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ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, ISSN 1292-8119, 03/2020, Volume 26, p. 26
A sequence of graphs with diverging number of nodes is a dense graph sequence if the number of edges grows approximately as for complete graphs... 
MATHEMATICS, APPLIED | CONTINUUM LIMITS | large graphs | Dense graph sequences | nonlocal variational problems | RELAXATION | bisection problem | CONVERGENT SEQUENCES | LOWER SEMICONTINUITY | Gamma-convergence | DISCRETE-SYSTEMS | Young measures | ENERGIES | AUTOMATION & CONTROL SYSTEMS
Journal Article
Information sciences, ISSN 0020-0255, 2019, Volume 490, pp. 59 - 73
Sequence-to-sequence (Seq2seq) models have played an important role in the recent success of various natural language processing methods, such as machine translation, text summarization, and speech recognition... 
Recurrent neural network | Auto-encoder | Document information vector | Variational method | Natural language processing | Sequence-to-sequence learning | Self attention mechanism | COMPUTER SCIENCE, INFORMATION SYSTEMS | Language processing | Computational linguistics | Neural networks | Analysis | Natural language interfaces
Journal Article
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 05/2016, Volume 12
This paper is a review containing new original results on the finite order variational sequence and its different representations with emphasis on applications in the theory of variational symmetries... 
Lagrangian formalism | Conservation law | Fibered manifold | Jet space | Variational derivative | Cohomology | Variational sequence | Symmetry | variational derivative | CONTACT SYMMETRIES | cohomology | CALCULUS | LEPAGE FORMS | PHYSICS, MATHEMATICAL | C-SPECTRAL SEQUENCE | LAGRANGIAN-FORMALISM | symmetry | fibered manifold | conservation law | variational sequence | CONSERVATION-LAWS | jet space
Journal Article
eLife, ISSN 2050-084X, 2019, Volume 8
Probabilistic models of adaptive immune repertoire sequence distributions can be used to infer the expansion of immune cells in response to stimulus, differentiate genetic from environmental factors... 
BIOLOGY | Adaptive Immunity | Genetic Variation | Models, Genetic | Recombination, Genetic | Receptors, Antigen, T-Cell, alpha-beta - genetics | Humans | Cell culture | Antigens | Vaccination | V(D)J recombination | Probability | T cell receptors | Lymphocytes T | Environmental factors | Cell differentiation | T-cell receptor | Proteins | Neural networks | Lymphocytes
Journal Article
Expositiones mathematicae, ISSN 0723-0869, 2014, Volume 32, Issue 3, pp. 284 - 295
Taking advantage of a recent critical point theorem, the existence of infinitely many solutions for an anisotropic problem with a parameter is established.... 
Infinitely many solutions | Anisotropic difference equations | Variational methods | Discrete nonlinear boundary value problems | MATHEMATICS
Journal Article
Optik, ISSN 0030-4026, 10/2016, Volume 127, Issue 20, pp. 8710 - 8727
In this paper, a fractional order variational model for estimating the optical flow is presented. In particular, the proposed model generalizes the integer... 
Partial differential equations | Variational methods | Image sequence | Optical flow | Fractional derivative | DENSE | FIELDS | DISPLACEMENT | COMPUTATION | OPTICS | Models | Algorithms | Analysis | Differential equations
Journal Article
Mathematical Communications, ISSN 1331-0623, 2019, Volume 24, Issue 1, pp. 39 - 59
In this paper we obtain a priori estimates for finite-energy sequences of Muller's functional I-alpha(epsilon)(v) = integral(1 )(0)(epsilon(2)v ''(2 )(S) +W- (v'(s)) + a(s)v(2... 
Gamma convergence | Modica-mortola functional | Asymptotic analysis | Young measures | Singular perturbation | MATHEMATICS, APPLIED | singular perturbation | PHASE-TRANSITIONS | asymptotic analysis | RELAXATION | TERM | MATHEMATICS | Modica-Mortola functional | VARIATIONAL-PROBLEMS | GRADIENT THEORY | CRITERION
Journal Article
Journal of Mathematical Sciences (United States), ISSN 1072-3374, 11/2018, Volume 235, Issue 2, pp. 199 - 207
We establish a connection between the limit characteristics of minimizing sequences of the energy functional of a two-phase elastic medium and the derivative... 
ELASTICITY | TEMPERATURE DEPENDENCE | MATHEMATICAL METHODS AND COMPUTING | VARIATIONAL METHODS | EQUILIBRIUM
Journal Article
Electronic Journal of Qualitative Theory of Differential Equations, ISSN 1417-3875, 2015, Volume 2015, Issue 25, pp. 1 - 10
Journal Article
International journal of computer vision, ISSN 1573-1405, 2013, Volume 105, Issue 3, pp. 269 - 297
Journal Article
Advances in Difference Equations, ISSN 1687-1839, 12/2016, Volume 2016, Issue 1, pp. 1 - 11
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2010, Volume 2010, Issue 1, pp. 1 - 16
The purpose of this paper is to consider the weak convergence of an iterative sequence for finding a common element in the set of solutions of generalized equilibrium problems, in the set of solutions... 
Mathematics, general | Mathematics | Applications of Mathematics | Analysis | MATHEMATICS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | THEOREMS | WEAK-CONVERGENCE | EXTRAGRADIENT METHOD | VARIATIONAL INEQUALITY | Studies | Problems | Hilbert space | Mathematical analysis | Convergence
Journal Article