Upper bounds on minimum cardinality of exact and approximate reducts
Chikalov, Igor
2010-01-01
In the paper, we consider the notions of exact and approximate decision reducts for binary decision tables. We present upper bounds on minimum cardinality of exact and approximate reducts depending on the number of rows (objects) in the decision table. We show that the bound for exact reducts is unimprovable in the general case, and the bound for approximate reducts is almost unimprovable in the general case. © 2010 Springer-Verlag Berlin Heidelberg.
Exact lower and upper bounds on stationary moments in stochastic biochemical systems
Ghusinga, Khem Raj; Vargas-Garcia, Cesar A.; Lamperski, Andrew; Singh, Abhyudai
2017-08-01
In the stochastic description of biochemical reaction systems, the time evolution of statistical moments for species population counts is described by a linear dynamical system. However, except for some ideal cases (such as zero- and first-order reaction kinetics), the moment dynamics is underdetermined as lower-order moments depend upon higher-order moments. Here, we propose a novel method to find exact lower and upper bounds on stationary moments for a given arbitrary system of biochemical reactions. The method exploits the fact that statistical moments of any positive-valued random variable must satisfy some constraints that are compactly represented through the positive semidefiniteness of moment matrices. Our analysis shows that solving moment equations at steady state in conjunction with constraints on moment matrices provides exact lower and upper bounds on the moments. These results are illustrated by three different examples—the commonly used logistic growth model, stochastic gene expression with auto-regulation and an activator-repressor gene network motif. Interestingly, in all cases the accuracy of the bounds is shown to improve as moment equations are expanded to include higher-order moments. Our results provide avenues for development of approximation methods that provide explicit bounds on moments for nonlinear stochastic systems that are otherwise analytically intractable.
Exact BPS bound for noncommutative baby Skyrmions
Energy Technology Data Exchange (ETDEWEB)
Domrin, Andrei, E-mail: domrin@mi.ras.ru [Department of Mathematics and Mechanics, Moscow State University, Leninskie gory, 119992, GSP-2, Moscow (Russian Federation); Lechtenfeld, Olaf, E-mail: lechtenf@itp.uni-hannover.de [Institut für Theoretische Physik and Riemann Center for Geometry and Physics, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover (Germany); Linares, Román, E-mail: lirr@xanum.uam.mx [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, San Rafael Atlixco 186, C.P. 09340, México D.F. (Mexico); Maceda, Marco, E-mail: mmac@xanum.uam.mx [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, San Rafael Atlixco 186, C.P. 09340, México D.F. (Mexico)
2013-11-25
The noncommutative baby Skyrme model is a Moyal deformation of the two-dimensional sigma model plus a Skyrme term, with a group-valued or Grassmannian target. Exact abelian solitonic solutions have been identified analytically in this model, with a singular commutative limit. Inside any given Grassmannian, we establish a BPS bound for the energy functional, which is saturated by these baby Skyrmions. This asserts their stability for unit charge, as we also test in second-order perturbation theory.
Upper bound on quantum stabilizer codes
Li, Zhuo; Xing, Li-Juan
2009-03-01
By studying sets of operators having constant weight, we present an analytical upper bound on the pure quantum stabilizer codes whose underlying quantum system can be of arbitrary dimension, which outperforms the well-known quantum Hamming bound, the optimal analytical upper bound so far for small code length.
Schroedinger upper bounds to semirelativistic eigenvalues
Energy Technology Data Exchange (ETDEWEB)
Hall, Richard L [Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, Quebec, H3G 1M8 (Canada); Lucha, Wolfgang [Institut fuer Hochenergiephysik, Oesterreichische Akademie der Wissenschaften, Nikolsdorfergasse 18, A-1050 Vienna (Austria)
2005-09-16
Problems posed by semirelativistic Hamiltonians of the form H = {radical}(m{sup 2} + p{sup 2}) + V(r) are studied. It is shown that energy upper bounds can be constructed in terms of certain related Schroedinger operators; these bounds include free parameters which can be chosen optimally.
Upper Bounds on Numerical Approximation Errors
DEFF Research Database (Denmark)
Raahauge, Peter
2004-01-01
This paper suggests a method for determining rigorous upper bounds on approximationerrors of numerical solutions to infinite horizon dynamic programming models.Bounds are provided for approximations of the value function and the policyfunction as well as the derivatives of the value function...
Improved bounds on the epidemic threshold of exact SIS models on complex networks
Ruhi, Navid Azizan
2017-01-05
The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a 2n-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and, in particular, determining the threshold of epidemic spread quite challenging. It has been shown that the exact marginal probabilities of infection can be upper bounded by an n-dimensional linear time-invariant system, a consequence of which is that the Markov chain is “fast-mixing” when the LTI system is stable, i.e. when equation (where β is the infection rate per link, δ is the recovery rate, and λmax(A) is the largest eigenvalue of the network\\'s adjacency matrix). This well-known threshold has been recently shown not to be tight in several cases, such as in a star network. In this paper, we provide tighter upper bounds on the exact marginal probabilities of infection, by also taking pairwise infection probabilities into account. Based on this improved bound, we derive tighter eigenvalue conditions that guarantee fast mixing (i.e., logarithmic mixing time) of the chain. We demonstrate the improvement of the threshold condition by comparing the new bound with the known one on various networks with various epidemic parameters.
Upper Bounds for Mutations of Potentials
Directory of Open Access Journals (Sweden)
John Alexander Cruz Morales
2013-01-01
Full Text Available In this note we provide a new, algebraic proof of the excessive Laurent phenomenon for mutations of potentials (in the sense of [Galkin S., Usnich A., Preprint IPMU 10-0100, 2010] by introducing to this theory the analogue of the upper bounds from [Berenstein A., Fomin S., Zelevinsky A., Duke Math. J. 126 (2005, 1-52].
The exact distribution of the Hansen-Jagannathan bound
Kan, R; Robotti, C
2008-01-01
Under the assumption of multivariate normality of asset returns, this paper presents a geometrical interpretation and the finite-sample distributions of the sample Hansen-Jagannathan (1991) bounds on the variance of admissible stochastic discount factors, with and without the nonnegativity constraint on the stochastic discount factors. In addition, since the sample Hansen-Jagannathan bounds can be very volatile, we propose a simple method to construct confidence intervals for the population H...
A sharp upper bound for departure from normality
Energy Technology Data Exchange (ETDEWEB)
Lee, S.L.
1993-08-01
The departure from normality of a matrix is a real scalar that is impractical to compute if a matrix is large and its eigenvalues are unknown. A simple formula is presented for computing an upper bound for departure from normality in the Frobenius norm. This new upper bound is cheaper to compute than the upper bound derived by Henrici. Moreover, the new bound is sharp for Hermitian matrices, skew-Hermitian matrices and, in general, any matrix with eigenvalues that are horizontally or vertically aligned in the complex plane. In terms of applications, the new bound can be used in computing bounds for the spectral norm of matrix functions or bounds for the sensitivity of eigenvalues to matrix perturbations.
Upper Bounds on Stream I/O Using Semantic Interpretations
Gaboardi, Marco; Péchoux, Romain
2009-01-01
The original publication is available at www.springerlink.com; International audience; This paper extends for the first time semantics interpretation tools to infinite data in order to ensure Input/Output upper bounds on first order Haskell like programs on streams. By I/O upper bounds, we mean temporal relations between the number of reads performed on the input stream elements and the number of output elements produced. We study several I/O upper bounds properties that are of both theoretic...
Inequalities involving upper bounds for certain matrix operators
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 116; Issue 3. Inequalities Involving Upper Bounds for Certain Matrix Operators. R Lashkaripour D Foroutannia. Volume ... Keywords. Inequality; norm; summability matrix; Hausdorff matrix; Hilbert matrix; weighted sequence space; Lorentz sequence space.
Upper bounds for domination related parameters in graphs on surfaces
Directory of Open Access Journals (Sweden)
Vladimir Samodivkin
2016-08-01
Full Text Available In this paper we give tight upper bounds on the total domination number, the weakly connected domination number and the connected domination number of a graph in terms of order and Euler characteristic. We also present upper bounds for the restrained bondage number, the total restrained bondage number and the restricted edge connectivity of graphs in terms of the orientable/nonorientable genus and maximum degree.
Thermodynamic Upper Bound on Broadband Light Coupling with Photonic Structures
Yu, Zongfu
2012-10-01
The coupling between free space radiation and optical media critically influences the performance of optical devices. We show that, for any given photonic structure, the sum of the external coupling rates for all its optical modes are subject to an upper bound dictated by the second law of thermodynamics. Such bound limits how efficient light can be coupled to any photonic structure. As one example of application, we use this upper bound to derive the limit of light absorption in broadband solar absorbers. © 2012 American Physical Society.
Communication: An exact bound on the bridge function in integral equation theories
Kast, Stefan M.; Tomazic, Daniel
2012-11-01
We show that the formal solution of the general closure relation occurring in Ornstein-Zernike-type integral equation theories in terms of the Lambert W function leads to an exact relation between the bridge function and correlation functions, most notably to an inequality that bounds possible bridge values. The analytical results are illustrated on the example of the Lennard-Jones fluid for which the exact bridge function is known from computer simulations under various conditions. The inequality has consequences for the development of bridge function models and rationalizes numerical convergence issues.
Communication: An exact bound on the bridge function in integral equation theories.
Kast, Stefan M; Tomazic, Daniel
2012-11-07
We show that the formal solution of the general closure relation occurring in Ornstein-Zernike-type integral equation theories in terms of the Lambert W function leads to an exact relation between the bridge function and correlation functions, most notably to an inequality that bounds possible bridge values. The analytical results are illustrated on the example of the Lennard-Jones fluid for which the exact bridge function is known from computer simulations under various conditions. The inequality has consequences for the development of bridge function models and rationalizes numerical convergence issues.
A Method for Upper Bounding on Network Access Speed
DEFF Research Database (Denmark)
Knudsen, Thomas Phillip; Patel, A.; Pedersen, Jens Myrup
2004-01-01
This paper presents a method for calculating an upper bound on network access speed growth and gives guidelines for further research experiments and simulations. The method is aimed at providing a basis for simulation of long term network development and resource management.......This paper presents a method for calculating an upper bound on network access speed growth and gives guidelines for further research experiments and simulations. The method is aimed at providing a basis for simulation of long term network development and resource management....
Upper bounds for Neyman-Pearson cooperative spectrum sensing
Zahabi, Sayed Jalal
2011-06-01
We consider a cooperative spectrum sensing scenario where the local sensors at the secondary users are viewed as one-level quantizers, and the quantized data are to be fused under Neyman-Pearson (N-P) criterion. We demonstrate how the N-P fusion results in a randomized test, which represents the total performance of our spectrum sensing scheme. We further introduce an upper performance bound for the overall primary user signal detection. An analytical procedure towards the upper bound and its relevant quantization setup at the local sensors are proposed and examined through simulations. © 2011 IEEE.
Upper bound on the radii of black-hole photonspheres
Energy Technology Data Exchange (ETDEWEB)
Hod, Shahar [The Ruppin Academic Center, Emeq Hefer 40250 (Israel); The Hadassah Institute, Jerusalem 91010 (Israel)
2013-11-25
One of the most remarkable predictions of the general theory of relativity is the existence of black-hole “photonspheres”, compact null hypersurfaces on which massless particles can orbit the central black hole. We prove that every spherically-symmetric asymptotically flat black-hole spacetime is characterized by a photonsphere whose radius is bounded from above by r{sub γ}⩽3M, where M is the total ADM mass of the black-hole spacetime. It is shown that hairy black-hole configurations conform to this upper bound. In particular, the null circular geodesic of the (bald) Schwarzschild black-hole spacetime saturates the bound.
Upper Bound Limit Load Solutions for Welded Joints with Cracks
Alexandrov, Sergey
2012-01-01
The present short monograph concerns analytic and semi-analytic techniques for finding an approximate value of the limit load. The limit load is an essential input parameter of flaw assessment procedures. In most cases, finding the limit load involves some numerical calculations of different levels of complexity, including numerical minimization of functions of one or several arguments, the slip-line technique and the finite element method. This book shows in particular how to use singular behavior of the real velocity field in the vicinity of bi-material interfaces in kinematically admissible velocity fields to increase the accuracy of upper bound solutions. An approach to recalculate the limit load for a class of structures with defects with the use of its value for the corresponding structure with no defect is discussed. The upper bound technique is applied to evaluate the limit load of overmatched and undermatched welded joints with cracks subject to various loading conditions of practical importance in c...
Upper bound on the Abelian gauge coupling from asymptotic safety
Eichhorn, Astrid; Versteegen, Fleur
2018-01-01
We explore the impact of asymptotically safe quantum gravity on the Abelian gauge coupling in a model including a charged scalar, confirming indications that asymptotically safe quantum fluctuations of gravity could trigger a power-law running towards a free fixed point for the gauge coupling above the Planck scale. Simultaneously, quantum gravity fluctuations balance against matter fluctuations to generate an interacting fixed point, which acts as a boundary of the basin of attraction of the free fixed point. This enforces an upper bound on the infrared value of the Abelian gauge coupling. In the regime of gravity couplings which in our approximation also allows for a prediction of the top quark and Higgs mass close to the experimental value [1], we obtain an upper bound approximately 35% above the infrared value of the hypercharge coupling in the Standard Model.
Upper Bound Performance Estimation for Copper Based Broadband Access
DEFF Research Database (Denmark)
Jensen, Michael; Gutierrez Lopez, Jose Manuel
2012-01-01
Around 70% of all broadband connections in the European Union are carried over copper, and the scenario is unlikely to change in the next few years as carriers still believe in the profitability of their copper infrastructure. In this paper we show how to estimate the performance upper bound of c...... to define the limitations of copper based broadband access. A case study in a municipality in Denmark shows how the estimated network dimension to be able to provide video conference services to the majority of the population might be too high to be implemented in reality.......Around 70% of all broadband connections in the European Union are carried over copper, and the scenario is unlikely to change in the next few years as carriers still believe in the profitability of their copper infrastructure. In this paper we show how to estimate the performance upper bound...
Upper and lower bounds of solutions for fractional integral equations
Directory of Open Access Journals (Sweden)
Shaher Momani
2008-03-01
Full Text Available In this paper we consider the integral equation offractional order in sense of Riemann-Liouville operatorum(t = a(t Iα [b(tu(t]+f(twith m ≥ 1, t ∈ [0, T], T < ∞ and 0< α <1. We discuss the existence, uniqueness, maximal, minimal and the upper and lower bounds of the solutions. Also we illustrate our results with examples.
Computing an upper bound on contact stress with surrogate duality
Xuan, Zhaocheng; Papadopoulos, Panayiotis
2016-07-01
We present a method for computing an upper bound on the contact stress of elastic bodies. The continuum model of elastic bodies with contact is first modeled as a constrained optimization problem by using finite elements. An explicit formulation of the total contact force, a fraction function with the numerator as a linear function and the denominator as a quadratic convex function, is derived with only the normalized nodal contact forces as the constrained variables in a standard simplex. Then two bounds are obtained for the sum of the nodal contact forces. The first is an explicit formulation of matrices of the finite element model, derived by maximizing the fraction function under the constraint that the sum of the normalized nodal contact forces is one. The second bound is solved by first maximizing the fraction function subject to the standard simplex and then using Dinkelbach's algorithm for fractional programming to find the maximum—since the fraction function is pseudo concave in a neighborhood of the solution. These two bounds are solved with the problem dimensions being only the number of contact nodes or node pairs, which are much smaller than the dimension for the original problem, namely, the number of degrees of freedom. Next, a scheme for constructing an upper bound on the contact stress is proposed that uses the bounds on the sum of the nodal contact forces obtained on a fine finite element mesh and the nodal contact forces obtained on a coarse finite element mesh, which are problems that can be solved at a lower computational cost. Finally, the proposed method is verified through some examples concerning both frictionless and frictional contact to demonstrate the method's feasibility, efficiency, and robustness.
New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities
Mceliece, R. J.; Rodemich, E. R.; Rumsey, H., Jr.; Welch, L. R.
1977-01-01
An upper bound on the rate of a binary code as a function of minimum code distance (using a Hamming code metric) is arrived at from Delsarte-MacWilliams inequalities. The upper bound so found is asymptotically less than Levenshtein's bound, and a fortiori less than Elias' bound. Appendices review properties of Krawtchouk polynomials and Q-polynomials utilized in the rigorous proofs.
Statistical Analysis of Upper Bound using Data with Uncertainties
Tng, Barry Jia Hao
2014-01-01
Let $F$ be the unknown distribution of a non-negative continuous random variable. We would like to determine if $supp(F) \\subseteq [0,c]$ where $c$ is a constant (a proposed upper bound). Instead of directly observing $X_1,...,X_n i.i.d. \\sim F$, we only get to observe as data $Y_1,...,Y_n$ where $Y_i = X_i + \\epsilon_i$, with $\\epsilon_i$ being random variables representing errors. In this paper, we will explore methods to handle this statistical problem for two primary cases - parametric and nonparametric. The data from deep inelastic scattering experiments on measurements of $R=\\sigma_L / \\sigma_T$ would be used to test code which has been written to implement the discussed methods.
An upper bound on the number of independent sets in a tree
DEFF Research Database (Denmark)
Vestergaard, Preben D.; Pedersen, Anders Sune
2007-01-01
The main result of this paper is an upper bound on the number of independent sets in a tree in terms of the order and diameter of the tree. This new upper bound is a refinement of the bound given by Prodinger and Tichy [ Fibonacci Q., 20 (1982), no. 1, 16-21]. Finally, we give a sufficient...... condition for the new upper bound to be better thatn the upper bound given by Brigham, Chandrasekharan and Dutton [ Fibonacci Q., 31 (1993), no. 2, 98-104]....
An upper bound on the number of independent sets in a tree
DEFF Research Database (Denmark)
Vestergaard, Preben Dahl; Pedersen, Anders Sune
The main result of this paper is an upper bound on the number of independent sets in a tree in terms of the order and diameter of the tree. This new upper bound is a refinement of the bound given by Prodinger and Tichy [Fibonacci Q., 20 (1982), no. 1, 16-21]. Finally, we give a sufficient condition...... for the new upper bound to be better than the upper bound given by Brigham, Chandrasekharan and Dutton [Fibonacci Q., 31 (1993), no. 2, 98-104]....
Upper Bounds on Performance Measures of Heterogeneous // Queues
Directory of Open Access Journals (Sweden)
F. S. Q. Alves
2011-01-01
Full Text Available In many real-life queueing systems, the servers are often heterogeneous, namely they work at different rates. This paper provides a simple method to compute tight upper bounds on two important performance measures of single-class heterogeneous multi-server Markovian queueing systems, namely the average number in queue and the average waiting time in queue. This method is based on an expansion of the state space that is followed by an approximate reduction of the state space, only considering the most probable states. In most cases tested, we were able to approximate the actual behavior of the system with smaller errors than those obtained from traditional homogeneous multiserver Markovian queues, as shown by GPSS simulations. In addition, we have correlated the quality of the approximation with the degree of heterogeneity of the system, which was evaluated using its Gini index. Finally, we have shown that the bounds are robust and still useful, even considering quite different allocation strategies. A large number of simulation results show the accuracy of the proposed method that is better than that of classical homogeneous multiserver Markovian formulae in many situations.
Upper bounds on the number of errors corrected by a convolutional code
DEFF Research Database (Denmark)
Justesen, Jørn
2004-01-01
We derive upper bounds on the weights of error patterns that can be corrected by a convolutional code with given parameters, or equivalently we give bounds on the code rate for a given set of error patterns. The bounds parallel the Hamming bound for block codes by relating the number of error...... patterns to the number of distinct syndromes....
New Upper Bounds for Taxicab and Cabtaxi Numbers
Boyer, Christian
2008-03-01
Hardy was surprised by Ramanujan's remark about a London taxi numbered 1729: "it is a very interesting number, it is the smallest number expressible as a sum of two cubes in two different ways". In memory of this story, this number is now called Taxicab(2) = 1729 = 9^3 + 10^33 = 1^33 + 12^33, Taxicab(n) being the smallest number expressible in n ways as a sum of two cubes. We can generalize the problem by also allowing differences of cubes: Cabtaxi(n) is the smallest number expressible in n ways as a sum or difference of two cubes. For example, Cabtaxi(2) = 91 = 3^3 + 4^3 = 6^3 - 5^3. Results were only known up to Taxicab(6) and Cabtaxi(9). This paper presents a history of the two problems since Fermat, Frenicle and Viete, and gives new upper bounds for Taxicab(7) to Taxicab(19), and for Cabtaxi(10) to Cabtaxi(30). Decompositions are explicitly given up to Taxicab(12) and Cabtaxi(20).
Power generation assets. Energy constraints, upper bounds and hedging strategies
Energy Technology Data Exchange (ETDEWEB)
Enge, Thomas
2010-09-20
The overall topic of this thesis is the valuation of power generation assets under energy and risk constraints. Our focus is on the modeling aspect i.e. to find the right balance between accuracy and computational feasibility. We define a new not yet investigated unit commitment problem that introduces an energy constraint to a thermal power plant. We define a continuous stochastic dynamic program with a nested mixed integer program (MIP). We introduce a fast implementation approach by replacing the MIP with an efficient matrix calculation and use principal component analysis to reduce the number of risk factors. We also provide a fast heuristic valuation approach for comparison. As both models can only provide lower bounds of the asset value, we investigate the theory of upper bounds for a proper validation of our power plant results. We review the primal dual algorithm for swing options by Meinshausen and Hambly and in particular clarify their notation and implementation. Then we provide an extension for swing options with multiple exercises at the same stage that we developed together with Prof. Bender, University of Braunschweig. We outline Prof. Bender's proof and describe the implementation in detail. Finally we provide a risk analysis for our thermal power plant. In particular we investigate strategies to reduce spot price risk to which power plants are significantly exposed. First, we focus on the measurement of spot price risk and propose three appropriate risk figures (Forward delta as opposed to Futures delta, synthetic spot delta and Earnings-at-Risk) and illustrate their application using a business case. Second we suggest risk mitigation strategies for both periods, before and in delivery. The latter tries to alter the dispatch policy i.e. pick less risky hours and accept a (desirably only slightly) smaller return. We introduce a benchmark that weighs risk versus return and that we will call EaR-efficient option value. We propose a mitigation
An upper bound on the number of errors corrected by a convolutional code
DEFF Research Database (Denmark)
Justesen, Jørn
2000-01-01
The number of errors that a convolutional codes can correct in a segment of the encoded sequence is upper bounded by the number of distinct syndrome sequences of the relevant length.......The number of errors that a convolutional codes can correct in a segment of the encoded sequence is upper bounded by the number of distinct syndrome sequences of the relevant length....
An Upper Bound on the Entropy of Constrained 2d Fields
DEFF Research Database (Denmark)
Forchhammer, Søren; Justesen, Jørn
1998-01-01
An upper bound on the entropy of constrained 2D fields is presented. The constraints have to be symmetric in (at least) one of the two directions. The bound generalizes (in a weaker form) the bound of Calkin and Wilf (see SIAM Journal of Discrete Mathematics, vol.11, p.54-60, 1998) which is valid...
New code upper bounds from the Terwilliger algebra and semidefinite programming
A. Schrijver (Alexander)
2005-01-01
textabstractWe give a new upper bound on the maximum size $A(n, d)$ of a binary code of word length $n$ and minimum distance at least $d$. It is based on block-diagonalising the Terwilliger algebra of the Hamming cube. The bound strengthens the Delsarte bound, and can be calculated with
Upper bounds on quantum uncertainty products and complexity measures
Energy Technology Data Exchange (ETDEWEB)
Guerrero, Angel; Sanchez-Moreno, Pablo; Dehesa, Jesus S. [Department of Atomic, Molecular and Nuclear Physics, University of Granada, Granada (Spain); Department of Applied Mathematics, University of Granada, Granada (Spain) and Institute Carlos I for Computational and Theoretical Physics, University of Granada, Granada (Spain); Department of Atomic, Molecular and Nuclear Physics, University of Granada, Granada (Spain); Institute Carlos I for Computational and Theoretical Physics, University of Granada, Granada (Spain)
2011-10-15
The position-momentum Shannon and Renyi uncertainty products of general quantum systems are shown to be bounded not only from below (through the known uncertainty relations), but also from above in terms of the Heisenberg-Kennard product . Moreover, the Cramer-Rao, Fisher-Shannon, and Lopez-Ruiz, Mancini, and Calbet shape measures of complexity (whose lower bounds have been recently found) are also bounded from above. The improvement of these bounds for systems subject to spherically symmetric potentials is also explicitly given. Finally, applications to hydrogenic and oscillator-like systems are done.
Gangaraj, Srihari Kumar
This dissertation addresses reliable finite element analysis of boundary value problems in engineering computations, where the solution quantities which are of interest to the engineer will be computed together with an estimate of their error. The solution quantities often computed during design and certification phases are the temperature/displacement, flux/stress in a region, flux/stress intensity factor at the crack tip or corner, reaction at a fixed end, etc. The existing finite element analysis software concentrate primarily on obtaining a solution rapidly and do not guarantee the accuracy of these solution quantities. Recent developments in error-estimation and adaptive mesh refinement strategies have led to new algorithms to compute solution quantities of interest within the prescribed tolerance. The drawback of these algorithms is that the quality of the estimate of the error in the solution quantities is not guaranteed, i.e., the estimated error could be greater or smaller than the exact error. Therefore, we have developed a new method of estimation of the error in the quantities of interest---computation of guaranteed upper and lower bounds for the errors in the quantities of interest. The guaranteed upper and lower bounds for the errors in the quantities of interest are based on the capability to compute bounds for the energy norm of the error. The tools for computation of bounds for the energy norm of the error are the solutions of the local residual problems, which are often implemented in finite element programs which have a posteriori error estimation capabilities. The main features of the upper and lower bounds given in this dissertation are: (1) The upper and lower bounds are guaranteed for the exact error in the quantities of interest, unlike the bounds proposed in recent literature which are guaranteed only for the energy norm of the error with respect to an enriched (truth-mesh) finite element solution; (2) The sharpness of the bounds can be
Energy Technology Data Exchange (ETDEWEB)
Requardt, M.
1985-01-01
For a large class of potentials the author proves upper bounds on the number of bound states in the various angular momentum channels below a certain energy E. As by-product he derives estimates on the maximal angular momentum etc. The class of allowed potentials enclose as typical candidate potentials with infinitely many bound states below the essential spectrum, respectively potentials which go to infinity for r ..-->.. infinity as e.g. the model potentials used in quarkonium physics like V(r) = -a(1/r) + br. Generalizations to the case of N-body quantum mechanics seem to be possible. (Auth.).
Energy Technology Data Exchange (ETDEWEB)
Ackroyd, R.T.
1978-02-01
A maximum principle for neutron transport in systems with extraneous sources is used with the method of source iteration to suggest a functional for a variational principle for self-sustaining systems. By using the general properties of the leakage and removal operators of the even-parity transport equation the variational principle is shown to give an upper bound to the lowest eigenvalue of the one-speed Boltzmann equation. Thus by making use of the method of Part III for a lower bound, the lowest eigenvalue can be bracketed. The variational principle leads to the finite element equations identical to those arising in the Williams/Galliara finite element formulation of the source-iteration methods, thus showing that the latter method always gives an upper bound to the lowest eigenvalue. Their upper bounds are very close to the exact value for some benchmark calculations.
Viñales, A D; Despósito, M A
2006-01-01
We study the effect of a disordered or fractal environment in the irreversible dynamics of a harmonic oscillator. Starting from a generalized Langevin equation and using Laplace analysis, we derive exact expressions for the mean values, variances, and velocity autocorrelation function of the particle in terms of generalized Mittag-Leffler functions. The long-time behaviors of these quantities are obtained and the presence of a whip-back effect is analyzed.
Upper Higgs boson mass bounds from a chirally invariant lattice Higgs-Yukawa Model
Energy Technology Data Exchange (ETDEWEB)
Gerhold, P. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; John von Neumann-Institut fuer Computing NIC/DESY, Zeuthen (Germany); Jansen, K. [John von Neumann-Institut fuer Computing NIC/DESY, Zeuthen (Germany)
2010-02-15
We establish the cutoff-dependent upper Higgs boson mass bound by means of direct lattice computations in the framework of a chirally invariant lattice Higgs-Yukawa model emulating the same chiral Yukawa coupling structure as in the Higgs-fermion sector of the Standard Model. As expected from the triviality picture of the Higgs sector, we observe the upper mass bound to decrease with rising cutoff parameter {lambda}. Moreover, the strength of the fermionic contribution to the upper mass bound is explored by comparing to the corresponding analysis in the pure {phi}{sup 4}-theory. (orig.)
Least Upper Bounds of the Powers Extracted and Scattered by Bi-anisotropic Particles
Liberal, Inigo; Gonzalo, Ramon; Ederra, Inigo; Tretyakov, Sergei A; Ziolkowski, Richard W
2014-01-01
The least upper bounds of the powers extracted and scattered by bi-anisotropic particles are investigated analytically. A rigorous derivation for particles having invertible polarizability tensors is presented, and the particles with singular polarizability tensors that have been reported in the literature are treated explicitly. The analysis concludes that previous upper bounds presented for isotropic particles can be extrapolated to bi-anisotropic particles. In particular, it is shown that neither nonreciprocal nor magnetoelectric coupling phenomena can further increase those upper bounds on the extracted and scattered powers. The outcomes are illustrated further with approximate circuit model examples of two dipole antennas connected via a generic lossless network.
Hadamard upper bound on optimum joint decoding capacity of Wyner Gaussian cellular MAC
Shakir, Muhammad
2011-09-01
This article presents an original analytical expression for an upper bound on the optimum joint decoding capacity of Wyner circular Gaussian cellular multiple access channel (C-GCMAC) for uniformly distributed mobile terminals (MTs). This upper bound is referred to as Hadamard upper bound (HUB) and is a novel application of the Hadamard inequality established by exploiting the Hadamard operation between the channel fading matrix G and the channel path gain matrix Ω. This article demonstrates that the actual capacity converges to the theoretical upper bound under the constraints like low signal-to-noise ratios and limiting channel path gain among the MTs and the respective base station of interest. In order to determine the usefulness of the HUB, the behavior of the theoretical upper bound is critically observed specially when the inter-cell and the intra-cell time sharing schemes are employed. In this context, we derive an analytical form of HUB by employing an approximation approach based on the estimation of probability density function of trace of Hadamard product of two matrices, i.e., G and Ω. A closed form of expression has been derived to capture the effect of the MT distribution on the optimum joint decoding capacity of C-GCMAC. This article demonstrates that the analytical HUB based on the proposed approximation approach converges to the theoretical upper bound results in the medium to high signal to noise ratio regime and shows a reasonably tighter bound on optimum joint decoding capacity of Wyner GCMAC.
Sublinear Upper Bounds for Stochastic Programs with Recourse. Revision.
1987-06-01
approximation procedures for (1.1) generally rely on discretizations of E (Huang, Ziemba , and Ben-Tal (1977), Kall and Stoyan (1982), Birge and Wets...Wright, Practical optimization (Academic Press, London and New York,1981). C.C. Huang, W. Ziemba , and A. Ben-Tal, "Bounds on the expectation of a con
Bounded Rationality and Cognitive Development: Upper Limits on Growth?
Shaklee, Harriet
1979-01-01
Piaget's characterization of formal operational thought and human judgment psychologists' model of bounded rationality are two conflicting models dealing with the nature and limits of mature thought. However, a look at the respective databases demonstrates their complementarity and their contribution to understanding mature cognition. (Author/RD)
Some upper and lower bounds on PSD-rank
T. J. Lee (Troy); Z. Wei (Zhaohui); R. M. de Wolf (Ronald)
2014-01-01
textabstractPositive semidefinite rank (PSD-rank) is a relatively new quantity with applications to combinatorial optimization and communication complexity. We first study several basic properties of PSD-rank, and then develop new techniques for showing lower bounds on the PSD-rank. All of these
Some upper and lower bounds on PSD-rank
Lee, T.; Wei, Z.; de Wolf, R.
Positive semidefinite rank (PSD-rank) is a relatively new complexity measure on matrices, with applications to combinatorial optimization and communication complexity. We first study several basic properties of PSD-rank, and then develop new techniques for showing lower bounds on the PSD-rank. All
Modifying the upper bound on the length of minimal synchronizing word
Trahtman, A N
2011-01-01
A word $w$ is called synchronizing (recurrent, reset, magic, directable) word of deterministic finite automaton (DFA) if $w$ sends all states of the automaton to a unique state. In 1964 Jan \\v{C}erny found a sequence of n-state complete DFA possessing a minimal synchronizing word of length $(n-1)^2$. He conjectured that it is an upper bound on the length of such words for complete DFA. Nevertheless, the best upper bound $(n^3-n)/6$ was found almost 30 years ago. We reduce the upper bound on the length of the minimal synchronizing word to $n(7n^2+12n-4)/48$. An implemented algorithm for finding synchronizing word with restricted upper bound is described. The work presents the distribution of all synchronizing automata of small size according to the length of an almost minimal synchronizing word.
A New Upper Bound on the Infinity Norm of the Inverse of Nekrasov Matrices
Directory of Open Access Journals (Sweden)
Lei Gao
2014-01-01
Full Text Available A new upper bound which involves a parameter for the infinity norm of the inverse of Nekrasov matrices is given. And we determine the optimal value of the parameter such that the bound improves the results of Kolotilina, 2013. Numerical examples are given to illustrate the corresponding results.
New Upper Bounds for Nonbinary Codes Based on the Terwilliger Algebra and Semidefinite Programming
Gijswijt, D.C.; Schrijver, A.
2006-01-01
Abstract: We give a new upper bound on the maximum size $A_q(n,d)$ of a code of word length $n$ and minimum Hamming distance at least $d$ over the alphabet of $q\\geq 3$ letters. By block-diagonalizing the Terwilliger algebra of the nonbinary Hamming scheme, the bound can be calculated in time
New upper bounds for nonbinary codes based on the Terwilliger algebra and semidefinite programming
D. Gijswijt (Dion); A. Schrijver (Alexander); H. Tanaka
2006-01-01
htmlabstractWe give a new upper bound on the maximum size $A_q(n,d)$ of a code of word length $n$ and minimum Hamming distance at least $d$ over the alphabet of $q\\geq 3$ letters. By block-diagonalizing the Terwilliger algebra of the nonbinary Hamming scheme, the bound can be calculated in time
Lower and Upper Bounds for Deniable Public-Key Encryption
DEFF Research Database (Denmark)
Bendlin, Rikke; Nielsen, Jesper Buus; Nordholt, Peter Sebastian
2011-01-01
A deniable cryptosystem allows a sender and a receiver to communicate over an insecure channel in such a way that the communication is still secure even if the adversary can threaten the parties into revealing their internal states after the execution of the protocol. This is done by allowing...... the parties to change their internal state to make it look like a given ciphertext decrypts to a message different from what it really decrypts to. Deniable encryption was in this way introduced to allow to deny a message exchange and hence combat coercion. Depending on which parties can be coerced...... that it is impossible to construct a non-interactive bi-deniable public-key encryption scheme with better than polynomial security. Specifically, we give an explicit bound relating the security of the scheme to how efficient the scheme is in terms of key size. Our impossibility result establishes a lower bound...
Upper and Lower Bounds of Frequency Interval Gramians for a Class of Perturbed Linear Systems
DEFF Research Database (Denmark)
Shaker, Hamid Reza
2012-01-01
if the system is controllable or observable, but also it is required to know the degree of controllability or observability of the system. Gramian matrices were introduced to address this issue by providing a quantitative measure for controllability and observability. In many applications, the information...... of uncertain systems. In this paper, we derive upper and lower bounds of frequency interval gramians under perturbations of an A-matrix in the state-space form. These bounds are obtained by solving algebraic Riccati equations. The results are further used to obtain upper and lower bounds of the frequency...
Upper and Lower Bound Limit Loads for Thin-Walled Pressure Vessels Used for Aerosol Cans
Directory of Open Access Journals (Sweden)
Stephen John Hardy
2009-01-01
Full Text Available The elastic compensation method proposed by Mackenzie and Boyle is used to estimate the upper and lower bound limit (collapse loads for one-piece aluminium aerosol cans, which are thin-walled pressure vessels subjected to internal pressure loading. Elastic-plastic finite element predictions for yield and collapse pressures are found using axisymmetric models. However, it is shown that predictions for the elastic-plastic buckling of the vessel base require the use of a full three-dimensional model with a small unsymmetrical imperfection introduced. The finite element predictions for the internal pressure to cause complete failure via collapse fall within the upper and lower bounds. Hence the method, which involves only elastic analyses, can be used in place of complex elastic-plastic finite element analyses when upper and lower bound estimates are adequate for design purposes. Similarly, the lower bound value underpredicts the pressure at which first yield occurs.
Analytical upper bound on optimum joint decoding capacity of Wyner GCMAC using hadamard inequality
Shakir, Muhammad
2011-11-01
This paper presents an original analytical expression for an upper bound on the optimum joint decoding capacity of Wyner circular Gaussian cellular multiple access channel (C-GCMAC) for uniformly distributed mobile terminals (MTs) across the cells. This upper bound is referred to as Hadamard upper bound (HUB) and is a novel application of the Hadamard inequality established by exploiting the Hadamard operation between the channel fading and channel path gain matrices. In this context, we employ an approximation approach based on the estimation of probability density function (PDF) of Hadamard product of two matrices. A closed-form expression has been derived to capture the effect of variable user density in adjacent cells on optimal joint decoding capacity. The results of this paper demonstrate that the analytical HUB based on the proposed approximation approach converges to the theoretical results for medium range of signal to noise ratios and shows a comparable tighter bound on optimum joint decoding capacity. © 2011 IEEE.
Weights of Exact Threshold Functions
DEFF Research Database (Denmark)
Babai, László; Hansen, Kristoffer Arnsfelt; Podolskii, Vladimir V.
2010-01-01
We consider Boolean exact threshold functions defined by linear equations, and in general degree d polynomials. We give upper and lower bounds on the maximum magnitude (absolute value) of the coefficients required to represent such functions. These bounds are very close and in the linear case...... and the Boolean cube {0,1} n . In the process we construct new families of ill-conditioned matrices. We further stratify the problem (in the linear case) in terms of the dimension k of the affine subspace spanned by the solutions, and give upper and lower bounds in this case as well. Our bounds here in terms of k...
Directory of Open Access Journals (Sweden)
Chao Lu
2016-01-01
Full Text Available This paper is concerned with the scheduling of Electrical Multiple Units (EMUs under the condition of their utilization on one sector or within several interacting sectors. Based on the introduction of the train connection graph which describes the possible connection relationship between trains, the integer programming model of EMU circulation planning is constructed. In order to analyzing the resolution of the model, a heuristic which shares the characteristics with the existing methods is introduced first. This method consists of two stages: one is a greedy strategy to construct a feasible circulation plan fragment, and another is to apply a stochastic disturbance to it to generate a whole feasible solution or get a new feasible solution. Then, an exact branch and bound method which is based on graph designing is proposed. Due to the complexity, the lower bound is computed through a polynomial approximation algorithm which is a modification from the one solving the degree constraint minimum 1-tree problem. Then, a branching strategy is designed to cope with the maintenance constraints. Finally, we report extensive computational results on a railway corridor in which the sectors possess the basic feature of railway networks.
Hadamard Upper Bound (HUB) on Optimum Joint Decoding Capacity of Wyner Gaussian Cellular MAC
Shakir, M Zeeshan; Alouini, Mohamed-Slim
2010-01-01
This paper presents an original analytical expression for an upper bound on the optimum joint decoding capacity of Wyner Circular Gaussian Cellular Multiple Access Channel (C-GCMAC) for uniformly distributed Mobile Terminals (MTs). This upper bound is referred to as Hadamard Upper Bound (HUB) and is a novel application of the Hadamard inequality established by exploiting the Hadamard operation between the channel fading and channel slow gain matrices. This paper demonstrates that the theoretical upper bound converges to the actual capacity under constraints like low range of signal to noise ratios and limiting channel slow gain among the MTs and the Base Station (BS) of interest. The behaviour of the theoretical upper bound is critically observed when the inter-cell and the intra-cell time sharing schemes are employed. In this context, we employ an approximation approach to evaluate the effect of the MT distribution on optimal joint decoding capacity for a variable user-density in C-GCMAC. This paper demonstr...
Upper bounds on secret-key agreement over lossy thermal bosonic channels
Kaur, Eneet; Wilde, Mark M.
2017-12-01
Upper bounds on the secret-key-agreement capacity of a quantum channel serve as a way to assess the performance of practical quantum-key-distribution protocols conducted over that channel. In particular, if a protocol employs a quantum repeater, achieving secret-key rates exceeding these upper bounds is evidence of having a working quantum repeater. In this paper, we extend a recent advance [Liuzzo-Scorpo et al., Phys. Rev. Lett. 119, 120503 (2017), 10.1103/PhysRevLett.119.120503] in the theory of the teleportation simulation of single-mode phase-insensitive Gaussian channels such that it now applies to the relative entropy of entanglement measure. As a consequence of this extension, we find tighter upper bounds on the nonasymptotic secret-key-agreement capacity of the lossy thermal bosonic channel than were previously known. The lossy thermal bosonic channel serves as a more realistic model of communication than the pure-loss bosonic channel, because it can model the effects of eavesdropper tampering and imperfect detectors. An implication of our result is that the previously known upper bounds on the secret-key-agreement capacity of the thermal channel are too pessimistic for the practical finite-size regime in which the channel is used a finite number of times, and so it should now be somewhat easier to witness a working quantum repeater when using secret-key-agreement capacity upper bounds as a benchmark.
Membrane-based ethylene/ethane separation: The upper bound and beyond
Rungta, Meha
2013-08-02
Ethylene/ethane separation via cryogenic distillation is extremely energy-intensive, and membrane separation may provide an attractive alternative. In this paper, ethylene/ethane separation performance using polymeric membranes is summarized, and an experimental ethylene/ethane polymeric upper bound based on literature data is presented. A theoretical prediction of the ethylene/ethane upper bound is also presented, and shows good agreement with the experimental upper bound. Further, two ways to overcome the ethylene/ethane upper bound, based on increasing the sorption or diffusion selectivity, is also discussed, and a review on advanced membrane types such as facilitated transport membranes, zeolite and metal organic framework based membranes, and carbon molecular sieve membranes is presented. Of these, carbon membranes have shown the potential to surpass the polymeric ethylene/ethane upper bound performance. Furthermore, a convenient, potentially scalable method for tailoring the performance of carbon membranes for ethylene/ethane separation based on tuning the pyrolysis conditions has also been demonstrated. © 2013 American Institute of Chemical Engineers.
The upper bound on the lowest mass halo
Jethwa, P.; Erkal, D.; Belokurov, V.
2018-01-01
We explore the connection between galaxies and dark matter haloes in the Milky Way (MW) and quantify the implications on properties of the dark matter particle and the phenomenology of low-mass galaxy formation. This is done through a probabilistic comparison of the luminosity function of MW dwarf satellite galaxies to models based on two suites of zoom-in simulations. One suite is dark-matter-only, while the other includes a disc component, therefore we can quantify the effect of the MW's baryonic disc on our results. We apply numerous stellar-mass-halo-mass (SMHM) relations allowing for multiple complexities: scatter, a characteristic break scale, and subhaloes which host no galaxy. In contrast to previous works, we push the model/data comparison to the faintest dwarfs by modelling observational incompleteness, allowing us to draw three new conclusions. First, we constrain the SMHM relation for 102 2.4 × 108 M⊙ (1σ). Secondly, by translating to a warm dark matter (WDM) cosmology, we bound the thermal relic mass mWDM > 2.9 keV at 95 per cent confidence, on a par with recent constraints from the Lyman-α forest. Lastly, we find that the observed number of ultra-faint MW dwarfs is in tension with the theoretical prediction that reionization prevents galaxy formation in almost all 108 M⊙ haloes. This can be tested with the next generation of deep imaging surveys. To this end, we predict the likely number of detectable satellite galaxies in the Subaru/Hyper Suprime-Cam survey and the Large Synoptic Survey Telescope. Confronting these predictions with future observations will be amongst our strongest tests of WDM and the effect reionization on low-mass systems.
Upper Bounds on the Number of Solutions of Binary Integer Programs
Jain, Siddhartha; Kadioglu, Serdar; Sellmann, Meinolf
We present a new method to compute upper bounds of the number of solutions of binary integer programming (BIP) problems. Given a BIP, we create a dynamic programming (DP) table for a redundant knapsack constraint which is obtained by surrogate relaxation. We then consider a Lagrangian relaxation of the original problem to obtain an initial weight bound on the knapsack. This bound is then refined through subgradient optimization. The latter provides a variety of Lagrange multipliers which allow us to filter infeasible edges in the DP table. The number of paths in the final table then provides an upper bound on the number of solutions. Numerical results show the effectiveness of our counting framework on automatic recording and market split problems.
A Method for Upper Bounding Long Term Growth of Network Access Speed
DEFF Research Database (Denmark)
Knudsen, Thomas Phillip; Pedersen, Jens Myrup; Madsen, Ole Brun
2004-01-01
The development in home Internet access speed has shown an exponential development with growth rates averaging 25% per year. For resource management in network provisioning it becomes an urgent question how long such growth can continue. This paper presents a method for calculating an upper bound...... to visual content driven growth, proceeding from datarate requirements for a full virtual environment. Scenarios and approaches for reducing datarate requirements are considered and discussed. The presented figures for an upper bound on network access speed are discussed and perspectives on further research...
Upper bounds on secret key agreement over lossy thermal bosonic channels
Kaur, Eneet; Wilde, Mark M.
2017-01-01
Upper bounds on the secret-key-agreement capacity of a quantum channel serve as a way to assess the performance of practical quantum-key-distribution protocols conducted over that channel. In particular, if a protocol employs a quantum repeater, achieving secret-key rates exceeding these upper bounds is a witness to having a working quantum repeater. In this paper, we extend a recent advance [Liuzzo-Scorpo et al., arXiv:1705.03017] in the theory of the teleportation simulation of single-mode ...
The upper bound of Pier Scour defined by selected laboratory and field data
Benedict, Stephen; Caldwell, Andral W.
2015-01-01
The U.S. Geological Survey, in cooperation with the South Carolina Department of Transportation, conducted several field investigations of pier scour in South Carolina (Benedict and Caldwell, 2006; Benedict and Caldwell, 2009) and used that data to develop envelope curves defining the upper bound of pier scour. To expand upon this previous work, an additional cooperative investigation was initiated to combine the South Carolina data with pier-scour data from other sources and evaluate the upper bound of pier scour with this larger data set. To facilitate this analysis, a literature review was made to identify potential sources of published pier-scour data, and selected data were compiled into a digital spreadsheet consisting of approximately 570 laboratory and 1,880 field measurements. These data encompass a wide range of laboratory and field conditions and represent field data from 24 states within the United States and six other countries. This extensive database was used to define the upper bound of pier-scour depth with respect to pier width encompassing the laboratory and field data. Pier width is a primary variable that influences pier-scour depth (Laursen and Toch, 1956; Melville and Coleman, 2000; Mueller and Wagner, 2005, Ettema et al. 2011, Arneson et al. 2012) and therefore, was used as the primary explanatory variable in developing the upper-bound envelope curve. The envelope curve provides a simple but useful tool for assessing the potential maximum pier-scour depth for pier widths of about 30 feet or less.
Computing arbitrage upper bounds on basket options in the presence of bid–ask spreads
Pena, J.; Vera, J.C.; Zuluaga, L.F.
2012-01-01
We study the problem of computing the sharpest static-arbitrage upper bound on the price of a European basket option, given the bid–ask prices of vanilla call options in the underlying securities. We show that this semi-infinite problem can be recast as a linear program whose size is linear in the
Upper and lower bounds for the ergodic capacity of MIMO Jacobi fading channels
Nafkha, Amor; Bonnefoi, Rémi
2017-05-01
In multi-(core/mode) optical fiber communication, the transmission channel can be modeled as a complex sub-matrix of the Haar-distributed unitary matrix (complex Jacobi unitary ensemble). In this letter, we present new analytical expressions of the upper and lower bounds for the ergodic capacity of multiple-input multiple-output Jacobi-fading channels. Recent results on the determinant of the Jacobi unitary ensemble are employed to derive a tight lower bound on the ergodic capacity. We use Jensen's inequality to provide an analytical closed-form upper bound to the ergodic capacity at any signal-to-noise ratio (SNR). Closed-form expressions of the ergodic capacity, at low and high SNR regimes, are also derived. Simulation results are presented to validate the accuracy of the derived expressions.
From, Steven G.
2010-01-01
We present several new bounds for certain sums of deviation probabilities involving sums of nonnegative random variables. These are based upon upper bounds for the moment generating functions of the sums. We compare these new bounds to those of Maurer [2], Bernstein [4], Pinelis [16], and Bentkus [3]. We also briefly discuss the infinitely divisible distributions case.
Non Uniform Selection of Solutions for Upper Bounding the 3-SAT Threshold
Hugel, Thomas
2010-01-01
We give a new insight into the upper bounding of the 3-SAT threshold by the first moment method. The best criteria developed so far to select the solutions to be counted discriminate among neighboring solutions on the basis of uniform information about each individual free variable. What we mean by uniform information, is information which does not depend on the solution: e.g. the number of positive/negative occurrences of the considered variable. What is new in our approach is that we use non uniform information about variables. Thus we are able to make a more precise tuning, resulting in a slight improvement on upper bounding the 3-SAT threshold for various models of formulas defined by their distributions.
An Improved Upper Bound for the Critical Probability of the Frog Model on Homogeneous Trees
Lebensztayn, Élcio; Machado, Fábio P.; Popov, Serguei
2005-04-01
We study the frog model on homogeneous trees, a discrete time system of simple symmetric random walks whose description is as follows. There are active and inactive particles living on the vertices. Each active particle performs a simple symmetric random walk having a geometrically distributed random lifetime with parameter (1 - p). When an active particle hits an inactive particle, the latter becomes active. We obtain an improved upper bound for the critical parameter for having indefinite survival of active particles, in the case of one-particle-per-vertex initial configuration. The main tool is to construct a class of branching processes which are dominated by the frog model and analyze their supercritical behavior. This approach allows us also to present an upper bound for the critical probability in the case of random initial configuration.
Some Upper Bounds on the Inverse Relative Dimension/Length Profile
Wang, Peisheng; Luo, Yuan; Vinck, A. J. Han
The generalized Hamming weight played an important role in coding theory. In the study of the wiretap channel of type II, the generalized Hamming weight was extended to a two-code format. Two equivalent concepts of the generalized Hamming weight hierarchy and its two-code format, are the inverse dimension/length profile (IDLP) and the inverse relative dimension/length profile (IRDLP), respectively. In this paper, the Singleton upper bound on the IRDLP is improved by using a quotient subcode set and a subset with respect to a generator matrix, respectively. If these new upper bounds on the IRDLP are achieved, in the corresponding coordinated two-party wire-tap channel of type II, the adversary cannot learn more from the illegitimate party.
Upper and lower bounds of ground-motion variabilities: implication for source properties
Cotton, Fabrice; Reddy-Kotha, Sreeram; Bora, Sanjay; Bindi, Dino
2017-04-01
One of the key challenges of seismology is to be able to analyse the physical factors that control earthquakes and ground-motion variabilities. Such analysis is particularly important to calibrate physics-based simulations and seismic hazard estimations at high frequencies. Within the framework of the development of ground-motion prediction equation (GMPE) developments, ground-motions residuals (differences between recorded ground motions and the values predicted by a GMPE) are computed. The exponential growth of seismological near-source records and modern GMPE analysis technics allow to partition these residuals into between- and a within-event components. In particular, the between-event term quantifies all those repeatable source effects (e.g. related to stress-drop or kappa-source variability) which have not been accounted by the magnitude-dependent term of the model. In this presentation, we first discuss the between-event variabilities computed both in the Fourier and Response Spectra domains, using recent high-quality global accelerometric datasets (e.g. NGA-west2, Resorce, Kiknet). These analysis lead to the assessment of upper bounds for the ground-motion variability. Then, we compare these upper bounds with lower bounds estimated by analysing seismic sequences which occurred on specific fault systems (e.g., located in Central Italy or in Japan). We show that the lower bounds of between-event variabilities are surprisingly large which indicates a large variability of earthquake dynamic properties even within the same fault system. Finally, these upper and lower bounds of ground-shaking variability are discussed in term of variability of earthquake physical properties (e.g., stress-drop and kappa_source).
Upper Bounds on the Degeneracy of the Ground State in Quantum Field Models
Directory of Open Access Journals (Sweden)
Asao Arai
2016-01-01
Full Text Available Axiomatic abstract formulations are presented to derive upper bounds on the degeneracy of the ground state in quantum field models including massless ones. In particular, given is a sufficient condition under which the degeneracy of the ground state of the perturbed Hamiltonian is less than or equal to the degeneracy of the ground state of the unperturbed one. Applications of the abstract theory to models in quantum field theory are outlined.
Some novel inequalities for fuzzy variables on the variance and its rational upper bound
Directory of Open Access Journals (Sweden)
Xiajie Yi
2016-02-01
Full Text Available Abstract Variance is of great significance in measuring the degree of deviation, which has gained extensive usage in many fields in practical scenarios. The definition of the variance on the basis of the credibility measure was first put forward in 2002. Following this idea, the calculation of the accurate value of the variance for some special fuzzy variables, like the symmetric and asymmetric triangular fuzzy numbers and the Gaussian fuzzy numbers, is presented in this paper, which turns out to be far more complicated. Thus, in order to better implement variance in real-life projects like risk control and quality management, we suggest a rational upper bound of the variance based on an inequality, together with its calculation formula, which can largely simplify the calculation process within a reasonable range. Meanwhile, some discussions between the variance and its rational upper bound are presented to show the rationality of the latter. Furthermore, two inequalities regarding the rational upper bound of variance and standard deviation of the sum of two fuzzy variables and their individual variances and standard deviations are proved. Subsequently, some numerical examples are illustrated to show the effectiveness and the feasibility of the proposed inequalities.
Upper bound on the gluino mass in supersymmetric models with extra matters
Directory of Open Access Journals (Sweden)
Takeo Moroi
2016-09-01
Full Text Available We discuss the upper bound on the gluino mass in supersymmetric models with vector-like extra matters. In order to realize the observed Higgs mass of 125 GeV, the gluino mass is bounded from above in supersymmetric models. With the existence of the vector-like extra matters at around TeV, we show that such an upper bound on the gluino mass is significantly reduced compared to the case of minimal supersymmetric standard model. This is due to the fact that radiatively generated stop masses as well the stop trilinear coupling are enhanced in the presence of the vector-like multiplets. In a wide range of parameter space of the model with extra matters, particularly with sizable tanβ (which is the ratio of the vacuum expectation values of the two Higgs bosons, the gluino is required to be lighter than ∼3 TeV, which is likely to be within the reach of forthcoming LHC experiment.
Tight upper bound for the maximal quantum value of the Svetlichny operators
Li, Ming; Shen, Shuqian; Jing, Naihuan; Fei, Shao-Ming; Li-Jost, Xianqing
2017-10-01
It is a challenging task to detect genuine multipartite nonlocality (GMNL). In this paper, the problem is considered via computing the maximal quantum value of Svetlichny operators for three-qubit systems and a tight upper bound is obtained. The constraints on the quantum states for the tightness of the bound are also presented. The approach enables us to give the necessary and sufficient conditions of violating the Svetlichny inequality (SI) for several quantum states, including the white and color noised Greenberger-Horne-Zeilinger (GHZ) states. The relation between the genuine multipartite entanglement concurrence and the maximal quantum value of the Svetlichny operators for mixed GHZ class states is also discussed. As the SI is useful for the investigation of GMNL, our results give an effective and operational method to detect the GMNL for three-qubit mixed states.
Wang, Dong; Tsui, Kwok-Leung
2018-01-01
Bearing-supported shafts are widely used in various machines. Due to harsh working environments, bearing performance degrades over time. To prevent unexpected bearing failures and accidents, bearing performance degradation assessment becomes an emerging topic in recent years. Bearing performance degradation assessment aims to evaluate the current health condition of a bearing through a bearing health indicator. In the past years, many signal processing and data mining based methods were proposed to construct bearing health indicators. However, the upper and lower bounds of these bearing health indicators were not theoretically calculated and they strongly depended on historical bearing data including normal and failure data. Besides, most health indicators are dimensional, which connotes that these health indicators are prone to be affected by varying operating conditions, such as varying speeds and loads. In this paper, based on the principle of squared envelope analysis, we focus on theoretical investigation of bearing performance degradation assessment in the case of additive Gaussian noises, including distribution establishment of squared envelope, construction of a generalized dimensionless bearing health indicator, and mathematical calculation of the upper and lower bounds of the generalized dimensionless bearing health indicator. Then, analyses of simulated and real bearing run to failure data are used as two case studies to illustrate how the generalized dimensionless health indicator works and demonstrate its effectiveness in bearing performance degradation assessment. Results show that squared envelope follows a noncentral chi-square distribution and the upper and lower bounds of the generalized dimensionless health indicator can be mathematically established. Moreover, the generalized dimensionless health indicator is sensitive to an incipient bearing defect in the process of bearing performance degradation.
Improved upper bounds on Kaluza-Klein gravity with current Solar System experiments and observations
Energy Technology Data Exchange (ETDEWEB)
Deng, Xue-Mei [Chinese Academy of Sciences, Purple Mountain Observatory, Nanjing (China); Xie, Yi [Nanjing University, School of Astronomy and Space Science, Nanjing (China); Shanghai Key Laboratory of Space Navigation and Position Techniques, Shanghai (China); Nanjing University, Ministry of Education, Key Laboratory of Modern Astronomy and Astrophysics, Nanjing (China)
2015-11-15
As an extension of previous works on classical tests of Kaluza-Klein (KK) gravity and as an attempt to find more stringent constraints on this theory, its effects on physical experiments and astronomical observations conducted in the Solar System are studied. We investigate the gravitational time delay at inferior conjunction caused by KK gravity, and use new Solar System ephemerides and the observation of Cassini to strengthen constraints on KK gravity by up to two orders of magnitude. These improved upper bounds mean that the fifth-dimensional space in the soliton case is a very flat extra dimension in the Solar System, even in the vicinity of the Sun. (orig.)
DEFF Research Database (Denmark)
Lange-Hansen, Preben
1998-01-01
Purpose: None of the published formulae for obtaining upper bounds for residual deflections in elastoplastic structures with quasistatically varying loads (shakedown problems) has been able to result in theoretical maximum values of residual deflections. Therefore, the purpose of the report...... deflection.Results: The assessment has resulted in placing Ponter's formula as the best, followed the formulae of Lange-Hansen and Nielsen, Capurso and finally that of Dorosz, the results of three last mentioned being found to lie in average 4%, 46% and 60%, respectively, over the average results from Ponter...... formulae.Keywords: Plastic analysis, shakedown, residual deflections...
Directory of Open Access Journals (Sweden)
Ali Tavasoli
2012-01-01
Full Text Available Nonlinear vehicle control allocation is achieved through distributing the task of vehicle control among individual tire forces, which are constrained to nonlinear saturation conditions. A high-level sliding mode control with adaptive upper bounds is considered to assess the body yaw moment and lateral force for the vehicle motion. The proposed controller only requires the online adaptation of control gains without acquiring the knowledge of upper bounds on system uncertainties. Static and dynamic control allocation approaches have been formulated to distribute high-level control objectives among the system inputs. For static control allocation, the interior-point method is applied to solve the formulated nonlinear optimization problem. Based on the dynamic control allocation method, a dynamic update law is derived to allocate vehicle control to tire forces. The allocated tire forces are fed into a low-level control module, where the applied torque and active steering angle at each wheel are determined through a slip-ratio controller and an inverse tire model. Computer simulations are used to prove the significant effects of the proposed control allocation methods on improving the stability and handling performance. The advantages and limitations of each method have been discussed, and conclusions have been derived.
Safe Upper-Bounds Inference of Energy Consumption for Java Bytecode Applications
Navas, Jorge; Mendez-Lojo, Mario; Hermenegildo, Manuel V.
2008-01-01
Many space applications such as sensor networks, on-board satellite-based platforms, on-board vehicle monitoring systems, etc. handle large amounts of data and analysis of such data is often critical for the scientific mission. Transmitting such large amounts of data to the remote control station for analysis is usually too expensive for time-critical applications. Instead, modern space applications are increasingly relying on autonomous on-board data analysis. All these applications face many resource constraints. A key requirement is to minimize energy consumption. Several approaches have been developed for estimating the energy consumption of such applications (e.g. [3, 1]) based on measuring actual consumption at run-time for large sets of random inputs. However, this approach has the limitation that it is in general not possible to cover all possible inputs. Using formal techniques offers the potential for inferring safe energy consumption bounds, thus being specially interesting for space exploration and safety-critical systems. We have proposed and implemented a general frame- work for resource usage analysis of Java bytecode [2]. The user defines a set of resource(s) of interest to be tracked and some annotations that describe the cost of some elementary elements of the program for those resources. These values can be constants or, more generally, functions of the input data sizes. The analysis then statically derives an upper bound on the amount of those resources that the program as a whole will consume or provide, also as functions of the input data sizes. This article develops a novel application of the analysis of [2] to inferring safe upper bounds on the energy consumption of Java bytecode applications. We first use a resource model that describes the cost of each bytecode instruction in terms of the joules it consumes. With this resource model, we then generate energy consumption cost relations, which are then used to infer safe upper bounds. How
Using a Water Balance Model to Bound Potential Irrigation Development in the Upper Blue Nile Basin
Jain Figueroa, A.; McLaughlin, D.
2016-12-01
The Grand Ethiopian Renaissance Dam (GERD), on the Blue Nile is an example of water resource management underpinning food, water and energy security. Downstream countries have long expressed concern about water projects in Ethiopia because of possible diversions to agricultural uses that could reduce flow in the Nile. Such diversions are attractive to Ethiopia as a partial solution to its food security problems but they could also conflict with hydropower revenue from GERD. This research estimates an upper bound on diversions above the GERD project by considering the potential for irrigated agriculture expansion and, in particular, the availability of water and land resources for crop production. Although many studies have aimed to simulate downstream flows for various Nile basin management plans, few have taken the perspective of bounding the likely impacts of upstream agricultural development. The approach is to construct an optimization model to establish a bound on Upper Blue Nile (UBN) agricultural development, paying particular attention to soil suitability and seasonal variability in climate. The results show that land and climate constraints impose significant limitations on crop production. Only 25% of the land area is suitable for irrigation due to the soil, slope and temperature constraints. When precipitation is also considered only 11% of current land area could be used in a way that increases water consumption. The results suggest that Ethiopia could consume an additional 3.75 billion cubic meters (bcm) of water per year, through changes in land use and storage capacity. By exploiting this irrigation potential, Ethiopia could potentially decrease the annual flow downstream of the UBN by 8 percent from the current 46 bcm/y to the modeled 42 bcm/y.
Luo, FuSheng; Lin, Qun; Xie, HeHu
2012-05-01
This article is devoted to computing the lower and upper bounds of the Laplace eigenvalue problem. By using the special nonconforming finite elements, i.e., enriched Crouzeix-Raviart element and extension $Q_1^{\\rm rot}$, we get the lower bound of the eigenvalue. Additionally, we also use conforming finite elements to do the postprocessing to get the upper bound of the eigenvalue. The postprocessing method need only to solve the corresponding source problems and a small eigenvalue problem if higher order postprocessing method is implemented. Thus, we can obtain the lower and upper bounds of the eigenvalues simultaneously by solving eigenvalue problem only once. Some numerical results are also presented to validate our theoretical analysis.
Local Model Checking of Weighted CTL with Upper-Bound Constraints
DEFF Research Database (Denmark)
Jensen, Jonas Finnemann; Larsen, Kim Guldstrand; Srba, Jiri
2013-01-01
We present a symbolic extension of dependency graphs by Liu and Smolka in order to model-check weighted Kripke structures against the logic CTL with upper-bound weight constraints. Our extension introduces a new type of edges into dependency graphs and lifts the computation of fixed-points from...... boolean domain to nonnegative integers in order to cope with the weights. We present both global and local algorithms for the fixed-point computation on symbolic dependency graphs and argue for the advantages of our approach compared to the direct encoding of the model checking problem into dependency...... graphs. We implement all algorithms in a publicly available tool prototype and evaluate them on several experiments. The principal conclusion is that our local algorithm is the most efficient one with an order of magnitude improvement for model checking problems with a high number of “witnesses”....
An upper-bound assessment of the benefits of reducing perchlorate in drinking water.
Lutter, Randall
2014-10-01
The Environmental Protection Agency plans to issue new federal regulations to limit drinking water concentrations of perchlorate, which occurs naturally and results from the combustion of rocket fuel. This article presents an upper-bound estimate of the potential benefits of alternative maximum contaminant levels for perchlorate in drinking water. The results suggest that the economic benefits of reducing perchlorate concentrations in drinking water are likely to be low, i.e., under $2.9 million per year nationally, for several reasons. First, the prevalence of detectable perchlorate in public drinking water systems is low. Second, the population especially sensitive to effects of perchlorate, pregnant women who are moderately iodide deficient, represents a minority of all pregnant women. Third, and perhaps most importantly, reducing exposure to perchlorate in drinking water is a relatively ineffective way of increasing iodide uptake, a crucial step linking perchlorate to health effects of concern. © 2014 Society for Risk Analysis.
Upper bounds for the number of limit cycles of polynomial differential systems
Directory of Open Access Journals (Sweden)
Selma Ellaggoune
2016-12-01
Full Text Available For $\\varepsilon$ small we consider the number of limit cycles of the polynomial differential system $$ \\dot{x}=y-f_1(x,yy, \\quad \\dot{y}=-x-g_2(x,y-f_2(x,yy, $$ where $f_1(x,y=\\varepsilon f_{11}(x,y+\\varepsilon^2f_{12}(x,y$, $g_2(x,y=\\varepsilon g_{21}(x,y+\\varepsilon^2 g_{22}(x,y$ and $f_2(x,y=\\varepsilon f_{21}(x,y+\\varepsilon^2 f_{22}(x,y$ where $f_{1i}, f_{2i}, g_{2i}$ have degree $l, n,m$ respectively for each $i=1,2$. We provide an accurate upper bound of the maximum number of limit cycles that this class of systems can have bifurcating from the periodic orbits of the linear center $\\dot{x}=y, \\dot{y}=-x$ using the averaging theory of first and second order. We give an example for which this bound is reached.
Energy Technology Data Exchange (ETDEWEB)
Saucier, Antoine [Ecole Polytechnique de Montreal, C.P. 6079, Station centre-ville, Montreal (Que.), H3C-3A7 (Canada)]. E-mail: Antoine.Saucier@polymtl.ca; Soumis, Francois [Ecole Polytechnique de Montreal, C.P. 6079, Station centre-ville, Montreal (Que.), H3C-3A7 (Canada)]. E-mail: Francois.Soumis@gerad.ca
2006-06-15
The characterization of irregular objects with fractal methods often leads to the estimation of the slope of a function which is plotted versus a scale parameter. The slope is usually obtained with a linear regression. The problem is that the fit is usually not acceptable from the statistical standpoint. We propose a new approach in which we use two straight lines to bound the data from above and from below. We call these lines the upper and lower linear bounds. We propose to define these bounds as the solution of an optimization problem. We discuss the solution of this problem and we give an algorithm to obtain its solution. We use the difference between the upper and lower linear bounds to define a measure of the degree of linearity in the scaling range. We illustrate our method by analyzing the fluctuations of the variogram in a microresistivity well log from an oil reservoir in the North Sea.
Energy Technology Data Exchange (ETDEWEB)
Datta, Nilanjana, E-mail: n.datta@statslab.cam.ac.uk [Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Hsieh, Min-Hsiu, E-mail: Min-Hsiu.Hsieh@uts.edu.au [Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, NSW 2007 (Australia); Oppenheim, Jonathan, E-mail: j.oppenheim@ucl.ac.uk [Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom); Department of Computer Science and Centre for Quantum Technologies, National University of Singapore, Singapore 119615 (Singapore)
2016-05-15
State redistribution is the protocol in which given an arbitrary tripartite quantum state, with two of the subsystems initially being with Alice and one being with Bob, the goal is for Alice to send one of her subsystems to Bob, possibly with the help of prior shared entanglement. We derive an upper bound on the second order asymptotic expansion for the quantum communication cost of achieving state redistribution with a given finite accuracy. In proving our result, we also obtain an upper bound on the quantum communication cost of this protocol in the one-shot setting, by using the protocol of coherent state merging as a primitive.
Frisbee, Joseph H., Jr.
2015-01-01
Upper bounds on high speed satellite collision probability, PC †, have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum PC. If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but potentially useful Pc upper bound.
Directory of Open Access Journals (Sweden)
Carolina Bermudo
2016-07-01
Full Text Available Focusing on incremental bulk metal forming processes, the indentation process is gaining interest as a fundamental part of these kinds of processes. This paper presents the analysis of the pressure obtained in indentation under the influence of different punch geometries. To this end, an innovative Upper Bound Theorem (UBT based solution is introduced. This new solution can be easily applied to estimate the necessary force that guarantees plastic deformation by an indentation process. In this work, we propose an accurate analytical approach to analyse indentation under different punches. The new Modular Upper Bound (MUB method presents a simpler and faster application. Additionally, its complexity is not considerably increased by the addition of more Triangular Rigid Zones. In addition, a two-dimensional indentation model is designed and implemented using the Finite Element Method (FEM. The comparison of the two methods applied to the indentation process analysed—the new Modular Upper Bound technique and the Finite Element Method—reveal close similarities, the new Modular Upper Bound being more computationally efficient.
Directory of Open Access Journals (Sweden)
Z. Li
2017-11-01
Full Text Available Export production reflects the amount of organic matter transferred from the ocean surface to depth through biological processes. This export is in large part controlled by nutrient and light availability, which are conditioned by mixed layer depth (MLD. In this study, building on Sverdrup's critical depth hypothesis, we derive a mechanistic model of an upper bound on carbon export based on the metabolic balance between photosynthesis and respiration as a function of MLD and temperature. We find that the upper bound is a positively skewed bell-shaped function of MLD. Specifically, the upper bound increases with deepening mixed layers down to a critical depth, beyond which a long tail of decreasing carbon export is associated with increasing heterotrophic activity and decreasing light availability. We also show that in cold regions the upper bound on carbon export decreases with increasing temperature when mixed layers are deep, but increases with temperature when mixed layers are shallow. A meta-analysis shows that our model envelopes field estimates of carbon export from the mixed layer. When compared to satellite export production estimates, our model indicates that export production in some regions of the Southern Ocean, particularly the subantarctic zone, is likely limited by light for a significant portion of the growing season.
Sun, Wei; Chou, Chih-Ping; Stacy, Alan W; Ma, Huiyan; Unger, Jennifer; Gallaher, Peggy
2007-02-01
Cronbach's a is widely used in social science research to estimate the internal consistency of reliability of a measurement scale. However, when items are not strictly parallel, the Cronbach's a coefficient provides a lower-bound estimate of true reliability, and this estimate may be further biased downward when items are dichotomous. The estimation of standardized Cronbach's a for a scale with dichotomous items can be improved by using the upper bound of coefficient phi. SAS and SPSS macros have been developed in this article to obtain standardized Cronbach's a via this method. The simulation analysis showed that Cronbach's a from upper-bound phi might be appropriate for estimating the real reliability when standardized Cronbach's a is problematic.
Upper Bounds on the Capacity of Binary Channels with Causal Adversaries
Dey, Bikash Kumar; Langberg, Michael; Sarwate, Anand D
2012-01-01
In this work we consider the communication of information in the presence of a causal adversarial jammer. In the setting under study, a sender wishes to communicate a message to a receiver by transmitting a codeword $\\mathbf{x}=(x_1,...,x_n)$ bit-by-bit over a communication channel. The sender and receiver do not share common randomness. The adversarial jammer can view the transmitted bits $x_i$ one at a time, and can change up to a $p$-fraction of them. However, the decisions of the jammer must be made in a causal manner. Namely, for each bit $x_i$ the jammer's decision on whether to corrupt it or not (and on how to change it) must depend only on $x_j$ for $j \\leq i$. This is in contrast to the "classical" adversarial jamming situations in which the jammer has no knowledge of $\\mathbf{x}$ or complete knowledge of $\\mathbf{x}$. In this work, we present upper bounds on the capacity which hold for both deterministic and stochastic encoding schemes.
Upper bound of errors in solving the inverse problem of identifying a voice source
Leonov, A. S.; Sorokin, V. N.
2017-09-01
The paper considers the inverse problem of finding the shape of a voice-source pulse from a specified segment of a speech signal using a special mathematical model that relates these quantities. A variational method for solving the formulated inverse problem for two new parametric classes of sources is proposed: a piecewise-linear source and an A-source. The error in the obtained approximate solutions of the inverse problem is considered, and a technique to numerically estimate this error is proposed, which is based on the theory of a posteriori estimates of the accuracy in solving ill-posed problems. A computer study of the adequacy of the proposed models of sources, and a study of the a posteriori estimates of the accuracy in solving inverse problems for such sources were performed using various types of voice signals. Numerical experiments for speech signals showed satisfactory properties of such a posteriori estimates, which represent the upper bounds of possible errors in solving the inverse problem. The estimate of the most probable error in determining the source-pulse shapes for the investigated speech material is on average 7%. It is noted that the a posteriori accuracy estimates can be used as a criterion for the quality of determining the voice-source pulse shape in the speaker-identification problem.
An Entropy-Based Upper Bound Methodology for Robust Predictive Multi-Mode RCPSP Schedules
Directory of Open Access Journals (Sweden)
Angela Hsiang-Ling Chen
2014-09-01
Full Text Available Projects are an important part of our activities and regardless of their magnitude, scheduling is at the very core of every project. In an ideal world makespan minimization, which is the most commonly sought objective, would give us an advantage. However, every time we execute a project we have to deal with uncertainty; part of it coming from known sources and part remaining unknown until it affects us. For this reason, it is much more practical to focus on making our schedules robust, capable of handling uncertainty, and even to determine a range in which the project could be completed. In this paper we focus on an approach to determine such a range for the Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP, a widely researched, NP-complete problem, but without adding any subjective considerations to its estimation. We do this by using a concept well known in the domain of thermodynamics, entropy and a three-stage approach. First we use Artificial Bee Colony (ABC—an effective and powerful meta-heuristic—to determine a schedule with minimized makespan which serves as a lower bound. The second stage defines buffer times and creates an upper bound makespan using an entropy function, with the advantage over other methods that it only considers elements which are inherent to the schedule itself and does not introduce any subjectivity to the buffer time generation. In the last stage, we use the ABC algorithm with an objective function that seeks to maximize robustness while staying within the makespan boundaries defined previously and in some cases even below the lower boundary. We evaluate our approach with two different benchmarks sets: when using the PSPLIB for the MRCPSP benchmark set, the computational results indicate that it is possible to generate robust schedules which generally result in an increase of less than 10% of the best known solutions while increasing the robustness in at least 20% for practically every
Explicit Lower and Upper Bounds on the Entangled Value of Multiplayer XOR Games
Briët, Jop; Vidick, Thomas
2013-07-01
The study of quantum-mechanical violations of Bell inequalities is motivated by the investigation, and the eventual demonstration, of the nonlocal properties of entanglement. In recent years, Bell inequalities have found a fruitful re-formulation using the language of multiplayer games originating from Computer Science. This paper studies the nonlocal properties of entanglement in the context of the simplest such games, called XOR games. When there are two players, it is well known that the maximum bias—the advantage over random play—of players using entanglement can be at most a constant times greater than that of classical players. Recently, Pérez-García et al. (Commun. Mathe. Phys. 279:455, 2008) showed that no such bound holds when there are three or more players: the use of entanglement can provide an unbounded advantage, and scale with the number of questions in the game. Their proof relies on non-trivial results from operator space theory, and gives a non-explicit existence proof, leading to a game with a very large number of questions and only a loose control over the local dimension of the players' shared entanglement. We give a new, simple and explicit (though still probabilistic) construction of a family of three-player XOR games which achieve a large quantum-classical gap (QC-gap). This QC-gap is exponentially larger than the one given by Pérez-García et. al. in terms of the size of the game, achieving a QC-gap of order {√{N}} with N 2 questions per player. In terms of the dimension of the entangled state required, we achieve the same (optimal) QC-gap of {√{N}} for a state of local dimension N per player. Moreover, the optimal entangled strategy is very simple, involving observables defined by tensor products of the Pauli matrices. Additionally, we give the first upper bound on the maximal QC-gap in terms of the number of questions per player, showing that our construction is only quadratically off in that respect. Our results rely on
Sources, transport, and mixing of particle-bound PAHs fluxes in the upper Neckar River basin
Schwientek, Marc; Rügner, Hermann; Qin, Xintong; Scherer, Ulrike; Grathwohl, Peter
2016-04-01
Transport of many urban pollutants in rivers is coupled to transport of suspended particles. The degree of contamination of these suspended particles depends on the mixture of "polluted" urban and "clean" background particles. Recent results have shown that, in several meso-scale catchments studied in southwestern and eastern Germany, the loading of particles with polycyclic aromatic hydrocarbons (PAHs) was stable over time and characteristic for each catchment. The absence of significant long-term trends or pronounced changes of the catchment-specific loadings indicate that either input and output of PAHs into the stream networks are largely at steady state or that storage of PAHs in the sediments within the stream network are sufficient to smooth out larger fluctuations. Moreover, it was shown that the contamination of sediments and suspended particles with PAHs is proportional to the number of inhabitants per suspended sediment flux in a catchment. These processes are being further studied at larger scale in the upper Neckar River basin (2300 km²) in southwestern Germany. This basin, located between the mountain ranges of the Black Forest and the Swabian Alb, comprises sub-catchments that are diverse in terms of urban impact, geology (ranging from gypsum and limetstones to siliceous sandstones) and hydrology (dynamics driven either by summerly convective events or by winterly frontal systems and snow melt). Accordingly, quality and quantity of particles being released in the sub-catchments as potential vectors for hydrophobic pollutants differ; and so do the events that mobilize the particles. These settings enable the investigation of how particle-bound pollutant fluxes generated at the meso-scale are mixed and transported at larger scales when introduced into a higher order river. A prominent research question is whether varying contributions from contrasting sub-catchments lead to changing contamination patterns in the main stem or if the sediment storage in
Paul L. Patterson; Mark Finco
2009-01-01
This paper explores the information FIA data can produce regarding forest types that were not sampled and develops the equations necessary to define the upper confidence bounds on not-sampled forest types. The problem is reduced to a Bernoulli variable. This simplification allows the upper confidence bounds to be calculated based on Cochran (1977). Examples are...
Paul L. Patterson; Mark Finco
2011-01-01
This paper explores the information forest inventory data can produce regarding forest types that were not sampled and develops the equations necessary to define the upper confidence bounds on not-sampled forest types. The problem is reduced to a Bernoulli variable. This simplification allows the upper confidence bounds to be calculated based on Cochran (1977)....
Energy Technology Data Exchange (ETDEWEB)
Ackroyd, R.T. (UKAEA Risley Nuclear Power Development Establishment. Technical Services and Planning Directorate); Splawski, B.A. (Queen Mary Coll., London (UK). Dept. of Nuclear Engineering)
1982-01-01
It is shown that the finite element method also shares with Monte Carlo the capability to bracket local characteristics of a solution, such as the reaction rate for a small locality. The bracketing bounds for the Monte Carlo method have a statistical error, whereas these bounds are rigorous for the finite element method. The latter bounds for a locality of a system are obtained by a bi-variational method with the aid of an associated system. For cell problems very tight bounds can be computed, but in deep-penetration problems for shields there are some difficulties to be overcome. Reasons are advanced for the difficulties.
Pre-Test Assessment of the Upper Bound of the Drag Coefficient Repeatability of a Wind Tunnel Model
Ulbrich, N.; L'Esperance, A.
2017-01-01
A new method is presented that computes a pre{test estimate of the upper bound of the drag coefficient repeatability of a wind tunnel model. This upper bound is a conservative estimate of the precision error of the drag coefficient. For clarity, precision error contributions associated with the measurement of the dynamic pressure are analyzed separately from those that are associated with the measurement of the aerodynamic loads. The upper bound is computed by using information about the model, the tunnel conditions, and the balance in combination with an estimate of the expected output variations as input. The model information consists of the reference area and an assumed angle of attack. The tunnel conditions are described by the Mach number and the total pressure or unit Reynolds number. The balance inputs are the partial derivatives of the axial and normal force with respect to all balance outputs. Finally, an empirical output variation of 1.0 microV/V is used to relate both random instrumentation and angle measurement errors to the precision error of the drag coefficient. Results of the analysis are reported by plotting the upper bound of the precision error versus the tunnel conditions. The analysis shows that the influence of the dynamic pressure measurement error on the precision error of the drag coefficient is often small when compared with the influence of errors that are associated with the load measurements. Consequently, the sensitivities of the axial and normal force gages of the balance have a significant influence on the overall magnitude of the drag coefficient's precision error. Therefore, results of the error analysis can be used for balance selection purposes as the drag prediction characteristics of balances of similar size and capacities can objectively be compared. Data from two wind tunnel models and three balances are used to illustrate the assessment of the precision error of the drag coefficient.
Upper and lower bounds for stochastic processes modern methods and classical problems
Talagrand, Michel
2014-01-01
The book develops modern methods and in particular the "generic chaining" to bound stochastic processes. This methods allows in particular to get optimal bounds for Gaussian and Bernoulli processes. Applications are given to stable processes, infinitely divisible processes, matching theorems, the convergence of random Fourier series, of orthogonal series, and to functional analysis. The complete solution of a number of classical problems is given in complete detail, and an ambitious program for future research is laid out.
Directory of Open Access Journals (Sweden)
Jie Liu
2014-01-01
discusses the nonconforming rotated Q1 finite element computable upper bound a posteriori error estimate of the boundary value problem established by M. Ainsworth and obtains efficient computable upper bound a posteriori error indicators for the eigenvalue problem associated with the boundary value problem. We extend the a posteriori error estimate to the Steklov eigenvalue problem and also derive efficient computable upper bound a posteriori error indicators. Finally, through numerical experiments, we verify the validity of the a posteriori error estimate of the boundary value problem; meanwhile, the numerical results show that the a posteriori error indicators of the eigenvalue problem and the Steklov eigenvalue problem are effective.
Determining Upper Bounds for the Clay-squirt Effect in Clay Bearing Sandstone
DEFF Research Database (Denmark)
Sørensen, Morten Kanne; Fabricius, Ida Lykke
2012-01-01
Sonic measurements of saturated bulk moduli of clay bearing sandstones show larger values than expected by Gassmann modelling from dry rock properties. This causes difficulties in extrapolation of laboratory data to different saturants or frequencies. Squirt flow from the clay phase of the rock...... have been proposed as the mechanism behind this stiffening. Low fluid mobility and low bulk modulus of the clay phase cause excess pore-pressures to be induced and retained in the phase leading to stiffening. A quantitative bound is formulated for this effect through the determination of the Hashin......-Shtrikman bounds for the case of a drained clay phase and an undrained clay phase. The bound is achieved by analyzing the influence of the relevant parameters with subsequent grouping using reasonable correlations. Through this approach only the saturated bulk modulus of the quartz phase and the clay fraction...
Energy Technology Data Exchange (ETDEWEB)
Luque, A., E-mail: a.luque@upm.es [Instituto de Energía Solar, Universidad Politécnica de Madrid (Spain); Mellor, A.; Tobías, I.; Antolín, E.; Linares, P.G.; Ramiro, I.; Martí, A. [Instituto de Energía Solar, Universidad Politécnica de Madrid (Spain)
2013-03-15
The effective mass Schrödinger equation of a QD of parallelepipedic shape with a square potential well is solved by diagonalizing the exact Hamiltonian matrix developed in a basis of separation-of-variables wavefunctions. The expected below bandgap bound states are found not to differ very much from the former approximate calculations. In addition, the presence of bound states within the conduction band is confirmed. Furthermore, filamentary states bounded in two dimensions and extended in one dimension and layered states with only one dimension bounded, all within the conduction band—which are similar to those originated in quantum wires and quantum wells—coexist with the ordinary continuum spectrum of plane waves. All these subtleties are absent in spherically shaped quantum dots, often used for modeling.
Energy Technology Data Exchange (ETDEWEB)
Gerhold, Philipp [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2009-12-15
We study a lattice Higgs-Yukawa model emulating the same Higgs-fermion coupling structure as in the Higgs sector of the electroweak Standard Model, in particular, obeying a Ginsparg- Wilson version of the underlying SU(2){sub L} x U(1){sub Y} symmetry, being a global symmetry here due to the neglection of gauge fields in this model. In this paper we present our results on the cutoffdependent upper Higgs boson mass bound at several selected values of the cutoff parameter {lambda}. (orig.)
1987-08-01
of the absolute difference between the random variable and its mean.Gassmann and Ziemba 119861 provide a weaker bound that does not require...2.8284, and EX4tV) -12 EX’iX) = -42. Hence C = -2 -€t* i-4’]= I-- . 1213. £1 2 5 COMPARISONS OF BOUNDS IN IIn Gassmann and Ziemba 11986) extend an idea...solution of the foLLowing Linear program: (see Gassmann, Ziemba (1986),Theorem 1) m m m-GZ=max(XT(vi) I: z. 1=1,Z vo=x io (5.1hk i-l i=i i=1 I I where 0
Directory of Open Access Journals (Sweden)
Hervé Le Sourne
2012-01-01
Full Text Available This paper presents a user-friendly rapid prediction tool of damage to struck and striking vessels in a ship collision event. To do this, the so-called upper bound theorem is applied to calculate internal forces and energies of any substructure involved in the ships crushing process. At each increment of indentation, the total crushing force is transmitted to the external dynamics MCOL program, which calculates the global ship motion correction by solving the hydrodynamic force equilibrium equations. As a first step, the paper gives a brief description of the upper bound method originally developed for perpendicular collisions and recently enhanced for oblique ones. Then, the theory developed in MCOL program for large rotational ship movements is detailed. By comparing results obtained with and without MCOL, the importance of hydrodynamic effects is highlighted. Some simulation results are compared with results provided by classical nonlinear finite element calculations. Finally, by using the developed analytical tool, which mixes internal and external dynamics, different crushing scenarios including oblique collisions are investigated and the influence of some collision parameters like longitudinal and vertical impact location, impact angle, and struck ship velocity is studied.
Bermudo, Carolina; Sevilla, Lorenzo; Martín, Francisco; Trujillo, Francisco Javier
2017-01-01
The application of incremental processes in the manufacturing industry is having a great development in recent years. The first stage of an Incremental Forming Process can be defined as an indentation. Because of this, the indentation process is starting to be widely studied, not only as a hardening test but also as a forming process. Thus, in this work, an analysis of the indentation process under the new Modular Upper Bound perspective has been performed. The modular implementation has several advantages, including the possibility of the introduction of different parameters to extend the study, such as the friction effect, the temperature or the hardening effect studied in this paper. The main objective of the present work is to analyze the three hardening models developed depending on the material characteristics. In order to support the validation of the hardening models, finite element analyses of diverse materials under an indentation are carried out. Results obtained from the Modular Upper Bound are in concordance with the results obtained from the numerical analyses. In addition, the numerical and analytical methods are in concordance with the results previously obtained in the experimental indentation of annealed aluminum A92030. Due to the introduction of the hardening factor, the new modular distribution is a suitable option for the analysis of indentation process. PMID:28772914
An upper bound on the minimum number of monomials required to separate dichotomies of {-1, 1}n.
Oztop, Erhan
2006-12-01
It is known that any dichotomy of {-1, 1}n can be learned (separated) with a higher-order neuron (polynomial function) with 2n inputs (monomials). In general, less than 2n monomials are sufficient to solve a given dichotomy. In spite of the efforts to develop algorithms for finding solutions with fewer monomials, there have been relatively fewer studies investigating maximum density (Pi(n)), the minimum number of monomials that would suffice to separate an arbitrary dichotomy of {-1, 1}n . This article derives a theoretical (upper) bound for this quantity, superseding previously known bounds. The main theorem here states that for any binary classification problem in {-1, 1}n (n > 1), one can always find a polynomial function solution with 2n -2n/4 or fewer monomials. In particular, any dichotomy of {-1, 1}n can be learned by a higher-order neuron with a fan-in of 2n -2n/4 or less. With this result, for the first time, a deterministic ratio bound independent of n is established as Pi(n)/2n < or = 0 75. The main theorem is constructive, so it provides a deterministic algorithm for achieving the theoretical result. The study presented provides the basic mathematical tools and forms the basis for further analyses that may have implications for neural computation mechanisms employed in the cerebral cortex.
Bounds for Asian basket options
Deelstra, Griselda; Diallo, Ibrahima; Vanmaele, Michèle
2008-09-01
In this paper we propose pricing bounds for European-style discrete arithmetic Asian basket options in a Black and Scholes framework. We start from methods used for basket options and Asian options. First, we use the general approach for deriving upper and lower bounds for stop-loss premia of sums of non-independent random variables as in Kaas et al. [Upper and lower bounds for sums of random variables, Insurance Math. Econom. 27 (2000) 151-168] or Dhaene et al. [The concept of comonotonicity in actuarial science and finance: theory, Insurance Math. Econom. 31(1) (2002) 3-33]. We generalize the methods in Deelstra et al. [Pricing of arithmetic basket options by conditioning, Insurance Math. Econom. 34 (2004) 55-57] and Vanmaele et al. [Bounds for the price of discrete sampled arithmetic Asian options, J. Comput. Appl. Math. 185(1) (2006) 51-90]. Afterwards we show how to derive an analytical closed-form expression for a lower bound in the non-comonotonic case. Finally, we derive upper bounds for Asian basket options by applying techniques as in Thompson [Fast narrow bounds on the value of Asian options, Working Paper, University of Cambridge, 1999] and Lord [Partially exact and bounded approximations for arithmetic Asian options, J. Comput. Finance 10 (2) (2006) 1-52]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and time-to-maturity.
Upper bounds on the non- 3-colourability threshold of random graphs
Directory of Open Access Journals (Sweden)
Nikolaos Fountoulakis
2002-12-01
Full Text Available We present a full analysis of the expected number of `rigid' 3-colourings of a sparse random graph. This shows that, if the average degree is at least 4.99, then as n → ∞ the expected number of such colourings tends to 0 and so the probability that the graph is 3-colourable tends to 0. (This result is tight, in that with average degree 4.989 the expected number tends to ∞. This bound appears independently in Kaporis et al. [Kap]. We then give a minor improvement, showing that the probability that the graph is 3-colourable tends to 0 if the average degree is at least 4.989.
$f(T)$ gravity: effects on astronomical observation and Solar System experiments and upper-bounds
Xie, Yi
2013-01-01
As an extension of a previous work in which perihelion advances are considered only and as an attempt to find more stringent constraints on its parameters, we investigate effects on astronomical observation and experiments conducted in the Solar System due to the $f(T)$ gravity which contains a quadratic correction of $\\alpha T^2$ ($\\alpha$ is a model parameter) and the cosmological constant $\\Lambda$. Using a spherical solution describing the Sun's gravitational field, the resulting secular evolution of planetary orbital motions, light deflection, gravitational time delay and frequency shift are calculated up to the leading contribution. Among them, we find qualitatively that the light deflection holds a unique bound on $\\alpha$, without dependence on $\\Lambda$, and the time delay experiments during inferior conjunction impose a clean constraint on $\\Lambda$, regardless of $\\alpha$. Based on observation and experiments, especially the supplementary advances in the perihelia provided by the INPOP10a ephemeris...
Shannon entropic temperature and its lower and upper bounds for non-Markovian stochastic dynamics
Ray, Somrita; Bag, Bidhan Chandra
2014-09-01
In this article we have studied Shannon entropic nonequilibrium temperature (NET) extensively for a system which is coupled to a thermal bath that may be Markovian or non-Markovian in nature. Using the phase-space distribution function, i.e., the solution of the generalized Fokker Planck equation, we have calculated the entropy production, NET, and their bounds. Other thermodynamic properties like internal energy of the system, heat, and work, etc. are also measured to study their relations with NET. The present study reveals that the heat flux is proportional to the difference between the temperature of the thermal bath and the nonequilibrium temperature of the system. It also reveals that heat capacity at nonequilibrium state is independent of both NET and time. Furthermore, we have demonstrated the time variations of the above-mentioned and related quantities to differentiate between the equilibration processes for the coupling of the system with the Markovian and the non-Markovian thermal baths, respectively. It implies that in contrast to the Markovian case, a certain time is required to develop maximum interaction between the system and the non-Markovian thermal bath (NMTB). It also implies that longer relaxation time is needed for a NMTB compared to a Markovian one. Quasidynamical behavior of the NMTB introduces an oscillation in the variation of properties with time. Finally, we have demonstrated how the nonequilibrium state is affected by the memory time of the thermal bath.
Xue, T.; Ma, X.; Rahn, C.; Roundy, S.
2014-11-01
Energy harvesting from human motion addresses the growing need for battery-free health and wellness sensors in wearable applications. The major obstacles to harvesting energy in such applications are low and random frequencies due to the nature of human motion. This paper presents a generalized rotational harvester model in 3 dimensions to determine the upper bound of power output from real world measured data. Simulation results indicate much space for improvement on power generation comparing to existing devices. We have developed a rotational energy harvester for human motion that attempts to close the gap between theoretical possibility and demonstrated devices. Like previous work, it makes use of magnetically plucked piezoelectric beams. However, it more fully utilizes the space available and has many degrees of freedom available for optimization. Finally we present a prototype harvester based on the coupled harvester model with preliminary experimental validation.
Capacity bounds for kth best path selection over generalized fading channels
Hanif, Muhammad Fainan
2014-02-01
Exact ergodic capacity calculation for fading wireless channels typically involves time-consuming numerical evaluation of infinite integrals. In this paper, lower and upper bounds on ergodic capacity for kth best path are presented. These bounds have simple analytic expressions which allow their fast evaluation. Numerical results show that the newly proposed bounds closely approximate the exact ergodic capacity for a large variety of system configurations. © 1997-2012 IEEE.
Upper and lower bounds for disadvantage factors as a test of an algorithm used in a synthesis method
Energy Technology Data Exchange (ETDEWEB)
Ackroyd, R.T.; Nanneh, M.M.
1988-01-01
A lower bound for the disadvantage factor of a lattice cell of arbitrary configuration is obtained using a finite element method which is based on a variational principle for the even-parity angular flux. An upper bound for the disadvantage factor is given by a finite element method using the complementary variational principle for the odd-parity angular flux. These theoretical results are illustrated by calculations for urnaium/graphite and uranium/water lattices. As the approximations are refined the fluxes obtained by the first method tend towards the actual flux from below in the moderator, and from above in the fuel. These trends are reversed for the second method. This derivation of benchmarks for disadvantage factors has been undertaken primarily as a test of an important algorithm used by the authors in a method of synthesising transport solutions starting with a diffusion theory approximation. The algorithm is used to convert odd-parity approximations for the angular flux into even-parity approximations and vice versa.
Upper bound on neutrino mass based on T2K neutrino timing measurements
Abe, K.; Adam, J.; Aihara, H.; Akiri, T.; Andreopoulos, C.; Aoki, S.; Ariga, A.; Assylbekov, S.; Autiero, D.; Barbi, M.; Barker, G. J.; Barr, G.; Bartet-Friburg, P.; Bass, M.; Batkiewicz, M.; Bay, F.; Berardi, V.; Berger, B. E.; Berkman, S.; Bhadra, S.; Blaszczyk, F. d. M.; Blondel, A.; Bojechko, C.; Bolognesi, S.; Bordoni, S.; Boyd, S. B.; Brailsford, D.; Bravar, A.; Bronner, C.; Buchanan, N.; Calland, R. G.; Caravaca Rodríguez, J.; Cartwright, S. L.; Castillo, R.; Catanesi, M. G.; Cervera, A.; Cherdack, D.; Chikuma, N.; Christodoulou, G.; Clifton, A.; Coleman, J.; Coleman, S. J.; Collazuol, G.; Connolly, K.; Cremonesi, L.; Dabrowska, A.; Danko, I.; Das, R.; Davis, S.; de Perio, P.; De Rosa, G.; Dealtry, T.; Dennis, S. R.; Densham, C.; Dewhurst, D.; Di Lodovico, F.; Di Luise, S.; Dolan, S.; Drapier, O.; Duboyski, T.; Duffy, K.; Dumarchez, J.; Dytman, S.; Dziewiecki, M.; Emery-Schrenk, S.; Ereditato, A.; Escudero, L.; Feusels, T.; Finch, A. J.; Fiorentini, G. A.; Friend, M.; Fujii, Y.; Fukuda, Y.; Furmanski, A. P.; Galymov, V.; Garcia, A.; Giffin, S.; Giganti, C.; Gilje, K.; Goeldi, D.; Golan, T.; Gonin, M.; Grant, N.; Gudin, D.; Hadley, D. R.; Haegel, L.; Haesler, A.; Haigh, M. D.; Hamilton, P.; Hansen, D.; Hara, T.; Hartz, M.; Hasegawa, T.; Hastings, N. C.; Hayashino, T.; Hayato, Y.; Hearty, C.; Helmer, R. L.; Hierholzer, M.; Hignight, J.; Hillairet, A.; Himmel, A.; Hiraki, T.; Hirota, S.; Holeczek, J.; Horikawa, S.; Hosomi, F.; Huang, K.; Ichikawa, A. K.; Ieki, K.; Ieva, M.; Ikeda, M.; Imber, J.; Insler, J.; Irvine, T. J.; Ishida, T.; Ishii, T.; Iwai, E.; Iwamoto, K.; Iyogi, K.; Izmaylov, A.; Jacob, A.; Jamieson, B.; Jiang, M.; Johnson, R. A.; Johnson, S.; Jo, J. H.; Jonsson, P.; Jung, C. K.; Kabirnezhad, M.; Kaboth, A. C.; Kajita, T.; Kakuno, H.; Kameda, J.; Kanazawa, Y.; Karlen, D.; Karpikov, I.; Katori, T.; Kearns, E.; Khabibullin, M.; Khotjantsev, A.; Kielczewska, D.; Kikawa, T.; Kilinski, A.; Kim, J.; King, S.; Kisiel, J.; Kitching, P.; Kobayashi, T.; Koch, L.; Koga, T.; Kolaceke, A.; Konaka, A.; Kopylov, A.; Kormos, L. L.; Korzenev, A.; Koshio, Y.; Kropp, W.; Kubo, H.; Kudenko, Y.; Kurjata, R.; Kutter, T.; Lagoda, J.; Lamont, I.; Larkin, E.; Laveder, M.; Lawe, M.; Lazos, M.; Lindner, T.; Lister, C.; Litchfield, R. P.; Longhin, A.; Lopez, J. P.; Ludovici, L.; Magaletti, L.; Mahn, K.; Malek, M.; Manly, S.; Marino, A. D.; Marteau, J.; Martin, J. F.; Martins, P.; Martynenko, S.; Maruyama, T.; Matveev, V.; Mavrokoridis, K.; Mazzucato, E.; McCarthy, M.; McCauley, N.; McFarland, K. S.; McGrew, C.; Mefodiev, A.; Metelko, C.; Mezzetto, M.; Mijakowski, P.; Miller, C. A.; Minamino, A.; Mineev, O.; Missert, A.; Miura, M.; Moriyama, S.; Mueller, Th. A.; Murakami, A.; Murdoch, M.; Murphy, S.; Myslik, J.; Nakadaira, T.; Nakahata, M.; Nakamura, K. G.; Nakamura, K.; Nakayama, S.; Nakaya, T.; Nakayoshi, K.; Nantais, C.; Nielsen, C.; Nirkko, M.; Nishikawa, K.; Nishimura, Y.; Nowak, J.; O'Keeffe, H. M.; Ohta, R.; Okumura, K.; Okusawa, T.; Oryszczak, W.; Oser, S. M.; Ovsyannikova, T.; Owen, R. A.; Oyama, Y.; Palladino, V.; Palomino, J. L.; Paolone, V.; Payne, D.; Perevozchikov, O.; Perkin, J. D.; Petrov, Y.; Pickard, L.; Pinzon Guerra, E. S.; Pistillo, C.; Plonski, P.; Poplawska, E.; Popov, B.; Posiadala-Zezula, M.; Poutissou, J.-M.; Poutissou, R.; Przewlocki, P.; Quilain, B.; Radicioni, E.; Ratoff, P. N.; Ravonel, M.; Rayner, M. A. M.; Redij, A.; Reeves, M.; Reinherz-Aronis, E.; Riccio, C.; Rodrigues, P. A.; Rojas, P.; Rondio, E.; Roth, S.; Rubbia, A.; Ruterbories, D.; Rychter, A.; Sacco, R.; Sakashita, K.; Sánchez, F.; Sato, F.; Scantamburlo, E.; Scholberg, K.; Schoppmann, S.; Schwehr, J.; Scott, M.; Seiya, Y.; Sekiguchi, T.; Sekiya, H.; Sgalaberna, D.; Shah, R.; Shaker, F.; Shaw, D.; Shiozawa, M.; Short, S.; Shustrov, Y.; Sinclair, P.; Smith, B.; Smy, M.; Sobczyk, J. T.; Sobel, H.; Sorel, M.; Southwell, L.; Stamoulis, P.; Steinmann, J.; Still, B.; Suda, Y.; Suzuki, A.; Suzuki, K.; Suzuki, S. Y.; Suzuki, Y.; Tacik, R.; Tada, M.; Takahashi, S.; Takeda, A.; Takeuchi, Y.; Tanaka, H. K.; Tanaka, H. A.; Tanaka, M. M.; Terhorst, D.; Terri, R.; Thompson, L. F.; Thorley, A.; Tobayama, S.; Toki, W.; Tomura, T.; Totsuka, Y.; Touramanis, C.; Tsukamoto, T.; Tzanov, M.; Uchida, Y.; Vacheret, A.; Vagins, M.; Vasseur, G.; Wachala, T.; Wakamatsu, K.; Walter, C. W.; Wark, D.; Warzycha, W.; Wascko, M. O.; Weber, A.; Wendell, R.; Wilkes, R. J.; Wilking, M. J.; Wilkinson, C.; Williamson, Z.; Wilson, J. R.; Wilson, R. J.; Wongjirad, T.; Yamada, Y.; Yamamoto, K.; Yanagisawa, C.; Yano, T.; Yen, S.; Yershov, N.; Yokoyama, M.; Yoo, J.; Yoshida, K.; Yuan, T.; Yu, M.; Zalewska, A.; Zalipska, J.; Zambelli, L.; Zaremba, K.; Ziembicki, M.; Zimmerman, E. D.; Zito, M.; Żmuda, J.; T2K Collaboration
2016-01-01
The Tokai to Kamioka (T2K) long-baseline neutrino experiment consists of a muon neutrino beam, produced at the J-PARC accelerator, a near detector complex and a large 295-km-distant far detector. The present work utilizes the T2K event timing measurements at the near and far detectors to study neutrino time of flight as a function of derived neutrino energy. Under the assumption of a relativistic relation between energy and time of flight, constraints on the neutrino rest mass can be derived. The sub-GeV neutrino beam in conjunction with timing precision of order tens of ns provide sensitivity to neutrino mass in the few MeV /c2 range. We study the distribution of relative arrival times of muon and electron neutrino candidate events at the T2K far detector as a function of neutrino energy. The 90% C.L. upper limit on the mixture of neutrino mass eigenstates represented in the data sample is found to be mν2<5.6 MeV2/c4 .
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Podolskii, Vladimir V.
2010-01-01
with the well-studied corresponding hierarchies defined using ordinary threshold gates. A major open problem in Boolean circuit complexity is to provide an explicit super-polynomial lower bound for depth two threshold circuits. We identify the class of depth two exact threshold circuits as a natural subclass...
Qiu, Shanwen
2012-07-01
In this article, we propose a new grid-free and exact solution method for computing solutions associated with an hybrid traffic flow model based on the Lighthill- Whitham-Richards (LWR) partial differential equation. In this hybrid flow model, the vehicles satisfy the LWR equation whenever possible, and have a fixed acceleration otherwise. We first present a grid-free solution method for the LWR equation based on the minimization of component functions. We then show that this solution method can be extended to compute the solutions to the hybrid model by proper modification of the component functions, for any concave fundamental diagram. We derive these functions analytically for the specific case of a triangular fundamental diagram. We also show that the proposed computational method can handle fixed or moving bottlenecks.
Qiu, Shanwen
2013-09-01
In this article, we propose a new exact and grid-free numerical scheme for computing solutions associated with an hybrid traffic flow model based on the Lighthill-Whitham-Richards (LWR) partial differential equation, for a class of fundamental diagrams. In this hybrid flow model, the vehicles satisfy the LWR equation whenever possible, and have a constant acceleration otherwise. We first propose a mathematical definition of the solution as a minimization problem. We use this formulation to build a grid-free solution method for this model based on the minimization of component function. We then derive these component functions analytically for triangular fundamental diagrams, which are commonly used to model traffic flow. We also show that the proposed computational method can handle fixed or moving bottlenecks. A toolbox implementation of the resulting algorithm is briefly discussed, and posted at https://dl.dropbox.com/u/1318701/Toolbox.zip. © 2013 Elsevier Ltd.
Directory of Open Access Journals (Sweden)
Daniel Khoshnoudirad
2015-09-01
Full Text Available The aim of the paper is to bring new combinatorial analytical properties of the Farey diagrams of order $(m,n$, which are associated to the $(m,n$-cubes. The latter are the pieces of discrete planes occurring in discrete geometry, theoretical computer sciences, and combinatorial number theory. We give a new upper bound for the number of Farey vertices $FV(m,n$ obtained as intersections points of Farey lines ([14]: $$\\exists C>0, \\forall (m,n\\in\\mathbb{N}^{*2},\\quad \\Big|FV(m,n\\Big| \\leq C m^2 n^2 (m+n \\ln^2 (mn$$ Using it, in particular, we show that the number of $(m,n$-cubes $\\mathcal{U}_{m,n}$ verifies: $$\\exists C>0, \\forall (m,n\\in\\mathbb{N}^{*2},\\quad \\Big|\\mathcal{U}_{m,n}\\Big| \\leq C m^3 n^3 (m+n \\ln^2 (mn$$ which is an important improvement of the result previously obtained in [6], which was a polynomial of degree 8. This work uses combinatorics, graph theory, and elementary and analytical number theory.
Toosizadeh, Nima; Joseph, Bellal; Heusser, Michelle R; Orouji Jokar, Tahereh; Mohler, Jane; Phelan, Herb A; Najafi, Bijan
2016-08-01
Despite increasing evidence that assessing frailty facilitates medical decision-making, a quick and clinically simple frailty assessment tool is not available for trauma settings. This study examined accuracy and acceptability of a novel wearable technology (upper-extremity frailty [UEF]) to objectively assess frailty status in older adults (65 years or older) admitted to the hospital due to traumatic ground-level falls. Frailty was measured using a validated modified Rockwood questionnaire, the Trauma-Specific Frailty Index (TSFI), as the gold standard. Participants performed a 20-second trial of rapid elbow flexion with the dominant elbow in a supine posture while wearing the UEF system. We recruited 101 eligible older adults (age 79 ± 9 years). Parameters of the UEF indicative of slowness, weakness, and exhaustion during elbow flexion were independent predictors of the TSFI score, while adjusted for age, sex, and body mass index. A high agreement (r = 0.72, p < 0.0001) was observed between TSFI score and the UEF model; sensitivity and specificity for predicting the frailty status were 78% and 82%, respectively. Of recruited participants, 57% were not able to walk at the time of measurements, suggesting a limitation for walking-based frailty assessments. Significant correlations were observed between UEF parameters and number of falls within a previous year, with highest correlation observed for elbow flexion slowness (r = -0.41). The results suggest that a simple test of 20-second elbow flexion may be practical and sensitive to identify frailty among hospitalized older adults. The UEF test is independent of walking assessments, reflects several frailty markers, and it is practical for bed-bound patients. Copyright © 2016 American College of Surgeons. Published by Elsevier Inc. All rights reserved.
A semidefinite programming based branch-and-bound framework for the quadratic assignment problem
Truetsch, U.
2014-01-01
The practical approach to calculate an exact solution for a quadratic assignment problem (QAP) via a branch-and-bound framework depends strongly on a "smart" choice of different strategies within the framework, for example the branching strategy, heuristics for the upper bound or relaxations for the
Guan, H.; Cook, P. G.; Simmons, C. T.; Brunner, P.; Gutierrez-Jurado, H. A.; Wang, H.
2013-12-01
Long-term evaporation pan observations worldwide constitute a good database to study effects of climate change. In many cases, however, actual evapotranspiration rather than pan evapotranspiration is of interest. In order to estimate land surface evapotranspiration based on pan observations, a relationship between pan evaporation and its surrounding actual evapotranspiration (ET) must be found. A complementary relationship has been developed in previous studies and is formulated as Epan = Ep + b(Ep-Ea), where Epan, Ep and Ea are pan evaporation, potential evaporation due to local radiation energy input, and actual areal evapotranspiration, respectively. We explore this model, based on long-term observations at seven evaporation pan sites in South Australia. Interestingly, we observe a clear edge in the lower-left corner of the data cloud in the (1/Ep, Epan/Ep) space for most months. This clear edge line is most likely caused by an upper bound in daily ET, which is observed at multiple AmeriFlux sites of various land covers. This upper bound in daily ET is likely associated with radiative energy partitioning and different timing of surface and root-zone soil wetting. It is simulated with physically-based numerical modelling at a vegetated semiarid environment. This upper bound in daily ET provides a mathematical basis for the lower edge in the (1/Ep, Epan/Ep) space. This edge line, when determined, can be used to estimate monthly b values. An automatic regression approach is presented to objectively determine the lower-left edge line. Preliminary calculation of Ea with the estimated b, appears to provide reasonable values for the three pan sites in areas with mean annual precipitation around and above 500 mm. We also examine under what a range of climate and surface conditions this upper ET bound exists. The significance of this phenomenon is not only in application of this evaporation pan based complementary-relationship method, but also in application of remote
Bounding the number of points on a curve using a generalization of Weierstrass semigroups
DEFF Research Database (Denmark)
Beelen, Peter; Ruano, Diego
2013-01-01
In this article we use techniques from coding theory to derive upper bounds for the number of rational places of the function field of an algebraic curve defined over a finite field. The used techniques yield upper bounds if the (generalized) Weierstrass semigroup (J Pure Appl Algebra 207(2), 243......–260, 2006) for an n-tuple of places is known, even if the exact defining equation of the curve is not known. As shown in examples, this sometimes enables one to get an upper bound for the number of rational places for families of function fields. Our results extend results in (J Pure Appl Algebra 213...
Thompson, Travis H.; Ochsenfeld, Christian
2017-10-01
We introduce both rigorous and non-rigorous distance-dependent integral estimates for four-center two-electron integrals derived from a distance-including Schwarz-type inequality. The estimates are even easier to implement than our so far most efficient distance-dependent estimates [S. A. Maurer et al., J. Chem. Phys. 136, 144107 (2012)] and, in addition, do not require well-separated charge-distributions. They are also applicable to a wide range of two-electron operators such as those found in explicitly correlated theories and in short-range hybrid density functionals. For two such operators with exponential distance decay [e-r12 and erfc (0.11 ṡr12 ) /r12], the rigorous bound is shown to be much tighter than the standard Schwarz estimate with virtually no error penalty. The non-rigorous estimate gives results very close to an exact screening for these operators and for the long-range 1/r12 operator, with errors that are completely controllable through the integral screening threshold. In addition, we present an alternative form of our non-rigorous bound that is particularly well-suited for improving the PreLinK method [J. Kussmann and C. Ochsenfeld, J. Chem. Phys. 138, 134114 (2013)] in the context of short-range exchange calculations.
Abdullah, Dahlan; Suwilo, Saib; Tulus; Mawengkang, Herman; Efendi, Syahril
2017-09-01
The higher education system in Indonesia can be considered not only as an important source of developing knowledge in the country, but also could create positive living conditions for the country. Therefore it is not surprising that enrollments in higher education continue to expand. However, the implication of this situation, the Indonesian government is necessarily to support more funds. In the interest of accountability, it is essential to measure the efficiency for this higher institution. Data envelopment analysis (DEA) is a method to evaluate the technical efficiency of production units which have multiple input and output. The higher learning institution considered in this paper is Malikussaleh University located in Lhokseumawe, a city in Aceh province of Indonesia. This paper develops a method to evaluate efficiency for all departments in Malikussaleh University using DEA with bounded output. Accordingly, we present some important differences in efficiency of those departments. Finally we discuss the effort should be done by these departments in order to become efficient.
Upper Bounds on r-Mode Amplitudes from Observations of Low-Mass X-Ray Binary Neutron Stars
Mahmoodifar, Simin; Strohmayer, Tod
2013-01-01
We present upper limits on the amplitude of r-mode oscillations and gravitational-radiation-induced spin-down rates in low-mass X-ray binary neutron stars, under the assumption that the quiescent neutron star luminosity is powered by dissipation from a steady-state r-mode. For masses <2M solar mass we find dimensionless r-mode amplitudes in the range from about 1×10(exp-8) to 1.5×10(exp-6). For the accreting millisecond X-ray pulsar sources with known quiescent spin-down rates, these limits suggest that approx. less than 1% of the observed rate can be due to an unstable r-mode. Interestingly, the source with the highest amplitude limit, NGC 6440, could have an r-mode spin-down rate comparable to the observed, quiescent rate for SAX J1808-3658. Thus, quiescent spin-down measurements for this source would be particularly interesting. For all sources considered here, our amplitude limits suggest that gravitational wave signals are likely too weak for detection with Advanced LIGO. Our highest mass model (2.21M solar mass) can support enhanced, direct Urca neutrino emission in the core and thus can have higher r-mode amplitudes. Indeed, the inferred r-mode spin-down rates at these higher amplitudes are inconsistent with the observed spin-down rates for some of the sources, such as IGR J00291+5934 and XTE J1751-305. In the absence of other significant sources of internal heat, these results could be used to place an upper limit on the masses of these sources if they were made of hadronic matter, or alternatively it could be used to probe the existence of exotic matter in them if their masses were known.
Naif, Samer
2018-01-01
Electrical conductivity soundings provide important constraints on the thermal and hydration state of the mantle. Recent seafloor magnetotelluric surveys have imaged the electrical conductivity structure of the oceanic upper mantle over a variety of plate ages. All regions show high conductivity (0.02 to 0.2 S/m) at 50 to 150 km depths that cannot be explained with a sub-solidus dry mantle regime without unrealistic temperature gradients. Instead, the conductivity observations require either a small amount of water stored in nominally anhydrous minerals or the presence of interconnected partial melts. This ambiguity leads to dramatically different interpretations on the origin of the asthenosphere. Here, I apply the damp peridotite solidus together with plate cooling models to determine the amount of H2O needed to induce dehydration melting as a function of depth and plate age. Then, I use the temperature and water content estimates to calculate the electrical conductivity of the oceanic mantle with a two-phase mixture of olivine and pyroxene from several competing empirical conductivity models. This represents the maximum potential conductivity of sub-solidus oceanic mantle at the limit of hydration. The results show that partial melt is required to explain the subset of the high conductivity observations beneath young seafloor, irrespective of which empirical model is applied. In contrast, the end-member empirical models predict either nearly dry (<20 wt ppm H2O) or slightly damp (<200 wt ppm H2O) asthenosphere for observations of mature seafloor. Since the former estimate is too dry compared with geochemical constraints from mid-ocean ridge basalts, this suggests the effect of water on mantle conductivity is less pronounced than currently predicted by the conductive end-member empirical model.
An upper bound for the
Haukkanen Pentti
2006-01-01
We find an upper bound for the norm of the matrix whose entry is , where and are the greatest common divisor and the least common multiple of and and where and are real numbers. In fact, we show that if and , then for all positive integers , where is the Riemann zeta function.
Physical Uncertainty Bounds (PUB)
Energy Technology Data Exchange (ETDEWEB)
Vaughan, Diane Elizabeth [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Preston, Dean L. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-03-19
This paper introduces and motivates the need for a new methodology for determining upper bounds on the uncertainties in simulations of engineered systems due to limited fidelity in the composite continuum-level physics models needed to simulate the systems. We show that traditional uncertainty quantification methods provide, at best, a lower bound on this uncertainty. We propose to obtain bounds on the simulation uncertainties by first determining bounds on the physical quantities or processes relevant to system performance. By bounding these physics processes, as opposed to carrying out statistical analyses of the parameter sets of specific physics models or simply switching out the available physics models, one can obtain upper bounds on the uncertainties in simulated quantities of interest.
Universal bounds in even-spin CFTs
Energy Technology Data Exchange (ETDEWEB)
Qualls, Joshua D. [Department of Physics, National Taiwan University,Taipei, Taiwan (China)
2015-12-01
We prove using invariance under the modular S− and ST−transformations that every unitary two-dimensional conformal field theory (CFT) having only even-spin primary operators (with no extended chiral algebra and with right- and left-central charges c,c̃>1) contains a primary operator with dimension Δ{sub 1} satisfying 0<Δ{sub 1}<((c+c̃)/24)+0.09280…. After deriving both analytical and numerical bounds, we discuss how to extend our methods to bound higher conformal dimensions before deriving lower and upper bounds on the number of primary operators in a given energy range. Using the AdS{sub 3}/CFT{sub 2} dictionary, the bound on Δ{sub 1} proves the lightest massive excitation in appropriate theories of 3D matter and gravity with cosmological constant Λ<0 can be no heavier than 1/8G{sub N}+O(√(−Λ)); the bounds on the number of operators are related via AdS/CFT to the entropy of states in the dual gravitational theory. In the flat-space approximation, the limiting mass is exactly that of the lightest BTZ black hole.
Exact and Adaptive Signed Distance Fields Computation for Rigid and Deformable Models on GPUs.
Liu, Fuchang; Kim, Young J
2014-05-01
Most techniques for real-time construction of a signed distance field, whether on a CPU or GPU, involve approximate distances. We use a GPU to build an exact adaptive distance field, constructed from an octree by using the Morton code. We use rectangle-swept spheres to construct a bounding volume hierarchy (BVH) around a triangulated model. To speed up BVH construction, we can use a multi-BVH structure to improve the workload balance between GPU processors. An upper bound on distance to the model provided by the octree itself allows us to reduce the number of BVHs involved in determining the distances from the centers of octree nodes at successively lower levels, prior to an exact distance query involving the remaining BVHs. Distance fields can be constructed 35-64 times as fast as a serial CPU implementation of a similar algorithm, allowing us to simulate a piece of fabric interacting with the Stanford Bunny at 20 frames per second.
Refining Multivariate Value Set Bounds
Smith, Luke Alexander
Over finite fields, if the image of a polynomial map is not the entire field, then its cardinality can be bounded above by a significantly smaller value. Earlier results bound the cardinality of the value set using the degree of the polynomial, but more recent results make use of the powers of all monomials. In this paper, we explore the geometric properties of the Newton polytope and show how they allow for tighter upper bounds on the cardinality of the multivariate value set. We then explore a method which allows for even stronger upper bounds, regardless of whether one uses the multivariate degree or the Newton polytope to bound the value set. Effectively, this provides an alternate proof of Kosters' degree bound, an improved Newton polytope-based bound, and an improvement of a degree matrix-based result given by Zan and Cao.
Energy Technology Data Exchange (ETDEWEB)
Singleton, Robert Jr. [Los Alamos National Laboratory; Israel, Daniel M. [Los Alamos National Laboratory; Doebling, Scott William [Los Alamos National Laboratory; Woods, Charles Nathan [Los Alamos National Laboratory; Kaul, Ann [Los Alamos National Laboratory; Walter, John William Jr [Los Alamos National Laboratory; Rogers, Michael Lloyd [Los Alamos National Laboratory
2016-05-09
For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.
Two-Sided A Posteriori Error Bounds for Electro-Magneto Static Problems
Pauly, Dirk; Repin, Sergey
2011-01-01
This paper is concerned with the derivation of computable and guaranteed upper and lower bounds of the difference between the exact and the approximate solution of a boundary value problem for static Maxwell equations. Our analysis is based upon purely functional argumentation and does not attract specific properties of an approximation method. Therefore, the estimates derived in the paper at hand are applicable to any approximate solution that belongs to the corresponding energy space. Such ...
Martin, Julien; Edwards, Holly H.; Bled, Florent; Fonnesbeck, Christopher J.; Dupuis, Jérôme A.; Gardner, Beth; Koslovsky, Stacie M.; Aven, Allen M.; Ward-Geiger, Leslie I.; Carmichael, Ruth H.; Fagan, Daniel E.; Ross, Monica A.; Reinert, Thomas R.
2014-01-01
The explosion of the Deepwater Horizon drilling platform created the largest marine oil spill in U.S. history. As part of the Natural Resource Damage Assessment process, we applied an innovative modeling approach to obtain upper estimates for occupancy and for number of manatees in areas potentially affected by the oil spill. Our data consisted of aerial survey counts in waters of the Florida Panhandle, Alabama and Mississippi. Our method, which uses a Bayesian approach, allows for the propagation of uncertainty associated with estimates from empirical data and from the published literature. We illustrate that it is possible to derive estimates of occupancy rate and upper estimates of the number of manatees present at the time of sampling, even when no manatees were observed in our sampled plots during surveys. We estimated that fewer than 2.4% of potentially affected manatee habitat in our Florida study area may have been occupied by manatees. The upper estimate for the number of manatees present in potentially impacted areas (within our study area) was estimated with our model to be 74 (95%CI 46 to 107). This upper estimate for the number of manatees was conditioned on the upper 95%CI value of the occupancy rate. In other words, based on our estimates, it is highly probable that there were 107 or fewer manatees in our study area during the time of our surveys. Because our analyses apply to habitats considered likely manatee habitats, our inference is restricted to these sites and to the time frame of our surveys. Given that manatees may be hard to see during aerial surveys, it was important to account for imperfect detection. The approach that we described can be useful for determining the best allocation of resources for monitoring and conservation. PMID:24670971
Directory of Open Access Journals (Sweden)
Julien Martin
Full Text Available The explosion of the Deepwater Horizon drilling platform created the largest marine oil spill in U.S. history. As part of the Natural Resource Damage Assessment process, we applied an innovative modeling approach to obtain upper estimates for occupancy and for number of manatees in areas potentially affected by the oil spill. Our data consisted of aerial survey counts in waters of the Florida Panhandle, Alabama and Mississippi. Our method, which uses a Bayesian approach, allows for the propagation of uncertainty associated with estimates from empirical data and from the published literature. We illustrate that it is possible to derive estimates of occupancy rate and upper estimates of the number of manatees present at the time of sampling, even when no manatees were observed in our sampled plots during surveys. We estimated that fewer than 2.4% of potentially affected manatee habitat in our Florida study area may have been occupied by manatees. The upper estimate for the number of manatees present in potentially impacted areas (within our study area was estimated with our model to be 74 (95%CI 46 to 107. This upper estimate for the number of manatees was conditioned on the upper 95%CI value of the occupancy rate. In other words, based on our estimates, it is highly probable that there were 107 or fewer manatees in our study area during the time of our surveys. Because our analyses apply to habitats considered likely manatee habitats, our inference is restricted to these sites and to the time frame of our surveys. Given that manatees may be hard to see during aerial surveys, it was important to account for imperfect detection. The approach that we described can be useful for determining the best allocation of resources for monitoring and conservation.
Communication waveform properties of an exact folded-band chaotic oscillator
Blakely, Jonathan N.; Hahs, Daniel W.; Corron, Ned J.
2013-11-01
We interpret the waveform of an exact folded-band oscillator as an on-off keyed communication waveform. Unlike most nonlinear systems, this oscillator has a general analytic solution that allows for unusually exact analysis. Using this solution, we identify the key differences between a deterministic chaotic oscillation and an ideal on-off keying waveform to be (1) an inherent form of intersymbol interference and (2) a grammar restriction giving rise to a built-in variable length code. We define a simple coherent receiver based on a matched filter, and consider transmission in the presence of additive white Gaussian noise. Analytic expressions for upper and lower bounds on the probability of errors in receiving code letters are derived and shown to be consistent with numerical simulations.
Improved Lower Bounds on the Price of Stability of Undirected Network Design Games
Bilò, Vittorio; Caragiannis, Ioannis; Fanelli, Angelo; Monaco, Gianpiero
Bounding the price of stability of undirected network design games with fair cost allocation is a challenging open problem in the Algorithmic Game Theory research agenda. Even though the generalization of such games in directed networks is well understood in terms of the price of stability (it is exactly H n , the n-th harmonic number, for games with n players), far less is known for network design games in undirected networks. The upper bound carries over to this case as well while the best known lower bound is 42/23 ≈ 1.826. For more restricted but interesting variants of such games such as broadcast and multicast games, sublogarithmic upper bounds are known while the best known lower bound is 12/7 ≈ 1.714. In the current paper, we improve the lower bounds as follows. We break the psychological barrier of 2 by showing that the price of stability of undirected network design games is at least 348/155 ≈ 2.245. Our proof uses a recursive construction of a network design game with a simple gadget as the main building block. For broadcast and multicast games, we present new lower bounds of 20/11 ≈ 1.818 and 1.862, respectively.
Translational diffusion of chain polymers. I. Improved variational bounds
Fixman, Marshall
1986-04-01
Variational estimates of an upper bound to the diffusion constant have been obtained from equilibrium simulations of Gaussian and cubic lattice chains. The trial functions that represent the deformation of the chain due to the external force have been inferred from the previous dynamical simulations of short Gaussian chains, which implied that local rather than large scale deformations were important. The variational results are in excellent agreement with the dynamical results for short Gaussian chains, and with exact results for rigid, planar, polygonal polymers. The variational results for long Gaussian chains (up to 896 beads) and cubic lattice chains (up to 448 beads), give an extrapolated reduction of the diffusion constant due to fluctuating hydrodynamic interaction of about 8% below the Kirkwood formula. The exact amount of the decrease may depend on friction constants and local chain structure.
National Research Council Canada - National Science Library
Ballester Pla, Coralio; Hernández, Penélope
2012-01-01
The observation of the actual behavior by economic decision makers in the lab and in the field justifies that bounded rationality has been a generally accepted assumption in many socio-economic models...
Gutiérrez-Rodríguez, A
2003-01-01
A bound on the nu /sup tau / magnetic moment is calculated through the reaction e/sup +/e/sup -/ to nu nu gamma at the Z/sub 1/-pole, and in the framework of a left-right symmetric model at LEP energies. We find that the bound is almost independent of the mixing angle phi of the model in the allowed experimental range for this parameter. (31 refs).
Exact Relativistic `Antigravity' Propulsion
Felber, Franklin S.
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Swaidan, Raja
2015-08-20
Intrinsically ultramicroporous (<7 Å) polymers represent a new paradigm in materials development for membrane-based gas separation. In particular, they demonstrate that uniting intrachain “rigidity”, the traditional design metric of highly permeable polymers of intrinsic microporosity (PIMs), with gas-sieving ultramicroporosity yields high-performance gas separation membranes. Highly ultramicroporous PIMs have redefined the state-of-the-art in large-scale air (e.g., O2/N2) and hydrogen recovery (e.g., H2/N2, H2/CH4) applications with unprecedented molecular sieving gas transport properties. Accordingly, presented herein are new 2015 permeability/selectivity “upper bounds” for large-scale commercial membrane-based air and hydrogen applications that accommodate the substantial performance enhancements of recent PIMs over preceding polymers. A subtle balance between intrachain rigidity and interchain spacing has been achieved in the amorphous microstructures of PIMs, fine-tuned using unique bridged-bicyclic building blocks (i.e., triptycene, ethanoanthracene and Tröger’s base) in both ladder and semiladder (e.g., polyimide) structures.
Efficient exact motif discovery.
Marschall, Tobias; Rahmann, Sven
2009-06-15
The motif discovery problem consists of finding over-represented patterns in a collection of biosequences. It is one of the classical sequence analysis problems, but still has not been satisfactorily solved in an exact and efficient manner. This is partly due to the large number of possibilities of defining the motif search space and the notion of over-representation. Even for well-defined formalizations, the problem is frequently solved in an ad hoc manner with heuristics that do not guarantee to find the best motif. We show how to solve the motif discovery problem (almost) exactly on a practically relevant space of IUPAC generalized string patterns, using the p-value with respect to an i.i.d. model or a Markov model as the measure of over-representation. In particular, (i) we use a highly accurate compound Poisson approximation for the null distribution of the number of motif occurrences. We show how to compute the exact clump size distribution using a recently introduced device called probabilistic arithmetic automaton (PAA). (ii) We define two p-value scores for over-representation, the first one based on the total number of motif occurrences, the second one based on the number of sequences in a collection with at least one occurrence. (iii) We describe an algorithm to discover the optimal pattern with respect to either of the scores. The method exploits monotonicity properties of the compound Poisson approximation and is by orders of magnitude faster than exhaustive enumeration of IUPAC strings (11.8 h compared with an extrapolated runtime of 4.8 years). (iv) We justify the use of the proposed scores for motif discovery by showing our method to outperform other motif discovery algorithms (e.g. MEME, Weeder) on benchmark datasets. We also propose new motifs on Mycobacterium tuberculosis. The method has been implemented in Java. It can be obtained from http://ls11-www.cs.tu-dortmund.de/people/marschal/paa_md/.
AbouEisha, Hassan M.
2014-01-01
The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts with minimum cardinality. This algorithm transforms the initial table to a decision table of a special kind, apply a set of simplification steps to this table, and use a dynamic programming algorithm to finish the construction of an optimal reduct. I present results of computer experiments for a collection of decision tables from UCIML Repository. For many of the experimented tables, the simplification steps solved the problem.
Directory of Open Access Journals (Sweden)
Jérôme Chenal
2009-09-01
Full Text Available © Benoît Vollmer, sans titre, Nouakchott, 2007. Le travail scientifique a toujours entretenu un rapport étroit avec l’image. Dans le domaine de la médecine, l’imagerie passe aujourd’hui pour être indispensable à la plupart des interventions sur les corps ; les scanners, irm et autres procédés montrent une utilisation possible de l’image dans le monde des sciences exactes. La police scientifique que popularisent Ncis ou Les Experts , qu’ils soient de Miami, de Manhattan ...
Ferreira, L. A.; Shnir, Ya.
2017-09-01
We introduce a Skyrme type model with the target space being the sphere S3 and with an action possessing, as usual, quadratic and quartic terms in field derivatives. The novel character of the model is that the strength of the couplings of those two terms are allowed to depend upon the space-time coordinates. The model should therefore be interpreted as an effective theory, such that those couplings correspond in fact to low energy expectation values of fields belonging to a more fundamental theory at high energies. The theory possesses a self-dual sector that saturates the Bogomolny bound leading to an energy depending linearly on the topological charge. The self-duality equations are conformally invariant in three space dimensions leading to a toroidal ansatz and exact self-dual Skyrmion solutions. Those solutions are labelled by two integers and, despite their toroidal character, the energy density is spherically symmetric when those integers are equal and oblate or prolate otherwise.
Directory of Open Access Journals (Sweden)
L.A. Ferreira
2017-09-01
Full Text Available We introduce a Skyrme type model with the target space being the sphere S3 and with an action possessing, as usual, quadratic and quartic terms in field derivatives. The novel character of the model is that the strength of the couplings of those two terms are allowed to depend upon the space–time coordinates. The model should therefore be interpreted as an effective theory, such that those couplings correspond in fact to low energy expectation values of fields belonging to a more fundamental theory at high energies. The theory possesses a self-dual sector that saturates the Bogomolny bound leading to an energy depending linearly on the topological charge. The self-duality equations are conformally invariant in three space dimensions leading to a toroidal ansatz and exact self-dual Skyrmion solutions. Those solutions are labelled by two integers and, despite their toroidal character, the energy density is spherically symmetric when those integers are equal and oblate or prolate otherwise.
Instantaneous Bethe-Salpeter equation with exact propagators
Energy Technology Data Exchange (ETDEWEB)
Lucha, Wolfgang [Institut fuer Hochenergiephysik, Oesterreichische Akademie der Wissenschaften, Nikolsdorfergasse 18, A-1050 Vienna (Austria); Schoeberl, Franz F [Institut fuer Theoretische Physik, Universitaet Wien, Boltzmanngasse 5, A-1090 Vienna (Austria)
2005-11-01
Consequent application of the instantaneous approximation to both the interaction and all propagators of the bound-state constituents allows us to forge, within the framework of the Bethe-Salpeter formalism for the description of bound states, an instantaneous form of the Bethe-Salpeter equation with exact (i.e., full) propagators of the bound-state constituents. This instantaneous equation generalizes the well-known Salpeter equation, the derivation of which needs the additional assumption of free propagation of the bound-state constituents.
ExtremeBounds: Extreme Bounds Analysis in R
Directory of Open Access Journals (Sweden)
Marek Hlavac
2016-08-01
Full Text Available This article introduces the R package ExtremeBounds to perform extreme bounds analysis (EBA, a sensitivity test that examines how robustly the dependent variable of a regression model is related to a variety of possible determinants. ExtremeBounds supports Leamer's EBA that focuses on the upper and lower extreme bounds of regression coefficients, as well as Sala-i-Martin's EBA which considers their entire distribution. In contrast to existing alternatives, it can estimate models of a variety of user-defined sizes, use regression models other than ordinary least squares, incorporate non-linearities in the model specification, and apply custom weights and standard errors. To alleviate concerns about the multicollinearity and conceptual overlap of examined variables, ExtremeBounds allows users to specify sets of mutually exclusive variables, and can restrict the analysis to coefficients from regression models that yield a variance inflation factor within a prespecified limit.
Model checking exact cost for attack scenarios
DEFF Research Database (Denmark)
Aslanyan, Zaruhi; Nielson, Flemming
2017-01-01
Attack trees constitute a powerful tool for modelling security threats. Many security analyses of attack trees can be seamlessly expressed as model checking of Markov Decision Processes obtained from the attack trees, thus reaping the benefits of a coherent framework and a mature tool support....... However, current model checking does not encompass the exact cost analysis of an attack, which is standard for attack trees. Our first contribution is the logic erPCTL with cost-related operators. The extended logic allows to analyse the probability of an event satisfying given cost bounds and to compute...... the exact cost of an event. Our second contribution is the model checking algorithm for erPCTL. Finally, we apply our framework to the analysis of attack trees....
Exact Solutions to Maccari's System
Pan, Jun-Ting; Gong, Lun-Xun
2007-07-01
Based on the generalized Riccati relation, an algebraic method to construct a series of exact solutions to nonlinear evolution equations is proposed. Being concise and straightforward, the method is applied to Maccari's system, and some exact solutions of the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations.
Spectral bisection algorithm for solving Schrodinger equation using upper and lower solutions
Directory of Open Access Journals (Sweden)
Qutaibeh Deeb Katatbeh
2007-10-01
Full Text Available This paper establishes a new criteria for obtaining a sequence of upper and lower bounds for the ground state eigenvalue of Schr"odinger equation $ -Deltapsi(r+V(rpsi(r=Epsi(r$ in $N$ spatial dimensions. Based on this proposed criteria, we prove a new comparison theorem in quantum mechanics for the ground state eigenfunctions of Schrodinger equation. We determine also lower and upper solutions for the exact wave function of the ground state eigenfunctions using the computed upper and lower bounds for the eigenvalues obtained by variational methods. In other words, by using this criteria, we prove that the substitution of the lower(upper bound of the eigenvalue in Schrodinger equation leads to an upper(lower solution. Finally, two proposed iteration approaches lead to an exact convergent sequence of solutions. The first one uses Raielgh-Ritz theorem. Meanwhile, the second approach uses a new numerical spectral bisection technique. We apply our results for a wide class of potentials in quantum mechanics such as sum of power-law potentials in quantum mechanics.
Exact Outage Probability of Dual-Hop CSI-Assisted AF Relaying Over Nakagami-m Fading Channels
Xia, Minghua
2012-10-01
In this correspondence, considering dual-hop channel state information (CSI)-assisted amplify-and-forward (AF) relaying over Nakagami- m fading channels, the cumulative distribution function (CDF) of the end-to-end signal-to-noise ratio (SNR) is derived. In particular, when the fading shape factors m1 and m2 at consecutive hops take non-integer values, the bivariate H-function and G -function are exploited to obtain an exact analytical expression for the CDF. The obtained CDF is then applied to evaluate the outage performance of the system under study. The analytical results of outage probability coincide exactly with Monte-Carlo simulation results and outperform the previously reported upper bounds in the low and medium SNR regions.
Capacity Bounds for Parallel Optical Wireless Channels
Chaaban, Anas
2016-01-01
A system consisting of parallel optical wireless channels with a total average intensity constraint is studied. Capacity upper and lower bounds for this system are derived. Under perfect channel-state information at the transmitter (CSIT), the bounds have to be optimized with respect to the power allocation over the parallel channels. The optimization of the lower bound is non-convex, however, the KKT conditions can be used to find a list of possible solutions one of which is optimal. The optimal solution can then be found by an exhaustive search algorithm, which is computationally expensive. To overcome this, we propose low-complexity power allocation algorithms which are nearly optimal. The optimized capacity lower bound nearly coincides with the capacity at high SNR. Without CSIT, our capacity bounds lead to upper and lower bounds on the outage probability. The outage probability bounds meet at high SNR. The system with average and peak intensity constraints is also discussed.
Isoperimetric upper bounds for the first eigenvalue
Indian Academy of Sciences (India)
v〉 for 1 ≤ i ≤ n. We also note that β2 = ∇Mr 2. Let v = d(expp0 )v ∈ TqM(κ) be orthogonal to ∇ r. Then it follows from the standard Jacobi field estimate that v 2 = sin2 κ r r2. ¯v 2. Hence n. ∑ i=1. 〈∇ fi ,ν〉2 = β2 n. ∑ i=1. 〈∇ fi ,v〉2. = ∇Mr 2 1.
How hairpin vortices emerge from exact invariant solutions
Schneider, Tobias M.; Farano, Mirko; de Palma, Pietro; Robinet, Jean-Christoph; Cherubini, Stefania
2017-11-01
Hairpin vortices are among the most commonly observed flow structures in wall-bounded shear flows. However, within the dynamical system approach to turbulence, those structures have not yet been described. They are not captured by known exact invariant solutions of the Navier-Stokes equations nor have other state-space structures supporting hairpins been identified. We show that hairpin structures are observed along an optimally growing trajectory leaving a well known exact traveling wave solution of plane Poiseuille flow. The perturbation triggering hairpins does not correspond to an unstable mode of the exact traveling wave but lies in the stable manifold where non-normality causes strong transient amplification.
Wronskian method for bound states
Energy Technology Data Exchange (ETDEWEB)
Fernandez, Francisco M, E-mail: fernande@quimica.unlp.edu.ar [INIFTA (UNLP, CONICET), Division Quimica Teorica, Boulevard 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2011-05-15
We propose a simple and straightforward method based on Wronskians for the calculation of bound-state energies and wavefunctions of one-dimensional quantum-mechanical problems. We explicitly discuss the asymptotic behaviour of the wavefunction and show that the allowed energies make the divergent part vanish. As illustrative examples we consider an exactly solvable model, the Gaussian potential well, and a two-well potential proposed earlier for the interpretation of the infrared spectrum of ammonia.
Distance bounds on quantum dynamics
Lidar, Daniel A.; Zanardi, Paolo; Khodjasteh, Kaveh
2008-07-01
We derive rigorous upper bounds on the distance between quantum states in an open-system setting in terms of the operator norm between Hamiltonians describing their evolution. We illustrate our results with an example taken from protection against decoherence using dynamical decoupling.
Bounds in the generalized Weber problem under locational uncertainty
DEFF Research Database (Denmark)
Juel, Henrik
1981-01-01
An existing analysis of the bounds on the Weber problem solution under uncertainty is incorrect. For the generalized problem with arbitrary measures of distance, we give easily computable ranges on the bounds and state the conditions under which the exact values of the bounds can be found...
Endom, Joerg
2014-05-01
negligible any more. Locating for example the exact position of joints, rebars on site, getting correct calibration information or overlaying measurements of independent methods requires high accuracy positioning for all data. Different technologies of synchronizing and stabilizing are discussed in this presentation. Furthermore a scale problem for interdisciplinary work between the geotechnical engineer, the civil engineer, the surveyor and the geophysicist is presented. Manufacturers as well as users are addressed to work on a unified methodology that could be implemented in future. This presentation is a contribution to COST Action TU1208.
Directory of Open Access Journals (Sweden)
Ballester Pla, Coralio
2012-03-01
Full Text Available The observation of the actual behavior by economic decision makers in the lab and in the field justifies that bounded rationality has been a generally accepted assumption in many socio-economic models. The goal of this paper is to illustrate the difficulties involved in providing a correct definition of what a rational (or irrational agent is. In this paper we describe two frameworks that employ different approaches for analyzing bounded rationality. The first is a spatial segregation set-up that encompasses two optimization methodologies: backward induction and forward induction. The main result is that, even under the same state of knowledge, rational and non-rational agents may match their actions. The second framework elaborates on the relationship between irrationality and informational restrictions. We use the beauty contest (Nagel, 1995 as a device to explain this relationship.
La observación del comportamiento de los agentes económicos tanto en el laboratorio como en la vida real justifica que la racionalidad acotada sea un supuesto aceptado en numerosos modelos socio-económicos. El objetivo de este artículo es ilustrar las dificultades que conlleva una correcta definición de qué es un agente racional (irracional. En este artículo se describen dos marcos que emplean diferentes metodologías para analizar la racionalidad acotada. El primero es un modelo de segregación espacial donde se contrastan dos metodologías de optimización: inducción hacia atrás y hacia adelante. El resultado principal es que, incluso con el mismo nivel de conocimiento, tanto agentes racionales como irracionales podrían coincidir en sus acciones. El segundo marco trabaja sobre la relación entre irracionalidad y restricción de información. Se utiliza el juego llamado “beauty contest” (Nagel 1995 como mecanismo para explicar dicha relación.
Energy Technology Data Exchange (ETDEWEB)
Buras, Andrzej J. [TUM Institute for Advanced Study,Lichtenbergstr. 2a, D-85748 Garching (Germany); Physik Department, TU München,James-Franck-Straße, D-85748 Garching (Germany); Gérard, Jean-Marc [Centre for Cosmology, Particle Physics and Phenomenology (CP3),Université catholique de Louvain,Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve (Belgium)
2015-12-01
We demonstrate that in the large N approach developed by the authors in collaboration with Bardeen, the parameters B{sub 6}{sup (1/2)} and B{sub 8}{sup (3/2)} parametrizing the K→ππ matrix elements 〈Q{sub 6}〉{sub 0} and 〈Q{sub 8}〉{sub 2} of the dominant QCD and electroweak operators receive both negativeO(1/N) corrections such that B{sub 6}{sup (1/2)}≤B{sub 8}{sup (3/2)}<1 in agreement with the recent lattice results of the RBC-UKQCD collaboration. We also point out that the pattern of the size of the hadronic matrix elements of all QCD and electroweak penguin operators Q{sub i} contributing to the K→ππ amplitudes A{sub 0} and A{sub 2}, obtained by this lattice collaboration, provides further support to our large N approach. In particular, the lattice result for the matrix element 〈Q{sub 8}〉{sub 0} implies for the corresponding parameter B{sub 8}{sup (1/2)}=1.0±0.2 to be compared with large N value B{sub 8}{sup (1/2)}=1.1±0.1. We discuss briefly the implications of these findings for the ratio ε{sup ′}/ε. In fact, with the precise value for B{sub 8}{sup (3/2)} from RBC-UKQCD collaboration, our upper bound on B{sub 6}{sup (1/2)} implies ε{sup ′}/ε in the SM roughly by a factor of two below its experimental value (16.6±2.3)×10{sup −4}. We also briefly comment on the parameter B̂{sub K} and the ΔI=1/2 rule.
Exact piecewise flat gravitational waves
van de Meent, M.|info:eu-repo/dai/nl/314007067
2011-01-01
We generalize our previous linear result (van de Meent 2011 Class. Quantum Grav 28 075005) in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly how to
An Error Bound for Solution of Fredholm Integral Equations by Adomian Method
Directory of Open Access Journals (Sweden)
A. Davari
2010-03-01
Full Text Available In this paper, we will obtain an efficient computable upper bound for approximate solution of linear Fredholm integral equations obtained by Adomian decomposition method. Numerical examples are presented to show the effectiveness of the upper bounds.
Exact cosmological solutions for MOG
Energy Technology Data Exchange (ETDEWEB)
Roshan, Mahmood [Ferdowsi University of Mashhad, Department of Physics, P.O. Box 1436, Mashhad (Iran, Islamic Republic of)
2015-09-15
We find some new exact cosmological solutions for the covariant scalar-tensor-vector gravity theory, the so-called modified gravity (MOG). The exact solution of the vacuum field equations has been derived. Also, for non-vacuum cases we have found some exact solutions with the aid of the Noether symmetry approach. More specifically, the symmetry vector and also the Noether conserved quantity associated to the point-like Lagrangian of the theory have been found. Also we find the exact form of the generic vector field potential of this theory by considering the behavior of the relevant point-like Lagrangian under the infinitesimal generator of the Noether symmetry. Finally, we discuss the cosmological implications of the solutions. (orig.)
Exact solution for generalized pairing
Pan, Feng; Draayer, J. P.
1997-01-01
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with some numerical examples.
de Cooman, Gert; Troffaes, Matthias C. M.; Miranda, Enrique
2008-11-01
We study n-monotone functionals, which constitute a generalisation of n-monotone set functions. We investigate their relation to the concepts of exactness and natural extension, which generalise coherence and natural extension in the behavioural theory of imprecise probabilities. We improve upon a number of results in the literature, and prove among other things a representation result for exact n-monotone functionals in terms of Choquet integrals.
Directory of Open Access Journals (Sweden)
Jan Kucera
1990-01-01
Full Text Available It is proved in [1] & [2] that a set bounded in an inductive limit E=indlim En of Fréchet spaces is also bounded in some En iff E is fast complete. In the case of arbitrary locally convex spaces En every bounded set in a fast complete indlim En is quasi-bounded in some En, though it may not be bounded or even contained in any En. Every bounded set is quasi-bounded. In a Fréchet space every quasi-bounded set is also bounded.
Computing Symmetric Boolean Functions by Circuits with Few Exact Threshold Gates
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt
2007-01-01
We consider constant depth circuits augmented with few exact threshold gates with arbitrary weights. We prove strong (up to exponential) size lower bounds for such circuits computing symmetric Boolean functions. Our lower bound is expressed in terms of a natural parameter, the balance, of symmetric...... functions. Furthermore, in the quasi-polynomial size setting our results provides an exact characterization of the class of symmetric functions in terms of their balance....
Bounding Averages Rigorously Using Semidefinite Programming: Mean Moments of the Lorenz System
Goluskin, David
2017-11-01
We describe methods for proving bounds on infinite-time averages in differential dynamical systems. The methods rely on the construction of nonnegative polynomials with certain properties, similarly to the way nonlinear stability can be proved using Lyapunov functions. Nonnegativity is enforced by requiring the polynomials to be sums of squares, a condition which is then formulated as a semidefinite program (SDP) that can be solved computationally. Although such computations are subject to numerical error, we demonstrate two ways to obtain rigorous results: using interval arithmetic to control the error of an approximate SDP solution, and finding exact analytical solutions to relatively small SDPs. Previous formulations are extended to allow for bounds depending analytically on parametric variables. These methods are illustrated using the Lorenz equations, a system with three state variables (x, y, z) and three parameters (β ,σ ,r) . Bounds are reported for infinite-time averages of all eighteen moments x^ly^mz^n up to quartic degree that are symmetric under (x,y)\\mapsto (-x,-y) . These bounds apply to all solutions regardless of stability, including chaotic trajectories, periodic orbits, and equilibrium points. The analytical approach yields two novel bounds that are sharp: the mean of z^3 can be no larger than its value of (r-1)^3 at the nonzero equilibria, and the mean of xy^3 must be nonnegative. The interval arithmetic approach is applied at the standard chaotic parameters to bound eleven average moments that all appear to be maximized on the shortest periodic orbit. Our best upper bound on each such average exceeds its value on the maximizing orbit by less than 1%. Many bounds reported here are much tighter than would be possible without computer assistance.
Directory of Open Access Journals (Sweden)
Juan Carlos Ceballos V.
2005-10-01
Full Text Available The exact boundary controllability of the higher order nonlinear Schrodinger equation with constant coefficients on a bounded domain with various boundary conditions is studied. We derive the exact boundary controllability for this equation for sufficiently small initial and final states.
Entropy Bounds for Constrained Two-Dimensional Fields
DEFF Research Database (Denmark)
Forchhammer, Søren Otto; Justesen, Jørn
1999-01-01
The maximum entropy and thereby the capacity of 2-D fields given by certain constraints on configurations are considered. Upper and lower bounds are derived.......The maximum entropy and thereby the capacity of 2-D fields given by certain constraints on configurations are considered. Upper and lower bounds are derived....
Exact discretization by Fourier transforms
Tarasov, Vasily E.
2016-08-01
A discretization of differential and integral operators of integer and non-integer orders is suggested. New type of differences, which are represented by infinite series, is proposed. A characteristic feature of the suggested differences is an implementation of the same algebraic properties that have the operator of differentiation (property of algebraic correspondence). Therefore the suggested differences are considered as an exact discretization of derivatives. These differences have a property of universality, which means that these operators do not depend on the form of differential equations and the parameters of these equations. The suggested differences operators allows us to have difference equations whose solutions are equal to the solutions of corresponding differential equations. The exact discretization of the derivatives of integer orders is given by the suggested differences of the same integer orders. Similarly, the exact discretization of the Riesz derivatives and integrals of integer and non-integer order is given by the proposed fractional differences of the same order.
Exact analysis of discrete data
Hirji, Karim F
2005-01-01
Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...
When 'exact recovery' is exact recovery in compressed sensing simulation
DEFF Research Database (Denmark)
Sturm, Bob L.
2012-01-01
In a simulation of compressed sensing (CS), one must test whether the recovered solution \\(\\vax\\) is the true solution \\(\\vx\\), i.e., ``exact recovery.'' Most CS simulations employ one of two criteria: 1) the recovered support is the true support; or 2) the normalized squared error is less than...
On the Applicability of Lower Bounds for Solving Rectilinear
DEFF Research Database (Denmark)
Clausen, Jens; Karisch, Stefan E.; Perregaard, M.
1998-01-01
The quadratic assignment problem (QAP) belongs to the hard core of NP-hard optimization problems. After almost forty years of research only relatively small instances can be solved to optimality. The reason is that the quality of the lower bounds available for exact methods is not sufficient....... Recently, lower bounds based on decomposition were proposed for the so called rectilinear QAP that proved to be the strongest for a large class of problem instances. We investigate the strength of these bounds when applied not only at the root node of a search tree but as the bound function used...... in a Branch-and-Bound code solving large scale QAPs....
Exact semiclassical expansions for one-dimensional quantum oscillators
Energy Technology Data Exchange (ETDEWEB)
Delabaere, E. [UMR CNRS J. A. Dieudonne No. 6621, University of Nice, 06108 Nice Cedex 2 (France); Dillinger, H.; Pham, F. [University of Nice, Department of Maths, UMR CNRS J.A. Dieudonne No. 6621, 06108 Nice Cedex 2 (France)
1997-12-01
A set of rules is given for dealing with WKB expansions in the one-dimensional analytic case, whereby such expansions are not considered as approximations but as exact encodings of wave functions, thus allowing for analytic continuation with respect to whichever parameters the potential function depends on, with an exact control of small exponential effects. These rules, which include also the case when there are double turning points, are illustrated on various examples, and applied to the study of bound state or resonance spectra. In the case of simple oscillators, it is thus shown that the Rayleigh{endash}Schr{umlt o}dinger series is Borel resummable, yielding the exact energy levels. In the case of the symmetrical anharmonic oscillator, one gets a simple and rigorous justification of the Zinn-Justin quantization condition, and of its solution in terms of {open_quotes}multi-instanton expansions.{close_quotes} {copyright} {ital 1997 American Institute of Physics.}
Semirelativistic N-boson systems bound by attractive pair potentials
Energy Technology Data Exchange (ETDEWEB)
Hall, Richard L [Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, Quebec, H3G 1M8 (Canada); Lucha, Wolfgang [Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna (Austria)], E-mail: rhall@mathstat.concordia.ca, E-mail: wolfgang.lucha@oeaw.ac.at
2009-10-02
We establish bounds on the energy of a system of N identical bosons bound by attractive pair potentials and obeying the semirelativistic Salpeter equation. The lower bound is provided by a 'reduction', with the aid of Jacobi relative coordinates, to a suitably scaled one-body Klein-Gordon problem. Complementary upper energy bounds are provided by means of a Gaussian trial function. Detailed results are presented for the exponential pair potential V(r) = -vexp(-r/a)
Huang, Wenxuan; Dacek, Stephen; Rong, Ziqin; Urban, Alexander; Cao, Shan; Luo, Chuan; Ceder, Gerbrand
2016-01-01
Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of solids, and fluid mechanics, among others. However, the problem of finding the true global ground state of a lattice model, which is essential for all of the aforementioned applications, has remained unresolved, with only a limited number of results for highly simplified systems known. In this article, we present the first general algorithm to find the exact ground states of complex lattice models and to prove their global optimality, resolving this fundamental problem in condensed matter and materials theory. We transform the infinite-discrete-optimization problem into a pair of combinatorial optimization (MAX-SAT) and non-smooth convex optimization (MAX-MIN) problems, which provide upper and lower bounds on the ground state energy respectively. By systematically converging th...
Energy Technology Data Exchange (ETDEWEB)
Voss, L.
1986-01-01
The accuracy can be improved, and the risk of complications can be reduced in the case of cytodiagnostic lung puncture, if one optimises the method whereby the puncture needle is inserted into the lesion. The author describes such a procedure incorporating the use of technical aids for marking the exact puncture point of the cannula. At the same time the procedure results in a reduction of radiation exposure of both doctor and patient.
Positivity bounds on double parton distributions
Energy Technology Data Exchange (ETDEWEB)
Diehl, Markus; Kasemets, Tomas
2013-03-15
Double hard scattering in proton-proton collisions is described in terms of double parton distributions. We derive bounds on these distributions that follow from their interpretation as probability densities, taking into account all possible spin correlations between two partons in an unpolarized proton. These bounds constrain the size of the polarized distributions and can for instance be used to set upper limits on the effects of spin correlations in double hard scattering. We show that the bounds are stable under leading-order DGLAP evolution to higher scales.
Bound states and the Bekenstein bound
Energy Technology Data Exchange (ETDEWEB)
Bousso, Raphael
2003-10-16
We explore the validity of the generalized Bekenstein bound, S<= pi M a. We define the entropy S as the logarithm of the number of states which have energy eigenvalue below M and are localized to a flat space region of width alpha. If boundary conditions that localize field modes are imposed by fiat, then the bound encounters well-known difficulties with negative Casimir energy and large species number, as well as novel problems arising only in the generalized form. In realistic systems, however, finite-size effects contribute additional energy. We study two different models for estimating such contributions. Our analysis suggests that the bound is both valid and nontrivial if interactions are properly included, so that the entropy S counts the bound states of interacting fields.
Directory of Open Access Journals (Sweden)
J.M. Valério de Carvalho
1996-04-01
Full Text Available Quando se pretende obter uma solução inteira para o problema de corte unidimensional, depois de se ter resolvido a sua relaxação linear, é frequente recorrer, quer a técnicas de arredondamento de soluções, quer a diversos tipos de heurísticas. Estas dificuldades decorrem do facto de não ser viável enumerar todas as variáveis estruturais do problema, cujo número pode ser da ordem dos milhões. Neste artigo, apresenta se uma formulação em que o número de variáveis e restrições é uma função polinomial da largura do stock e do número de pedidos. Para algumas classes de problemas, é possível enumerar todas as variáveis e obter a solução óptima usando o método da partição e avaliação sucessivas. Para instâncias de maiores dimensões, apresenta se um procedimento que combina a geração diferida de colunas e o método da partição e avaliação sucessivas. Define se o subproblema e o modo como é modificado durante a fase de partição e avaliação sucessivas. São apresentados resultados de testes computacionais para diversos problemas de teste.If an integer solution to the one-dimensional cutting stock problem is required, after solving the linear programming relaxation, one frequently resorts to heuristics based on rounding up and down the continuos solution, or other heuristics similar type. The difficulties arise from the fact that it may not be practically possible to enumerate all the structural variables of the problem, whose number may be in the order of millions, even for instances of moderate size. In this article we present a formulation with a number of variables and constraints that is polinomial with respect to the width of the stock and the number of orders. For some classes of instances, it is possible to enumerate completely all the variables and to obtain an integer optional solution using a branch-and-bound method. For larger instances, we present a procedure that combines column generation and
Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates
DEFF Research Database (Denmark)
Gal, A.; Hansen, Kristoffer Arnsfelt; Koucky, Michal
2013-01-01
We bound the minimum number w of wires needed to compute any (asymptotically good) error-correcting code C:{0,1}Ω(n)→{0,1}n with minimum distance Ω(n), using unbounded fan-in circuits of depth d with arbitrary gates. Our main results are: 1) if d=2, then w=Θ(n (lgn/lglgn)2); 2) if d=3, then w...... bound gives the largest known lower bound for computing any linear map. The upper bounds imply that a (necessarily dense) generator matrix for our code can be written as the product of two sparse matrices. Using known techniques, we also obtain similar (but not tight) bounds for computing pairwise......-independent hash functions. Our lower bounds are based on a superconcentrator-like condition that the graphs of circuits computing good codes must satisfy. This condition is provably intermediate between superconcentrators and their weakenings considered before...
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates
DEFF Research Database (Denmark)
Gál, Anna; Hansen, Kristoffer Arnsfelt; Koucký, Michal
2011-01-01
We bound the minimum number w of wires needed to compute any (asymptotically good) error-correcting code C:01(n)01n with minimum distance (n), using unbounded fan-in circuits of depth d with arbitrary gates. Our main results are: (1) If d=2 then w=(n(lognloglogn)2) . (2) If d=3 then w=(nlglgn). (3......, our (n(lognloglogn)2) lower bound gives the largest known lower bound for computing any linear map, improving on the (nlg32n) bound of Pudlak and Rodl (Discrete Mathematics '94). We find the upper bounds surprising. They imply that a (necessarily dense) generator matrix for the code can be written...... as the product of two sparse matrices. The upper bounds are non-explicit: we show the existence of circuits (consisting of only XOR gates) computing good codes within the stated bounds. Using a result by Ishai, Kushilevitz, Ostrovsky, and Sahai (STOC '08), we also obtain similar bounds for computing pairwise...
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Breinbjerg, Olav
2011-01-01
A new lower bound for the radiation $Q$ of electrically small spherical magnetic dipole antennas with solid magnetodielectric core is derived in closed form using the exact theory. The new bound approaches the Chu lower bound from above as the antenna electrical size decreases. For $ka, the new...
Tight lower bound for percolation threshold on an infinite graph.
Hamilton, Kathleen E; Pryadko, Leonid P
2014-11-14
We construct a tight lower bound for the site percolation threshold on an infinite graph, which becomes exact for an infinite tree. The bound is given by the inverse of the maximal eigenvalue of the Hashimoto matrix used to count nonbacktracking walks on the original graph. Our bound always exceeds the inverse spectral radius of the graph's adjacency matrix, and it is also generally tighter than the existing bound in terms of the maximum degree. We give a constructive proof for existence of such an eigenvalue in the case of a connected infinite quasitransitive graph, a graph-theoretic analog of a translationally invariant system.
Spectral computations for bounded operators
Ahues, Mario; Limaye, Balmohan
2001-01-01
Exact eigenvalues, eigenvectors, and principal vectors of operators with infinite dimensional ranges can rarely be found. Therefore, one must approximate such operators by finite rank operators, then solve the original eigenvalue problem approximately. Serving as both an outstanding text for graduate students and as a source of current results for research scientists, Spectral Computations for Bounded Operators addresses the issue of solving eigenvalue problems for operators on infinite dimensional spaces. From a review of classical spectral theory through concrete approximation techniques to finite dimensional situations that can be implemented on a computer, this volume illustrates the marriage of pure and applied mathematics. It contains a variety of recent developments, including a new type of approximation that encompasses a variety of approximation methods but is simple to verify in practice. It also suggests a new stopping criterion for the QR Method and outlines advances in both the iterative refineme...
AESS: Accelerated Exact Stochastic Simulation
Jenkins, David D.; Peterson, Gregory D.
2011-12-01
The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution
A polynomial bound on solutions of quadratic equations in free groups
Lysenok, Igor; Myasnikov, Alexei
2011-01-01
We provide polynomial upper bounds on the size of a shortest solution for quadratic equations in a free group. A similar bound is given for parametric solutions in the description of solutions sets of quadratic equations in a free group.
Cosmological bounds on neutrino degeneracy and the Dirac neutrino magnetic moment
Semikoz, V. B.
2017-11-01
The amplification of a seed cosmological magnetic field (CMF) in a hot electroweak plasma of early Universe driven by neutrino degeneracy (asymmetry) is provided by a lower bound on such asymmetries that is in agreement with the known upper (BBN) bound on the electron neutrino asymmetry. Independently of a mechanism for CMF generation one predicts a stringent upper bound on the Dirac neutrino magnetic moment using the lower bound on CMF amplitude found from the Fermi satellite experiment.
DEFF Research Database (Denmark)
Emiris, Ioannis Z.; Mourrain, Bernard; Tsigaridas, Elias
2010-01-01
In this paper we derive aggregate separation bounds, named after Davenport-Mahler-Mignotte (DMM), on the isolated roots of polynomial systems, specifically on the minimum distance between any two such roots. The bounds exploit the structure of the system and the height of the sparse (or toric) re...... bound on the number of steps that subdivision-based algorithms perform in order to isolate all real roots of a polynomial system. This leads to the first complexity bound of Milne's algorithm [22] in 2D....
Exact solutions to relativistic singular fractional power potentials
Agboola, Davids; Zhang, Yao-Zhong
2013-12-01
We present (exact) solutions of the Dirac equation with equally mixed interactions for a single fermion bounded by the family of fractional power singular potentials. Closed-form expressions as well as numerical values for the energies were obtained. The wave functions and the allowed values of the potential parameters for the first two members of the family are obtained in terms of a set of algebraic equations. The non-relativistic limit is also discussed and using the Hellmann-Feynmann theorem, some useful expectation values are obtained.
Mass Deformed Exact S-parameter in Conformal Theories
DEFF Research Database (Denmark)
Sannino, Francesco
2010-01-01
the existence of a universal lower bound on the opportunely normalized S parameter and explore its theoretical and phenomenological implications. Our exact results constitute an ideal framework to correctly interpret the lattice studies of the conformal window of strongly interacting theories....... leads to drastically different limiting values of S. Our results apply to any fermion matter representation and can be used as benchmark for the determination of certain relevant properties of the conformal window of any generic vector like gauge theory with fermionic matter. We finally suggest...
A bounds on the resonant frequency of rectangular microstrip antennas
Bailey, M. C.
1980-01-01
The calculation of currents induced by a transverse electric plane wave normally incident upon an infinite strip embedded in a grounded dielectric slab is used to infer a lower bound on the resonant frequency (or resonant-E-plane dimension) for rectangular microstrip antennas. An upper bound is provided by the frequency for which the E-plane dimension is a half-wavelength.
Bounds on the Effect of Progressive Structural Degradation
DEFF Research Database (Denmark)
Achtziger, Wolfgang; Bendsøe, Martin P; Taylor, John E.
1997-01-01
Problem formulations are presented for the evaluation of upper and lower bounds on the effect of progressive structural degradation. For the purposes of this study, degradation effect is measured by an increase in global structural compliance (flexibility). Thus the stated bounds are given simply...
Exact method for numerically analyzing a model of local denaturation in superhelically stressed DNA
Fye, Richard M.; Benham, Craig J.
1999-03-01
Local denaturation, the separation at specific sites of the two strands comprising the DNA double helix, is one of the most fundamental processes in biology, required to allow the base sequence to be read both in DNA transcription and in replication. In living organisms this process can be mediated by enzymes which regulate the amount of superhelical stress imposed on the DNA. We present a numerically exact technique for analyzing a model of denaturation in superhelically stressed DNA. This approach is capable of predicting the locations and extents of transition in circular superhelical DNA molecules of kilobase lengths and specified base pair sequences. It can also be used for closed loops of DNA which are typically found in vivo to be kilobases long. The analytic method consists of an integration over the DNA twist degrees of freedom followed by the introduction of auxiliary variables to decouple the remaining degrees of freedom, which allows the use of the transfer matrix method. The algorithm implementing our technique requires O(N2) operations and O(N) memory to analyze a DNA domain containing N base pairs. However, to analyze kilobase length DNA molecules it must be implemented in high precision floating point arithmetic. An accelerated algorithm is constructed by imposing an upper bound M on the number of base pairs that can simultaneously denature in a state. This accelerated algorithm requires O(MN) operations, and has an analytically bounded error. Sample calculations show that it achieves high accuracy (greater than 15 decimal digits) with relatively small values of M (Myeast show that this approach can also accurately treat in vivo denaturation.
Directory of Open Access Journals (Sweden)
Michaël Cadilhac
2011-08-01
Full Text Available The Parikh finite word automaton model (PA was introduced and studied by Klaedtke and Ruess in 2003. Here, by means of related models, it is shown that the bounded languages recognized by PA are the same as those recognized by deterministic PA. Moreover, this class of languages is the class of bounded languages whose set of iterations is semilinear.
Bounded Gaussian process regression
DEFF Research Database (Denmark)
Jensen, Bjørn Sand; Nielsen, Jens Brehm; Larsen, Jan
2013-01-01
We extend the Gaussian process (GP) framework for bounded regression by introducing two bounded likelihood functions that model the noise on the dependent variable explicitly. This is fundamentally different from the implicit noise assumption in the previously suggested warped GP framework. We...
Nonequilibrium quantum bounds to Landauer's principle: Tightness and effectiveness
Campbell, Steve; Guarnieri, Giacomo; Paternostro, Mauro; Vacchini, Bassano
2017-10-01
We assess two different nonequilibrium quantum Landauer bounds: the traditional approach based on the change in entropy, referred to as the "entropic bound," and one based on the details of the dynamical map, referred to as the "thermodynamic bound." By first restricting to a simple exactly solvable model of a single two-level system coupled to a finite-dimensional thermal environment and by exploiting an excitation-preserving interaction, we establish the dominant role played by the population terms in dictating the tightness of these bounds with respect to the dissipated heat and clearly establish that coherences only affect the entropic bound. Furthermore, we show that sharp boundaries between the relative performance of the two quantities emerge and find that there are clear instances where both approaches return a bound weaker than Clausius' statement of the second law, rendering them ineffective. Finally, we show that our results extend to generic interaction terms.
Bounding Species Distribution Models
Stohlgren, Thomas J.; Jarnevich, Cahterine S.; Morisette, Jeffrey T.; Esaias, Wayne E.
2011-01-01
Species distribution models are increasing in popularity for mapping suitable habitat for species of management concern. Many investigators now recognize that extrapolations of these models with geographic information systems (GIS) might be sensitive to the environmental bounds of the data used in their development, yet there is no recommended best practice for "clamping" model extrapolations. We relied on two commonly used modeling approaches: classification and regression tree (CART) and maximum entropy (Maxent) models, and we tested a simple alteration of the model extrapolations, bounding extrapolations to the maximum and minimum values of primary environmental predictors, to provide a more realistic map of suitable habitat of hybridized Africanized honey bees in the southwestern United States. Findings suggest that multiple models of bounding, and the most conservative bounding of species distribution models, like those presented here, should probably replace the unbounded or loosely bounded techniques currently used [Current Zoology 57 (5): 642-647, 2011].
Huang, Wenxuan; Kitchaev, Daniil A.; Dacek, Stephen T.; Rong, Ziqin; Urban, Alexander; Cao, Shan; Luo, Chuan; Ceder, Gerbrand
2016-10-01
Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to the study of alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of solids, fluid mechanics, and others. However, the problem of finding and proving the global ground state of a lattice model, which is essential for all of the aforementioned applications, has remained unresolved for relatively complex practical systems, with only a limited number of results for highly simplified systems known. In this paper, we present a practical and general algorithm that provides a provable periodically constrained ground state of a complex lattice model up to a given unit cell size and in many cases is able to prove global optimality over all other choices of unit cell. We transform the infinite-discrete-optimization problem into a pair of combinatorial optimization (MAX-SAT) and nonsmooth convex optimization (MAX-MIN) problems, which provide upper and lower bounds on the ground state energy, respectively. By systematically converging these bounds to each other, we may find and prove the exact ground state of realistic Hamiltonians whose exact solutions are difficult, if not impossible, to obtain via traditional methods. Considering that currently such practical Hamiltonians are solved using simulated annealing and genetic algorithms that are often unable to find the true global energy minimum and inherently cannot prove the optimality of their result, our paper opens the door to resolving longstanding uncertainties in lattice models of physical phenomena. An implementation of the algorithm is available at https://github.com/dkitch/maxsat-ising.
Exact Probability Distribution versus Entropy
Directory of Open Access Journals (Sweden)
Kerstin Andersson
2014-10-01
Full Text Available The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations to a natural language are considered. The guessing strategy used is guessing words in decreasing order of probability. When word and alphabet sizes are large, approximations are necessary in order to estimate the number of guesses. Several kinds of approximations are discussed demonstrating moderate requirements regarding both memory and central processing unit (CPU time. When considering realistic sizes of alphabets and words (100, the number of guesses can be estimated within minutes with reasonable accuracy (a few percent and may therefore constitute an alternative to, e.g., various entropy expressions. For many probability distributions, the density of the logarithm of probability products is close to a normal distribution. For those cases, it is possible to derive an analytical expression for the average number of guesses. The proportion of guesses needed on average compared to the total number decreases almost exponentially with the word length. The leading term in an asymptotic expansion can be used to estimate the number of guesses for large word lengths. Comparisons with analytical lower bounds and entropy expressions are also provided.
Azbel‧, Mark Ya.
2005-08-01
The exact law of mortality dynamics in changing populations and environment is derived. It includes no explicit characteristics of animal-environment interactions (metabolism, etc.) which are a must for life; it is universal for all animals, from single-cell yeast to humans, with their drastically different biology, evolutionary history, and complexity; it is rapidly (within few percent of life span) reversible. Such a law is unique for live systems with their homeostatic self-adjustment to environment (cf. thermodynamics of liquids and glasses). The law which is valid for all live, and only live, systems is their specific natural law. Mortality is an instrument of natural selection and biological diversity. Its law, which is preserved in evolution of all species, is a conservation law of mortality, selection, evolution, biology. The law implies new kinds of intrinsic mortality and adaptation which dominate in evolutionary unprecedented protected populations and, in contrast to species-specific natural selection, proceed via universal stepwise rungs and reduce to universal cellular mechanism. The law demonstrates that intrinsic mortality and at least certain aspects of aging are disposable evolutionary byproducts, and directed genetic and/or biological changes may yield healthy and vital Methuselah lifespan. This is consistent with experiments. Universality implies that single-cell yeast may provide a master key to the cellular mechanism of universal mortality, aging, selection, evolution, and its regulation in all animals. One may look for its manifestations in animal cells also, e.g., in their replicative senescence and cancer. Evolutionary origin and genetic nature of universality are suggested.
Bounds on fake weighted projective space
Kasprzyk, Alexander M.
2009-01-01
A fake weighted projective space X is a Q-factorial toric variety with Picard number one. As with weighted projective space, X comes equipped with a set of weights (λ0, ..., λn). We see how the singularities of P (λ0, ..., λn) influence the singularities of X, and how the weights bound the number of possible fake weighted projective spaces for a fixed dimension. Finally, we present an upper bound on the ratios λj/Σλi if we wish X to have only terminal (or canonical) singularities.
Bagherinejad, Jafar; Niknam, Azar
2017-06-01
In this paper, a leader-follower competitive facility location problem considering the reactions of the competitors is studied. A model for locating new facilities and determining levels of quality for the facilities of the leader firm is proposed. Moreover, changes in the location and quality of existing facilities in a competitive market where a competitor offers the same goods or services are taken into account. The competitor could react by opening new facilities, closing existing ones, and adjusting the quality levels of its existing facilities. The market share, captured by each facility, depends on its distance to customer and its quality that is calculated based on the probabilistic Huff's model. Each firm aims to maximize its profit subject to constraints on quality levels and budget of setting up new facilities. This problem is formulated as a bi-level mixed integer non-linear model. The model is solved using a combination of Tabu Search with an exact method. The performance of the proposed algorithm is compared with an upper bound that is achieved by applying Karush-Kuhn-Tucker conditions. Computational results show that our algorithm finds near the upper bound solutions in a reasonable time.
Exact Solutions in Modified Gravity Models
Directory of Open Access Journals (Sweden)
Valery V. Obukhov
2012-06-01
Full Text Available We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations. In this paper we consider a number of exact solutions obtained by the method of separation of variables. Some applications to Cosmology and BH entropy are briefly mentioned.
Directory of Open Access Journals (Sweden)
Igor Papalia
Full Text Available End-to-side nerve coaptation brings regenerating axons from the donor to the recipient nerve. Several techniques have been used to perform coaptation: microsurgical sutures with and without opening a window into the epi(perineurial connective tissue; among these, window techniques have been proven more effective in inducing axonal regeneration. The authors developed a sutureless model of end-to-side coaptation in the rat upper limb. In 19 adult Wistar rats, the median and the ulnar nerves of the left arm were approached from the axillary region, the median nerve transected and the proximal stump sutured to the pectoral muscle to prevent regeneration. Animals were then randomly divided in two experimental groups (7 animals each, 5 animals acting as control: Group 1: the distal stump of the transected median nerve was fixed to the ulnar nerve by applying cyanoacrylate solution; Group 2: a small epineurial window was opened into the epineurium of the ulnar nerve, caring to avoid damage to the nerve fibres; the distal stump of the transected median nerve was then fixed to the ulnar nerve by applying cyanoacrylate solution. The grasping test for functional evaluation was repeated every 10-11 weeks starting from week-15, up to the sacrifice (week 36. At week 36, the animals were sacrificed and the regenerated nerves harvested and processed for morphological investigations (high-resolution light microscopy as well as stereological and morphometrical analysis. This study shows that a cyanoacrylate in end-to-side coaptation produces scarless axon regeneration without toxic effects; b axonal regeneration and myelination occur even without opening an epineurial window, but c the window is related to a larger number of regenerating fibres, especially myelinated and mature, and better functional outcomes.
Papalia, Igor; Magaudda, Ludovico; Righi, Maria; Ronchi, Giulia; Viano, Nicoletta; Geuna, Stefano; Colonna, Michele Rosario
2016-01-01
End-to-side nerve coaptation brings regenerating axons from the donor to the recipient nerve. Several techniques have been used to perform coaptation: microsurgical sutures with and without opening a window into the epi(peri)neurial connective tissue; among these, window techniques have been proven more effective in inducing axonal regeneration. The authors developed a sutureless model of end-to-side coaptation in the rat upper limb. In 19 adult Wistar rats, the median and the ulnar nerves of the left arm were approached from the axillary region, the median nerve transected and the proximal stump sutured to the pectoral muscle to prevent regeneration. Animals were then randomly divided in two experimental groups (7 animals each, 5 animals acting as control): Group 1: the distal stump of the transected median nerve was fixed to the ulnar nerve by applying cyanoacrylate solution; Group 2: a small epineurial window was opened into the epineurium of the ulnar nerve, caring to avoid damage to the nerve fibres; the distal stump of the transected median nerve was then fixed to the ulnar nerve by applying cyanoacrylate solution. The grasping test for functional evaluation was repeated every 10-11 weeks starting from week-15, up to the sacrifice (week 36). At week 36, the animals were sacrificed and the regenerated nerves harvested and processed for morphological investigations (high-resolution light microscopy as well as stereological and morphometrical analysis). This study shows that a) cyanoacrylate in end-to-side coaptation produces scarless axon regeneration without toxic effects; b) axonal regeneration and myelination occur even without opening an epineurial window, but c) the window is related to a larger number of regenerating fibres, especially myelinated and mature, and better functional outcomes.
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Cangalovic, Mirjana; Schreuder, J.A.M.
1991-01-01
An exact algorithm is presented for determining the interval chromatic number of a weighted graph. The algorithm is based on enumeration and the Branch-and-Bound principle. Computational experiments with the application of the algorithm to random weighted graphs are given. The algorithm and its
Exit times for a class of random walks: exact distribution results
DEFF Research Database (Denmark)
Jacobsen, Martin
2011-01-01
the exit possible has a Laplace transform which is a rational function. The expected exit time is also determined and the paper concludes with exact distribution results concerning exits from bounded intervals. The proofs use simple martingale techniques together with some classical expansions...
Exact analytic solutions for a Dirac electron moving in graphene under magnetic fields
Energy Technology Data Exchange (ETDEWEB)
Kuru, S [Department of Physics, Faculty of Science, Ankara University, 06100 Ankara (Turkey); Negro, J; Nieto, L M, E-mail: sengul.kuru@science.ankara.edu.t, E-mail: jnegro@fta.uva.e, E-mail: luismi@metodos.fam.cie.uva.e [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, E-47071 Valladolid (Spain)
2009-11-11
Exact analytical solutions for the bound states of a graphene Dirac electron in various magnetic fields with translational symmetry are obtained. In order to solve the time-independent Dirac-Weyl equation the factorization method used in supersymmetric quantum mechanics is adapted to this problem. The behavior of the discrete spectrum, probability and current densities are discussed.
Exact analytic solutions for a Dirac electron moving in graphene under magnetic fields.
Kuru, S; Negro, J; Nieto, L M
2009-11-11
Exact analytical solutions for the bound states of a graphene Dirac electron in various magnetic fields with translational symmetry are obtained. In order to solve the time-independent Dirac-Weyl equation the factorization method used in supersymmetric quantum mechanics is adapted to this problem. The behavior of the discrete spectrum, probability and current densities are discussed.
Tate, Stephen James
2013-10-01
In the 1960s, the technique of using cluster expansion bounds in order to achieve bounds on the virial expansion was developed by Lebowitz and Penrose (J. Math. Phys. 5:841, 1964) and Ruelle (Statistical Mechanics: Rigorous Results. Benjamin, Elmsford, 1969). This technique is generalised to more recent cluster expansion bounds by Poghosyan and Ueltschi (J. Math. Phys. 50:053509, 2009), which are related to the work of Procacci (J. Stat. Phys. 129:171, 2007) and the tree-graph identity, detailed by Brydges (Phénomènes Critiques, Systèmes Aléatoires, Théories de Jauge. Les Houches 1984, pp. 129-183, 1986). The bounds achieved by Lebowitz and Penrose can also be sharpened by doing the actual optimisation and achieving expressions in terms of the Lambert W-function. The different bound from the cluster expansion shows some improvements for bounds on the convergence of the virial expansion in the case of positive potentials, which are allowed to have a hard core.
Resistivity bound for hydrodynamic bad metals
Lucas, Andrew; Hartnoll, Sean A.
2017-10-01
We obtain a rigorous upper bound on the resistivity ρ of an electron fluid whose electronic mean free path is short compared with the scale of spatial inhomogeneities. When such a hydrodynamic electron fluid supports a nonthermal diffusion process—such as an imbalance mode between different bands—we show that the resistivity bound becomes ρ≲AΓ. The coefficient A is independent of temperature and inhomogeneity lengthscale, and Γ is a microscopic momentum-preserving scattering rate. In this way, we obtain a unified mechanism—without umklapp—for ρ˜T2 in a Fermi liquid and the crossover to ρ˜T in quantum critical regimes. This behavior is widely observed in transition metal oxides, organic metals, pnictides, and heavy fermion compounds and has presented a long-standing challenge to transport theory. Our hydrodynamic bound allows phonon contributions to diffusion constants, including thermal diffusion, to directly affect the electrical resistivity.
Quasi exact solution of the Rabi Hamiltonian
Koç, R; Tuetuencueler, H
2002-01-01
A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of orthogonal polynomials. It is also demonstrated that the Rabi system, in a particular case, coincides with the quasi exactly solvable Poeschl-Teller potential.
Quantum algorithm for exact Monte Carlo sampling
Destainville, Nicolas; Georgeot, Bertrand; Giraud, Olivier
2010-01-01
We build a quantum algorithm which uses the Grover quantum search procedure in order to sample the exact equilibrium distribution of a wide range of classical statistical mechanics systems. The algorithm is based on recently developed exact Monte Carlo sampling methods, and yields a polynomial gain compared to classical procedures.
Exact, almost and delayed fault detection
DEFF Research Database (Denmark)
Niemann, Hans Henrik; Saberi, Ali; Stoorvogel, Anton A.
1999-01-01
Considers the problem of fault detection and isolation while using zero or almost zero threshold. A number of different fault detection and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability conditions are given for the formulated design problems....... The l-step delayed fault detection problem is also considered for discrete-time systems....
New exact wave solutions for Hirota equation
Indian Academy of Sciences (India)
... integrals in polynomial form with a high accuracy for two-dimensional plane autonomous systems. Exact soliton solution is constructed through the established first integrals. This method is a powerful tool for searching exact travelling solutions of nonlinear partial differential equations (NPDEs) in mathematical physics.
Fitness levels with tail bounds for the analysis of randomized search heuristics
DEFF Research Database (Denmark)
Witt, Carsten
2014-01-01
The fitness-level method, also called the method of f-based partitions, is an intuitive and widely used technique for the running time analysis of randomized search heuristics. It was originally defined to prove upper and lower bounds on the expected running time. Recently, upper tail bounds were...
Andreev bound states. Some quasiclassical reflections
Energy Technology Data Exchange (ETDEWEB)
Lin, Y., E-mail: yiriolin@illinois.edu; Leggett, A. J. [University of Illinois at Urhana-Champaign, Dept. of Physics (United States)
2014-12-15
We discuss a very simple and essentially exactly solvable model problem which illustrates some nice features of Andreev bound states, namely, the trapping of a single Bogoliubov quasiparticle in a neutral s-wave BCS superfluid by a wide and shallow Zeeman trap. In the quasiclassical limit, the ground state is a doublet with a splitting which is proportional to the exponentially small amplitude for “normal” reflection by the edges of the trap. We comment briefly on a prima facie paradox concerning the continuity equation and conjecture a resolution to it.
Energy Technology Data Exchange (ETDEWEB)
Warne, L.K.; Merewether, K.O.; Chen, K.C.; Jorgenson, R.E.; Morris, M.E.; Solberg, J.E.; Lewis, J.G. [Sandia National Labs., Albuquerque, NM (United States); Derr, W. [Derr Enterprises, Albuquerque, NM (United States)
1996-07-01
Test data on canonical weapon-like fixtures are used to validate previously developed analytical bounding results. The test fixtures were constructed to simulate (but be slightly worse than) weapon ports of entry but have known geometries (and electrical points of contact). The exterior of the test fixtures exhibited exterior resonant enhancement of the incident fields at the ports of entry with magnitudes equal to those of weapon geometries. The interior consisted of loaded transmission lines adjusted to maximize received energy or voltage but incorporating practical weapon geometrical constraints. New analytical results are also presented for bounding the energies associated with multiple bolt joints and for bounding the exterior resonant enhancement of the exciting fields.
Bounds for entanglement of formation of two mode squeezed thermal states
Energy Technology Data Exchange (ETDEWEB)
Chen, Xiao-Yu; Qiu, Pei-Liang
2003-07-28
The upper and lower bounds of entanglement of formation are given for two mode squeezed thermal state. The bounds are compared with other entanglement measure or bounds. The entanglement distillation and the relative entropy of entanglement of infinitive squeezed state are obtained at the postulation of hashing inequality.
Bounds on Threshold of Regular Random $k$-SAT
Rathi, Vishwambhar; Rasmussen, Lars; Skoglund, Mikael
2010-01-01
We consider the regular model of formula generation in conjunctive normal form (CNF) introduced by Boufkhad et. al. We derive an upper bound on the satisfiability threshold and NAE-satisfiability threshold for regular random $k$-SAT for any $k \\geq 3$. We show that these bounds matches with the corresponding bound for the uniform model of formula generation. We derive lower bound on the threshold by applying the second moment method to the number of satisfying assignments. For large $k$, we note that the obtained lower bounds on the threshold of a regular random formula converges to the lower bound obtained for the uniform model. Thus, we answer the question posed in \\cite{AcM06} regarding the performance of the second moment method for regular random formulas.
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Faust, Sebastian; Mukherjee, Pratyay
2013-01-01
a bounded tamper and leakage resilient CCA secure public key cryptosystem based on the DDH assumption. We first define a weaker CPA-like security notion that we can instantiate based on DDH, and then we give a general compiler that yields CCA-security with tamper and leakage resilience. This requires...... a public tamper-proof common reference string. Finally, we explain how to boost bounded tampering and leakage resilience (as in 1. and 2. above) to continuous tampering and leakage resilience, in the so-called floppy model where each user has a personal hardware token (containing leak- and tamper...
Reduced description of exact coherent states in parallel shear flows.
Beaume, Cédric; Chini, Gregory P; Julien, Keith; Knobloch, Edgar
2015-04-01
A reduced description of exact coherent structures in the transition regime of plane parallel shear flows is developed, based on the Reynolds number scaling of streamwise-averaged (mean) and streamwise-varying (fluctuation) velocities observed in numerical simulations. The resulting system is characterized by an effective unit Reynolds number mean equation coupled to linear equations for the fluctuations, regularized by formally higher-order diffusion. Stationary coherent states are computed by solving the resulting equations simultaneously using a robust numerical algorithm developed for this purpose. The algorithm determines self-consistently the amplitude of the fluctuations for which the associated mean flow is just such that the fluctuations neither grow nor decay. The procedure is used to compute exact coherent states of a flow introduced by Drazin and Reid [Hydrodynamic Stability (Cambridge University Press, Cambridge, UK, 1981)] and studied by Waleffe [Phys. Fluids 9, 883 (1997)]: a linearly stable, plane parallel shear flow confined between stationary stress-free walls and driven by a sinusoidal body force. Numerical continuation of the lower-branch states to lower Reynolds numbers reveals the presence of a saddle node; the saddle node allows access to upper-branch states that are, like the lower-branch states, self-consistently described by the reduced equations. Both lower- and upper-branch states are characterized in detail.
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Appell, Jürgen; Merentes Díaz, Nelson José
2013-01-01
This monographis a self-contained exposition of the definition and properties of functionsof bounded variation and their various generalizations; the analytical properties of nonlinear composition operators in spaces of such functions; applications to Fourier analysis, nonlinear integral equations, and boundary value problems. The book is written for non-specialists. Every chapter closes with a list of exercises and open problems.
Hoyer, Paul
2017-05-01
Bound state poles in the S-matrix of perturbative QED are generated by the divergence of the expansion in α . The perturbative corrections are necessarily singular when expanding around free, {O}( α ^0 ) in and out states that have no overlap with finite-sized atomic wave functions. Nevertheless, measurables such as binding energies do have well-behaved expansions in powers of α (and log α ). It is desirable to formulate the concept of "lowest order" for gauge theory bound states such that higher order corrections vanish in the α → 0 limit. This may allow to determine a lowest order term for QCD hadrons which incorporates essential features such as confinement and chiral symmetry breaking, and thus can serve as the starting point of a useful perturbative expansion. I discuss a "Born" (no loop, lowest order in \\hbar ) approximation. Born level states are bound by gauge fields which satisfy the classical field equations. Gauss' law determines a distinct field A^0({\\varvec{x}}) for each instantaneous position of the charges. A Poincaré covariant boundary condition for the gluon field leads to a confining potential for q\\bar{q} and qqq states. In frames where the bound state is in motion the classical gauge field is obtained by a Lorentz boost of the rest frame field.
Exact Tests for Hardy-Weinberg Proportions
National Research Council Canada - National Science Library
Engels, William R
2009-01-01
Exact conditional tests are often required to evaluate statistically whether a sample of diploids comes from a population with Hardy-Weinberg proportions or to confirm the accuracy of genotype assignments...
Fast Exact Euclidean Distance (FEED) Transformation
Schouten, Theo; Kittler, J.; van den Broek, Egon; Petrou, M.; Nixon, M.
2004-01-01
Fast Exact Euclidean Distance (FEED) transformation is introduced, starting from the inverse of the distance transformation. The prohibitive computational cost of a naive implementation of traditional Euclidean Distance Transformation, is tackled by three operations: restriction of both the number
Exact Test of Independence Using Mutual Information
Directory of Open Access Journals (Sweden)
Shawn D. Pethel
2014-05-01
Full Text Available Using a recently discovered method for producing random symbol sequences with prescribed transition counts, we present an exact null hypothesis significance test (NHST for mutual information between two random variables, the null hypothesis being that the mutual information is zero (i.e., independence. The exact tests reported in the literature assume that data samples for each variable are sequentially independent and identically distributed (iid. In general, time series data have dependencies (Markov structure that violate this condition. The algorithm given in this paper is the first exact significance test of mutual information that takes into account the Markov structure. When the Markov order is not known or indefinite, an exact test is used to determine an effective Markov order.
Exact Algorithms for Solving Stochastic Games
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels
2012-01-01
Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games.......Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....
Tight bounds on accessible information and informational power
Dall'Arno, Michele; Buscemi, Francesco; Ozawa, Masanao
2014-06-01
The accessible information quantifies the amount of classical information that can be extracted from an ensemble of quantum states. Analogously, the informational power quantifies the amount of classical information that can be extracted by a quantum measurement. For both quantities, we provide upper and lower bounds that depend only on the dimension of the system, and we prove their tightness. In the case of symmetric informationally complete (SIC) ensembles and measurements, stronger bounds are provided and their tightness proved for qubits and qutrits. From our upper bounds, we notice, perhaps surprisingly, that the statistics generated by SIC ensembles or measurements in arbitrary dimension, though optimal for tomographic purposes, in fact never contain more than just one bit of information, the rest being constituted by completely random bits. On the other hand, from our lower bounds, we obtain an explicit strategy beating the so-called pretty-good one for the extraction of mutual information in the case of SIC ensembles and measurements.
Exact Fundamental Limits of the First and Second Hyperpolarizabilities
Lytel, Rick; Mossman, Sean; Crowell, Ethan; Kuzyk, Mark G.
2017-08-01
Nonlinear optical interactions of light with materials originate in the microscopic response of the molecular constituents to excitation by an optical field, and are expressed by the first (β ) and second (γ ) hyperpolarizabilities. Upper bounds to these quantities were derived seventeen years ago using approximate, truncated state models that violated completeness and unitarity, and far exceed those achieved by potential optimization of analytical systems. This Letter determines the fundamental limits of the first and second hyperpolarizability tensors using Monte Carlo sampling of energy spectra and transition moments constrained by the diagonal Thomas-Reiche-Kuhn (TRK) sum rules and filtered by the off-diagonal TRK sum rules. The upper bounds of β and γ are determined from these quantities by applying error-refined extrapolation to perfect compliance with the sum rules. The method yields the largest diagonal component of the hyperpolarizabilities for an arbitrary number of interacting electrons in any number of dimensions. The new method provides design insight to the synthetic chemist and nanophysicist for approaching the limits. This analysis also reveals that the special cases which lead to divergent nonlinearities in the many-state catastrophe are not physically realizable.
Inequalities involving upper bounds for certain matrix operators
Indian Academy of Sciences (India)
Copson and Hilbert matrix operators, which are recently considered in [5] and [6] and similar to that in [10]. Keywords. Inequality; norm; summability matrix; Hausdorff matrix; Hilbert matrix; weighted sequence space; Lorentz sequence space. 1. Introduction. We study the norm of a certain matrix operator on lp(w) and Lorentz ...
Upper and Lower Bounds for Numerical Radii of Block Shifts
Gau, Hwa-Long; Wu, Pei Yuan
2014-01-01
For any $n$-by-$n$ matrix $A$ of the form \\[[\\begin{array}{cccc} 0 & A_1 & & \\\\ & 0 & \\ddots & \\\\ & & \\ddots & A_{k-1} \\\\ & & & 0\\end{array}],\\] we consider two $k$-by-$k$ matrices \\[A'=[\\begin{array}{cccc} 0 & \\|A_1\\| & & \\\\ & 0 & \\ddots & \\\\ & & \\ddots & \\|A_{k-1}\\| \\\\ & & & 0\\end{array}] \\ {and} \\ A''=[\\begin{array}{cccc} 0 & m(A_1) & & \\\\ & 0 & \\ddots & \\\\ & & \\ddots & m(A_{k-1}) \\\\ & & & 0\\end{array}],\\] where $\\|\\cdot\\|$ and $m(\\cdot)$ denote the operator norm and minimum modulus of a m...
Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
Bender, Carl M.; Mannheim, Philip D.
2008-07-01
In a recent paper Bender and Mannheim showed that the unequal-frequency fourth-order derivative Pais-Uhlenbeck oscillator model has a realization in which the energy eigenvalues are real and bounded below, the Hilbert-space inner product is positive definite, and time evolution is unitary. Central to that analysis was the recognition that the Hamiltonian HPU of the model is PT symmetric. This Hamiltonian was mapped to a conventional Dirac-Hermitian Hamiltonian via a similarity transformation whose form was found exactly. The present paper explores the equal-frequency limit of the same model. It is shown that in this limit the similarity transform that was used for the unequal-frequency case becomes singular and that HPU becomes a Jordan-block operator, which is nondiagonalizable and has fewer energy eigenstates than eigenvalues. Such a Hamiltonian has no Hermitian counterpart. Thus, the equal-frequency PT theory emerges as a distinct realization of quantum mechanics. The quantum mechanics associated with this Jordan-block Hamiltonian can be treated exactly. It is shown that the Hilbert space is complete with a set of nonstationary solutions to the Schrödinger equation replacing the missing stationary ones. These nonstationary states are needed to establish that the Jordan-block Hamiltonian of the equal-frequency Pais-Uhlenbeck model generates unitary time evolution.
Meyer, B. K.
In the preceding chapter, we concentrated on the properties of free excitons. These free excitons may move through the sample and hit a trap, a nonradiative or a radiative recombination center. At low temperatures, the latter case gives rise to either deep center luminescence, mentioned in Sect. 7.1 and discussed in detail in Chap. 9, or to the luminescence of bound exciton complexes (BE or BEC). The chapter continues with the most prominent of these BECs, namely A-excitons bound to neutral donors. The next aspects are the more weakly BEs at ionized donors. The Sect. 7.4 treats the binding or localization energies of BEC from a theoretical point of view, while Sect. 7.5 is dedicated to excited states of BECs, which contain either holes from deeper valence bands or an envelope function with higher quantum numbers. The last section is devoted to donor-acceptor pair transitions. There is no section devoted specifically to excitons bound to neutral acceptors, because this topic is still partly controversially discussed. Instead, information on these A0X complexes is scattered over the whole chapter, however, with some special emphasis seen in Sects. 7.1, 7.4, and 7.5.
Prüstel, Thorsten; Meier-Schellersheim, Martin
2012-01-01
We derive an exact Green's function of the diffusion equation for a pair of disk-shaped interacting particles in two dimensions subject to a backreaction boundary condition. Furthermore, we use the obtained function to calculate exact expressions for the survival probability and the time-dependent rate coefficient for the initially unbound pair and the survival probability of the bound state. The derived expressions will be of particular utility for the description of reversible membrane-bound reactions in cell biology. PMID:22894329
Any Two Learning Algorithms Are (Almost) Exactly Identical
Wolpert, David H.
2000-01-01
This paper shows that if one is provided with a loss function, it can be used in a natural way to specify a distance measure quantifying the similarity of any two supervised learning algorithms, even non-parametric algorithms. Intuitively, this measure gives the fraction of targets and training sets for which the expected performance of the two algorithms differs significantly. Bounds on the value of this distance are calculated for the case of binary outputs and 0-1 loss, indicating that any two learning algorithms are almost exactly identical for such scenarios. As an example, for any two algorithms A and B, even for small input spaces and training sets, for less than 2e(-50) of all targets will the difference between A's and B's generalization performance of exceed 1%. In particular, this is true if B is bagging applied to A, or boosting applied to A. These bounds can be viewed alternatively as telling us, for example, that the simple English phrase 'I expect that algorithm A will generalize from the training set with an accuracy of at least 75% on the rest of the target' conveys 20,000 bytes of information concerning the target. The paper ends by discussing some of the subtleties of extending the distance measure to give a full (non-parametric) differential geometry of the manifold of learning algorithms.
Landscape of the exact energy functional
Cohen, Aron J
2015-01-01
One of the great challenges of electronic structure theory is the search for the exact functional of density functional theory (DFT). Its existence is undoubted but it is hard to even conceptualize it as it is a surface in a massively multidimensional space. However, the asymmetric two-site Hubbard model has a two-dimensional universe of density matrices and the exact functional simply becomes a function of two variables whose landscape can be calculated, visualized and explored. This one unique surface contains all the possible physics of any system in this universe. A walk on this landscape, moved to the angle of any one-electron Hamiltonian, gives a valley whose minimum is the exact total energy. We show concrete examples of pure-state density matrices that are not v-representable due to the underlying non-convex nature of the exact functional. Using the Perdew, Parr, Levy and Balduz extension to fractional ensembles we calculate the exact functional for all numbers of electrons. The derivative discontinui...
Full Text Available ... Upper Endoscopy (EGD) The Latest Practice Guidelines Technology Reviews Articles Videos Events & Products Ensuring the Safety of ... S0016-5107(98)70268-8 View more Technology Reviews Members-only content Document Link: ASGE Leading Edge: ...
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Bounds for departure from normality and the Frobenius norm of matrix eigenvalues
Energy Technology Data Exchange (ETDEWEB)
Lee, S.L.
1994-12-01
New lower and upper bounds for the departure from normality and the Frobenius norm of the eigenvalues of a matrix axe given. The significant properties of these bounds axe also described. For example, the upper bound for matrix eigenvalues improves upon the one derived by Kress, de Vries and Wegmann in [Lin. Alg. Appl., 8 (1974), pp. 109-120]. The upper bound for departure from normality is sharp for any matrix whose eigenvalues are collinear in the complex plane. Moreover, the latter formula is a practical estimate that costs (at most) 2m multiplications, where m is the number of nonzeros in the matrix. In terms of applications, the results can be used to bound from above the sensitivity of eigenvalues to matrix perturbations or bound from below the condition number of the eigenbasis of a matrix.
Quantum quenches to the attractive one-dimensional Bose gas: exact results
Directory of Open Access Journals (Sweden)
Lorenzo Piroli, Pasquale Calabrese, Fabian H. L. Essler
2016-09-01
Full Text Available We study quantum quenches to the one-dimensional Bose gas with attractive interactions in the case when the initial state is an ideal one-dimensional Bose condensate. We focus on properties of the stationary state reached at late times after the quench. This displays a finite density of multi-particle bound states, whose rapidity distribution is determined exactly by means of the quench action method. We discuss the relevance of the multi-particle bound states for the physical properties of the system, computing in particular the stationary value of the local pair correlation function $g_2$.
Finite energy bounds for $\\piN$ scattering
Grassberger, P; Schwela, D
1974-01-01
Upper bounds on energy averaged pi N cross sections are given. Using low energy data and data from pi N backward scattering and NN to pi pi annihilation, it is found that sigma /sub tot/
OPRA capacity bounds for selection diversity over generalized fading channels
Hanif, Muhammad Fainan
2014-05-01
Channel side information at the transmitter can increase the average capacity by enabling optimal power and rate adaptation. The resulting optimal power and rate adaptation (OPRA) capacity rarely has a closed-form analytic expression. In this paper, lower and upper bounds on OPRA capacity for selection diversity scheme are presented. These bounds hold for variety of fading channels including log-normal and generalized Gamma distributed models and have very simple analytic expressions for easy evaluation even for kth best path selection. Some selected numerical results show that the newly proposed bounds closely approximate the actual OPRA capacity. © 2014 IEEE.
Bounds of memory strength for power-law series
Guo, Fangjian; Yang, Dan; Yang, Zimo; Zhao, Zhi-Dan; Zhou, Tao
2017-05-01
Many time series produced by complex systems are empirically found to follow power-law distributions with different exponents α . By permuting the independently drawn samples from a power-law distribution, we present nontrivial bounds on the memory strength (first-order autocorrelation) as a function of α , which are markedly different from the ordinary ±1 bounds for Gaussian or uniform distributions. When 1 3 , the upper bound remains +1 while the lower bound descends below 0. Theoretical bounds agree well with numerical simulations. Based on the posts on Twitter, ratings of MovieLens, calling records of the mobile operator Orange, and the browsing behavior of Taobao, we find that empirical power-law-distributed data produced by human activities obey such constraints. The present findings explain some observed constraints in bursty time series and scale-free networks and challenge the validity of measures such as autocorrelation and assortativity coefficient in heterogeneous systems.
Exact solutions in three-dimensional gravity
Garcia-Diaz, Alberto A
2017-01-01
A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...
Exact and approximate calculation of giant resonances
Energy Technology Data Exchange (ETDEWEB)
Vertse, T. [Magyar Tudomanyos Akademia, Debrecen (Hungary). Atommag Kutato Intezete; Liotta, R.J. [Royal Inst. of Tech., Stockholm (Sweden); Maglione, E. [Padua Univ. (Italy). Ist. di Fisica
1995-02-13
Energies, sum rules and partial decay widths of giant resonances in {sup 208}Pb are calculated solving exactly the continuum RPA equations corresponding to a central Woods-Saxon potential. For comparison an approximate treatment of those quantities in terms of pole expansions of the Green function (Berggren and Mittag-Leffler) is also performed. It is found that the approximated results agree well with the exact ones. Comparison with experimental data is made and a search for physically meaningful resonances is carried out. ((orig.))
Exact Asymptotics of Bivariate Scale Mixture Distributions
Hashorva, Enkelejd
2009-01-01
Let (RU_1, R U_2) be a given bivariate scale mixture random vector, with R>0 being independent of the bivariate random vector (U_1,U_2). In this paper we derive exact asymptotic expansions of the tail probability P{RU_1> x, RU_2> ax}, a \\in (0,1] as x tends infintiy assuming that R has distribution function in the Gumbel max-domain of attraction and (U_1,U_2) has a specific tail behaviour around some absorbing point. As a special case of our results we retrieve the exact asymptotic behaviour ...
Energy Technology Data Exchange (ETDEWEB)
Maccari, Attilio
2003-03-01
The asymptotic perturbation (AP) method is applied to the study of the nonlinear Klein-Gordon equation in 3+1 dimensions with harmonic potential and external periodic excitation supposed to be in primary resonance with the frequency of a generic mode. The AP method uses two different procedures for the solutions: introducing an asymptotic temporal rescaling and balancing of the harmonic terms with a simple iteration. Standard quantum mechanics can be used to derive the lowest order approximate solution and amplitude and phase modulation equations are obtained. External force-response and frequency-response curves are found and the existence of dromions trapped in bound states is demonstrated.
A useful strong lower bound on two-qubit concurrence
Jafarpour, Mojtaba; Sabour, Abbass
2012-12-01
A new strong lower bound on concurrence for two-qubit states is derived. Its equality with the concurrence itself for the pure- and X-states is proved analytically; while extensive numerical computations show that equality for a general mixed state may also exist. Being a very simple function and easy to calculate, it is more convenient and practical than the exact value in some cases, including entanglement investigations in spin chains. We study thermal localizable entanglement in spin chains as an example, to demonstrate the convenience of this bound.
The number of minimal surfaces bounded by Enneper's wire
Beeson, Michael
2015-01-01
Enneper's wire, the image of the circle of radius $R$ under Enneper's surface, bounds exactly three minimal surfaces for $R$ between 1 and $\\sqrt 3$, and these three surfaces depend continuously on $R$. The other two surfaces (besides Enneper's surface) are absolute minima of area among disk-type surfaces bounded by Enneper's wire. These surfaces each have a unique horizontal tangent plane, whose height can be computed from $R$, and they are invariant under reflections in the planes $x_1=0$ a...
Verbal Interference Suppresses Exact Numerical Representation
Frank, Michael C.; Fedorenko, Evelina; Lai, Peter; Saxe, Rebecca; Gibson, Edward
2012-01-01
Language for number is an important case study of the relationship between language and cognition because the mechanisms of non-verbal numerical cognition are well-understood. When the Piraha (an Amazonian hunter-gatherer tribe who have no exact number words) are tested in non-verbal numerical tasks, they are able to perform one-to-one matching…
The Exact Renormalization Group -- renormalization theory revisited --
Sonoda, Hidenori
2007-01-01
We overview the entire renormalization theory, both perturbative and non-perturbative, by the method of the exact renormalization group (ERG). We emphasize particularly on the perturbative application of the ERG to the phi4 theory and QED in the four dimensional euclidean space.
Python for Education: The Exact Cover Problem
Directory of Open Access Journals (Sweden)
2011-06-01
Full Text Available
Python implementation of Algorithm X by Knuth is presented.
Algorithm X finds all solutions to the exact cover problem.
The exemplary results for pentominoes, Latin squares and Sudoku
are given.
On exact solutions of the Bogoyavlenskii equation
Indian Academy of Sciences (India)
Abstract. Exact solutions for the Bogoyavlenskii equation are studied by the travelling wave method and the singular manifold method. It is found that the linear superposition of the shock wave solution and the complex solitary wave solution for the physical field is still a solution of the equation of interest, except for a ...
Compiling Relational Bayesian Networks for Exact Inference
DEFF Research Database (Denmark)
Jaeger, Manfred; Chavira, Mark; Darwiche, Adnan
2004-01-01
We describe a system for exact inference with relational Bayesian networks as defined in the publicly available \\primula\\ tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating and ...
Exact Optimum Design of Segmented Thermoelectric Generators
Directory of Open Access Journals (Sweden)
M. Zare
2016-01-01
Full Text Available A considerable difference between experimental and theoretical results has been observed in the studies of segmented thermoelectric generators (STEGs. Because of simplicity, the approximate methods are widely used for design and optimization of the STEGs. This study is focused on employment of exact method for design and optimization of STEGs and comparison of exact and approximate results. Thus, using new highly efficient thermoelectric materials, four STEGs are proposed to operate in the temperature range of 300 to 1300 kelvins. The proposed STEGs are optimally designed to achieve maximum efficiency. Design and performance characteristics of the optimized generators including maximum conversion efficiency and length of elements are calculated through both exact and approximate methods. The comparison indicates that the approximate method can cause a difference up to 20% in calculation of some design characteristics despite its appropriate results in efficiency calculation. The results also show that the maximum theoretical efficiency of 23.08% is achievable using the new proposed STEGs. Compatibility factor of the selected materials for the proposed STEGs is also calculated using both exact and approximate methods. The comparison indicates a negligible difference in calculation of compatibility factor, despite the considerable difference in calculation of reduced efficiency (temperature independence efficiency.
Exact solutions for the biadjoint scalar field
Energy Technology Data Exchange (ETDEWEB)
White, C.D., E-mail: Christopher.White@glasgow.ac.uk [School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, Scotland (United Kingdom); Centre for Research in String Theory, Queen Mary University of London, London E1 4NS (United Kingdom)
2016-12-10
Biadjoint scalar theories are novel field theories that arise in the study of non-abelian gauge and gravity amplitudes. In this short paper, we present exact nonperturbative solutions of the field equations, and compare their properties with monopole-like solutions in non-abelian gauge theory. Our results may pave the way for nonperturbative studies of the double copy.
New exact wave solutions for Hirota equation
Indian Academy of Sciences (India)
Nonlinear partial differential equations (NPDEs) of mathematical physics are major sub- jects in physical science. With the development of soliton theory, many useful methods for obtaining exact solutions of NPDEs have been presented. Some of them are: the (G /G)- expansion method [1–4], the simplest equation method ...
The exact solution of the Schrödinger equation with a polynomially spatially varying mass
Bednarik, Michal; Cervenka, Milan
2017-07-01
The Schrödinger equation with a position-dependent mass (SEPDM) is employed in many areas of quantum physics. Exact solutions for the SEPDM lie at the center of interest of the professional public because it helps us to understand the behavior of quantum particles in the cases in which their mass varies spatially. For this purpose, we used the mass function represented by a quartic polynomial and a quadratic potential function, which extends the current class of exact solutions of the SEPDM. The exact analytical solution of the problem is expressed as a linear combination of local Heun functions. Heun's equation contains many parameters, resulting in its general nature. We studied how limit changes in some of these parameters will affect the solution of the SEPDM. The obtained solutions are particularly suitable for the transfer matrix method and solutions of scattering problems; this is demonstrated by the calculation of bound states.
Stieltjes electrostatic model interpretation for bound state problems
Indian Academy of Sciences (India)
+ iQ(xk) = 0, 1 ≤ k ≤ n. (17) the solution for the differential eq. (17), for an exactly solvable potential that is for cer- tain Q(xk), are the zeros of appropriate orthogonal polynomials. The interval is fixed by the fixed poles of the potential. It is well known that the classical orthogonal poly- nomials arise as solutions to the bound ...
Bounds for the variance of an inverse binomial estimator
A. Sahai; J.M. Buhrman
1979-01-01
textabstractSummary Best [1] found the variance of the minimum variance unbiased estimator of the parameter p of the negative binomial distribution. Mikulski and Sm [2] gave an upper bound to it, easier to calculate than Best's expression and a good approximation for small values of p and large
Semidefinite bounds for nonbinary codes based on quadruples
B. Litjens (Bart); S.C. Polak (Sven); A. Schrijver (Alexander)
2017-01-01
textabstractFor nonnegative integers q, n, d, let Aq(n, d) denote the maximum cardinality of a code of length n over an alphabet [q] with q letters and with minimum distance at least d. We consider the following upper bound on Aq(n, d). For any k, let Ck be the collection of codes of
Sharp Bounds by Probability-Generating Functions and Variable Drift
DEFF Research Database (Denmark)
Doerr, Benjamin; Fouz, Mahmoud; Witt, Carsten
2011-01-01
We introduce to the runtime analysis of evolutionary algorithms two powerful techniques: probability-generating functions and variable drift analysis. They are shown to provide a clean framework for proving sharp upper and lower bounds. As an application, we improve the results by Doerr et al...
Optimal portfolio selection for cashflows with bounded capital at risk
Vyncke, D.; Goovaerts, M.J.; Dhaene, J.L.M.; Vanduffel, S.
2005-01-01
We consider a continuous-time Markowitz type portfolio problem that consists of minimizing the discounted cost of a given cash-fl ow under the constraint of a restricted Capital at Risk. In a Black-Scholes setting, upper and lower bounds are obtained by means of simple analytical expressions that
Solving the minimum flow problem with interval bounds and flows
Indian Academy of Sciences (India)
The minimum cost ﬂow problem with interval data can be solved using two minimum cost ﬂow problems with crisp data. In this paper, the idea of Ghiyasvand was extended for solving the minimum ﬂow problem with interval-valued lower, upper bounds and ﬂows. This problem can be solved using two minimum ﬂow ...
Hartree–Fock variational bounds for ground state energy of ...
Indian Academy of Sciences (India)
We use different determinantal Hartree–Fock (HF) wave functions to calculate true variational upper bounds for the ground state energy of spin-half fermions in volume 0, with mass , electric charge zero, and magnetic moment , interacting through magnetic dipole–dipole interaction. We ﬁnd that at high densities ...
Viscosity bound for anisotropic superfluids in higher derivative gravity
Energy Technology Data Exchange (ETDEWEB)
Bhattacharyya, Arpan; Roychowdhury, Dibakar [Centre for High Energy Physics, Indian Institute of Science,C.V. Raman Avenue, Bangalore 560012 (India)
2015-03-11
In the present paper, based on the principles of gauge/gravity duality we analytically compute the shear viscosity to entropy (η/s) ratio corresponding to the super fluid phase in Einstein Gauss-Bonnet gravity. From our analysis we note that the ratio indeed receives a finite temperature correction below certain critical temperature (T
The Exact Limit of Some Cubic Towers
DEFF Research Database (Denmark)
Anbar Meidl, Nurdagül; Beelen, Peter; Nguyen, Nhut
2017-01-01
Recently, a new explicit tower of function fields was introduced by Bassa, Beelen, Garcia and Stichtenoth (BBGS). This resulted in currently the best known lower bound for Ihara’s constant in the case of non-prime finite fields. In particular over cubic fields, the tower’s limit is at least as good...
On the Content Bound for Real Quadratic Field Extensions
Directory of Open Access Journals (Sweden)
Robert G. Underwood
2012-12-01
Full Text Available Let K be a finite extension of Q and let S = {ν} denote the collection of K normalized absolute values on K. Let V+K denote the additive group of adeles over K and let K ≥0 c : V + → R denote the content map defined as c({aν } = Q K ν ∈S ν (aν for {aν } ∈ V+K A classical result of J. W. S. Cassels states that there is a constant c > 0 depending only on the field K with the following property: if {aν } ∈ V+K with c({aν } > c, then there exists a non-zero element b ∈ K for which ν (b ≤ ν (aν , ∀ν ∈ S. Let cK be the greatest lower bound of the set of all c that satisfy this property. In the case that K is a real quadratic extension there is a known upper bound for cK due to S. Lang. The purpose of this paper is to construct a new upper bound for cK in the case that K has class number one. We compare our new bound with Lang’s bound for various real quadratic extensions and find that our new bound is better than Lang’s in many instances.
An exact algorithm for generating homogenous two-segment cutting patterns
Cui, Y.
2007-04-01
An exact algorithm is proposed for generating homogenous two-segment patterns for the constrained two-dimensional guillotine-cutting problems of rectangular items. It is a bottom-up approach combined with branch-and-bound techniques. The stock plate is divided into two segments. Each segment consists of strips of the same length and direction. Only homogenous strips are considered, each of which contains items of the same type. The strip directions of the two segments may be either the same or perpendicular to each other. The algorithm uses a tree-search procedure. It starts from an initial lower bound, implicitly generates all possible segments through the assembly of strips, and constructs possible patterns through the combination of two segments. Tighter bounds are established to discard non-promising segments. The computational results indicate that the algorithm is efficient both in computation time and in material utilization, and is able to deal with relatively large-scale problems.
Exact solution to fractional logistic equation
West, Bruce J.
2015-07-01
The logistic equation is one of the most familiar nonlinear differential equations in the biological and social sciences. Herein we provide an exact solution to an extension of this equation to incorporate memory through the use of fractional derivatives in time. The solution to the fractional logistic equation (FLE) is obtained using the Carleman embedding technique that allows the nonlinear equation to be replaced by an infinite-order set of linear equations, which we then solve exactly. The formal series expansion for the initial value solution of the FLE is shown to be expressed in terms of a series of weighted Mittag-Leffler functions that reduces to the well known analytic solution in the limit where the fractional index for the derivative approaches unity. The numerical integration to the FLE provides an excellent fit to the analytic solution. We propose this approach as a general technique for solving a class of nonlinear fractional differential equations.
The maximal family of exactly solvable chaos
Umeno, K
1996-01-01
A new two-parameter family of ergordic transformations with non-uniform invariant measures on the unit interval (I=[0,1]) is found here. The family has a special property that their invariant measures can be explicitly written in terms of algebraic functions of parameters and a dynamical variable. Furthermore, it is also proven here that this family is the most generalized class of exactly solvable chaos on (I) including the Ulam=Neumann map (y=4x(1-x)). Unpredictably, by choosing certain parameters, the maximal class of exactly solvable chaos is found to describe the asymmetric shape of the experimentally obtained first return maps of the Beloussof-Zhabotinski chemical reaction.
Exact Relativistic Magnetized Haloes around Rotating Disks
Directory of Open Access Journals (Sweden)
Antonio C. Gutiérrez-Piñeres
2015-01-01
Full Text Available The study of the dynamics of magnetic fields in galaxies is one of important problems in formation and evolution of galaxies. In this paper, we present the exact relativistic treatment of a rotating disk surrounded by a magnetized material halo. The features of the halo and disk are described by the distributional energy-momentum tensor of a general fluid in canonical form. All the relevant quantities and the metric and electromagnetic potentials are exactly determined by an arbitrary harmonic function only. For instance, the generalized Kuzmin-disk potential is used. The particular class of solutions obtained is asymptotically flat and satisfies all the energy conditions. Moreover, the motion of a charged particle on the halo is described. As far as we know, this is the first relativistic model describing analytically the magnetized halo of a rotating disk.
Exact solutions for helical magnetohydrodynamic equilibria
Energy Technology Data Exchange (ETDEWEB)
Villata, M. (Istituto di Fisica Generale, Universita di Torino, Via Pietro Giuria 1, I-10125 Torino (Italy)); Tsinganos, K. (Department of Physics, University of Crete and Research Center of Crete, GR-71409, Heraklion, Crete (Greece))
1993-07-01
Three novel classes of exact solutions of the generalized Grad--Shafranov equation for helically symmetric magnetohydrodynamic (MHD) equilibria are presented. The first two classes may be applied to helical MHD equilibria for plasma confined between two coaxial cylinders, while the third one to the modeling of helicoidal magnetic fields and flows in several recently observed astrophysical jets. The same solutions can be also used for the testing of sophisticated numerical codes. It is also shown that all helically symmetric MHD equilibria can be treated by the same general method which is employed to generate exact MHD solutions for systems possessing an ignorable coordinate in a system of three orthogonal basis vectors, although in the case of helical symmetry an [ital orthogonal] ignorable coordinate does not exist, contrary to what happens in the well-known cases of axial and translational symmetries.
Exact geodesic distances in FLRW spacetimes
Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri
2017-11-01
Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.
Introduction to Hubbard model and exact diagonalization
Directory of Open Access Journals (Sweden)
S. Akbar Jafari
2008-06-01
Full Text Available Hubbard model is an important model in the theory of strongly correlated electron systems. In this contribution we introduce this model and the concepts of electron correlation by building on a tight binding model. After enumerating various methods of tackling the Hubbard model, we introduce the numerical method of exact diagonalization in detail. The book keeping and practical implementation aspects are illustrated with analytically solvable example of two-site Hubbard model.
Introduction to Hubbard model and exact diagonalization
S. Akbar Jafari
2008-01-01
Hubbard model is an important model in the theory of strongly correlated electron systems. In this contribution we introduce this model and the concepts of electron correlation by building on a tight binding model. After enumerating various methods of tackling the Hubbard model, we introduce the numerical method of exact diagonalization in detail. The book keeping and practical implementation aspects are illustrated with analytically solvable example of two-site Hubbard model.
Vaidya-like exact solutions with torsion
Blagojević, M
2015-01-01
Starting from the Oliva-Tempo-Troncoso black hole, a solution of the Bergshoeff-Hohm-Townsend massive gravity, a new class of the Vaidya-like exact solutions with torsion is constructed in the three-dimensional Poincar\\'e gauge theory. A particular subclass of these solutions is shown to possess the asymptotic conformal symmetry. The related canonical energy contains a contribution stemming from torsion.
New exact cosmologies on the brane
Astashenok, Artyom V.; Yurov, Artyom V.; Chervon, Sergey V.; Shabanov, Evgeniy V.; Sami, Mohammad
2014-10-01
We develop a method for constructing exact cosmological solutions in brane world cosmology. New classes of cosmological solutions on Randall-Sandrum brane are obtained. The superpotential and Hubble parameter are represented in quadratures. These solutions have inflationary phases under general assumptions and also describe an exit from the inflationary phase without a fine tuning of the parameters. Another class solutions can describe the current phase of accelerated expansion with or without possible exit from it.
Exact tests for Hardy-Weinberg proportions.
Engels, William R
2009-12-01
Exact conditional tests are often required to evaluate statistically whether a sample of diploids comes from a population with Hardy-Weinberg proportions or to confirm the accuracy of genotype assignments. This requirement is especially common when the sample includes multiple alleles and sparse data, thus rendering asymptotic methods, such as the common chi(2)-test, unreliable. Such an exact test can be performed using the likelihood ratio as its test statistic rather than the more commonly used probability test. Conceptual advantages in using the likelihood ratio are discussed. A substantially improved algorithm is described to permit the performance of a full-enumeration exact test on sample sizes that are too large for previous methods. An improved Monte Carlo algorithm is also proposed for samples that preclude full enumeration. These algorithms are about two orders of magnitude faster than those currently in use. Finally, methods are derived to compute the number of possible samples with a given set of allele counts, a useful quantity for evaluating the feasibility of the full enumeration procedure. Software implementing these methods, ExactoHW, is provided.
Exact Eigenfunctions of a Chaotic System
Ausländer, O M
1997-01-01
The interest in the properties of quantum systems, whose classical dynamics are chaotic, derives from their abundance in nature. The spectrum of such systems can be related, in the semiclassical approximation (SCA), to the unstable classical periodic orbits, through Gutzwiller's trace formula. The class of systems studied in this work, tiling billiards on the pseudo-sphere, is special in this correspondence being exact, via Selberg's trace formula. In this work, an exact expression for Green's function (GF) and the eigenfunctions (EF) of tiling billiards on the pseudo-sphere, whose classical dynamics are chaotic, is derived. GF is shown to be equal to the quotient of two infinite sums over periodic orbits, where the denominator is the spectral determinant. Such a result is known to be true for typical chaotic systems, in the leading SCA. From the exact expression for GF, individual EF can be identified. In order to obtain a SCA by finite series for the infinite sums encountered, resummation by analytic contin...
On the exactness of soft theorems
Guerrieri, Andrea L.; Huang, Yu-tin; Li, Zhizhong; Wen, Congkao
2017-12-01
Soft behaviours of S-matrix for massless theories reflect the underlying symmetry principle that enforces its masslessness. As an expansion in soft momenta, sub-leading soft theorems can arise either due to (I) unique structure of the fundamental vertex or (II) presence of enhanced broken-symmetries. While the former is expected to be modified by infrared or ultraviolet divergences, the latter should remain exact to all orders in perturbation theory. Using current algebra, we clarify such distinction for spontaneously broken (super) Poincaré and (super) conformal symmetry. We compute the UV divergences of DBI, conformal DBI, and A-V theory to verify the exactness of type (II) soft theorems, while type (I) are shown to be broken and the soft-modifying higher-dimensional operators are identified. As further evidence for the exactness of type (II) soft theorems, we consider the α' expansion of both super and bosonic open strings amplitudes, and verify the validity of the translation symmetry breaking soft-theorems up to O({α}^' 6}) . Thus the massless S-matrix of string theory "knows" about the presence of D-branes.
Estimation variance bounds of importance sampling simulations in digital communication systems
Lu, D.; Yao, K.
1991-01-01
In practical applications of importance sampling (IS) simulation, two basic problems are encountered, that of determining the estimation variance and that of evaluating the proper IS parameters needed in the simulations. The authors derive new upper and lower bounds on the estimation variance which are applicable to IS techniques. The upper bound is simple to evaluate and may be minimized by the proper selection of the IS parameter. Thus, lower and upper bounds on the improvement ratio of various IS techniques relative to the direct Monte Carlo simulation are also available. These bounds are shown to be useful and computationally simple to obtain. Based on the proposed technique, one can readily find practical suboptimum IS parameters. Numerical results indicate that these bounding techniques are useful for IS simulations of linear and nonlinear communication systems with intersymbol interference in which bit error rate and IS estimation variances cannot be obtained readily using prior techniques.
BOUNDS FOR THE ABSOLUTE REGULARITY COEFFICIENT OF A STATIONARY RENEWAL PROCESS
Heinrich, Lothar
1992-01-01
We give an upper bound for the absolute regularity coefficient of a stationary renewal process in terms of the total variation of the difference between the corresponding Palm and the usual renewal measure.
Hung, Tran Loc; Giang, Le Truong
2016-01-01
Using the Stein-Chen method some upper bounds in Poisson approximation for distributions of row-wise triangular arrays of independent negative-binomial distributed random variables are established in this note.
Betti numbers of space curves bounded by Hilbert functions
Directory of Open Access Journals (Sweden)
Renato Maggioni
1997-05-01
Full Text Available We study relationships between Hilbert functions and graded Betti numbers of two space curves C and C_0 bilinked by a sequence of basic double linkages; precisely we obtain bounds for the graded Betti numbers of C by means of the Hilbert functions of the two curves and the graded Betti numbers of C_0 . On the other hand for every set of integers satisfying these bounds we can construct a curve with these integers as its graded Betti numbers. As a consequence we get a Dubreil-type theorem for a curve C which strongly dominates C_0 at height h which is exactly the Amasaki bound for Buchsbaum curves. Moreover we deduce for biliaison classes of Buchsbaum curves that a strong Lazarsfeld-Rao property holds.
Bubble-bound state of triple-stranded DNA: Efimov physics in DNA with repulsion
Maji, Jaya; Seno, Flavio; Trovato, Antonio; Bhattacharjee, Somendra M.
2017-07-01
The presence of a thermodynamic phase of a three-stranded DNA, namely, a mixed phase of bubbles of two bound strands and a single one, is established for large dimensions (d≥slant 5 ) by using exact real space renormalization group transformations and exact computations of specific heat for finite length chains. Similar exact computations for the fractal Sierpinski gasket of dimension d stability of the phase in the presence of a repulsive three chain interaction. Although, for d DNA, where three strands are bound though no two are bound, the mixed phase appears at temperatures less than the two chain melting temperature. Both the Efimov-DNA and the mixed phase are formed essentially due to the strand exchange mechanism.
Capacity bounds for parallel IM-DD optical wireless channels
Chaaban, Anas
2016-07-26
A system consisting of parallel intensity-modulation direct-detection optical wireless channels with a total average intensity constraint is studied. Capacity upper and lower bounds for this system are derived. If channel-state information is available at the transmitter, the bounds have to be optimized with respect to intensity allocation over the parallel channels. The optimization of the lower bound is non-convex, however, the Karush-Kuhn-Tucker conditions can be used to find a list of possible solutions one of which is optimal. The optimal solution can then be found by an exhaustive search algorithm, which is computationally expensive. To overcome this, we propose a low-complexity intensity allocation algorithm which is nearly optimal. The optimized capacity lower bound coincides with the capacity at high signal-to-noise ratio. © 2016 IEEE.
Bounding approaches to system identification
Norton, John; Piet-Lahanier, Hélène; Walter, Éric
1996-01-01
In response to the growing interest in bounding error approaches, the editors of this volume offer the first collection of papers to describe advances in techniques and applications of bounding of the parameters, or state variables, of uncertain dynamical systems. Contributors explore the application of the bounding approach as an alternative to the probabilistic analysis of such systems, relating its importance to robust control-system design.
with Bounded Failure Intensity
Directory of Open Access Journals (Sweden)
Preeti Wanti Srivastava
2011-01-01
Full Text Available This paper deals with the Bayes prediction of the future failures of a deteriorating repairable mechanical system subject to minimal repairs and periodic overhauls. To model the effect of overhauls on the reliability of the system a proportional age reduction model is assumed and the 2-parameter Engelhardt-Bain process (2-EBP is used to model the failure process between two successive overhauls. 2-EBP has an advantage over Power Law Process (PLP models. It is found that the failure intensity of deteriorating repairable systems attains a finite bound when repeated minimal repair actions are combined with some overhauls. If such a data is analyzed through models with unbounded increasing failure intensity, such as the PLP, then pessimistic estimates of the system reliability will arise and incorrect preventive maintenance policy may be defined. On the basis of the observed data and of a number of suitable prior densities reflecting varied degrees of belief on the failure/repair process and effectiveness of overhauls, the prediction of the future failure times and the number of failures in a future time interval is found. Finally, a numerical application is used to illustrate the advantages from overhauls and sensitivity analysis of the improvement parameter carried out.
Bounding the number of points on a curve using a generalization of Weierstrass semigroups
DEFF Research Database (Denmark)
Beelen, Peter; Ruano, Diego
2011-01-01
In [5] an upper bound for the number of points on an al- gebraic curve dened over a nite eld was derived. In this article we generalize their result by considering Weierstrass groups of several points simultaneously.......In [5] an upper bound for the number of points on an al- gebraic curve dened over a nite eld was derived. In this article we generalize their result by considering Weierstrass groups of several points simultaneously....
Combinatorial bounds on the α-divergence of univariate mixture models
Nielsen, Frank
2017-06-20
We derive lower- and upper-bounds of α-divergence between univariate mixture models with components in the exponential family. Three pairs of bounds are presented in order with increasing quality and increasing computational cost. They are verified empirically through simulated Gaussian mixture models. The presented methodology generalizes to other divergence families relying on Hellinger-type integrals.
Bounds for right tails of deterministic and stochastic sums of random variables
Darkiewicz, G.; Deelstra, G.; Dhaene, J.; Hoedemakers, T.; Vanmaele, M.
2009-01-01
We investigate lower and upper bounds for right tails (stop-loss premiums) of deterministic and stochastic sums of nonindependent random variables. The bounds are derived using the concepts of comonotonicity, convex order, and conditioning. The performance of the presented approximations is
Fundamentals of the exact renormalization group
Rosten, Oliver J.
2012-02-01
Various aspects of the Exact Renormalization Group (ERG) are explored, starting with a review of the concepts underpinning the framework and the circumstances under which it is expected to be useful. A particular emphasis is placed on the intuitive picture provided for both renormalization in quantum field theory and universality associated with second order phase transitions. A qualitative discussion of triviality, asymptotic freedom and asymptotic safety is presented. Focusing on scalar field theory, the construction of assorted flow equations is considered using a general approach, whereby different ERGs follow from field redefinitions. It is recalled that Polchinski’s equation can be cast as a heat equation, which provides intuition and computational techniques for what follows. The analysis of properties of exact solutions to flow equations includes a proof that the spectrum of the anomalous dimension at critical fixed-points is quantized. Two alternative methods for computing the β-function in λϕ4 theory are considered. For one of these it is found that all explicit dependence on the non-universal differences between a family of ERGs cancels out, exactly. The Wilson-Fisher fixed-point is rediscovered in a rather novel way. The discussion of nonperturbative approximation schemes focuses on the derivative expansion, and includes a refinement of the arguments that, at the lowest order in this approximation, a function can be constructed which decreases monotonically along the flow. A new perspective is provided on the relationship between the renormalizability of the Wilsonian effective action and of correlation functions, following which the construction of manifestly gauge invariant ERGs is sketched, and some new insights are given. Drawing these strands together suggests a new approach to quantum field theory.
Supersymmetric QCD: exact results and strong coupling
Dine, Michael; Festuccia, Guido; Pack, Lawrence; Park, Chang-Soon; Ubaldi, Lorenzo; Wu, Weitao
2011-05-01
We revisit two longstanding puzzles in supersymmetric gauge theories. The first concerns the question of the holomorphy of the coupling, and related to this the possible definition of an exact (NSVZ) beta function. The second concerns instantons in pure gluodynamics, which appear to give sensible, exact results for certain correlation functions, which nonetheless differ from those obtained using systematic weak coupling expansions. For the first question, we extend an earlier proposal of Arkani-Hamed and Murayama, showing that if their regulated action is written suitably, the holomorphy of the couplings is manifest, and it is easy to determine the renormalization scheme for which the NSVZ formula holds. This scheme, however, is seen to be one of an infinite class of schemes, each leading to an exact beta function; the NSVZ scheme, while simple, is not selected by any compelling physical consideration. For the second question, we explain why the instanton computation in the pure supersymmetric gauge theory is not reliable, even at short distances. The semiclassical expansion about the instanton is purely formal; if infrared divergences appear, they spoil arguments based on holomorphy. We demonstrate that infrared divergences do not occur in the perturbation expansion about the instanton, but explain that there is no reason to think this captures all contributions from the sector with unit topological charge. That one expects additional contributions is illustrated by dilute gas corrections. These are infrared divergent, and so difficult to define, but if non-zero give order one, holomorphic, corrections to the leading result. Exploiting an earlier analysis of Davies et al, we demonstrate that in the theory compactified on a circle of radius β, due to infrared effects, finite contributions indeed arise which are not visible in the formal β → ∞ limit.
Exact formation of hairy planar black holes
Fan, Zhong-Ying; Chen, Bin
2015-01-01
We consider Einstein gravity minimally coupled to a scalar field with a given potential in general dimensions. We obtain large classes of static hairy planar black holes which are asymptotic to AdS space-times. In particular, for a special case $\\mu=(n-2)/2$, we obtain new classes of exact dynamical solutions describing black holes formation. We find there are two classes of collapse solutions. The first class solutions describe the evolution start from AdS space-time with a naked singularity...
Compiling Relational Bayesian Networks for Exact Inference
DEFF Research Database (Denmark)
Jaeger, Manfred; Darwiche, Adnan; Chavira, Mark
2006-01-01
We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available PRIMULA tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference...... by evaluating and differentiating these circuits in time linear in their size. We report on experimental results showing successful compilation and efficient inference on relational Bayesian networks, whose PRIMULA--generated propositional instances have thousands of variables, and whose jointrees have clusters...
Yamazaki, T
2000-01-01
A new type of nuclear spectroscopy to study hadron-nucleus bound states is described. The first successful experiment was to search for deeply bound pi sup - states in heavy nuclei using the sup 2 sup 0 sup 8 Pb(d, sup 3 He) reaction at GSI, in which a narrow peak arising from the 2p pi sup - orbital coupled with the neutron-hole states was observed at 135 MeV excitation energy. An improved experiment has just been carried out to separately identify the 1s and 2p pi sup - states. These experiments provide important information on the local potential strength, from which the effective mass of pi sup - is deduced to be 20 MeV. This method will be extended to search for eta and omega bound states as well as for K sup - bound states. The advantage of the bound-state spectroscopy versus invariant mass spectroscopy is emphasized.
Market Access through Bound Tariffs
DEFF Research Database (Denmark)
Sala, Davide; Schröder, Philipp J.H.; Yalcin, Erdal
on the risk that exporters face in destination markets. The present paper formalizes the underlying interaction of risk, fixed export costs and firms' market entry decisions based on techniques known from the real options literature; doing so we highlight the important role of bound tariffs at the extensive......WTO negotiations deal predominantly with bound - besides applied - tariff rates. But, how can reductions in tariffs ceilings, i.e. tariff rates that no exporter may ever actually be confronted with, generate market access? The answer to this question relates to the effects of tariff bindings...... margin of trade. We find that bound tariffs are more effective with higher risk destination markets, that a large binding overhang may still command substantial market access, and that reductions in bound tariffs generate effective market access even when bound rates are above current and long...
Market access through bound tariffs
DEFF Research Database (Denmark)
Sala, Davide; Schröder, Philipp J.H.; Yalcin, Erdal
2010-01-01
on the risk that exporters face in destination markets. The present paper formalizes the underlying interaction of risk, fixed export costs and firms' market entry decisions based on techniques known from the real options literature; doing so we highlight the important role of bound tariffs at the extensive......WTO negotiations deal predominantly with bound - besides applied - tariff rates. But, how can reductions in tariffs ceilings, i.e. tariff rates that no exporter may ever actually be confronted with, generate market access? The answer to this question relates to the effects of tariff bindings...... margin of trade. We find that bound tariffs are more effective with higher risk destination markets, that a large binding overhang may still command substantial market access, and that reductions in bound tariffs generate effective market access even when bound rates are above current and longterm...
Entanglement and relaxation in exactly solvable models
Lychkovskiy, O.
2011-11-01
A system put in contact with a large heat bath normally thermalizes. This means that the state of the system ρℐ( t) approaches an equilibrium state ρ{eq/ℐ}, the latter depending only on macroscopic characteristics of the bath (e.g. temperature), but not on the initial state of the system. The above statement is the cornerstone of the equilibrium statistical mechanics; its validity and its domain of applicability are central questions in the studies of the foundations of statistical mechanics. In the present contribution we discuss the recently proven general theorems about thermalization and demonstrate how they work in exactly solvable models. In particular, we review a necessary condition for the system initial state independence (ISI) of ρ{eq/ℐ}, which was proven in our previous work, and apply it for two exactly solvable models, the XX spin chain and a central spin model with a special interaction with the environment. In the latter case we are able to prove the absence of the system ISI. Also the Eigenstate Thermalization Hypothesis is discussed. It is pointed out that although it is supposed to be generically true in essentially not-integrable ( chaotic) quantum systems, it is how-ever also valid in the integrable XX model.
Exact Solution for a Gravitational Wave Detector
Rabounski, Dmitri; Borissova, Larissa
2008-04-01
The experimental statement on gravitational waves proceeds from the equation for deviating geodesic lines and the equation for deviating non-geodesics. Weber's result was not based upon an exact solution to the equations, but on an approximate analysis of what could be expected: he expected that a plane weak wave of the space metric may displace two resting particles with respect to each other. In this work, exact solutions are presented for the deviation equation of both free and spring-connected particles. The solutions show that a gravitational wave may displace particles in a two-particle system only if they are in motion with respect to each other or the local space (there is no effect if they are at rest). Thus, gravitational waves produce a parametric effect on a two-particle system. According to the solutions, an altered detector construction can be proposed such that it might interact with gravitational waves: 1) a horizontally suspended cylindrical pig, whose butt-ends have basic relative oscillations induced by a laboratory source; 2) a free-mass detector where suspended mirrors have laboratory induced basic oscillations relative to each other.
Phase-space dynamics of opposition control in wall-bounded turbulent flows
Hwang, Yongyun; Ibrahim, Joseph; Yang, Qiang; Doohan, Patrick
2017-11-01
The phase-space dynamics of wall-bounded shear flow in the presence of opposition control is explored by examining the behaviours of a pair of nonlinear equilibrium solutions (exact coherent structures), edge state and life time of turbulence at low Reynolds numbers. While the control modifies statistics and phase-space location of the edge state and the lower-branch equilibrium solution very little, it is also found to regularise the periodic orbit on the edge state by reverting a period-doubling bifurcation. Only the upper-branch equilibrium solution and mean turbulent state are significantly modified by the control, and, in phase space, they gradually approach the edge state on increasing the control gain. It is found that this behaviour results in a significant reduction of the life time of turbulence, indicating that the opposition control significantly increases the probability that the turbulent solution trajectory passes through the edge state. Finally, it is shown that the opposition control increases the critical Reynolds number of the onset of the equilibrium solutions, indicating its capability of transition delay. This work is sponsored by the Engineering and Physical Sciences Research Council (EPSRC) in the UK (EP/N019342/1).
EXACT SIMULATION OF A BOOLEAN MODEL
Directory of Open Access Journals (Sweden)
Christian Lantuéjoul
2013-06-01
Full Text Available A Boolean model is a union of independent objects (compact random subsets located at Poisson points. Two algorithms are proposed for simulating a Boolean model in a bounded domain. The first one applies only to stationary models. It generates the objects prior to their Poisson locations. Two examples illustrate its applicability. The second algorithm applies to stationary and non-stationary models. It generates the Poisson points prior to the objects. Its practical difficulties of implementation are discussed. Both algorithms are based on importance sampling techniques, and the generated objects are weighted.
Experimental bounds on collapse models from gravitational wave detectors
Carlesso, Matteo; Bassi, Angelo; Falferi, Paolo; Vinante, Andrea
2016-12-01
Wave function collapse models postulate a fundamental breakdown of the quantum superposition principle at the macroscale. Therefore, experimental tests of collapse models are also fundamental tests of quantum mechanics. Here, we compute the upper bounds on the collapse parameters, which can be inferred by the gravitational wave detectors LIGO, LISA Pathfinder, and AURIGA. We consider the most widely used collapse model, the continuous spontaneous localization (CSL) model. We show that these experiments exclude a huge portion of the CSL parameter space, the strongest bound being set by the recently launched space mission LISA Pathfinder. We also rule out a proposal for quantum-gravity-induced decoherence.
Bounds on Block Error Probability for Multilevel Concatenated Codes
Lin, Shu; Moorthy, Hari T.; Stojanovic, Diana
1996-01-01
Maximum likelihood decoding of long block codes is not feasable due to large complexity. Some classes of codes are shown to be decomposable into multilevel concatenated codes (MLCC). For these codes, multistage decoding provides good trade-off between performance and complexity. In this paper, we derive an upper bound on the probability of block error for MLCC. We use this bound to evaluate difference in performance for different decompositions of some codes. Examples given show that a significant reduction in complexity can be achieved when increasing number of stages of decoding. Resulting performance degradation varies for different decompositions. A guideline is given for finding good m-level decompositions.
Exact, E = 0, classical and quantum solutions for general power-law oscillators
Energy Technology Data Exchange (ETDEWEB)
Nieto, M.M. [Los Alamos National Lab., NM (United States); Daboul, J. [Ben Gurion Univ. of the Negev, Beer Sheva (Israel)
1994-07-01
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = {minus}{gamma}/r{sup {nu}}, {gamma} > 0 and {minus}{infinity} < {nu} < {infinity}. When the angular momentum is non-zero, these solutions lead to the classical orbits {rho}(t) = [cos {mu}({var_phi}(t) {minus} {var_phi}{sub 0}(t))]{sup 1/{mu}}, with {mu} = {nu}/2 {minus} 1 {ne} 0. For {nu} > 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when {nu} > 2 the solutions are normalizable (bound), as in the classical case. Also, there are normalizable discrete, yet unbound, state which correspond to unbound classical particles which reach infinity in a finite time. These and other interesting comparisons to the classical system will be discussed.
Frehlich, Rod
1993-01-01
Calculations of the exact Cramer-Rao Bound (CRB) for unbiased estimates of the mean frequency, signal power, and spectral width of Doppler radar/lidar signals (a Gaussian random process) are presented. Approximate CRB's are derived using the Discrete Fourier Transform (DFT). These approximate results are equal to the exact CRB when the DFT coefficients are mutually uncorrelated. Previous high SNR limits for CRB's are shown to be inaccurate because the discrete summations cannot be approximated with integration. The performance of an approximate maximum likelihood estimator for mean frequency approaches the exact CRB for moderate signal to noise ratio and moderate spectral width.
Generalized zig-zag products of regular digraphs and bounds on their spectral expansions
Nomura, Shunichi; Takemura, Akimichi
2007-01-01
We introduce a generalization of the zig-zag product of regular digraphs (directed graphs), which allows us to construct regular digraphs with m ore flexible choices of the degrees. In our generalization, we can control the connectivity of the resulting graph measured by its spectral expansion. We derive an upper bound on the spectral expansion of the generalized zig-zag product. Our upper bound improves on known bounds when applied to the zig-zag product. We also consider a special case of t...
Exact renormalization group study of fermionic theories
Comellas, Jordi; Kubyshin, Yuri; Moreno, Enrique
1997-02-01
The exact renormalization group approach (ERG) is developed for the case of pure fermionic theories by deriving a Grassmann version of the ERG equation and applying it to the study of fixed point solutions and critical exponents of the two-dimensional chiral Gross-Neveu model. An approximation based on the derivative expansion and a further truncation in the number of fields is used. Two solutions are obtained analytically in the limit N → ∞, with N being the number of fermionic species. For finite N some fixed point solutions, with their anomalous dimensions and critical exponents, are computed numerically. The issue of separation of physical results from the numerous spurious ones is discussed. We argue that one of the solutions we find can be identified with that of Dashen and Frishman, whereas the others seem to be new ones.
On truncations of the exact renormalization group
Morris, T R
1994-01-01
We investigate the Exact Renormalization Group (ERG) description of (Z_2 invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. Concentrating on the non-perturbative three dimensional Wilson fixed point, we then show that the sequence of truncations n=2,3,\\dots, obtained by expanding about the field \\varphi=0 and discarding all powers \\varphi^{2n+2} and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. No completely reliable method exists to reject the many spurious solutions that are also found. These properties are explained in terms of the analytic behaviour of the untruncated solutions -- which we describe in some detail.
Interference-exact radiative transfer equation
DEFF Research Database (Denmark)
Partanen, Mikko; Haÿrynen, Teppo; Oksanen, Jani
2017-01-01
Maxwell's equations with stochastic or quantum optical source terms accounting for the quantum nature of light. We show that both the nonlocal wave and local particle features associated with interference and emission of propagating fields in stratified geometries can be fully captured by local damping...... equation (RTE) as a physically transparent interference-exact model that extends the useful range of computationally efficient and quantum optically accurate interference-aware optical models from simple structures to full optical devices.......The Purcell effect, i.e., the modification of the spontaneous emission rate by optical interference, profoundly affects the light-matter coupling in optical resonators. Fully describing the optical absorption, emission, and interference of light hence conventionally requires combining the full...
An exactly solvable system from quantum optics
Energy Technology Data Exchange (ETDEWEB)
Maciejewski, Andrzej J., E-mail: maciejka@astro.ia.uz.zgora.pl [J. Kepler Institute of Astronomy, University of Zielona Góra, Licealna 9, PL-65-417 Zielona Góra (Poland); Przybylska, Maria, E-mail: M.Przybylska@if.uz.zgora.pl [Institute of Physics, University of Zielona Góra, Licealna 9, 65-417 Zielona Góra (Poland); Stachowiak, Tomasz, E-mail: stachowiak@cft.edu.pl [Center for Theoretical Physics PAS, Al. Lotników 32/46, 02-668 Warsaw (Poland)
2015-07-31
We investigate a generalisation of the Rabi system in the Bargmann–Fock representation. In this representation the eigenproblem of the considered quantum model is described by a system of two linear differential equations with one independent variable. The system has only one irregular singular point at infinity. We show how the quantisation of the model is related to asymptotic behaviour of solutions in a vicinity of this point. The explicit formulae for the spectrum and eigenfunctions of the model follow from an analysis of the Stokes phenomenon. An interpretation of the obtained results in terms of differential Galois group of the system is also given. - Highlights: • New exactly solvable system from quantum optics is found. • Normalisation condition for system in Bargmann representation is used. • Formulae for spectrum and eigenfunctions from analysis of Stokes phenomenon are given.
Exact eigenfunctions and the open topological string
Mariño, Marcos; Zakany, Szabolcs
2017-08-01
Mirror curves to toric Calabi-Yau threefolds can be quantized and lead to trace class operators on the real line. The eigenvalues of these operators are encoded in the BPS invariants of the underlying threefold, but much less is known about their eigenfunctions. In this paper, we first develop methods in spectral theory to compute these eigenfunctions. We also provide an integral matrix representation which allows them to be studied in a ’t Hooft limit, where they are described by standard topological open string amplitudes. Based on these results, we propose a conjecture for the exact eigenfunctions, which involves both the WKB wavefunction and the standard topological string wavefunction. This conjecture can be made completely explicit in the maximally supersymmetric, or self-dual case, which we work out in detail for local \
Exact and Efficient Sampling of Conditioned Walks
Adorisio, Matteo; Pezzotta, Alberto; de Mulatier, Clélia; Micheletti, Cristian; Celani, Antonio
2017-11-01
A computationally challenging and open problem is how to efficiently generate equilibrated samples of conditioned walks. We present here a general stochastic approach that allows one to produce these samples with their correct statistical weight and without rejections. The method is illustrated for a jump process conditioned to evolve within a cylindrical channel and forced to reach one of its ends. We obtain analytically the exact probability density function of the jumps and offer a direct method for gathering equilibrated samples of a random walk conditioned to stay in a channel with suitable boundary conditions. Unbiased walks of arbitrary length can thus be generated with linear computational complexity—even when the channel width is much smaller than the typical bond length of the unconditioned walk. By profiling the metric properties of the generated walks for various bond lengths we characterize the crossover between weak and strong confinement regimes with great detail.
Combining Alphas via Bounded Regression
Directory of Open Access Journals (Sweden)
Zura Kakushadze
2015-11-01
Full Text Available We give an explicit algorithm and source code for combining alpha streams via bounded regression. In practical applications, typically, there is insufficient history to compute a sample covariance matrix (SCM for a large number of alphas. To compute alpha allocation weights, one then resorts to (weighted regression over SCM principal components. Regression often produces alpha weights with insufficient diversification and/or skewed distribution against, e.g., turnover. This can be rectified by imposing bounds on alpha weights within the regression procedure. Bounded regression can also be applied to stock and other asset portfolio construction. We discuss illustrative examples.
Butterfly velocity bound and reverse isoperimetric inequality
Feng, Xing-Hui; Lü, H.
2017-03-01
We study the butterfly effect of the AdS planar black holes in the framework of Einstein's general relativity. We find that the butterfly velocities can be expressed by a universal formula vB2=T S /(2 VthP ). In doing so, we come upon a near-horizon geometrical formula for the thermodynamical volume Vth . We verify the volume formula by examining a variety of AdS black holes. We also show that the volume formula implies that the conjectured reverse isoperimetric inequality follows straightforwardly from the null-energy condition, for static AdS black holes. The inequality is thus related to an upper bound of the butterfly velocities.
Computational Lower Bounds Using Diagonalization
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 14; Issue 7. Computational Lower Bounds Using Diagonalization - Languages, Turing Machines and Complexity Classes. M V Panduranga Rao. General Article Volume 14 Issue 7 July 2009 pp 682-690 ...
Bounded Rationality in Transposition Processes
DEFF Research Database (Denmark)
Vollaard, Hans; Martinsen, Dorte Sindbjerg
2014-01-01
perspective may affect the commonly employed explanatory factors of administrative capacities, misfit and the heterogeneity of preferences among veto players. To prevent retrospective rationalisation of the transposition process, this paper traces this process as it unfolded in Denmark and the Netherlands....... As bounded rationality is apparent in the transposition processes in these relatively well-organised countries, future transposition studies should devote greater consideration to the bounded rationality perspective....
Constraining a fourth generation of quarks: non-perturbative Higgs boson mass bounds
Bulava, J.; Nagy, A.
2013-01-01
We present a non-perturbative determination of the upper and lower Higgs boson mass bounds with a heavy fourth generation of quarks from numerical lattice computations in a chirally symmetric Higgs-Yukawa model. We find that the upper bound only moderately rises with the quark mass while the lower bound increases significantly, providing additional constraints on the existence of a straight-forward fourth quark generation. We examine the stability of the lower bound under the addition of a higher dimensional operator to the scalar field potential using perturbation theory, demonstrating that it is not significantly altered for small values of the coupling of this operator. For a Higgs boson mass of $\\sim125\\mathrm{GeV}$ we find that the maximum value of the fourth generation quark mass is $\\sim300\\mathrm{GeV}$, which is already in conflict with bounds from direct searches.
Bounding the quantum limits of precision for phase estimation with loss and thermal noise
Gagatsos, Christos N.; Bash, Boulat A.; Guha, Saikat; Datta, Animesh
2017-12-01
We consider the problem of estimating an unknown but constant carrier phase modulation θ using a general, possibly entangled, n -mode optical probe through n independent and identical uses of a lossy bosonic channel with additive thermal noise. We find an upper bound to the quantum Fisher information (QFI) of estimating θ as a function of n , the mean and variance of the total number of photons NS in the n -mode probe, the transmissivity η , and mean thermal photon number per mode n¯B of the bosonic channel. Since the inverse of QFI provides a lower bound to the mean-square error (MSE) of an unbiased estimator θ ˜ of θ , our upper bound to the QFI provides a lower bound to the MSE. It already has found use in proving fundamental limits of covert sensing and could find other applications requiring bounding the fundamental limits of sensing an unknown parameter embedded in a correlated field.
Computing a Non-trivial Lower Bound on the Joint Entropy between Two Images
Energy Technology Data Exchange (ETDEWEB)
Perumalla, Kalyan S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2017-03-01
In this report, a non-trivial lower bound on the joint entropy of two non-identical images is developed, which is greater than the individual entropies of the images. The lower bound is the least joint entropy possible among all pairs of images that have the same histograms as those of the given images. New algorithms are presented to compute the joint entropy lower bound with a computation time proportional to S log S where S is the number of histogram bins of the images. This is faster than the traditional methods of computing the exact joint entropy with a computation time that is quadratic in S .
Improved lower bounds for the atomic charge density at the nucleus
Energy Technology Data Exchange (ETDEWEB)
Galvez, F.J.; Porras, I.; Angulo, J.C.; Dehesa, J.S.
1988-06-14
Lower bounds F(..cap alpha.., ..beta..) for the electronic charge density of atomic systems with N electrons at the nucleus, p (O), are given by means of any two radial expectation values
Bound on local unambiguous discrimination between multipartite quantum states
Yang, Ying-Hui; Gao, Fei; Tian, Guo-Jing; Cao, Tian-Qing; Zuo, Hui-Juan; Wen, Qiao-Yan
2015-02-01
We investigate the upper bound on unambiguous discrimination by local operations and classical communication. We demonstrate that any set of linearly independent multipartite pure quantum states can be locally unambiguously discriminated if the number of states in the set is no more than , where the space spanned by the set can be expressed in the irreducible form and is the optimal local dimension of the party. That is, is an upper bound. We also show that it is tight, namely there exists a set of states, in which at least one of the states cannot be locally unambiguously discriminated. Our result gives the reason why the multiqubit system is the only exception when any three quantum states are locally unambiguously distinguished.
Speeding Up Exact Solutions of Interactive Dynamic Influence Diagrams Using Action Equivalence
DEFF Research Database (Denmark)
Zeng, Yifeng; Prashant, Doshi
2009-01-01
Interactive dynamic influence diagrams (I-DIDs) are graphical models for sequential decision making in partially observable settings shared by other agents. Algorithms for solving I-DIDs face the challenge of an exponentially growing space of candidate models ascribed to other agents, over time. ...... at a single time step. We show how to update these augmented classes and prove that our method is exact. The new approach enables us to bound the aggregated model space by the cardinality of other agents' actions. We evaluate its performance and provide empirical results in support....
Semidefinite bounds for nonbinary codes based on quadruples
Litjens, B.; Polak, S.; Schrijver, A.
For nonnegative integers q, n, d, let Aq(n, d) denote the maximum cardinality of a code of length n over an alphabet [q] with q letters and with minimum distance at least d. We consider the following upper bound on Aq(n, d). For any k, let Ck be the collection of codes of cardinality at most k. Then
FLAG: Exact Fourier-Laguerre transform on the ball
Leistedt, Boris; McEwen, Jason
2017-10-01
FLAG is a fast implementation of the Fourier-Laguerre Transform, a novel 3D transform exploiting an exact quadrature rule of the ball to construct an exact harmonic transform in 3D spherical coordinates. The angular part of the Fourier-Laguerre transform uses the MW sampling theorem and the exact spherical harmonic transform implemented in the SSHT code. The radial sampling scheme arises from an exact quadrature of the radial half-line using damped Laguerre polynomials. The radial transform can in fact be used to compute the spherical Bessel transform exactly, and the Fourier-Laguerre transform is thus closely related to the Fourier-Bessel transform.
Bounds for the propagation speed of combustion flames
Energy Technology Data Exchange (ETDEWEB)
Fort, Joaquim [Departament de FIsica, Universitat de Girona, Campus de Montilivi, 17071 Girona, Catalonia (Spain); Campos, Daniel [Grup de FIsica EstadIstica, Departament de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterra (Spain); Gonzalez, Josep R [Grup de Mecanica de Fluids, Departament d' Enginyeria Mecanica, Universitat de Girona, Campus de Montilivi, 17071 Girona, Catalonia (Spain); Velayos, Joaquim [Grup de Mecanica de Fluids, Departament d' Enginyeria Mecanica, Universitat de Girona, Campus de Montilivi, 17071 Girona, Catalonia (Spain)
2004-07-23
We focus on a combustion model for premixed flames based on two coupled equations determining the spatial dynamics of temperature and fuel density. We rewrite these equations as a classical reaction-diffusion model, so that we can apply some known methods for the prediction of lower and upper bounds to the front speed. The predictions are compared to simulations, which show that our new bounds substantially improve those following from the linearization method, used in the previous work of Fort et al (2000 J. Phys. A: Math. Gen. 33 6953). Radiative losses lead to pulses rather than fronts. We find a bound for their speed which (in contrast to the linearization one) correctly predicts the order of magnitude of the flame speed.
On truncations of the exact renormalization group
Morris, Tim R.
1994-08-01
We investigate the Exact Renormalization Group (ERG) description of ( Z2 invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. The approximation is seen to be a good one, both qualitatively and quantitatively. We then consider the further approximation of truncating the lagrangian to polynomial in the field dependence. Concentrating on the non-perturbative three dimensional Wilson fixed point, we show that the sequence of truncations n = 2,3,…, obtained by expanding about the field ϕ = 0 and discarding all powers ϕ2 n+2 and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. Within the sequence of truncations, no completely reliable method exists to reject the many spurious solutions that are also generated. These properties are explained in terms of the analytic behaviour of the untruncated solutions - which we describe in some detail.
Exact Fit of Simple Finite Mixture Models
Directory of Open Access Journals (Sweden)
Dirk Tasche
2014-11-01
Full Text Available How to forecast next year’s portfolio-wide credit default rate based on last year’s default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score distribution. This is a special (simple case of a finite mixture model where the mixture components are fixed and only the weights of the components are estimated. The optimum weights provide a forecast of next year’s portfolio-wide default rate. We point out that the maximum-likelihood (ML approach to fitting the mixture distribution not only gives an optimum but even an exact fit if we allow the mixture components to vary but keep their density ratio fixed. From this observation we can conclude that the standard default rate forecast based on last year’s conditional default rates will always be located between last year’s portfolio-wide default rate and the ML forecast for next year. As an application example, cost quantification is then discussed. We also discuss how the mixture model based estimation methods can be used to forecast total loss. This involves the reinterpretation of an individual classification problem as a collective quantification problem.
STELLAR: fast and exact local alignments
Directory of Open Access Journals (Sweden)
Weese David
2011-10-01
Full Text Available Abstract Background Large-scale comparison of genomic sequences requires reliable tools for the search of local alignments. Practical local aligners are in general fast, but heuristic, and hence sometimes miss significant matches. Results We present here the local pairwise aligner STELLAR that has full sensitivity for ε-alignments, i.e. guarantees to report all local alignments of a given minimal length and maximal error rate. The aligner is composed of two steps, filtering and verification. We apply the SWIFT algorithm for lossless filtering, and have developed a new verification strategy that we prove to be exact. Our results on simulated and real genomic data confirm and quantify the conjecture that heuristic tools like BLAST or BLAT miss a large percentage of significant local alignments. Conclusions STELLAR is very practical and fast on very long sequences which makes it a suitable new tool for finding local alignments between genomic sequences under the edit distance model. Binaries are freely available for Linux, Windows, and Mac OS X at http://www.seqan.de/projects/stellar. The source code is freely distributed with the SeqAn C++ library version 1.3 and later at http://www.seqan.de.
Low-frequency flute instabilities of a bounded plasma column.
Rognlien, T. D.
1973-01-01
Derivation of exact solutions for unstable waves (called flute waves) which occur in a radially bounded plasma column at frequencies below the ion cyclotron frequency. Both analytical and numerical solutions are presented for the m = 1 and m = 2 azimuthal modes for a variety of radial electric field profiles. It is shown that the behavior of the flute waves can depend sensitively on the radial extent of the plasma column. Moreover, it is found that the m = 1 mode and the m = 2 mode do not respond in the same way to changes in the radial boundary position or in the electric field profile.
Exact Hypothesis Tests for Log-linear Models with exactLoglinTest
Directory of Open Access Journals (Sweden)
Brian Caffo
2006-11-01
Full Text Available This manuscript overviews exact testing of goodness of fit for log-linear models using the R package exactLoglinTest. This package evaluates model fit for Poisson log-linear models by conditioning on minimal sufficient statistics to remove nuisance parameters. A Monte Carlo algorithm is proposed to estimate P values from the resulting conditional distribution. In particular, this package implements a sequentially rounded normal approximation and importance sampling to approximate probabilities from the conditional distribution. Usually, this results in a high percentage of valid samples. However, in instances where this is not the case, a Metropolis Hastings algorithm can be implemented that makes more localized jumps within the reference set. The manuscript details how some conditional tests for binomial logit models can also be viewed as conditional Poisson log-linear models and hence can be performed via exactLoglinTest. A diverse battery of examples is considered to highlight use, features and extensions of the software. Notably, potential extensions to evaluating disclosure risk are also considered.
Dynamics of logistic equations with non-autonomous bounded coefficients
Directory of Open Access Journals (Sweden)
. N. Nkashama
2000-01-01
Full Text Available We prove that the Verhulst logistic equation with positive non-autonomous bounded coefficients has exactly one bounded solution that is positive, and that does not approach the zero-solution in the past and in the future. We also show that this solution is an attractor for all positive solutions, some of which are shown to blow-up in finite time backward. Since the zero-solution is shown to be a repeller for all solutions that remain below the afore-mentioned one, we obtain an attractor-repeller pair, and hence (connecting heteroclinic orbits. The almost-periodic attractor case is also discussed. Our techniques apply to the critical threshold-level equation as well.
Exact sampling hardness of Ising spin models
Fefferman, B.; Foss-Feig, M.; Gorshkov, A. V.
2017-09-01
We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of exact classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.
Space-bounded communication complexity
DEFF Research Database (Denmark)
Brody, Joshua Eric; Chen, Shiteng; Papakonstantinou, Periklis A.
2013-01-01
-obliviousness shows up. For this model we also introduce new techniques through which certain limitations of space-bounded computation are revealed. One of the main motivations of this work is in understanding the difference in the use of space when computing the following functions: Equality (EQ), Inner Product (IP......In the past thirty years, Communication Complexity has emerged as a foundational tool to proving lower bounds in many areas of computer science. Its power comes from its generality, but this generality comes at a price---no superlinear communication lower bound is possible, since a player may...... communicate his entire input. However, what if the players are limited in their ability to recall parts of their interaction? We introduce memory models for 2-party communication complexity. Our general model is as follows: two computationally unrestricted players, Alice and Bob, each have s(n) bits of memory...
Quasitraces on exact C*-algebras are traces
DEFF Research Database (Denmark)
Haagerup, Uffe
2014-01-01
It is shown that all 2-quasitraces on a unital exact C ∗ -algebra are traces. As consequences one gets: (1) Every stably finite exact unital C ∗ -algebra has a tracial state, and (2) if an AW ∗ -factor of type II 1 is generated (as an AW ∗ -algebra) by an exact C ∗ -subalgebra, then i...
New exact travelling wave solutions of some complex nonlinear equations
Bekir, Ahmet
2009-04-01
In this paper, we establish exact solutions for complex nonlinear equations. The tanh-coth and the sine-cosine methods are used to construct exact periodic and soliton solutions of these equations. Many new families of exact travelling wave solutions of the coupled Higgs and Maccari equations are successfully obtained. These solutions may be important of significance for the explanation of some practical physical problems.
Bounded Densities and Their Derivatives
DEFF Research Database (Denmark)
Kozine, Igor; Krymsky, V.
2009-01-01
This paper describes how one can compute interval-valued statistical measures given limited information about the underlying distribution. The particular focus is on a bounded derivative of a probability density function and its combination with other available statistical evidence for computing ...
Physics with loosely bound nuclei
Indian Academy of Sciences (India)
nuclear physics changed drastically as the new generation of accelerators started providing more and more rare isotopes, which are away from the line of stability. These weakly bound nuclei are found to exhibit new forms of nuclear matter and unprecedented exotic behaviour. The low breakup thresholds of these rare ...
Moderate deviations for bounded subsequences
Directory of Open Access Journals (Sweden)
George Stoica
2006-01-01
Full Text Available We study Davis' series of moderate deviations probabilities for Lp-bounded sequences of random variables (p>2. A certain subseries therein is convergent for the same range of parameters as in the case of martingale difference or i.i.d. sequences.
Bounds for percolation thresholds on directed and undirected graphs
Hamilton, Kathleen; Pryadko, Leonid
2015-03-01
Percolation theory is an efficient approach to problems with strong disorder, e.g., in quantum or classical transport, composite materials, and diluted magnets. Recently, the growing role of big data in scientific and industrial applications has led to a renewed interest in graph theory as a tool for describing complex connections in various kinds of networks: social, biological, technological, etc. In particular, percolation on graphs has been used to describe internet stability, spread of contagious diseases and computer viruses; related models describe market crashes and viral spread in social networks. We consider site-dependent percolation on directed and undirected graphs, and present several exact bounds for location of the percolation transition in terms of the eigenvalues of matrices associated with graphs, including the adjacency matrix and the Hashimoto matrix used to enumerate non-backtracking walks. These bounds correspond t0 a mean field approximation and become asymptotically exact for graphs with no short cycles. We illustrate this convergence numerically by simulating percolation on several families of graphs with different cycle lengths. This research was supported in part by the NSF Grant PHY-1416578 and by the ARO Grant W911NF-11-1-0027.
Bounds for cell entries in contingency tables given marginal totals and decomposable graphs
Dobra, Adrian; Fienberg, Stephen E.
2000-01-01
Upper and lower bounds on cell counts in cross-classifications of nonnegative counts play important roles in a number of practical problems, including statistical disclosure limitation, computer tomography, mass transportation, cell suppression, and data swapping. Some features of the Fréchet bounds are well known, intuitive, and regularly used by those working on disclosure limitation methods, especially those for two-dimensional tables. We previously have describ...
A bound for the convergence rate of parallel tempering for sampling restricted Boltzmann machines
DEFF Research Database (Denmark)
Fischer, Asja; Igel, Christian
2015-01-01
Abstract Sampling from restricted Boltzmann machines (RBMs) is done by Markov chain Monte Carlo (MCMC) methods. The faster the convergence of the Markov chain, the more efficiently can high quality samples be obtained. This is also important for robust training of RBMs, which usually relies...... for contrastive divergence learning, our bound on the mixing time implies an upper bound on the error of the gradient approximation when the method is used for RBM training....
Exact Algorithms for the Clustered Vehicle Routing Problem
Battarra, M.; Erdogan, G.; Vigo, D.
2014-01-01
This study presents new exact algorithms for the clustered vehicle routing problem (CluVRP). The CluVRP is a generalization of the capacitated vehicle routing problem (CVRP), in which the customers are grouped into clusters. As in the CVRP, all the customers must be visited exactly once, but a
Classical charged fluids at equilibrium near an interface: Exact ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 64; Issue 5. Classical charged fluids at equilibrium near an interface: Exact analytical density profiles and surface tension. Françoise Cornu. Invited Talks:- Topic 1. Rigorous results and exact solutions; general aspects of statistical physics; thermodynamics Volume 64 ...
Exact solutions of some nonlinear partial differential equations using ...
Indian Academy of Sciences (India)
Research Articles Volume 81 Issue 2 August 2013 pp 225-236 ... Abstract. The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper ... By using this useful method, we found some exact solutions of the above-mentioned equations.
New exact solutions of the generalized Zakharov–Kuznetsov ...
Indian Academy of Sciences (India)
In §2, an extended trial equation method is described for finding exact travelling wave solutions of nonlinear evolution equations with higher-order nonlinearity. In §3, as an application, some exact solutions to nonlinear partial differential equation such as the generalized Zakharov–Kuznetsov modified equal-width equation ...
New exact travelling wave solutions of bidirectional wave equations
Indian Academy of Sciences (India)
where , , and d are real constants. In general, the exact travelling wave solutions will be helpful in the theoretical and numerical study of the nonlinear evolution systems. In this paper, we obtain exact travelling wave solutions of system (1) using the modiﬁed tanh–coth function method with computerized symbolic ...
Rusak, Z.; Luijten, J.; Kooijman, A.
2015-01-01
The present invention relates a wearable exoskeleton for a user having a torso with an upper limb to support motion of the said upper limb. The wearable exoskeleton comprises a first fixed frame mountable to the torso, an upper arm brace and a first group of actuators for moving the upper arm brace
Lower bounds in differential privacy
De, Anindya
2011-01-01
This is a paper about private data analysis, in which a trusted curator holding a confidential database responds to real vector-valued queries. A common approach to ensuring privacy for the database elements is to add appropriately generated random noise to the answers, releasing only these {\\em noisy} responses. In this paper, we investigate various lower bounds on the noise required to maintain different kind of privacy guarantees.
Geometry of Homogeneous Bounded Domains
Vesentini, E
2011-01-01
This title includes: S.G. Gindikin, I.I. Pjateckii-Sapiro, E.B. Vinberg: Homogeneous Kahler manifolds; S.G. Greenfield: Extendibility properties of real submanifolds of Cn; W. Kaup: Holomorphische Abbildungen in Hyperbolische Raume; A. Koranyi: Holomorphic and harmonic functions on bounded symmetric domains; J.L. Koszul: Formes harmoniques vectorielles sur les espaces localement symetriques; S. Murakami: Plongements holomorphes de domaines symetriques; and E.M. Stein: The analogues of Fatous' theorem and estimates for maximal functions.
An exact factorization perspective on quantum interferences in nonadiabatic dynamics.
Curchod, Basile F E; Agostini, Federica; Gross, E K U
2016-07-21
Nonadiabatic quantum interferences emerge whenever nuclear wavefunctions in different electronic states meet and interact in a nonadiabatic region. In this work, we analyze how nonadiabatic quantum interferences translate in the context of the exact factorization of the molecular wavefunction. In particular, we focus our attention on the shape of the time-dependent potential energy surface-the exact surface on which the nuclear dynamics takes place. We use a one-dimensional exactly solvable model to reproduce different conditions for quantum interferences, whose characteristic features already appear in one-dimension. The time-dependent potential energy surface develops complex features when strong interferences are present, in clear contrast to the observed behavior in simple nonadiabatic crossing cases. Nevertheless, independent classical trajectories propagated on the exact time-dependent potential energy surface reasonably conserve a distribution in configuration space that mimics one of the exact nuclear probability densities.
Cyclotron transitions of bound ions
Bezchastnov, Victor G.; Pavlov, George G.
2017-06-01
A charged particle in a magnetic field possesses discrete energy levels associated with particle rotation around the field lines. The radiative transitions between these levels are the well-known cyclotron transitions. We show that a bound complex of particles with a nonzero net charge displays analogous transitions between the states of confined motion of the entire complex in the field. The latter bound-ion cyclotron transitions are affected by a coupling between the collective and internal motions of the complex and, as a result, differ from the transitions of a "reference" bare ion with the same mass and charge. We analyze the cyclotron transitions for complex ions by including the coupling within a rigorous quantum approach. Particular attention is paid to comparison of the transition energies and oscillator strengths to those of the bare ion. Selection rules based on integrals of collective motion are derived for the bound-ion cyclotron transitions analytically, and the perturbation and coupled-channel approaches are developed to study the transitions quantitatively. Representative examples are considered and discussed for positive and negative atomic and cluster ions.
Congenital eversion of upper eyelids: Case report and management
Directory of Open Access Journals (Sweden)
Maheshwari Rajat
2006-01-01
Full Text Available Congenital eversion of the upper eyelids is a rare condition, the exact cause of which remains unknown. It is more frequently associated with Down′s syndrome and black babies. If diagnosed early and treated properly, the condition can be managed without surgery. We report a case of congenital bilateral severe upper eyelid eversion in a normal infant, born by vaginal delivery. The case was conservatively managed by lubricants, antibiotics and eyelid patching.
Bounds on Average Time Complexity of Decision Trees
Chikalov, Igor
2011-01-01
In this chapter, bounds on the average depth and the average weighted depth of decision trees are considered. Similar problems are studied in search theory [1], coding theory [77], design and analysis of algorithms (e.g., sorting) [38]. For any diagnostic problem, the minimum average depth of decision tree is bounded from below by the entropy of probability distribution (with a multiplier 1/log2 k for a problem over a k-valued information system). Among diagnostic problems, the problems with a complete set of attributes have the lowest minimum average depth of decision trees (e.g, the problem of building optimal prefix code [1] and a blood test study in assumption that exactly one patient is ill [23]). For such problems, the minimum average depth of decision tree exceeds the lower bound by at most one. The minimum average depth reaches the maximum on the problems in which each attribute is "indispensable" [44] (e.g., a diagnostic problem with n attributes and kn pairwise different rows in the decision table and the problem of implementing the modulo 2 summation function). These problems have the minimum average depth of decision tree equal to the number of attributes in the problem description. © Springer-Verlag Berlin Heidelberg 2011.
Tight bounds on the size of neural networks for classification problems
Energy Technology Data Exchange (ETDEWEB)
Beiu, V. [Los Alamos National Lab., NM (United States); Pauw, T. de [Universite Catholique de Louvain, Louvain-la-Neuve (Belgium). Dept. de Mathematique
1997-06-01
This paper relies on the entropy of a data-set (i.e., number-of-bits) to prove tight bounds on the size of neural networks solving a classification problem. First, based on a sequence of geometrical steps, the authors constructively compute an upper bound of O(mn) on the number-of-bits for a given data-set - here m is the number of examples and n is the number of dimensions (i.e., R{sup n}). This result is used further in a nonconstructive way to bound the size of neural networks which correctly classify that data-set.
Bounds for the Hilbert function of polynomial ideals and for the degrees in the Nullstellensatz
Sombra, M
1996-01-01
We present a new effective Nullstellensatz with bounds for the degrees which depend not only on the number of variables and on the degrees of the input polynomials but also on an additional parameter called the {\\it geometric degree of the system of equations}. The obtained bound is polynomial in these parameters. It is essentially optimal in the general case, and it substantially improves the existent bounds in some special cases. The proof of this result is combinatorial, and it relies on global estimations for the Hilbert function of homogeneous polynomial ideals. In this direction, we obtain a lower bound for the Hilbert function of an arbitrary homogeneous polynomial ideal, and an upper bound for the Hilbert function of a generic hypersurface section of an unmixed radical polynomial ideal.
On Parameterized Gallager's First Bounds for Binary Linear Codes over AWGN Channels
Ma, Xiao; Bai, Baoming
2012-01-01
In this paper, nested Gallager regions with a single parameter is introduced to exploit Gallager's first bounding technique (GFBT). We present a necessary and sufficient condition on the optimal parameter. We also present a sufficient condition (with a simple geometrical explanation) under which the optimal parameter does not depend on the signal-to-noise ratio (SNR). With this general framework, three existing upper bounds are revisited, including the tangential bound (TB) of Berlekamp, the sphere bound (SB) of Herzberg and Poltyrev, and the tangential-sphere bound (TSB) of Poltyrev. This paper also reveals that the SB of Herzberg and Poltyrev is equivalent to the SB of Kasami et al., which was rarely cited in literature.
Termination Proofs for String Rewriting Systems via Inverse Match-Bounds
Butler, Ricky (Technical Monitor); Geser, Alfons; Hofbauer, Dieter; Waldmann, Johannes
2004-01-01
Annotating a letter by a number, one can record information about its history during a reduction. A string rewriting system is called match-bounded if there is a global upper bound to these numbers. In earlier papers we established match-boundedness as a strong sufficient criterion for both termination and preservation of regular languages. We show now that the string rewriting system whose inverse (left and right hand sides exchanged) is match-bounded, also have exceptional properties, but slightly different ones. Inverse match-bounded systems effectively preserve context-free languages; their sets of normalized strings and their sets of immortal strings are effectively regular. These sets of strings can be used to decide the normalization, the termination and the uniform termination problems of inverse match-bounded systems. We also show that the termination problem is decidable in linear time, and that a certain strong reachability problem is deciable, thus solving two open problems of McNaughton's.
Chaaban, Anas
2016-02-03
The capacity of the free-space optical channel is studied. A new recursive approach for bounding the capacity of the channel based on sphere-packing is proposed. This approach leads to new capacity upper bounds for a channel with a peak intensity constraint or an average intensity constraint. Under an average constraint only, the derived bound is tighter than an existing sphere-packing bound derived earlier by Farid and Hranilovic. The achievable rate of a truncated-Gaussian input distribution is also derived. It is shown that under both average and peak constraints, this achievable rate and the sphere-packing bounds are within a small gap at high SNR, leading to a simple high-SNR capacity approximation. Simple fitting functions that capture the best known achievable rate for the channel are provided. These functions can be of practical importance especially for the study of systems operating under atmospheric turbulence and misalignment conditions.
Dissociation between exact and approximate addition in developmental dyslexia.
Yang, Xiujie; Meng, Xiangzhi
2016-09-01
Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. Copyright © 2016 Elsevier Ltd. All rights reserved.
Lower bounds for randomized Exclusive Write PRAMs
Energy Technology Data Exchange (ETDEWEB)
MacKenzie, P.D.
1995-05-02
In this paper we study the question: How useful is randomization in speeding up Exclusive Write PRAM computations? Our results give further evidence that randomization is of limited use in these types of computations. First we examine a compaction problem on both the CREW and EREW PRAM models, and we present randomized lower bounds which match the best deterministic lower bounds known. (For the CREW PRAM model, the lower bound is asymptotically optimal.) These are the first non-trivial randomized lower bounds known for the compaction problem on these models. We show that our lower bounds also apply to the problem of approximate compaction. Next we examine the problem of computing boolean functions on the CREW PRAM model, and we present a randomized lower bound, which improves on the previous best randomized lower bound for many boolean functions, including the OR function. (The previous lower bounds for these functions were asymptotically optimal, but we improve the constant multiplicative factor.) We also give an alternate proof for the randomized lower bound on PARITY, which was already optimal to within a constant additive factor. Lastly, we give a randomized lower bound for integer merging on an EREW PRAM which matches the best deterministic lower bound known. In all our proofs, we use the Random Adversary method, which has previously only been used for proving lower bounds on models with Concurrent Write capabilities. Thus this paper also serves to illustrate the power and generality of this method for proving parallel randomized lower bounds.
Yavorskii, N. I.
2017-09-01
Magnetohydrodynamic (MHD) flow of a viscous electrically conducting incompressible fluid between two stationary impermeable disks is considered. A homogeneous electric current density vector normal to the surface is specified on the upper disk, and the lower disk is nonconducting. The exact von Karman solution of the complete system of MHD equations is studied in which the axial velocity and the magnetic field depend only on the axial coordinate. The problem contains two dimensionless parameters: the electric current density on the upper plate Y and the Batchelor number (magnetic Prandtl number). It is assumed that there is no external source that produces an axial magnetic field. The problem is solved for a Batchelor number of 0-2. Fluid flow is caused by the electric current. It is shown that for small values of Y, the fluid velocity vector has only axial and radial components. The velocity of motion increases with increasing Y, and at a critical value of Y, there is a bifurcation of the new steady flow regime with fluid rotation, while the flow without rotation becomes unstable. A feature of the obtained new exact solution is the absence of an axial magnetic field necessary for the occurrence of an azimuthal component of the ponderomotive force, as is the case in the MHD dynamo. A new mechanism for the bifurcation of rotation in MHD flow is found.
Bounding the Speed of Gravity with Gravitational Wave Observations
Cornish, Neil; Blas, Diego; Nardini, Germano
2017-10-01
The time delay between gravitational wave signals arriving at widely separated detectors can be used to place upper and lower bounds on the speed of gravitational wave propagation. Using a Bayesian approach that combines the first three gravitational wave detections reported by the LIGO Scientific and Virgo Collaborations we constrain the gravitational waves propagation speed cgw to the 90% credible interval 0.55 c light in vacuum. These bounds will improve as more detections are made and as more detectors join the worldwide network. Of order 20 detections by the two LIGO detectors will constrain the speed of gravity to within 20% of the speed of light, while just five detections by the LIGO-Virgo-Kagra network will constrain the speed of gravity to within 1% of the speed of light.
Thermodynamic models for bounding pressurant mass requirements of cryogenic tanks
Vandresar, Neil T.; Haberbusch, Mark S.
1994-01-01
Thermodynamic models have been formulated to predict lower and upper bounds for the mass of pressurant gas required to pressurize a cryogenic tank and then expel liquid from the tank. Limiting conditions are based on either thermal equilibrium or zero energy exchange between the pressurant gas and initial tank contents. The models are independent of gravity level and allow specification of autogenous or non-condensible pressurants. Partial liquid fill levels may be specified for initial and final conditions. Model predictions are shown to successfully bound results from limited normal-gravity tests with condensable and non-condensable pressurant gases. Representative maximum collapse factor maps are presented for liquid hydrogen to show the effects of initial and final fill level on the range of pressurant gas requirements. Maximum collapse factors occur for partial expulsions with large final liquid fill fractions.
Bounds on the Effect of Progressive Structural Degradation
DEFF Research Database (Denmark)
Achtziger, W.; Bendsøe, Martin P; Taylor, John E.
1998-01-01
" interpretations. Several formulations for extremal "loss of stiffness", each with one or another form of model for local degradation, are compared and evaluated. An isoperimetric constraint controls the degree of loss in overall structural stiffness. Results obtained sequentially for a set of specified......Problem formulations are presented for the evaluation of upper and lower bounds on the effect of progressive structural degradation. For the purposes of this study, degradation effect is measured by an increase in global structural compliance (flexibility). Thus the slated bounds are given simply...... by the maximum and minimum values, respectively, of the increase in compliance corresponding to a specified global interval of degradation. Solutions to these optimization problems identify the particular patterns of local degradation associated with the respective "worst case" and "least degrading...
Robust Adaptive PID Control of Robot Manipulator with Bounded Disturbances
Directory of Open Access Journals (Sweden)
Jian Xu
2013-01-01
Full Text Available To solve the strong nonlinearity and coupling problems in robot manipulator control, two novel robust adaptive PID control schemes are proposed in this paper with known or unknown upper bound of the external disturbances. Invoking the two proposed controllers, the unknown bounded external disturbances can be compensated and the global asymptotical stability with respect to the manipulator positions and velocities is able to be guaranteed. As compared with the existing adaptive PD control methods, the designed control laws can enlarge the tolerable external disturbances, enhance the accuracy in finite-time trajectory tracking control, and improve the dynamic performance of the manipulator systems. The stability and convergence properties of the closed-loop system are analytically proved using Lyapunov stability theory and Barbalat’s lemma. Simulations are performed for a planner manipulator with two rotary degrees of freedom to illustrate the viability and the advantages of the proposed controllers.
Exact Cover Problem in Milton Babbitt's All-partition Array
DEFF Research Database (Denmark)
Bemman, Brian; Meredith, David
2015-01-01
One aspect of analyzing Milton Babbitt’s (1916–2011) all- partition arrays requires finding a sequence of distinct, non-overlapping aggregate regions that completely and exactly covers an irregular matrix of pitch class integers. This is an example of the so-called exact cover problem. Given a set......, A, and a collection of distinct subsets of this set, S, then a subset of S is an exact cover of A if it exhaustively and exclu- sively partitions A. We provide a backtracking algorithm for solving this problem in an all-partition array and compare the output of this algorithm with an analysis...
Exact and approximate computations of watersheds on triangulated terrains
DEFF Research Database (Denmark)
Tsirogiannis, Konstantinos; de Berg, Mark
2011-01-01
The natural way of modeling water flow on a triangulated terrain is to make the fundamental assumption that water follows the direction of steepest descent (dsd). However, computing watersheds and other flow-related structures according to the dsd model in an exact manner is difficult: the dsd...... implementation that computes watersheds on triangulated terrains following strictly the dsd model and using exact arithmetic, and we experimentally investigate its computational cost. Our experiments show that the algorithm cannot handle large data sets effectively, due to the bit-sizes needed in the exact...
Diffusion induced by bounded noise in a two-dimensional coupled memory system
Directory of Open Access Journals (Sweden)
Pengfei Xu
2014-01-01
Full Text Available The diffusion behavior driven by bounded noise under the influence of a coupled harmonic potential is investigated in a two-dimensional coupled-damped model. With the help of the Laplace analysis we obtain exact descriptions for a particle's two-time dynamics which is subjected to a coupled harmonic potential and a coupled damping. The time lag is used to describe the velocity autocorrelation function and mean square displacement of the diffusing particle. The diffusion behavior for the time lag is also discussed with respect to the coupled items and the amplitude of bounded noise.
Atmospheric inverse modeling with known physical bounds: an example from trace gas emissions
Directory of Open Access Journals (Sweden)
S. M. Miller
2014-02-01
the relative merits of each. This paper investigates the applicability of several approaches to bounded inverse problems. A common method of data transformations is found to unrealistically skew estimates for the examined example application. The method of Lagrange multipliers and two Markov chain Monte Carlo (MCMC methods yield more realistic and accurate results. In general, the examined MCMC approaches produce the most realistic result but can require substantial computational time. Lagrange multipliers offer an appealing option for large, computationally intensive problems when exact uncertainty bounds are less central to the analysis. A synthetic data inversion of US anthropogenic methane emissions illustrates the strengths and weaknesses of each approach.
Towards Automatic Resource Bound Analysis for OCaml
Hoffmann, Jan; Das, Ankush; Weng, Shu-Chun
2016-01-01
This article presents a resource analysis system for OCaml programs. This system automatically derives worst-case resource bounds for higher-order polymorphic programs with user-defined inductive types. The technique is parametric in the resource and can derive bounds for time, memory allocations and energy usage. The derived bounds are multivariate resource polynomials which are functions of different size parameters that depend on the standard OCaml types. Bound inference is fully automatic...
Distance hijacking attacks on distance bounding protocols
Cremers, Cas; Rasmussen, Kasper Bonne; Čapkun, Srdjan
2011-01-01
Distance bounding protocols are typically analyzed with respect to three types of attacks: Distance Fraud, Mafia Fraud, and Terrorist Fraud. We define and analyze a fourth main type of attack on distance bounding protocols, called Distance Hijacking. We show that many proposed distance bounding protocols are vulnerable to this type of attack, and we propose solutions to make these protocols resilient to Distance Hijacking. We further show that verifying distance bounding protocols using exist...
Purity- and Gaussianity-bounded uncertainty relations
Mandilara, A.; Karpov, E.; Cerf, N. J.
2014-01-01
Bounded uncertainty relations provide the minimum value of the uncertainty assuming some additional information on the state. We derive analytically an uncertainty relation bounded by a pair of constraints, those of purity and Gaussianity. In a limiting case this uncertainty relation reproduces the purity-bounded derived by Man’ko and Dodonov and the Gaussianity-bounded one (Mandilara and Cerf 2012 Phys. Rev. A 86 030102R).
An interval-valued reliability model with bounded failure rates
DEFF Research Database (Denmark)
Kozine, Igor; Krymsky, Victor
2012-01-01
The approach to deriving interval-valued reliability measures described in this paper is distinctive from other imprecise reliability models in that it overcomes the issue of having to impose an upper bound on time to failure. It rests on the presupposition that a constant interval-valued failure...... rate is known possibly along with other reliability measures, precise or imprecise. The Lagrange method is used to solve the constrained optimization problem to derive new reliability measures of interest. The obtained results call for an exponential-wise approximation of failure probability density...... function if only partial failure information is available. An example is provided. © 2012 Copyright Taylor and Francis Group, LLC....
Energy bounds for the spinless Salpeter equation: harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Hall, Richard L. [Department of Mathematics and Statistics, Concordia University, Montreal, PQ (Canada)]. E-mail: rhall@mathstat.concordia.ca; Lucha, Wolfgang [Institut fuer Hochenergiephysik, Oesterreichische Akademie der Wissenschaften, Vienna (Austria)]. E-mail: wolfgang.lucha@oeaw.ac.at; Schoeberl, Franz F. [Institut fuer Theoretische Physik, Universitaet Wien, Vienna (Austria)]. E-mail: franz.schoeberl@univie.ac.at
2001-06-22
We study the eigenvalues E{sub nl} of the Salpeter Hamiltonian H={beta}(m{sup 2}+p{sup 2}){sup 1/2}+vr{sup 2}, v>0, {beta}>0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided, the simple semiclassical formula E{sub nl}{approx}min{sub r>0}{l_brace}v(P{sub nl}/r){sup 2}+{beta}(m{sup 2}+r{sup 2}){sup 1/2}{r_brace} provides both upper and lower energy bounds for all the eigenvalues of the problem. (author)
Bounded rationality and heterogeneous expectations in macroeconomics
Massaro, D.
2012-01-01
This thesis studies the effect of individual bounded rationality on aggregate macroeconomic dynamics. Boundedly rational agents are specified as using simple heuristics in their decision making. An important aspect of the type of bounded rationality described in this thesis is that the population of
Labeling schemes for bounded degree graphs
DEFF Research Database (Denmark)
Adjiashvili, David; Rotbart, Noy Galil
2014-01-01
graphs. Our results complement a similar bound recently obtained for bounded depth trees [Fraigniaud and Korman, SODA 2010], and may provide new insights for closing the long standing gap for adjacency in trees [Alstrup and Rauhe, FOCS 2002]. We also provide improved labeling schemes for bounded degree...
Massive Axial Gauge in the Exact Renormalization Group Approach
Panza, P.; Soldati, R.
The Exact Renormalization Group (ERG) approach to massive gauge theories in the axial gauge is studied and the smoothness of the massless limit is analysed for a formally gauge invariant quantity such as the Euclidean Wilson loop.
Exactly solvable models for multiatomic molecular Bose-Einstein condensates
Energy Technology Data Exchange (ETDEWEB)
Santos, G, E-mail: gfilho@if.ufrgs.br, E-mail: gfilho@cbpf.br [Instituto de Fisica da UFRGS, Av. Bento Goncalves, 9500, Agronomia, Porto Alegre, RS (Brazil)
2011-08-26
I introduce two families of exactly solvable models for multiatomic hetero-nuclear and homo-nuclear molecular Bose-Einstein condensates through the algebraic Bethe ansatz method. The conserved quantities of the respective models are also shown. (paper)
An exact test of the Hardy-Weinberg law.
Chapco, W
1976-03-01
An exact distribution of a finite sample drawn from an infinite population in Hardy-Weinberg Equilibrium is described for k-alleles. Accordingly, an exact test of the law is presented and compared with two x2-tests for two and three alleles. For two alleles, it is shown that the "classical" c2-test is very adequate for sample sizes as small as ten. For three alleles, it is shown that a simpler formulation based on Leven's distribution approximates the exact test of this paper rather closely. However, it is recommended that researchers continue to employ the standard x2-test for all sample sizes and abide by it if the corresponding probability value is not "too close" to the critical level; otherwise, an exact test should be used.
Exact complex integrals in two dimensions for shifted harmonic ...
Indian Academy of Sciences (India)
symmetric. Hamiltonians appear to be special cases of such transformations. In the present work we carry out the ECPS approach to obtain exact complex integrals of a two-dimensional classical dynamical system [14,15]. Rationalization method ...
Exact solutions for the differential equations in fractal heat transfer
Directory of Open Access Journals (Sweden)
Yang Chun-Yu
2016-01-01
Full Text Available In this article we consider the boundary value problems for differential equations in fractal heat transfer. The exact solutions of non-differentiable type are obtained by using the local fractional differential transform method.
Exact and approximate expressions for the period of anharmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (Conicet, UNLP), Blvd. 113 y 64 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2005-07-01
In this paper, we present a straightforward systematic method for the exact and approximate calculation of integrals that appear in formulae for the period of anharmonic oscillators and other problems of interest in classical mechanics.
Exact solutions and spacetime singularities in nonlocal gravity
National Research Council Canada - National Science Library
Li, Yao-Dong; Modesto, Leonardo; Rachwał, Lesław
2015-01-01
.... We prove that maximally symmetric spacetimes are exact solutions in both classes, while in dimension higher than four we can also have Anti-de Sitter solutions in the presence of positive cosmological constant...
DEFF Research Database (Denmark)
Nørrelykke, Simon F; Flyvbjerg, Henrik
2011-01-01
-lapse recordings. Three applications are discussed: (i) The effects of finite sampling rate and time, described exactly here, are similar for other stochastic dynamical systems-e.g., motile microorganisms and their time-lapse-recorded trajectories. (ii) The same statistics is satisfied by any experimental system......The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...... of finite sampling rate and sampling time for these models as well....
... obstruction - acute upper Images Throat anatomy Choking Respiratory system References Cukor J, Manno M. Pediatric respiratory emergencies: upper airway obstruction and infections. In: Marx J, ed. Rosen's Emergency Medicine: Concepts and Clinical Practice . 8th ed. Philadelphia, PA: Elsevier ...
US Fish and Wildlife Service, Department of the Interior — The Upper Kenai Corridor study describes and evaluates the Upper Kenai River and the land which embraces it. It also places the river corridor in its regional...
Corollary from the Exact Expression for Enthalpy of Vaporization
Directory of Open Access Journals (Sweden)
A. A. Sobko
2011-01-01
Full Text Available A problem on determining effective volumes for atoms and molecules becomes actual due to rapidly developing nanotechnologies. In the present study an exact expression for enthalpy of vaporization is obtained, from which an exact expression is derived for effective volumes of atoms and molecules, and under certain assumptions on the form of an atom (molecule it is possible to find their linear dimensions. The accuracy is only determined by the accuracy of measurements of thermodynamic parameters at the critical point.
Exact Mean Computation in Dynamic Time Warping Spaces
Brill, Markus; Fluschnik, Till; Froese, Vincent; Jain, Brijnesh; Niedermeier, Rolf; Schultz, David
2017-01-01
Dynamic time warping constitutes a major tool for analyzing time series. In particular, computing a mean series of a given sample of series in dynamic time warping spaces (by minimizing the Fr\\'echet function) is a challenging computational problem, so far solved by several heuristic, inexact strategies. We spot several inaccuracies in the literature on exact mean computation in dynamic time warping spaces. Our contributions comprise an exact dynamic program computing a mean (useful for bench...
Rusak, Z.; Luijten, J.; Kooijman, A.
2015-01-01
The present invention relates a wearable exoskeleton for a user having a torso with an upper limb to support motion of the said upper limb. The wearable exoskeleton comprises a first fixed frame mountable to the torso, an upper arm brace and a first group of actuators for moving the upper arm brace relative to the first fixed frame. In an example the present invention is for use in post-stroke therapy.
Exact Solution of the Three-Body Santilli-Shillady Model of the Hydrogen Molecule
Directory of Open Access Journals (Sweden)
Pérez-Enríquez R.
2007-04-01
Full Text Available The conventional representation of the H 2 molecule characterizes a 4-body system due to the independence of the orbitals of the two valence electrons as requested by quantum chemistry, under which conditions no exact solution is possible. To overcome this problem, Santilli and Shillady introduced in 1999 a new model of the H 2 -molecu- le in which the two valence electrons are deeply bounded-correlated into a single quasi-particle they called isoelectronium that is permitted by the covering hadronic chemistry. They pointed out that their new H 2 -model is a restricted 3-body system that, as such, is expected to admit an exact solution and suggested independent studies for its identification due to its relevance, e.g., for other molecules. In 2000, Aringazin and Kucherenko did study the Santilli-Shillady restricted 3-body model of the H 2 molecules, but they presented a variational solution that, as such, is not exact. In any case, the latter approach produced significant deviations from experimental data, such as a 19.6% inter-nuclear distance greater than the experimental value. In this paper we present, apparently for the first time, an exact solution of the Santilli-Shillady restricted 3-body model of the Hydrogen molecule along the lines of its originators and show that it does indeed represent correctly all basic data. Intriguingly, our solution confirms that the orbital of the isoelectronium (referred to as its charge distribution around the nuclei must be concentrated in a limited region of space given by the Santilli-Shillady oo-shaped orbits. Our exact solution is constructed by following the Ley-Koo solution to the Schr ̈ odinger equation for a confined hydrogen molecular ion, H + 2 . We show that a confined model to the 3-body molecule reproduces the ground state curve as calculated by Kolos, Szalewics and Monkhorst with a precision up to the 4-th digit and a precision in the representation of the binding energy up to the 5-th digit.
A simple but usually fast branch-and-bound algorithm for the capacitated facility location problem
DEFF Research Database (Denmark)
Görtz, Simon; Klose, Andreas
2012-01-01
This paper presents a simple branch-and-bound method based on Lagrangean relaxation and subgradient optimization for solving large instances of the capacitated facility location problem (CFLP) to optimality. To guess a primal solution to the Lagrangean dual, we average solutions to the Lagrangean...... subproblem. Branching decisions are then based on this estimated (fractional) primal solution. Extensive numerical results reveal that the method is much faster and more robust than other state-of-the-art methods for solving the CFLP exactly....
Morse potential, symmetric Morse potential and bracketed bound-state energies
Czech Academy of Sciences Publication Activity Database
Znojil, Miloslav
2016-01-01
Roč. 31, č. 14 (2016), s. 1650088 ISSN 0217-7323 R&D Projects: GA ČR GA16-22945S Institutional support: RVO:61389005 Keywords : quantum bound states * special functions * Morse potential * symmetrized Morse potential * upper and lower energy estimates * computer-assisted symbolic manipulations Subject RIV: BE - Theoretical Physics Impact factor: 1.165, year: 2016
Bounds of the Spectral Radius and the Nordhaus-Gaddum Type of the Graphs
Directory of Open Access Journals (Sweden)
Tianfei Wang
2013-01-01
Full Text Available The Laplacian spectra are the eigenvalues of Laplacian matrix L(G=D(G-A(G, where D(G and A(G are the diagonal matrix of vertex degrees and the adjacency matrix of a graph G, respectively, and the spectral radius of a graph G is the largest eigenvalue of A(G. The spectra of the graph and corresponding eigenvalues are closely linked to the molecular stability and related chemical properties. In quantum chemistry, spectral radius of a graph is the maximum energy level of molecules. Therefore, good upper bounds for the spectral radius are conducive to evaluate the energy of molecules. In this paper, we first give several sharp upper bounds on the adjacency spectral radius in terms of some invariants of graphs, such as the vertex degree, the average 2-degree, and the number of the triangles. Then, we give some numerical examples which indicate that the results are better than the mentioned upper bounds in some sense. Finally, an upper bound of the Nordhaus-Gaddum type is obtained for the sum of Laplacian spectral radius of a connected graph and its complement. Moreover, some examples are applied to illustrate that our result is valuable.
Bounds for the price of a European-style Asian option in a binary tree model
Reynaerts, H; Vanmaele, M.; Dhaene, J.L.M.; Deelstra, G.
2006-01-01
Inspired by the ideas of Rogers and Shi [J. Appl. Prob. 32 (1995) 1077], Chalasani et al. [J. Comput. Finance 1(4) (1998) 11] derived accurate lower and upper bounds for the price of a European-style Asian option with continuous averaging over the full lifetime of the option, using a discrete-time
Bounds on Correlation Decay for Long-Range Vector Spin Glasses
Enter, Aernout C.D. van
1985-01-01
We give upper bounds on the decay of correlation functions for long-range SO(N)-symmetric spin-glass models in one and two dimensions using McBryan-Spencer techniques. In doing so we extend other's recent results.
Performance Bounds of Quaternion Estimators.
Xia, Yili; Jahanchahi, Cyrus; Nitta, Tohru; Mandic, Danilo P
2015-12-01
The quaternion widely linear (WL) estimator has been recently introduced for optimal second-order modeling of the generality of quaternion data, both second-order circular (proper) and second-order noncircular (improper). Experimental evidence exists of its performance advantage over the conventional strictly linear (SL) as well as the semi-WL (SWL) estimators for improper data. However, rigorous theoretical and practical performance bounds are still missing in the literature, yet this is crucial for the development of quaternion valued learning systems for 3-D and 4-D data. To this end, based on the orthogonality principle, we introduce a rigorous closed-form solution to quantify the degree of performance benefits, in terms of the mean square error, obtained when using the WL models. The cases when the optimal WL estimation can simplify into the SWL or the SL estimation are also discussed.
On order bounded subsets of locally solid Riesz spaces | Hong ...
African Journals Online (AJOL)
In a topological Riesz space there are two types of bounded subsets: order bounded subsets and topologically bounded subsets. It is natural to ask (1) whether an order bounded subset is topologically bounded and (2) whether a topologically bounded subset is order bounded. A classical result gives a partial answer to (1) ...
Exact dimension estimation of interacting qubit systems assisted by a single quantum probe
Sone, Akira; Cappellaro, Paola
2017-12-01
Estimating the dimension of an Hilbert space is an important component of quantum system identification. In quantum technologies, the dimension of a quantum system (or its corresponding accessible Hilbert space) is an important resource, as larger dimensions determine, e.g., the performance of quantum computation protocols or the sensitivity of quantum sensors. Despite being a critical task in quantum system identification, estimating the Hilbert space dimension is experimentally challenging. While there have been proposals for various dimension witnesses capable of putting a lower bound on the dimension from measuring collective observables that encode correlations, in many practical scenarios, especially for multiqubit systems, the experimental control might not be able to engineer the required initialization, dynamics, and observables. Here we propose a more practical strategy that relies not on directly measuring an unknown multiqubit target system, but on the indirect interaction with a local quantum probe under the experimenter's control. Assuming only that the interaction model is given and the evolution correlates all the qubits with the probe, we combine a graph-theoretical approach and realization theory to demonstrate that the system dimension can be exactly estimated from the model order of the system. We further analyze the robustness in the presence of background noise of the proposed estimation method based on realization theory, finding that despite stringent constrains on the allowed noise level, exact dimension estimation can still be achieved.
Morrison, Abigail; Straube, Sirko; Plesser, Hans Ekkehard; Diesmann, Markus
2007-01-01
Very large networks of spiking neurons can be simulated efficiently in parallel under the constraint that spike times are bound to an equidistant time grid. Within this scheme, the subthreshold dynamics of a wide class of integrate-and-fire-type neuron models can be integrated exactly from one grid point to the next. However, the loss in accuracy caused by restricting spike times to the grid can have undesirable consequences, which has led to interest in interpolating spike times between the grid points to retrieve an adequate representation of network dynamics. We demonstrate that the exact integration scheme can be combined naturally with off-grid spike events found by interpolation. We show that by exploiting the existence of a minimal synaptic propagation delay, the need for a central event queue is removed, so that the precision of event-driven simulation on the level of single neurons is combined with the efficiency of time-driven global scheduling. Further, for neuron models with linear subthreshold dynamics, even local event queuing can be avoided, resulting in much greater efficiency on the single-neuron level. These ideas are exemplified by two implementations of a widely used neuron model. We present a measure for the efficiency of network simulations in terms of their integration error and show that for a wide range of input spike rates, the novel techniques we present are both more accurate and faster than standard techniques.
Ishkhanyan, A. M.
2016-09-01
We introduce two potentials explicitly given by the Lambert-W function for which the exact solution of the one-dimensional stationary Schrödinger equation is written through the first derivative of a double-confluent Heun function. One of these potentials is a singular potential that behaves as the inverse square root in the vicinity of the origin and vanishes exponentially at the infinity. The exact solution of the Schrödinger equation for this potential is given through fundamental solutions each of which presents an irreducible linear combination of two confluent hypergeometric functions. Since the potential is effectively a short-range one, it supports only a finite number of bound states.
Information-Theoretic Bounds and Approximations in Neural Population Coding.
Huang, Wentao; Zhang, Kechen
2018-01-17
While Shannon's mutual information has widespread applications in many disciplines, for practical applications it is often difficult to calculate its value accurately for high-dimensional variables because of the curse of dimensionality. This article focuses on effective approximation methods for evaluating mutual information in the context of neural population coding. For large but finite neural populations, we derive several information-theoretic asymptotic bounds and approximation formulas that remain valid in high-dimensional spaces. We prove that optimizing the population density distribution based on these approximation formulas is a convex optimization problem that allows efficient numerical solutions. Numerical simulation results confirmed that our asymptotic formulas were highly accurate for approximating mutual information for large neural populations. In special cases, the approximation formulas are exactly equal to the true mutual information. We also discuss techniques of variable transformation and dimensionality reduction to facilitate computation of the approximations.
Latency-Bounded Minimum Influential Node Selection in Social Networks
Zou, Feng; Zhang, Zhao; Wu, Weili
As one of the essential problems in information diffusion process, how to select a set of influential nodes as the starting nodes has been studied by lots of researchers. All the existing solutions focus on how to maximize the influence of the initially selected “influential nodes”, paying no attention on how the influential nodes selection could maximize the speed of the diffusion. In this paper, we consider the problem of influential nodes selection regarding to the propagation speed in social network information diffusion. We define a discrete optimization problem, called Fast Information Propagation Problem. We show that this problem is NP-hard problem when the time requirement for information propagation is exactly 1-hop. We also propose a Latency-bounded Minimum Influential Node Selection Algorithm to solve the problem in this case.
Volume of a vortex and the Bradlow bound
Adam, C.; Speight, J. M.; Wereszczynski, A.
2017-06-01
We demonstrate that the geometric volume of a soliton coincides with the thermodynamical volume also for field theories with higher-dimensional vacuum manifolds (e.g., for gauged scalar field theories supporting vortices or monopoles), generalizing the recent results of Ref. [C. Adam, M. Haberichter, and A. Wereszczynski, Phys. Lett. B 754, 18 (2016)., 10.1016/j.physletb.2016.01.009]. We apply this observation to understand Bradlow-type bounds for general Abelian gauge theories supporting vortices, as well as some thermodynamical aspects of said theories. In the case of SDiff Bogomolny-Prasad-Sommerfield (BPS) models (being examples of perfect fluid models) we show that the base-space independent geometric volume (area) of the vortex is exactly equal to the Bradlow volume (a minimal volume for which BPS soliton solutions exist). This volume can be finite for compactons or infinite for infinitely extended solitons (in flat Minkowski space-time).
Bounds on the Coupling of the Majoron to Light Neutrinos from Supernova Cooling
Energy Technology Data Exchange (ETDEWEB)
Farzan, Yasaman
2002-12-02
We explore the role of Majoron (J) emission in the supernova cooling process, as a source of upper bound on the neutrino-Majoron coupling. We show that the strongest upper bound on the coupling to {nu}{sub 3} comes from the {nu}{sub e}{nu}{sub e} {yields} J process in the core of a supernova. We also find bounds on diagonal couplings of the Majoron to {nu}{sub {mu}({tau})}{nu}{sub {mu}({tau})} and on off-diagonal {nu}{sub e}{nu}{sub {mu}({tau})} couplings in various regions of the parameter space. We discuss the evaluation of cross-section for four-particle interactions ({nu}{nu} {yields} JJ and {nu}J {yields} {nu}J). We show that these are typically dominated by three-particle sub-processes and do not give new independent constraints.
Full counting statistics approach to the quantum non-equilibrium Landauer bound
Guarnieri, Giacomo; Campbell, Steve; Goold, John; Pigeon, Simon; Vacchini, Bassano; Paternostro, Mauro
2017-10-01
We develop the full counting statistics of dissipated heat to explore the relation with Landauer’s principle. Combining the two-time measurement protocol for the reconstruction of the statistics of heat with the minimal set of assumptions for Landauer’s principle to hold, we derive a general one-parameter family of upper and lower bounds on the mean dissipated heat from a system to its environment. Furthermore, we establish a connection with the degree of non-unitality of the system’s dynamics and show that, if a large deviation function exists as stationary limit of the above cumulant generating function, then our family of lower and upper bounds can be used to witness and understand first-order dynamical phase transitions. For the purpose of demonstration, we apply these bounds to an externally pumped three level system coupled to a finite sized thermal environment.
Ghinita, Gabriel
2010-12-15
Mobile devices with global positioning capabilities allow users to retrieve points of interest (POI) in their proximity. To protect user privacy, it is important not to disclose exact user coordinates to un-trusted entities that provide location-based services. Currently, there are two main approaches to protect the location privacy of users: (i) hiding locations inside cloaking regions (CRs) and (ii) encrypting location data using private information retrieval (PIR) protocols. Previous work focused on finding good trade-offs between privacy and performance of user protection techniques, but disregarded the important issue of protecting the POI dataset D. For instance, location cloaking requires large-sized CRs, leading to excessive disclosure of POIs (O({pipe}D{pipe}) in the worst case). PIR, on the other hand, reduces this bound to O(√{pipe}D{pipe}), but at the expense of high processing and communication overhead. We propose hybrid, two-step approaches for private location-based queries which provide protection for both the users and the database. In the first step, user locations are generalized to coarse-grained CRs which provide strong privacy. Next, a PIR protocol is applied with respect to the obtained query CR. To protect against excessive disclosure of POI locations, we devise two cryptographic protocols that privately evaluate whether a point is enclosed inside a rectangular region or a convex polygon. We also introduce algorithms to efficiently support PIR on dynamic POI sub-sets. We provide solutions for both approximate and exact NN queries. In the approximate case, our method discloses O(1) POI, orders of magnitude fewer than CR- or PIR-based techniques. For the exact case, we obtain optimal disclosure of a single POI, although with slightly higher computational overhead. Experimental results show that the hybrid approaches are scalable in practice, and outperform the pure-PIR approach in terms of computational and communication overhead. © 2010
Is regional species diversity bounded or unbounded?
Cornell, Howard V
2013-02-01
Two conflicting hypotheses have been proposed to explain large-scale species diversity patterns and dynamics. The unbounded hypothesis proposes that regional diversity depends only on time and diversification rate and increases without limit. The bounded hypothesis proposes that ecological constraints place upper limits on regional diversity and that diversity is usually close to its limit. Recent evidence from the fossil record, phylogenetic analysis, biogeography, and phenotypic disparity during lineage diversification suggests that diversity is constrained by ecological processes but that it is rarely asymptotic. Niche space is often unfilled or can be more finely subdivided and still permit coexistence, and new niche space is often created before ecological limits are reached. Damped increases in diversity over time are the prevalent pattern, suggesting the need for a new 'damped increase hypothesis'. The damped increase hypothesis predicts that diversity generally increases through time but that its rate of increase is often slowed by ecological constraints. However, slowing due to niche limitation must be distinguished from other possible mechanisms creating similar patterns. These include sampling artifacts, the inability to detect extinctions or declines in clade diversity with some methods, the distorting effects of correlated speciation-extinction dynamics, the likelihood that opportunities for allopatric speciation will vary in space and time, and the role of undetected natural enemies in reducing host ranges and thus slowing speciation rates. The taxonomic scope of regional diversity studies must be broadened to include all ecologically similar species so that ecological constraints may be accurately inferred. The damped increase hypothesis suggests that information on evolutionary processes such as time-for-speciation and intrinsic diversification rates as well as ecological factors will be required to explain why regional diversity varies among times
Using tolerance bounds in scientific investigations
Energy Technology Data Exchange (ETDEWEB)
Wendelberger, J.R.
1996-07-01
Assessment of the variability in population values plays an important role in the analysis of scientific data. Analysis of scientific data often involves developing a bound on a proportion of a population. Sometimes simple probability bounds are obtained using formulas involving known mean and variance parameters and replacing the parameters by sample estimates. The resulting bounds are only approximate and fail to account for the variability in the estimated parameters. Tolerance bounds provide bounds on population proportions which account for the variation resulting from the estimated mean and variance parameters. A beta content, gamma confidence tolerance interval is constructed so that a proportion beta of the population lies within the region bounded by the interval with confidence gamma. An application involving corrosion measurements is used to illustrate the use of tolerance bounds for different situations. Extensions of standard tolerance intervals are applied to generate regression tolerance bounds, tolerance bounds for more general models of measurements collected over time, and tolerance intervals for varying precision data. Tolerance bounds also provide useful information for designing the collection of future data.
Exact multilocal renormalization group and applications to disordered problems
Chauve, Pascal; Le Doussal, Pierre
2001-11-01
We develop a method, the exact multilocal renormalization group (EMRG) which applies to a broad set of theories. It is based on the systematic multilocal expansion of the Polchinski-Wilson exact renormalization group (ERG) equation together with a scheme to compute correlation functions. Integrating out explicitly the nonlocal interactions, we reduce the ERG equation obeyed by the full interaction functional to a flow equation for a function, its local part. This is done perturbatively around fixed points, but exactly to any given order in the local part. It is thus controlled, at variance with projection methods, e.g., derivative expansions or local potential approximations. Our EMRG method is well-suited to problems such as the pinning of disordered elastic systems, previously described via functional renormalization group (FRG) approach based on a hard cutoff scheme. Since it involves arbitrary cutoff functions, we explicitly verify universality to O(ɛ=4-D), both of the T=0 FRG equation and of correlations. Extension to finite temperature T yields the finite size (L) susceptibility fluctuations characterizing mesoscopic behavior (Δχ)2¯~Lθ/T, where θ is the energy exponent. Finally, we obtain the universal scaling function to O(ɛ1/3) which describes the ground state of a domain wall in a random field confined by a field gradient, compare with exact results and variational method. Explicit two loop exact RG equations are derived and the application to the FRG problem is sketched.
Cannon, Dirk; Brayshaw, David; Methven, John; Drew, Daniel
2017-04-01
State-of-the-art wind power forecasts beyond a few hours ahead rely on global numerical weather prediction models to forecast the future large-scale atmospheric state. Often they provide initial and boundary conditions for nested high resolution simulations. In this work, both upper and lower bounds on forecast range are identified within which global ensemble forecasts provide skilful information for system-wide wind power applications. An upper bound on forecast range is associated with the limit of predictability, beyond which forecasts have no more skill than predictions based on climatological statistics. A lower bound is defined at the lead time beyond which the resolved uncertainty associated with estimating the future large-scale atmospheric state is larger than the unresolved uncertainty associated with estimating the system-wide wind power response to a given large-scale state. The bounds of skillful ensemble forecast range are quantified for three leading global forecast systems. The power system of Great Britain (GB) is used as an example because independent verifying data is available from National Grid. The upper bound defined by forecasts of GB-total wind power generation at a specific point in time is found to be 6-8 days. The lower bound is found to be 1.4-2.4 days. Both bounds depend on the global forecast system and vary seasonally. In addition, forecasts of the probability of an extreme power ramp event were found to possess a shorter limit of predictability (4.5-5.5 days). The upper bound on this forecast range can only be extended by improving the global forecast system (outside the control of most users) or by changing the metric used in the probability forecast. Improved downscaling and microscale modelling of the wind farm response may act to decrease the lower bound. The potential gain from such improvements have diminishing returns beyond the short-range (out to around 2 days).
Bound anionic states of adenine
Energy Technology Data Exchange (ETDEWEB)
Haranczyk, Maciej; Gutowski, Maciej S; Li, Xiang; Bowen, Kit H
2007-03-20
Anionic states of nucleic acid bases are involved in DNA damage by low-energy electrons and in charge transfer through DNA. Previous gas phase studies of free, unsolvated nucleic acid base parent anions probed only dipole-bound states, which are not present in condensed phase environments, but did not observe valence anionic states, which for purine bases, are thought to be adiabatically unbound. Contrary to this expectation, we have demonstrated that some thus far ignored tautomers of adenine, which result from enamine-imine transformations, support valence anionic states with electron vertical detachment energies as large as 2.2 eV, and at least one of these anionic tautomers is adiabatically bound. Moreover, we predict that the new anionic tautomers should also dominate in solutions and should be characterized by larger values of electron vertical detachment energy than the canonical valence anion. All of the new-found anionic tautomers might be formed in the course of dissociative electron attachment followed by a hydrogen atom attachment to a carbon atom, and they might affect the structure and properties of DNA and RNA exposed to low-energy electrons. The discovery of these valence anionic states of adenine was facilitated by the development of: (i) a new experimental method for preparing parent anions of nucleic acid bases for photoelectron experiments, and (ii) a new combinatorial/ quantum chemical approach for identification of the most stable tautomers of organic molecules. The computational portion of this work was supported by the: (i) Polish State Committee for Scientific Research (KBN) Grants: DS/8000-4-0140-7 (M.G.) and N204 127 31/2963 (M.H.), (ii) European Social Funds (EFS) ZPORR/2.22/II/2.6/ARP/U/2/05 (M.H.), and (iii) US DOE Office of Biological and Environmental Research, Low Dose Radiation Research Program (M.G.). M.H. holds the Foundation for Polish Science (FNP) award for young scientists. The calculations were performed at the Academic
On field redefinitions and exact solutions in string theory
Tseytlin, Arkady A
1993-01-01
String backgrounds associated with gauged $G/H$ WZNW models in general depend non-trivially on $\\alpha'$. We note, however, that there exists a local covariant $\\a'$-dependent field redefinition that relates the exact metric-dilaton background corresponding to the $SL(2,R)/U(1)$ model to its leading-order form ($D=2$ black hole). As a consequence, there exists a `scheme' in which the string effective equations have the latter as an exact solution. However, the corresponding equation for the tachyon (which, like other Weyl anomaly coefficients, has scheme-dependent form) still contains corrections of all orders in $\\alpha'$. As a result, the `probes' (the tachyons) still feel the $\\alpha'$-corrected background. The field redefinitions we discuss contain the dilaton terms in the metric transformation law. We comment on exact forms of the duality transformation in different `schemes'.
Exact renormalization flow and domain walls from holography
Ketov, Sergei V.
2001-03-01
The holographic correspondence between 2d, N=2 quantum field theories and classical 4d, N=2 supergravity coupled to hypermultiplet matter is proposed. The geometrical constraints on the target space of the 4d, N=2 non-linear sigma-models in N=2 supergravity background are interpreted as the exact renormalization group flow equations in two dimensions. Our geometrical description of the renormalization flow is manifestly covariant under general reparametrization of the 2d coupling constants. An explicit exact solution to the 2d renormalization flow, based on its dual holographic description in terms of the Zamolodchikov metric, is considered in the particular case of the four-dimensional NLSM target space described by the SU(2)-invariant (Weyl) anti-self-dual Einstein metrics. The exact regular (Tod-Hitchin) solutions to these metrics are governed by the Painlevé VI equation, and describe domain walls.
Fuzziness and Foundations of Exact and Inexact Sciences
Dompere, Kofi Kissi
2013-01-01
The monograph is an examination of the fuzzy rational foundations of the structure of exact and inexact sciences over the epistemological space which is distinguished from the ontological space. It is thus concerned with the demarcation problem. It examines exact science and its critique of inexact science. The role of fuzzy rationality in these examinations is presented. The driving force of the discussions is the nature of the information that connects the cognitive relational structure of the epistemological space to the ontological space for knowing. The knowing action is undertaken by decision-choice agents who must process information to derive exact-inexact or true-false conclusions. The information processing is done with a paradigm and laws of thought that constitute the input-output machine. The nature of the paradigm selected depends on the nature of the information structure that is taken as input of the thought processing. Generally, the information structure received from the ontological space i...
Exact solution of the two-axis countertwisting Hamiltonian
Pan, Feng; Zhang, Yao-Zhong; Draayer, Jerry P.
2017-01-01
It is shown that the two-axis countertwisting Hamiltonian is exactly solvable when the quantum number of the total angular momentum of the system is an integer after the Jordan-Schwinger (differential) boson realization of the SU(2) algebra. Algebraic Bethe ansatz is used to get the exact solution with the help of the SU(1,1) algebraic structure, from which a set of Bethe ansatz equations of the problem is derived. It is shown that solutions of the Bethe ansatz equations can be obtained as zeros of the Heine-Stieltjes polynomials. The total number of the four sets of the zeros equals exactly 2 J + 1 for a given integer angular momentum quantum number J, which proves the completeness of the solutions. It is also shown that double degeneracy in level energies may also occur in the J → ∞ limit for integer J case except a unique non-degenerate level with zero excitation energy.
Exact deconstruction of the 6D (2,0) theory
Hayling, J.; Papageorgakis, C.; Pomoni, E.; Rodríguez-Gómez, D.
2017-06-01
The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T 2, starting from a four-dimensional N=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: in the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N=2 quiver to the "half-BPS" limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S 4 to the (2,0) partition function on S 4 × T 2. In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.
Upper Limit in the Periodic Table of Elements
Directory of Open Access Journals (Sweden)
Khazan A.
2007-01-01
Full Text Available The method of rectangular hyperbolas is developed for the first time, by which a means for estimating the upper bound of the Periodic Table is established in calculating that its last element has an atom mass of 411.663243 and an atomic number (the nuclear charge of 155. The formulating law is given.
Instanton bound states in ABJM theory
Energy Technology Data Exchange (ETDEWEB)
Hatsuda, Yasuyuki [DESY Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst. and Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics
2013-06-15
The partition function of the ABJM theory receives non-perturbative corrections due to instanton effects. We study these non-perturbative corrections, including bound states of worldsheet instantons and membrane instantons, in the Fermi-gas approach. We require that the total non-perturbative correction should be always finite for arbitrary Chern-Simons level. This finiteness is realized quite non-trivially because each bound state contribution naively diverges at some levels. The poles of each contribution should be canceled out in total. We use this pole cancellation mechanism to find unknown bound state corrections from known ones. We conjecture a general expression of the bound state contribution. Summing up all the bound state contributions, we find that the effect of bound states is simply incorporated into the worldsheet instanton correction by a redefinition of the chemical potential in the Fermi-gas system. Analytic expressions of the 3- and 4-membrane instanton corrections are also proposed.
Universality of the Volume Bound in Slow-Roll Eternal Inflation
Energy Technology Data Exchange (ETDEWEB)
Dubovsky, Sergei; Senatore, Leonardo; Villadoro, Giovanni
2012-03-28
It has recently been shown that in single field slow-roll inflation the total volume cannot grow by a factor larger than e{sup S{sub dS}/2} without becoming infinite. The bound is saturated exactly at the phase transition to eternal inflation where the probability to produce infinite volume becomes non zero. We show that the bound holds sharply also in any space-time dimensions, when arbitrary higher-dimensional operators are included and in the multi-field inflationary case. The relation with the entropy of de Sitter and the universality of the bound strengthen the case for a deeper holographic interpretation. As a spin-off we provide the formalism to compute the probability distribution of the volume after inflation for generic multi-field models, which might help to address questions about the population of vacua of the landscape during slow-roll inflation.
Optimality Bounds for a Variational Relaxation of the Image Partitioning Problem
Lellmann, Jan
2012-11-09
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation methods for finite-dimensional problems. While for the latter several optimality bounds are known, to our knowledge no such bounds exist in the infinite-dimensional setting. We provide such a bound by analyzing a probabilistic rounding method, showing that it is possible to obtain an integral solution of the original partitioning problem from a solution of the relaxed problem with an a priori upper bound on the objective. The approach has a natural interpretation as an approximate, multiclass variant of the celebrated coarea formula. © 2012 Springer Science+Business Media New York.
Distance hijacking attacks on distance bounding protocols
Cremers, Cas; Rasmussen, Kasper Bonne; Čapkun, Srdjan
2011-01-01
Distance bounding protocols are typically analyzed with respect to three types of attacks: Distance Fraud, Mafia Fraud, and Terrorist Fraud. We define a fourth main type of attacks on distance bounding protocols, called Distance Hijacking attacks. We show that many proposed distance bounding protocols are vulnerable to these attacks, and we propose solutions to make these protocols resilient to Distance Hijacking. Additionally, we generalize Distance Hijacking to Location Hijacking, to which ...
Boundedly UC spaces: characterisations and preservation | Jain ...
African Journals Online (AJOL)
A metric space (X, d) is called a boundedly UC space if every closed and bounded subset of X is a UC space. A metric space (X, d) is called a UC space if each real-valued continuous function on (X, d) is uniformly continuous. In this paper, we study twenty-two equivalent conditions for a metric space to be a boundedly UC ...
The Problem of Understanding of Nature in Exact Science
Directory of Open Access Journals (Sweden)
Leo Näpinen
2014-10-01
Full Text Available In this short inquiry I would like to defend the statement that exact science deals with the explanation of models, but not with the understanding (comprehending of nature. By the word ‘nature’ I mean nature as physis (as a self-moving and self-developing living organism to which humans also belong, not nature as natura naturata (as a nonevolving creature created by someone or something. The Estonian philosopher of science Rein Vihalemm (2008 has shown with his conception of phi-science (φ-science that exact science is itself an idealized model or theoretical object derived from Galilean mathematical physics.
Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2013-01-01
Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.
Exact asymmetric Skyrmion in anisotropic ferromagnet and its helimagnetic application
Directory of Open Access Journals (Sweden)
Anjan Kundu
2016-08-01
Full Text Available Topological Skyrmions as intricate spin textures were observed experimentally in helimagnets on 2d plane. Theoretical foundation of such solitonic states to appear in pure ferromagnetic model, as exact solutions expressed through any analytic function, was made long ago by Belavin and Polyakov (BP. We propose an innovative generalization of the BP solution for an anisotropic ferromagnet, based on a physically motivated geometric (in-equality, which takes the exact Skyrmion to a new class of functions beyond analyticity. The possibility of stabilizing such metastable states in helimagnets is discussed with the construction of individual Skyrmion, Skyrmion crystal and lattice with asymmetry, likely to be detected in precision experiments.
Exact asymmetric Skyrmion in anisotropic ferromagnet and its helimagnetic application
Energy Technology Data Exchange (ETDEWEB)
Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in
2016-08-15
Topological Skyrmions as intricate spin textures were observed experimentally in helimagnets on 2d plane. Theoretical foundation of such solitonic states to appear in pure ferromagnetic model, as exact solutions expressed through any analytic function, was made long ago by Belavin and Polyakov (BP). We propose an innovative generalization of the BP solution for an anisotropic ferromagnet, based on a physically motivated geometric (in-)equality, which takes the exact Skyrmion to a new class of functions beyond analyticity. The possibility of stabilizing such metastable states in helimagnets is discussed with the construction of individual Skyrmion, Skyrmion crystal and lattice with asymmetry, likely to be detected in precision experiments.
Quantifying risks with exact analytical solutions of derivative pricing distribution
Zhang, Kun; Liu, Jing; Wang, Erkang; Wang, Jin
2017-04-01
Derivative (i.e. option) pricing is essential for modern financial instrumentations. Despite of the previous efforts, the exact analytical forms of the derivative pricing distributions are still challenging to obtain. In this study, we established a quantitative framework using path integrals to obtain the exact analytical solutions of the statistical distribution for bond and bond option pricing for the Vasicek model. We discuss the importance of statistical fluctuations away from the expected option pricing characterized by the distribution tail and their associations to value at risk (VaR). The framework established here is general and can be applied to other financial derivatives for quantifying the underlying statistical distributions.
Clock Math — a System for Solving SLEs Exactly
Directory of Open Access Journals (Sweden)
Jakub Hladík
2013-01-01
Full Text Available In this paper, we present a GPU-accelerated hybrid system that solves ill-conditioned systems of linear equations exactly. Exactly means without rounding errors due to using integer arithmetics. First, we scale floating-point numbers up to integers, then we solve dozens of SLEs within different modular arithmetics and then we assemble sub-solutions back using the Chinese remainder theorem. This approach effectively bypasses current CPU floating-point limitations. The system is capable of solving Hilbert’s matrix without losing a single bit of precision, and with a significant speedup compared to existing CPU solvers.
Bounded cohomology of discrete groups
Frigerio, Roberto
2017-01-01
The author manages a near perfect equilibrium between necessary technicalities (always well motivated) and geometric intuition, leading the readers from the first simple definition to the most striking applications of the theory in 13 very pleasant chapters. This book can serve as an ideal textbook for a graduate topics course on the subject and become the much-needed standard reference on Gromov's beautiful theory. -Michelle Bucher The theory of bounded cohomology, introduced by Gromov in the late 1980s, has had powerful applications in geometric group theory and the geometry and topology of manifolds, and has been the topic of active research continuing to this day. This monograph provides a unified, self-contained introduction to the theory and its applications, making it accessible to a student who has completed a first course in algebraic topology and manifold theory. The book can be used as a source for research projects for master's students, as a thorough introduction to the field for graduate student...
Colloid Bound Transport of Contaminats In The Unsaturated Zone
Hofmann, T.; Christ, A.
Colloids can play a major role in the relocation of contaminants in the unsaturated zone. The amount of colloid driven transport is defined by soil chemistry, soil water chemistry and water flow velocity as well as colloid composition and formation. In a current research project we investigate the filtration and mobilization of colloids in unsaturated column studies. We use different soil types, chosen by a wide range of mean grain size and heterogeneity. Particle tracers are polystyrene solids with a de- fined negative surface charge and defined size from 50 nm to 10 µm. In addition, we use natural colloids extracted from a wide range of contaminated and uncontaminated land. Experimental conditions are exactly controlled throughout all the time. We alter mainly flow velocity ionic strength in order to study the filtration behaviour of the soils. In addition, Pyrene and Lead are are used as model contaminants. First results show the colloids are not retarded in many coarse structured soil types. Preferential colloid flow shows a major impact in breakthrough behaviour. Colloid bound lead is relocated significant through the unsaturated zone, whereas non colloid bound lead species are strongly retarded. In the presentation we will show results of contami- nant processes and present new results on the filtration behaviour of colloids in the unsaturated zone depending on flow velocity, soil type and colloid size.
Bounded sets in fast complete inductive limits
Directory of Open Access Journals (Sweden)
Jan Kucera
1984-01-01
Full Text Available Let E1⊂E2⊂… be a sequence of locally convex spaces with all identity maps: En→En+1 continuous and E=indlim En fast complete. Then each set bounded in E is also bounded in some En iff for any Banach disk B bounded in E and n∈N, the closure of B⋂En in B is bounded in some Em. This holds, in particular, if all spaces En are webbed.
Valuation models and Simon's bounded rationality
National Research Council Canada - National Science Library
Alexandra Strommer de Farias Godoi
2009-01-01
This paper aims at reconciling the evidence that sophisticated valuation models are increasingly used by companies in their investment appraisal with the literature of bounded rationality, according...
Some Improved Nonperturbative Bounds for Fermionic Expansions
Energy Technology Data Exchange (ETDEWEB)
Lohmann, Martin, E-mail: marlohmann@gmail.com [Universita di Roma Tre, Dipartimento di Matematica (Italy)
2016-06-15
We reconsider the Gram-Hadamard bound as it is used in constructive quantum field theory and many body physics to prove convergence of Fermionic perturbative expansions. Our approach uses a recursion for the amplitudes of the expansion, discovered in a model problem by Djokic (2013). It explains the standard way to bound the expansion from a new point of view, and for some of the amplitudes provides new bounds, which avoid the use of Fourier transform, and are therefore superior to the standard bounds for models like the cold interacting Fermi gas.
A strongly quasiconvex PAC-Bayesian bound
DEFF Research Database (Denmark)
Thiemann, Niklas; Igel, Christian; Wintenberger, Olivier
We propose a new PAC-Bayesian bound and a way of constructing a hypothesis space, so that the bound is convex in the posterior distribution and also convex in a trade-off parameter between empirical performance of the posterior distribution and its complexity. The complexity is measured by the Ku......We propose a new PAC-Bayesian bound and a way of constructing a hypothesis space, so that the bound is convex in the posterior distribution and also convex in a trade-off parameter between empirical performance of the posterior distribution and its complexity. The complexity is measured...
Coexistence of neurofibroma and meningioma at exactly the same level of the cervical spine
Directory of Open Access Journals (Sweden)
Kai-Yuan Chen
2014-11-01
Full Text Available We report a case of the coexistence of different spinal tumors at the same level of the cervical spine, without neurofibromatosis (NF, which was successfully treated with surgery. A 72-year-old female presented with right upper-limb clumsiness and weakness. Magnetic resonance imaging revealed an intradural, extramedullary tumor mass at the right C3–4 level with extradural extension into the intervertebral foramen. The extradural tumor was removed, and the pathology showed neurofibroma. After incision of the dura, the intradural tumor was removed, and was identified as meningioma in the pathological report. The patient did not meet the criteria of NF. Coexistence of neurofibroma and meningioma at exactly the same level of the spine without NF is extremely rare. Exploration of the intradural space may be necessary after resection of an extradural tumor if the surgical finding does not correlate well with the preoperative images.
New lower bound for the Capacitated Arc Routing Problem
DEFF Research Database (Denmark)
Wøhlk, Sanne
2006-01-01
We present a new lower bound, the Multiple Cuts Node Duplication Lower Bound, for the undirected Capacitated Arc Routing Problem.We prove that this new bound dominates the existing bounds for the problem. Computational results are also provided.......We present a new lower bound, the Multiple Cuts Node Duplication Lower Bound, for the undirected Capacitated Arc Routing Problem.We prove that this new bound dominates the existing bounds for the problem. Computational results are also provided....
Exact interacting Green's function for the Anderson impurity at high bias voltages
Oguri, Akira; Sakano, Rui
2013-10-01
We describe some exact high-energy properties of a single Anderson impurity connected to two noninteracting leads in a nonequilibrium steady state. In the limit of high bias voltages, and also in the high-temperature limit at thermal equilibrium, the model can be mapped onto an effective non-Hermitian Hamiltonian consisting of two sites, which correspond to the original impurity and its image that is defined in a doubled Hilbert space referred to as Liouville-Fock space. For this, we provide a heuristic derivation using a path-integral representation of the Keldysh contour and the thermal field theory, in which the time evolution along the backward contour is replicated by extra degrees of freedom corresponding to the image. We find that the effective Hamiltonian can also be expressed in terms of charges and currents. From this, it can be deduced that the dynamic susceptibilities for the charges and the current fluctuations become independent of the Coulomb repulsion U in the high bias limit. Furthermore, the equations of motion for the Green's function and two other higher-order correlation functions constitute a closed system. The exact solution obtained from the three coupled equations extends the atomic-limit solution such that the self-energy correctly captures the imaginary part caused by the relaxation processes at high energies. The spectral weights of the upper and lower Hubbard levels depend sensitively on the asymmetry in the tunneling couplings to the left and right leads.
Exact equivalent straight waveguide model for bent and twisted waveguides
DEFF Research Database (Denmark)
Shyroki, Dzmitry
2008-01-01
Exact equivalent straight waveguide representation is given for a waveguide of arbitrary curvature and torsion. No assumptions regarding refractive index contrast, isotropy of materials, or particular morphology in the waveguide cross section are made. This enables rigorous full-vector modeling o...
Thermodynamics of Rh nuclear spins calculated by exact diagonalization
DEFF Research Database (Denmark)
Lefmann, K.; Ipsen, J.; Rasmussen, F.B.
2000-01-01
We have employed the method of exact diagonalization to obtain the full-energy spectrum of a cluster of 16 Rh nuclear spins, having dipolar and RK interactions between first and second nearest neighbours only. We have used this to calculate the nuclear spin entropy, and our results at both positi...
Exact solution for a one-dimensional model for reptation.
Drzewiński, Andrzej; van Leeuwen, J M J
2006-05-01
We discuss the exact solution for the properties of the recently introduced "necklace" model for reptation. The solution gives the drift velocity, diffusion constant, and renewal time for asymptotically long chains. Its properties are also related to a special case of the Rubinstein-Duke model in one dimension.
The functional variable method for finding exact solutions of some ...
Indian Academy of Sciences (India)
and KEWANG CHEN. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, ... Introduction. The effort in finding exact solutions of nonlinear equations is very important for understanding most nonlinear physical phenomena. For instance, the nonlinear wave phenomena observed ...
Exact overflow asymptotics for queues with many Gaussian inputs
Debicki, Krzysztof; Mandjes, M.R.H.
2003-01-01
In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the
Dynamic Programming Approach for Exact Decision Rule Optimization
Amin, Talha
2013-01-01
This chapter is devoted to the study of an extension of dynamic programming approach that allows sequential optimization of exact decision rules relative to the length and coverage. It contains also results of experiments with decision tables from UCI Machine Learning Repository. © Springer-Verlag Berlin Heidelberg 2013.
More exact tunneling solutions in scalar field theory
Energy Technology Data Exchange (ETDEWEB)
Dutta, Koushik; Hector, Cecelie; Vaudrevange, Pascal M.; Westphal, Alexander
2011-11-15
We present exact bounce solutions and amplitudes for tunneling in (i) a piecewise linear-quartic potential and (ii) a piecewise quartic-quartic potential. We cross check their correctness by comparing with results obtained through the thin-wall approximation and with a piecewise linear-linear potential. We briefly comment on applications in cosmology. (orig.)
Exact solutions for nonlinear variants of Kadomtsev–Petviashvili (n ...
Indian Academy of Sciences (India)
Exact solutions for nonlinear variants of Kadomtsev–Petviashvili (, ) equation using functional variable method. M Mirzazadeh M Eslami. Volume 81 Issue ... The functional variable method is used to establish compactons, solitons, solitary patterns and periodic solutions for these variants. This method is a powerful tool for ...
Timed Fast Exact Euclidean Distance (tFEED) maps
Kehtarnavaz, Nasser; Schouten, Theo E.; Laplante, Philip A.; Kuppens, Harco; van den Broek, Egon
2005-01-01
In image and video analysis, distance maps are frequently used. They provide the (Euclidean) distance (ED) of background pixels to the nearest object pixel. In a naive implementation, each object pixel feeds its (exact) ED to each background pixel; then the minimum of these values denotes the ED to
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
problems. More precisely, there is no unified method that can be used to handle all types of nonlinear problems. A powerful and effective method for finding exact ... Explicit solutions to nonlinear problems are of fundamental importance. ... fluid dynamics, fluid flow, quantum field theory, electromagnetic waves and so on [7].
Exact rational expectations, cointegration, and reduced rank regression
DEFF Research Database (Denmark)
Johansen, Søren; Swensen, Anders Rygh
We interpret the linear relations from exact rational expectations models as restrictions on the parameters of the statistical model called the cointegrated vector autoregressive model for non-stationary variables. We then show how reduced rank regression, Anderson (1951), plays an important role...
Exact rational expectations, cointegration, and reduced rank regression
DEFF Research Database (Denmark)
Johansen, Søren; Swensen, Anders Rygh
2008-01-01
We interpret the linear relations from exact rational expectations models as restrictions on the parameters of the statistical model called the cointegrated vector autoregressive model for non-stationary variables. We then show how reduced rank regression, Anderson (1951), plays an important role...
Exact Rational Expectations, Cointegration, and Reduced Rank Regression
DEFF Research Database (Denmark)
Johansen, Søren; Swensen, Anders Rygh
We interpret the linear relations from exact rational expectations models as restrictions on the parameters of the statistical model called the cointegrated vector autoregressive model for non-stationary variables. We then show how reduced rank regression, Anderson (1951), plays an important role...
An Exactly Solvable Model for the Spread of Disease
Mickens, Ronald E.
2012-01-01
We present a new SIR epidemiological model whose exact analytical solution can be calculated. In this model, unlike previous models, the infective population becomes zero at a finite time. Remarkably, these results can be derived from only an elementary knowledge of differential equations.
The Alleged Crisis and the Illusion of Exact Replication
Stroebe, Wolfgang; Strack, Fritz
There has been increasing criticism of the way psychologists conduct and analyze studies. These critiques as well as failures to replicate several high-profile studies have been used as justification to proclaim a replication crisis in psychology. Psychologists are encouraged to conduct more exact
A SAS/IML algorithm for an exact permutation test
Directory of Open Access Journals (Sweden)
Neuhäuser, Markus
2009-03-01
Full Text Available An algorithm written in SAS/IML is presented that can perform an exact permutation test for a two-sample comparison. All possible permutations are considered. The Baumgartner-Weiß-Schindler statistic is exemplarily used as the test statistic for the permutation test.
Exact angular momentum projection based on cranked HFB solution
Energy Technology Data Exchange (ETDEWEB)
Enami, Kenichi; Tanabe, Kosai; Yosinaga, Naotaka [Saitama Univ., Urawa (Japan). Dept. of Physics
1998-03-01
Exact angular momentum projection of cranked HFB solutions is carried out. It is reconfirmed from this calculation that cranked HFB solutions reproduce the intrinsic structure of deformed nucleus. The result also indicates that the energy correction from projection is important for further investigation of nuclear structure. (author)
Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.
1998-01-01
We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...
Exact solution for the interior of a black hole
Nieuwenhuizen, T.M.
2008-01-01
Within the Relativistic Theory of Gravitation it is shown that the equation of state p = rho holds near the center of a black hole. For the stiff equation of state p = rho - rho(c) the interior metric is solved exactly. It is matched with the Schwarzschild metric, which is deformed in a narrow range
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical ...
Construction of an exact solution of time-dependent Ginzburg ...
Indian Academy of Sciences (India)
A new approach is taken to calculate the speed of front propagation at which the interface moves from a superconducting to a normal region in a superconducting sample. Using time-dependent Ginzburg–Landau (TDGL) equations we have calculated the speed by constructing a new exact solution. This approach is based ...
Electromagnetic shock wave in nonlinear vacuum: exact solution.
Kovachev, Lubomir M; Georgieva, Daniela A; Kovachev, Kamen L
2012-10-01
An analytical approach to the theory of electromagnetic waves in nonlinear vacuum is developed. The evolution of the pulse is governed by a system of nonlinear wave vector equations. An exact solution with its own angular momentum in the form of a shock wave is obtained.
Adaptive filtering for stochastic volatility by using exact sampling
Aihara, ShinIchi; Bagchi, Arunabha; Saha, S.
2013-01-01
We study the sequential identification problem for Bates stochastic volatility model, which is widely used as the model of a stock in finance. By using the exact simulation method, a particle filter for estimating stochastic volatility is constructed. The systems parameters are sequentially
Exact boundary controllability of nodal profile for quasilinear hyperbolic systems
Li, Tatsien; Gu, Qilong
2016-01-01
This book provides a comprehensive overview of the exact boundary controllability of nodal profile, a new kind of exact boundary controllability stimulated by some practical applications. This kind of controllability is useful in practice as it does not require any precisely given final state to be attained at a suitable time t=T by means of boundary controls, instead it requires the state to exactly fit any given demand (profile) on one or more nodes after a suitable time t=T by means of boundary controls. In this book we present a general discussion of this kind of controllability for general 1-D first order quasilinear hyperbolic systems and for general 1-D quasilinear wave equations on an interval as well as on a tree-like network using a modular-structure construtive method, suggested in LI Tatsien's monograph "Controllability and Observability for Quasilinear Hyperbolic Systems"(2010), and we establish a complete theory on the local exact boundary controllability of nodal profile for 1-D quasilinear hyp...
Construction of an exact solution of time-dependent Ginzburg ...
Indian Academy of Sciences (India)
Abstract. A new approach is taken to calculate the speed of front propagation at which the interface moves from a superconducting to a normal region in a superconducting sample. Using time-dependent Ginzburg–Landau (TDGL) equations we have calculated the speed by constructing a new exact solution. This approach ...
New exact solutions of the generalized Zakharov–Kuznetsov ...
Indian Academy of Sciences (India)
In this paper, new exact solutions, including soliton, rational and elliptic integral function solutions, for the generalized Zakharov–Kuznetsov modified equal-width equation are obtained using a new approach called the extended trial equation method. In this discussion, a new version of the trial equation method for the ...
Exact solutions, energy, and charge of stable Q-balls
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D.; Marques, M.A. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Menezes, R. [Universidade Federal da Paraiba, Departamento de Ciencias Exatas, Rio Tinto, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil)
2016-05-15
In this work we deal with nontopological solutions of the Q-ball type in two spacetime dimensions. We study models of current interest, described by a Higgs-like and other, similar potentials which unveil the presence of exact solutions. We use the analytic results to investigate how to control the energy and charge to make the Q-balls stable. (orig.)
The exact solutions of differential equation with delay
Hasebe, K; Sugiyama, Y
1998-01-01
The exact solutions of the first order differential equation with delay are derived. The equation has been introduced as a model of traffic flow. The solution describes the traveling cluster of jam, which is characterized by Jacobi's elliptic function. We also obtain the family of solutions of such type of equations.
Exact results on the steady state of a hopping model
Zhang, M. Q.
1987-03-01
A hopping model described by Katz, Lebowitz, and Spohn [J. Stat. Phys. 34, 497 (1983)] and by Valles and Marro [J. Stat. Phys. 43, 441 (1986)] is studied analytically for small lattice systems. The dependence of the nonequilibrium steady state on various parameters and transition rate functions is obtained exactly. The results are compared with simulations on large systems.
Exact solution of the neutron transport equation in spherical geometry
Energy Technology Data Exchange (ETDEWEB)
Anli, Fikret; Akkurt, Abdullah; Yildirim, Hueseyin; Ates, Kemal [Kahramanmaras Suetcue Imam Univ. (Turkey). Faculty of Sciences and Letters
2017-03-15
Solution of the neutron transport equation in one dimensional slab geometry construct a basis for the solution of neutron transport equation in a curvilinear geometry. Therefore, in this work, we attempt to derive an exact analytical benchmark solution for both neutron transport equations in slab and spherical medium by using P{sub N} approximation which is widely used in neutron transport theory.
Exact boundary controllability for a series of membranes elastically connected
Directory of Open Access Journals (Sweden)
Waldemar D. Bastos
2017-01-01
Full Text Available In this article we study the exact controllability with Neumann boundary controls for a system of linear wave equations coupled in parallel by lower order terms on piecewise smooth domains of the plane. We obtain square integrable controls for initial state with finite energy and time of controllability near the optimal value.
Method for generating exact Bianchi type II cosmological models
Energy Technology Data Exchange (ETDEWEB)
Hajj-Boutros, J.
1986-06-01
A method for generating exact Bianchi type II cosmological models with a perfect fluid distribution of matter is presented. Two new classes of Bianchi type II solutions have been generated from Lorenz's solution (D. Lorenz, Phys. Lett. A 79, 19 (1980)). A detailed study of physical and kinematic properties of one of them has been carried out.
A procedure to construct exact solutions of nonlinear evolution ...
Indian Academy of Sciences (India)
physics pp. 337–344. A procedure to construct exact solutions of nonlinear evolution equations. ADEM CENGIZ ÇEVIKEL1,∗, AHMET BEKIR2, MUTLU AKAR3 and. SAIT SAN2. 1Yildiz Technical University, Faculty of Education, Department of Mathematics Education,. Davutpasa Campus, 34210, Esenler, Istanbul, Turkey.
Bounded rationality and learning in complex markets
Hommes, C.H.; Barkely Rosser Jr, J.
2009-01-01
This chapter reviews some work on bounded rationality, expectation formation and learning in complex markets, using the familiar demand-supply cobweb model. We emphasize two stories of bounded rationality, one story of adaptive learning and another story of evolutionary selection. According to the
Bounded rationality and learning in complex markets
Hommes, C.H.
2007-01-01
This chapter reviews some work on bounded rationality, expectation formation and learning in complex markets, using the familiar demand-supply cobweb model. We emphasize two stories of bounded rationality, one story of adaptive learning and another story of evolutionary selection. According to the
Spatial coagulation with bounded coagulation rate
Bailleul, Ismael
2010-01-01
We prove that the spatial coagulation equation with bounded coagulation rate is well-posed for all times in a given class of kernels if the convection term of the underlying particle dynamics has divergence bounded below by a positive constant. Multiple coagulations, fragmentation and scattering are also considered.
No-arbitrage bounds for financial scenarios
DEFF Research Database (Denmark)
Geyer, Alois; Hanke, Michael; Weissensteiner, Alex
2014-01-01
We derive no-arbitrage bounds for expected excess returns to generate scenarios used in financial applications. The bounds allow to distinguish three regions: one where arbitrage opportunities will never exist, a second where arbitrage may be present, and a third, where arbitrage opportunities...
Nonatomic dual bakery algorithm with bounded tokens
Aravind, Alex A.; Hesselink, Wim H.
A simple mutual exclusion algorithm is presented that only uses nonatomic shared variables of bounded size, and that satisfies bounded overtaking. When the shared variables behave atomically, it has the first-come-first-served property (FCFS). Nonatomic access makes information vulnerable. The
Polynomially Bounded Sequences and Polynomial Sequences
Directory of Open Access Journals (Sweden)
Okazaki Hiroyuki
2015-09-01
Full Text Available In this article, we formalize polynomially bounded sequences that plays an important role in computational complexity theory. Class P is a fundamental computational complexity class that contains all polynomial-time decision problems [11], [12]. It takes polynomially bounded amount of computation time to solve polynomial-time decision problems by the deterministic Turing machine. Moreover we formalize polynomial sequences [5].
On the range of completely bounded maps
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Richard I. Loebl
1978-01-01
Full Text Available It is shown that if every bounded linear map from a C*-algebra α to a von Neumann algebra β is completely bounded, then either α is finite-dimensional or β⫅⊗Mn, where is a commutative von Neumann algebra and Mn is the algebra of n×n complex matrices.
A polynomial lower bound for testing monotonicity
A. Belovs (Aleksandr); Blais, E. (Eric)
2016-01-01
textabstractWe show that every algorithm for testing n-variate Boolean functions for monotonicity has query complexity Ω(n1/4). All previous lower bounds for this problem were designed for nonadaptive algorithms and, as a result, the best previous lower bound for general (possibly adaptive)
Directory of Open Access Journals (Sweden)
Feng HE
2017-12-01
Full Text Available The state of the art avionics system adopts switched networks for airborne communications. A major concern in the design of the networks is the end-to-end guarantee ability. Analytic methods have been developed to compute the worst-case delays according to the detailed configurations of flows and networks within avionics context, such as network calculus and trajectory approach. It still lacks a relevant method to make a rapid performance estimation according to some typically switched networking features, such as networking scale, bandwidth utilization and average flow rate. The goal of this paper is to establish a deterministic upper bound analysis method by using these networking features instead of the complete network configurations. Two deterministic upper bounds are proposed from network calculus perspective: one is for a basic estimation, and another just shows the benefits from grouping strategy. Besides, a mathematic expression for grouping ability is established based on the concept of network connecting degree, which illustrates the possibly minimal grouping benefit. For a fully connected network with 4 switches and 12 end systems, the grouping ability coming from grouping strategy is 15â20%, which just coincides with the statistical data (18â22% from the actual grouping advantage. Compared with the complete network calculus analysis method for individual flows, the effectiveness of the two deterministic upper bounds is no less than 38% even with remarkably varied packet lengths. Finally, the paper illustrates the design process for an industrial Avionics Full DupleX switched Ethernet (AFDX networking case according to the two deterministic upper bounds and shows that a better control for network connecting, when designing a switched network, can improve the worst-case delays dramatically. Keywords: Deterministic bound, Grouping ability, Network calculus, Networking features, Switched networks