Are the invariance principles really truly Lorentz covariant?
International Nuclear Information System (INIS)
Arunasalam, V.
1994-02-01
It is shown that some sections of the invariance (or symmetry) principles such as the space reversal symmetry (or parity P) and time reversal symmetry T (of elementary particle and condensed matter physics, etc.) are not really truly Lorentz covariant. Indeed, I find that the Dirac-Wigner sense of Lorentz invariance is not in full compliance with the Einstein-Minkowski reguirements of the Lorentz covariance of all physical laws (i.e., the world space Mach principle)
Invariance principle, multifractional Gaussian processes and long-range dependence
Cohen, Serge; Marty, Renaud
2008-01-01
This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in $(1/2,1)$. Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional Brownian motion.
A strong invariance principle for the elephant random walk
Coletti, Cristian F.; Gava, Renato; Schütz, Gunter M.
2017-12-01
We consider a non-Markovian discrete-time random walk on {Z} with unbounded memory, called the elephant random walk (ERW). We prove a strong invariance principle for the ERW. More specifically, we prove that, under a suitable scaling and in the diffusive regime as well as at the critical value p_c=3/4 where the model is marginally superdiffusive, the ERW is almost surely well approximated by a Brownian motion. As a by-product of our result we get the law of iterated logarithm and the central limit theorem for the ERW.
An Invariance Principle to Ferrari-Spohn Diffusions
Ioffe, Dmitry; Shlosman, Senya; Velenik, Yvan
2015-06-01
We prove an invariance principle for a class of tilted 1 + 1-dimensional SOS models or, equivalently, for a class of tilted random walk bridges in . The limiting objects are stationary reversible ergodic diffusions with drifts given by the logarithmic derivatives of the ground states of associated singular Sturm-Liouville operators. In the case of a linear area tilt, we recover the Ferrari-Spohn diffusion with log-Airy drift, which was derived in Ferrari and Spohn (Ann Probab 33(4):1302—1325, 2005) in the context of Brownian motions conditioned to stay above circular and parabolic barriers.
Measurement Invariance: A Foundational Principle for Quantitative Theory Building
Nimon, Kim; Reio, Thomas G., Jr.
2011-01-01
This article describes why measurement invariance is a critical issue to quantitative theory building within the field of human resource development. Readers will learn what measurement invariance is and how to test for its presence using techniques that are accessible to applied researchers. Using data from a LibQUAL+[TM] study of user…
The `principle of invariance' in currency systems: a comment on Caianiello et al.
Bouhdaoui, Y.; Bounie, D.; Van Hove, L.
2012-04-01
In an often-cited article in this journal, Caianiello et al. (1982. International Journal of General Systems, 8 (2), 81-92) formulate a 'principle of invariance' for currency systems. They build on this principle to explain the distribution of the coins and banknotes in circulation over the different denominations, and analyse how a currency system adjusts to inflation. This paper shows that Caianiello et al.'s distribution law is flawed because the principle of invariance is false.
Indian Academy of Sciences (India)
removed two cells of the same color. Whenever you are putting a 2 × 1 rectangle you are covering one black and one white cell. So the total number of white cells you have covered minus the total number of black cells you have covered after putting some 2 × 1 rectangles is always zero. So this difference is an invariant! You.
Sonnino, Giorgio; Steinbrecher, György; Cardinali, Alessandro; Sonnino, Alberto; Tlidi, Mustapha
2013-01-01
Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing the minimum entropy production and the maximum entropy principle under the scale invariance restrictions. The obtained probability distribution presents a singularity that has immediate physical interpretation in terms of the intermittency models. The derived reference probability distribution function is interpreted as time and ensemble average of the real physical one. A generic family of stochastic processes describing noise-driven intermittency, where the stationary density distribution coincides exactly with the one resulted from entropy maximization, is presented.
Testing the Equivalence Principle and Lorentz Invariance with PeV Neutrinos from Blazar Flares.
Wang, Zi-Yi; Liu, Ruo-Yu; Wang, Xiang-Yu
2016-04-15
It was recently proposed that a giant flare of the blazar PKS B1424-418 at redshift z=1.522 is in association with a PeV-energy neutrino event detected by IceCube. Based on this association we here suggest that the flight time difference between the PeV neutrino and gamma-ray photons from blazar flares can be used to constrain the violations of equivalence principle and the Lorentz invariance for neutrinos. From the calculated Shapiro delay due to clusters or superclusters in the nearby universe, we find that violation of the equivalence principle for neutrinos and photons is constrained to an accuracy of at least 10^{-5}, which is 2 orders of magnitude tighter than the constraint placed by MeV neutrinos from supernova 1987A. Lorentz invariance violation (LIV) arises in various quantum-gravity theories, which predicts an energy-dependent velocity of propagation in vacuum for particles. We find that the association of the PeV neutrino with the gamma-ray outburst set limits on the energy scale of possible LIV to >0.01E_{pl} for linear LIV models and >6×10^{-8}E_{pl} for quadratic order LIV models, where E_{pl} is the Planck energy scale. These are the most stringent constraints on neutrino LIV for subluminal neutrinos.
International Nuclear Information System (INIS)
Marumori, Toshio; Hayashi, Akihisa; Tomoda, Toshiaki; Kuriyama, Atsushi; Maskawa, Toshihide
1980-01-01
The aim of this series of papers is to propose a microscopic theory to go beyond the situations where collective motions are described by the random phase approximation, i.e., by small amplitude harmonic oscillations about equilibrium. The theory is thus appropriate for the microscopic description of the large amplitude collective motion of soft nuclei. The essential idea is to develop a method to determine the collective subspace (or submanifold) in the many-particle Hilbert space in an optimal way, on the basis of a fundamental principle called the invariance principle of the Schroedinger equation. By using the principle within the framework of the Hartree-Fock theory, it is shown that the theory can clarify the structure of the so-called ''phonon-bands'' by self-consistently deriving the collective Hamiltonian where the number of the ''physical phonon'' is conserved. The purpose of this paper is not to go into detailed quantitative discussion, but rather to develop the basic idea. (author)
Korepanov, Alexey
2017-12-01
Let {T : M \\to M} be a nonuniformly expanding dynamical system, such as logistic or intermittent map. Let {v : M \\to R^d} be an observable and {v_n = \\sum_{k=0}^{n-1} v circ T^k} denote the Birkhoff sums. Given a probability measure {μ} on M, we consider v n as a discrete time random process on the probability space {(M, μ)} . In smooth ergodic theory there are various natural choices of {μ} , such as the Lebesgue measure, or the absolutely continuous T-invariant measure. They give rise to different random processes. We investigate relation between such processes. We show that in a large class of measures, it is possible to couple (redefine on a new probability space) every two processes so that they are almost surely close to each other, with explicit estimates of "closeness". The purpose of this work is to close a gap in the proof of the almost sure invariance principle for nonuniformly hyperbolic transformations by Melbourne and Nicol.
Flambaum, V V
2016-08-12
Local Lorentz invariance violating (LLIV) and Einstein equivalence principle violating (EEPV) effects in atomic experiments are discussed. The EEPV effects are strongly enhanced in the narrow 7.8 eV transition in the _{90}^{229}Th nucleus. The nuclear LLIV tensors describing the anisotropy in the maximal attainable speed for massive particles (analog of the Michelson-Morley experiment for light) are expressed in terms of the experimental values of the nuclear quadrupole moments. Calculations for nuclei of experimental interest _{55}^{133}Cs, _{37}^{85}Rb, _{37}^{87}Rb, _{80}^{201}Hg, _{54}^{131}Xe, and _{10}^{21}Ne are performed. The results for _{10}^{21}Ne are used to improve the limits on the proton LLIV interaction constants by 4 orders of magnitude.
Czech Academy of Sciences Publication Activity Database
Chen, G.; Zhou, J.; Čelikovský, Sergej
2005-01-01
Roč. 50, č. 6 (2005), s. 869-874 ISSN 0018-9286 R&D Projects: GA ČR GA102/05/0011 Institutional research plan: CEZ:AV0Z10750506 Keywords : chaos synchronization * duffing oscillator * LaSalle's invariance principle Subject RIV: BC - Control Systems Theory Impact factor: 2.159, year: 2005
Murase, M.
1996-01-01
with self-organization, has been thought to underlie `creative' aspects of biological phenomena such as the origin of life, adaptive evolution of viruses, immune recognition and brain function. It therefore must be surprising to find that the same principles will also underlie `non-creative' aspects, for example, the development of cancer and the aging of complex organisms. Although self-organization has extensively been studied in nonliving things such as chemical reactions and laser physics, it is undoubtedly true that the similar sources of the order are available to living things at different levels and scales. Several paradigm shifts are, however, required to realize how the general principles of natural selection can be extensible to non-DNA molecules which do not possess the intrinsic nature of self-reproduction. One of them is, from the traditional, genetic inheritance view that DNA (or RNA) molecules are the ultimate unit of heritable variations and natural selection at any organization level, to the epigenetic (nongenetic) inheritance view that any non-DNA molecule can be the target of heritable variations and molecular selection to accumulate in certain biochemical environment. Because they are all enriched with a β-sheet content, ready to mostly interact with one another, different denatured proteins like β-amyloid, PHF and prions can individually undergo self-templating or self-aggregating processes out of gene control. Other paradigm shifts requisite for a break-through in the etiology of neurodegenerative disorders will be discussed. As it is based on the scale-invariant principles, the present theory also predicts plausible mechanisms underlying quite different classes of disorders such as amyotrophic lateral sclerosis (ALS), atherosclerosis, senile cataract and many other symptoms of aging. The present theory, thus, provides the consistent and comprehensive account to the origin of aging by means of natural selection and self-organization.
Csörgő, Miklós; Szyszkowicz, Barbara; Wang, Lihong
2006-01-01
In this paper we study strong approximations (invariance principles) of the sequential uniform and general Bahadur--Kiefer processes of long-range dependent sequences. We also investigate the strong and weak asymptotic behavior of the sequential Vervaat process, that is, the integrated sequential Bahadur--Kiefer process, properly normalized, as well as that of its deviation from its limiting process, the so-called Vervaat error process. It is well known that the Bahadur--Kiefer and the Vervaa...
International Nuclear Information System (INIS)
Kaku, M.
1988-01-01
We present an entirely new approach to closed-string field theory, called Igeometric string field theory R, which avoids the complications found in Becchi-Rouet-Stora-Tyutin string field theory (e.g., ghost counting, infinite overcounting of diagrams, midpoints, lack of modular invariance). Following the analogy with general relativity and Yang-Mills theory, we define a new infinite-dimensional local gauge group, called the unified string group, which uniquely specifies the connection fields, the curvature tensor, the measure and tensor calculus, and finally the action itself. Geometric field theory, when gauge fixed, yields an entirely new class of gauges called the interpolating gauge which allows us to smoothly interpolate between the midpoint gauge and the end-point gauge (''covariantized light-cone gauge''). We can show that geometric string field theory reproduces one copy of the Shapiro-Virasoro model. Surprisingly, after the gauge is broken, a new Iclosed four-string interactionR emerges as the counterpart of the instantaneous four-fermion Coulomb term in QED. This term restores modular invariance and precisely fills the missing region of the complex plane
Pressler, David E.
2012-03-01
A great discrepancy exists - the speed of light and the neutrino speed must be identical; as indicated by supernova1987A; yet, OPERA predicts faster-than-light neutrinos. Einstein's theories are based on the invariance of the speed of light, and no privileged Galilean frame of reference exists. Both of these hypotheses are in error and must be reconciled in order to solve the dilemma. The Michelson-Morley Experiment was misinterpreted - my Neoclassical Theory postulates that BOTH mirrors of the interferometer physically and absolutely move towards its center. The result is a three-directional-Contraction, (x, y, z axis), an actual distortion of space itself; a C-Space condition. ``PRESSLER'S LAW OF C-SPACE: The speed of light, c, will always be measured the same speed in all three directions (˜300,000 km/sec), in ones own inertial reference system, and will always be measured as having a different speed in all other inertial frames which are at a different kinetic energy level or at a location with a different strength gravity field'' Thus, the faster you go, motion, or the stronger the gravity field the smaller you get in all three directions. OPERA results are explained; at the surface of Earth, the strength of gravity field is at maximum -- below the earth's surface, time and space is less distorted; therefore, time is absolutely faster accordingly. Reference OPERA's preprint: Neutrino's faster time-effect due to altitude difference; (10-13ns) x c (299792458m) = 2.9 x 10-5 m/ns x distance (730085m) + 21.8m.) This is consistent with the OPERA result.
Radjavi, Heydar
2003-01-01
This broad survey spans a wealth of studies on invariant subspaces, focusing on operators on separable Hilbert space. Largely self-contained, it requires only a working knowledge of measure theory, complex analysis, and elementary functional analysis. Subjects include normal operators, analytic functions of operators, shift operators, examples of invariant subspace lattices, compact operators, and the existence of invariant and hyperinvariant subspaces. Additional chapters cover certain results on von Neumann algebras, transitive operator algebras, algebras associated with invariant subspaces,
Lorentz invariance with an invariant energy scale.
Magueijo, João; Smolin, Lee
2002-05-13
We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.
The gauge principle vs. the equivalence principle
International Nuclear Information System (INIS)
Gates, S.J. Jr.
1984-01-01
Within the context of field theory, it is argued that the role of the equivalence principle may be replaced by the principle of gauge invariance to provide a logical framework for theories of gravitation
Permutationally invariant state reconstruction
DEFF Research Database (Denmark)
Moroder, Tobias; Hyllus, Philipp; Tóth, Géza
2012-01-01
Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large-scale opti......Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large......-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum...... likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex...
Testing Lorentz invariance of dark matter
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [Theory Group, Physics Department, CERN, CH-1211 Geneva 23 (Switzerland); Ivanov, Mikhail M.; Sibiryakov, Sergey, E-mail: diego.blas@cern.ch, E-mail: mm.ivanov@physics.msu.ru, E-mail: sibir@inr.ac.ru [Faculty of Physics, Moscow State University, Vorobjevy Gory, 119991 Moscow (Russian Federation)
2012-10-01
We study the possibility to constrain deviations from Lorentz invariance in dark matter (DM) with cosmological observations. Breaking of Lorentz invariance generically introduces new light gravitational degrees of freedom, which we represent through a dynamical timelike vector field. If DM does not obey Lorentz invariance, it couples to this vector field. We find that this coupling affects the inertial mass of small DM halos which no longer satisfy the equivalence principle. For large enough lumps of DM we identify a (chameleon) mechanism that restores the inertial mass to its standard value. As a consequence, the dynamics of gravitational clustering are modified. Two prominent effects are a scale dependent enhancement in the growth of large scale structure and a scale dependent bias between DM and baryon density perturbations. The comparison with the measured linear matter power spectrum in principle allows to bound the departure from Lorentz invariance of DM at the per cent level.
Testing Lorentz invariance of dark matter
Blas, Diego; Sibiryakov, Sergey
2012-01-01
We study the possibility to constrain deviations from Lorentz invariance in dark matter (DM) with cosmological observations. Breaking of Lorentz invariance generically introduces new light gravitational degrees of freedom, which we represent through a dynamical timelike vector field. If DM does not obey Lorentz invariance, it couples to this vector field. We find that this coupling affects the inertial mass of small DM halos which no longer satisfy the equivalence principle. For large enough lumps of DM we identify a (chameleon) mechanism that restores the inertial mass to its standard value. As a consequence, the dynamics of gravitational clustering are modified. Two prominent effects are a scale dependent enhancement in the growth of large scale structure and a scale dependent bias between DM and baryon density perturbations. The comparison with the measured linear matter power spectrum in principle allows to bound the departure from Lorentz invariance of DM at the per cent level.
Computational invariant theory
Derksen, Harm
2015-01-01
This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be ...
Physical Invariants of Intelligence
Zak, Michail
2010-01-01
A program of research is dedicated to development of a mathematical formalism that could provide, among other things, means by which living systems could be distinguished from non-living ones. A major issue that arises in this research is the following question: What invariants of mathematical models of the physics of systems are (1) characteristic of the behaviors of intelligent living systems and (2) do not depend on specific features of material compositions heretofore considered to be characteristic of life? This research at earlier stages has been reported, albeit from different perspectives, in numerous previous NASA Tech Briefs articles. To recapitulate: One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Mathematical models of motor dynamics are used to simulate the observable physical behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. At the time of reporting the information for this article, the focus of this research was upon the following aspects of the formalism: Intelligence is considered to be a means by which a living system preserves itself and improves its ability to survive and is further considered to manifest itself in feedback from the mental dynamics to the motor dynamics. Because of the feedback from the mental dynamics, the motor dynamics attains quantum-like properties: The trajectory of the physical aspect of the system in the space of dynamical variables splits into a family of different trajectories, and each of those trajectories can be chosen with a probability prescribed by the mental dynamics. From a slightly different perspective
General relativity invariance and string field theory
International Nuclear Information System (INIS)
Aref'eva, I.Ya.; Volovich, I.V.
1987-04-01
The general covariance principle in the string field theory is considered. The algebraic properties of the string Lie derivative are discussed. The string vielbein and spin connection are introduced and an action invariant under general co-ordinate transformation is proposed. (author). 18 refs
Measurement invariance versus selection invariance : Is fair selection possible?
Borsboom, Denny; Romeijn, Jan-Willem; Wicherts, Jelte M.
This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement
Morozov, Albert D; Dragunov, Timothy N; Malysheva, Olga V
1999-01-01
This book deals with the visualization and exploration of invariant sets (fractals, strange attractors, resonance structures, patterns etc.) for various kinds of nonlinear dynamical systems. The authors have created a special Windows 95 application called WInSet, which allows one to visualize the invariant sets. A WInSet installation disk is enclosed with the book.The book consists of two parts. Part I contains a description of WInSet and a list of the built-in invariant sets which can be plotted using the program. This part is intended for a wide audience with interests ranging from dynamical
Algorithms in invariant theory
Sturmfels, Bernd
2008-01-01
J. Kung and G.-C. Rota, in their 1984 paper, write: "Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics". The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students will find the book an easy introduction to this "classical and new" area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to a wealth of research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems.
International Nuclear Information System (INIS)
Tian Chou.
1991-05-01
It is important but difficult to find the invariant groups for the differential equations. We found a new invariant group for the MKdV equation. In this paper, we present a new invariance for the CDF equation. By using this invariance, we obtain some new solutions of CDF equation. (author). 5 refs
Lorentz invariance in shape dynamics
International Nuclear Information System (INIS)
Carlip, S; Gomes, Henrique
2015-01-01
Shape dynamics is a reframing of canonical general relativity in which time reparametrization invariance is ‘traded’ for a local conformal invariance. We explore the emergence of Lorentz invariance in this model in three contexts: as a maximal symmetry, an asymptotic symmetry and a local invariance. (paper)
Chirality invariance and 'chiral' fields
International Nuclear Information System (INIS)
Ziino, G.
1978-01-01
The new field model derived in the present paper actually gives a definite answer to three fundamental questions concerning elementary-particle physics: 1) The phenomenological dualism between parity and chirality invariance: it would be only an apparent display of a general 'duality' principle underlying the intrinsic nature itself of (spin 1/2) fermions and expressed by the anticommutativity property between scalar and pseudoscalar charges. 2) The real physical meaning of V - A current structure: it would exclusively be connected to the one (just pointed out) of chiral fields themselves. 3) The unjustified apparent oddness shown by Nature in weak interactions, for the fact of picking out only one of the two (left- and right-handed) fermion 'chiral' projections: the key to such a 'mystery' would just be provided by the consequences of the dual and partial character of the two fermion-antifermion field bases. (Auth.)
Robust Affine Invariant Descriptors
Directory of Open Access Journals (Sweden)
Jianwei Yang
2011-01-01
Full Text Available An approach is developed for the extraction of affine invariant descriptors by cutting object into slices. Gray values associated with every pixel in each slice are summed up to construct affine invariant descriptors. As a result, these descriptors are very robust to additive noise. In order to establish slices of correspondence between an object and its affine transformed version, general contour (GC of the object is constructed by performing projection along lines with different polar angles. Consequently, affine in-variant division curves are derived. A slice is formed by points fall in the region enclosed by two adjacent division curves. To test and evaluate the proposed method, several experiments have been conducted. Experimental results show that the proposed method is very robust to noise.
Energy Technology Data Exchange (ETDEWEB)
Perez-Nadal, Guillem [Universidad de Buenos Aires, Buenos Aires (Argentina)
2017-07-15
We consider a non-relativistic free scalar field theory with a type of anisotropic scale invariance in which the number of coordinates ''scaling like time'' is generically greater than one. We propose the Cartesian product of two curved spaces, the metric of each space being parameterized by the other space, as a notion of curved background to which the theory can be extended. We study this type of geometries, and find a family of extensions of the theory to curved backgrounds in which the anisotropic scale invariance is promoted to a local, Weyl-type symmetry. (orig.)
Modular invariant gaugino condensation
Energy Technology Data Exchange (ETDEWEB)
Gaillard, M.K.
1991-05-09
The construction of effective supergravity lagrangians for gaugino condensation is reviewed and recent results are presented that are consistent with modular invariance and yield a positive definite potential of the noscale type. Possible implications for phenomenology are briefly discussed. 29 refs.
Invariant differential operators
Dobrev, Vladimir K
2016-01-01
With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory.
Perspective Projection Invariants,
1986-02-01
AD-AI67 793 PERSPECTIVE PROJECTION INVARIANTS(U) MASSACHUSETTS INST 1/1~ OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB VERRI ET AL , FEB 86 AI-M-832...some stability properties. On the contrary, zeros of curvature of arbitrary 3D curves do not present any simple kindi of stability. Thus zeros of
International Nuclear Information System (INIS)
Bramson, B.D.
1978-01-01
An isolated system in general relativity makes a transition between stationary states. It is shown that the spin vectors of the system, long before and long after the emission of radiation, are supertranslation invariant and, hence, independent of the choice of Minkowski observation space. (author)
Invariants of generalized Lie algebras
International Nuclear Information System (INIS)
Agrawala, V.K.
1981-01-01
Invariants and invariant multilinear forms are defined for generalized Lie algebras with arbitrary grading and commutation factor. Explicit constructions of invariants and vector operators are given by contracting invariant forms with basic elements of the generalized Lie algebra. The use of the matrix of a linear map between graded vector spaces is emphasized. With the help of this matrix, the concept of graded trace of a linear operator is introduced, which is a rich source of multilinear forms of degree zero. To illustrate the use of invariants, a characteristic identity similar to that of Green is derived and a few Racah coefficients are evaluated in terms of invariants
Existence of a last invariant of conservative motion
International Nuclear Information System (INIS)
Hall, L.S.
1982-01-01
A general theory of integrable systems in two dimensions is formulated and applied. (The theory also has applications to more dimensions). The constraints are found which admit to general integrability of the orbits for magnetic forces as well as for forces derivable from a potential. When a system admits a given invariant, the invariant is found. A number of examples including known and apparently previously unknown invariants are given. The theory of exact integrals of the motion also can be extended to the derivation of approximate invariants. The general theory admits a variational principle, among other approximation techniques, for the computation of a best approximate invariant. The problem of the general cubic potential with one symmetric coordinate, V = 1/2 Ax 2 + 1/2 By 2 + Cx 2 y + 1/3 Dy 3 (of which the well-studied Henon-Heiles potential is the special case for A = B and C = -D), is examined in detail
Analytic invariants of boundary links
Garoufalidis, Stavros; Levine, Jerome
2001-01-01
Using basic topology and linear algebra, we define a plethora of invariants of boundary links whose values are power series with noncommuting variables. These turn out to be useful and elementary reformulations of an invariant originally defined by M. Farber.
Continuous Integrated Invariant Inference Project
National Aeronautics and Space Administration — The proposed project will develop a new technique for invariant inference and embed this and other current invariant inference and checking techniques in an...
Status of time reversal invariance
International Nuclear Information System (INIS)
Henley, E.M.
1989-01-01
Time Reversal Invariance is introduced, and theories for its violation are reviewed. The present experimental and theoretical status of Time Reversal Invariance and tests thereof will be presented. Possible future tests will be discussed
Conformal invariance of curvature perturbation
Gong, Jinn-Ouk; Park, Wan Il; Sasaki, Misao; Song, Yong-Seon
2011-01-01
We show that in the single component situation all perturbation variables in the comoving gauge are conformally invariant to all perturbation orders. Generally we identify a special time slicing, the uniform-conformal transformation slicing, where all perturbations are again conformally invariant to all perturbation orders. We apply this result to the delta N formalism, and show its conformal invariance.
Invariant scattering convolution networks.
Bruna, Joan; Mallat, Stéphane
2013-08-01
A wavelet scattering network computes a translation invariant image representation which is stable to deformations and preserves high-frequency information for classification. It cascades wavelet transform convolutions with nonlinear modulus and averaging operators. The first network layer outputs SIFT-type descriptors, whereas the next layers provide complementary invariant information that improves classification. The mathematical analysis of wavelet scattering networks explains important properties of deep convolution networks for classification. A scattering representation of stationary processes incorporates higher order moments and can thus discriminate textures having the same Fourier power spectrum. State-of-the-art classification results are obtained for handwritten digits and texture discrimination, with a Gaussian kernel SVM and a generative PCA classifier.
Conformal invariance in supergravity
International Nuclear Information System (INIS)
Bergshoeff, E.A.
1983-01-01
In this thesis the author explains the role of conformal invariance in supergravity. He presents the complete structure of extended conformal supergravity for N <= 4. The outline of this work is as follows. In chapter 2 he briefly summarizes the essential properties of supersymmetry and supergravity and indicates the use of conformal invariance in supergravity. The idea that the introduction of additional symmetry transformations can make clear the structure of a field theory is not reserved to supergravity only. By means of some simple examples it is shown in chapter 3 how one can always introduce additional gauge transformations in a theory of massive vector fields. Moreover it is shown how the gauge invariant formulation sometimes explains the quantum mechanical properties of the theory. In chapter 4 the author defines the conformal transformations and summarizes their main properties. He explains how these conformal transformations can be used to analyse the structure of gravity. The supersymmetric extension of these results is discussed in chapter 5. Here he describes as an example how N=1 supergravity can be reformulated in a conformally-invariant way. He also shows that beyond N=1 the gauge fields of the superconformal symmetries do not constitute an off-shell field representation of extended conformal supergravity. Therefore, in chapter 6, a systematic method to construct the off-shell formulation of all extended conformal supergravity theories with N <= 4 is developed. As an example he uses this method to construct N=1 conformal supergravity. Finally, in chapter 7 N=4 conformal supergravity is discussed. (Auth.)
2010-12-02
evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and thus we can employ various...tractable linear programming, spectral, and SDP relaxations of QAP [40, 11, 33]. In particular we discuss recent work [14] on exploiting group...symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many interesting cases. Finally in
Czech Academy of Sciences Publication Activity Database
Flusser, Jan; Kautský, J.; Šroubek, Filip
2010-01-01
Roč. 86, č. 1 (2010), s. 72-86 ISSN 0920-5691 R&D Projects: GA MŠk 1M0572; GA ČR GA102/08/1593 Institutional research plan: CEZ:AV0Z10750506 Keywords : Implicit invariants * Orthogonal polynomials * Polynomial image deformation Subject RIV: BD - Theory of Information Impact factor: 4.930, year: 2010 http://library.utia.cas.cz/separaty/2009/ZOI/flusser-0329394.pdf
Czech Academy of Sciences Publication Activity Database
Suk, Tomáš; Flusser, Jan
2004-01-01
Roč. 26, č. 10 (2004), s. 1364-1367 ISSN 0162-8828 R&D Projects: GA ČR GA201/03/0675 Institutional research plan: CEZ:AV0Z1075907 Keywords : projective transform * moment invariants * object recognition Subject RIV: JD - Computer Applications, Robotics Impact factor: 4.352, year: 2004 http://library.utia.cas.cz/prace/20040112.pdf
Polynomial invariants to quantify Four-body Correlations
Sharma, Santosh Shelly; Sharma, Naresh Kumar
2013-03-01
Local unitary invariance and notion of negativity fonts are used as the principle tools to construct four qubit polynomial invariants of degree 8, 12, and 24. Determinants of negativity fonts are linked to matrices obtained from state operator through selective partial transposition. Our general aim is to construct the polynomial invariants that quantify entanglement due to K - body correlations in an N-qubit (N ? K) pure state. This is done by constructing N-qubit invariants from multivariate forms with (K - 1)-qubit invariants as coefficients. In particular, the invariant that quantifies entanglement due to N-body correlations is obtained from a biform having as coefficients the N - 1 qubit invariants. A polynomial invariant that is non-zero on four qubit pure states with four-body correlations and zero on all other states, is identified. Classification of four qubit states into seven major classes, using criterion based on the nature of correlations, is discussed. We gratefully acknowledge financial support from CNPq Brazil and Faep, UEL, Brazil.
Probability density functions for CP-violating rephasing invariants
Fortin, Jean-François; Giasson, Nicolas; Marleau, Luc
2018-05-01
The implications of the anarchy principle on CP violation in the lepton sector are investigated. A systematic method is introduced to compute the probability density functions for the CP-violating rephasing invariants of the PMNS matrix from the Haar measure relevant to the anarchy principle. Contrary to the CKM matrix which is hierarchical, it is shown that the Haar measure, and hence the anarchy principle, are very likely to lead to the observed PMNS matrix. Predictions on the CP-violating Dirac rephasing invariant |jD | and Majorana rephasing invariant |j1 | are also obtained. They correspond to 〈 |jD | 〉 Haar = π / 105 ≈ 0.030 and 〈 |j1 | 〉 Haar = 1 / (6 π) ≈ 0.053 respectively, in agreement with the experimental hint from T2K of |jDexp | ≈ 0.032 ± 0.005 (or ≈ 0.033 ± 0.003) for the normal (or inverted) hierarchy.
Viability, invariance and applications
Carja, Ovidiu; Vrabie, Ioan I
2007-01-01
The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time.The book includes the most important necessary and sufficient conditions for viability starting with Nagumo's Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In th...
Invariants in probabilistic reasoning.
Costello, Fintan; Watts, Paul
2018-02-01
Recent research has identified three invariants or identities that appear to hold in people's probabilistic reasoning: the QQ identity, the addition law identity, and the Bayes rule identity (Costello and Watts, 2014, 2016a, Fisher and Wolfe, 2014, Wang and Busemeyer, 2013, Wang et al., 2014). Each of these identities represent specific agreement with the requirements of normative probability theory; strikingly, these identities seem to hold in people's judgements despite the presence of strong and systematic biases against the requirements of normative probability theory in those very same judgements. These results suggest that the systematic biases seen in people's probabilistic reasoning follow mathematical rules: for these particular identities, these rules cause an overall cancellation of biases and so produce agreement with normative requirements. We assess two competing mathematical models of probabilistic reasoning (the 'probability theory plus noise' model and the 'quantum probability' model) in terms of their ability to account for this pattern of systematic biases and invariant identities. Copyright © 2017 Elsevier Inc. All rights reserved.
Prediction of critical properties of freon using the new invariants of weighted graphs
Directory of Open Access Journals (Sweden)
Юрий Алексеевич Кругляк
2014-10-01
Full Text Available It is proposed a new approach to the "structure – property" problems with usage the invariants of the fully weighted graphs for quantitative description of the critical properties of freon. A general principle of topological invariants construction of fully weighted graphs is formulated and propose two new invariants applied to calculate the critical properties of freon of methane, ethane and propane series without the involvement of experimental data and patterns.
Stable pair invariants of surfaces and Seiberg-Witten invariants
Kool, M.
2016-01-01
The moduli space of stable pairs on a local surface X = KS is in general non-compact. The action of C ∗ on the fibres of X induces an action on the moduli space and the stable pair invariants of X are defined by the virtual localization formula. We study the contribution to these invariants of
Wulan, Hasi
2017-01-01
This monograph summarizes the recent major achievements in Möbius invariant QK spaces. First introduced by Hasi Wulan and his collaborators, the theory of QK spaces has developed immensely in the last two decades, and the topics covered in this book will be helpful to graduate students and new researchers interested in the field. Featuring a wide range of subjects, including an overview of QK spaces, QK-Teichmüller spaces, K-Carleson measures and analysis of weight functions, this book serves as an important resource for analysts interested in this area of complex analysis. Notes, numerous exercises, and a comprehensive up-to-date bibliography provide an accessible entry to anyone with a standard graduate background in real and complex analysis.
Electromagnetic field and the theory of conformal and biholomorphic invariants
International Nuclear Information System (INIS)
Lawrynowicz, J.
1976-01-01
This paper contains sections on: 1. Conformal invariance and variational principles in electrodynamics. 2. The principles of Dirichlet and Thomson as a physical motivation for the methods of conformal capacities and extremal lengths. 3. Extension to pseudoriemannian manifolds. 4. Extension to hermitian manifolds. 5. An extension of Schwarz's lemma for hermitian manifolds and its physical significance. 6. Variation of ''complex'' capacities within the admissible class of plurisubharmonic functions. The author concentrates on motivations and interpretations connected with the electromagnetic field. (author)
International Nuclear Information System (INIS)
Habegger, N.; Thompson, G.
1999-11-01
Let Z LMO be the 3-manifold invariant of [LMO]. It is shown that Z LMO (M) = 1, if the first Betti number of M, b 1 (M), is greater than 3. If b 1 (M) = 3, then Z LMO (M) is completely determined by the cohomology ring of M. A relation of Z LMO with the Rozansky-Witten invariants Z X RW [M] is established at a physical level of rigour. We show that Z X RW [M] satisfies appropriate connected sum properties suggesting that the generalized Casson invariant ought to be computable from the LMO invariant. (author)
On the generalized Casson invariant
International Nuclear Information System (INIS)
Thompson, G.
1998-11-01
The path integral generalization of the Casson invariant as developed by Rozansky and Witten is investigated. The path integral for various three manifolds is explicitly evaluated. A new class of topological observables are introduced that may allow for more effective invariants. Finally it is shown how the dimensional reduction of these theories correspond to a generalization of the topological B sigma model. (author)
Hidden scale invariance of metals
DEFF Research Database (Denmark)
Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.
2015-01-01
Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between the thermal fluctuations of the virial and the potential energy in the isochoric ensemble. This demonstrates a general “hidden” scale invariance...... of metals making the condensed part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Grüneisen parameter, are in good agreement with experimental values for the 16 elements where reliable data were...... available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant...
Invariant and semi-invariant probabilistic normed spaces
Energy Technology Data Exchange (ETDEWEB)
Ghaemi, M.B. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: mghaemi@iust.ac.ir; Lafuerza-Guillen, B. [Departamento de Estadistica y Matematica Aplicada, Universidad de Almeria, Almeria E-04120 (Spain)], E-mail: blafuerz@ual.es; Saiedinezhad, S. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: ssaiedinezhad@yahoo.com
2009-10-15
Probabilistic metric spaces were introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of probabilistic normed space based on the definition of Menger . We introduce the concept of semi-invariance among the PN spaces. In this paper we will find a sufficient condition for some PN spaces to be semi-invariant. We will show that PN spaces are normal spaces. Urysohn's lemma, and Tietze extension theorem for them are proved.
The invariant theory of matrices
Concini, Corrado De
2017-01-01
This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of m\\times m matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving the first fundamental theorem that describes a set of generators in the ring of invariants, and the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case...
Modern Tests of Lorentz Invariance
Directory of Open Access Journals (Sweden)
Mattingly David
2005-09-01
Full Text Available Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made new high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented.
CPT invariance in classical electrodynamics
Kaplan, Aaron D.; Tsankov, Tsvetelin D.
2017-11-01
The transformation properties of classical electrodynamic variables under charge conjugation C, parity reversal P, and time inversion T are considered both for standard and atypical assumptions for the nature of charge. We have shown that four distinct behaviours of charge under space and time inversion are consistent with the invariance of Maxwell’s equations under CPT and P. No prior knowledge of CPT invariance is assumed and the material is accessible to undergraduate students.
Invariant measures for Chebyshev maps
Directory of Open Access Journals (Sweden)
Abraham Boyarsky
2001-01-01
Full Text Available Let Tλ(x=cos(λarccosx, −1≤x≤1, where λ>1 is not an integer. For a certain set of λ's which are irrational, the density of the unique absolutely continuous measure invariant under Tλ is determined exactly. This is accomplished by showing that Tλ is differentially conjugate to a piecewise linear Markov map whose unique invariant density can be computed as the unique left eigenvector of a matrix.
Invariant Bayesian estimation on manifolds
Jermyn, Ian H.
2005-01-01
A frequent and well-founded criticism of the maximum a posteriori (MAP) and minimum mean squared error (MMSE) estimates of a continuous parameter \\gamma taking values in a differentiable manifold \\Gamma is that they are not invariant to arbitrary ``reparameterizations'' of \\Gamma. This paper clarifies the issues surrounding this problem, by pointing out the difference between coordinate invariance, which is a sine qua non for a mathematically well-defined problem, and diffeomorphism invarianc...
Object recognition by implicit invariants
Czech Academy of Sciences Publication Activity Database
Flusser, Jan; Kautsky, J.; Šroubek, Filip
2007-01-01
Roč. 2007, č. 4673 (2007), s. 856-863 ISSN 0302-9743. [Computer Analysis of Images and Patterns. Vienna, 27.08.2007-29.08.2007] R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : Invariants * implicit invariants * moments * orthogonal polynomials * nonlinear object deformation Subject RIV: JD - Computer Applications, Robotics Impact factor: 0.402, year: 2005 http://staff.utia.cas.cz/sroubekf/papers/CAIP_07.pdf
Classification of simple current invariants
Gato-Rivera, Beatriz
1992-01-01
We summarize recent work on the classification of modular invariant partition functions that can be obtained with simple currents in theories with a center (Z_p)^k with p prime. New empirical results for other centers are also presented. Our observation that the total number of invariants is monodromy-independent for (Z_p)^k appears to be true in general as well. (Talk presented in the parallel session on string theory of the Lepton-Photon/EPS Conference, Geneva, 1991.)
An almost sure invariance principle for trimmed sums of random ...
Indian Academy of Sciences (India)
the definition of α0, and observing that n − i. 2 ≤ E|X|2I (δ cn ≤ |X| ≤ cn) for some δ > 0, we can similarly get. ∞. ∑ n=1. 1 n. P. ( max. 1≤k≤n. ∣. ∣. ∣. ∣. ∣ k. ∑ i=1. ( n − i)Yi. ∣. ∣. ∣. ∣. ∣. ≥ εcn. ) ≤ C. ∞. ∑ n=1. 1 n exp. (. − ε2c2 n. 2p. ∑n i=1 n − i. 2. ) ≤ C. ∞. ∑ n=1. 1 n exp. (. − ε2c2 n. 4p. ∑Dn i=1 n − i. 2. ) + C.
Cosmological principles. II. Physical principles
International Nuclear Information System (INIS)
Harrison, E.R.
1974-01-01
The discussion of cosmological principle covers the uniformity principle of the laws of physics, the gravitation and cognizability principles, and the Dirac creation, chaos, and bootstrap principles. (U.S.)
Invariant Matsumoto metrics on homogeneous spaces
Salimi Moghaddam, H.R.
2014-01-01
In this paper we consider invariant Matsumoto metrics which are induced by invariant Riemannian metrics and invariant vector fields on homogeneous spaces, and then we give the flag curvature formula of them. Also we study the special cases of naturally reductive spaces and bi-invariant metrics. We end the article by giving some examples of geodesically complete Matsumoto spaces.
A gauge principle yielding consistent chiral theories
International Nuclear Information System (INIS)
Thompson, G.; Zhang, R.
1987-02-01
We propose a new principle in gauge theories: namely that in a given action, fields should be replaced by gauge invariant equivalents. Using this principle we study anomalous gauge theories and find that the resulting models are anomaly free, unitary and power counting renormalizable. (author). 8 refs
A cyclic symmetry principle in physics
International Nuclear Information System (INIS)
Green, H.S.; Adelaide Univ., SA
1994-01-01
Many areas of modern physics are illuminated by the application of a symmetry principle, requiring the invariance of the relevant laws of physics under a group of transformations. This paper examines the implications and some of the applications of the principle of cyclic symmetry, especially in the areas of statistical mechanics and quantum mechanics, including quantized field theory. This principle requires invariance under the transformations of a finite group, which may be a Sylow π-group, a group of Lie type, or a symmetric group. The utility of the principle of cyclic invariance is demonstrated in finding solutions of the Yang-Baxter equation that include and generalize known solutions. It is shown that the Sylow π-groups have other uses, in providing a basis for a type of generalized quantum statistics, and in parametrising a new generalization of Lie groups, with associated algebras that include quantized algebras. 31 refs
Energy Invariance in Capillary Systems
Ruiz-Gutiérrez, Élfego; Guan, Jian H.; Xu, Ben; McHale, Glen; Wells, Gary G.; Ledesma-Aguilar, Rodrigo
2017-05-01
We demonstrate the continuous translational invariance of the energy of a capillary surface in contact with reconfigurable solid boundaries. We present a theoretical approach to find the energy-invariant equilibria of spherical capillary surfaces in contact with solid boundaries of arbitrary shape and examine the implications of dynamic frictional forces upon a reconfiguration of the boundaries. Experimentally, we realize our ideas by manipulating the position of a droplet in a wedge geometry using lubricant-impregnated solid surfaces, which eliminate the contact-angle hysteresis and provide a test bed for quantifying dissipative losses out of equilibrium. Our experiments show that dissipative energy losses for an otherwise energy-invariant reconfiguration are relatively small, provided that the actuation time scale is longer than the typical relaxation time scale of the capillary surface. We discuss the wider applicability of our ideas as a pathway for liquid manipulation at no potential energy cost in low-pinning, low-friction situations.
Invariants of triangular Lie algebras
International Nuclear Information System (INIS)
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman
2007-01-01
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated
Dark coupling and gauge invariance
International Nuclear Information System (INIS)
Gavela, M.B.; Honorez, L. Lopez; Mena, O.; Rigolin, S.
2010-01-01
We study a coupled dark energy-dark matter model in which the energy-momentum exchange is proportional to the Hubble expansion rate. The inclusion of its perturbation is required by gauge invariance. We derive the linear perturbation equations for the gauge invariant energy density contrast and velocity of the coupled fluids, and we determine the initial conditions. The latter turn out to be adiabatic for dark energy, when assuming adiabatic initial conditions for all the standard fluids. We perform a full Monte Carlo Markov Chain likelihood analysis of the model, using WMAP 7-year data
Numeric invariants from multidimensional persistence
Energy Technology Data Exchange (ETDEWEB)
Skryzalin, Jacek [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Carlsson, Gunnar [Stanford Univ., Stanford, CA (United States)
2017-05-19
In this paper, we analyze the space of multidimensional persistence modules from the perspectives of algebraic geometry. We first build a moduli space of a certain subclass of easily analyzed multidimensional persistence modules, which we construct specifically to capture much of the information which can be gained by using multidimensional persistence over one-dimensional persistence. We argue that the global sections of this space provide interesting numeric invariants when evaluated against our subclass of multidimensional persistence modules. Lastly, we extend these global sections to the space of all multidimensional persistence modules and discuss how the resulting numeric invariants might be used to study data.
Trace Invariance for Quaternion Matrices
Directory of Open Access Journals (Sweden)
Ralph John de la Cruz
2015-12-01
Full Text Available Let F be a f ield. It is a classical result in linear algebra that for each A, P ϵ Mn (F such that P is nonsingular, tr A = tr (PAP-1. We show in this paper that the preceding property does not hold true if F is the division ring of real quaternions. We show that the only quaternion matrices that have their trace invariant under unitary similarity are Hermitian matrices, and that the only matrices that have their trace invariant under similarity are real scalar matrices.
Supersymmetric gauge invariant interaction revisited
International Nuclear Information System (INIS)
Smith, A.W.; Pontificia Univ. Catolica do Rio de Janeiro; Barcelos Neto, J.
1983-01-01
A supersymmetric Lagrangian invariant under local U(1) gauge transformations is written in terms of a non-chiral superfield which substitute the usual vector supermultiplet together with chiral and anti-chiral superfields. The Euler equations allow us to obtain the off-shell version of the usual Lagrangian for supersymmetric quantum-electrodynamics (SQED). (Author) [pt
On renormalization-invariant masses
International Nuclear Information System (INIS)
Fleming, H.; Furuya, K.
1978-02-01
It is shown that spontaneous generation of renormalization invariant mass is possible in infra-red stable theories with more than one coupling constant. If relations among the coupling constants are permitted the effect can be made compatible with pertubation theory
Moment Invariants in Image Analysis
Czech Academy of Sciences Publication Activity Database
Flusser, Jan
2006-01-01
Roč. 11, č. 2 (2006), s. 196-201 ISSN 1305-5313 R&D Projects: GA MŠk 1M0572; GA ČR GA102/04/0155 Institutional research plan: CEZ:AV0Z10750506 Keywords : moment invariants * pattern recognition Subject RIV: JD - Computer Applications, Robotics
A Many Particle Adiabatic Invariant
DEFF Research Database (Denmark)
Hjorth, Poul G.
1999-01-01
For a system of N charged particles moving in a homogeneous, sufficiently strong magnetic field, a many-particle adiabatic invariant constrains the collisional exchange of energy between the degrees of freedom perpendicular to and parallel to the magnetic field. A description of the phenomenon...
Computing with scale-invariant neural representations
Howard, Marc; Shankar, Karthik
The Weber-Fechner law is perhaps the oldest quantitative relationship in psychology. Consider the problem of the brain representing a function f (x) . Different neurons have receptive fields that support different parts of the range, such that the ith neuron has a receptive field at xi. Weber-Fechner scaling refers to the finding that the width of the receptive field scales with xi as does the difference between the centers of adjacent receptive fields. Weber-Fechner scaling is exponentially resource-conserving. Neurophysiological evidence suggests that neural representations obey Weber-Fechner scaling in the visual system and perhaps other systems as well. We describe an optimality constraint that is solved by Weber-Fechner scaling, providing an information-theoretic rationale for this principle of neural coding. Weber-Fechner scaling can be generated within a mathematical framework using the Laplace transform. Within this framework, simple computations such as translation, correlation and cross-correlation can be accomplished. This framework can in principle be extended to provide a general computational language for brain-inspired cognitive computation on scale-invariant representations. Supported by NSF PHY 1444389 and the BU Initiative for the Physics and Mathematics of Neural Systems,.
Continuous Integrated Invariant Inference, Phase I
National Aeronautics and Space Administration — The proposed project will develop a new technique for invariant inference and embed this and other current invariant inference and checking techniques in an...
Local unitary invariants for multipartite quantum systems
Energy Technology Data Exchange (ETDEWEB)
Vrana, Peter, E-mail: vranap@math.bme.hu [Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1111 Budapest (Hungary)
2011-03-18
A method is presented to obtain local unitary invariants for multipartite quantum systems consisting of fermions or distinguishable particles. The invariants are organized into infinite families, in particular, the generalization to higher dimensional single-particle Hilbert spaces is straightforward. Many well-known invariants and their generalizations are also included.
Gauge invariant fractional electromagnetic fields
Energy Technology Data Exchange (ETDEWEB)
Lazo, Matheus Jatkoske, E-mail: matheuslazo@furg.br [Instituto de Matematica, Estatistica e Fisica - FURG, Rio Grande, RS (Brazil)
2011-09-26
Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators. -- Highlights: → We propose a fractional Lagrangian formulation for fractional Maxwell's fields. → We obtain gauge invariant fractional electromagnetic fields. → Our generalized fractional Maxwell's field is spatially symmetrical. → We discuss the non-causality of the theory.
Invariance for Single Curved Manifold
Castro, Pedro Machado Manhaes de
2012-08-01
Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.
Holographic multiverse and conformal invariance
Energy Technology Data Exchange (ETDEWEB)
Garriga, Jaume [Departament de Física Fonamental i Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès 1, 08193 Barcelona (Spain); Vilenkin, Alexander, E-mail: jaume.garriga@ub.edu, E-mail: vilenkin@cosmos.phy.tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, 212 College Ave., Medford, MA 02155 (United States)
2009-11-01
We consider a holographic description of the inflationary multiverse, according to which the wave function of the universe is interpreted as the generating functional for a lower dimensional Euclidean theory. We analyze a simple model where transitions between inflationary vacua occur through bubble nucleation, and the inflating part of spacetime consists of de Sitter regions separated by thin bubble walls. In this model, we present some evidence that the dual theory is conformally invariant in the UV.
Molecular invariants: atomic group valence
International Nuclear Information System (INIS)
Mundim, K.C.; Giambiagi, M.; Giambiagi, M.S. de.
1988-01-01
Molecular invariants may be deduced in a very compact way through Grassman algebra. In this work, a generalized valence is defined for an atomic group; it reduces to the Known expressions for the case of an atom in a molecule. It is the same of the correlations between the fluctions of the atomic charges qc and qd (C belongs to the group and D does not) around their average values. Numerical results agree with chemical expectation. (author) [pt
Homotopy invariants of Gauss words
Gibson, Andrew
2009-01-01
By defining combinatorial moves, we can define an equivalence relation on Gauss words called homotopy. In this paper we define a homotopy invariant of Gauss words. We use this to show that there exist Gauss words that are not homotopically equivalent to the empty Gauss word, disproving a conjecture by Turaev. In fact, we show that there are an infinite number of equivalence classes of Gauss words under homotopy.
Random SU(2) invariant tensors
Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei
2018-04-01
SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n = 4. In this paper, we show that for n > 4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.
Indian Academy of Sciences (India)
Example 5 (Chameleons): In a certain island there are 13 grey, 15 brown and 17 crimson chameleons. If two chameleons of different colors meet, both of them change to the third color. No other color changes are ... permutation)?' is the question. Well, the set of per- mutations are divided into two classes, odd and even.
Blur invariants constructed from arbitrary moments.
Kautsky, Jaroslav; Flusser, Jan
2011-12-01
This paper deals with moment invariants with respect to image blurring. It is mainly a reaction to the works of Zhang and Chen , recently published in these Transactions. We present a general method on how to construct blur invariants from arbitrary moments and show that it is no longer necessary to separately derive the invariants for each polynomial basis. We show how to discard dependent terms in blur invariants definition and discuss a proper implementation of the invariants in orthogonal bases using recurrent relations. An example for Legendre moments is given. © 2011 IEEE
Cartan invariants and event horizon detection
Brooks, D.; Chavy-Waddy, P. C.; Coley, A. A.; Forget, A.; Gregoris, D.; MacCallum, M. A. H.; McNutt, D. D.
2018-04-01
We show that it is possible to locate the event horizon of a black hole (in arbitrary dimensions) by the zeros of certain Cartan invariants. This approach accounts for the recent results on the detection of stationary horizons using scalar polynomial curvature invariants, and improves upon them since the proposed method is computationally less expensive. As an application, we produce Cartan invariants that locate the event horizons for various exact four-dimensional and five-dimensional stationary, asymptotically flat (or (anti) de Sitter), black hole solutions and compare the Cartan invariants with the corresponding scalar curvature invariants that detect the event horizon.
Invariant recognition drives neural representations of action sequences.
Directory of Open Access Journals (Sweden)
Andrea Tacchetti
2017-12-01
Full Text Available Recognizing the actions of others from visual stimuli is a crucial aspect of human perception that allows individuals to respond to social cues. Humans are able to discriminate between similar actions despite transformations, like changes in viewpoint or actor, that substantially alter the visual appearance of a scene. This ability to generalize across complex transformations is a hallmark of human visual intelligence. Advances in understanding action recognition at the neural level have not always translated into precise accounts of the computational principles underlying what representations of action sequences are constructed by human visual cortex. Here we test the hypothesis that invariant action discrimination might fill this gap. Recently, the study of artificial systems for static object perception has produced models, Convolutional Neural Networks (CNNs, that achieve human level performance in complex discriminative tasks. Within this class, architectures that better support invariant object recognition also produce image representations that better match those implied by human and primate neural data. However, whether these models produce representations of action sequences that support recognition across complex transformations and closely follow neural representations of actions remains unknown. Here we show that spatiotemporal CNNs accurately categorize video stimuli into action classes, and that deliberate model modifications that improve performance on an invariant action recognition task lead to data representations that better match human neural recordings. Our results support our hypothesis that performance on invariant discrimination dictates the neural representations of actions computed in the brain. These results broaden the scope of the invariant recognition framework for understanding visual intelligence from perception of inanimate objects and faces in static images to the study of human perception of action sequences.
Invariant recognition drives neural representations of action sequences.
Tacchetti, Andrea; Isik, Leyla; Poggio, Tomaso
2017-12-01
Recognizing the actions of others from visual stimuli is a crucial aspect of human perception that allows individuals to respond to social cues. Humans are able to discriminate between similar actions despite transformations, like changes in viewpoint or actor, that substantially alter the visual appearance of a scene. This ability to generalize across complex transformations is a hallmark of human visual intelligence. Advances in understanding action recognition at the neural level have not always translated into precise accounts of the computational principles underlying what representations of action sequences are constructed by human visual cortex. Here we test the hypothesis that invariant action discrimination might fill this gap. Recently, the study of artificial systems for static object perception has produced models, Convolutional Neural Networks (CNNs), that achieve human level performance in complex discriminative tasks. Within this class, architectures that better support invariant object recognition also produce image representations that better match those implied by human and primate neural data. However, whether these models produce representations of action sequences that support recognition across complex transformations and closely follow neural representations of actions remains unknown. Here we show that spatiotemporal CNNs accurately categorize video stimuli into action classes, and that deliberate model modifications that improve performance on an invariant action recognition task lead to data representations that better match human neural recordings. Our results support our hypothesis that performance on invariant discrimination dictates the neural representations of actions computed in the brain. These results broaden the scope of the invariant recognition framework for understanding visual intelligence from perception of inanimate objects and faces in static images to the study of human perception of action sequences.
Invariant Classification of Gait Types
DEFF Research Database (Denmark)
Fihl, Preben; Moeslund, Thomas B.
2008-01-01
This paper presents a method of classifying human gait in an invariant manner based on silhouette comparison. A database of artificially generated silhouettes is created representing the three main types of gait, i.e. walking, jogging, and running. Silhouettes generated from different camera angles....... Input silhouettes are matched to the database using the Hungarian method. A classifier is defined based on the dissimilarity between the input silhouettes and the gait actions of the database. The overall recognition rate is 88.2% on a large and diverse test set. The recognition rate is better than...
Quantum Weyl invariance and cosmology
Energy Technology Data Exchange (ETDEWEB)
Dabholkar, Atish, E-mail: atish@ictp.it [International Centre for Theoretical Physics, ICTP-UNESCO, Strada Costiera 11, Trieste 34151 (Italy); Sorbonne Universités, UPMC Univ Paris 06, CNRS UMR 7589, LPTHE, F-75005, Paris (France)
2016-09-10
Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly decaying vacuum energy. A natural generalization to four dimensions implies a quantum modification of Einstein field equations at long distances. It offers a new perspective on time-dependence of couplings and naturalness with potentially far-reaching consequences for the cosmological constant problem, inflation, and dark energy.
Invariant metrics for Hamiltonian systems
International Nuclear Information System (INIS)
Rangarajan, G.; Dragt, A.J.; Neri, F.
1991-05-01
In this paper, invariant metrics are constructed for Hamiltonian systems. These metrics give rise to norms on the space of homeogeneous polynomials of phase-space variables. For an accelerator lattice described by a Hamiltonian, these norms characterize the nonlinear content of the lattice. Therefore, the performance of the lattice can be improved by minimizing the norm as a function of parameters describing the beam-line elements in the lattice. A four-fold increase in the dynamic aperture of a model FODO cell is obtained using this procedure. 7 refs
Tensor network methods for invariant theory
Biamonte, Jacob; Bergholm, Ville; Lanzagorta, Marco
2013-11-01
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical approach provides an alternative to the polynomial equations that describe invariants, which often contain a large number of terms with coefficients raised to high powers. This approach also enables one to use known methods from tensor network theory (such as the matrix product state (MPS) factorization) when studying polynomial invariants. As our main example, we consider invariants of MPSs. We generate a family of tensor contractions resulting in a complete set of local unitary invariants that can be used to express the Rényi entropies. We find that the graphical approach to representing invariants can provide structural insight into the invariants being contracted, as well as an alternative, and sometimes much simpler, means to study polynomial invariants of quantum states. In addition, many tensor network methods, such as MPSs, contain excellent tools that can be applied in the study of invariants.
Numerical continuation of normally hyperbolic invariant manifolds
Broer, H. W.; Hagen, A.; Vegter, G.
2007-06-01
This paper deals with the numerical continuation of invariant manifolds regardless of the restricted dynamics. Common examples of such manifolds include limit sets, codimension 1 manifolds separating basins of attraction (separatrices), stable/unstable/centre manifolds, nested hierarchies of attracting manifolds in dissipative systems and manifolds appearing in bifurcations. The approach is based on the general principle of normal hyperbolicity, where the graph transform leads to the numerical algorithms. This gives a highly multiple purpose method. The graph transform and linear graph transform compute the perturbed manifold with its hyperbolic splitting. To globally discretize manifolds, a discrete tubular neighbourhood is used, induced by a transverse bundle composed of discrete stable and unstable bundles. This approach allows the development of the discrete graph transform/linear graph transform analogous to the usual smooth case. Convergence results are given. The discrete vector bundle construction and associated local k-plane interpolation may be of independent interest. A practical numerical implementation for solving the global equations underlying the graph transform is proposed. Relevant numerical techniques are discussed and computational tests included. An additional application is the computation of the 'slow-transient' surface of an enzyme reaction.
The four variational principles of mechanics
International Nuclear Information System (INIS)
Gray, C.G.; Karl, G.; Novikov, V.A.
1996-01-01
We argue that there are four basic forms of the variational principles of mechanics: Hamilton close-quote s least action principle (HP), the generalized Maupertuis principle (MP), and their two reciprocal principles, RHP and RMP. This set is invariant under reciprocity and Legendre transformations. One of these forms (HP) is in the literature: only special cases of the other three are known. The generalized MP has a weaker constraint compared to the traditional formulation, only the mean energy bar E is kept fixed between virtual paths. This reformulation of MP alleviates several weaknesses of the old version. The reciprocal Maupertuis principle (RMP) is the classical limit of Schroedinger close-quote s variational principle of quantum mechanics, and this connection emphasizes the importance of the reciprocity transformation for variational principles. Two unconstrained formulations (UHP and UMP) of these four principles are also proposed, with completely specified Lagrange multipliers Percival close-quote s variational principle for invariant tori and variational principles for scattering orbits are derived from the RMP. The RMP is very convenient for approximate variational solutions to problems in mechanics using Ritz type methods Examples are provided. Copyright copyright 1996 Academic Press, Inc
Limit Cycles and Conformal Invariance
Fortin, Jean-Francois; Stergiou, Andreas
2013-01-01
There is a widely held belief that conformal field theories (CFTs) require zero beta functions. Nevertheless, the work of Jack and Osborn implies that the beta functions are not actually the quantites that decide conformality, but until recently no such behavior had been exhibited. Our recent work has led to the discovery of CFTs with nonzero beta functions, more precisely CFTs that live on recurrent trajectories, e.g., limit cycles, of the beta-function vector field. To demonstrate this we study the S function of Jack and Osborn. We use Weyl consistency conditions to show that it vanishes at fixed points and agrees with the generator Q of limit cycles on them. Moreover, we compute S to third order in perturbation theory, and explicitly verify that it agrees with our previous determinations of Q. A byproduct of our analysis is that, in perturbation theory, unitarity and scale invariance imply conformal invariance in four-dimensional quantum field theories. Finally, we study some properties of these new, "cycl...
Remark on shape invariant potential
International Nuclear Information System (INIS)
Drigo Filho, Elso; Ricotta, Regina Maria
1997-01-01
For more than a decade, Supersymmetry has provided new information about ordinary quantum mechanical problems, and Supersymmetric Quantum Mechanics has become a field research by itself. If has been shown that the symmetry between two different systems that share energy spectra can be interpreted in terms of supersymmetry. From the knowledge of the ground state of a given potential it is possible to find another potential with the same energy spectrum, except for the ground state. In fact, from the use of supersymmetric partner Hamiltonians and their degeneracy spectra it has become possible to determine a ladder of Hamiltonians and their spectra, only through the ground states of the ladder. Concerning the partner Hamiltonians with potentials V + and V - that are similar in shape but Differ in the parameters. Gedenshtein introduced in 1983 the concept of shape invariance. Here we propose an extension of this concept. It is formulated in terms of the functional form of the whole super-family and not only between any two members of the ladder. We give two examples where all the members of the super-family can be written in a general functional form and conclude that Gedenshtein's conditions of shape invariance is sufficient but not necessary in order to obtain the super-family. (author)
Scale-invariant gravity: geometrodynamics
International Nuclear Information System (INIS)
Anderson, Edward; Barbour, Julian; Foster, Brendan; Murchadha, Niall O
2003-01-01
We present a scale-invariant theory, conformal gravity, which closely resembles the geometrodynamical formulation of general relativity (GR). While previous attempts to create scale-invariant theories of gravity have been based on Weyl's idea of a compensating field, our direct approach dispenses with this and is built by extension of the method of best matching w.r.t. scaling developed in the parallel particle dynamics paper by one of the authors. In spatially compact GR, there is an infinity of degrees of freedom that describe the shape of 3-space which interact with a single volume degree of freedom. In conformal gravity, the shape degrees of freedom remain, but the volume is no longer a dynamical variable. Further theories and formulations related to GR and conformal gravity are presented. Conformal gravity is successfully coupled to scalars and the gauge fields of nature. It should describe the solar system observations as well as GR does, but its cosmology and quantization will be completely different
Wilson loop invariants from WN conformal blocks
Directory of Open Access Journals (Sweden)
Oleg Alekseev
2015-12-01
Full Text Available Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern–Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate crossing and braiding matrices for WN conformal blocks with one component in the fundamental representation and another component in a rectangular representation of SU(N, which can be used to obtain HOMFLY knot and link invariants for these cases. We also discuss how our approach can be generalized to invariants in higher-representations of WN algebra.
Scale invariance in road networks.
Kalapala, Vamsi; Sanwalani, Vishal; Clauset, Aaron; Moore, Cristopher
2006-02-01
We study the topological and geographic structure of the national road networks of the United States, England, and Denmark. By transforming these networks into their dual representation, where roads are vertices and an edge connects two vertices if the corresponding roads ever intersect, we show that they exhibit both topological and geographic scale invariance. That is, we show that for sufficiently large geographic areas, the dual degree distribution follows a power law with exponent 2.2< or = alpha < or =2.4, and that journeys, regardless of their length, have a largely identical structure. To explain these properties, we introduce and analyze a simple fractal model of road placement that reproduces the observed structure, and suggests a testable connection between the scaling exponent and the fractal dimensions governing the placement of roads and intersections.
Invariants of DNA genomic signals
Cristea, Paul Dan A.
2005-02-01
For large scale analysis purposes, the conversion of genomic sequences into digital signals opens the possibility to use powerful signal processing methods for handling genomic information. The study of complex genomic signals reveals large scale features, maintained over the scale of whole chromosomes, that would be difficult to find by using only the symbolic representation. Based on genomic signal methods and on statistical techniques, the paper defines parameters of DNA sequences which are invariant to transformations induced by SNPs, splicing or crossover. Re-orienting concatenated coding regions in the same direction, regularities shared by the genomic material in all exons are revealed, pointing towards the hypothesis of a regular ancestral structure from which the current chromosome structures have evolved. This property is not found in non-nuclear genomic material, e.g., plasmids.
Local invariance via comparison functions
Directory of Open Access Journals (Sweden)
Ovidiu Carja
2004-04-01
Full Text Available We consider the ordinary differential equation $u'(t=f(t,u(t$, where $f:[a,b]imes Do mathbb{R}^n$ is a given function, while $D$ is an open subset in $mathbb{R}^n$. We prove that, if $Ksubset D$ is locally closed and there exists a comparison function $omega:[a,b]imesmathbb{R}_+o mathbb{R}$ such that $$ liminf_{hdownarrow 0}frac{1}{h}ig[d(xi+hf(t,xi;K-d(xi;Kig] leqomega(t,d(xi;K $$ for each $(t,xiin [a,b]imes D$, then $K$ is locally invariant with respect to $f$. We show further that, under some natural extra condition, the converse statement is also true.
Asymptotic invariants of homotopy groups
Manin, Fedor
We study the homotopy groups of a finite CW complex X via constraints on the geometry of representatives of their elements. For example, one can measure the "size" of alpha ∈ pi n (X) by the optimal Lipschitz constant or volume of a representative. By comparing the geometrical structure thus obtained with the algebraic structure of the group, one can define functions such as growth and distortion in pin(X), analogously to the way that such functions are studied in asymptotic geometric group theory. We provide a number of examples and techniques for studying these invariants, with a special focus on spaces with few rational homotopy groups. Our main theorem characterizes those X in which all non-torsion homotopy classes are undistorted, that is, their volume distortion functions, and hence also their Lipschitz distortion functions, are linear.
Scale-invariant extended inflation
International Nuclear Information System (INIS)
Holman, R.; Kolb, E.W.; Vadas, S.L.; Wang, Y.
1991-01-01
We propose a model of extended inflation which makes use of the nonlinear realization of scale invariance involving the dilaton coupled to an inflaton field whose potential admits a metastable ground state. The resulting theory resembles the Jordan-Brans-Dicke version of extended inflation. However, quantum effects, in the form of the conformal anomaly, generate a mass for the dilaton, thus allowing our model to evade the problems of the original version of extended inflation. We show that extended inflation can occur for a wide range of inflaton potentials with no fine-tuning of dimensionless parameters required. Furthermore, we also find that it is quite natural for the extended-inflation period to be followed by an epoch of slow-rollover inflation as the dilaton settles down to the minimum of its induced potential
Negation switching invariant signed graphs
Directory of Open Access Journals (Sweden)
Deepa Sinha
2014-04-01
Full Text Available A signed graph (or, $sigraph$ in short is a graph G in which each edge x carries a value $\\sigma(x \\in \\{-, +\\}$ called its sign. Given a sigraph S, the negation $\\eta(S$ of the sigraph S is a sigraph obtained from S by reversing the sign of every edge of S. Two sigraphs $S_{1}$ and $S_{2}$ on the same underlying graph are switching equivalent if it is possible to assign signs `+' (`plus' or `-' (`minus' to vertices of $S_{1}$ such that by reversing the sign of each of its edges that has received opposite signs at its ends, one obtains $S_{2}$. In this paper, we characterize sigraphs which are negation switching invariant and also see for what sigraphs, S and $\\eta (S$ are signed isomorphic.
Graudenz, Dirk
1996-01-01
We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an infinite-dimensional vector bundle over the space-time manifold. The time evolution equation and the dynamical equations for the matter fields are invariant under an arbitrary local change of frames along the restriction of the bundle to the worldline of an observer, thus implementing a ``quantum gauge principle''. We derive dynamical equations for the connection and a complex scalar quantum field based on a gauge field action. In the limit of vanishing curvature of the vector bundle, we recover the standard equation of motion of a scalar field in a curved background space-time.
Spontaneously broken abelian gauge invariant supersymmetric model
International Nuclear Information System (INIS)
Mainland, G.B.; Tanaka, K.
A model is presented that is invariant under an Abelian gauge transformation and a modified supersymmetry transformation. This model is broken spontaneously, and the interplay between symmetry breaking, Goldstone particles, and mass breaking is studied. In the present model, spontaneously breaking the Abelian symmetry of the vacuum restores the invariance of the vacuum under a modified supersymmetry transformation. (U.S.)
Invariant subsets under compact quantum group actions
Huang, Huichi
2012-01-01
We investigate compact quantum group actions on unital $C^*$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact metrizable spaces with infinitely many points are not quantum homogeneous spaces.
Scale invariant Volkov–Akulov supergravity
Directory of Open Access Journals (Sweden)
S. Ferrara
2015-10-01
Full Text Available A scale invariant goldstino theory coupled to supergravity is obtained as a standard supergravity dual of a rigidly scale-invariant higher-curvature supergravity with a nilpotent chiral scalar curvature. The bosonic part of this theory describes a massless scalaron and a massive axion in a de Sitter Universe.
Superfield approach to symmetry invariance in quantum ...
Indian Academy of Sciences (India)
invariance for the Abelian and non-Abelian 1-form gauge theories where there is an explicit coupling between the 1-form gauge fields and the Dirac fields. It has been established, in the above works [26–28], that the (anti-)BRST invariance of the 4D Lagrangian densities is encoded in the Grassmannian independence of ...
Real object recognition using moment invariants
Indian Academy of Sciences (India)
contour-based shape descriptors and region-based shape descriptors (Kim & Sung 2000). Regular moment invariants are one of the most popular and widely used contour-based shape descriptors is a set of derived by Hu (1962). These geometrical moment invariants have been then extended to larger sets by Wong & Siu ...
Gromov–Witten invariants and quantum cohomology
Indian Academy of Sciences (India)
no local invariant in symplectic geometry, like, for example, the curvature in Riemannian geometry. The only possible invariants have to be global. The Darboux ..... that earlier Donaldson [D] used similar arguments for the orientation of Yang–Mills moduli spaces. Part (b) uses an infinite dimensional version of Sard–Smale ...
A test for ordinal measurement invariance
Ligtvoet, R.; Millsap, R.E.; Bolt, D.M.; van der Ark, L.A.; Wang, W.-C.
2015-01-01
One problem with the analysis of measurement invariance is the reliance of the analysis on having a parametric model that accurately describes the data. In this paper an ordinal version of the property of measurement invariance is proposed, which relies only on nonparametric restrictions. This
Constructing Invariant Fairness Measures for Surfaces
DEFF Research Database (Denmark)
Gravesen, Jens; Ungstrup, Michael
1998-01-01
This paper presents a general method which from an invariant curve fairness measure constructs an invariant surface fairness measure. Besides the curve fairness measure one only needs a class of curves on the surface for which one wants to apply the curve measure. The surface measure at a point...... variation.The method is extended to the case where one considers, not the fairness of one curve, but the fairness of a one parameter family of curves. Such a family is generated by the flow of a vector field, orthogonal to the curves. The first, respectively the second order derivative along the curve...... of the size of this vector field is used as the fairness measure on the family.Six basic 3rd order invariants satisfying two quadratic equations are defined. They form a complete set in the sense that any invariant 3rd order function can be written as a function of the six basic invariants together...
The usage of color invariance in SURF
Meng, Gang; Jiang, Zhiguo; Zhao, Danpei
2009-10-01
SURF (Scale Invariant Feature Transform) is a robust local invariant feature descriptor. However, SURF is mainly designed for gray images. In order to make use of the information provided by color (mainly RGB channels), this paper presents a novel colored local invariant feature descriptor, CISURF (Color Invariance based SURF). The proposed approach builds the descriptors in a color invariant space, which stems from Kubelka-Munk model and provides more valuable information than the gray space. Compared with the conventional SURF and SIFT descriptors, the experimental results show that descriptors created by CISURF is more robust to the circumstance changes such as the illumination direction, illumination intensity, and the viewpoints, and are more suitable for the deep space background objects.
Scale invariant transfer matrices and Hamiltionians
Jones, Vaughan F. R.
2018-03-01
Given a direct system of Hilbert spaces s\\mapsto {\\mathcal H}s (with isometric inclusion maps \\iota_s^t:{\\mathcal H}_s→ {\\mathcal H}t for s≤slant t ) corresponding to quantum systems on scales s, we define notions of scale invariant and weakly scale invariant operators. In some cases of quantum spin chains we find conditions for transfer matrices and nearest neighbour Hamiltonians to be scale invariant or weakly so. Scale invariance forces spatial inhomogeneity of the spectral parameter. But weakly scale invariant transfer matrices may be spatially homogeneous in which case the change of spectral parameter from one scale to another is governed by a classical dynamical system exhibiting fractal behaviour.
Three invariant Hi-C interaction patterns: applications to genome assembly.
Oddes, Sivan; Zelig, Aviv; Kaplan, Noam
2018-04-20
Assembly of reference-quality genomes from next-generation sequencing data is a key challenge in genomics. Recently, we and others have shown that Hi-C data can be used to address several outstanding challenges in the field of genome assembly. This principle has since been developed in academia and industry, and has been used in the assembly of several major genomes. In this paper, we explore the central principles underlying Hi-C-based assembly approaches, by quantitatively defining and characterizing three invariant Hi-C interaction patterns on which these approaches can build: Intrachromosomal interaction enrichment, distance-dependent interaction decay and local interaction smoothness. Specifically, we evaluate to what degree each invariant pattern holds on a single locus level in different species, cell types and Hi-C map resolutions. We find that these patterns are generally consistent across species and cell types but are affected by sequencing depth, and that matrix balancing improves consistency of loci with all three invariant patterns. Finally, we overview current Hi-C-based assembly approaches in light of these invariant patterns and demonstrate how local interaction smoothness can be used to easily detect scaffolding errors in extremely sparse Hi-C maps. We suggest that simultaneously considering all three invariant patterns may lead to better Hi-C-based genome assembly methods. Copyright © 2018 Elsevier Inc. All rights reserved.
Rotational Invariant Dimensionality Reduction Algorithms.
Lai, Zhihui; Xu, Yong; Yang, Jian; Shen, Linlin; Zhang, David
2017-11-01
A common intrinsic limitation of the traditional subspace learning methods is the sensitivity to the outliers and the image variations of the object since they use the norm as the metric. In this paper, a series of methods based on the -norm are proposed for linear dimensionality reduction. Since the -norm based objective function is robust to the image variations, the proposed algorithms can perform robust image feature extraction for classification. We use different ideas to design different algorithms and obtain a unified rotational invariant (RI) dimensionality reduction framework, which extends the well-known graph embedding algorithm framework to a more generalized form. We provide the comprehensive analyses to show the essential properties of the proposed algorithm framework. This paper indicates that the optimization problems have global optimal solutions when all the orthogonal projections of the data space are computed and used. Experimental results on popular image datasets indicate that the proposed RI dimensionality reduction algorithms can obtain competitive performance compared with the previous norm based subspace learning algorithms.
Stereo Correspondence Using Moment Invariants
Premaratne, Prashan; Safaei, Farzad
Autonomous navigation is seen as a vital tool in harnessing the enormous potential of Unmanned Aerial Vehicles (UAV) and small robotic vehicles for both military and civilian use. Even though, laser based scanning solutions for Simultaneous Location And Mapping (SLAM) is considered as the most reliable for depth estimation, they are not feasible for use in UAV and land-based small vehicles due to their physical size and weight. Stereovision is considered as the best approach for any autonomous navigation solution as stereo rigs are considered to be lightweight and inexpensive. However, stereoscopy which estimates the depth information through pairs of stereo images can still be computationally expensive and unreliable. This is mainly due to some of the algorithms used in successful stereovision solutions require high computational requirements that cannot be met by small robotic vehicles. In our research, we implement a feature-based stereovision solution using moment invariants as a metric to find corresponding regions in image pairs that will reduce the computational complexity and improve the accuracy of the disparity measures that will be significant for the use in UAVs and in small robotic vehicles.
A scale invariance criterion for LES parametrizations
Directory of Open Access Journals (Sweden)
Urs Schaefer-Rolffs
2015-01-01
Full Text Available Turbulent kinetic energy cascades in fluid dynamical systems are usually characterized by scale invariance. However, representations of subgrid scales in large eddy simulations do not necessarily fulfill this constraint. So far, scale invariance has been considered in the context of isotropic, incompressible, and three-dimensional turbulence. In the present paper, the theory is extended to compressible flows that obey the hydrostatic approximation, as well as to corresponding subgrid-scale parametrizations. A criterion is presented to check if the symmetries of the governing equations are correctly translated into the equations used in numerical models. By applying scaling transformations to the model equations, relations between the scaling factors are obtained by demanding that the mathematical structure of the equations does not change.The criterion is validated by recovering the breakdown of scale invariance in the classical Smagorinsky model and confirming scale invariance for the Dynamic Smagorinsky Model. The criterion also shows that the compressible continuity equation is intrinsically scale-invariant. The criterion also proves that a scale-invariant turbulent kinetic energy equation or a scale-invariant equation of motion for a passive tracer is obtained only with a dynamic mixing length. For large-scale atmospheric flows governed by the hydrostatic balance the energy cascade is due to horizontal advection and the vertical length scale exhibits a scaling behaviour that is different from that derived for horizontal length scales.
Feedback-Driven Dynamic Invariant Discovery
Zhang, Lingming; Yang, Guowei; Rungta, Neha S.; Person, Suzette; Khurshid, Sarfraz
2014-01-01
Program invariants can help software developers identify program properties that must be preserved as the software evolves, however, formulating correct invariants can be challenging. In this work, we introduce iDiscovery, a technique which leverages symbolic execution to improve the quality of dynamically discovered invariants computed by Daikon. Candidate invariants generated by Daikon are synthesized into assertions and instrumented onto the program. The instrumented code is executed symbolically to generate new test cases that are fed back to Daikon to help further re ne the set of candidate invariants. This feedback loop is executed until a x-point is reached. To mitigate the cost of symbolic execution, we present optimizations to prune the symbolic state space and to reduce the complexity of the generated path conditions. We also leverage recent advances in constraint solution reuse techniques to avoid computing results for the same constraints across iterations. Experimental results show that iDiscovery converges to a set of higher quality invariants compared to the initial set of candidate invariants in a small number of iterations.
Principle or constructive relativity
Frisch, Mathias
Appealing to Albert Einstein's distinction between principle and constructive theories, Harvey Brown has argued for an interpretation of the theory of relativity as a dynamic and constructive theory. Brown's view has been challenged by Michel Janssen and in this paper I investigate their dispute. I argue that their disagreement appears larger than it actually is due to the two frameworks used by Brown and Janssen to express their respective views: Brown's appeal to Einstein's principle-constructive distinction and Janssen's framing of the disagreement as one over the question whether relativity provides a kinematic or a dynamic constraint. I appeal to a distinction between types of theories drawn by H. A. Lorentz two decades before Einstein's distinction to argue that Einstein's distinction represents a false dichotomy. I argue further that the disagreement concerning the kinematics-dynamics distinction is a disagreement about labels but not about substance. There remains a genuine disagreement over the explanatory role of spacetime geometry and here I agree with Brown arguing that Janssen sees a pressing need for an explanation of Lorentz invariance where no further explanation is needed.
Gromov–Witten invariants and localization
International Nuclear Information System (INIS)
Morrison, David R
2017-01-01
We give a pedagogical review of the computation of Gromov–Witten invariants via localization in 2D gauged linear sigma models. We explain the relationship between the two-sphere partition function of the theory and the Kähler potential on the conformal manifold. We show how the Kähler potential can be assembled from classical, perturbative, and non-perturbative contributions, and explain how the non-perturbative contributions are related to the Gromov–Witten invariants of the corresponding Calabi–Yau manifold. We then explain how localization enables efficient calculation of the two-sphere partition function and, ultimately, the Gromov–Witten invariants themselves. (topical review)
Topological excitations in U(1) -invariant theories
International Nuclear Information System (INIS)
Savit, R.
1977-01-01
A class of U(1) -invariant theories in d dimensions is introduced on a lattice. These theories are labeled by a simplex number s, with 1 < or = s < d. The case with s = 1 is the X-Y model; and s = 2 gives compact photodynamics. An exact duality transformation is applied to show that the U(1) -invariant theory in d dimensions with simplex number s is the same as a similar theory in d dimensions but which is Z /sub infinity/-invariant and has simplex number s = d-s. This dual theory describes the topological excitations of the original theory. These excitations are of dimension s - 1
Comment on ``Pairing interaction and Galilei invariance''
Arias, J. M.; Gallardo, M.; Gómez-Camacho, J.
1999-05-01
A recent article by Dussel, Sofia, and Tonina studies the relation between Galilei invariance and dipole energy weighted sum rule (EWSR). The authors find that the pairing interaction, which is neither Galilei nor Lorentz invariant, produces big changes in the EWSR and in effective masses of the nucleons. They argue that these effects of the pairing force could be realistic. In this Comment we stress the validity of Galilei invariance to a very good approximation in this context of low-energy nuclear physics and show that the effective masses and the observed change in the EWSR for the electric dipole operator relative to its classical value are compatible with this symmetry.
Simultaneity as an Invariant Equivalence Relation
Mamone-Capria, Marco
2012-11-01
This paper deals with the concept of simultaneity in classical and relativistic physics as construed in terms of group-invariant equivalence relations. A full examination of Newton, Galilei and Poincaré invariant equivalence relations in ℝ4 is presented, which provides alternative proofs, additions and occasionally corrections of results in the literature, including Malament's theorem and some of its variants. It is argued that the interpretation of simultaneity as an invariant equivalence relation, although interesting for its own sake, does not cut in the debate concerning the conventionality of simultaneity in special relativity.
Multiperiod Maximum Loss is time unit invariant.
Kovacevic, Raimund M; Breuer, Thomas
2016-01-01
Time unit invariance is introduced as an additional requirement for multiperiod risk measures: for a constant portfolio under an i.i.d. risk factor process, the multiperiod risk should equal the one period risk of the aggregated loss, for an appropriate choice of parameters and independent of the portfolio and its distribution. Multiperiod Maximum Loss over a sequence of Kullback-Leibler balls is time unit invariant. This is also the case for the entropic risk measure. On the other hand, multiperiod Value at Risk and multiperiod Expected Shortfall are not time unit invariant.
Physical Consequences of Mathematical Principles
Directory of Open Access Journals (Sweden)
Comay E.
2009-10-01
Full Text Available Physical consequences are derived from the following mathematical structures: the variational principle, Wigner’s classifications of the irreducible representations of the Poincar ́ e group and the duality invariance of the homogeneous Maxwell equations. The analysis is carried out within the validity domain of special relativity. Hierarchical re- lations between physical theories are used. Some new results are pointed out together with their comparison with experimental data. It is also predicted that a genuine Higgs particle will not be detected.
Invariant Measures of Genetic Recombination Processes
Akopyan, Arseniy V.; Pirogov, Sergey A.; Rybko, Aleksandr N.
2015-07-01
We construct a non-linear Markov process connected with a biological model of a bacterial genome recombination. The description of invariant measures of this process gives us the solution of one problem in elementary probability theory.
Ermakov–Lewis invariants and Reid systems
International Nuclear Information System (INIS)
Mancas, Stefan C.; Rosu, Haret C.
2014-01-01
Reid's mth-order generalized Ermakov systems of nonlinear coupling constant α are equivalent to an integrable Emden–Fowler equation. The standard Ermakov–Lewis invariant is discussed from this perspective, and a closed formula for the invariant is obtained for the higher-order Reid systems (m≥3). We also discuss the parametric solutions of these systems of equations through the integration of the Emden–Fowler equation and present an example of a dynamical system for which the invariant is equivalent to the total energy. - Highlights: • Reid systems of order m are connected to Emden–Fowler equations. • General expressions for the Ermakov–Lewis invariants both for m=2 and m≥3 are obtained. • Parametric solutions of the Emden–Fowler equations related to Reid systems are obtained
Borromean surgery formula for the Casson invariant
DEFF Research Database (Denmark)
Meilhan, Jean-Baptiste Odet Thierry
2008-01-01
It is known that every oriented integral homology 3-sphere can be obtained from S3 by a finite sequence of Borromean surgeries. We give an explicit formula for the variation of the Casson invariant under such a surgery move. The formula involves simple classical invariants, namely the framing, li......, linking number and Milnor's triple linking number. A more general statement, for n independent Borromean surgeries, is also provided.......It is known that every oriented integral homology 3-sphere can be obtained from S3 by a finite sequence of Borromean surgeries. We give an explicit formula for the variation of the Casson invariant under such a surgery move. The formula involves simple classical invariants, namely the framing...
Ermakov–Lewis invariants and Reid systems
Energy Technology Data Exchange (ETDEWEB)
Mancas, Stefan C., E-mail: stefan.mancas@erau.edu [Department of Mathematics, Embry-Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Camino a la presa San José 2055, Col. Lomas 4a Sección, 78216 San Luis Potosí, S.L.P. (Mexico)
2014-06-13
Reid's mth-order generalized Ermakov systems of nonlinear coupling constant α are equivalent to an integrable Emden–Fowler equation. The standard Ermakov–Lewis invariant is discussed from this perspective, and a closed formula for the invariant is obtained for the higher-order Reid systems (m≥3). We also discuss the parametric solutions of these systems of equations through the integration of the Emden–Fowler equation and present an example of a dynamical system for which the invariant is equivalent to the total energy. - Highlights: • Reid systems of order m are connected to Emden–Fowler equations. • General expressions for the Ermakov–Lewis invariants both for m=2 and m≥3 are obtained. • Parametric solutions of the Emden–Fowler equations related to Reid systems are obtained.
Modified dispersion relations, inflation, and scale invariance
Bianco, Stefano; Friedhoff, Victor Nicolai; Wilson-Ewing, Edward
2018-02-01
For a certain type of modified dispersion relations, the vacuum quantum state for very short wavelength cosmological perturbations is scale-invariant and it has been suggested that this may be the source of the scale-invariance observed in the temperature anisotropies in the cosmic microwave background. We point out that for this scenario to be possible, it is necessary to redshift these short wavelength modes to cosmological scales in such a way that the scale-invariance is not lost. This requires nontrivial background dynamics before the onset of standard radiation-dominated cosmology; we demonstrate that one possible solution is inflation with a sufficiently large Hubble rate, for this slow roll is not necessary. In addition, we also show that if the slow-roll condition is added to inflation with a large Hubble rate, then for any power law modified dispersion relation quantum vacuum fluctuations become nearly scale-invariant when they exit the Hubble radius.
Moiseiwitsch, B L
2004-01-01
This graduate-level text's primary objective is to demonstrate the expression of the equations of the various branches of mathematical physics in the succinct and elegant form of variational principles (and thereby illuminate their interrelationship). Its related intentions are to show how variational principles may be employed to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities (such as the phase shifts) that arise in the theory of scattering. Chapter-by-chapter treatment consists of analytical dynamics; optics, wave mecha
Is quantum entanglement invariant in special relativity?
Ahn, D.; Lee, H. J.; Hwang, S. W.; Kim, M. S.
2003-01-01
Quantum entanglements are of fundamental importance in quantum physics ranging from the quantum information processing to the physics of black hole. Here, we show that the quantum entanglement is not invariant in special relativity. This suggests that nearly all aspects of quantum information processing would be affected significantly when relativistic effects are considered because present schemes are based on the general assumption that entanglement is invariant. There should be additional ...
Computer calculation of Witten's 3-manifold invariant
International Nuclear Information System (INIS)
Freed, D.S.; Gompf, R.E.
1991-01-01
Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant. (orig.)
Indian Academy of Sciences (India)
that allows one to write down the laws of motion and arrive at the concept of inertia is somehow intimately re- lated to the background of distant parts of the universe. This argument is known as `Mach's principle' and we will analyse its implications further. When expressed in the framework of the absolute space,. Newton's ...
Directory of Open Access Journals (Sweden)
V. A. Grinenko
2011-06-01
Full Text Available The offered material in the article is picked up so that the reader could have a complete representation about concept “safety”, intrinsic characteristics and formalization possibilities. Principles and possible strategy of safety are considered. A material of the article is destined for the experts who are taking up the problems of safety.
Indian Academy of Sciences (India)
popularize science. The underlying idea in Mach's principle is that the origin of inertia or mass of a particle is a dynamical quantity determined by the environ- ... Knowing the latitude of the location of the pendulum it is possible to calculate the Earth's spin period. The two methods give the same answer. At first sight this does ...
Chern-Simons invariants on hyperbolic manifolds and topological quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Bonora, L. [International School for Advanced Studies (SISSA/ISAS), Trieste (Italy); INFN, Sezione di Trieste (Italy); Bytsenko, A.A.; Goncalves, A.E. [Universidade Estadual de Londrina, Departamento de Fisica, Londrina-Parana (Brazil)
2016-11-15
We derive formulas for the classical Chern-Simons invariant of irreducible SU(n)-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of the Labastida-Marino-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities. (orig.)
Learning optimized features for hierarchical models of invariant object recognition.
Wersing, Heiko; Körner, Edgar
2003-07-01
There is an ongoing debate over the capabilities of hierarchical neural feedforward architectures for performing real-world invariant object recognition. Although a variety of hierarchical models exists, appropriate supervised and unsupervised learning methods are still an issue of intense research. We propose a feedforward model for recognition that shares components like weight sharing, pooling stages, and competitive nonlinearities with earlier approaches but focuses on new methods for learning optimal feature-detecting cells in intermediate stages of the hierarchical network. We show that principles of sparse coding, which were previously mostly applied to the initial feature detection stages, can also be employed to obtain optimized intermediate complex features. We suggest a new approach to optimize the learning of sparse features under the constraints of a weight-sharing or convolutional architecture that uses pooling operations to achieve gradual invariance in the feature hierarchy. The approach explicitly enforces symmetry constraints like translation invariance on the feature set. This leads to a dimension reduction in the search space of optimal features and allows determining more efficiently the basis representatives, which achieve a sparse decomposition of the input. We analyze the quality of the learned feature representation by investigating the recognition performance of the resulting hierarchical network on object and face databases. We show that a hierarchy with features learned on a single object data set can also be applied to face recognition without parameter changes and is competitive with other recent machine learning recognition approaches. To investigate the effect of the interplay between sparse coding and processing nonlinearities, we also consider alternative feedforward pooling nonlinearities such as presynaptic maximum selection and sum-of-squares integration. The comparison shows that a combination of strong competitive
The avian egg exhibits general allometric invariances in mechanical design.
Juang, Jia-Yang; Chen, Pin-Yi; Yang, Da-Chang; Wu, Shang-Ping; Yen, An; Hsieh, Hsin-I
2017-10-27
The avian egg exhibits extraordinary diversity in size, shape and color, and has a key role in avian adaptive radiations. Despite extensive work, our understanding of the underlying principles that guide the "design" of the egg as a load-bearing structure remains incomplete, especially over broad taxonomic scales. Here we define a dimensionless number C, a function of egg weight, stiffness and dimensions, to quantify how stiff an egg is with respect to its weight after removing geometry-induced rigidity. We analyze eggs of 463 bird species in 36 orders across five orders of magnitude in body mass, and find that C number is nearly invariant for most species, including tiny hummingbirds and giant elephant birds. This invariance or "design guideline" dictates that evolutionary changes in shell thickness and Young's modulus, both contributing to shell stiffness, are constrained by changes in egg weight. Our analysis illuminates unique reproductive strategies of brood parasites, kiwis, and megapodes, and quantifies the loss of safety margin for contact incubation due to artificial selection and environmental toxins. Our approach provides a mechanistic framework for a better understanding of the mechanical design of the avian egg, and may provide clues to the evolutionary origin of contact incubation of amniote eggs.
Holography beyond conformal invariance and AdS isometry?
Barvinsky, A.O.
2015-01-01
We suggest that the principle of holographic duality can be extended beyond conformal invariance and AdS isometry. Such an extension is based on a special relation between functional determinants of the operators acting in the bulk and on its boundary, provided that the boundary operator represents the inverse propagators of the theory induced on the boundary by the Dirichlet boundary value problem from the bulk spacetime. This relation holds for operators of general spin-tensor structure on generic manifolds with boundaries irrespective of their background geometry and conformal invariance, and it apparently underlies numerous $O(N^0)$ tests of AdS/CFT correspondence, based on direct calculation of the bulk and boundary partition functions, Casimir energies and conformal anomalies. The generalized holographic duality is discussed within the concept of the "double-trace" deformation of the boundary theory, which is responsible in the case of large $N$ CFT coupled to the tower of higher spin gauge fields for t...
Scale Invariance in Lateral Head Scans During Spatial Exploration
Yadav, Chetan K.; Doreswamy, Yoganarasimha
2017-04-01
Universality connects various natural phenomena through physical principles governing their dynamics, and has provided broadly accepted answers to many complex questions, including information processing in neuronal systems. However, its significance in behavioral systems is still elusive. Lateral head scanning (LHS) behavior in rodents might contribute to spatial navigation by actively managing (optimizing) the available sensory information. Our findings of scale invariant distributions in LHS lifetimes, interevent intervals and event magnitudes, provide evidence for the first time that the optimization takes place at a critical point in LHS dynamics. We propose that the LHS behavior is responsible for preprocessing of the spatial information content, critical for subsequent foolproof encoding by the respective downstream neural networks.
On the Construction of a Geometric Invariant Measuring the Deviation from Kerr Data
Bäckdahl, Thomas; Valiente Kroon, Juan A.
2010-11-01
This article contains a detailed and rigorous proof of the construction of a geometric invariant for initial data sets for the Einstein vacuum field equations. This geometric invariant vanishes if and only if the initial data set corresponds to data for the Kerr spacetime, and thus, it characterises this type of data. The construction presented is valid for boosted and non-boosted initial data sets which are, in a sense, asymptotically Schwarzschildean. As a preliminary step to the construction of the geometric invariant, an analysis of a characterisation of the Kerr spacetime in terms of Killing spinors is carried out. A space spinor split of the (spacetime) Killing spinor equation is performed, to obtain a set of three conditions ensuring the existence of a Killing spinor of the development of the initial data set. In order to construct the geometric invariant, we introduce the notion of approximate Killing spinors. These spinors are symmetric valence 2 spinors intrinsic to the initial hypersurface and satisfy a certain second order elliptic equation ---the approximate Killing spinor equation. This equation arises as the Euler-Lagrange equation of a non-negative integral functional. This functional constitutes part of our geometric invariant ---however, the whole functional does not come from a variational principle. The asymptotic behaviour of solutions to the approximate Killing spinor equation is studied and an existence theorem is presented.
Change of adiabatic invariant near the separatrix
International Nuclear Information System (INIS)
Bulanov, S.V.
1995-10-01
The properties of particle motion in the vicinity of the separatrix in a phase plane are investigated. The change of adiabatic invariant value due to the separatrix crossing is evaluated as a function of a perturbation parameter magnitude and a phase of a particle for time dependent Hamiltonians. It is demonstrated that the change of adiabatic invariant value near the separatrix birth is much larger than that in the case of the separatrix crossing near the saddle point in a phase plane. The conditions of a stochastic regime to appear around the separatrix are found. The results are applied to study the longitudinal invariant behaviour of charged particles near singular lines of the magnetic field. (author). 22 refs, 9 figs
Spin foam diagrammatics and topological invariance
International Nuclear Information System (INIS)
Girelli, Florian; Oeckl, Robert; Perez, Alejandro
2002-01-01
We provide a simple proof of the topological invariance of the Turaev-Viro model (corresponding to simplicial 3D pure Euclidean gravity with cosmological constant) by means of a novel diagrammatic formulation of the state sum models for quantum BF theories. Moreover, we prove the invariance under more general conditions allowing the state sum to be defined on arbitrary cellular decompositions of the underlying manifold. Invariance is governed by a set of identities corresponding to local gluing and rearrangement of cells in the complex. Due to the fully algebraic nature of these identities our results extend to a vast class of quantum groups. The techniques introduced here could be relevant for investigating the scaling properties of non-topological state sums, proposed as models of quantum gravity in 4D, under refinement of the cellular decomposition
Blurred image recognition by legendre moment invariants
Zhang, Hui; Shu, Huazhong; Han, Guo-Niu; Coatrieux, Gouenou; Luo, Limin; Coatrieux, Jean-Louis
2010-01-01
Processing blurred images is a key problem in many image applications. Existing methods to obtain blur invariants which are invariant with respect to centrally symmetric blur are based on geometric moments or complex moments. In this paper, we propose a new method to construct a set of blur invariants using the orthogonal Legendre moments. Some important properties of Legendre moments for the blurred image are presented and proved. The performance of the proposed descriptors is evaluated with various point-spread functions and different image noises. The comparison of the present approach with previous methods in terms of pattern recognition accuracy is also provided. The experimental results show that the proposed descriptors are more robust to noise and have better discriminative power than the methods based on geometric or complex moments. PMID:19933003
Knot invariants and higher representation theory
Webster, Ben
2018-01-01
The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for \\mathfrak{sl}_2 and \\mathfrak{sl}_3 and by Mazorchuk-Stroppel and Sussan for \\mathfrak{sl}_n. The author's technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These are the representation categories of certain finite dimensional algebras with an explicit diagrammatic presentation, generalizing the cyclotomic quotient of the KLR algebra. When the Lie algebra under consideration is \\mathfrak{sl}_n, the author shows that these categories agree with certain subcategories of parabolic category \\mathcal{O} for \\mathfrak{gl}_k.
Differential invariants in nonclassical models of hydrodynamics
Bublik, Vasily V.
2017-10-01
In this paper, differential invariants are used to construct solutions for equations of the dynamics of a viscous heat-conducting gas and the dynamics of a viscous incompressible fluid modified by nanopowder inoculators. To describe the dynamics of a viscous heat-conducting gas, we use the complete system of Navier—Stokes equations with allowance for heat fluxes. Mathematical description of the dynamics of liquid metals under high-energy external influences (laser radiation or plasma flow) includes, in addition to the Navier—Stokes system of an incompressible viscous fluid, also heat fluxes and processes of nonequilibrium crystallization of a deformable fluid. Differentially invariant solutions are a generalization of partially invariant solutions, and their active study for various models of continuous medium mechanics is just beginning. Differentially invariant solutions can also be considered as solutions with differential constraints; therefore, when developing them, the approaches and methods developed by the science schools of academicians N. N. Yanenko and A. F. Sidorov will be actively used. In the construction of partially invariant and differentially invariant solutions, there are overdetermined systems of differential equations that require a compatibility analysis. The algorithms for reducing such systems to involution in a finite number of steps are described by Cartan, Finikov, Kuranishi, and other authors. However, the difficultly foreseeable volume of intermediate calculations complicates their practical application. Therefore, the methods of computer algebra are actively used here, which largely helps in solving this difficult problem. It is proposed to use the constructed exact solutions as tests for formulas, algorithms and their software implementations when developing and creating numerical methods and computational program complexes. This combination of effective numerical methods, capable of solving a wide class of problems, with
Wilkesman, Jeff; Kurz, Liliana
2017-01-01
Zymography, the detection, identification, and even quantification of enzyme activity fractionated by gel electrophoresis, has received increasing attention in the last years, as revealed by the number of articles published. A number of enzymes are routinely detected by zymography, especially with clinical interest. This introductory chapter reviews the major principles behind zymography. New advances of this method are basically focused towards two-dimensional zymography and transfer zymography as will be explained in the rest of the chapters. Some general considerations when performing the experiments are outlined as well as the major troubleshooting and safety issues necessary for correct development of the electrophoresis.
International Nuclear Information System (INIS)
Wilson, P.D.
1996-01-01
Some basic explanations are given of the principles underlying the nuclear fuel cycle, starting with the physics of atomic and nuclear structure and continuing with nuclear energy and reactors, fuel and waste management and finally a discussion of economics and the future. An important aspect of the fuel cycle concerns the possibility of ''closing the back end'' i.e. reprocessing the waste or unused fuel in order to re-use it in reactors of various kinds. The alternative, the ''oncethrough'' cycle, discards the discharged fuel completely. An interim measure involves the prolonged storage of highly radioactive waste fuel. (UK)
On the Einstein equivalence principle
International Nuclear Information System (INIS)
Gabriel, M.D.
1989-01-01
The Einstein equivalence principle, the cornerstone of our present day understanding of gravity, is used to explore a deeper connection between the deflection of starlight by a spinning object and the Lense-Thirring dragging of inertial frames. It is also noted that experiment has not established that the gravitomagnetic coupling to currents of particle rest-mass energy, to currents of electromagnetic energy, and to currents of all other types of energy are identical as predicted by the Einstein equivalence principle. The detailed analysis of how atomic physics experiments originated by Hughes and by Drever can constrain such possible violations of the Einstein equivalence principle is given. Atomic clocks are also important tools used to test local Lorentz invariance and hence one important aspect of Einstein equivalence principle. The sensitivity of atomic clocks to preferred-frame effects is studied here for the first time, and the behavior of the hydrogen-maser clocks of the Gravity Probe A experiment is analyzed to illustrate use of the techniques involved
The haling principle-true or false?
International Nuclear Information System (INIS)
Sun, S.X.; Kropaczek, D.J.; Turinsky, P.J.
1993-01-01
The Haling principle has long been viewed as an idealized control strategy for maximizing thermal margin over the operating cycle of a nuclear reactor core. In essence, the Haling principle states that the time-dependent power distribution that minimizes power peaking over the cycle is that power distribution which remains invariant throughout cycle. Applicable but not strictly limited to boiling water reactor (BWR) operation, maintaining a constant power Haling distribution through manipulation of control materials should, in theory, yield an optimum beyond which further reductions in thermal margin remain unachievable, given a particular arrangement of fuel inventory
Invariant distances and metrics in complex analysis
Jarnicki, Marek
2013-01-01
As in the field of ""Invariant Distances and Metrics in Complex Analysis"" there was and is a continuous progress this is the second extended edition of the corresponding monograph. This comprehensive book is about the study of invariant pseudodistances (non-negative functions on pairs of points) and pseudometrics (non-negative functions on the tangent bundle) in several complex variables. It is an overview over a highly active research area at the borderline between complex analysis, functional analysis and differential geometry. New chapters are covering the Wu, Bergman and several other met
The decomposition of global conformal invariants
Alexakis, Spyros
2012-01-01
This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. These functionals act on a metric by first constructing a Riemannian scalar out of it, and then integrating this scalar over the manifold. Suppose this integral remains invariant under conformal re-scalings of the underlying metric. What information can one then deduce about the Riemannian scalar? Dese
Application of invariant embedding to reactor physics
Shimizu, Akinao; Parsegian, V L
1972-01-01
Application of Invariant Embedding to Reactor Physics describes the application of the method of invariant embedding to radiation shielding and to criticality calculations of atomic reactors. The authors intend to show how this method has been applied to realistic problems, together with the results of applications which will be useful to shielding design. The book is organized into two parts. Part A deals with the reflection and transmission of gamma rays by slabs. The chapters in this section cover topics such as the reflection and transmission problem of gamma rays; formulation of the probl
Approaching Moons from Resonance via Invariant Manifolds
Anderson, Rodney L.
2012-01-01
In this work, the approach phase from the final resonance of the endgame scenario in a tour design is examined within the context of invariant manifolds. Previous analyses have typically solved this problem either by using numerical techniques or by computing a catalog of suitable trajectories. The invariant manifolds of a selected set of libration orbits and unstable resonant orbits are computed here to serve as guides for desirable approach trajectories. The analysis focuses on designing an approach phase that may be tied into the final resonance in the endgame sequence while also targeting desired conditions at the moon.
Conformal invariants topics in geometric function theory
Ahlfors, Lars V
2010-01-01
Most conformal invariants can be described in terms of extremal properties. Conformal invariants and extremal problems are therefore intimately linked and form together the central theme of this classic book which is primarily intended for students with approximately a year's background in complex variable theory. The book emphasizes the geometric approach as well as classical and semi-classical results which Lars Ahlfors felt every student of complex analysis should know before embarking on independent research. At the time of the book's original appearance, much of this material had never ap
Supersymmetric models with broken Lorentz invariance.
Directory of Open Access Journals (Sweden)
Marakulin Arthur
2017-01-01
Full Text Available Several supersymmetric theories with broken Lorentz invariance are considered. We study at the component level Lorentz violating representations of the supersymmetry algebra and construct Lagrangians for the scalar and vector supermultiplets with broken Lorentz invariance. Lorentz violating model for the gravitational supermultiplet is constructed using the superfield formalism as supersymmetric extension of the linearized Einstein-aether theory. The most general Lagrangian of the linearized Einstein-aether supergravity is constructed. We show that the Lagrangian for this model is unique and obtain its bosonic part in components. The constraints imposed by supersymmetry on the parameters of the theory are obtained. The phenomenological consequences of the model are discussed.
Perturbative string theory in BRST invariant formalism
International Nuclear Information System (INIS)
Di Vecchia, P.; Hornfeck, K.; Frau, M.; Lerda, A.
1988-01-01
In this talk we present a constructive and very explicit way of calculating multiloop amplitudes in string theories. The main ingredients are the BRST invariant N String Vertex and the BRST invariant twisted propagator. This approach naturally leads to the Schottky parametrization of moduli space in terms of multipliers and fixed points of the g projective transformations which characterize a Riemann surface of genus g. The complete expression (including measure) of the multiloop corrections to the N String Vertex for the bosonic string is exhibited. (orig.)
Lorentz invariance as a low energy phenomenon
International Nuclear Information System (INIS)
Chadha, S.
1982-09-01
It is propsed that the various symmetries observed in nature be regarded as infrared attractive fixed points of a large class of theories which are not endowed with these symmetries a priori. That this hypothesis is feasible is explicitly demonstrated for the case of Lorentz invariance. The strategy is to consider a suitable noncovariant model of electrodynamics, and to show by calculating the relevant β-functions that this model simulates Lorentz invariance better and better as the energy scale is progressively lowered. (Auth.)
Reparametrization invariance and the Schroedinger equation
International Nuclear Information System (INIS)
Tkach, V.I.; Pashnev, A.I.; Rosales, J.J.
1999-01-01
A time-dependent Schroedinger equation for systems invariant under the reparametrization of time is considered. We develop the two-stage procedure of construction such systems from a given initial ones, which are not invariant under the time reparametrization. One of the first-class constraints of the systems in such description becomes the time-dependent Schroedinger equation. The procedure is applicable in the supersymmetric theories as well. The n = 2 supersymmetric quantum mechanics is coupled to world-line supergravity, and the local supersymmetric action is constructed leading to the square root representation of the time-dependent Schroedinger equation
Quantized Hall conductance as a topological invariant
International Nuclear Information System (INIS)
Niu, Q.; Thouless, Ds.J.; Wu, Y.S.
1984-10-01
Whenever the Fermi level lies in a gap (or mobility gap) the bulk Hall conductance can be expressed in a topologically invariant form showing the quantization explicitly. The new formulation generalizes the earlier result by TKNN to the situation where many body interaction and substrate disorder are also present. When applying to the fractional quantized Hall effect we draw the conclusion that there must be a symmetry breaking in the many body ground state. The possibility of writing the fractionally quantized Hall conductance as a topological invariant is also carefully discussed. 19 references
Scaling theory of {{{Z}}_{2}} topological invariants
Chen, Wei; Sigrist, Manfred; Schnyder, Andreas P.
2016-09-01
For inversion-symmetric topological insulators and superconductors characterized by {{{Z}}2} topological invariants, two scaling schemes are proposed to judge topological phase transitions driven by an energy parameter. The scaling schemes renormalize either the phase gradient or the second derivative of the Pfaffian of the time-reversal operator, through which the renormalization group flow of the driving energy parameter can be obtained. The Pfaffian near the time-reversal invariant momentum is revealed to display a universal critical behavior for a great variety of models examined.
Invariant of dynamical systems: A generalized entropy
International Nuclear Information System (INIS)
Meson, A.M.; Vericat, F.
1996-01-01
In this work the concept of entropy of a dynamical system, as given by Kolmogorov, is generalized in the sense of Tsallis. It is shown that this entropy is an isomorphism invariant, being complete for Bernoulli schemes. copyright 1996 American Institute of Physics
Field transformations, collective coordinates and BRST invariance
International Nuclear Information System (INIS)
Alfaro, J.; Damgaard, P.H.
1989-12-01
A very large class of general field transformations can be viewed as a field theory generalization of the method of collective coordinates. The introduction of new variables induces a gauge invariance in the transformed theory, and the freedom left in gauge fixing this new invariance can be used to find equivalent formulations of the same theory. First the Batalin-Fradkin-Vilkovisky formalism is applied to the Hamiltonian formulation of physical systems that can be described in terms of collective coordinates. We then show how this type of collective coordinate scheme can be generalized to field transformations, and discuss the War Identities of the associated BRST invariance. For Yang-Mills theory a connection to topological field theory and the background field method is explained in detail. In general the resulting BRST invariance we find hidden in any quantum field theory can be viewed as a consequence of our freedom in choosing a basis of coordinates φ(χ) in the action S[φ]. (orig.)
Learning the Lie groups of visual invariance.
Miao, Xu; Rao, Rajesh P N
2007-10-01
A fundamental problem in biological and machine vision is visual invariance: How are objects perceived to be the same despite transformations such as translations, rotations, and scaling? In this letter, we describe a new, unsupervised approach to learning invariances based on Lie group theory. Unlike traditional approaches that sacrifice information about transformations to achieve invariance, the Lie group approach explicitly models the effects of transformations in images. As a result, estimates of transformations are available for other purposes, such as pose estimation and visuomotor control. Previous approaches based on first-order Taylor series expansions of images can be regarded as special cases of the Lie group approach, which utilizes a matrix-exponential-based generative model of images and can handle arbitrarily large transformations. We present an unsupervised expectation-maximization algorithm for learning Lie transformation operators directly from image data containing examples of transformations. Our experimental results show that the Lie operators learned by the algorithm from an artificial data set containing six types of affine transformations closely match the analytically predicted affine operators. We then demonstrate that the algorithm can also recover novel transformation operators from natural image sequences. We conclude by showing that the learned operators can be used to both generate and estimate transformations in images, thereby providing a basis for achieving visual invariance.
Gauge invariance and fractional quantized Hall effect
International Nuclear Information System (INIS)
Tao, R.; Wu, Y.S.
1984-01-01
It is shown that gauge invariance arguments imply the possibility of fractional quantized Hall effect; the Hall conductance is accurately quantized to a rational value. The ground state of a system showing the fractional quantized Hall effect must be degenerate; the non-degenerate ground state can only produce the integral quantized Hall effect. 12 references
Invariant metric for nonlinear symplectic maps
Indian Academy of Sciences (India)
a function of system parameters, we demonstrate that the performance of a nonlinear Hamiltonian system is enhanced. Keywords. Invariant metric; symplectic maps; performance optimization. PACS Nos 05.45. ...... [7] A Nijenhuis and H S Wilf, Computational algorithms for computers and calculators (Academic. Press, New ...
Neutrinos as Probes of Lorentz Invariance
Directory of Open Access Journals (Sweden)
Jorge S. Díaz
2014-01-01
Full Text Available Neutrinos can be used to search for deviations from exact Lorentz invariance. The worldwide experimental program in neutrino physics makes these particles a remarkable tool to search for a variety of signals that could reveal minute relativity violations. This paper reviews the generic experimental signatures of the breakdown of Lorentz symmetry in the neutrino sector.
Testing Lorentz and CPT Invariance with Neutrinos
Directory of Open Access Journals (Sweden)
Jorge S. Díaz
2016-10-01
Full Text Available Neutrino experiments can be considered sensitive tools to test Lorentz and CPT invariance. Taking advantage of the great variety of neutrino experiments, including neutrino oscillations, weak decays, and astrophysical neutrinos, the generic experimental signatures of the breakdown of these fundamental symmetries in the neutrino sector are presented.
Automatic invariant detection in dynamic web applications
Groeneveld, F.; Mesbah, A.; Van Deursen, A.
2010-01-01
The complexity of modern web applications increases as client-side JavaScript and dynamic DOM programming are used to offer a more interactive web experience. In this paper, we focus on improving the dependability of such applications by automatically inferring invariants from the client-side and
Constitutive laws, tensorial invariance and chocolate cake
Rundle, John B.; Passman, S. L.
1982-04-01
Although constitutive modeling is a well-established branch of mathematics which has found wide industrial application, geophysicists often do not take full advantage of its known results. We present a synopsis of the theory of constitutive modeling, couched in terms of the ‘simple material’, which has been extensively studied and is complex enough to include most of the correct models proposed to describe the behavior of geological materials. Critical in the development of the theory are various invariance requirements, the principal ones being coordinate invariance, peer group invariance (isotropy), and frame-indifference. Each places distinet restrictions on constitutive equations. A noncomprehensive list of properly invariant and commonly used constitutive equations is given. To exemplify use of the equations, we consider two problems in detail: steady extension, which models the commonly performed constant strain rate triaxial test, and simple shearing. We note that each test is so restricted kinematically that only the most trivial aspects of material behavior are manifested in these tests, no matter how complex the material. Furthermore, the results of one test do not generally determine the results of the other.
Invariant metric for nonlinear symplectic maps
Indian Academy of Sciences (India)
In this paper, we construct an invariant metric in the space of homogeneous polynomials of a given degree (≥ 3). The homogeneous polynomials specify a nonlinear symplectic map which in turn represents a Hamiltonian system. By minimizing the norm constructed out of this metric as a function of system parameters, we ...
Joint local quasinilpotence and common invariant subspaces
Indian Academy of Sciences (India)
MS received 27 November 2005; revised 3 February 2006. Abstract. In this article we obtain some positive results about the existence of a common nontrivial invariant subspace for N-tuples of not necessarily commuting operators on. Banach spaces with a Schauder basis. The concept of joint quasinilpotence plays a basic.
Notes on the knot concordance invariant Upsilon
Livingston, Charles
2014-01-01
The knot concordance invariant Upsilon, recently defined by Ozsvath, Stipsicz, and Szabo, takes values in the group of piecewise linear functions on the closed interval [0,2]. This paper presents a description of one approach to defining Upsilon and of proving its basic properties related to the knot 3-genus, 4-genus, and concordance genus.
Translationally invariant self-consistent field theories
International Nuclear Information System (INIS)
Shakin, C.M.; Weiss, M.S.
1977-01-01
We present a self-consistent field theory which is translationally invariant. The equations obtained go over to the usual Hartree-Fock equations in the limit of large particle number. In addition to deriving the dynamic equations for the self-consistent amplitudes we discuss the calculation of form factors and various other observables
Question of Lorentz invariance in muon decay
Noordmans, J.P.; Onderwater, C. J. G.; Wilschut, H. W.; Timmermans, R. G. E.
2014-01-01
Possibilities to test the Lorentz invariance of the weak interaction in muon decay are considered. We derive the general Lorentz-violating muon-decay rate and discuss measurements of the directional and boost dependence of the Michel parameters and of the muon lifetime as function of absolute
Adaptivity and group invariance in mathematical morphology
Roerdink, Jos B.T.M.
2009-01-01
The standard morphological operators are (i) defined on Euclidean space, (ii) based on structuring elements, and (iii) invariant with respect to translation. There are several ways to generalise this. One way is to make the operators adaptive by letting the size or shape of structuring elements
Superfield approach to symmetry invariance in quantum ...
Indian Academy of Sciences (India)
vectors Ei and Bi are the electric and magnetic fields and totally antisymmetric εijk is the 3D Levi–Civita tensor. ... origin to the exterior derivative (i.e. d = dxµ∂µ) of the differential geometry, remains invariant. ... of the Langrangian density (2.1), modulo some total ordinary space-time derivative terms, which do not affect the ...
Real object recognition using moment invariants
Indian Academy of Sciences (India)
associative memory was used to create a system, recognizing objects regardless of changes in rotation or scale by Wechsler & Zimmerman (1998) 3-D object simulations were ..... Hu M 1962 Visual pattern recognition by moment invariants. IRE Trans. Inf. Theor. IT-8: 179–187. Khotanzad A, Lu J-H 1990 Classification of ...
Invariant properties between stroke features in handwriting
Teulings, H L; Schomaker, L R
A handwriting pattern is considered as a sequence of ballistic strokes. Replications of a pattern may be generated from a single, higher-level memory representation, acting as a motor program. Therefore, those stroke features which show the most invariant pattern are probably related to the
Invariant Theory (IT) & Standard Monomial Theory (SMT)
Indian Academy of Sciences (India)
2013-07-06
Jul 6, 2013 ... Introducing co-ordinate axes in the usual fashion (with origin at the central point), we can represent the points by ordered pairs (xred, yred), (xblue, yblue), (xgreen, ygreen),. (xyellow, yyellow). ..... What are the (polynomial) invariants in this case? The dot products x2 red + y2 red, . . . (of every point with itself) ...
Conformal branching rules and modular invariants
International Nuclear Information System (INIS)
Walton, M.A.
1989-01-01
Using the outer automorphisms of the affine algebra SU(n), we show how the branching rules for the conformal subalgebra SU(pq) contains SU(p) x SU(q) may be simply calculated. We demonstrate that new modular invariant combinations of SU(n) characters are obtainable from the branching rules. (orig.)
DEFF Research Database (Denmark)
Nobaew, Banphot; Ryberg, Thomas
2011-01-01
developed by Buckingham. It supplements and extends this framework by offering a more detailed account of how visual principles and elements in games can be analysed. In developing this visual grammar we draw theoretically on existing approaches within: the arts, history, film study, semiotics, multimodal...... analysis, and game studies. We illustrate the theoretical and analytical framework by analysing samples of screenshots and video clips collected from the online game “World of Warcraft” (WoW) where we have conducted our online research. The research data is supplemented by ethnographic data (observation......This paper proposes a new theoretical framework or visual grammar for analysing visual aspects of digital 3D games, and for understanding more deeply the notion of Visual Digital Game Literacy. The framework focuses on the development of a visual grammar by drawing on the digital literacy framework...
Foundations of gravitation theory: the principle of equivalence
International Nuclear Information System (INIS)
Haugan, M.P.
1978-01-01
A new framework is presented within which to discuss the principle of equivalence and its experimental tests. The framework incorporates a special structure imposed on the equivalence principle by the principle of energy conservation. This structure includes relations among the conceptual components of the equivalence principle as well as quantitative relations among the outcomes of its experimental tests. One of the most striking new results obtained through use of this framework is a connection between the breakdown of local Lorentz invariance and the breakdown of the principle that all bodies fall with the same acceleration in a gravitational field. An extensive discussion of experimental tests of the equivalence principle and their significance is also presented. Within the above framework, theory-independent analyses of a broad range of equivalence principle tests are possible. Gravitational redshift experiments. Doppler-shift experiments, the Turner-Hill and Hughes-Drever experiments, and a number of solar-system tests of gravitation theories are analyzed. Application of the techniques of theoretical nuclear physics to the quantitative interpretation of equivalence principle tests using laboratory materials of different composition yields a number of important results. It is found that current Eotvos experiments significantly demonstrate the compatibility of the weak interactions with the equivalence principle. It is also shown that the Hughes-Drever experiment is the most precise test of local Lorentz invariance yet performed. The work leads to a strong, tightly knit empirical basis for the principle of equivalence, the central pillar of the foundations of gravitation theory
On organizing principles of discrete differential geometry. Geometry of spheres
International Nuclear Information System (INIS)
Bobenko, Alexander I; Suris, Yury B
2007-01-01
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.
Dimensional analysis using toric ideals: primitive invariants.
Directory of Open Access Journals (Sweden)
Mark A Atherton
Full Text Available Classical dimensional analysis in its original form starts by expressing the units for derived quantities, such as force, in terms of power products of basic units [Formula: see text] etc. This suggests the use of toric ideal theory from algebraic geometry. Within this the Graver basis provides a unique primitive basis in a well-defined sense, which typically has more terms than the standard Buckingham approach. Some textbook examples are revisited and the full set of primitive invariants found. First, a worked example based on convection is introduced to recall the Buckingham method, but using computer algebra to obtain an integer [Formula: see text] matrix from the initial integer [Formula: see text] matrix holding the exponents for the derived quantities. The [Formula: see text] matrix defines the dimensionless variables. But, rather than this integer linear algebra approach it is shown how, by staying with the power product representation, the full set of invariants (dimensionless groups is obtained directly from the toric ideal defined by [Formula: see text]. One candidate for the set of invariants is a simple basis of the toric ideal. This, although larger than the rank of [Formula: see text], is typically not unique. However, the alternative Graver basis is unique and defines a maximal set of invariants, which are primitive in a simple sense. In addition to the running example four examples are taken from: a windmill, convection, electrodynamics and the hydrogen atom. The method reveals some named invariants. A selection of computer algebra packages is used to show the considerable ease with which both a simple basis and a Graver basis can be found.
The chronos principle and the interactions of fields of spin 0 and 1
International Nuclear Information System (INIS)
Christodoulou, D.
1977-01-01
The definition of time for a physical system consisting of the geometry of space in which there is any number of scalar and vector fields, is established as a fundamental physical principle. From this principle, called 'chronos principle', in combination with the relativity principle, the Yang-Mills type of field interaction is uniquely deduced, without making any assumption about the form of the gauge transformation of the fields which leaves the action invariant. (Auth.)
Quantization of a conformal invariant pure spinor model
International Nuclear Information System (INIS)
Akdeniz, K.G.; Hortacsu, M.; Pak, N.K.; Arik, M.
1982-08-01
The Gursey model, a conformally invariant pure spinor model in four dimensions, is shown to yield a renormalizable field theory, which is asymptotically free in the phase which has discrete ν 5 -invariance. (author)
Through the Looking Glass: Symmetry in Behavioral Principles?
Marr, M. Jackson
2006-01-01
In this article, the author discusses and presents seven possibilities that describe how symmetry principles are reflected in behavior analysis. First, if there are apparently no functional distinctions to be made between positive and negative reinforcement, then reinforcer effectiveness (by various measures) is invariant under a simple inversion…
The principle of relativity and the special relativity triple
International Nuclear Information System (INIS)
Guo Hanying; Wu Hongtu; Zhou Bin
2009-01-01
Based on the principle of relativity and the postulate on universal invariant constants (c,l) as well as Einstein's isotropy conditions, three kinds of special relativity form a triple with a common Lorentz group as isotropy group under full Umov-Weyl-Fock-Lorentz transformations among inertial motions
Action principles for the Vlasov equation
International Nuclear Information System (INIS)
Ye, H.; Morrison, P.J.
1992-01-01
Five action principles for the Vlasov--Poisson and Vlasov--Maxwell equations, which differ by the variables incorporated to describe the distribution of particles in phase space, are presented. Three action principles previously known for the Vlasov--Maxwell equations are altered so as to produce the Vlasov--Poisson equation upon variation with respect to only the particle variables, and one action principle previously known for the Vlasov--Poisson equation is altered to produce the Vlasov--Maxwell equations upon variations with respect to particle and field variables independently. Also, a new action principle for both systems, which is called the leaf action, is presented. This new action has the desirable features of using only a single generating function as the dynamical variable for describing the particle distribution, and manifestly preserving invariants of the system known as Casimir invariants. The relationships between the various actions are described, and it is shown that the leaf action is a link between actions written in terms of Lagrangian and Eulerian variables
A scale invariant covariance structure on jet space
DEFF Research Database (Denmark)
Pedersen, Kim Steenstrup; Loog, Marco; Markussen, Bo
2005-01-01
This paper considers scale invariance of statistical image models. We study statistical scale invariance of the covariance structure of jet space under scale space blurring and derive the necessary structure and conditions of the jet covariance matrix in order for it to be scale invariant. As part...... results where we estimate the scale invariant jet covariance of natural images and show that it resembles that of Brownian images....
How to Find Invariants for Coloured Petri Nets
DEFF Research Database (Denmark)
Jensen, Kurt
1981-01-01
This paper shows how invariants can be found for coloured Petri Nets. We define a set of transformation rules, which can be used to transform the incidence matrix, without changing the set of invariants.......This paper shows how invariants can be found for coloured Petri Nets. We define a set of transformation rules, which can be used to transform the incidence matrix, without changing the set of invariants....
International Nuclear Information System (INIS)
Gulati, S.P.; Gulati, S.
1979-01-01
An attempt has been made to replace the principle of relativity with the principle of covariance. This amounts to modification of the theory of relativity based on the two postulates (i) the principle of covariance and (ii) the light principle. Some of the fundamental results and the laws of relativistic mechanics, electromagnetodynamics and quantum mechanics are re-examined. The principle of invariance is questioned. (A.K.)
Movement timing and invariance arise from several geometries.
Directory of Open Access Journals (Sweden)
Daniel Bennequin
2009-07-01
Full Text Available Human movements show several prominent features; movement duration is nearly independent of movement size (the isochrony principle, instantaneous speed depends on movement curvature (captured by the 2/3 power law, and complex movements are composed of simpler elements (movement compositionality. No existing theory can successfully account for all of these features, and the nature of the underlying motion primitives is still unknown. Also unknown is how the brain selects movement duration. Here we present a new theory of movement timing based on geometrical invariance. We propose that movement duration and compositionality arise from cooperation among Euclidian, equi-affine and full affine geometries. Each geometry posses a canonical measure of distance along curves, an invariant arc-length parameter. We suggest that for continuous movements, the actual movement duration reflects a particular tensorial mixture of these canonical parameters. Near geometrical singularities, specific combinations are selected to compensate for time expansion or compression in individual parameters. The theory was mathematically formulated using Cartan's moving frame method. Its predictions were tested on three data sets: drawings of elliptical curves, locomotion and drawing trajectories of complex figural forms (cloverleaves, lemniscates and limaçons, with varying ratios between the sizes of the large versus the small loops. Our theory accounted well for the kinematic and temporal features of these movements, in most cases better than the constrained Minimum Jerk model, even when taking into account the number of estimated free parameters. During both drawing and locomotion equi-affine geometry was the most dominant geometry, with affine geometry second most important during drawing; Euclidian geometry was second most important during locomotion. We further discuss the implications of this theory: the origin of the dominance of equi-affine geometry, the possibility
Movement Timing and Invariance Arise from Several Geometries
Bennequin, Daniel; Fuchs, Ronit; Berthoz, Alain; Flash, Tamar
2009-01-01
Human movements show several prominent features; movement duration is nearly independent of movement size (the isochrony principle), instantaneous speed depends on movement curvature (captured by the 2/3 power law), and complex movements are composed of simpler elements (movement compositionality). No existing theory can successfully account for all of these features, and the nature of the underlying motion primitives is still unknown. Also unknown is how the brain selects movement duration. Here we present a new theory of movement timing based on geometrical invariance. We propose that movement duration and compositionality arise from cooperation among Euclidian, equi-affine and full affine geometries. Each geometry posses a canonical measure of distance along curves, an invariant arc-length parameter. We suggest that for continuous movements, the actual movement duration reflects a particular tensorial mixture of these canonical parameters. Near geometrical singularities, specific combinations are selected to compensate for time expansion or compression in individual parameters. The theory was mathematically formulated using Cartan's moving frame method. Its predictions were tested on three data sets: drawings of elliptical curves, locomotion and drawing trajectories of complex figural forms (cloverleaves, lemniscates and limaçons, with varying ratios between the sizes of the large versus the small loops). Our theory accounted well for the kinematic and temporal features of these movements, in most cases better than the constrained Minimum Jerk model, even when taking into account the number of estimated free parameters. During both drawing and locomotion equi-affine geometry was the most dominant geometry, with affine geometry second most important during drawing; Euclidian geometry was second most important during locomotion. We further discuss the implications of this theory: the origin of the dominance of equi-affine geometry, the possibility that the brain
The gauge invariant Lagrangian for Seiberg-Witten topological monopoles
International Nuclear Information System (INIS)
Gianvittorio, R.; Martin, I.; Restuccia, A.
1995-04-01
A topological gauge invariant Lagrangian for Seiberg-Witten monopole equations is constructed. The actions is invariant under a huge class of gauge transformations which after BRST fixing leads to the BRST invariant actin associated to Seiberg-Witten monopole topological theory. The supersymmetric transformation of the fields involved in the construction is obtained from the nilpotent BRST algebra. (author). 6 refs
Complex dynamical invariants for two-dimensional complex potentials
Indian Academy of Sciences (India)
that the cubic oscillator and shifted harmonic oscillator admit quadratic complex invariants. The obtained invariants ..... where α, β, α1,α2,β1,β2,δ3 and δ4 are arbitrary constants of integration. Pramana – J. Phys. ..... An invariant for a shifted harmonic oscillator in complex plane can be derived by substi- tuting δ3 = 0,δ2 = −1.
Invariant Einstein metrics on Ledger-Obata spaces
Chen, Zhiqi; Nikonorov, Yuriĭ; Nikonorova, Yulia
2016-01-01
In this paper, we study invariant Einstein metrics on Ledger-Obata spaces $F^m/\\operatorname{diag}(F)$. In particular, we classify invariant Einstein metrics on $F^4/\\operatorname{diag}(F)$ and estimate the number of invariant Einstein metrics on general Ledger-Obata spaces $F^{m}/\\operatorname{diag}(F)$.
Image indexing using composite color and shape invariant features
Gevers, Th.; Smeulders, A.W.M.
1998-01-01
New sets of color models are proposed for object recognition invariant to a change in view point, object geometry and illumination. Further, computational methods are presented to combine color and shape invariants to produce a high-dimensional invariant feature set for discriminatory object
The need for invariant assessments in South African education
African Journals Online (AJOL)
Even though we cannot conclude at this stage that the Marko-D satisfies the requirements of invariance and unidimensionality com- pletely, this study provides an elucidation of the need for invariant assessments in South African education. Keywords: foundation phase learners; invariance; mathematical competence; ...
The geometric Hopf invariant and surgery theory
Crabb, Michael
2017-01-01
Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. .
Scale invariance from phase transitions to turbulence
Lesne, Annick
2012-01-01
During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance. The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos ...
Odor concentration invariance by chemical ratio coding
Directory of Open Access Journals (Sweden)
Naoshige Uchida
2008-08-01
Full Text Available Many animal species rely on chemical signals to extract ecologically important information from the environment. Yet in natural conditions chemical signals will frequently undergo concentration changes that produce differences in both level and pattern of activation of olfactory receptor neurons. Thus, a central problem in olfactory processing is how the system is able to recognize the same stimulus across different concentrations. To signal species identity for mate recognition, some insects use the ratio of two components in a binary chemical mixture to produce a code that is invariant to dilution. Here, using psychophysical methods, we show that rats also classify binary odor mixtures according to the molar ratios of their components, spontaneously generalizing over at least a tenfold concentration range. These results indicate that extracting chemical ratio information is not restricted to pheromone signaling and suggest a general solution for concentration-invariant odor recognition by the mammalian olfactory system.
Mutation, Witten index, and quiver invariant
International Nuclear Information System (INIS)
Kim, Heeyeon; Lee, Seung-Joo; Yi, Piljin
2015-01-01
We explore Seiberg-like dualities, or mutations, for N=4 quiver quantum mechanics in the context of wall-crossing. In contrast to higher dimensions, the 1d Seiberg-duality must be performed with much care. With fixed Fayet-Iliopoulos constants, at most two nodes can be mutated, one left and the other right, mapping a chamber of a quiver into a chamber of a mutated quiver. We delineate this complex pattern for triangle quivers and show how the Witten indices are preserved under such finely chosen mutations. On the other hand, the quiver invariants, or wall-crossing-safe part of supersymmetric spectra, mutate more straightforwardly, whereby a quiver is mapped to a quiver. The mutation rule that preserves the quiver invariant is different from the usual one, however, which we explore and confirm numerically.
BRS invariant stochastic quantization of Einstein gravity
International Nuclear Information System (INIS)
Nakazawa, Naohito.
1989-11-01
We study stochastic quantization of gravity in terms of a BRS invariant canonical operator formalism. By introducing artificially canonical momentum variables for the original field variables, a canonical formulation of stochastic quantization is proposed in the sense that the Fokker-Planck hamiltonian is the generator of the fictitious time translation. Then we show that there exists a nilpotent BRS symmetry in an enlarged phase space of the first-class constrained systems. The phase space is spanned by the dynamical variables, their canonical conjugate momentum variables, Faddeev-Popov ghost and anti-ghost. We apply the general BRS invariant formulation to stochastic quantization of gravity which is described as a second-class constrained system in terms of a pair of Langevin equations coupled with white noises. It is shown that the stochastic action of gravity includes explicitly the De Witt's type superspace metric which leads to a geometrical interpretation of quantum gravity analogous to nonlinear σ-models. (author)
Role of Lifshitz Invariants in Liquid Crystals
Directory of Open Access Journals (Sweden)
Amelia Sparavigna
2009-06-01
Full Text Available The interaction between an external action and the order parameter, via a dependence described by a so-called Lifshitz invariant, is very important to determine the final configuration of liquid crystal cells. The external action can be an electric field applied to the bulk or the confinement due to free surfaces or cell walls. The Lifshitz invariant includes the order parameter in the form of an elastic strain. This coupling between elastic strains and fields, inserted in a Landau-Ginzburg formalism, is well known and gives rise to striction effects causing undulations in the director configuration. We want to discuss here the role of Lifshitz coupling terms, following an approach similar to that introduced by Dzyaloshinskii for magnetic materials. Case studies on nematics in planar and cylindrical cells are also proposed.
CP invariance: a point of view
International Nuclear Information System (INIS)
Mohan, Gyan
1983-01-01
That the longlived component L of K 0 has both CP = +1 and CP = -1 modes of decay is often cited as evidence of violation of CP invariance. The careful ones find the compelling evidence to be the non-dilution of the regeneration interference pattern when the incident K 0 beam is mixed even substantially with anti-K 0 . However the two phenomena comprehensively imply that L has a CP = +1 component Lsub(+) and CP = -1 component Lsub(-) and that the longlived component of both K 0 and anti-K 0 are one and the same L. This does not demand abandoning CP invariance. It does imply that anti-K 0 is not the CP conjugate of K 0 . (author)
Gauge-invariant variables and entanglement entropy
Agarwal, Abhishek; Karabali, Dimitra; Nair, V. P.
2017-12-01
The entanglement entropy (EE) of gauge theories in three spacetime dimensions is analyzed using manifestly gauge-invariant variables defined directly in the continuum. Specifically, we focus on the Maxwell, Maxwell-Chern-Simons (MCS), and non-Abelian Yang-Mills theories. Special attention is paid to the analysis of edge modes and their contribution to EE. The contact term is derived without invoking the replica method and its physical origin is traced to the phase space volume measure for the edge modes. The topological contribution to the EE for the MCS case is calculated. For all the Abelian cases, the EE presented in this paper agrees with known results in the literature. The EE for the non-Abelian theory is computed in a gauge-invariant Gaussian approximation, which incorporates the dynamically generated mass gap. A formulation of the contact term for the non-Abelian case is also presented.
Revisiting R-invariant direct gauge mediation
Energy Technology Data Exchange (ETDEWEB)
Chiang, Cheng-Wei [Center for Mathematics and Theoretical Physics andDepartment of Physics, National Central University,Taoyuan, Taiwan 32001, R.O.C. (China); Institute of Physics, Academia Sinica,Taipei, Taiwan 11529, R.O.C. (China); Physics Division, National Center for Theoretical Sciences,Hsinchu, Taiwan 30013, R.O.C. (China); Kavli IPMU (WPI), UTIAS, University of Tokyo,Kashiwa, Chiba 277-8583 (Japan); Harigaya, Keisuke [Department of Physics, University of California,Berkeley, California 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory,Berkeley, California 94720 (United States); ICRR, University of Tokyo,Kashiwa, Chiba 277-8582 (Japan); Ibe, Masahiro [Kavli IPMU (WPI), UTIAS, University of Tokyo,Kashiwa, Chiba 277-8583 (Japan); ICRR, University of Tokyo,Kashiwa, Chiba 277-8582 (Japan); Yanagida, Tsutomu T. [Kavli IPMU (WPI), UTIAS, University of Tokyo,Kashiwa, Chiba 277-8583 (Japan)
2016-03-21
We revisit a special model of gauge mediated supersymmetry breaking, the “R-invariant direct gauge mediation.” We pay particular attention to whether the model is consistent with the minimal model of the μ-term, i.e., a simple mass term of the Higgs doublets in the superpotential. Although the incompatibility is highlighted in view of the current experimental constraints on the superparticle masses and the observed Higgs boson mass, the minimal μ-term can be consistent with the R-invariant gauge mediation model via a careful choice of model parameters. We derive an upper limit on the gluino mass from the observed Higgs boson mass. We also discuss whether the model can explain the 3σ excess of the Z+jets+E{sub T}{sup miss} events reported by the ATLAS collaboration.
Monopoles, Abelian projection, and gauge invariance
International Nuclear Information System (INIS)
Bonati, Claudio; Di Giacomo, Adriano; Lepori, Luca; Pucci, Fabrizio
2010-01-01
A direct connection is proved between the non-Abelian Bianchi Identities (NABI's) and the Abelian Bianchi identities for the 't Hooft tensor. As a consequence, the existence of a nonzero magnetic current is related to the violation of the NABI's and is a gauge-invariant property. The construction allows us to show that not all Abelian projections can be used to expose monopoles in lattice configurations: each field configuration with nonzero magnetic charge identifies its natural projection, up to gauge transformations which tend to unity at large distances. It is shown that the so-called maximal-Abelian gauge is a legitimate choice. It is also proven, starting from the NABI, that monopole condensation is a physical gauge-invariant phenomenon, independent of the choice of the Abelian projection.
Adiabatic invariants for field-reversed configurations
International Nuclear Information System (INIS)
Schwarzmeier, J.L.; Lewis, H.R.; Seyler, C.E.
1982-01-01
Field reversed configurations (FRCs) are characterized by azimuthal symmetry, so two exact constants of the particle motion are the total particle energy E and the canonical angular momentum P/sub theta/. For many purposes it is desirable to construct a third (diabatic) constant of the motion if this is possible. It is shown that for parameters characteristic of current FRCs that the magnetic moment μ is a poor adiabatic invariant, while the radial action J is conserved rather well
Liaison, Schottky Problem and Invariant Theory
Alonso, Maria Emilia; Mallavibarrena, Raquel; Sols, Ignacio
2010-01-01
This volume is a homage to the memory of the Spanish mathematician Federico Gaeta (1923-2007). Apart from a historical presentation of his life and interaction with the classical Italian school of algebraic geometry, the volume presents surveys and original research papers on the mathematics he studied. Specifically, it is divided into three parts: linkage theory, Schottky problem and invariant theory. On this last topic a hitherto unpublished article by Federico Gaeta is also included.
3D rotation invariants by complex moments
Czech Academy of Sciences Publication Activity Database
Suk, Tomáš; Flusser, Jan; Boldyš, Jiří
2015-01-01
Roč. 48, č. 11 (2015), s. 3516-3526 ISSN 0031-3203 R&D Projects: GA ČR(CZ) GA13-29225S; GA ČR(CZ) GA15-16928S Institutional support: RVO:67985556 Keywords : Complex moment * spherical harmonic * group representation theory * 3D rotation invariant Subject RIV: IN - Informatics, Computer Science Impact factor: 3.399, year: 2015 http://library.utia.cas.cz/separaty/2015/ZOI/suk-0445882.pdf
Invariant dependence structures and Archimedean copulas
Czech Academy of Sciences Publication Activity Database
Durante, F.; Jaworski, P.; Mesiar, Radko
2011-01-01
Roč. 81, č. 12 (2011), s. 1995-2003 ISSN 0167-7152 R&D Projects: GA ČR GAP402/11/0378 Institutional research plan: CEZ:AV0Z10750506 Keywords : Archimedean copula * Tail dependence * Clayton model Subject RIV: BA - General Mathematics Impact factor: 0.498, year: 2011 http://library.utia.cas.cz/separaty/2011/E/mesiar-invariant dependence structures and archimedean copulas.pdf
Coordinate invariant conservation laws in Schwarzschild geometry
Energy Technology Data Exchange (ETDEWEB)
Burghardt, R.
1983-01-01
Einstein's field equations can be written in a special way to give expressions free of any quantities which cannot be measured. These expressions are fully coordinate invariant but observer dependent. Generalized Lorentz transformations according to Treder's theory serve as connecting links between the measured values of different observer systems. The field equations contain expressions for gravitational energy stresses which satisfy covariant conservation laws.
Affine Moment Invariants Generated by Graph Method
Czech Academy of Sciences Publication Activity Database
Suk, Tomáš; Flusser, Jan
2011-01-01
Roč. 44, č. 9 (2011), 2047 – 2056 ISSN 0031-3203 R&D Projects: GA ČR(CZ) GA102/08/1593 Institutional research plan: CEZ:AV0Z10750506 Keywords : Image moments * Object recognition * Affine transformation * Affine moment invariants * Pseudoinvariants * Graph representation * Irreducibility * Independence Subject RIV: IN - Informatics, Computer Science Impact factor: 2.292, year: 2011 http://library.utia.cas.cz/separaty/2011/ZOI/suk-0359752.pdf
Invariance and inconsistency in utility ratings.
Bravata, Dena M; Nelson, Lorene M; Garber, Alan M; Goldstein, Mary K
2005-01-01
To assess utilities of composite health states for dependence in activities of daily living (ADLs) for invariance (i.e., when subjects provide a utility of 1 for all health states) and order inconsistency (i.e., when subjects order their utilities such that their utility for a combination of ADL dependencies is greater than their utility for any subset of the combination). Each of the 400 subjects, age 65 y and older, enrolled in one of several regional medical centers of the Kaiser Permanente Medical Care Program of Northern California and provided standard-gamble utilities for single ADL dependencies (e.g., bathing, dressing, continence) and for dependence in 8 other combinations of ADL dependencies. For order-inconsistent responses, the authors calculated the maximum magnitude of inconsistency as the maximum difference between the utility for the combined ADL dependence health state and that of its inconsistent subset. A total of 76 subjects (19%) gave a utility of 1.0 for all health states presented to them; 19 (5%) gave the same utility other than 1.0 for all health states; 130 (33%) gave at least 1 utility Invariance was associated with a Mini-Mental Status Examination score invariant (0.88 [0.24]) was higher than among inconsistent subjects (0.80 [0.27]; P = 0.01). Invariance and order inconsistencies in utility ratings for complex health states occur frequently. Utilities of consistent subjects may differ from those of inconsistent subjects. Utility assessments should attempt to measure and report these patterns.
Visual Distinctness Determined by Partially Invariant Features
2000-03-01
DISTINCTNESS DETERMINED BY PARTIALLY INVARIANT FEATURES. J.A. Garcia, J. Fdez-Valdivia Departamento de Ciencias de la Computacion e I.A. Univ. de Granada...constant, independently of the viewing distance.The perceptual organization capabilities of human in a complex rural background. vision seem to exhibit...designed and 5.1.2. Clarity of separation at stage j organized by NVESD (Night Vision & Electro-optic Sensors Here we introduce the criterion by which we
O(3)-invariant tunneling in general relativity
International Nuclear Information System (INIS)
Berezin, V.A.; Tkachev, I.I.; Kuzmin, V.A.; AN SSSR, Moscow. Inst. Yadernykh Issledovanij)
1987-12-01
We derived a general formula for the action for any O(3)-invariant tunneling processes in false vacuum decay in general relativity. The general classification of the bubble Euclidean trajectories is elaborated and explicit expressions for bounces for some processes like the vacuum creation of a double bubble, in particular in the vicinity of a black hole; the subbarrier creation of the Einstein-Rosen bridge, creation from nothing of two Minkowski worlds connected by a shell etc., are given. (orig.)
On local invariants of singular symplectic forms
Domitrz, Wojciech
2017-04-01
We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a 2 n-dimensional manifold. In the C-analytic category this set consists of the Martinet hypersurface Σ2, the restriction of the singular symplectic form ω to TΣ2 and the kernel of ω n - 1 at the point p ∈Σ2. In the R-analytic and smooth categories this set contains one more invariant: the canonical orientation of Σ2. We find the conditions to determine the kernel of ω n - 1 at p by the other invariants. In dimension 4 we find sufficient conditions to determine the equivalence class of a singular symplectic form-germ with the structurally smooth Martinet hypersurface by the Martinet hypersurface and the restriction of the singular symplectic form to it. We also study the singular symplectic forms with singular Martinet hypersurfaces. We prove that the equivalence class of such singular symplectic form-germ is determined by the Martinet hypersurface, the canonical orientation of its regular part and the restriction of the singular symplectic form to its regular part if the Martinet hypersurface is a quasi-homogeneous hypersurface with an isolated singularity.
Equivalence principles and electromagnetism
Ni, W.-T.
1977-01-01
The implications of the weak equivalence principles are investigated in detail for electromagnetic systems in a general framework. In particular, it is shown that the universality of free-fall trajectories (Galileo weak equivalence principle) does not imply the validity of the Einstein equivalence principle. However, the Galileo principle plus the universality of free-fall rotation states does imply the Einstein principle.
Constructing invariant fairness measures for surfaces
DEFF Research Database (Denmark)
Gravesen, Jens; Ungstrup, Michael
2002-01-01
The paper proposes a rational method to derive fairness measures for surfaces. It works in cases where isophotes, reflection lines, planar intersection curves, or other curves are used to judge the fairness of the surface. The surface fairness measure is derived by demanding that all the given cu...... of curves. Six basic third order invariants by which the fairing measures can be expressed are defined. Furthermore, the geometry of a plane intersection curve is studied, and the variation of the total, the normal, and the geodesic curvature and the geodesic torsion is determined....
Invariant measures of mass migration processes
Czech Academy of Sciences Publication Activity Database
Fajfrová, Lucie; Gobron, T.; Saada, E.
2016-01-01
Roč. 21, č. 1 (2016), s. 1-52, č. článku 60. ISSN 1083-6489 R&D Projects: GA ČR GAP201/12/2613; GA ČR(CZ) GA16-15238S Institutional support: RVO:67985556 Keywords : interacting particle systems * product invariant measures * zero range process * target process * mass migration process * condensation Subject RIV: BA - General Mathematics Impact factor: 0.904, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/fajfrova-0464455.pdf
Origin of gauge invariance in string theory
Horowitz, G. T.; Strominger, A.
1986-01-01
A first quantization of the space-time embedding Chi exp mu and the world-sheet metric rho of the open bosonic string. The world-sheet metric rho decouples from S-matrix elements in 26 dimensions. This formulation of the theory naturally includes 26-dimensional gauge transformations. The gauge invariance of S-matrix elements is a direct consequence of the decoupling of rho. Second quantization leads to a string field Phi(Chi exp mu, rho) with a gauge-covariant equation of motion.
Translational invariant shell model for Λ hypernuclei
Directory of Open Access Journals (Sweden)
Jolos R.V.
2016-01-01
Full Text Available We extend shell model for Λ hypernuclei suggested by Gal and Millener by including 2ћω excitations in the translation invariant version to estimate yields of different hyperfragments from primary p-shell hypernuclei. We are inspired by the first successful experiment done at MAMI which opens way to study baryon decay of hypernuclei. We use quantum numbers of group SU(4, [f], and SU(3, (λμ, to classify basis wave functions and calculate coefficients of fractional parentage.
The axion mass in modular invariant supergravity
International Nuclear Information System (INIS)
Butter, Daniel; Gaillard, Mary K.
2005-01-01
When supersymmetry is broken by condensates with a single condensing gauge group, there is a nonanomalous R-symmetry that prevents the universal axion from acquiring a mass. It has been argued that, in the context of supergravity, higher dimension operators will break this symmetry and may generate an axion mass too large to allow the identification of the universal axion with the QCD axion. We show that such contributions to the axion mass are highly suppressed in a class of models where the effective Lagrangian for gaugino and matter condensation respects modular invariance (T-duality)
Scale invariants from Gaussian-Hermite moments
Czech Academy of Sciences Publication Activity Database
Yang, B.; Kostková, Jitka; Flusser, Jan; Suk, Tomáš
2017-01-01
Roč. 132, č. 1 (2017), s. 77-84 ISSN 0165-1684 R&D Projects: GA ČR GA15-16928S Institutional support: RVO:67985556 Keywords : Scale invariants * Gaussian–Hermite moments * Variable modulation * Normalization * Zernike moments Subject RIV: JD - Computer Applications, Robotics OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 3.110, year: 2016 http://library.utia.cas.cz/separaty/2016/ZOI/flusser-0466031.pdf
Testing Lorentz invariance in β decay
Directory of Open Access Journals (Sweden)
Sytema A.
2014-03-01
Experimentally we exploit the Gamow-Teller transition of polarized 20Na, where we can test the dependence of the β-decay rate on the spin orientation of 20Na. The polarization degree is measured using the β asymmetry, while the decay rate is measured by the γ yield. A change in the γ rate, when reversing the spin, implies Lorentz invariance violation. The decay rate should depend on sidereal time and the polarization direction relative to the rotation axis of the earth. The method of the measurement will be presented, together with the first results.
Structure of BRS-invariant local functionals
International Nuclear Information System (INIS)
Brandt, F.
1993-01-01
For a large class of gauge theories a nilpotent BRS-operator s is constructed and its cohomology in the space of local functionals of the off-shell fields is shown to be isomorphic to the cohomology of s=s+d on functions f(C,T) of tensor fields T and of variables C which are constructed of the ghosts and the connection forms. The result allows general statements about the structure of invariant classical actions and anomaly cadidates whose BRS-variation vanishes off-shell. The assumptions under which the result holds are thoroughly discussed. (orig.)
Modular invariance and covariant loop calculus
International Nuclear Information System (INIS)
Petersen, J.L.; Roland, K.O.; Sidenius, J.R.
1988-01-01
The covariant loop calculus provides an efficient technique for computing explicit expressions for the density on moduli space corresponding to arbitrary (bosonic string) loop diagrams. Since modular invariance is not manifest, however, we carry out a detailed comparison with known explicit two- and three-loop results derived using analytic geometry (one loop is known to be okay). We establish identity to 'high' order in some moduli and exactly in others. Agreement is found as a result of various nontrivial cancellations, in part related to number theory. We feel our results provide very strong support for the correctness of the covariant loop calculus approach. (orig.)
Gauge invariant actions for string models
International Nuclear Information System (INIS)
Banks, T.
1986-06-01
String models of unified interactions are elegant sets of Feynman rules for the scattering of gravitons, gauge bosons, and a host of massive excitations. The purpose of these lectures is to describe the progress towards a nonperturbative formulation of the theory. Such a formulation should make the geometrical meaning of string theory manifest and explain the many ''miracles'' exhibited by the string Feynman rules. There are some new results on gauge invariant observables, on the cosmological constant, and on the symmetries of interacting string field theory. 49 refs
Hidden Scale Invariance in Condensed Matter
DEFF Research Database (Denmark)
Dyre, J. C.
2014-01-01
. This means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. Liquids and solids with isomorphs include most or all van der Waals bonded systems and metals, as well as weakly ionic or dipolar systems. On the other hand, systems with directional bonding...... (hydrogen bonds or covalent bonds) or strong Coulomb forces generally do not exhibit hidden scale invariance. The article reviews the theory behind this picture of condensed matter and the evidence for it coming from computer simulations and experiments...
Modular invariance and covariant loop calculus
International Nuclear Information System (INIS)
Petersen, J.L.; Roland, K.O.; Sidenius, J.R.
1988-01-01
The covariant loop calculus provides and efficient technique for computing explicit expressions for the density on moduli space corresponding to arbitrary (bosonic string) loop diagrams. Since modular invariance is not manifest, however, we carry out a detailed comparison with known explicit 2- and 3- loop results derived using analytic geometry (1 loop is known to be ok). We establish identity to 'high' order in some moduli and exactly in others. Agreement is found as a result of various non-trivial cancellations, in part related to number theory. We feel our results provide very strong support for the correctness of the covariant loop calculus approach. (orig.)
Multi-Centered Invariants, Plethysm and Grassmannians
Cacciatori, Sergio L.; van Geemen, Bert
2013-01-01
Motivated by multi-centered black hole solutions of Maxwell-Einstein theories of (super)gravity in D=4 space-time dimensions, we develop some general methods, that can be used to determine all homogeneous invariant polynomials on the irreducible (SL_h(p,R) x G4)-representation (p,R), where p denotes the number of centers, and SL_h(p,R) is the "horizontal" symmetry of the system, acting upon the indices labelling the centers. The black hole electric and magnetic charges sit in the symplectic representation R of the generalized electric-magnetic (U-)duality group G4. We start with an algebraic approach based on classical invariant theory, using Schur polynomials and the Cauchy formula. Then, we perform a geometric analysis, involving Grassmannians, Pluecker coordinates, and exploiting Bott's Theorem. We focus on non-degenerate groups G4 "of type E7" relevant for (super)gravities whose (vector multiplets') scalar manifold is a symmetric space. In the triality-symmetric stu model of N=2 supergravity, we explicitl...
Duality invariant class of exact string backgrounds
Klimcík, C
1994-01-01
We consider a class of $2+D$ - dimensional string backgrounds with a target space metric having a covariantly constant null Killing vector and flat `transverse' part. The corresponding sigma models are invariant under $D$ abelian isometries and are transformed by $O(D,D)$ duality into models belonging to the same class. The leading-order solutions of the conformal invariance equations (metric, antisymmetric tensor and dilaton), as well as the action of $O(D,D)$ duality transformations on them, are exact, i.e. are not modified by $\\a'$-corrections. This makes a discussion of different space-time representations of the same string solution (related by $O(D,D|Z)$ duality subgroup) rather explicit. We show that the $O(D,D)$ duality may connect curved $2+D$-dimensional backgrounds with solutions having flat metric but, in general, non-trivial antisymmetric tensor and dilaton. We discuss several particular examples including the $2+D=4$ - dimensional background that was recently interpreted in terms of a WZW model.
Natural inflation with hidden scale invariance
Directory of Open Access Journals (Sweden)
Neil D. Barrie
2016-05-01
Full Text Available We propose a new class of natural inflation models based on a hidden scale invariance. In a very generic Wilsonian effective field theory with an arbitrary number of scalar fields, which exhibits scale invariance via the dilaton, the potential necessarily contains a flat direction in the classical limit. This flat direction is lifted by small quantum corrections and inflation is realised without need for an unnatural fine-tuning. In the conformal limit, the effective potential becomes linear in the inflaton field, yielding to specific predictions for the spectral index and the tensor-to-scalar ratio, being respectively: ns−1≈−0.025(N⋆60−1 and r≈0.0667(N⋆60−1, where N⋆≈30–65 is a number of efolds during observable inflation. This predictions are in reasonable agreement with cosmological measurements. Further improvement of the accuracy of these measurements may turn out to be critical in falsifying our scenario.
Asymptotically free theory with scale invariant thermodynamics
Ferrari, Gabriel N.; Kneur, Jean-Loïc; Pinto, Marcus Benghi; Ramos, Rudnei O.
2017-12-01
A recently developed variational resummation technique, incorporating renormalization group properties consistently, has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g., within the framework of approximations such as in the hard-thermal-loop resummed perturbation theory. This method is used in the present work to evaluate thermodynamical quantities within the two-dimensional nonlinear sigma model, which, apart from providing a technically simpler testing ground, shares some common features with Yang-Mills theories, like asymptotic freedom, trace anomaly and the nonperturbative generation of a mass gap. The present application confirms that nonperturbative results can be readily generated solely by considering the lowest-order (quasiparticle) contribution to the thermodynamic effective potential, when this quantity is required to be renormalization group invariant. We also show that when the next-to-leading correction from the method is accounted for, the results indicate convergence, apart from optimally preserving, within the approximations here considered, the sought-after scale invariance.
Conformal invariance in conditioned stochastic particle systems
Schütz, Gunter M.
2017-08-01
We consider space-time correlations in generic one-dimensional stochastic interacting particle systems with short-range interactions that undergo a fluctuation with an atypically activity of particle jumps or reactions or spin flips. We briefly review the approach in the framework of the quantum Hamiltonian formalism and present examples where the dynamics during such large fluctuations is governed not by the typical stationary dynamics, but by ballistic universality classes with dynamical exponent z=1 that are described unitary conformally invariant field theories with central charge c. For reaction-diffusion and spin flip dynamics we identify critical points (a) in the Ising universality class with c=1/2 , and (b) in the universality class of the three-states Potts model with c=4/5 . For the Ising universality class we obtain a universal scaling form for the generating function of cumulants of the jump activity. For repulsive driven diffusive systems with one conservation law the regime of an atypically high current or hopping activity is generically conformally invariant with central charge c=1 .
On logarithmic extensions of local scale-invariance
Energy Technology Data Exchange (ETDEWEB)
Henkel, Malte, E-mail: malte.henkel@ijl.nancy-universite.fr [Groupe de Physique Statistique, Département de Physique de la Matière et des Matériaux, Institut Jean Lamour (CNRS UMR 7198), Université de Lorraine Nancy, B.P. 70239, F-54506 Vandoeuvre lès Nancy Cedex (France)
2013-04-11
Ageing phenomena far from equilibrium naturally present dynamical scaling and in many situations this may be generalised to local scale-invariance. Generically, the absence of time-translation-invariance implies that each scaling operator is characterised by two independent scaling dimensions. Building on analogies with logarithmic conformal invariance and logarithmic Schrödinger-invariance, this work proposes a logarithmic extension of local scale-invariance, without time-translation-invariance. Carrying this out requires in general to replace both scaling dimensions of each scaling operator by Jordan cells. Co-variant two-point functions are derived for the most simple case of a two-dimensional logarithmic extension. Their form is compared to simulational data for autoresponse functions in several universality classes of non-equilibrium ageing phenomena.
Conformal invariance in the long-range Ising model
Directory of Open Access Journals (Sweden)
Miguel F. Paulos
2016-01-01
Full Text Available We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.
Skein Invariants of Links and Their State Sum Models
Directory of Open Access Journals (Sweden)
Louis H. Kauffman
2017-10-01
Full Text Available We present the new skein invariants of classical links, H [ H ] , K [ K ] and D [ D ] , based on the invariants of links, H, K and D, denoting the regular isotopy version of the Homflypt polynomial, the Kauffman polynomial and the Dubrovnik polynomial. The invariants are obtained by abstracting the skein relation of the corresponding invariant and making a new skein algorithm comprising two computational levels: first producing unlinked knotted components, then evaluating the resulting knots. The invariants in this paper, were revealed through the skein theoretic definition of the invariants Θ d related to the Yokonuma–Hecke algebras and their 3-variable generalization Θ , which generalizes the Homflypt polynomial. H [ H ] is the regular isotopy counterpart of Θ . The invariants K [ K ] and D [ D ] are new generalizations of the Kauffman and the Dubrovnik polynomials. We sketch skein theoretic proofs of the well-definedness and topological properties of these invariants. The invariants of this paper are reformulated into summations of the generating invariants (H, K, D on sublinks of the given link L, obtained by partitioning L into collections of sublinks. The first such reformulation was achieved by W.B.R. Lickorish for the invariant Θ and we generalize it to the Kauffman and Dubrovnik polynomial cases. State sum models are formulated for all the invariants. These state summation models are based on our skein template algorithm which formalizes the skein theoretic process as an analogue of a statistical mechanics partition function. Relationships with statistical mechanics models are articulated. Finally, we discuss physical situations where a multi-leveled course of action is taken naturally.
Differential invariants for higher-rank tensors. A progress report
International Nuclear Information System (INIS)
Tapial, V.
2004-07-01
We outline the construction of differential invariants for higher-rank tensors. In section 2 we outline the general method for the construction of differential invariants. A first result is that the simplest tensor differential invariant contains derivatives of the same order as the rank of the tensor. In section 3 we review the construction for the first-rank tensors (vectors) and second-rank tensors (metrics). In section 4 we outline the same construction for higher-rank tensors. (author)
Dimuon Level-1 invariant mass in 2017 data
CMS Collaboration
2018-01-01
This document shows the Level-1 (L1) dimuon invariant mass with and without L1 muon track extrapolation to the collision vertex and how it compares with the offline reconstructed dimuon invariant mass. The plots are made with the data sample collected in 2017. The event selection, the matching algorithm and the results of the L1 dimuon invariant mass are described in the next pages.
Geometric Invariant Measuring the Deviation from Kerr Data
Bäckdahl, Thomas; Kroon, Juan A. Valiente
2010-01-01
A geometrical invariant for regular asymptotically Euclidean data for the vacuum Einstein field equations is constructed. This invariant vanishes if and only if the data correspond to a slice of the Kerr black hole spacetime --thus, it provides a measure of the non-Kerr-like behavior of generic data. In order to proceed with the construction of the geometric invariant, we introduce the notion of approximate Killing spinors.
Geometric Invariant Measuring the Deviation from Kerr Data
Bäckdahl, Thomas; Valiente Kroon, Juan A.
2010-06-01
A geometrical invariant for regular asymptotically Euclidean data for the vacuum Einstein field equations is constructed. This invariant vanishes if and only if the data correspond to a slice of the Kerr black hole spacetime—thus, it provides a measure of the non-Kerr-like behavior of generic data. In order to proceed with the construction of the geometric invariant, we introduce the notion of approximate Killing spinors.
Cotton-Type and Joint Invariants for Linear Elliptic Systems
Directory of Open Access Journals (Sweden)
A. Aslam
2013-01-01
that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results.
Scale-invariance underlying the logistic equation and its social applications
International Nuclear Information System (INIS)
Hernando, A.; Plastino, A.
2013-01-01
On the basis of dynamical principles we i) advance a derivation of the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and ii) demonstrate that scale-invariance and a mean-value constraint are sufficient and necessary conditions for obtaining it. We also generalize the LE to multi-component systems and show that the above dynamical mechanisms underlie a large number of scale-free processes. Examples are presented regarding city-populations, diffusion in complex networks, and popularity of technological products, all of them obeying the multi-component logistic equation in an either stochastic or deterministic way.
Scale-invariance underlying the logistic equation and its social applications
Energy Technology Data Exchange (ETDEWEB)
Hernando, A., E-mail: alberto.hernando@irsamc.ups-tlse.fr [Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex 09 (France); Plastino, A., E-mail: plastino@fisica.unlp.edu.ar [National University La Plata, IFLP-CCT-CONICET, C.C. 727, 1900 La Plata (Argentina); Universitat de les Illes Balears and IFISC-CSIC, 07122 Palma de Mallorca (Spain)
2013-01-03
On the basis of dynamical principles we i) advance a derivation of the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and ii) demonstrate that scale-invariance and a mean-value constraint are sufficient and necessary conditions for obtaining it. We also generalize the LE to multi-component systems and show that the above dynamical mechanisms underlie a large number of scale-free processes. Examples are presented regarding city-populations, diffusion in complex networks, and popularity of technological products, all of them obeying the multi-component logistic equation in an either stochastic or deterministic way.
Binary optical filters for scale invariant pattern recognition
Reid, Max B.; Downie, John D.; Hine, Butler P.
1992-01-01
Binary synthetic discriminant function (BSDF) optical filters which are invariant to scale changes in the target object of more than 50 percent are demonstrated in simulation and experiment. Efficient databases of scale invariant BSDF filters can be designed which discriminate between two very similar objects at any view scaled over a factor of 2 or more. The BSDF technique has considerable advantages over other methods for achieving scale invariant object recognition, as it also allows determination of the object's scale. In addition to scale, the technique can be used to design recognition systems invariant to other geometric distortions.
Experimental Design for Testing Local Lorentz Invariance Violations in Gravity
Directory of Open Access Journals (Sweden)
Ya-Fen Chen
2017-10-01
Full Text Available Local Lorentz invariance is an important component of General Relativity. Testing for Local Lorentz invariance can not only probe the foundation stone of General Relativity but also help to explore the unified theory for General Relativity and quantum mechanics. In this paper, we search the Local Lorentz invariance violation associated with operators of mass dimension d = 6 in the pure-gravity sector with short-range gravitational experiments. To enlarge the Local Lorentz invariance violation signal effectively, we design a new experiment in which the constraints of all fourteen violation coefficients may be improved by about one order of magnitude.
On the invariance of residues of Feynman graphs
International Nuclear Information System (INIS)
Bierenbaum, Isabella; Kreckel, Richard; Kreimer, Dirk
2002-01-01
We use simple iterated one-loop graphs in massless Yukawa theory and QED to pose the following question: what are the symmetries of the residues of a graph under a permutation of places to insert subdivergences. The investigation confirms partial invariance of the residue under such permutations: the highest weight transcendental is invariant under such a permutation. For QED this result is gauge invariant, i.e., the permutation invariance holds for any gauge. Computations are done making use of the Hopf algebra structure of graphs and employing GiNaC to automate the calculations
Experimental Design for Testing Local Lorentz Invariance Violations in Gravity
Chen, Ya-Fen; Tan, Yu-Jie; Shao, Cheng-Gang
2017-09-01
Local Lorentz invariance is an important component of General Relativity. Testing for Local Lorentz invariance can not only probe the foundation stone of General Relativity but also help to explore the unified theory for General Relativity and quantum mechanics. In this paper, we search the Local Lorentz invariance violation associated with operators of mass dimension d=6 in the pure-gravity sector with short-range gravitational experiments. To enlarge the Local Lorentz invariance violation signal effectively, we design a new experiment in which the constraints of all fourteen violation coefficients may be improved by about one order of magnitude
Note on Weyl versus conformal invariance in field theory
Energy Technology Data Exchange (ETDEWEB)
Wu, Feng [Nanchang University, Department of Physics, Nanchang (China)
2017-12-15
It was argued recently that conformal invariance in flat spacetime implies Weyl invariance in a general curved background for unitary theories and possible anomalies in the Weyl variation of scalar operators are identified. We argue that generically unitarity alone is not sufficient for a conformal field theory to be Weyl invariant. Furthermore, we show explicitly that when a unitary conformal field theory couples to gravity in a Weyl-invariant way, each primary scalar operator that is either relevant or marginal in the unitary conformal field theory corresponds to a Weyl-covariant operator in the curved background. (orig.)
Metric Ranking of Invariant Networks with Belief Propagation
Energy Technology Data Exchange (ETDEWEB)
Tao, Changxia [Xi' an Jiaotong University, China; Ge, Yong [University of North Carolina, Charlotte; Song, Qinbao [Xi' an Jiaotong University, China; Ge, Yuan [Anhui Polytechnic University, China; Omitaomu, Olufemi A [ORNL
2014-01-01
The management of large-scale distributed information systems relies on the effective use and modeling of monitoring data collected at various points in the distributed information systems. A promising approach is to discover invariant relationships among the monitoring data and generate invariant networks, where a node is a monitoring data source (metric) and a link indicates an invariant relationship between two monitoring data. Such an invariant network representation can help system experts to localize and diagnose the system faults by examining those broken invariant relationships and their related metrics, because system faults usually propagate among the monitoring data and eventually lead to some broken invariant relationships. However, at one time, there are usually a lot of broken links (invariant relationships) within an invariant network. Without proper guidance, it is difficult for system experts to manually inspect this large number of broken links. Thus, a critical challenge is how to effectively and efficiently rank metrics (nodes) of invariant networks according to the anomaly levels of metrics. The ranked list of metrics will provide system experts with useful guidance for them to localize and diagnose the system faults. To this end, we propose to model the nodes and the broken links as a Markov Random Field (MRF), and develop an iteration algorithm to infer the anomaly of each node based on belief propagation (BP). Finally, we validate the proposed algorithm on both realworld and synthetic data sets to illustrate its effectiveness.
Invariant relationships deriving from classical scaling transformations
International Nuclear Information System (INIS)
Bludman, Sidney; Kennedy, Dallas C.
2011-01-01
Because scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action, they do not lead to conservation laws. Instead, an extension of Noether's theorem reduces the equations of motion to evolutionary laws that prove useful, even if the transformations are not symmetries of the equations of motion. In the case of scaling, symmetry leads to a scaling evolutionary law, a first-order equation in terms of scale invariants, linearly relating kinematic and dynamic degrees of freedom. This scaling evolutionary law appears in dynamical and in static systems. Applied to dynamical central-force systems, the scaling evolutionary equation leads to generalized virial laws, which linearly connect the kinetic and potential energies. Applied to barotropic hydrostatic spheres, the scaling evolutionary equation linearly connects the gravitational and internal energy densities. This implies well-known properties of polytropes, describing degenerate stars and chemically homogeneous nondegenerate stellar cores.
Kahler stabilized, modular invariant heterotic string models
Energy Technology Data Exchange (ETDEWEB)
Gaillard, Mary K.; Gaillard, Mary K.; Nelson, Brent D.
2007-03-19
We review the theory and phenomenology of effective supergravity theories based on orbifold compactifications of the weakly-coupled heterotic string. In particular, we consider theories in which the four-dimensional theory displays target space modular invariance and where the dilatonic mode undergoes Kahler stabilization. A self-contained exposition of effective Lagrangian approaches to gaugino condensation and heterotic string theory is presented, leading to the development of the models of Binétruy, Gaillard and Wu. Various aspects of the phenomenology of this class of models are considered. These include issues of supersymmetry breaking and superpartner spectra, the role of anomalous U(1) factors, issues of flavor and R-parity conservation, collider signatures, axion physics, and early universe cosmology. For the vast majority of phenomenological considerations the theories reviewed here compare quite favorably to other string-derived models in the literature. Theoretical objections to the framework and directions for further research are identified and discussed.
Blocks of finite groups and their invariants
Sambale, Benjamin
2014-01-01
Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern theory of fusion systems introduced by Puig, the geometry of numbers developed by Minkowski, the classification of finite simple groups, and various computer assisted methods. In a powerful combination, these tools are applied to solve many special cases of famous open conjectures in the representation theory of finite groups. Most of the material is drawn from peer-reviewed journal articles, but there are also new previously unpublished results. In order to make the text self-contained, detailed proofs are given whenever possible. Several tables add to the text's usefulness as a reference. The book is aimed at experts in group theory or representation theory who may wish to make use of the presented ideas in their research.
Gauge invariance and Weyl-polymer quantization
Strocchi, Franco
2016-01-01
The book gives an introduction to Weyl non-regular quantization suitable for the description of physically interesting quantum systems, where the traditional Dirac-Heisenberg quantization is not applicable. The latter implicitly assumes that the canonical variables describe observables, entailing necessarily the regularity of their exponentials (Weyl operators). However, in physically interesting cases -- typically in the presence of a gauge symmetry -- non-observable canonical variables are introduced for the description of the states, namely of the relevant representations of the observable algebra. In general, a gauge invariant ground state defines a non-regular representation of the gauge dependent Weyl operators, providing a mathematically consistent treatment of familiar quantum systems -- such as the electron in a periodic potential (Bloch electron), the Quantum Hall electron, or the quantum particle on a circle -- where the gauge transformations are, respectively, the lattice translations, the magne...
Joint survival probability via truncated invariant copula
International Nuclear Information System (INIS)
Kim, Jeong-Hoon; Ma, Yong-Ki; Park, Chan Yeol
2016-01-01
Highlights: • We have studied an issue of dependence structure between default intensities. • We use a multivariate shot noise intensity process, where jumps occur simultaneously and their sizes are correlated. • We obtain the joint survival probability of the integrated intensities by using a copula. • We apply our theoretical result to pricing basket default swap spread. - Abstract: Given an intensity-based credit risk model, this paper studies dependence structure between default intensities. To model this structure, we use a multivariate shot noise intensity process, where jumps occur simultaneously and their sizes are correlated. Through very lengthy algebra, we obtain explicitly the joint survival probability of the integrated intensities by using the truncated invariant Farlie–Gumbel–Morgenstern copula with exponential marginal distributions. We also apply our theoretical result to pricing basket default swap spreads. This result can provide a useful guide for credit risk management.
Scale-invariance in soft gamma repeaters
Chang, Zhe; Lin, Hai-Nan; Sang, Yu; Wang, Ping
2017-06-01
The statistical properties of the soft gamma repeater SGR J1550-5418 are investigated carefully. We find that the cumulative distributions of fluence, peak flux and duration can be well fitted by a bent power law, while the cumulative distribution of waiting time follows a simple power law. In particular, the probability density functions of fluctuations of fluence, peak flux, and duration have a sharp peak and fat tails, which can be well fitted by a q-Gaussian function. The q values keep approximately steady for different scale intervals, indicating a scale-invariant structure of soft gamma repeaters. Those results support that the origin of soft gamma repeaters is crustquakes of neutron stars with extremely strong magnetic fields. Supported by National Natural Science Foundation of China (11375203, 11675182, 11690022, 11603005), and Fundamental Research Funds for Central Universities (106112016CDJCR301206)
Quantum critical phenomena and conformal invariance
International Nuclear Information System (INIS)
Zhe Chang.
1995-05-01
We show that the Abelian bosonization of continuum limit of the 1D Hubbard model corresponds to the 2D explicitly conformal invariant Gaussian model at weak coupling limit. A universality argument is used to extend the equivalence to an entire segment of the critical line of the strongly correlated electron system. An integral equation satisfied by the mapping function between critical lines of the 1D Hubbard model and 2D Gaussian model is obtained and then solved in some limiting cases. By making use of the fact that the free Hubbard system reduces to four fermions and each of them is related to a c = 1/2 conformal field theory, we present exactly the partition function of the Hubbard model on a finite 1D lattice. (author). 16 refs
Null tests of time-reversal invariance
International Nuclear Information System (INIS)
Conzett, H.E.
1993-01-01
Because null tests of parity conservation exist in nuclear and particle reactions, it has been possible to measure very precisely the (weak-interaction) parity nonconserving contribution to the process. There is, however, a proof of the nonexistence of a comparable null test of time-reversal invariance. As a result, reaction tests of T symmetry have, at best, achieved precisions several orders of magnitude below that of the tests of P symmetry. Since transmission experiments are not included in the nonexistence proof, the existing formalism used to describe spin observables in neutron transmission experiments has been expanded to include explicitly the target spin. Through this formalism, the time-reversal-violating (and parity nonconserving) forward scattering amplitudes are identified, along with the corresponding spin observables. It is noted that new and more precise tests of T symmetry are provided in transmission experiments, and that such investigations are applicable more generally in nuclear and particle physics
Conformally invariant braneworld and the cosmological constant
International Nuclear Information System (INIS)
Guendelman, E.I.
2004-01-01
A six-dimensional braneworld scenario based on a model describing the interaction of gravity, gauge fields and 3+1 branes in a conformally invariant way is described. The action of the model is defined using a measure of integration built of degrees of freedom independent of the metric. There is no need to fine tune any bulk cosmological constant or the tension of the two (in the scenario described here) parallel branes to obtain zero cosmological constant, the only solutions are those with zero 4D cosmological constant. The two extra dimensions are compactified in a 'football' fashion and the branes lie on the two opposite poles of the compact 'football-shaped' sphere
Time reversal invariance in polarized neutron decay
Energy Technology Data Exchange (ETDEWEB)
Wasserman, Eric G. [Harvard Univ., Cambridge, MA (United States)
1994-03-01
An experiment to measure the time reversal invariance violating (T-violating) triple correlation (D) in the decay of free polarized neutrons has been developed. The detector design incorporates a detector geometry that provides a significant improvement in the sensitivity over that used in the most sensitive of previous experiments. A prototype detector was tested in measurements with a cold neutron beam. Data resulting from the tests are presented. A detailed calculation of systematic effects has been performed and new diagnostic techniques that allow these effects to be measured have been developed. As the result of this work, a new experiment is under way that will improve the sensitivity to D to 3 x 10^{-4} or better. With higher neutron flux a statistical sensitivity of the order 3 x 10^{-5} is ultimately expected. The decay of free polarized neutrons (n → p + e + $\\bar{v}$_{e}) is used to search for T-violation by measuring the triple correlation of the neutron spin polarization, and the electron and proton momenta (σ_{n} • p_{p} x p_{e}). This correlation changes sign under reversal of the motion. Since final state effects in neutron decay are small, a nonzero coefficient, D, of this correlation indicates the violation of time reversal invariance. D is measured by comparing the numbers of coincidences in electron and proton detectors arranged symmetrically about a longitudinally polarized neutron beam. Particular care must be taken to eliminate residual asymmetries in the detectors or beam as these can lead to significant false effects. The Standard Model predicts negligible T-violating effects in neutron decay. Extensions to the Standard Model include new interactions some of which include CP-violating components. Some of these make first order contributions to D.
Conformally invariant processes in the plane
International Nuclear Information System (INIS)
Lawler, G.F.
2004-01-01
These lectures will focus on recent rigorous work on continuum limits of planar lattice models from statistical physics at criticality. For an introduction, I would like to discuss the general problem of critical exponents and scaling limits for lattice models in equilibrium statistical mechanics. There are a number of models, [e.g., self-avoiding walk (polymers), percolation, loop-erased random walk (uniform spanning trees, domino tilings), Ising model, Potts model, nonintersecting simple random walks] that fall under this general framework. These lectures will consider the case d = 2. Mathematicians are now starting to understand rigorously the scaling limit of two-dimensional systems. For most of these models, the general strategy can be described as: Construct possible continuum limits for these models. Show that there are only a limited number of such limits that are conformally invariant. Prove that the lattice model approaches the continuum limit. We should think of the first step as being similar for all of these models. We will spend the next couple of lectures discussing the continuum limits. One example you should already know - the scaling limit of simple random walk is Brownian motion (which in two dimensions is conformally invariant). The important new ideas are restriction measures and stochastic Loewner evolution (SLE). The later lectures will discuss rigorous results about lattice models approaching the continuum limit - we will discuss nonintersecting random walks (which can be shown to be equivalent to problems about exceptional sets of Brownian paths), percolation on the triangular lattice, and the loop-erased random walk. As a rule, the methods used for the second step are particular to each model
Time reversal invariance in polarized neutron decay
International Nuclear Information System (INIS)
Wasserman, E.G.
1994-03-01
An experiment to measure the time reversal invariance violating (T-violating) triple correlation (D) in the decay of free polarized neutrons has been developed. The detector design incorporates a detector geometry that provides a significant improvement in the sensitivity over that used in the most sensitive of previous experiments. A prototype detector was tested in measurements with a cold neutron beam. Data resulting from the tests are presented. A detailed calculation of systematic effects has been performed and new diagnostic techniques that allow these effects to be measured have been developed. As the result of this work, a new experiment is under way that will improve the sensitivity to D to 3 x 10 -4 or better. With higher neutron flux a statistical sensitivity of the order 3 x 10 -5 is ultimately expected. The decay of free polarized neutrons (n → p + e + bar v e ) is used to search for T-violation by measuring the triple correlation of the neutron spin polarization, and the electron and proton momenta (σ n · p p x p e ). This correlation changes sign under reversal of the motion. Since final state effects in neutron decay are small, a nonzero coefficient, D, of this correlation indicates the violation of time reversal invariance. D is measured by comparing the numbers of coincidences in electron and proton detectors arranged symmetrically about a longitudinally polarized neutron beam. Particular care must be taken to eliminate residual asymmetries in the detectors or beam as these can lead to significant false effects. The Standard Model predicts negligible T-violating effects in neutron decay. Extensions to the Standard Model include new interactions some of which include CP-violating components. Some of these make first order contributions to D
A review of the generalized uncertainty principle
International Nuclear Information System (INIS)
Tawfik, Abdel Nasser; Diab, Abdel Magied
2015-01-01
Based on string theory, black hole physics, doubly special relativity and some ‘thought’ experiments, minimal distance and/or maximum momentum are proposed. As alternatives to the generalized uncertainty principle (GUP), the modified dispersion relation, the space noncommutativity, the Lorentz invariance violation, and the quantum-gravity-induced birefringence effects are summarized. The origin of minimal measurable quantities and the different GUP approaches are reviewed and the corresponding observations are analysed. Bounds on the GUP parameter are discussed and implemented in the understanding of recent PLANCK observations of cosmic inflation. The higher-order GUP approaches predict minimal length uncertainty with and without maximum momenta. Possible arguments against the GUP are discussed; for instance, the concern about its compatibility with the equivalence principles, the universality of gravitational redshift and the free fall and law of reciprocal action are addressed. (review)
On a class of invariant coframe operators with application to gravity
Itin, Yakov; Kaniel, Shmuel
2000-09-01
Let a differential 4D-manifold with a smooth coframe field be given. Consider the operators on it that are linear in the second order derivatives and quadratic in the first order derivatives of the coframe, both with coefficients that depend on the coframe variables. The article exhibits the class of operators that are invariant under a general change of coordinates, and, also, invariant under the global SO(1,3)-transformation of the coframe. A general class of field equations is constructed. We display two subclasses in it. The subclass of field equations that are derivable from action principles by free variations and the subclass of field equations for which spherical-symmetric solutions, Minkowskian at infinity, exist. Then, for the spherical-symmetric solutions, the resulting metric is computed. Invoking the geodesic postulate, we find all the equations that are experimentally (by the three classical tests) indistinguishable from Einstein field equations. This family also includes, of course, Einstein equations. Moreover, it is shown, explicitly, how to exhibit it. The basic tool employed in the article is an invariant formulation reminiscent of Cartan's structural equations. The article sheds light on the possibilities and limitations of the coframe gravity. It may also serve as a general procedure to derive covariant field equations.
Pen, I.R.; Weissing, F.J.
Recently, Charnov (1996) investigated the consequences of sperm competition for optimal sex allocation in simultaneous hermaphrodites. Charnov argued that the optimal sex allocation strategy can be derived on the basis of the 'sperm displacement rule'; that is, the function describing the
Rigid invariance as derived from BRS invariance. The abelian Higgs model
International Nuclear Information System (INIS)
Kraus, E.
1995-02-01
Consequences of a symmetry, e.g. relations amongst Green functions, are renormalization scheme independently expressed in terms of a rigid Ward identity. The corresponding local version yields information on the respective current. In the case of spontaneous breakdown one has to define the theory via the BRS invariance and thus to construct rigid and current Ward identity non-trivially in accordance with it. We performed this construction to all orders of perturbation theory in the abelian Higgs model as a prelude to the standard model. A technical tool of interest in itself is the use of a doublet of external scalar ''background'' fields. The Callan-Symanzik equation has an interesting form and follows easily once the rigid invariance is established. (orig.)
The parametrization invariant and gauge invariant effective actions in quantum field theory
International Nuclear Information System (INIS)
Odintsov, S.D.
1990-01-01
The review of formulation and methods of calculation of the parametrization and gauge invariant effective actions in quantum field theory is given. As an example the Vilkovisky-De Witt Effective action (EA) is studied (this EA is a natural representative of gauge and parametrization invariant EA's). The examples where the use of the standard EA leads to the ambiguity are demonstrated. This happens as the result of dependence of the standard EA upon the choice of gauge condition. These examples are as follows: Coleman-Weinberg potential in the finite theories and symmetry breaking, EA in quantum gravity with matter and d=5 gauged supergravity, the possibility of spontaneous supersymmetry breaking in N=1 supergravity and the spontaneous compactification in the multidimensional R 2 -gravity. In all these cases the one-loop Vilkovisky-De Witt EA is found and therefore the problem of gauge dependence of EA is solved. The dependence of standard EA of composite fields upon the gauge is studied for the general gauge theories. The class of gauge and parametrization invariant EA's of the composite fields is offered. (author)
Projective invariants in a conformal finsler space - I
International Nuclear Information System (INIS)
Mishra, C.K.; Singh, M.P.
1989-12-01
The projective invariants in a conformal Finsler space have been studied in regard to certain tensor and scalar which are invariant under projective transformation in a Finsler space. They have been the subject of further investigation by the present authors. (author). 8 refs
N=2 supergravity in superspace: the invariant action
International Nuclear Information System (INIS)
Gal'perin, A.S.; Sokachev, E.
1987-01-01
This paper continues the formulation of harmonic superspace supergravity. We write down the invariant action for the first off-shell version of the theory. The proof of the invariance relies on the existence of a new 'hybrid' basis in harmonic superspace in which semi-chirality combined with analyticity are manifest
Measurement Invariance of the Pay Satisfaction Questionnaire across Three Countries
Lievens, Filip; Anseel, Frederik; Harris, Michael M.; Eisenberg, Jacob
2007-01-01
In recent years, pay satisfaction has been increasingly studied in an international context, prompting the importance of examining whether the Pay Satisfaction Questionnaire (PSQ) is invariant across countries other than the United States. This study investigated the measurement invariance across three countries, namely, the United States (N =…
Rotation-invariant fingerprint matching using radon and DCT
Indian Academy of Sciences (India)
Sangita Bharkad
2017-11-20
Nov 20, 2017 ... invariant features using radon transform and translation invariance is achieved using DCT. ... et al [11] introduced a convolutional neural-network-based approach for automatic extraction of minutiae points ...... recognition, machine intelligence and biometrics (PRMI),. Chapter 17, Springer, pp. 417–455.
On Action Invariance under Linear Spinor-Vector Supersymmetry
Directory of Open Access Journals (Sweden)
Kazunari Shima
2006-01-01
Full Text Available We show explicitly that a free Lagrangian expressed in terms of scalar, spinor, vector and Rarita-Schwinger (RS fields is invariant under linear supersymmetry transformations generated by a global spinor-vector parameter. A (generalized gauge invariance of the Lagrangian for the RS field is also discussed.
The Scale Invariant Synchrotron Jet of Flat Spectrum Radio Quasars
Indian Academy of Sciences (India)
2016-01-27
Jan 27, 2016 ... In this paper, the scale invariance of the synchrotron jet of Flat Spectrum Radio Quasars has been studied using a sample of combined sources from FKM04 and from SDSS DR3 catalogue. Since the research of scale invariance has been focused on sub-Eddington cases that can be fitted onto the ...
Conformal invariance in the long-range Ising model
Paulos, M.F.; Rychkov, S.; van Rees, B.C.; Zan, B.
We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to
The undergeneration of permutation invariance as a criterion for logicality
Dutilh Novaes, Catarina
2014-01-01
Permutation invariance is often presented as the correct criterion for logicality. The basic idea is that one can demarcate the realm of logic by isolating speciﬁc entities—logical notions or constants—and that permutation invariance would provide a philosophically motivated and technically
Integrable lattice models, graphs and modular invariant conformal field theories
International Nuclear Information System (INIS)
Francesco, P.
1992-01-01
This paper reviews the construction of integrable height models attached to graphs in connection with compact Lie groups. The continuum limit of these models yields conformally invariant field theories. A direct relation between graphs and (Kac-Moody or coset) modular invariants is proposed
Construction of exact complex dynamical invariant of a two ...
Indian Academy of Sciences (India)
physics pp. 999–1009. Construction of exact complex dynamical invariant of a two-dimensional classical system. FAKIR CHAND and S C MISHRA. Department ... namical invariants for both time-dependent and time-independent classical systems. [1–3]. .... where [·, ·] is the Poisson bracket, which in view of the definition eq.
International Nuclear Information System (INIS)
Huang, Young-Sea
2010-01-01
The differential Lorentz transformation is formulated solely from the principle of relativity and the invariance of the speed of light. The differential Lorentz transformation transforms physical quantities, instead of space-time coordinates, to keep laws of nature form-invariant among inertial frames. The new relativistic transformation fulfills the principle of relativity, whereas the usual Lorentz transformation of space-time coordinates does not. Furthermore, the new relativistic transformation is compatible with quantum mechanics. The formulation herein provides theoretical foundations for the differential Lorentz transformation as the fundamental relativistic transformation.
Principles of project management
1982-01-01
The basic principles of project management as practiced by NASA management personnel are presented. These principles are given as ground rules and guidelines to be used in the performance of research, development, construction or operational assignments.
On Gauge Invariance and Minimal Coupling
Jenkins, Elizabeth E; Trott, Michael
2013-01-01
The principle of minimal coupling has been used in the study of Higgs boson interactions to argue that certain higher dimensional operators in the low-energy effective theory generalization of the Standard Model are suppressed by loop factors, and thus smaller than others. It also has been extensively used to analyze beyond-the-standard-model theories. We show that in field theory, and even in quantum mechanics, the concept of minimal coupling is ill-defined and inapplicable as a general principle, and give many pedagogical examples which illustrate this fact. We also clarify some related misconceptions about the dynamics of strongly coupled gauge theories. Many arguments in the literature on Higgs boson interactions that use minimal coupling, particularly in pseudo-Goldstone Higgs theories, are inherently flawed.
AN ILLUMINATION INVARIANT TEXTURE BASED FACE RECOGNITION
Directory of Open Access Journals (Sweden)
K. Meena
2013-11-01
Full Text Available Automatic face recognition remains an interesting but challenging computer vision open problem. Poor illumination is considered as one of the major issue, since illumination changes cause large variation in the facial features. To resolve this, illumination normalization preprocessing techniques are employed in this paper to enhance the face recognition rate. The methods such as Histogram Equalization (HE, Gamma Intensity Correction (GIC, Normalization chain and Modified Homomorphic Filtering (MHF are used for preprocessing. Owing to great success, the texture features are commonly used for face recognition. But these features are severely affected by lighting changes. Hence texture based models Local Binary Pattern (LBP, Local Derivative Pattern (LDP, Local Texture Pattern (LTP and Local Tetra Patterns (LTrPs are experimented under different lighting conditions. In this paper, illumination invariant face recognition technique is developed based on the fusion of illumination preprocessing with local texture descriptors. The performance has been evaluated using YALE B and CMU-PIE databases containing more than 1500 images. The results demonstrate that MHF based normalization gives significant improvement in recognition rate for the face images with large illumination conditions.
Achieving Translationally Invariant Trapped Ion Rings
Urban, Erik; Li, Hao-Kun; Noel, Crystal; Hemmerling, Boerge; Zhang, Xiang; Haeffner, Hartmut
2017-04-01
We present the design and implementation of a novel surface ion trap design in a ring configuration. By eliminating the need for wire bonds through the use of electrical vias and using a rotationally invariant electrode configuration, we have realized a trap that is able to trap up to 20 ions in a ring geometry 45um in diameter, 400um above the trap surface. This large trapping height to ring diameter ratio allows for global addressing of the ring with both lasers and electric fields in the chamber, thereby increasing our ability to control the ring as a whole. Applying compensating electric fields, we measure very low tangential trap frequencies (less than 20kHz) corresponding to rotational barriers down to 4mK. This measurement is currently limited by the temperature of the ions but extrapolation indicates the barrier can be reduced much further with more advanced cooling techniques. Finally, we show that we are able to reduce this energy barrier sufficiently such that the ions are able to overcome it either through thermal motion or rotational motion and delocalize over the full extent of the ring. This work was funded by the Keck Foundation and the NSF.
Scale-invariant gravity: spacetime recovered
International Nuclear Information System (INIS)
Kelleher, Bryan
2004-01-01
The configuration space of general relativity is superspace-the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace-the space of all Riemannian 3-metrics modulo diffeomorphisms and conformal transformations. Recently a manifestly three-dimensional theory was constructed with conformal superspace as the configuration space. Here a fully four-dimensional action is constructed so as to be invariant under conformal transformations of the 4-metric using general relativity as a guide. This action is then decomposed to a (3 + 1)-dimensional form and from this to its Jacobi form. The surprising thing is that the new theory turns out to be precisely the original three-dimensional theory. The physical data are identified and used to find the physical representation of the theory. In this representation the theory is extremely similar to general relativity. The clarity of the four-dimensional picture should prove very useful for comparing the theory with those aspects of general relativity which are usually treated in the four-dimensional framework
ICECUBE NEUTRINOS AND LORENTZ INVARIANCE VIOLATION
Energy Technology Data Exchange (ETDEWEB)
Amelino-Camelia, Giovanni [Dipartimento di Fisica, Sapienza Università di Roma and INFN, Sez. Roma1, P.le A. Moro 2, I-00185 Roma (Italy); Guetta, D. [Osservatorio astronomico di Roma, v. Frascati 33, I-00040 Monte Porzio Catone (Italy); Piran, Tsvi [The Racah Institute for Physics, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
2015-06-20
The IceCube neutrino telescope has found so far no evidence of gamma-ray burst (GRB) neutrinos. We here notice that these results assume the same travel times from source to telescope for neutrinos and photons, an assumption that is challenged by some much-studied pictures of spacetime quantization. We briefly review previous results suggesting that limits on quantum-spacetime effects obtained for photons might not be applicable to neutrinos, and we then observe that the outcome of GRB-neutrino searches could depend strongly on whether one allows for neutrinos to be affected by the minute effects of Lorentz invariance violation (LIV) predicted by some relevant quantum-spacetime models. We discuss some relevant issues using as an illustrative example three neutrinos that were detected by IceCube in good spatial coincidence with GRBs, but hours before the corresponding gamma rays. In general, this could happen if the earlier arrival reflects quantum-spacetime-induced LIV, but, as we stress, some consistency criteria must be enforced in order to properly test such a hypothesis. Our analysis sets the stage for future GRB-neutrino searches that could systematically test the possibility of quantum-spacetime-induced LIV.
Implications of conformal invariance in momentum space
Bzowski, Adam; McFadden, Paul; Skenderis, Kostas
2014-03-01
We present a comprehensive analysis of the implications of conformal invariance for 3-point functions of the stress-energy tensor, conserved currents and scalar operators in general dimension and in momentum space. Our starting point is a novel and very effective decomposition of tensor correlators which reduces their computation to that of a number of scalar form factors. For example, the most general 3-point function of a conserved and traceless stress-energy tensor is determined by only five form factors. Dilatations and special conformal Ward identities then impose additional conditions on these form factors. The special conformal Ward identities become a set of first and second order differential equations, whose general solution is given in terms of integrals involving a product of three Bessel functions (`triple- K integrals'). All in all, the correlators are completely determined up to a number of constants, in agreement with well-known position space results. In odd dimensions 3-point functions are finite without renormalisation while in even dimensions non-trivial renormalisation in required. In this paper we restrict ourselves to odd dimensions. A comprehensive analysis of renormalisation will be discussed elsewhere. This paper contains two parts that can be read independently of each other. In the first part, we explain the method that leads to the solution for the correlators in terms of triple- K integrals while the second part contains a self-contained presentation of all results. Readers interested only in results may directly consult the second part of the paper.
Lifshitz invariants from ab initio lattice dynamics
Schiaffino, Andrea; Stengel, Massimiliano
The interaction between different order parameters is vital to explain the emergence of new functionalities (hybrid improper ferroelectricity, magnetoelectricity) in multiferroic systems. While considerable theoretical efforts have been directed in the past at studying couplings (e.g. trilinear or biquadratic) that occur in a homogeneous sample, recent research has revealed an increasing number of cases where the interesting physics emerges from inhomogeneities in some order parameter (e.g. flexoelectricity, domain walls), rather than the uniform bulk phase itself. These are usually described in phenomenological theories via symmetry-allowed gradient-mediated terms, the so-called Lifshitz invariants. Here I will present a general method to calculate such couplings ab initio, within the framework of density-functional perturbation theory. I will start with a brief overview on the most challenging aspects of these calculations, i.e. how to deal with the breakdown of the translational symmetry, and with the unusual electrostatic effects that occur in such a regime. Next, I will demonstrate this strategy in practice by presenting calculations of the most relevant gradient coefficients involving strain, octahedral tilts and polarization in ferroelastic SrTiO3. MINECO-Spain through Grants No. FIS2013-48668-C2-2-P and No. SEV-2015-0496, and by Generalitat de Catalunya (Grant No. 2014SRG301).
Parity and time invariance violation in mercury
International Nuclear Information System (INIS)
Ginges, J.S.M.; Dzuba, V.A.; Flambaum, V.V.; Kozlov, M.G.
2002-01-01
Full text: In a recent experiment, a stringent upper limit was placed on the atomic electric dipole moment (EDM) of 199 Hg corresponding to the best limit on an atomic EDM to date. This limit can be interpreted in terms of a limit on a parity-and time-invariance violating (P,T-odd) nuclear electric moment, the Schiff moment. This moment can arise in the nucleus due to an intrinsic EDM of an unpaired nucleon or a P,T-odd interaction between nucleons. In previous calculations the electrostatic potential of the Schiff moment was expressed in a singular form which must be treated carefully to avoid divergences in the electronic matrix elements. We have shown that the electric field distribution inside the nucleus arising from the Schiff moment is constant and directed along the nuclear spin. This allows us to express the Schiff moment in a form more convenient for numerical relativistic atomic calculations. We have calculated the atomic EDM induced in Hg due to the Schiff moment (for which no direct calculation has previously been performed) and have placed new limits on the fundamental P,T-odd parameters. These limits strongly constrain competing theories of CP-violation
Spatially invariant computations in stereoscopic vision.
Vidal-Naquet, Michel; Gepshtein, Sergei
2012-01-01
PERCEPTION OF STEREOSCOPIC DEPTH REQUIRES THAT VISUAL SYSTEMS SOLVE A CORRESPONDENCE PROBLEM: find parts of the left-eye view of the visual scene that correspond to parts of the right-eye view. The standard model of binocular matching implies that similarity of left and right images is computed by inter-ocular correlation. But the left and right images of the same object are normally distorted relative to one another by the binocular projection, in particular when slanted surfaces are viewed from close distance. Correlation often fails to detect correct correspondences between such image parts. We investigate a measure of inter-ocular similarity that takes advantage of spatially invariant computations similar to the computations performed by complex cells in biological visual systems. This measure tolerates distortions of corresponding image parts and yields excellent performance over a much larger range of surface slants than the standard model. The results suggest that, rather than serving as disparity detectors, multiple binocular complex cells take part in the computation of inter-ocular similarity, and that visual systems are likely to postpone commitment to particular binocular disparities until later stages in the visual process.
Invariant measures of the 2D Euler and Vlasov equations
International Nuclear Information System (INIS)
Bouchet, Freddy; Corvellec, Marianne
2010-01-01
We discuss invariant measures of partial differential equations such as the 2D Euler or Vlasov equations. For the 2D Euler equations, starting from the Liouville theorem, valid for N-dimensional approximations of the dynamics, we define the microcanonical measure as a limit measure where N goes to infinity. When only the energy and enstrophy invariants are taken into account, we give an explicit computation to prove the following result: the microcanonical measure is actually a Young measure corresponding to the maximization of a mean-field entropy. We explain why this result remains true for more general microcanonical measures, when all the dynamical invariants are taken into account. We give an explicit proof that these microcanonical measures are invariant measures for the dynamics of the 2D Euler equations. We describe a more general set of invariant measures and discuss briefly their stability and their consequence for the ergodicity of the 2D Euler equations. The extension of these results to the Vlasov equations is also discussed, together with a proof of the uniqueness of statistical equilibria, for Vlasov equations with repulsive convex potentials. Even if we consider, in this paper, invariant measures only for Hamiltonian equations, with no fluxes of conserved quantities, we think this work is an important step towards the description of non-equilibrium invariant measures with fluxes
Static analysis of class invariants in Java programs
Bonilla-Quintero, Lidia Dionisia
2011-12-01
This paper presents a technique for the automatic inference of class invariants from Java bytecode. Class invariants are very important for both compiler optimization and as an aid to programmers in their efforts to reduce the number of software defects. We present the original DC-invariant analysis from Adam Webber, talk about its shortcomings and suggest several different ways to improve it. To apply the DC-invariant analysis to identify DC-invariant assertions, all that one needs is a monotonic method analysis function and a suitable assertion domain. The DC-invariant algorithm is very general; however, the method analysis can be highly tuned to the problem in hand. For example, one could choose shape analysis as the method analysis function and use the DC-invariant analysis to simply extend it to an analysis that would yield class-wide invariants describing the shapes of linked data structures. We have a prototype implementation: a system we refer to as "the analyzer" that infers DC-invariant unary and binary relations and provides them to the user in a human readable format. The analyzer uses those relations to identify unnecessary array bounds checks in Java programs and perform null-reference analysis. It uses Adam Webber's relational constraint technique for the class-invariant binary relations. Early results with the analyzer were very imprecise in the presence of "dirty-called" methods. A dirty-called method is one that is called, either directly or transitively, from any constructor of the class, or from any method of the class at a point at which a disciplined field has been altered. This result was unexpected and forced an extensive search for improved techniques. An important contribution of this paper is the suggestion of several ways to improve the results by changing the way dirty-called methods are handled. The new techniques expand the set of class invariants that can be inferred over Webber's original results. The technique that produces better
Invariants for minimal conformal supergravity in six dimensions
Energy Technology Data Exchange (ETDEWEB)
Butter, Daniel [Nikhef Theory Group,Science Park 105, 1098 XG Amsterdam (Netherlands); Kuzenko, Sergei M. [School of Physics M013, The University of Western Australia,35 Stirling Highway, Crawley W.A. 6009 (Australia); Novak, Joseph; Theisen, Stefan [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,Am Mühlenberg 1, D-14476 Golm (Germany)
2016-12-15
We develop a new off-shell formulation for six-dimensional conformal supergravity obtained by gauging the 6D N=(1,0) superconformal algebra in superspace. This formulation is employed to construct two invariants for 6D N=(1,0) conformal supergravity, which contain C{sup 3} and C◻C terms at the component level. Using a conformal supercurrent analysis, we prove that these exhaust all such invariants in minimal conformal supergravity. Finally, we show how to construct the supersymmetric F◻F invariant in curved superspace.
Hermite-symmetry and super-gauge-invariance
Energy Technology Data Exchange (ETDEWEB)
Treder, H.J. (Akademie der Wissenschaften der DDR, Potsdam-Babelsberg. Einstein-Laboratorium fuer Theoretische Physik)
1985-03-01
Within a unitary general relativistic field theory the metric fundamental tensor and the affinities are to be considered as independent field variables under the condition that besides the coordinate covariance the invariance for 'transformations preserving parallelism' (Einstein's A-gauge-invariance) exists. For a (non-degenerate) hermitian fundamental tensor the demand for super-gauge-invariance leads to the hermitian symmetry of both the affinities and the Ricci tensor. The hermitian continuation of general relativity into the complex domain leads therefore to the Einstein-Schroedinger field equations.
Verification of Java Programs using Symbolic Execution and Invariant Generation
Pasareanu, Corina; Visser, Willem
2004-01-01
Software verification is recognized as an important and difficult problem. We present a norel framework, based on symbolic execution, for the automated verification of software. The framework uses annotations in the form of method specifications an3 loop invariants. We present a novel iterative technique that uses invariant strengthening and approximation for discovering these loop invariants automatically. The technique handles different types of data (e.g. boolean and numeric constraints, dynamically allocated structures and arrays) and it allows for checking universally quantified formulas. Our framework is built on top of the Java PathFinder model checking toolset and it was used for the verification of several non-trivial Java programs.
Gauge invariance properties and singularity cancellations in a modified PQCD
Cabo-Montes de Oca, Alejandro; Cabo, Alejandro; Rigol, Marcos
2006-01-01
The gauge-invariance properties and singularity elimination of the modified perturbation theory for QCD introduced in previous works, are investigated. The construction of the modified free propagators is generalized to include the dependence on the gauge parameter $\\alpha $. Further, a functional proof of the independence of the theory under the changes of the quantum and classical gauges is given. The singularities appearing in the perturbative expansion are eliminated by properly combining dimensional regularization with the Nakanishi infrared regularization for the invariant functions in the operator quantization of the $\\alpha$-dependent gauge theory. First-order evaluations of various quantities are presented, illustrating the gauge invariance-properties.
Assessing the Gender Invariance of the Modern Homonegativity Scale.
Romero, Daniel H; Morera, Osvaldo F; Wiebe, John S
2015-01-01
The measurement invariance of the Modern Homonegativity Scale (MHS) was examined among heterosexual female (n = 449) and male (n = 329) university students who were predominantly Mexican American. The MHS demonstrated full invariance of factor loadings and partial invariance of latent intercepts. At the latent mean level, heterosexual men compared to heterosexual women held more negative attitudes toward both gay men and lesbian women. There were no latent mean differences in attitudes toward gay men and lesbian women when rated by either heterosexual men or heterosexual women. The MHS can be used by heterosexual men and heterosexual women to assess their homonegativity.
Evolution of Brain Tumor and Stability of Geometric Invariants
Directory of Open Access Journals (Sweden)
K. Tawbe
2008-01-01
Full Text Available This paper presents a method to reconstruct and to calculate geometric invariants on brain tumors. The geometric invariants considered in the paper are the volume, the area, the discrete Gauss curvature, and the discrete mean curvature. The volume of a tumor is an important aspect that helps doctors to make a medical diagnosis. And as doctors seek a stable calculation, we propose to prove the stability of some invariants. Finally, we study the evolution of brain tumor as a function of time in two or three years depending on patients with MR images every three or six months.
Invariant renormalization method for nonlinear realizations of dynamical symmetries
International Nuclear Information System (INIS)
Kazakov, D.I.; Pervushin, V.N.; Pushkin, S.V.
1977-01-01
The structure of ultraviolet divergences is investigated for the field theoretical models with nonlinear realization of the arbitrary semisimple Lie group, with spontaneously broken symmetry of vacuum. An invariant formulation of the background field method of renormalization is proposed which gives the manifest invariant counterterms off mass shell. A simple algorithm for construction of counterterms is developed. It is based on invariants of the group of dynamical symmetry in terms of the Cartan forms. The results of one-loop and two-loop calculations are reported
Dimensional cosmological principles
International Nuclear Information System (INIS)
Chi, L.K.
1985-01-01
The dimensional cosmological principles proposed by Wesson require that the density, pressure, and mass of cosmological models be functions of the dimensionless variables which are themselves combinations of the gravitational constant, the speed of light, and the spacetime coordinates. The space coordinate is not the comoving coordinate. In this paper, the dimensional cosmological principle and the dimensional perfect cosmological principle are reformulated by using the comoving coordinate. The dimensional perfect cosmological principle is further modified to allow the possibility that mass creation may occur. Self-similar spacetimes are found to be models obeying the new dimensional cosmological principle
Modeling the violation of reward maximization and invariance in reinforcement schedules.
Directory of Open Access Journals (Sweden)
Giancarlo La Camera
2008-08-01
Full Text Available It is often assumed that animals and people adjust their behavior to maximize reward acquisition. In visually cued reinforcement schedules, monkeys make errors in trials that are not immediately rewarded, despite having to repeat error trials. Here we show that error rates are typically smaller in trials equally distant from reward but belonging to longer schedules (referred to as "schedule length effect". This violates the principles of reward maximization and invariance and cannot be predicted by the standard methods of Reinforcement Learning, such as the method of temporal differences. We develop a heuristic model that accounts for all of the properties of the behavior in the reinforcement schedule task but whose predictions are not different from those of the standard temporal difference model in choice tasks. In the modification of temporal difference learning introduced here, the effect of schedule length emerges spontaneously from the sensitivity to the immediately preceding trial. We also introduce a policy for general Markov Decision Processes, where the decision made at each node is conditioned on the motivation to perform an instrumental action, and show that the application of our model to the reinforcement schedule task and the choice task are special cases of this general theoretical framework. Within this framework, Reinforcement Learning can approach contextual learning with the mixture of empirical findings and principled assumptions that seem to coexist in the best descriptions of animal behavior. As examples, we discuss two phenomena observed in humans that often derive from the violation of the principle of invariance: "framing," wherein equivalent options are treated differently depending on the context in which they are presented, and the "sunk cost" effect, the greater tendency to continue an endeavor once an investment in money, effort, or time has been made. The schedule length effect might be a manifestation of these
A quantization scheme for scale-invariant pure gauge theories
International Nuclear Information System (INIS)
Hortacsu, M.
1988-01-01
A scheme is suggested for the quantization of the recently proposed scale-invariant gauge theories in higher dimensions. The model is minimally coupled to a spinor field. Regularization algorithms are proposed. (orig.)
Gauge-invariant two- and three- density correlators
Alexandrou, C; Tsapalis, A; Forcrand, Ph. de
2003-01-01
Gauge-invariant spatial correlations between two and three quarks inside a hadron are measured within quenched and unquenched QCD. These correlators provide information on the shape and multipole moments of the pion, the rho, the nucleon and the $\\Delta$.
About Shape Identification Methods of Objects Invariant to Projective Transformations
Directory of Open Access Journals (Sweden)
Gostev Ivan M.
2016-01-01
Full Text Available Diffculties concerning the choice of the invariants of the projective transformation groups used for the identification of the shapes of planar objects are illustrated and solutions allowing the derivation of robust identification criteria are discussed.
Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI
Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.
2015-01-01
Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085
Gauge field improvement, form-scalar duality and conformal invariance
Deser, Stanley
1994-01-01
The problem of maintaining scale and conformal invariance in Maxwell and general N-form gauge theories away from their critical dimension d=2(N+1) is analyzed.We first exhibit the underlying group-theoretical clash between locality,gauge,Lorentz and conformal invariance require- ments. "Improved" traceless stress tensors are then constructed;each violates one of the above criteria.However,when d=N+2,there is a duality equivalence between N-form models and massless scalars.Here we show that conformal invariance is not lost,by constructing a quasilocal gauge invariant improved stress tensor.The correlators of the scalar theory are then reproduced including the latter's trace anomaly.
Chiral gauge theories on the lattice with exact gauge invariance
Lüscher, Martin
1999-01-01
A recently proposed formulation of chiral lattice gauge theories is reviewed, in which the locality and gauge invariance of the theory can be preserved if the fermion representation of the gauge group is anomaly-free.
Canopy spectral invariants for remote sensing and model applications
Huang, D.; Knyazikhin, Y.; Dickinson, R.E.; Rautiainen, M.; Stenberg, P.; Disney, M.; Lewis, P.; Cescatti, A.; Tian, Y.; Verhoef, W.; Martonchik, J.V.; Myneni, R.B.
2007-01-01
The concept of canopy spectral invariants expresses the observation that simple algebraic combinations of leaf and canopy spectral transmittance and reflectance become wavelength independent and determine a small set of canopy structure specific variables. This set includes the canopy interceptance,
The component structure of conformal supergravity invariants in six dimensions
Butter, Daniel; Novak, Joseph; Tartaglino-Mazzucchelli, Gabriele
2017-05-01
In the recent paper arXiv:1606.02921, the two invariant actions for 6D N=(1,0) conformal supergravity were constructed in superspace, corresponding to the supersymmetrization of C 3 and C□ C. In this paper, we provide the translation from superspace to the component formulation of superconformal tensor calculus, and we give the full component actions of these two invariants. As a second application, we build the component form for the supersymmetric F□ F action coupled to conformal supergravity. Exploiting the fact that the N=(2,0) Weyl multiplet has a consistent truncation to N=(1,0), we then verify that there is indeed only a single N=(2,0) conformal supergravity invariant and reconstruct most of its bosonic terms by uplifting a certain linear combination of N=(1,0) invariants.
Invariance properties of the Dirac equation with external electro ...
Indian Academy of Sciences (India)
. Introduction. The objective of this short paper is to investigate the invariance properties of the Dirac equation with external electro-magnetic field. There exists a large number of literatures on the problem beginning almost from the formulation ...
Generalized N-coupled maps with invariant measure in Bose ...
Indian Academy of Sciences (India)
- bility of the ..... One-parameter families of chaotic maps of the interval [0, ...... their invariant measure and Lyapunov exponent in order to simplify the generation of coupled map model based on Bose–Mesner algebra: 1. Bernuli shift map:.
Inertial Spontaneous Symmetry Breaking and Quantum Scale Invariance
Energy Technology Data Exchange (ETDEWEB)
Ferreira, Pedro G. [Oxford U.; Hill, Christopher T. [Fermilab; Ross, Graham G. [Oxford U., Theor. Phys.
2018-01-23
Weyl invariant theories of scalars and gravity can generate all mass scales spontaneously, initiated by a dynamical process of "inertial spontaneous symmetry breaking" that does not involve a potential. This is dictated by the structure of the Weyl current, $K_\\mu$, and a cosmological phase during which the universe expands and the Einstein-Hilbert effective action is formed. Maintaining exact Weyl invariance in the renormalised quantum theory is straightforward when renormalisation conditions are referred back to the VEV's of fields in the action of the theory, which implies a conserved Weyl current. We do not require scale invariant regulators. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential.
Manifestly scale-invariant regularization and quantum effective operators
Ghilencea, D.M.
2016-01-01
Scale invariant theories are often used to address the hierarchy problem, however the regularization of their quantum corrections introduces a dimensionful coupling (dimensional regularization) or scale (Pauli-Villars, etc) which break this symmetry explicitly. We show how to avoid this problem and study the implications of a manifestly scale invariant regularization in (classical) scale invariant theories. We use a dilaton-dependent subtraction function $\\mu(\\sigma)$ which after spontaneous breaking of scale symmetry generates the usual DR subtraction scale $\\mu(\\langle\\sigma\\rangle)$. One consequence is that "evanescent" interactions generated by scale invariance of the action in $d=4-2\\epsilon$ (but vanishing in $d=4$), give rise to new, finite quantum corrections. We find a (finite) correction $\\Delta U(\\phi,\\sigma)$ to the one-loop scalar potential for $\\phi$ and $\\sigma$, beyond the Coleman-Weinberg term. $\\Delta U$ is due to an evanescent correction ($\\propto\\epsilon$) to the field-dependent masses (of...
Trace anomaly and invariance under transformation of units
Namavarian, Nadereh
2017-05-01
Paying attention to conformal invariance as the invariance under local transformations of units of measure, we take a conformal-invariant quantum field as a quantum matter theory in which one has the freedom to choose the values of units of mass, length, and time arbitrarily at each point. To be able to have this view, it is necessary that the background on which the quantum field is based be conformal invariant as well. Consequently, defining the unambiguous expectation value of the energy-momentum tensor of such a quantum field through the Wald renormalizing prescription necessitates breaking down the conformal symmetry of the background. Then, noticing the field equations suitable for describing the backreaction effect, we show that the existence of the "trace anomaly," known for indicating the brokenness of conformal symmetry in quantum field theory, can also indicate the above "gravitational" conformal symmetry brokenness.
Testing measurement invariance of composites using partial least squares
Henseler, Jörg; Ringle, Christian M.; Sarstedt, Marko
2016-01-01
Purpose Research on international marketing usually involves comparing different groups of respondents. When using structural equation modeling (SEM), group comparisons can be misleading unless researchers establish the invariance of their measures. While methods have been proposed to analyze
Construction of exact complex dynamical invariant of a two ...
Indian Academy of Sciences (India)
dimensional classical dynamical system on an extended complex space utilizing Lie algebraic approach. These invariants are expected to play a vital role in understanding the complex trajectories of both classical and quantum systems.
Wavelet subspaces invariant under groups of translation operators
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Tα(Vj ) ⊂ Vj for all j ∈ Z and for all α ∈ R. Madych proved that the only translation invariant MRAs are those for which the Fourier transform of the scaling function is the characteristic function of a set. In other words, the associated wavelet is an MSF wavelet. Walter [10,11] modified the definition of translation invariance to ...
Construction of Lie algebras and invariant tensors through abelian semigroups
International Nuclear Information System (INIS)
Izaurieta, Fernando; RodrIguez, Eduardo; Salgado, Patricio
2008-01-01
The Abelian Semigroup Expansion Method for Lie Algebras is briefly explained. Given a Lie Algebra and a discrete abelian semigroup, the method allows us to directly build new Lie Algebras with their corresponding non-trivial invariant tensors. The Method is especially interesting in the context of M-Theory, because it allows us to construct M-Algebra Invariant Chern-Simons/Transgression Lagrangians in d = 11.
Skewed base compositions, asymmetric transition matrices, and phylogenetic invariants.
Ferretti, V; Lang, B F; Sankoff, D
1994-01-01
Evolutionary inference methods that assume equal DNA base compositions and symmetric nucleotide substitution matrices, where these assumptions do not hold, are likely to group species on the basis of similar base compositions rather than true phylogenetic relationships. We propose an invariants-based method for dealing with this problem. An invariant QT of a tree T under a k-state Markov model, where a generalized time parameter is identified with the E edges of T, allows us to recognize whether data on N observed species can be associated with the N terminal vertices of T in the sense of having been generated on T rather than on any other tree with N terminals. The form of the generalized time parameter is a positive determinant matrix in some semigroup S of stochastic matrices. The invariance is with respect to the choice of the set of E matrices in S, one associated with each of the E edges of T. We apply a general "empirical" method of finding invariants of a parametrized functional form. It involves calculating the probability f of all KN data possibilities for each of m sets of E matrices in S to associate with the edges of T, then solving for the parameters using the m equations of form Q(f) = 0. We discuss the problems of finding asymmetric models satisfying the property of semigroup closure, of finding asymmetric models that admit invariants at all, and of the computational complexity of the method. We propose a class of semigroups Sc containing matrices of form [formula: see text] to account for A+T versus G+C asymmetries in DNA base composition. Quadratic invariants are obtained for rooted trees with three and with four terminals. In the latter case the smallest set of algebraically independent invariants is sought. These invariants are applied to data pertaining the fungal evolution and to the origin of mitochondria as bacterial endosymbionts.
RG Cycles, Scale vs Conformal Invariance, and All That...
Fortin, J.-F.; Grinstein, B.; Stergiou, A.
Two long-standing questions in Quantum Field Theory have been recently answered, at least in perturbation theory. The first one is, are there recursive flows as solutions of the renormalization group equation (answer: yes). The second one is, can a theory display invariance under dilatations but not be conformally invariant? (answer: no). We review these results. In so doing we give a hopefully pedagogic derivation of the trace anomaly equation and of the Weyl consistency conditions of Jack and Osborn.
Modular invariant partition functions for toroidally compactified bosonic string
International Nuclear Information System (INIS)
Ardalan, F.; Arfaei, H.
1988-06-01
We systematically find all the modular invariant partition functions for the toroidally compactified closed bosonic string defined on a subset of a simply laced simple Lie algebra lattice, or equivalently for the closed bosonic string moving on a group manifold with the WZW coefficient k=1. We examine the relation between modular invariance of partition function and the possibility of describing it by an even Lorentzian self dual lattice in our context. (author). 23 refs
Rotation invariants from Gaussian-Hermite moments of color images
Czech Academy of Sciences Publication Activity Database
Yang, B.; Suk, Tomáš; Flusser, Jan; Shi, Z.; Chen, X.
2018-01-01
Roč. 143, č. 1 (2018), s. 282-291 ISSN 0165-1684 R&D Projects: GA ČR GA15-16928S Institutional support: RVO:67985556 Keywords : Color images * Object recognition * Rotation invariants * Gaussian–Hermite moments * Joint invariants Subject RIV: JD - Computer Applications, Robotics Impact factor: 3.110, year: 2016 http://library.utia.cas.cz/separaty/2017/ZOI/suk-0479748. pdf
Gender invariance of the College Student Stress Scale.
Feldt, Ronald C; Updegraff, Christina
2013-10-01
Assessment of perceived stress may be an important prerequisite to deployment of effective coping in efforts to help college students adjust to academic and social demands of college. The study examined the extent to which a seven-item measure of the College Student Stress Scale is invariant across gender. Results indicated invariance of factor loadings, factor variance, and all but one item intercept. No statistically significant gender difference was observed between latent variable means.
The supersymmetric t-J model with quantum group invariance
International Nuclear Information System (INIS)
Foerster, A.; Karowski, M.
1993-04-01
An integrable quantum group deformation of the supersymmetric t-J model is introduced. Open boundary conditions lead to an spl q (2, 1) invariant hamiltonian. A general procedure to obtain such invariant models is proposed. To solve the model a generalized nested algebraic Bethe ansatz is constructed and the Bethe ansatz equations are obtained. The quantum supergroup structure of the model is investigated. (orig.)
Modular invariants from simple currents. An explicit proof
International Nuclear Information System (INIS)
Schellekens, A.N.; Yankielowicz, S.
1989-01-01
In a previous paper an orbifold construction was used to demonstrate that the existence of primary fields with simple fusion rules in a conformal field theory implies the existence of non-diagonal modular invariant partition functions. Here we present a direct and explicit proof of modular invariance, which also covers a few cases that could not be obtained with the orbifold method. We also give a very simple general formula for the modular matrix M. (orig.)
QCD, monopoles on the lattice and gauge invariance
International Nuclear Information System (INIS)
Bonati, C.; Di Giacomo, A.; D'Elia, M.
2011-01-01
The number and the location of the monopoles observed on the lattice in QCD configurations happens to depend strongly on the choice of the gauge used to expose them, in contrast to the physical expectation that monopoles be gauge invariant objects. It is proved by use of the non abelian Bianchi identities (NABI) that monopoles are indeed gauge invariant, but the method used to detect them depends, in a controllable way, on the choice of the abelian projection. Numerical checks are presented.
Observation of the Efimovian Expansion in Scale Invariant Fermi Gases
Deng, Shujin; Shi, Zhe-Yu; Diao, Pengpeng; Yu, Qianli; Zhai, Hui; Qi, Ran; Wu, Haibin
2015-01-01
Scale invariance emerges and plays an important role in strongly correlated many-body systems such as critical regimes nearby phase transitions and the unitary Fermi gases. Discrete scaling symmetry also manifests itself in quantum few-body systems such as the Efimov effect. Here we report both theoretical predication and experimental observation of a novel type expansion dynamics for scale invariant quantum gases. When the frequency of the harmonic trap holding the gas decreases continuously...
3D rotation invariants of Gaussian-Hermite moments
Czech Academy of Sciences Publication Activity Database
Yang, Bo; Flusser, Jan; Suk, Tomáš
2015-01-01
Roč. 54, č. 1 (2015), s. 18-26 ISSN 0167-8655 R&D Projects: GA ČR GAP103/11/1552 Institutional support: RVO:67985556 Keywords : Rotation invariants * Orthogonal moments * Gaussian–Hermite moments * 3D moment invariants Subject RIV: IN - Informatics, Computer Science Impact factor: 1.586, year: 2015 http://library.utia.cas.cz/separaty/2014/ZOI/yang-0438325.pdf
Invariance as a Tool for Ontology of Information
Directory of Open Access Journals (Sweden)
Marcin J. Schroeder
2016-03-01
Full Text Available Attempts to answer questions regarding the ontological status of information are frequently based on the assumption that information should be placed within an already existing framework of concepts of established ontological statuses related to science, in particular to physics. However, many concepts of physics have undetermined or questionable ontological foundations. We can look for a solution in the recognition of the fundamental role of invariance with respect to a change of reference frame and to other transformations as a criterion for objective existence. The importance of invariance (symmetry as a criterion for a primary ontological status can be identified in the methodology of physics from its beginnings in the work of Galileo, to modern classifications of elementary particles. Thus, the study of the invariance of the theoretical description of information is proposed as the first step towards ontology of information. With the exception of only a few works among publications which set the paradigm of information studies, the issues of invariance were neglected. Orthodox analysis of information lacks conceptual framework for the study of invariance. The present paper shows how invariance can be formalized for the definition of information and, accompanying it, mathematical formalism proposed by the author in his earlier publications.
Adiabatic invariants of the extended KdV equation
Energy Technology Data Exchange (ETDEWEB)
Karczewska, Anna [Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Rozmej, Piotr, E-mail: p.rozmej@if.uz.zgora.pl [Institute of Physics, Faculty of Physics and Astronomy, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Infeld, Eryk [National Centre for Nuclear Research, Hoża 69, 00-681 Warszawa (Poland); Rowlands, George [Department of Physics, University of Warwick, Coventry, CV4 7A (United Kingdom)
2017-01-30
When the Euler equations for shallow water are taken to the next order, beyond KdV, momentum and energy are no longer exact invariants. (The only one is mass.) However, adiabatic invariants (AI) can be found. When the KdV expansion parameters are zero, exact invariants are recovered. Existence of adiabatic invariants results from general theory of near-identity transformations (NIT) which allow us to transform higher order nonintegrable equations to asymptotically equivalent (when small parameters tend to zero) integrable form. Here we present a direct method of calculations of adiabatic invariants. It does not need a transformation to a moving reference frame nor performing a near-identity transformation. Numerical tests show that deviations of AI from constant values are indeed small. - Highlights: • We suggest a new and simple method for calculating adiabatic invariants of second order wave equations. • It is easy to use and we hope that it will be useful if published. • Interesting numerics included.
Quantum tunneling, adiabatic invariance and black hole spectroscopy
Li, Guo-Ping; Pu, Jin; Jiang, Qing-Quan; Zu, Xiao-Tao
2017-05-01
In the tunneling framework, one of us, Jiang, together with Han has studied the black hole spectroscopy via adiabatic invariance, where the adiabatic invariant quantity has been intriguingly obtained by investigating the oscillating velocity of the black hole horizon. In this paper, we attempt to improve Jiang-Han's proposal in two ways. Firstly, we once again examine the fact that, in different types (Schwarzschild and Painlevé) of coordinates as well as in different gravity frames, the adiabatic invariant I_adia = \\oint p_i dq_i introduced by Jiang and Han is canonically invariant. Secondly, we attempt to confirm Jiang-Han's proposal reasonably in more general gravity frames (including Einstein's gravity, EGB gravity and HL gravity). Concurrently, for improving this proposal, we interestingly find in more general gravity theories that the entropy of the black hole is an adiabatic invariant action variable, but the horizon area is only an adiabatic invariant. In this sense, we emphasize the concept that the quantum of the black hole entropy is more natural than that of the horizon area.
Quantum tunneling, adiabatic invariance and black hole spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Li, Guo-Ping; Zu, Xiao-Tao [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Pu, Jin [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); China West Normal University, College of Physics and Space Science, Nanchong (China); Jiang, Qing-Quan [China West Normal University, College of Physics and Space Science, Nanchong (China)
2017-05-15
In the tunneling framework, one of us, Jiang, together with Han has studied the black hole spectroscopy via adiabatic invariance, where the adiabatic invariant quantity has been intriguingly obtained by investigating the oscillating velocity of the black hole horizon. In this paper, we attempt to improve Jiang-Han's proposal in two ways. Firstly, we once again examine the fact that, in different types (Schwarzschild and Painleve) of coordinates as well as in different gravity frames, the adiabatic invariant I{sub adia} = circular integral p{sub i}dq{sub i} introduced by Jiang and Han is canonically invariant. Secondly, we attempt to confirm Jiang-Han's proposal reasonably in more general gravity frames (including Einstein's gravity, EGB gravity and HL gravity). Concurrently, for improving this proposal, we interestingly find in more general gravity theories that the entropy of the black hole is an adiabatic invariant action variable, but the horizon area is only an adiabatic invariant. In this sense, we emphasize the concept that the quantum of the black hole entropy is more natural than that of the horizon area. (orig.)
Biomechanics principles and practices
Peterson, Donald R
2014-01-01
Presents Current Principles and ApplicationsBiomedical engineering is considered to be the most expansive of all the engineering sciences. Its function involves the direct combination of core engineering sciences as well as knowledge of nonengineering disciplines such as biology and medicine. Drawing on material from the biomechanics section of The Biomedical Engineering Handbook, Fourth Edition and utilizing the expert knowledge of respected published scientists in the application and research of biomechanics, Biomechanics: Principles and Practices discusses the latest principles and applicat
Dolan, Thomas James
2013-01-01
Fusion Research, Volume I: Principles provides a general description of the methods and problems of fusion research. The book contains three main parts: Principles, Experiments, and Technology. The Principles part describes the conditions necessary for a fusion reaction, as well as the fundamentals of plasma confinement, heating, and diagnostics. The Experiments part details about forty plasma confinement schemes and experiments. The last part explores various engineering problems associated with reactor design, vacuum and magnet systems, materials, plasma purity, fueling, blankets, neutronics
Database principles programming performance
O'Neil, Patrick
2014-01-01
Database: Principles Programming Performance provides an introduction to the fundamental principles of database systems. This book focuses on database programming and the relationships between principles, programming, and performance.Organized into 10 chapters, this book begins with an overview of database design principles and presents a comprehensive introduction to the concepts used by a DBA. This text then provides grounding in many abstract concepts of the relational model. Other chapters introduce SQL, describing its capabilities and covering the statements and functions of the programmi
National Research Council Canada - National Science Library
Walker, C. H
2012-01-01
"Now in its fourth edition, this exceptionally accessible text provides students with a multidisciplinary perspective and a grounding in the fundamental principles required for research in toxicology today...
Directory of Open Access Journals (Sweden)
Tristan J Webb
2014-04-01
Full Text Available When we see a human sitting down, standing up, or walking, we can recognise one of these poses independently of the individual, or we can recognise the individual person, independently of the pose. The same issues arise for deforming objects. For example, if we see a flag deformed by the wind, either blowing out or hanging languidly, we can usually recognise the flag, independently of its deformation; or we can recognise the deformation independently of the identity of the flag. We hypothesize that these types of recognition can be implemented by the primate visual system using temporo-spatial continuity as objects transform as a learning principle. In particular, we hypothesize that pose or deformation can be learned under conditions in which large numbers of different people are successively seen in the same pose, or objects in the same deformation. We also hypothesize that person-specific representations that are independent of pose, and object-specific representations that are independent of deformation and view, could be built, when individual people or objects are observed successively transforming from one pose or deformation and view to another. These hypotheses were tested in a simulation of the ventral visual system, VisNet, that uses temporal continuity, implemented in a synaptic learning rule with a short-term memory trace of previous neuronal activity, to learn invariant representations. It was found that depending on the statistics of the visual input, either pose-specific or deformation-specific representations could be built that were invariant with respect to individual and view; or that identity-specific representations could be built that were invariant with respect to pose or deformation and view. We propose that this is how pose-specific and pose-invariant, and deformation-specific and deformation-invariant, perceptual representations are built in the brain.
Assessment principles and tools.
Golnik, Karl C
2014-01-01
The goal of ophthalmology residency training is to produce competent ophthalmologists. Competence can only be determined by appropriately assessing resident performance. There are accepted guiding principles that should be applied to competence assessment methods. These principles are enumerated herein and ophthalmology-specific assessment tools that are available are described.
International Nuclear Information System (INIS)
Unnikrishnan, C.S.
1994-01-01
Principle of equivalence was the fundamental guiding principle in the formulation of the general theory of relativity. What are its key elements? What are the empirical observations which establish it? What is its relevance to some new experiments? These questions are discussed in this article. (author). 11 refs., 5 figs
Principles of Critical Dialogue.
Lankford, E. Louis
1986-01-01
Proposes four principles of critical dialog designed to suggest a consistent pattern of preparation for criticism. The principles concern the characteristics of the intended audience, establishing the goals of art criticism, making a commitment to a context of relevant dialogue, and clarifying one's concept of art in qualifying an object for…
International Nuclear Information System (INIS)
Carr, B.J.
1982-01-01
The anthropic principle (the conjecture that certain features of the world are determined by the existence of Man) is discussed with the listing of the objections, and is stated that nearly all the constants of nature may be determined by the anthropic principle which does not give exact values for the constants but only their orders of magnitude. (J.T.)
Denning, Peter J.
2008-01-01
The Great Principles of Computing is a framework for understanding computing as a field of science. The website ...April 2008 (Rev. 8/31/08) The Great Principles of Computing is a framework for understanding computing as a field of science.
International Nuclear Information System (INIS)
Khoury, Justin; Parikh, Maulik
2009-01-01
Mach's principle is the proposition that inertial frames are determined by matter. We put forth and implement a precise correspondence between matter and geometry that realizes Mach's principle. Einstein's equations are not modified and no selection principle is applied to their solutions; Mach's principle is realized wholly within Einstein's general theory of relativity. The key insight is the observation that, in addition to bulk matter, one can also add boundary matter. Given a space-time, and thus the inertial frames, we can read off both boundary and bulk stress tensors, thereby relating matter and geometry. We consider some global conditions that are necessary for the space-time to be reconstructible, in principle, from bulk and boundary matter. Our framework is similar to that of the black hole membrane paradigm and, in asymptotically anti-de Sitter space-times, is consistent with holographic duality.
Variational principles in physics
Basdevant, Jean-Louis
2007-01-01
Optimization under constraints is an essential part of everyday life. Indeed, we routinely solve problems by striking a balance between contradictory interests, individual desires and material contingencies. This notion of equilibrium was dear to thinkers of the enlightenment, as illustrated by Montesquieu’s famous formulation: "In all magistracies, the greatness of the power must be compensated by the brevity of the duration." Astonishingly, natural laws are guided by a similar principle. Variational principles have proven to be surprisingly fertile. For example, Fermat used variational methods to demonstrate that light follows the fastest route from one point to another, an idea which came to be known as Fermat’s principle, a cornerstone of geometrical optics. Variational Principles in Physics explains variational principles and charts their use throughout modern physics. The heart of the book is devoted to the analytical mechanics of Lagrange and Hamilton, the basic tools of any physicist. Prof. Basdev...
U(1 )×SU (2 ) gauge invariance made simple for density functional approximations
Pittalis, S.; Vignale, G.; Eich, F. G.
2017-07-01
A semirelativistic density-functional theory that includes spin-orbit couplings and Zeeman fields on equal footing with the electromagnetic potentials, is an appealing framework to develop a unified first-principles computational approach for noncollinear magnetism, spintronics, orbitronics, and topological states. The basic variables of this theory include the paramagnetic current and the spin-current density, besides the particle and the spin density, and the corresponding exchange-correlation (xc) energy functional is invariant under local U (1 )×SU (2 ) gauge transformations. The xc-energy functional must be approximated to enable practical applications, but, contrary to the case of the standard density functional theory, finding simple approximations suited to deal with realistic atomistic inhomogeneities has been a long-standing challenge. Here we propose a way out of this impasse by showing that approximate gauge-invariant functionals can be easily generated from existing approximate functionals of ordinary density-functional theory by applying a simple minimal substitution on the kinetic energy density, which controls the short-range behavior of the exchange hole. Our proposal opens the way to the construction of approximate, yet nonempirical functionals, which do not assume weak inhomogeneity and therefore may have a wide range of applicability in atomic, molecular, and condensed matter physics.
Multi-clues image retrieval based on improved color invariants
Liu, Liu; Li, Jian-Xun
2012-05-01
At present, image retrieval has a great progress in indexing efficiency and memory usage, which mainly benefits from the utilization of the text retrieval technology, such as the bag-of-features (BOF) model and the inverted-file structure. Meanwhile, because the robust local feature invariants are selected to establish BOF, the retrieval precision of BOF is enhanced, especially when it is applied to a large-scale database. However, these local feature invariants mainly consider the geometric variance of the objects in the images, and thus the color information of the objects fails to be made use of. Because of the development of the information technology and Internet, the majority of our retrieval objects is color images. Therefore, retrieval performance can be further improved through proper utilization of the color information. We propose an improved method through analyzing the flaw of shadow-shading quasi-invariant. The response and performance of shadow-shading quasi-invariant for the object edge with the variance of lighting are enhanced. The color descriptors of the invariant regions are extracted and integrated into BOF based on the local feature. The robustness of the algorithm and the improvement of the performance are verified in the final experiments.
An Advanced Rotation Invariant Descriptor for SAR Image Registration
Directory of Open Access Journals (Sweden)
Yuming Xiang
2017-07-01
Full Text Available The Scale-Invariant Feature Transform (SIFT algorithm and its many variants have been widely used in Synthetic Aperture Radar (SAR image registration. The SIFT-like algorithms maintain rotation invariance by assigning a dominant orientation for each keypoint, while the calculation of dominant orientation is not robust due to the effect of speckle noise in SAR imagery. In this paper, we propose an advanced local descriptor for SAR image registration to achieve rotation invariance without assigning a dominant orientation. Based on the improved intensity orders, we first divide a circular neighborhood into several sub-regions. Second, rotation-invariant ratio orientation histograms of each sub-region are proposed by accumulating the ratio values of different directions in a rotation-invariant coordinate system. The proposed descriptor is composed of the concatenation of the histograms of each sub-region. In order to increase the distinctiveness of the proposed descriptor, multiple image neighborhoods are aggregated. Experimental results on several satellite SAR images have shown an improvement in the matching performance over other state-of-the-art algorithms.
Color-invariant shape moments for object recognition
Zhou, Qiang; Celenk, Mehmet
2001-05-01
Geometric moments have been widely used in many shape recognition and object classification tasks. These monomials are usually computed from binary or gray-level images for the object shape recognition invariant to rotation, translation, and scaling. In this paper, we attempt to calculate the shape related moments from color images, and study their noise immunity and color invariance property for the application areas of face recognition and content based image retrieval. To this end, we describe a computationally efficient method of converting a vector-valued color image into a gray scale for robust moment computation. Geometric moments are calculated from the resultant scalar representation of a color image data, and proven to be robust shape descriptors for the face and flower images. The generated shape invariants appear to have better noise immunity than the Hu moments and exhibit characteristics invariant to hue changes in the object colors. As compared to the Zernike polynomials, the proposed feature set has higher discriminatory power although the Zernike polynomials present superior noise rejection capability. Robust performance, computational efficiency, high noise immunity, and hue invariance property of the new approach are particularly useful for fast image retrieval tasks requiring high query accuracy.
Phylogenetic mixtures and linear invariants for equal input models.
Casanellas, Marta; Steel, Mike
2017-04-01
The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987).
Uniqueness of the gauge invariant action for cosmological perturbations
Energy Technology Data Exchange (ETDEWEB)
Prokopec, Tomislav; Weenink, Jan, E-mail: t.prokopec@uu.nl, E-mail: j.g.weenink@uu.nl [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3585 CE Utrecht (Netherlands)
2012-12-01
In second order perturbation theory different definitions are known of gauge invariant perturbations in single field inflationary models. Consequently the corresponding gauge invariant cubic actions do not have the same form. Here we show that the cubic action for one choice of gauge invariant variables is unique in the following sense: the action for any other, non-linearly related variable can be brought to the same bulk action, plus additional boundary terms. These boundary terms correspond to the choice of hypersurface and generate extra, disconnected contributions to the bispectrum. We also discuss uniqueness of the action with respect to conformal frames. When expressed in terms of the gauge invariant curvature perturbation on uniform field hypersurfaces the action for cosmological perturbations has a unique form, independent of the original Einstein or Jordan frame. Crucial is that the gauge invariant comoving curvature perturbation is frame independent, which makes it extremely helpful in showing the quantum equivalence of the two frames, and therefore in calculating quantum effects in nonminimally coupled theories such as Higgs inflation.
Arthur's invariant trace formula and comparison of inner forms
Flicker, Yuval Z
2016-01-01
This monograph provides an accessible and comprehensive introduction to James Arthur’s invariant trace formula, a crucial tool in the theory of automorphic representations. It synthesizes two decades of Arthur’s research and writing into one volume, treating a highly detailed and often difficult subject in a clearer and more uniform manner without sacrificing any technical details. The book begins with a brief overview of Arthur’s work and a proof of the correspondence between GL(n) and its inner forms in general. Subsequent chapters develop the invariant trace formula in a form fit for applications, starting with Arthur’s proof of the basic, non-invariant trace formula, followed by a study of the non-invariance of the terms in the basic trace formula, and, finally, an in-depth look at the development of the invariant formula. The final chapter illustrates the use of the formula by comparing it for G’ = GL(n) and its inner form G and for functions with matching orbital integrals. Arthur’s Invarian...
Robust Frequency Invariant Beamforming with Low Sidelobe for Speech Enhancement
Zhu, Yiting; Pan, Xiang
2018-01-01
Frequency invariant beamformers (FIBs) are widely used in speech enhancement and source localization. There are two traditional optimization methods for FIB design. The first one is convex optimization, which is simple but the frequency invariant characteristic of the beam pattern is poor with respect to frequency band of five octaves. The least squares (LS) approach using spatial response variation (SRV) constraint is another optimization method. Although, it can provide good frequency invariant property, it usually couldn’t be used in speech enhancement for its lack of weight norm constraint which is related to the robustness of a beamformer. In this paper, a robust wideband beamforming method with a constant beamwidth is proposed. The frequency invariant beam pattern is achieved by resolving an optimization problem of the SRV constraint to cover speech frequency band. With the control of sidelobe level, it is available for the frequency invariant beamformer (FIB) to prevent distortion of interference from the undesirable direction. The approach is completed in time-domain by placing tapped delay lines(TDL) and finite impulse response (FIR) filter at the output of each sensor which is more convenient than the Frost processor. By invoking the weight norm constraint, the robustness of the beamformer is further improved against random errors. Experiment results show that the proposed method has a constant beamwidth and almost the same white noise gain as traditional delay-and-sum (DAS) beamformer.
Gauge-invariant three-gluon vertex in QCD
International Nuclear Information System (INIS)
Cornwall, J.M.; Papavassiliou, J.
1989-01-01
By resumming the Feynman graphs which contribute to any gauge-invariant process we explicitly construct, at one-loop order, a three-gluon vertex for QCD which is completely independent of the choice of gauge. This vertex satisfies a Ward identity of the type encountered in ghost-free gauges, relating the vertex to the proper self-energy of a previously constructed gluon propagator, also found by resumming graphs; like the vertex, this self-energy is completely gauge invariant. We also derive the gauge-invariant propagator and vertex via a second related technique which minimizes the dependence on embedding these objects in a gauge-invariant process; the same results are found as in the first technique. These results motivate a toy model of the nonlinear Schwinger-Dyson equation satisfied by the exact gauge-invariant three-gluon vertex. This model is nonperturbative and has infrared singularities, which we can remove via gluon mass generation; it shows many interesting features expected of QCD, such as a β function which is not Borel summable in perturbation theory
Superconformal invariants for scattering amplitudes in N=4 SYM theory
Energy Technology Data Exchange (ETDEWEB)
Korchemsky, G.P., E-mail: korchems@th.u-psud.f [Institut de Physique Theorique, CEA Saclay, 91191 Gif-sur-Yvette Cedex (France); Sokatchev, E. [LAPTH, Universite de Savoie, CNRS, B.P. 110, F-74941 Annecy-le-Vieux (France)
2010-11-11
Recent studies of scattering amplitudes in planar N=4 SYM theory revealed the existence of a hidden dual superconformal symmetry. Together with the conventional superconformal symmetry it gives rise to powerful restrictions on the planar scattering amplitudes to all loops. We study the general form of the invariants of both symmetries. We first construct an integral representation for the most general dual superconformal invariants and show that it allows a considerable freedom in the choice of the integration measure. We then perform a half-Fourier transform to twistor space, where conventional conformal symmetry is realized locally, derive the resulting conformal Ward identity for the integration measure and show that it admits a unique solution. Thus, the combination of dual and conventional superconformal symmetries, together with invariance under helicity rescalings, completely fixes the form of the invariants. The expressions obtained generalize the known tree and one-loop superconformal invariants and coincide with the recently proposed coefficients of the leading singularities of the scattering amplitudes as contour integrals over Grassmannians.
Tests of local Lorentz invariance violation of gravity in the standard model extension with pulsars.
Shao, Lijing
2014-03-21
The standard model extension is an effective field theory introducing all possible Lorentz-violating (LV) operators to the standard model and general relativity (GR). In the pure-gravity sector of minimal standard model extension, nine coefficients describe dominant observable deviations from GR. We systematically implemented 27 tests from 13 pulsar systems to tightly constrain eight linear combinations of these coefficients with extensive Monte Carlo simulations. It constitutes the first detailed and systematic test of the pure-gravity sector of minimal standard model extension with the state-of-the-art pulsar observations. No deviation from GR was detected. The limits of LV coefficients are expressed in the canonical Sun-centered celestial-equatorial frame for the convenience of further studies. They are all improved by significant factors of tens to hundreds with existing ones. As a consequence, Einstein's equivalence principle is verified substantially further by pulsar experiments in terms of local Lorentz invariance in gravity.
Invariant potential for elastic pion--nucleus scattering. Technical report No. 75-075
International Nuclear Information System (INIS)
Cammarata, J.B.; Banerjee, M.K.
1975-04-01
From the Wick-Dyson expansion of the exact propagator of a pion in the presence of a nucleus an invariant potential for crossing symmetric, elastic pion-nucleus scattering is obtained in terms of a series of pion-nucleon diagrams. The Chew-Low theory is used to develop a model in which the most important class of diagrams is effectively summed. Included in this model is the Exclusion Principle restriction on the pion-bound nucleon interaction, the effects of the binding of nucleons, a kinematic transformation of energy from the lab to the πN center of mass frames, and the Fermi motion and recoil of the target nucleons. From a numerical study of the effects of these processes on the π- 12 C total cross section, the relative importance of each is determined. Other processes contributing to the elastic scattering of pions not included in the present model are also discussed. (9 figures) (U.S.)
Gauge theories under incorporation of a generalized uncertainty principle
International Nuclear Information System (INIS)
Kober, Martin
2010-01-01
There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of matter field equations like the Dirac equation. If there is postulated invariance of such a generalized field equation under local gauge transformations, the usual covariant derivative containing the gauge potential has to be replaced by a generalized covariant derivative. This leads to a generalized interaction between the matter field and the gauge field as well as to an additional self-interaction of the gauge field. Since the existence of a minimal length scale seems to be a necessary assumption of any consistent quantum theory of gravity, the gauge principle is a constitutive ingredient of the standard model, and even gravity can be described as gauge theory of local translations or Lorentz transformations, the presented extension of gauge theories appears as a very important consideration.
Hill, Rodney
2013-01-01
Principles of Dynamics presents classical dynamics primarily as an exemplar of scientific theory and method. This book is divided into three major parts concerned with gravitational theory of planetary systems; general principles of the foundations of mechanics; and general motion of a rigid body. Some of the specific topics covered are Keplerian Laws of Planetary Motion; gravitational potential and potential energy; and fields of axisymmetric bodies. The principles of work and energy, fictitious body-forces, and inertial mass are also looked into. Other specific topics examined are kinematics
Modern electronic maintenance principles
Garland, DJ
2013-01-01
Modern Electronic Maintenance Principles reviews the principles of maintaining modern, complex electronic equipment, with emphasis on preventive and corrective maintenance. Unfamiliar subjects such as the half-split method of fault location, functional diagrams, and fault finding guides are explained. This book consists of 12 chapters and begins by stressing the need for maintenance principles and discussing the problem of complexity as well as the requirements for a maintenance technician. The next chapter deals with the connection between reliability and maintenance and defines the terms fai
Pérez-Soba Díez del Corral, Juan José
2008-01-01
Bioethics emerges about the tecnological problems of acting in human life. Emerges also the problem of the moral limits determination, because they seem exterior of this practice. The Bioethics of Principles, take his rationality of the teleological thinking, and the autonomism. These divergence manifest the epistemological fragility and the great difficulty of hmoralñ thinking. This is evident in the determination of autonomy's principle, it has not the ethical content of Kant's propose. We need a new ethic rationality with a new refelxion of new Principles whose emerges of the basic ethic experiences.
Hamilton's principle for beginners
International Nuclear Information System (INIS)
Brun, J L
2007-01-01
I find that students have difficulty with Hamilton's principle, at least the first time they come into contact with it, and therefore it is worth designing some examples to help students grasp its complex meaning. This paper supplies the simplest example to consolidate the learning of the quoted principle: that of a free particle moving along a line. Next, students are challenged to add gravity to reinforce the argument and, finally, a two-dimensional motion in a vertical plane is considered. Furthermore these examples force us to be very clear about such an abstract principle
Limitations of Boltzmann's principle
International Nuclear Information System (INIS)
Lavenda, B.H.
1995-01-01
The usual form of Boltzmann's principle assures that maximum entropy, or entropy reduction, occurs with maximum probability, implying a unimodal distribution. Boltzmann's principle cannot be applied to nonunimodal distributions, like the arcsine law, because the entropy may be concave only over a limited portion of the interval. The method of subordination shows that the arcsine distribution corresponds to a process with a single degree of freedom, thereby confirming the invalidation of Boltzmann's principle. The fractalization of time leads to a new distribution in which arcsine and Cauchy distributions can coexist simultaneously for nonintegral degrees of freedom between √2 and 2
Biomedical engineering principles
Ritter, Arthur B; Valdevit, Antonio; Ascione, Alfred N
2011-01-01
Introduction: Modeling of Physiological ProcessesCell Physiology and TransportPrinciples and Biomedical Applications of HemodynamicsA Systems Approach to PhysiologyThe Cardiovascular SystemBiomedical Signal ProcessingSignal Acquisition and ProcessingTechniques for Physiological Signal ProcessingExamples of Physiological Signal ProcessingPrinciples of BiomechanicsPractical Applications of BiomechanicsBiomaterialsPrinciples of Biomedical Capstone DesignUnmet Clinical NeedsEntrepreneurship: Reasons why Most Good Designs Never Get to MarketAn Engineering Solution in Search of a Biomedical Problem
Fuzzy based finger vein recognition with rotation invariant feature matching
Ezhilmaran, D.; Joseph, Rose Bindu
2017-11-01
Finger vein recognition is a promising biometric with commercial applications which is explored widely in the recent years. In this paper, a finger vein recognition system is proposed using rotation invariant feature descriptors for matching after enhancing the finger vein images with an interval type-2 fuzzy method. SIFT features are extracted and matched using a matching score based on Euclidian distance. Rotation invariance of the proposed method is verified in the experiment and the results are compared with SURF matching and minutiae matching. It is seen that rotation invariance is verified and the poor quality issues are solved efficiently with the designed system of finger vein recognition during the analysis. The experiments underlines the robustness and reliability of the interval type-2 fuzzy enhancement and SIFT feature matching.
Measurement Invariance of Discipline in Different Cultural Contexts.
Huang, Li; Malone, Patrick S; Lansford, Jennifer E; Deater-Deckard, Kirby; Di Giunta, Laura; Bombi, Anna Silvia; Bornstein, Marc H; Chang, Lei; Dodge, Kenneth A; Oburu, Paul; Pastorelli, Concetta; Skinner, Ann T; Sorbring, Emma; Tapanya, Sombat; Tirado, Liliana Maria Uribe; Zelli, Arnaldo; Alampay, Liane; Al-Hassan, Suha M; Bacchini, Dario
2011-07-01
The measurement invariance of mother-reported use of 18 discipline strategies was examined in samples from 13 different ethnic/cultural groups in nine countries (China, Colombia, Italy, Jordan, Kenya, the Philippines, Sweden, Thailand, and the United States). Participants included approximately 100-120 mothers and their children aged 7 to 10 years from each group. The results of exploratory factor analyses and multigroup categorical confirmatory factor analyses (MCCFA) indicated that a seven-factor solution was feasible across the cultural groups, as shown by marginally sufficient evidence for configural and metric invariance for the mother-reported frequency on the discipline interview. This study makes a contribution on measurement invariance to the parenting literature, and establishes the mother-report aspect of the discipline interview as an instrument for use in further cross-cultural research on discipline.
ASIFT: An Algorithm for Fully Affine Invariant Comparison
Directory of Open Access Journals (Sweden)
Guoshen Yu
2011-02-01
Full Text Available If a physical object has a smooth or piecewise smooth boundary, its images obtained by cameras in varying positions undergo smooth apparent deformations. These deformations are locally well approximated by affine transforms of the image plane. In consequence the solid object recognition problem has often been led back to the computation of affine invariant image local features. The similarity invariance (invariance to translation, rotation, and zoom is dealt with rigorously by the SIFT method The method illustrated and demonstrated in this work, Affine-SIFT (ASIFT, simulates a set of sample views of the initial images, obtainable by varying the two camera axis orientation parameters, namely the latitude and the longitude angles, which are not treated by the SIFT method. Then it applies the SIFT method itself to all images thus generated. Thus, ASIFT covers effectively all six parameters of the affine transform.
Isomorph invariance of the structure and dynamics of classical crystals
DEFF Research Database (Denmark)
Albrechtsen, Dan; Olsen, Andreas Elmerdahl; Pedersen, Ulf Rørbæk
2014-01-01
This paper shows by computer simulations that some crystalline systems have curves in their thermodynamic phase diagrams, so-called isomorphs, along which structure and dynamics in reduced units are invariant to a good approximation. The crystals are studied in a classical-mechanical framework......, which is generally a good description except significantly below melting. The existence of isomorphs for crystals is validated by simulations of particles interacting via the Lennard-Jones pair potential arranged into a face-centered cubic (fcc) crystalline structure; the slow vacancy-jump dynamics...... of a defective fcc crystal is also shown to be isomorph invariant. In contrast, a NaCl crystal model does not exhibit isomorph invariances. Other systems simulated, though in less detail, are the Wahnström binary Lennard-Jones crystal with the MgZn2 Laves crystal structure, monatomic fcc crystals of particles...
SPEEDY: An Eclipse-based IDE for invariant inference
Directory of Open Access Journals (Sweden)
David R. Cok
2014-04-01
Full Text Available SPEEDY is an Eclipse-based IDE for exploring techniques that assist users in generating correct specifications, particularly including invariant inference algorithms and tools. It integrates with several back-end tools that propose invariants and will incorporate published algorithms for inferring object and loop invariants. Though the architecture is language-neutral, current SPEEDY targets C programs. Building and using SPEEDY has confirmed earlier experience demonstrating the importance of showing and editing specifications in the IDEs that developers customarily use, automating as much of the production and checking of specifications as possible, and showing counterexample information directly in the source code editing environment. As in previous work, automation of specification checking is provided by back-end SMT solvers. However, reducing the effort demanded of software developers using formal methods also requires a GUI design that guides users in writing, reviewing, and correcting specifications and automates specification inference.
Open Gromov-Witten Invariants from the Augmentation Polynomial
Directory of Open Access Journals (Sweden)
Matthew Mahowald
2017-10-01
Full Text Available A conjecture of Aganagic and Vafa relates the open Gromov-Witten theory of X = O P 1 ( − 1 , − 1 to the augmentation polynomial of Legendrian contact homology. We describe how to use this conjecture to compute genus zero, one boundary component open Gromov-Witten invariants for Lagrangian submanifolds L K ⊂ X obtained from the conormal bundles of knots K ⊂ S 3 . This computation is then performed for two non-toric examples (the figure-eight and three-twist knots. For ( r , s torus knots, the open Gromov-Witten invariants can also be computed using Atiyah-Bott localization. Using this result for the unknot and the ( 3 , 2 torus knot, we show that the augmentation polynomial can be derived from these open Gromov-Witten invariants.
Machine learning strategies for systems with invariance properties
Ling, Julia; Jones, Reese; Templeton, Jeremy
2016-08-01
In many scientific fields, empirical models are employed to facilitate computational simulations of engineering systems. For example, in fluid mechanics, empirical Reynolds stress closures enable computationally-efficient Reynolds Averaged Navier Stokes simulations. Likewise, in solid mechanics, constitutive relations between the stress and strain in a material are required in deformation analysis. Traditional methods for developing and tuning empirical models usually combine physical intuition with simple regression techniques on limited data sets. The rise of high performance computing has led to a growing availability of high fidelity simulation data. These data open up the possibility of using machine learning algorithms, such as random forests or neural networks, to develop more accurate and general empirical models. A key question when using data-driven algorithms to develop these empirical models is how domain knowledge should be incorporated into the machine learning process. This paper will specifically address physical systems that possess symmetry or invariance properties. Two different methods for teaching a machine learning model an invariance property are compared. In the first method, a basis of invariant inputs is constructed, and the machine learning model is trained upon this basis, thereby embedding the invariance into the model. In the second method, the algorithm is trained on multiple transformations of the raw input data until the model learns invariance to that transformation. Results are discussed for two case studies: one in turbulence modeling and one in crystal elasticity. It is shown that in both cases embedding the invariance property into the input features yields higher performance at significantly reduced computational training costs.
Synaptotagmin 7 confers frequency invariance onto specialized depressing synapses
Turecek, Josef; Jackman, Skyler L.; Regehr, Wade G.
2017-11-01
At most synapses in the brain, short-term plasticity dynamically modulates synaptic strength. Rapid frequency-dependent changes in synaptic strength have key roles in sensory adaptation, gain control and many other neural computations. However, some auditory, vestibular and cerebellar synapses maintain constant strength over a wide range of firing frequencies, and as a result efficiently encode firing rates. Despite its apparent simplicity, frequency-invariant transmission is difficult to achieve because of inherent synaptic nonlinearities. Here we study frequency-invariant transmission at synapses from Purkinje cells to deep cerebellar nuclei and at vestibular synapses in mice. Prolonged activation of these synapses leads to initial depression, which is followed by steady-state responses that are frequency invariant for their physiological activity range. We find that synaptotagmin 7 (Syt7), a calcium sensor for short-term facilitation, is present at both synapses. It was unclear why a sensor for facilitation would be present at these and other depressing synapses. We find that at Purkinje cell and vestibular synapses, Syt7 supports facilitation that is normally masked by depression, which can be revealed in wild-type mice but is absent in Syt7 knockout mice. In wild-type mice, facilitation increases with firing frequency and counteracts depression to produce frequency-invariant transmission. In Syt7-knockout mice, Purkinje cell and vestibular synapses exhibit conventional use-dependent depression, weakening to a greater extent as the firing frequency is increased. Presynaptic rescue of Syt7 expression restores both facilitation and frequency-invariant transmission. Our results identify a function for Syt7 at synapses that exhibit overall depression, and demonstrate that facilitation has an unexpected and important function in producing frequency-invariant transmission.
Spectral invariants of operators of Dirac type on partitioned manifolds
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Bleecker, D.
2004-01-01
We review the concepts of the index of a Fredholm operator, the spectral flow of a curve of self-adjoint Fredholm operators, the Maslov index of a curve of Lagrangian subspaces in symplectic Hilbert space, and the eta invariant of operators of Dirac type on closed manifolds and manifolds...... with boundary. We emphasize various (occasionally overlooked) aspects of rigorous definitions and explain the quite different stability properties. Moreover, we utilize the heat equation approach in various settings and show how these topological and spectral invariants are mutually related in the study...
Weyl versus conformal invariance in quantum field theory
Farnsworth, Kara; Luty, Markus A.; Prilepina, Valentina
2017-10-01
We argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions d ≤ 10. We also study possible curvature corrections to the Weyl transformations of operators, and show that these are absent for operators of sufficiently low dimensionality and spin. We find possible `anomalous' Weyl transformations proportional to the Weyl (Cotton) tensor for d > 3 ( d = 3). The arguments are based on algebraic consistency conditions similar to the Wess-Zumino consistency conditions that classify possible local anomalies. The arguments can be straightforwardly extended to larger operator dimensions and higher d with additional algebraic complexity.
Trace Maps, Invariants, and Some of Their Applications
Baake, M.; Grimm, U.; Joseph, D.
Trace maps of two-letter substitution rules are investigated with special emphasis on the underlying algebraic structure and on the existence of invariants. We illustrate the results with the generalized Fibonacci chains and show that the well-known Fricke character I(x, y, z)=x2+y2+z2-2xyz-1 is not the only type of invariant that can occur. We discuss several physical applications to electronic spectra including the gap-labeling theorem, to kicked two-level systems, and to the classical 1D Ising model with non-commuting transfer matrices.
Gauge invariant treatment of the electroweak phase transition
International Nuclear Information System (INIS)
Buchmueller, W.; Fodor, Z.; Hebecker, A.
1994-03-01
We evaluate the gauge invariant effective potential for the composite field σ = 2Φ † Φin the SU(2)-Higgs model at finite temperature. Symmetric and broken phases correspond to the domains σ ≤ T 2 /3 and σ > T 2 /3, respectively. The effective potential increases very steeply at small values of σ. Predictions for several observables, derived from the ordinary and the gauge invariant effective potential, are compared. Good agreement is found for the critical temperature and the jump in the order parameter. The results for the latent heat differ significantly for large Higgs masses. (orig.)
Bidirectional log-polar mapping for invariant object recognition
Mehanian, Courosh; Rak, Steven J.
1991-08-01
The representation of visual information in human striate cortex is of significance to machine vision. Invariance to certain geometrical transformations in the field-of-view may be provided by the computational anatomy of the visual cortex. For example, there is evidence that the retino-cortical mapping is closely approximated by a log-polar transform. When combined with the foveation response, log-polar mapping can provide a basis for translation, rotation, and scale-invariant perception. There is also evidence that the visual system is sensitive to the spatial frequency content of its input. Although a Fourier transform is physiologically implausible, some authors have suggested its use for invariant object recognition because the magnitude of the Fourier transform is shift invariant. The Fourier transform magnitude operation followed by log-polar mapping can also provide a basis for translation, rotation, and scale-invariant perception. Both of these image-transform (feature mapping) algorithms give mathematical invariance to translation, rotation, and dilation. For an automatic recognition system, however, the feature mapping module has to be robust to discretization error, noise, and possible obscuration. Robustness considerations led to the development of the bi- directional log-polar mapping (BPM) algorithm. The BPM algorithm overcomes the pixel- dropout problems associated with conventional approaches to log-polar mapping. The authors evaluate several feature mapping models, both biologically and mathematically inspired, for their effect on recognition performance when embedded in a neural-network-based, object- recognition system. The modular recognition system, consisting of image restoration, detection, segmentation, feature extraction, invariant mapping, and classification, is being developed to classify objects in laser radar range imagery. Synthetic laser radar range images of four vehicles rotated in the field-of-view, scaled to various ranges, and
Object detection based on improved color and scale invariant features
Chen, Mengyang; Men, Aidong; Fan, Peng; Yang, Bo
2009-10-01
A novel object detection method which combines color and scale invariant features is presented in this paper. The detection system mainly adopts the widely used framework of SIFT (Scale Invariant Feature Transform), which consists of both a keypoint detector and descriptor. Although SIFT has some impressive advantages, it is not only computationally expensive, but also vulnerable to color images. To overcome these drawbacks, we employ the local color kernel histograms and Haar Wavelet Responses to enhance the descriptor's distinctiveness and computational efficiency. Extensive experimental evaluations show that the method has better robustness and lower computation costs.
Seven Experiments to Test the Local Lorentz Invariance of c
Gezari, Daniel Y.
2005-01-01
The speed of light has never been measured directly with a moving detector to test the fundamental assertion of special relativity that c is invariant to motion of the observer. Seven simple experiments are proposed, four of which could test the invariance of c to motion of the detector. Three other observations of moving sources could test Einstein s second postulate and the relativity of stellar aberration. There are lingering concerns that the speed of light may depend on the motion of the observer, after all. This issue can now be resolved by experiment.
Translation invariant time-dependent massive gravity: Hamiltonian analysis
Energy Technology Data Exchange (ETDEWEB)
Mourad, Jihad; Steer, Danièle A. [Laboratoire APC -- Astroparticule et Cosmologie, Université Paris Diderot, 75013 Paris (France); Noui, Karim, E-mail: mourad@apc.univ-paris7.fr, E-mail: karim.noui@lmpt.univ-tours.fr, E-mail: steer@apc.univ-paris7.fr [Laboratoire de Mathématiques et Physique Théorique, Université François Rabelais, Parc de Grandmont, 37200 Tours (France)
2014-09-01
The canonical structure of the massive gravity in the first order moving frame formalism is studied. We work in the simplified context of translation invariant fields, with mass terms given by general non-derivative interactions, invariant under the diagonal Lorentz group, depending on the moving frame as well as a fixed reference frame. We prove that the only mass terms which give 5 propagating degrees of freedom are the dRGT mass terms, namely those which are linear in the lapse. We also complete the Hamiltonian analysis with the dynamical evolution of the system.
Breakdown of invariant attractors for the dissipative standard map.
Calleja, Renato; Celletti, Alessandra
2010-03-01
We implement different methods for the computation of the breakdown threshold of invariant attractors in the dissipative standard mapping. A first approach is based on the computation of the Sobolev norms of the function parametrizing the solution. Then we look for the approximating periodic orbits and we analyze their stability in order to compute the critical threshold at which an invariant attractor breaks down. We also determine the domain of convergence of the dissipative standard mapping by extending the computations to the complex parameter space as well as by investigating a two-frequency model.
Scaling theory of [Formula: see text] topological invariants.
Chen, Wei; Sigrist, Manfred; Schnyder, Andreas P
2016-09-14
For inversion-symmetric topological insulators and superconductors characterized by [Formula: see text] topological invariants, two scaling schemes are proposed to judge topological phase transitions driven by an energy parameter. The scaling schemes renormalize either the phase gradient or the second derivative of the Pfaffian of the time-reversal operator, through which the renormalization group flow of the driving energy parameter can be obtained. The Pfaffian near the time-reversal invariant momentum is revealed to display a universal critical behavior for a great variety of models examined.
Projection Operators and Moment Invariants to Image Blurring
Czech Academy of Sciences Publication Activity Database
Flusser, Jan; Suk, Tomáš; Boldyš, Jiří; Zitová, Barbara
2015-01-01
Roč. 37, č. 4 (2015), s. 786-802 ISSN 0162-8828 R&D Projects: GA ČR GA13-29225S; GA ČR GAP103/11/1552 Institutional support: RVO:67985556 Keywords : Blurred image * N-fold rotation symmetry * projection operators * image moments * moment invariants * blur invariants * object recognition Subject RIV: JD - Computer Applications, Robotics Impact factor: 6.077, year: 2015 http://library.utia.cas.cz/separaty/2014/ZOI/flusser-0434521.pdf
Polarization particle drift and quasi-particle invariants
International Nuclear Information System (INIS)
Sosenko, P.P.
1995-01-01
The second-order approximation in quasi-particle description of magnetized plasmas is studied. Reduced particle and guiding-centre velocities are derived taking account of the second-order renormalization and polarization drift modified owing to finite-Larmor-radius effects. The second-order adiabatic invariant of quasi-particle motion is found. Global adiabatic invariants for the magnetized plasma are revealed, and their possible role in energy exchange between particles and fields, nonlinear mode cascades and global plasma stability is shown. 49 refs
Smooth invariant densities for random switching on the torus
Bakhtin, Yuri; Hurth, Tobias; Lawley, Sean D.; Mattingly, Jonathan C.
2018-04-01
We consider a random dynamical system obtained by switching between the flows generated by two smooth vector fields on the 2d-torus, with the random switchings happening according to a Poisson process. Assuming that the driving vector fields are transversal to each other at all points of the torus and that each of them allows for a smooth invariant density and no periodic orbits, we prove that the switched system also has a smooth invariant density, for every switching rate. Our approach is based on an integration by parts formula inspired by techniques from Malliavin calculus.
Variational principle for linear stability of flowing plasmas in Hall magnetohydrodynamics
International Nuclear Information System (INIS)
Hirota, M.; Yoshida, Z.; Hameiri, E.
2006-01-01
Linear stability of equilibrium states with flow is studied by means of the variational principle in Hall magnetohydrodynamics (MHD). The Lagrangian representation of the linearized Hall MHD equation is performed by considering special perturbations that preserves some constants of motion (the Casimir invariants). The resultant equation has a Hamiltonian structure which enables the variational principle. There is however some difficulties in showing the positive definiteness of the quadratic form in the presence of flow. The dynamically accessible variation is a more restricted class of perturbations which, by definition, preserves all the Casimir invariants. For such variations, the quadratic form (the second variation of Hamiltonian) can be positive definite. Some conditions for stability are derived by applying this variational principle to the double Beltrami equilibrium
Darvas, Gyrgy
2009-01-01
The paper discusses the mathematical consequences of the application of derived variables in gauge fields. Physics is aware of several phenomena, which depend first of all on velocities (like e.g., the force caused by charges moving in a magnetic field, or the Lorentz transformation). Applying the property of the second Noether theorem, that allowed generalised variables, this paper extends the article by Al-Kuwari and Taha (1991) with a new conclusion. They concluded that there are no extra conserved currents associated with local gauge invariance. We show, that in a more general case, there are further conserved Noether currents. In its method the paper reconstructs the clue introduced by Utiyama (1956, 1959) and followed by Al-Kuwari and Taha (1991) in the presence of a gauge field that depends on the co-ordinates of the velocity space. In this course we apply certain (but not full) analogies with Mills (1989). We show, that handling the space-time coordinates as implicit variables in the gauge field, reproduces the same results that have been derived in the configuration space (i.e., we do not lose information), while the proposed new treatment gives additional information extending those. The result is an extra conserved Noether current.
Archimedes' Principle in Action
Kires, Marian
2007-01-01
The conceptual understanding of Archimedes' principle can be verified in experimental procedures which determine mass and density using a floating object. This is demonstrated by simple experiments using graduated beakers. (Contains 5 figures.)
Design Principles for Security
National Research Council Canada - National Science Library
Benzel, Terry V; Irvine, Cynthia E; Levin, Timothy E; Bhaskara, Ganesha; Nguyen, Thuy D; Clark, Paul C
2005-01-01
As a prelude to the clean-slate design for the SecureCore project, the fundamental security principles from more than four decades of research and development in information security technology were reviewed...
Principles of applied statistics
National Research Council Canada - National Science Library
Cox, D. R; Donnelly, Christl A
2011-01-01
.... David Cox and Christl Donnelly distil decades of scientific experience into usable principles for the successful application of statistics, showing how good statistical strategy shapes every stage of an investigation...
Minimum entropy production principle
Czech Academy of Sciences Publication Activity Database
Maes, C.; Netočný, Karel
2013-01-01
Roč. 8, č. 7 (2013), s. 9664-9677 ISSN 1941-6016 Institutional support: RVO:68378271 Keywords : MINEP Subject RIV: BE - Theoretical Physics http://www.scholarpedia.org/article/Minimum_entropy_production_principle
Vaccinology: principles and practice
National Research Council Canada - National Science Library
Morrow, John
2012-01-01
... principles to implementation. This is an authoritative textbook that details a comprehensive and systematic approach to the science of vaccinology focusing on not only basic science, but the many stages required to commercialize...
Electrical and electronic principles
Knight, S A
1991-01-01
Electrical and Electronic Principles, 2, Second Edition covers the syllabus requirements of BTEC Unit U86/329, including the principles of control systems and elements of data transmission. The book first tackles series and parallel circuits, electrical networks, and capacitors and capacitance. Discussions focus on flux density, electric force, permittivity, Kirchhoff's laws, superposition theorem, arrangement of resistors, internal resistance, and powers in a circuit. The text then takes a look at capacitors in circuit, magnetism and magnetization, electromagnetic induction, and alternating v
Electrical and electronic principles
Knight, SA
1988-01-01
Electrical and Electronic Principles, 3 focuses on the principles involved in electrical and electronic circuits, including impedance, inductance, capacitance, and resistance.The book first deals with circuit elements and theorems, D.C. transients, and the series circuits of alternating current. Discussions focus on inductance and resistance in series, resistance and capacitance in series, power factor, impedance, circuit magnification, equation of charge, discharge of a capacitor, transfer of power, and decibels and attenuation. The manuscript then examines the parallel circuits of alternatin
Remark on Heisenberg's principle
International Nuclear Information System (INIS)
Noguez, G.
1988-01-01
Application of Heisenberg's principle to inertial frame transformations allows a distinction between three commutative groups of reciprocal transformations along one direction: Galilean transformations, dual transformations, and Lorentz transformations. These are three conjugate groups and for a given direction, the related commutators are all proportional to one single conjugation transformation which compensates for uniform and rectilinear motions. The three transformation groups correspond to three complementary ways of measuring space-time as a whole. Heisenberg's Principle then gets another explanation [fr
Microprocessors principles and applications
Debenham, Michael J
1979-01-01
Microprocessors: Principles and Applications deals with the principles and applications of microprocessors and covers topics ranging from computer architecture and programmed machines to microprocessor programming, support systems and software, and system design. A number of microprocessor applications are considered, including data processing, process control, and telephone switching. This book is comprised of 10 chapters and begins with a historical overview of computers and computing, followed by a discussion on computer architecture and programmed machines, paying particular attention to t
Microwave system engineering principles
Raff, Samuel J
1977-01-01
Microwave System Engineering Principles focuses on the calculus, differential equations, and transforms of microwave systems. This book discusses the basic nature and principles that can be derived from thermal noise; statistical concepts and binomial distribution; incoherent signal processing; basic properties of antennas; and beam widths and useful approximations. The fundamentals of propagation; LaPlace's Equation and Transmission Line (TEM) waves; interfaces between homogeneous media; modulation, bandwidth, and noise; and communications satellites are also deliberated in this text. This bo
Principles of general relativity theory in terms of the present day physics
International Nuclear Information System (INIS)
Pervushin, V.N.
1986-01-01
A hystory of gradual unification of general relativity theory and quantum field theory on the basis of unified geometrical principles is detected. The gauge invariance principles became universal for construction of all physical theories. Quantum mechanics, electrodynamics and Einstein gravitation theory were used to form geometrical principles. Identity of inertial and gravitational masses is an experimental basis of the general relativity theory (GRT). It is shown that correct understanding of GRT bases is a developing process related to the development of the present physics and stimulating this development
Perturbation of frame sequences in shift-invariant spaces
DEFF Research Database (Denmark)
Christensen, Ole; Kim, Hong Oh; Kim, Rae Young
2005-01-01
We prove a new perturbation criteria for frame sequences, which generalizes previous results and is easier to apply. In the special case of frames infinitely generated shift-invariant subspaces of L2(ℝd) the condition can be formulated in terms of the norm of a finite Gram matrix and a correspond...
Three-dimensional low-energy topological invariants
International Nuclear Information System (INIS)
Bakalarska, M.; Broda, B.
2000-01-01
A description of the one-loop approximation formula for the partition function of a three-dimensional abelian version of the Donaldson-Witten theory is proposed. The one-loop expression is shown to contain such topological invariants of a three-dimensional manifold M like the Reidemeister-Ray-Singer torsion τ R and Betti numbers. (orig.)
Conserved currents and gauge invariance in Yang-Mills theory
International Nuclear Information System (INIS)
Barnich, G.; Brandt, F.; Henneaux, M.
1994-01-01
It is shown that in the absence of free abelian gauge fields, the conserved currents of (classical) Yang-Mills gauge models coupled to matter fields can be always redefined so as to be gauge invariant. This is a direct consequence of the general analysis of the Wess-Zumino consistency condition for Yang-Mills theory that we have provided recently. (orig.)
Gauge invariance and equations of motion for closed string modes
Directory of Open Access Journals (Sweden)
B. Sathiapalan
2014-12-01
Full Text Available We continue earlier discussions on loop variables and the exact renormalization group on the string world sheet for closed and open string backgrounds. The world sheet action with a UV regulator is written in a generally background covariant way by introducing a background metric. It is shown that the renormalization group gives background covariant equations of motion – this is the gauge invariance of the graviton. Interaction is written in terms of gauge invariant and generally covariant field strength tensors. The basic idea is to work in Riemann normal coordinates and covariantize the final equation. It turns out that the equations for massive modes are gauge invariant only if the space–time curvature of the (arbitrary background is zero. The exact RG equations give quadratic equations of motion for all the modes including the physical graviton. The level (2,2¯ massive field equations are used to illustrate the techniques. At this level there are mixed symmetry tensors. Gauge invariant interacting equations can be written down. In flat space an action can also be written for the free theory.
Rotation-invariant fingerprint matching using radon and DCT
Indian Academy of Sciences (India)
A new set of promising rotation-invariant features based on radon and discrete cosine transform (DCT) is proposed for fingerprint matching. The radon and DCT of a tiny area in the region of core point of fingerprint image is computed. In the proposed method only 34% DCT coefficients are used for feature extraction.
An invariant symmetric non-selfadjoint differential operator
Thomas, Erik G.F.
2002-01-01
Let D be a symmetric left invariant differential operator on a unimodular Lie group G of type I. Then we show that D is essentially self-adjoint if and only if for almost all pi is an element of (G) over cap, with respect to the Plancherel measure, the operator pi(D) is essentially self-adjoint.
Transformations and invariants for dihedral Gauss hypergeometric functions
Vidunas, Raimundas
2011-01-01
Hypergeometric equations with a dihedral monodromy group can be solved in terms of elementary functions. This paper gives explicit general expressions for quadratic monodromy invariants for these hypergeometric equations, using a generalization of Clausen's formula and terminating double hypergeometric sums. Besides, pull-back transformations for the dihedral hypergeometric equations are presented, including Klein's pullback transformations for the equations with a finite (dihedral) monodromy...
Second invariant for two-dimensional classical super systems
Indian Academy of Sciences (India)
In §3, we obtain a set of coupled linear equations using graded bracket relation for the canonical conjugate variable where the existence of the second-order invariant for the super dynamical system under consideration is being as- sumed. A consistent solution of these equations yields the systems which are integrable.
Existence domains for invariant reactions in binary regular solution ...
Indian Academy of Sciences (India)
Home; Journals; Bulletin of Materials Science; Volume 26; Issue 4. Existence domains for invariant reactions in binary regular solution phase diagrams exhibiting two phases. B Nageswara Sarma S Srinivas Prasad S Vijayvergiya V Bharath Kumar S Lele. Biomaterials Volume 26 Issue 4 June 2003 pp 423-430 ...
Graph parameters and invariants of the orthogonal group
Regts, G.
2013-01-01
This thesis is concerned with links between certain graph parameters and the invariant theory of the orthogonal group and some of its subgroups. These links are given through so-called partition functions of edge-coloring models. These partition functions can be seen as graph parameters as well as
The Satisfaction with Life Scale: : Measurement invariance across immigrant groups
Ponizovsky, Y.; Dimitrova, R.; Schachner, M.K.; Van de Schoot, R.
2013-01-01
The current study examined measurement invariance of the Satisfaction With Life Scale (SWLS; Diener, Emmons, Larsen, & Griffin, 1985) across three immigrant groups, namely, immigrants from the Former Soviet Union (FSU) in Israel, Turkish-Bulgarians, and Turkish-Germans. The results demonstrate
The Satisfaction With Life Scale : Measurement invariance across immigrant groups
Ponizovsky, Y.; Dimitrova, R.; Schachner, M.; van de Schoot, R.
2013-01-01
The current study examined measurement invariance of the Satisfaction With Life Scale (SWLS; Diener, Emmons, Larsen, & Griffin, 1985) across three immigrant groups, namely, immigrants from the Former Soviet Union (FSU) in Israel, Turkish-Bulgarians, and Turkish-Germans. The results demonstrate
Factorial invariance of the Adult State Hope Scale
Directory of Open Access Journals (Sweden)
Petrus Nel
2014-05-01
Research purpose: The purpose of the study was to assess the degree of factorial invariance across race and gender by using a sample of aspiring chartered accountants. Motivation for the study: Previous research on the hope construct and associated measuring instruments have been conducted, using homogenous samples from Westernised cultures. Researchers need to be careful to assume that hope looks and behaves in exactly the same manner across cultures and groups. Research approach, design and method: A cross-sectional quantitative research design was used. A sample of 295 aspiring chartered accountants participated in the study. Exploratory factor analysis was used to determine the degree of factor similarity across groups, utilising Tucker’s coefficient of congruence. To supplement the exploratory factor analysis, a series of increasingly restrictive multi-group analyses were conducted to test the invariance of model parameters across the groups. Main findings: No significant differences were found in the factor patterns for the agency and pathways factors for (1 the white and designated groups and (2 females and males. Practical/managerial implications: Evidence related to factorial invariance was found. This should inform researchers and practitioners that both pathways and agency look similar across racial and gender groups. Contribution/value-add: Researchers are urged to use various statistical techniques, in combination, to determine the degree of factorial invariance across groups.
Invariant Nonrecurrent Fatou Components of Automorphisms of $C^2$
Jupiter, Daniel; Lilov, Krastio
2003-01-01
We examine invariant nonrecurrent Fatou components of automorphisms of $\\mathbb{C}^2$ in the case where all limit maps are constant. We show that except in special cases there cannot be more than one such limit map. We also briefly examine such Fatou components where the limit maps may be nonconstant. Lastly we present a few examples of such Fatou components.
Dynamical constraints and adiabatic invariants in chemical reactions.
Lorquet, J C
2007-08-23
For long-range electrostatic potentials and, more generally, when the topography of the potential energy surface is locally simple, the reaction path coordinate is adiabatically separable from the perpendicular degrees of freedom. For the ion-permanent dipole and ion-quadrupole interactions, the Poisson bracket of the adiabatic invariant decreases with the interfragment distance more rapidly than the electrostatic potential. The smaller the translational momentum, the moment of inertia of the neutral fragment, and the dipole or quadrupole moments are, the more reliable the adiabatic approximation is, as expected from the usual argumentation. Closed-form expressions for an effective one-dimensional potential in an adiabatic Hamiltonian are given. Connection with a model where the decoupling is exact is obtained in the limit of an infinitely heavy dipole. The dynamics is also constrained by adiabatic invariance for a harmonic valley about a curved reaction path, as shown by the reaction path Hamiltonian method. The maximum entropy method reveals that, as a result of the invariance properties of the entropy, constraints whose validity has been demonstrated locally only subsist in all parts of phase space. However, their form varies continuously, and they are not necessarily expressed in simple terms as they are in the asymptotic region. Therefore, although the influence of adiabatic invariance has been demonstrated at asymptotically large values of the reaction coordinate only, it persists in more interesting ranges.
DU and UD-invariants of unitary groups
International Nuclear Information System (INIS)
Aguilera-Navarro, M.C.K.
1977-01-01
Four distint ways of obtaining the eigenvalues of unitary groups, in any irreducible representation, are presented. The invariants are defined according to two different contraction conventions. Their eigenvalue can be given in terms of two classes of special partial hooks associated with the young diagram characterizing the irreducible representation considered
The need for invariant assessments in South African education ...
African Journals Online (AJOL)
Presently, a plethora of instruments designed to assess a mathematical skill, disposition, or competence prevail in South Africa. Yet few of them adhere to the basic requirements of the unidimensionality and invariance of measures. The Marko-D is a mathematical instrument designed to test learners between the ages of 4 ...
Generation of shape-invariant flat-top laser beams
CSIR Research Space (South Africa)
Ait-Ameur, K
2015-02-01
Full Text Available -1 Generation of shape-invariant flat-top laser beams Kamel Ait-Ameur, Darryl Naidoo, Sandile Ngcobo, Michael Fromager, Igor Litvin, Abdelkrim Hasnaoui, Ali Harfouche, Andrew Forbes ABSTRACT A great number of laser applications need in place of the usual...
The Scale Invariant Synchrotron Jet of Flat Spectrum Radio Quasars
Indian Academy of Sciences (India)
2016-01-27
Jan 27, 2016 ... The results are in good agreement with theoretical expectations of Heinz & Sunyaev (2003). Therefore, the jet synchrotron is shown to be scale independent, regardless of the accretion modes. Results in this article thus lend support to the scale invariant model of the jet synchrotron throughout the mass ...
A filter bank for rotationally invariant image recognition | Rodtook ...
African Journals Online (AJOL)
We present new rotation moment invariants based on multiresolution filter bank techniques. The multiresolution pyramid motivates our simple but efficient feature selection procedure based on the fuzzy C-mean clustering methodology combined with the Mahalanobis distance measure. The proposed procedure verifies an ...
Perturbation analysis of Lagrangian invariant subspaces of symplectic matrices
Ran, A.C.M.; Mehl, Ch.; Mehrmann, V.; Rodman, L.
2009-01-01
Lagrangian invariant subspaces for symplectic matrices play an important role in the numerical solution of discrete time, robust and optimal control problems. The sensitivity (perturbation) analysis of these subspaces, however, is a difficult problem, in particular, when the eigenvalues are on or
Invariant Subspace Method and Fractional Modified Kuramoto-Sivashinsky Equation
Ouhadan, A.; Kinani, E. H. El
2015-01-01
In this paper, the invariant subspace method is applied to the time fractional modified Kuramoto-Sivashinsky partial differential equation. The obtained reduced system of nonlinear ordinary fractional equations is solved by the Laplace transform method and with using of some useful properties of Mittag-Leffler function. Then, some exact solutions of the time fractional nonlinear studied equation are found.
Invariance of reactor location with the outaging of critical lines ...
African Journals Online (AJOL)
Remember me, or Register. DOWNLOAD FULL TEXT Open Access DOWNLOAD FULL TEXT Subscription or Fee Access. Invariance of reactor location with the outaging of critical lines. SOA Ogunjuyigbe, COA Awosope. Abstract. No Abstract. Journal of Applied Science, Engineering and Technology Vol. 4(2) 2004: 49-54 ...
Waveguide invariant broadband target detection and reverberation estimation.
Goldhahn, Ryan; Hickman, Granger; Krolik, Jeffrey
2008-11-01
Reverberation often limits the performance of active sonar systems. In particular, backscatter off of a rough ocean floor can obscure target returns and/or large bottom scatterers can be easily confused with water column targets of interest. Conventional active sonar detection involves constant false alarm rate (CFAR) normalization of the reverberation return which does not account for the frequency-selective fading caused by multipath propagation. This paper presents an alternative to conventional reverberation estimation motivated by striations observed in time-frequency analysis of active sonar data. A mathematical model for these reverberation striations is derived using waveguide invariant theory. This model is then used to motivate waveguide invariant reverberation estimation which involves averaging the time-frequency spectrum along these striations. An evaluation of this reverberation estimate using real Mediterranean data is given and its use in a generalized likelihood ratio test based CFAR detector is demonstrated. CFAR detection using waveguide invariant reverberation estimates is shown to outperform conventional cell-averaged and frequency-invariant CFAR detection methods in shallow water environments producing strong reverberation returns which exhibit the described striations.
Electromagnetic properties of off-shell particles and gauge invariance
Nagorny, S. I.; Dieperink, A. E. L.
1998-01-01
Abstract: Electromagnetic properties of off-shell particles are discussed on the basis of a purely electromagnetic reaction: virtual Compton scattering off a proton. It is shown that the definition of off-shell electromagnetic form factors is not gauge invariant and that these cannot be investigated
Deformed special relativity with an invariant minimum speed and its ...
Indian Academy of Sciences (India)
On the other hand, according to special relativity (SR), the momentum cannot ... Deformed special relativity with an invariant minimum speed ..... However, we need to show that there is an anti-gravitational interaction between the ordinary proof mass m and the big sphere with a 'dark mass' of vacuum (MΛ), but let us first ...
Characteristics of thermalization of boost-invariant plasma from holography
Heller, M.P.; Janik, R.A.; Witaszczyk, P.
2012-01-01
We report on the approach toward the hydrodynamic regime of boost-invariant N=4 super Yang-Mills plasma at strong coupling starting from various far-from-equilibrium states at τ=0. The results are obtained through a numerical solution of Einstein’s equations for the dual geometries, as described in
Higher dimensional gravity invariant under the Poincare group
International Nuclear Information System (INIS)
Salgado, P.; Cataldo, M.; Campo, S. del
2002-01-01
It is shown that the Stelle-West Grignani-Nardelli formalism allows, both when odd dimensions and when even dimensions are considered, constructing actions for higher dimensional gravity invariant under local Lorentz rotations and under local Poincare translations. It is also proved that such actions have the same coefficients as those obtained by Troncoso and Zanelli [Class. Quantum Grav. 17, 4451 (2000)
The Loneliness Questionnaire: Establishing Measurement Invariance Across Ethnic Groups.
Ritchwood, Tiarney D; Ebesutani, Chad K; Chin, Eu Gene; Young, John
2017-09-01
A state of loneliness describes an individual's perception of having dissatisfying social connections to others. Though it is notable across the life span, it may have particularly deleterious effects in childhood and adolescence, leading to increased risk of emotional impairment. The current study evaluates a widely used test of loneliness, the Loneliness Questionnaire, for measurement invariance across ethnic groups in a large, representative sample of youth in the 2nd to 12th grades ( N = 12,344; 41% African American) in Mississippi. Analyses were conducted using multigroup confirmatory factor analysis following a published, sequential method to examine invariance in form, factor loadings, and item intercepts. Overall, our results indicated that the instrument was invariant across ethnicities, suggesting that youth with equivalent manifest scores can be discerned as having comparable levels of latent loneliness. The loneliness scores also corresponded significantly with depression and anxiety scores for most subsamples, with one exception. These findings are discussed in the context of previous results comparing levels of loneliness across ethnicities. Additionally, the broader context of the need to expand invariance studies in instrumentation work is highlighted.
On the Galilean Non-Invariance of Classical Electromagnetism
Preti, Giovanni; de Felice, Fernando; Masiero, Luca
2009-01-01
When asked to explain the Galilean non-invariance of classical electromagnetism on the basis of pre-relativistic considerations alone, students--and sometimes their teachers too--may face an impasse. Indeed, they often argue that a pre-relativistic physicist could most obviously have provided the explanation "at a glance", on the basis of the…
A characterization of scale invariant responses in enzymatic networks.
Directory of Open Access Journals (Sweden)
Maja Skataric
Full Text Available An ubiquitous property of biological sensory systems is adaptation: a step increase in stimulus triggers an initial change in a biochemical or physiological response, followed by a more gradual relaxation toward a basal, pre-stimulus level. Adaptation helps maintain essential variables within acceptable bounds and allows organisms to readjust themselves to an optimum and non-saturating sensitivity range when faced with a prolonged change in their environment. Recently, it was shown theoretically and experimentally that many adapting systems, both at the organism and single-cell level, enjoy a remarkable additional feature: scale invariance, meaning that the initial, transient behavior remains (approximately the same even when the background signal level is scaled. In this work, we set out to investigate under what conditions a broadly used model of biochemical enzymatic networks will exhibit scale-invariant behavior. An exhaustive computational study led us to discover a new property of surprising simplicity and generality, uniform linearizations with fast output (ULFO, whose validity we show is both necessary and sufficient for scale invariance of three-node enzymatic networks (and sufficient for any number of nodes. Based on this study, we go on to develop a mathematical explanation of how ULFO results in scale invariance. Our work provides a surprisingly consistent, simple, and general framework for understanding this phenomenon, and results in concrete experimental predictions.
A filter bank for rotationally invariant image recognition
African Journals Online (AJOL)
2005-07-18
Jul 18, 2005 ... We present new rotation moment invariants based on multiresolution filter bank techniques. The multiresolution pyramid motivates our simple but efficient feature selection procedure based on the fuzzy C-mean clustering methodology combined with the Mahalanobis distance measure. The proposed ...
Invariant-Based Automatic Testing of AJAX User Interfaces
Mesbah, A.; Van Deursen, A.
2009-01-01
This paper is a pre-print of: Ali Mesbah and Arie van Deursen. Invariant-Based Automatic Testing of AJAX User Interfaces. In Proceedings of the 31st International Conference on Software Engineering (ICSE’09), Research Papers, Vancouver, Canada, IEEE Computer Society, 2009. AJAX-based Web 2.0
Global operator expansions in conformally invariant relativistic quantum field theory
International Nuclear Information System (INIS)
Schoer, B.; Swieca, J.A.; Voelkel, A.H.
1974-01-01
A global conformal operator expansions in the Minkowski region in several models and their formulation in the general theory is presented. Whereas the vacuum expansions are termwise manisfestly conformal invariant, the expansions away from the vacuum do not share this property
Another scheme for quantization of scale invariant gauge theories
International Nuclear Information System (INIS)
Hortacsu, M.
1987-10-01
A new scheme is proposed for the quantization of scale invariant gauge theories for all even dimensions when they are minimally coupled to a spinor field. A cut-off procedure suggests an algorithm which may regularize the theory. (author). 10 refs
Boundary behaviour of the Bergman invariant and related guantities
Czech Academy of Sciences Publication Activity Database
Engliš, Miroslav
2008-01-01
Roč. 154, č. 1 (2008), s. 19-37 ISSN 0026-9255 R&D Projects: GA AV ČR IAA1019304 Institutional research plan: CEZ:AV0Z10190503 Keywords : Bergman invariant * Bergman metric * Fefferman´s expansion Subject RIV: BA - General Mathematics Impact factor: 0.584, year: 2008
Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations
Directory of Open Access Journals (Sweden)
Waheed A. Ahmed
2017-11-01
Full Text Available Approximate symmetries of a class of perturbed nonlinear wave equations are computed using two newly-developed methods. Invariant solutions associated with the approximate symmetries are constructed for both methods. Symmetries and solutions are compared through discussing the advantages and disadvantages of each method.
Complex dynamical invariants for two-dimensional complex potentials
Indian Academy of Sciences (India)
Abstract. Complex dynamical invariants are searched out for two-dimensional complex poten- tials using rationalization method within the framework of an extended complex phase space characterized by x = x1 + ip3, y = x2 + ip4, px = p1 + ix3, py = p2 + ix4. It is found that the cubic oscillator and shifted harmonic oscillator ...
Invariant Handwriting Features Useful in Cursive-Script Recognition
Teulings, Hans-leo L; Schomaker, L R; Impedovo, S.
1994-01-01
A handwriting pattern is considered as a sequence of ballistic strokes. Replications of a pattern may be generated from a single, higher-level memory representation, acting as a motor program. Therefore, those stroke features which show the most invariant pattern are probably related to the
Lorentz Invariant Spectrum of Minimal Chiral Schwinger Model
Kim, Yong-Wan; Kim, Seung-Kook; Kim, Won-Tae; Park, Young-Jai; Kim, Kee Yong; Kim, Yongduk
We study the Lorentz transformation of the minimal chiral Schwinger model in terms of the alternative action. We automatically obtain a chiral constraint, which is equivalent to the frame constraint introduced by McCabe, in order to solve the frame problem in phase space. As a result we obtain the Lorentz invariant spectrum in any moving frame by choosing a frame parameter.
Invariant Distributionally Scrambled Manifolds for an Annihilation Operator
Directory of Open Access Journals (Sweden)
Xinxing Wu
2014-01-01
Full Text Available This note proves that the annihilation operator of a quantum harmonic oscillator admits an invariant distributionally ε-scrambled linear manifold for any 0<ε<2. This is a positive answer to Question 1 by Wu and Chen (2013.
Residual gauge invariance of Hamiltonian lattice gauge theories
International Nuclear Information System (INIS)
Ryang, S.; Saito, T.; Shigemoto, K.
1984-01-01
The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegengauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically. (orig.)
Selected papers on harmonic analysis, groups, and invariants
Nomizu, Katsumi
1997-01-01
This volume contains papers that originally appeared in Japanese in the journal Sūgaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication the Society has chosen to publish them as a volume of selected papers. The papers range over a variety of topics, including representation theory, differential geometry, invariant theory, and complex analysis.
Localization of Compact Invariant Sets of the Lorenz'1984 System
Directory of Open Access Journals (Sweden)
Kh. M. Ramazanova
2015-01-01
Full Text Available Localization of compact invariant sets of a dynamical system is one way to conduct a qualitative analysis of dynamical system. The localization task is aimed at evaluating the location of invariant compact sets of systems, which are equilibrium, periodic trajectories, attractors and repellers, and invariant tori. Such sets and their properties largely determine the structure of the phase portrait of the system. For this purpose, one can use a localization set, i.e. a set in the phase space of the system that contains all invariant compact sets.This article considers the problem of localization of invariant compact sets of an Autonomous version of the Lorenz-84 system. The system represents a simple model of the General circulation of the atmosphere in middle latitudes. The model was used in various climatological studies. To build localization set of the system the so-called functional localization method is applied. The article describes the main provisions of this method, lists the main properties of the localization sets. The simplest version of the Lorenz-84 system when there are no thermal loads is analyzed, and a common variant of the Autonomous Lorenz-84 system, in which for some values of system parameters chaotic dynamics occurs is investigated. In the first case it is shown that the only invariant compact set of the system is its equilibrium position, and localization function turned out to be a Lyapunov function of the system. For the General version of the system a family of localization sets is built and the intersection of this family is described. Graphical illustration for the localization set at fixed values of the parameters is shown. The result of the study partially overlaps with the result of K.E. Starkov on the subject, but provides additional information.The theme of localization of invariant compact sets is discussed quite actively in the literature. Research focuses both on the development of the method and its
International Nuclear Information System (INIS)
Rozansky, L.
1996-01-01
We establish a relation between the coefficients of asymptotic expansion of the trivial connection contribution to Witten's invariant of rational homology spheres and the invariants that T. Ohtsuki extracted from Witten's invariant at prime values of K. We also rederive the properties of prime K invariants discovered by H. Murakami and T. Ohtsuki. We do this by using the bounds on Taylor series expansion of the Jones polynomial of algebraically split links, studied in our previous paper. These bounds are enough to prove that Ohtsuki's invariants are of finite type. The relation between Ohtsuki's invariants and trivial connection contribution is verified explicitly for lens spaces and Seifert manifolds. (orig.)
Skew semi-invariant submanifolds of generalized quasi-Sasakian manifolds
Directory of Open Access Journals (Sweden)
M. D. Siddiqi
2017-12-01
Full Text Available In the present paper, we study a new class of submanifolds of a generalized Quasi-Sasakian manifold, called skew semi-invariant submanifold. We obtain integrability conditions of the distributions on a skew semi-invariant submanifold and also find the condition for a skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold to be mixed totally geodesic. Also it is shown that a skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold will be anti-invariant if and only if $A_{\\xi}=0$; and the submanifold will be skew semi-invariant submanifold if $\
Directory of Open Access Journals (Sweden)
Elena ANGHEL
2016-05-01
Full Text Available According to Professor Djuvara “law can be a science, and legal knowledge can also become science when, referring to a number as large as possible of acts of those covered by law, sorts and connects them by their essential characters upon legal concepts or principles which are universally valid, just like the laws of nature”. The general principles of law take a privileged place in the positive legal order and represent the foundation of any legal construction. The essence of the legal principles resides in their generality. In respect of the term “general”, Franck Moderne raised the question on the degree of generality used in order to define a principle as being general – at the level of an institution, of a branch of the law or at the level of the entire legal order. The purpose of this study is to find out the characteristics of law principles. In our opinion, four characteristics can be mentioned.
Ethical principles of scientific communication
Directory of Open Access Journals (Sweden)
Baranov G. V.
2017-03-01
Full Text Available the article presents the principles of ethical management of scientific communication. The author approves the priority of ethical principle of social responsibility of the scientist.
Deep generative learning of location-invariant visual word recognition
Di Bono, Maria Grazia; Zorzi, Marco
2013-01-01
It is widely believed that orthographic processing implies an approximate, flexible coding of letter position, as shown by relative-position and transposition priming effects in visual word recognition. These findings have inspired alternative proposals about the representation of letter position, ranging from noisy coding across the ordinal positions to relative position coding based on open bigrams. This debate can be cast within the broader problem of learning location-invariant representations of written words, that is, a coding scheme abstracting the identity and position of letters (and combinations of letters) from their eye-centered (i.e., retinal) locations. We asked whether location-invariance would emerge from deep unsupervised learning on letter strings and what type of intermediate coding would emerge in the resulting hierarchical generative model. We trained a deep network with three hidden layers on an artificial dataset of letter strings presented at five possible retinal locations. Though word-level information (i.e., word identity) was never provided to the network during training, linear decoding from the activity of the deepest hidden layer yielded near-perfect accuracy in location-invariant word recognition. Conversely, decoding from lower layers yielded a large number of transposition errors. Analyses of emergent internal representations showed that word selectivity and location invariance increased as a function of layer depth. Word-tuning and location-invariance were found at the level of single neurons, but there was no evidence for bigram coding. Finally, the distributed internal representation of words at the deepest layer showed higher similarity to the representation elicited by the two exterior letters than by other combinations of two contiguous letters, in agreement with the hypothesis that word edges have special status. These results reveal that the efficient coding of written words—which was the model's learning objective
Developing principles of growth
DEFF Research Database (Denmark)
Neergaard, Helle; Fleck, Emma
of the principles of growth among women-owned firms. Using an in-depth case study methodology, data was collected from women-owned firms in Denmark and Ireland, as these countries are similar in contextual terms, e.g. population and business composition, dominated by micro, small and medium-sized enterprises......Although it has been widely recognized that the growth of women-owned businesses is central to wealth creation, innovation and economic development; limited attention has been devoted to understanding small business growth from a female perspective.This research seeks to develop an understanding....... Extending on principles put forward in effectuation theory, we propose that women grow their firms according to five principles which enable women’s enterprises to survive in the face of crises such as the current financial world crisis....
Principles of musical acoustics
Hartmann, William M
2013-01-01
Principles of Musical Acoustics focuses on the basic principles in the science and technology of music. Musical examples and specific musical instruments demonstrate the principles. The book begins with a study of vibrations and waves, in that order. These topics constitute the basic physical properties of sound, one of two pillars supporting the science of musical acoustics. The second pillar is the human element, the physiological and psychological aspects of acoustical science. The perceptual topics include loudness, pitch, tone color, and localization of sound. With these two pillars in place, it is possible to go in a variety of directions. The book treats in turn, the topics of room acoustics, audio both analog and digital, broadcasting, and speech. It ends with chapters on the traditional musical instruments, organized by family. The mathematical level of this book assumes that the reader is familiar with elementary algebra. Trigonometric functions, logarithms and powers also appear in the book, but co...
Why Do We Believe the Speed of Light is an Invariant of Nature?
Smith, Felix T.
2014-03-01
We believe it, obviously, because we believe in relativity, and Einstein based his treatment of relativity on what he named ``The Principle of Constancy of the Velocity of Light.'' From Einstein's own writings between 1905 and about 1912 we know that in defining what this meant he was concerned especially about two issues: One was to deny the notion that the transmission of light required a privileged ``ether'' frame; the other was that the velocity of a light signal measured by an observer is independent of the velocity of the source that emitted the signal with respect to the observer. In relativity Einstein's two Principles made a handy brief basis from which he could deduce the requirement of covariance under the transformations of the Lorentz group. These transformations had been developed earlier by Lorentz to conform with the results of experiments, without requiring constancy of c. The Lorentz group only requires that c be an upper bound greater than all observed particle or signal velocities. The assumption of its invariance over cosmological time seems justified mostly by its convenience as a teaching and mnemonic oversimplification.
Electrical principles 3 checkbook
Bird, J O
2013-01-01
Electrical Principles 3 Checkbook aims to introduce students to the basic electrical principles needed by technicians in electrical engineering, electronics, and telecommunications.The book first tackles circuit theorems, single-phase series A.C. circuits, and single-phase parallel A.C. circuits. Discussions focus on worked problems on parallel A.C. circuits, worked problems on series A.C. circuits, main points concerned with D.C. circuit analysis, worked problems on circuit theorems, and further problems on circuit theorems. The manuscript then examines three-phase systems and D.C. transients
Bulmer, M G
1979-01-01
There are many textbooks which describe current methods of statistical analysis, while neglecting related theory. There are equally many advanced textbooks which delve into the far reaches of statistical theory, while bypassing practical applications. But between these two approaches is an unfilled gap, in which theory and practice merge at an intermediate level. Professor M. G. Bulmer's Principles of Statistics, originally published in 1965, was created to fill that need. The new, corrected Dover edition of Principles of Statistics makes this invaluable mid-level text available once again fo
Hankins, D. B.; Wake, W. H.
1981-01-01
The potential remote sensing user community is enormous, and the teaching and training tasks are even larger; however, some underlying principles may be synthesized and applied at all levels from elementary school children to sophisticated and knowledgeable adults. The basic rules applying to each of the six major elements of any training course and the underlying principle involved in each rule are summarized. The six identified major elements are: (1) field sites for problems and practice; (2) lectures and inside study; (3) learning materials and resources (the kit); (4) the field experience; (5) laboratory sessions; and (6) testing and evaluation.
Principles of quantum electronics
Marcuse, Dietrich
1980-01-01
Principles of Quantum Electronics focuses on the concept of quantum electronics as the application of quantum theory to engineering problems. It examines the principles that govern specific quantum electronics devices and presents their theoretical applications to typical problems. Comprised of 10 chapters, this book starts with an overview of the Dirac formulation of quantum mechanics. This text then considers the derivation of the formalism of field quantization and discusses the properties of photons and phonons. Other chapters examine the interaction between the electromagnetic field and c
Mechanical engineering principles
Bird, John
2014-01-01
A student-friendly introduction to core engineering topicsThis book introduces mechanical principles and technology through examples and applications, enabling students to develop a sound understanding of both engineering principles and their use in practice. These theoretical concepts are supported by 400 fully worked problems, 700 further problems with answers, and 300 multiple-choice questions, all of which add up to give the reader a firm grounding on each topic.The new edition is up to date with the latest BTEC National specifications and can also be used on undergraduate courses in mecha
International Nuclear Information System (INIS)
Abdelmalik, W.E.Y.
2011-01-01
This work presents a summary of the IAEA Safety Standards Series publication No. SF-1 entitled F UDAMENTAL Safety PRINCIPLES p ublished on 2006. This publication states the fundamental safety objective and ten associated safety principles, and briefly describes their intent and purposes. Safety measures and security measures have in common the aim of protecting human life and health and the environment. These safety principles are: 1) Responsibility for safety, 2) Role of the government, 3) Leadership and management for safety, 4) Justification of facilities and activities, 5) Optimization of protection, 6) Limitation of risks to individuals, 7) Protection of present and future generations, 8) Prevention of accidents, 9)Emergency preparedness and response and 10) Protective action to reduce existing or unregulated radiation risks. The safety principles concern the security of facilities and activities to the extent that they apply to measures that contribute to both safety and security. Safety measures and security measures must be designed and implemented in an integrated manner so that security measures do not compromise safety and safety measures do not compromise security.
DEFF Research Database (Denmark)
Sharp, Robin
This is a new and updated edition of a book first published in 1994. The book introduces the reader to the principles used in the construction of a large range of modern data communication protocols, as used in distributed computer systems of all kinds. The approach taken is rather a formal one...
Principles of Bridge Reliability
DEFF Research Database (Denmark)
Thoft-Christensen, Palle; Nowak, Andrzej S.
The paper gives a brief introduction to the basic principles of structural reliability theory and its application to bridge engineering. Fundamental concepts like failure probability and reliability index are introduced. Ultimate as well as serviceability limit states for bridges are formulated...
Pattern recognition principles
Tou, J. T.; Gonzalez, R. C.
1974-01-01
The present work gives an account of basic principles and available techniques for the analysis and design of pattern processing and recognition systems. Areas covered include decision functions, pattern classification by distance functions, pattern classification by likelihood functions, the perceptron and the potential function approaches to trainable pattern classifiers, statistical approach to trainable classifiers, pattern preprocessing and feature selection, and syntactic pattern recognition.
Indian Academy of Sciences (India)
IAS Admin
The Handicap Principle is an idea proposed by the husband and wife scientist team of Amotz and Avishag Zahavi from. Israel in the 1970's. It is among the most innovative ideas of the 20th century in the field of behavioural biology and attempts to explain several long-standing puzzles that have baffled naturalists since the ...
Schrodinger's Uncertainty Principle?
Indian Academy of Sciences (India)
correlation between x and p. The virtue of Schrodinger's version (5) is that it accounts for this correlation. In spe- cial cases like the free particle and the harmonic oscillator, the 'Schrodinger uncertainty product' even remains constant with time, whereas Heisenberg's does not. The glory of giving the uncertainty principle to ...
The traveltime holographic principle
Huang, Y.
2014-11-06
Fermat\\'s interferometric principle is used to compute interior transmission traveltimes τpq from exterior transmission traveltimes τsp and τsq. Here, the exterior traveltimes are computed for sources s on a boundary B that encloses a volume V of interior points p and q. Once the exterior traveltimes are computed, no further ray tracing is needed to calculate the interior times τpq. Therefore this interferometric approach can be more efficient than explicitly computing interior traveltimes τpq by ray tracing. Moreover, the memory requirement of the traveltimes is reduced by one dimension, because the boundary B is of one fewer dimension than the volume V. An application of this approach is demonstrated with interbed multiple (IM) elimination. Here, the IMs in the observed data are predicted from the migration image and are subsequently removed by adaptive subtraction. This prediction is enabled by the knowledge of interior transmission traveltimes τpq computed according to Fermat\\'s interferometric principle. We denote this principle as the ‘traveltime holographic principle’, by analogy with the holographic principle in cosmology where information in a volume is encoded on the region\\'s boundary.
Cooperatives, Principles and Practices.
Schaars, Marvin A.
A teaching aid and information source on activities, principles, and practices of cooperatives is presented. The following topics are included: (1) Basic Interests of People, (2) Legal Organization of Business in the United States, (3) What Is a Cooperative? (4) Procedure for Organizing Cooperatives, (5) How Cooperatives Are Run and Managed, (6)…
Principles of economics textbooks
DEFF Research Database (Denmark)
Madsen, Poul Thøis
2012-01-01
Has the financial crisis already changed US principles of economics textbooks? Rather little has changed in individual textbooks, but taken as a whole ten of the best-selling textbooks suggest rather encompassing changes of core curriculum. A critical analysis of these changes shows how individual...
Principles of Proper Validation
DEFF Research Database (Denmark)
Esbensen, Kim; Geladi, Paul
2010-01-01
Validation in chemometrics is presented using the exemplar context of multivariate calibration/prediction. A phenomenological analysis of common validation practices in data analysis and chemometrics leads to formulation of a set of generic Principles of Proper Validation (PPV), which is based...
Schrodinger's Uncertainty Principle?
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 2. Schrödinger's Uncertainty Principle? - Lilies can be Painted. Rajaram Nityananda. General Article Volume 4 Issue 2 February 1999 pp 24-26. Fulltext. Click here to view fulltext PDF. Permanent link:
Euthanasia: Buddhist principles.
Barnes, M
1996-04-01
Religions provide various forms of motivation for moral action. This chapter takes Buddhism as an example from within the Indian "family' of religions and seeks to identify the doctrinal and cultural principles on which ethical decisions are taken. Although beginning from very different religious premises, it is argued that the conclusions to which Buddhism tends are broadly similar to those found within mainstream Christianity.
DEFF Research Database (Denmark)
Hodgdon, Jennifer A.; Sethna, James P.
1993-01-01
We derive a general crack-propagation law for slow brittle cracking, in two and three dimensions, using discrete symmetries, gauge invariance, and gradient expansions. Our derivation provides explicit justification for the ‘‘principle of local symmetry,’’ which has been used extensively to describe...
Kaufman, Allan N.
1987-01-01
The covariant coupled equations for plasma dynamics and the Maxwell field are expressed as a phase-space-Lagrangian action principle. The linear interaction is transformed to the bilinear beat Hamiltonian by a gauge-invariant Lagrangian Lie transform. The result yields the generalized linear susceptibility directly.
Gauge-invariant fields and flow equations for Yang-Mills theories
Wetterich, C.
2017-01-01
We discuss the concept of gauge-invariant fields for non-abelian gauge theories. Infinitesimal fluctuations around a given gauge field can be split into physical and gauge fluctuations. Starting from some reference field the gauge-invariant fields are constructed by consecutively adding physical fluctuations. An effective action that depends on gauge-invariant fields becomes a gauge-invariant functional of arbitrary gauge fields by associating to every gauge field the corresponding gauge-inva...
Black hole complementarity with the generalized uncertainty principle in Gravity's Rainbow
Gim, Yongwan; Um, Hwajin; Kim, Wontae
2018-02-01
When gravitation is combined with quantum theory, the Heisenberg uncertainty principle could be extended to the generalized uncertainty principle accompanying a minimal length. To see how the generalized uncertainty principle works in the context of black hole complementarity, we calculate the required energy to duplicate information for the Schwarzschild black hole. It shows that the duplication of information is not allowed and black hole complementarity is still valid even assuming the generalized uncertainty principle. On the other hand, the generalized uncertainty principle with the minimal length could lead to a modification of the conventional dispersion relation in light of Gravity's Rainbow, where the minimal length is also invariant as well as the speed of light. Revisiting the gedanken experiment, we show that the no-cloning theorem for black hole complementarity can be made valid in the regime of Gravity's Rainbow on a certain combination of parameters.
The principle of locality: Effectiveness, fate, and challenges
International Nuclear Information System (INIS)
Doplicher, Sergio
2010-01-01
The special theory of relativity and quantum mechanics merge in the key principle of quantum field theory, the principle of locality. We review some examples of its 'unreasonable effectiveness' in giving rise to most of the conceptual and structural frame of quantum field theory, especially in the absence of massless particles. This effectiveness shows up best in the formulation of quantum field theory in terms of operator algebras of local observables; this formulation is successful in digging out the roots of global gauge invariance, through the analysis of superselection structure and statistics, in the structure of the local observable quantities alone, at least for purely massive theories; but so far it seems unfit to cope with the principle of local gauge invariance. This problem emerges also if one attempts to figure out the fate of the principle of locality in theories describing the gravitational forces between elementary particles as well. An approach based on the need to keep an operational meaning, in terms of localization of events, of the notion of space-time, shows that, in the small, the latter must loose any meaning as a classical pseudo-Riemannian manifold, locally based on Minkowski space, but should acquire a quantum structure at the Planck scale. We review the geometry of a basic model of quantum space-time and some attempts to formulate interaction of quantum fields on quantum space-time. The principle of locality is necessarily lost at the Planck scale, and it is a crucial open problem to unravel a replacement in such theories which is equally mathematically sharp, namely, a principle where the general theory of relativity and quantum mechanics merge, which reduces to the principle of locality at larger scales. Besides exploring its fate, many challenges for the principle of locality remain; among them, the analysis of superselection structure and statistics also in the presence of massless particles, and to give a precise mathematical
Normal Anti-Invariant Submanifolds of Paraquaternionic Kähler Manifolds
Directory of Open Access Journals (Sweden)
Novac-Claudiu Chiriac
2006-12-01
Full Text Available We introduce normal anti-invariant submanifolds of paraquaternionic Kähler manifolds and study the geometric structures induced on them. We obtain necessary and sufficient conditions for the integrability of the distributions defined on a normal anti-invariant submanifold. Also, we present characterizations of local (global anti-invariant products.
Jak, Suzanne; Oort, Frans J.; Dolan, Conor V.
2013-01-01
We present a test for cluster bias, which can be used to detect violations of measurement invariance across clusters in 2-level data. We show how measurement invariance assumptions across clusters imply measurement invariance across levels in a 2-level factor model. Cluster bias is investigated by testing whether the within-level factor loadings…
Local conservation laws for principle chiral fields (d=1)
International Nuclear Information System (INIS)
Cherednik, I.V.
1979-01-01
The Beklund transformation for chiral fields in the two-dimensional Minkovski space is found. As a result an infinite series of conservation laws for principle chiral Osub(n) fields (d=1) has been built. It is shown that these laws are local, the infinite series of global invariants which do not depend on xi, eta, and which is rather rapidly decrease along xi (or along eta) solutions being connected with these laws (xi, eta - coordinates of the light cone). It is noted that with the help of the construction proposed it is possible to obtain conservation laws of principle chiral G fields, including G in the suitable ortogonal groups. Symmetry permits to exchange xi and eta. The construction of conservation laws may be carried out without supposition that lambda has a multiplicity equal to 1, however the proof of the locality applied does not transfer on the laws obtained
Extremum principles for irreversible processes
International Nuclear Information System (INIS)
Hillert, M.; Agren, J.
2006-01-01
Hamilton's extremum principle is a powerful mathematical tool in classical mechanics. Onsager's extremum principle may play a similar role in irreversible thermodynamics and may also become a valuable tool. His principle may formally be regarded as a principle of maximum rate of entropy production but does not have a clear physical interpretation. Prigogine's principle of minimum rate of entropy production has a physical interpretation when it applies, but is not strictly valid except for a very special case
Yang–Baxter invariance of the Nappi–Witten model
International Nuclear Information System (INIS)
Kyono, Hideki; Yoshida, Kentaroh
2016-01-01
We study Yang–Baxter deformations of the Nappi–Witten model with a prescription invented by Delduc, Magro and Vicedo. The deformations are specified by skew-symmetric classical r-matrices satisfying (modified) classical Yang–Baxter equations. We show that the sigma-model metric is invariant under arbitrary deformations (while the coefficient of B-field is changed) by utilizing the most general classical r-matrix. Furthermore, the coefficient of B-field is determined to be the original value from the requirement that the one-loop β-function should vanish. After all, the Nappi–Witten model is the unique conformal theory within the class of the Yang–Baxter deformations preserving the conformal invariance.
Experiment of Azimuth-invariant Bistatic UHF UWB SAR
Xie, Hongtu; Shi, Shaoying; Mao, Junfa; Li, Fuhai; An, Daoxiang; Zhou, Zhimin; Wang, Guoqian
2018-01-01
Bistatic ultrahigh frequency ultrawideband synthetic aperture radar (UHF UWB SAR) has the well ability of the penetrating the foliage, high-resolution imaging and providing the increased information. In the paper, an imaging experiment of the azimuth-invariant bistatic UHF UWB SAR is described and the result is proposed. In August 2015, an along-track bistatic UHF UWB SAR experiment was conducted in China, and the raw data was collected. In this bistatic SAR system, the transmitter and receiver are both carried by a vehicle and separated by an invariable distance. The aim was to investigate the imaging property of the bistatic UHF UWB SAR system. Bistatic image was obtained using the subaperture spectrum-equilibrium method integrated with the fast factorized back projection algorithm (FFBPA). Experiment results prove the validity of the bistatic UHF UWB SAR experiment.
Background Independence and Duality Invariance in String Theory.
Hohm, Olaf
2017-03-31
Closed string theory exhibits an O(D,D) duality symmetry on tori, which in double field theory is manifest before compactification. I prove that to first order in α^{'} there is no manifestly background independent and duality invariant formulation of bosonic string theory in terms of a metric, b field, and dilaton. To this end I use O(D,D) invariant second order perturbation theory around flat space to show that the unique background independent candidate expression for the gauge algebra at order α^{'} is inconsistent with the Jacobi identity. A background independent formulation exists instead for frame variables subject to α^{'}-deformed frame transformations (generalized Green-Schwarz transformations). Potential applications for curved backgrounds, as in cosmology, are discussed.
Assessment of Rotationally-Invariant Clustering Using Streamlet Tractography
DEFF Research Database (Denmark)
Liptrot, Matthew George; Lauze, François
2016-01-01
We present a novel visualisation-based strategy for the assessment of a recently proposed clustering technique for raw DWI volumes which derives rotationally-invariant metrics to classify voxels. The validity of the division of all brain tissue voxels into such classes was assessed using the rece......We present a novel visualisation-based strategy for the assessment of a recently proposed clustering technique for raw DWI volumes which derives rotationally-invariant metrics to classify voxels. The validity of the division of all brain tissue voxels into such classes was assessed using...... the recently developed streamlets visualisation technique, which aims to represent brain fibres by collections of many short streamlines. Under the assumption that streamlines seeded in a cluster should stay within it, we were able to assess how well perceptual tracing could occur across the boundaries...... of the clusters....
Invariants and labels for Lie-Poisson Systems
International Nuclear Information System (INIS)
Thiffeault, J.L.; Morrison, P.J.
1998-04-01
Reduction is a process that uses symmetry to lower the order of a Hamiltonian system. The new variables in the reduced picture are often not canonical: there are no clear variables representing positions and momenta, and the Poisson bracket obtained is not of the canonical type. Specifically, we give two examples that give rise to brackets of the noncanonical Lie-Poisson form: the rigid body and the two-dimensional ideal fluid. From these simple cases, we then use the semidirect product extension of algebras to describe more complex physical systems. The Casimir invariants in these systems are examined, and some are shown to be linked to the recovery of information about the configuration of the system. We discuss a case in which the extension is not a semidirect product, namely compressible reduced MHD, and find for this case that the Casimir invariants lend partial information about the configuration of the system
Statistical analysis of complex systems with nonclassical invariant measures
Fratalocchi, Andrea
2011-02-28
I investigate the problem of finding a statistical description of a complex many-body system whose invariant measure cannot be constructed stemming from classical thermodynamics ensembles. By taking solitons as a reference system and by employing a general formalism based on the Ablowitz-Kaup-Newell-Segur scheme, I demonstrate how to build an invariant measure and, within a one-dimensional phase space, how to develop a suitable thermodynamics. A detailed example is provided with a universal model of wave propagation, with reference to a transparent potential sustaining gray solitons. The system shows a rich thermodynamic scenario, with a free-energy landscape supporting phase transitions and controllable emergent properties. I finally discuss the origin of such behavior, trying to identify common denominators in the area of complex dynamics.
Gauge invariant determination of charged hadron masses arXiv
Hansen, Martin; Patella, Agostino; Tantalo, Nazario
In this paper we show, for the first time, that charged-hadron masses can be calculated on the lattice without relying on gauge fixing at any stage of the calculations. In our simulations we follow a recent proposal and formulate full QCD+QED on a finite volume, without spoiling locality, by imposing C-periodic boundary conditions in the spatial directions. Electrically charged states are interpolated with a class of operators, originally suggested by Dirac and built as functionals of the photon field, that are invariant under local gauge transformations. We show that the quality of the numerical signal of charged-hadron masses is the same as in the neutral sector and that charged-neutral mass splittings can be calculated with satisfactory accuracy in this setup. We also discuss how to describe states of charged hadrons with real photons in a fully gauge-invariant way by providing a first evidence that the proposed strategy can be numerically viable.
Evaluating Forecasts, Narratives and Policy Using a Test of Invariance
Directory of Open Access Journals (Sweden)
Jennifer L. Castle
2017-09-01
Full Text Available Economic policy agencies produce forecasts with accompanying narratives, and base policy changes on the resulting anticipated developments in the target variables. Systematic forecast failure, defined as large, persistent deviations of the outturns from the numerical forecasts, can make the associated narrative false, which would in turn question the validity of the entailed policy implementation. We establish when systematic forecast failure entails failure of the accompanying narrative, which we call forediction failure, and when that in turn implies policy invalidity. Most policy regime changes involve location shifts, which can induce forediction failure unless the policy variable is super exogenous in the policy model. We propose a step-indicator saturation test to check in advance for invariance to policy changes. Systematic forecast failure, or a lack of invariance, previously justified by narratives reveals such stories to be economic fiction.
Can confinement ensure natural CP-invariance of strong interactions
International Nuclear Information System (INIS)
Shifman, M.A.; Vainshtein, A.I.; Zakharov, V.I.
1979-01-01
P- and T-invariance violation in quantum chromodynamics (QCD) due to the so called THETA term Δα=THETAxgsub(s)sup(2)/32πsup(2)xGsub(μν)sup(a)xGsub(μν)sup(a) tilde, where Gsub(μν)sup(a) is the gluon field strength tensor, and gsub(s) is the quark-gluon coupling constant is discussed. It is shown that irrespectively of how the confinement works there emerge observable P- and T-odd effects. The proof is based on the assumption that QCD resolves the upsilon(1) problem, i.e. the mass of the singlet pseudoscalar meson does not vanish in the chiral limit. A modification of the axion scheme which restores the natural P and T invariance of the theory is suggested and cannot be ruled out experimentally
Completed local ternary pattern for rotation invariant texture classification.
Rassem, Taha H; Khoo, Bee Ee
2014-01-01
Despite the fact that the two texture descriptors, the completed modeling of Local Binary Pattern (CLBP) and the Completed Local Binary Count (CLBC), have achieved a remarkable accuracy for invariant rotation texture classification, they inherit some Local Binary Pattern (LBP) drawbacks. The LBP is sensitive to noise, and different patterns of LBP may be classified into the same class that reduces its discriminating property. Although, the Local Ternary Pattern (LTP) is proposed to be more robust to noise than LBP, however, the latter's weakness may appear with the LTP as well as with LBP. In this paper, a novel completed modeling of the Local Ternary Pattern (LTP) operator is proposed to overcome both LBP drawbacks, and an associated completed Local Ternary Pattern (CLTP) scheme is developed for rotation invariant texture classification. The experimental results using four different texture databases show that the proposed CLTP achieved an impressive classification accuracy as compared to the CLBP and CLBC descriptors.
MEG source localization using invariance of noise space.
Zhang, Junpeng; Raij, Tommi; Hämäläinen, Matti; Yao, Dezhong
2013-01-01
We propose INvariance of Noise (INN) space as a novel method for source localization of magnetoencephalography (MEG) data. The method is based on the fact that modulations of source strengths across time change the energy in signal subspace but leave the noise subspace invariant. We compare INN with classical MUSIC, RAP-MUSIC, and beamformer approaches using simulated data while varying signal-to-noise ratios as well as distance and temporal correlation between two sources. We also demonstrate the utility of INN with actual auditory evoked MEG responses in eight subjects. In all cases, INN performed well, especially when the sources were closely spaced, highly correlated, or one source was considerably stronger than the other.
MEG source localization using invariance of noise space.
Directory of Open Access Journals (Sweden)
Junpeng Zhang
Full Text Available We propose INvariance of Noise (INN space as a novel method for source localization of magnetoencephalography (MEG data. The method is based on the fact that modulations of source strengths across time change the energy in signal subspace but leave the noise subspace invariant. We compare INN with classical MUSIC, RAP-MUSIC, and beamformer approaches using simulated data while varying signal-to-noise ratios as well as distance and temporal correlation between two sources. We also demonstrate the utility of INN with actual auditory evoked MEG responses in eight subjects. In all cases, INN performed well, especially when the sources were closely spaced, highly correlated, or one source was considerably stronger than the other.