is recovered by averaging over different stochastic trajectories while fluctuations beyond mean-field are observed. Finally, the nature of the fluctuations is discussed. (author)

Inflation in a Scale Invariant Universe

Energy Technology Data Exchange (ETDEWEB)

Ferreira, Pedro G. [Oxford U.; Hill, Christopher T. [Fermilab; Noller, Johannes [Zurich U.; Ross, Graham G. [Oxford U., Theor. Phys.

2018-02-16

A scale-invariant universe can have a period of accelerated expansion at early times: inflation. We use a frame-invariant approach to calculate inflationary observables in a scale invariant theory of gravity involving two scalar fields - the spectral indices, the tensor to scalar ratio, the level of isocurvature modes and non-Gaussianity. We show that scale symmetry leads to an exact cancellation of isocurvature modes and that, in the scale-symmetry broken phase, this theory is well described by a single scalar field theory. We find the predictions of this theory strongly compatible with current observations.

Adiabatic invariants of the extended KdV equation

Energy Technology Data Exchange (ETDEWEB)

Karczewska, Anna [Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Rozmej, Piotr, E-mail: p.rozmej@if.uz.zgora.pl [Institute of Physics, Faculty of Physics and Astronomy, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Infeld, Eryk [National Centre for Nuclear Research, Hoża 69, 00-681 Warszawa (Poland); Rowlands, George [Department of Physics, University of Warwick, Coventry, CV4 7A (United Kingdom)

2017-01-30

When the Euler equations for shallow water are taken to the next order, beyond KdV, momentum and energy are no longer exact invariants. (The only one is mass.) However, adiabatic invariants (AI) can be found. When the KdV expansion parameters are zero, exact invariants are recovered. Existence of adiabatic invariants results from general theory of near-identity transformations (NIT) which allow us to transform higher order nonintegrable equations to asymptotically equivalent (when small parameters tend to zero) integrable form. Here we present a direct method of calculations of adiabatic invariants. It does not need a transformation to a moving reference frame nor performing a near-identity transformation. Numerical tests show that deviations of AI from constant values are indeed small. - Highlights: • We suggest a new and simple method for calculating adiabatic invariants of second order wave equations. • It is easy to use and we hope that it will be useful if published. • Interesting numerics included.

Gromov-Witten invariants and localization

Science.gov (United States)

Morrison, David R.

2017-11-01

We give a pedagogical review of the computation of Gromov-Witten invariants via localization in 2D gauged linear sigma models. We explain the relationship between the two-sphere partition function of the theory and the Kähler potential on the conformal manifold. We show how the Kähler potential can be assembled from classical, perturbative, and non-perturbative contributions, and explain how the non-perturbative contributions are related to the Gromov-Witten invariants of the corresponding Calabi-Yau manifold. We then explain how localization enables efficient calculation of the two-sphere partition function and, ultimately, the Gromov-Witten invariants themselves. This is a contribution to the review issue ‘Localization techniques in quantum field theories’ (ed V Pestun and M Zabzine) which contains 17 chapters, available at [1].

Modelling the evolution and diversity of cumulative culture

Science.gov (United States)

Enquist, Magnus; Ghirlanda, Stefano; Eriksson, Kimmo

2011-01-01

Previous work on mathematical models of cultural evolution has mainly focused on the diffusion of simple cultural elements. However, a characteristic feature of human cultural evolution is the seemingly limitless appearance of new and increasingly complex cultural elements. Here, we develop a general modelling framework to study such cumulative processes, in which we assume that the appearance and disappearance of cultural elements are stochastic events that depend on the current state of culture. Five scenarios are explored: evolution of independent cultural elements, stepwise modification of elements, differentiation or combination of elements and systems of cultural elements. As one application of our framework, we study the evolution of cultural diversity (in time as well as between groups). PMID:21199845

Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras

Energy Technology Data Exchange (ETDEWEB)

Dobay, M. P. D., E-mail: maria.pamela.david@physik.uni-muenchen.de; Alberola, A. Piera; Mendoza, E. R.; Raedler, J. O., E-mail: joachim.raedler@physik.uni-muenchen.de [Ludwig-Maximilians University, Faculty of Physics, Center for NanoScience (Germany)

2012-03-15

Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.

Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras

International Nuclear Information System (INIS)

Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.

2012-01-01

Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.

Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras

Science.gov (United States)

Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.

2012-03-01

Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.

Thirty Years Later: Evolution of Treatment for Acute Left Main Coronary Artery Occlusion

Directory of Open Access Journals (Sweden)

Moshe Y. Flugelman

2016-01-01

Full Text Available Acute occlusion of left main coronary artery is a catastrophic event. We describe two patients with acute occlusion of the left main coronary artery treated thirty years apart. The first patient was treated in 1982 and survived the event without revascularization but developed severe heart failure. His survival was so unusual that it merited a case report at that time. The second patient was treated at the end of 2015. Early revascularization resulted in myocardial reperfusion and near normal left ventricular function. These patients exemplify the progress in therapeutic cardiology over the last 30 years.

Sequential stochastic optimization

CERN Document Server

Cairoli, Renzo

1996-01-01

Sequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved. Offering much material that is either new or has never before appeared in book form, it lucidly presents a unified theory of optimal stopping and optimal sequential control of stochastic processes. This book has been carefully organized so that little prior knowledge of the subject is assumed; its only prerequisites are a standard graduate course in probability theory and some familiarity with discrete-paramet

Stochastic modeling of mode interactions via linear parabolized stability equations

Science.gov (United States)

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

2017-11-01

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

Testing Lorentz invariance of dark matter

CERN Document Server

Blas, Diego; Sibiryakov, Sergey

2012-01-01

We study the possibility to constrain deviations from Lorentz invariance in dark matter (DM) with cosmological observations. Breaking of Lorentz invariance generically introduces new light gravitational degrees of freedom, which we represent through a dynamical timelike vector field. If DM does not obey Lorentz invariance, it couples to this vector field. We find that this coupling affects the inertial mass of small DM halos which no longer satisfy the equivalence principle. For large enough lumps of DM we identify a (chameleon) mechanism that restores the inertial mass to its standard value. As a consequence, the dynamics of gravitational clustering are modified. Two prominent effects are a scale dependent enhancement in the growth of large scale structure and a scale dependent bias between DM and baryon density perturbations. The comparison with the measured linear matter power spectrum in principle allows to bound the departure from Lorentz invariance of DM at the per cent level.

Testing Lorentz invariance of dark matter

Energy Technology Data Exchange (ETDEWEB)

Blas, Diego [Theory Group, Physics Department, CERN, CH-1211 Geneva 23 (Switzerland); Ivanov, Mikhail M.; Sibiryakov, Sergey, E-mail: diego.blas@cern.ch, E-mail: mm.ivanov@physics.msu.ru, E-mail: sibir@inr.ac.ru [Faculty of Physics, Moscow State University, Vorobjevy Gory, 119991 Moscow (Russian Federation)

2012-10-01

We study the possibility to constrain deviations from Lorentz invariance in dark matter (DM) with cosmological observations. Breaking of Lorentz invariance generically introduces new light gravitational degrees of freedom, which we represent through a dynamical timelike vector field. If DM does not obey Lorentz invariance, it couples to this vector field. We find that this coupling affects the inertial mass of small DM halos which no longer satisfy the equivalence principle. For large enough lumps of DM we identify a (chameleon) mechanism that restores the inertial mass to its standard value. As a consequence, the dynamics of gravitational clustering are modified. Two prominent effects are a scale dependent enhancement in the growth of large scale structure and a scale dependent bias between DM and baryon density perturbations. The comparison with the measured linear matter power spectrum in principle allows to bound the departure from Lorentz invariance of DM at the per cent level.

Affine invariants of convex polygons.

Science.gov (United States)

Flusser, Jan

2002-01-01

In this correspondence, we prove that the affine invariants, for image registration and object recognition, proposed recently by Yang and Cohen (see ibid., vol.8, no.7, p.934-46, July 1999) are algebraically dependent. We show how to select an independent and complete set of the invariants. The use of this new set leads to a significant reduction of the computing complexity without decreasing the discrimination power.

Geometric phases for mixed states during cyclic evolutions

International Nuclear Information System (INIS)

Fu Libin; Chen Jingling

2004-01-01

The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical 1-form is defined whose line integral gives the geometric phase, which is gauge invariant. It reduces to the Aharonov and Anandan phase in the pure state case. Our definition is consistent with the phase shift in the proposed experiment (Sjoeqvist et al 2000 Phys. Rev. Lett. 85 2845) for a cyclic evolution if the unitary transformation satisfies the parallel transport condition. A comprehensive geometric interpretation is also given. It shows that the geometric phases for mixed states share the same geometric sense with the pure states

Simulation of Stochastic Processes by Coupled ODE-PDE

Science.gov (United States)

Zak, Michail

2008-01-01

A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.

Uncertainty calculation for modal parameters used with stochastic subspace identification: an application to a bridge structure

Science.gov (United States)

Hsu, Wei-Ting; Loh, Chin-Hsiung; Chao, Shu-Hsien

2015-03-01

Stochastic subspace identification method (SSI) has been proven to be an efficient algorithm for the identification of liner-time-invariant system using multivariate measurements. Generally, the estimated modal parameters through SSI may be afflicted with statistical uncertainty, e.g. undefined measurement noises, non-stationary excitation, finite number of data samples etc. Therefore, the identified results are subjected to variance errors. Accordingly, the concept of the stabilization diagram can help users to identify the correct model, i.e. through removing the spurious modes. Modal parameters are estimated at successive model orders where the physical modes of the system are extracted and separated from the spurious modes. Besides, an uncertainty computation scheme was derived for the calculation of uncertainty bounds for modal parameters at some given model order. The uncertainty bounds of damping ratios are particularly interesting, as the estimation of damping ratios are difficult to obtain. In this paper, an automated stochastic subspace identification algorithm is addressed. First, the identification of modal parameters through covariance-driven stochastic subspace identification from the output-only measurements is used for discussion. A systematic way of investigation on the criteria for the stabilization diagram is presented. Secondly, an automated algorithm of post-processing on stabilization diagram is demonstrated. Finally, the computation of uncertainty bounds for each mode with all model order in the stabilization diagram is utilized to determine system natural frequencies and damping ratios. Demonstration of this study on the system identification of a three-span steel bridge under operation condition is presented. It is shown that the proposed new operation procedure for the automated covariance-driven stochastic subspace identification can enhance the robustness and reliability in structural health monitoring.

Topological structure of the solution set for evolution inclusions

CERN Document Server

Zhou, Yong; Peng, Li

2017-01-01

This book systematically presents the topological structure of solution sets and attractability for nonlinear evolution inclusions, together with its relevant applications in control problems and partial differential equations. It provides readers the background material needed to delve deeper into the subject and explore the rich research literature.  In addition, the book addresses many of the basic techniques and results recently developed in connection with this theory, including the structure of solution sets for evolution inclusions with m-dissipative operators; quasi-autonomous and non-autonomous evolution inclusions and control systems;evolution inclusions with the Hille-Yosida operator; functional evolution inclusions; impulsive evolution inclusions; and stochastic evolution inclusions. Several applications of evolution inclusions and control systems are also discussed in detail.  Based on extensive research work conducted by the authors and other experts over the past four years, the information p...

Notes on algebraic invariants for non-commutative dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Longo, R [Rome Univ. (Italy). Istituto di Matematica

1979-11-01

We consider an algebraic invariant for non-commutative dynamical systems naturally arising as the spectrum of the modular operator associated to an invariant state, provided certain conditions of mixing type are present. This invariant turns out to be exactly the annihilator of the invariant T of Connes. Further comments are included, in particular on the type of certain algebras of local observables

Stochastic Optimization of Wind Turbine Power Factor Using Stochastic Model of Wind Power

DEFF Research Database (Denmark)

Chen, Peiyuan; Siano, Pierluigi; Bak-Jensen, Birgitte

2010-01-01

This paper proposes a stochastic optimization algorithm that aims to minimize the expectation of the system power losses by controlling wind turbine (WT) power factors. This objective of the optimization is subject to the probability constraints of bus voltage and line current requirements....... The optimization algorithm utilizes the stochastic models of wind power generation (WPG) and load demand to take into account their stochastic variation. The stochastic model of WPG is developed on the basis of a limited autoregressive integrated moving average (LARIMA) model by introducing a crosscorrelation...... structure to the LARIMA model. The proposed stochastic optimization is carried out on a 69-bus distribution system. Simulation results confirm that, under various combinations of WPG and load demand, the system power losses are considerably reduced with the optimal setting of WT power factor as compared...

Singular stochastic differential equations

CERN Document Server

Cherny, Alexander S

2005-01-01

The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.

STOCHASTIC MODEL OF THE SPIN DISTRIBUTION OF DARK MATTER HALOS

Energy Technology Data Exchange (ETDEWEB)

Kim, Juhan [Center for Advanced Computation, Korea Institute for Advanced Study, Heogiro 85, Seoul 130-722 (Korea, Republic of); Choi, Yun-Young [Department of Astronomy and Space Science, Kyung Hee University, Gyeonggi 446-701 (Korea, Republic of); Kim, Sungsoo S.; Lee, Jeong-Eun [School of Space Research, Kyung Hee University, Gyeonggi 446-701 (Korea, Republic of)

2015-09-15

We employ a stochastic approach to probing the origin of the log-normal distributions of halo spin in N-body simulations. After analyzing spin evolution in halo merging trees, it was found that a spin change can be characterized by a stochastic random walk of angular momentum. Also, spin distributions generated by random walks are fairly consistent with those directly obtained from N-body simulations. We derived a stochastic differential equation from a widely used spin definition and measured the probability distributions of the derived angular momentum change from a massive set of halo merging trees. The roles of major merging and accretion are also statistically analyzed in evolving spin distributions. Several factors (local environment, halo mass, merging mass ratio, and redshift) are found to influence the angular momentum change. The spin distributions generated in the mean-field or void regions tend to shift slightly to a higher spin value compared with simulated spin distributions, which seems to be caused by the correlated random walks. We verified the assumption of randomness in the angular momentum change observed in the N-body simulation and detected several degrees of correlation between walks, which may provide a clue for the discrepancies between the simulated and generated spin distributions in the voids. However, the generated spin distributions in the group and cluster regions successfully match the simulated spin distribution. We also demonstrated that the log-normality of the spin distribution is a natural consequence of the stochastic differential equation of the halo spin, which is well described by the Geometric Brownian Motion model.

Conformal invariance in supergravity

International Nuclear Information System (INIS)

Bergshoeff, E.A.

1983-01-01

In this thesis the author explains the role of conformal invariance in supergravity. He presents the complete structure of extended conformal supergravity for N <= 4. The outline of this work is as follows. In chapter 2 he briefly summarizes the essential properties of supersymmetry and supergravity and indicates the use of conformal invariance in supergravity. The idea that the introduction of additional symmetry transformations can make clear the structure of a field theory is not reserved to supergravity only. By means of some simple examples it is shown in chapter 3 how one can always introduce additional gauge transformations in a theory of massive vector fields. Moreover it is shown how the gauge invariant formulation sometimes explains the quantum mechanical properties of the theory. In chapter 4 the author defines the conformal transformations and summarizes their main properties. He explains how these conformal transformations can be used to analyse the structure of gravity. The supersymmetric extension of these results is discussed in chapter 5. Here he describes as an example how N=1 supergravity can be reformulated in a conformally-invariant way. He also shows that beyond N=1 the gauge fields of the superconformal symmetries do not constitute an off-shell field representation of extended conformal supergravity. Therefore, in chapter 6, a systematic method to construct the off-shell formulation of all extended conformal supergravity theories with N <= 4 is developed. As an example he uses this method to construct N=1 conformal supergravity. Finally, in chapter 7 N=4 conformal supergravity is discussed. (Auth.)