Nonlinearity, ISSN 0951-7715, 03/2016, Volume 29, Issue 5, pp. 1507 - 1536

.... We prove the uniqueness and non-degeneracy of minimizers in a weakly anisotropic medium. In addition, for a wide range of anisotropic media, we derive the symmetry...

Choquard-Pekar | linearized operator | polaron | non-degeneracy | EXISTENCE | MATHEMATICS, APPLIED | STATES | SYMMETRY | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | PHYSICS, MATHEMATICAL | Kernels | Operators | Anisotropy | Mathematical analysis | Uniqueness | Translations | Symmetry | Polarons | Mathematical Physics | Analysis of PDEs | Mathematics

Choquard-Pekar | linearized operator | polaron | non-degeneracy | EXISTENCE | MATHEMATICS, APPLIED | STATES | SYMMETRY | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | PHYSICS, MATHEMATICAL | Kernels | Operators | Anisotropy | Mathematical analysis | Uniqueness | Translations | Symmetry | Polarons | Mathematical Physics | Analysis of PDEs | Mathematics

Journal Article

ACM Transactions on Algorithms (TALG), ISSN 1549-6325, 12/2012, Volume 9, Issue 1, pp. 1 - 23

...Polynomial Kernels for Dominating Set in Graphs of Bounded Degeneracy and Beyond GEEVARGHESE PHILIP and VENKATESH RAMAN, The Institute of Mathematical Sciences...

Degenerate graphs | dominating set | fixed parameter tractability | kernelization | PARAMETERIZED ALGORITHMS | MATHEMATICS, APPLIED | Theory | GENUS | SIZE | EXPONENTIAL SPEED-UP | Algorithms | TIME ALGORITHMS | COMPUTER SCIENCE, THEORY & METHODS | FPT ALGORITHMS | Integers | Kernels | Graphs | Construction | Polynomials

Degenerate graphs | dominating set | fixed parameter tractability | kernelization | PARAMETERIZED ALGORITHMS | MATHEMATICS, APPLIED | Theory | GENUS | SIZE | EXPONENTIAL SPEED-UP | Algorithms | TIME ALGORITHMS | COMPUTER SCIENCE, THEORY & METHODS | FPT ALGORITHMS | Integers | Kernels | Graphs | Construction | Polynomials

Journal Article

Memoirs of the American Mathematical Society, ISSN 0065-9266, 05/2012, Volume 217, Issue 1019, pp. 1 - 90

This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve...

Kernels | Degenerate elliptic | Spectral values | CR equations | Asymptotic behavior | Semilinear | Vector fields | Normalization | Fundamental matrix | fundamental matrix | semilinear | vector fields | VECTOR-FIELDS | CAUCHY-RIEMANN SYSTEM | MATHEMATICS | spectral values | asymptotic behavior | degenerate elliptic | normalization | SINGULARITY | kernels

Kernels | Degenerate elliptic | Spectral values | CR equations | Asymptotic behavior | Semilinear | Vector fields | Normalization | Fundamental matrix | fundamental matrix | semilinear | vector fields | VECTOR-FIELDS | CAUCHY-RIEMANN SYSTEM | MATHEMATICS | spectral values | asymptotic behavior | degenerate elliptic | normalization | SINGULARITY | kernels

Journal Article

Journal of Econometrics, ISSN 0304-4076, 01/2017, Volume 196, Issue 1, pp. 180 - 195

.... The reason for this breakdown is a kernel-induced degeneracy in the weighted signal matrix associated with the nonstationary regressors, a new phenomenon in the kernel regression literature...

Kernel degeneracy | Super-consistency | Endogeneity | Cointegration | Time varying coefficients | Nonparametric regression | REGRESSION | ASYMPTOTIC THEORY | INTEGRATED TIME-SERIES | STATISTICAL-INFERENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | VARYING COEFFICIENT MODELS | SYSTEMS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | Studies | Nonlinear equations | Estimating techniques | Cointegration analysis | Approximations

Kernel degeneracy | Super-consistency | Endogeneity | Cointegration | Time varying coefficients | Nonparametric regression | REGRESSION | ASYMPTOTIC THEORY | INTEGRATED TIME-SERIES | STATISTICAL-INFERENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | VARYING COEFFICIENT MODELS | SYSTEMS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | Studies | Nonlinear equations | Estimating techniques | Cointegration analysis | Approximations

Journal Article

Journal of Statistical Planning and Inference, ISSN 0378-3758, 03/2016, Volume 170, pp. 117 - 128

We study pathwise invariances and degeneracies of random fields with motivating applications in Gaussian process modelling...

Structural priors | RKHS | Covariance kernels | Linear operators | RATES | STATISTICS & PROBABILITY | KERNELS | Models | Gaussian processes | Modeling and Simulation | Computer Science

Structural priors | RKHS | Covariance kernels | Linear operators | RATES | STATISTICS & PROBABILITY | KERNELS | Models | Gaussian processes | Modeling and Simulation | Computer Science

Journal Article

Journal of Econometrics, ISSN 0304-4076, 04/2020, Volume 215, Issue 2, pp. 607 - 632

... and deterministic trends, complications which result in asymptotic degeneracy of the kernel-weighted signal matrix...

FM-kernel estimation | Generalized Wald test | Super-consistency | Cointegration | Local rotation | Time-varying coefficients | Kernel degeneracy | Global rotation | STATISTICAL-INFERENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | SERIES MODELS | Monte Carlo method | Analysis | Interest rates

FM-kernel estimation | Generalized Wald test | Super-consistency | Cointegration | Local rotation | Time-varying coefficients | Kernel degeneracy | Global rotation | STATISTICAL-INFERENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | SERIES MODELS | Monte Carlo method | Analysis | Interest rates

Journal Article

Physical Review D (Particles, Fields, Gravitation and Cosmology), ISSN 1550-7998, 04/2015, Volume 91, Issue 8

.... We take advantage of this to explore the degeneracies between gravitational parameters in weak lensing observations.

Kernels | Gravitation | Separation | Integrals | Relativity | Cosmology | Convergence

Kernels | Gravitation | Separation | Integrals | Relativity | Cosmology | Convergence

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 10/2008, Volume 56, Issue 10, pp. 5001 - 5012

Risk-sensitive filters (RSF) put a penalty to higher-order moments of the estimation error compared to conventional filters as the Kalman filter minimizing the...

Estimation error | sample degeneracy | Delay estimation | particle filter | Monte Carlo methods | Depletion | sample impoverishment | risk sensitive | Mean square error methods | Computer applications | Signal processing | Sampling methods | Particle filters | Kernel | Nonlinear systems | Risk sensitive | Sample impoverishment | Sample degeneracy | Particle filter | depletion | ENGINEERING, ELECTRICAL & ELECTRONIC | Kalman filtering | Research | Chaos theory | Analysis | Studies | Mean square errors | Errors | Mean square values | Approximation | Simulation | Mathematical analysis | Roughening | Risk | Dynamical systems

Estimation error | sample degeneracy | Delay estimation | particle filter | Monte Carlo methods | Depletion | sample impoverishment | risk sensitive | Mean square error methods | Computer applications | Signal processing | Sampling methods | Particle filters | Kernel | Nonlinear systems | Risk sensitive | Sample impoverishment | Sample degeneracy | Particle filter | depletion | ENGINEERING, ELECTRICAL & ELECTRONIC | Kalman filtering | Research | Chaos theory | Analysis | Studies | Mean square errors | Errors | Mean square values | Approximation | Simulation | Mathematical analysis | Roughening | Risk | Dynamical systems

Journal Article

Methodology and Computing in Applied Probability, ISSN 1387-5841, 12/2008, Volume 10, Issue 4, pp. 471 - 505

Although importance sampling is an established and effective sampling and estimation technique, it becomes unstable and unreliable for high-dimensional...

Exact sampling | Economics general | Combinatorial counting | Statistics, general | 65C60 | Statistics | Rare-event probability estimation | Electronic and Computer Engineering | 65C40 | Life Sciences, general | Likelihood ratio degeneracy | Business/Management Science, general | 65C05 | Kernel density estimation | 68Q32 | Importance sampling | kernel density estimation | rare-event probability estimation | STATISTICS & PROBABILITY | exact sampling | CROSS-ENTROPY METHOD | importance sampling | likelihood ratio degeneracy | combinatorial counting | Markov processes | Monte Carlo method | Usage | Algorithms | Mathematical optimization | Studies | Efficiency | Probability | Estimating techniques | Sampling | Combinatorics | Monte Carlo methods | Asymptotic properties | Likelihood ratio | Mathematical models | Combinatorial analysis | Counting | Optimization

Exact sampling | Economics general | Combinatorial counting | Statistics, general | 65C60 | Statistics | Rare-event probability estimation | Electronic and Computer Engineering | 65C40 | Life Sciences, general | Likelihood ratio degeneracy | Business/Management Science, general | 65C05 | Kernel density estimation | 68Q32 | Importance sampling | kernel density estimation | rare-event probability estimation | STATISTICS & PROBABILITY | exact sampling | CROSS-ENTROPY METHOD | importance sampling | likelihood ratio degeneracy | combinatorial counting | Markov processes | Monte Carlo method | Usage | Algorithms | Mathematical optimization | Studies | Efficiency | Probability | Estimating techniques | Sampling | Combinatorics | Monte Carlo methods | Asymptotic properties | Likelihood ratio | Mathematical models | Combinatorial analysis | Counting | Optimization

Journal Article

Applied Numerical Mathematics, ISSN 0168-9274, 2009, Volume 59, Issue 3, pp. 656 - 670

The method of normal spline-collocation (NSC), applicable to a wide class of ordinary linear singular differential and integral equations, is specified for the...

Reproducing kernel | Hilbertâ€“Sobolev space | Equations on the semi-axis | Differential-algebraic equations | Variable degeneracy | Normal splines | Hilbert-Sobolev space | MATHEMATICS, APPLIED | PARAMETERIZATION METHOD | Methods | Algorithms

Reproducing kernel | Hilbertâ€“Sobolev space | Equations on the semi-axis | Differential-algebraic equations | Variable degeneracy | Normal splines | Hilbert-Sobolev space | MATHEMATICS, APPLIED | PARAMETERIZATION METHOD | Methods | Algorithms

Journal Article

2009, ISBN 0521791928, xiii, 349

Machine learning methods originated from artificial intelligence and are now used in various fields in environmental sciences today. This is the first...

Kernel functions | Environmental sciences | Neural networks (Computer science) | Machine learning

Kernel functions | Environmental sciences | Neural networks (Computer science) | Machine learning

Book

Journal of High Energy Physics, ISSN 1126-6708, 1/2014, Volume 2014, Issue 1, pp. 1 - 35

In this paper quantum effects are investigated in a very special two-scalar field model having a moduli space of BPS topological defects. In a (1 +...

Renormalization Regularization and Renormalons | Solitons Monopoles and Instantons | Field Theories in Lower Dimensions | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | ENERGY | VORTICES | FIELD-THEORY | STABILITY | CENTRAL CHARGE | MODELS | MASS | ONE-LOOP CORRECTIONS | KINKS | REGULARIZATION | PHYSICS, PARTICLES & FIELDS | Kernels | Operators | Fluctuation | Domain walls | Surface tension | Mathematical models | Spectra | Defects | Physics - High Energy Physics - Theory | NATURAL SCIENCES::Physics [Research Subject Categories] | Nuclear and High Energy Physics | Renormalization Regularization | High Energy Physics - Theory | Renormalons

Renormalization Regularization and Renormalons | Solitons Monopoles and Instantons | Field Theories in Lower Dimensions | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | ENERGY | VORTICES | FIELD-THEORY | STABILITY | CENTRAL CHARGE | MODELS | MASS | ONE-LOOP CORRECTIONS | KINKS | REGULARIZATION | PHYSICS, PARTICLES & FIELDS | Kernels | Operators | Fluctuation | Domain walls | Surface tension | Mathematical models | Spectra | Defects | Physics - High Energy Physics - Theory | NATURAL SCIENCES::Physics [Research Subject Categories] | Nuclear and High Energy Physics | Renormalization Regularization | High Energy Physics - Theory | Renormalons

Journal Article

Theoretical computer science, ISSN 0304-3975, 2011, Volume 412, Issue 41, pp. 5744 - 5751

.... The second parameterization is W[1]-complete, but the introduction of an additional parameter, the degeneracy of the hypergraph H = ( V , F...

Hypergraph | Hitting set | Parameterized problems | Fixed-parameter tractable | Kernel | COMPUTER SCIENCE, THEORY & METHODS | SMALL TRANSVERSALS | Integers | Kernels | Parametrization | Upper bounds | Collection | Grounds | Graphs | Graph theory

Hypergraph | Hitting set | Parameterized problems | Fixed-parameter tractable | Kernel | COMPUTER SCIENCE, THEORY & METHODS | SMALL TRANSVERSALS | Integers | Kernels | Parametrization | Upper bounds | Collection | Grounds | Graphs | Graph theory

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 11/2014, Volume 461, pp. 271 - 317

.... We address two problems. 1Â° In the presence of degeneracy, it is not possible to reproduce function values as inner products with a kernel function in the usual way...

Reproducing kernel | Degenerate inner product | Indefinite inner product | Completion | Almost Pontryagin space | MATHEMATICS | MATHEMATICS, APPLIED | DIRICHLET SPACE | KREIN SPACES | OPERATORS

Reproducing kernel | Degenerate inner product | Indefinite inner product | Completion | Almost Pontryagin space | MATHEMATICS | MATHEMATICS, APPLIED | DIRICHLET SPACE | KREIN SPACES | OPERATORS

Journal Article

15.
Full Text
Concentrated solution for some non-local and non-variational singularly perturbed problems

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 10/2019, Volume 58, Issue 5, pp. 1 - 31

In the present paper, we prove the existence of concentrated solution for the following non-local and non-variational singularly perturbed problem,...

58C15 | 47H11 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 35B40 | 34E15 | SEMICLASSICAL BOUND-STATES | BREZIS-NIRENBERG PROBLEM | FRACTIONAL LAPLACIAN | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | KIRCHHOFF-TYPE EQUATIONS | NONLINEAR SCHRODINGER-EQUATIONS | SOLITARY WAVES | POSITIVE SOLUTIONS | ELLIPTIC EQUATION | GROUND-STATES

58C15 | 47H11 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 35B40 | 34E15 | SEMICLASSICAL BOUND-STATES | BREZIS-NIRENBERG PROBLEM | FRACTIONAL LAPLACIAN | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | KIRCHHOFF-TYPE EQUATIONS | NONLINEAR SCHRODINGER-EQUATIONS | SOLITARY WAVES | POSITIVE SOLUTIONS | ELLIPTIC EQUATION | GROUND-STATES

Journal Article

Europhysics letters, ISSN 1286-4854, 2015, Volume 112, Issue 6, pp. 60001 - 60001

The ground-state properties of N spinless free fermions in a d-dimensional confining potential are studied. We find that any n-point correlation function has a...

DISTRIBUTIONS | DENSITY | MATRIX | PHYSICS, MULTIDISCIPLINARY | EDGE | Kernels | Correlation | Fermions | Mathematical analysis | Mathematical models | Matrix theory | Confining | Density | Mathematical Physics | Physics

DISTRIBUTIONS | DENSITY | MATRIX | PHYSICS, MULTIDISCIPLINARY | EDGE | Kernels | Correlation | Fermions | Mathematical analysis | Mathematical models | Matrix theory | Confining | Density | Mathematical Physics | Physics

Journal Article

IEEE transactions on signal processing, ISSN 1941-0476, 2019, Volume 67, Issue 9, pp. 2499 - 2512

.... One of the most effective non-linear filtering approaches, particle filtering, suffers from weight degeneracy in high-dimensional filtering scenarios...

Monte Carlo methods | Hidden Markov models | Signal processing algorithms | Markov chain Monte Carlo | high-dimensional filtering | Markov processes | Approximation algorithms | state-space model | Proposals | particle flow | Kernel | Gaussian mixture model | LANGEVIN | FILTERS | ENGINEERING, ELECTRICAL & ELECTRONIC | Kernels | Monte Carlo method | Algorithms | Filtration | Computer simulation | Signal processing | Markov chains | Markov analysis | State estimation | Monte Carlo simulation | Weight

Monte Carlo methods | Hidden Markov models | Signal processing algorithms | Markov chain Monte Carlo | high-dimensional filtering | Markov processes | Approximation algorithms | state-space model | Proposals | particle flow | Kernel | Gaussian mixture model | LANGEVIN | FILTERS | ENGINEERING, ELECTRICAL & ELECTRONIC | Kernels | Monte Carlo method | Algorithms | Filtration | Computer simulation | Signal processing | Markov chains | Markov analysis | State estimation | Monte Carlo simulation | Weight

Journal Article

Sensors (Basel, Switzerland), ISSN 1424-8220, 05/2019, Volume 19, Issue 10, p. 2290

Under realistic environmental conditions, heuristic-based data association and map management routines often result in divergent map and trajectory estimates...

Electrical engineering | Routines | Automation | Tracking | Random sampling | Computer simulation | Heuristic methods | Mapping | Associations | Ground truth | Noise control | Robotics | Vehicles | Kernels | Multiple target tracking | Algorithms | Data sets | Parallel processing | International conferences | Sensors | Localization | Trajectory analysis | Kalman filters | Robots | robotics | SLAM | random finite sets | tracking

Electrical engineering | Routines | Automation | Tracking | Random sampling | Computer simulation | Heuristic methods | Mapping | Associations | Ground truth | Noise control | Robotics | Vehicles | Kernels | Multiple target tracking | Algorithms | Data sets | Parallel processing | International conferences | Sensors | Localization | Trajectory analysis | Kalman filters | Robots | robotics | SLAM | random finite sets | tracking

Journal Article

The journal of high energy physics, ISSN 1029-8479, 2018, Volume 2018, Issue 11, pp. 1 - 62

In this note we consider the problem of extracting the corrections to CFT data induced by the exchange of a primary operator and its descendents in the crossed...

Conformal Field Theory | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | 1/N Expansion | Elementary Particles, Quantum Field Theory | Higher Spin Symmetry | COEFFICIENTS | SIGMA-MODEL | PHYSICS, PARTICLES & FIELDS | Kernels | Operators (mathematics) | Polynomials | Mathematical analysis | Integrals | Physics - High Energy Physics - Theory

Conformal Field Theory | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | 1/N Expansion | Elementary Particles, Quantum Field Theory | Higher Spin Symmetry | COEFFICIENTS | SIGMA-MODEL | PHYSICS, PARTICLES & FIELDS | Kernels | Operators (mathematics) | Polynomials | Mathematical analysis | Integrals | Physics - High Energy Physics - Theory

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2017, Volume 369, Issue 9, pp. 6263 - 6278

Brownian motion by a random walk in the setting of a sub-Riemannian manifold M. To construct such a random walk we first address several issues related to the degeneracy of such a...

Brownian motion | Hypoelliptic operator | Sub-Riemannian manifold | Random walk | hypoelliptic operator | MATHEMATICS | random walk | HEISENBERG-GROUP | INEQUALITIES | sub-Riemannian manifold | HEAT KERNEL

Brownian motion | Hypoelliptic operator | Sub-Riemannian manifold | Random walk | hypoelliptic operator | MATHEMATICS | random walk | HEISENBERG-GROUP | INEQUALITIES | sub-Riemannian manifold | HEAT KERNEL

Journal Article