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We present a new framework for the analysis and design of randomized algorithms for solving various types of linear systems, including consistent or inconsistent, full rank or rank-deficient. Our method is formulated with four randomized…
We improve recently introduced consensus-based optimization method, proposed in [R. Pinnau, C. Totzeck, O. Tse and S. Martin, Math. Models Methods Appl. Sci., 27(01):183--204, 2017], which is a gradient-free optimization method for general…
The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth optimization problems. These algorithms are based on the theory and calculations of…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
Renormalization plays an important role in the theoretically and mathematically careful analysis of models in condensed-matter physics. I review selected results about correlated-fermion systems, ranging from mathematical theorems to…
Motivated by the supersymmetric version of Dirac's theory, chiral models in field theory, and the quest of a geometric fundament for the Standard Model, we describe an approach to the differential geometry of vector bundles on…
We show that a recently introduced generalized scheme of quantum mechanics has connections to Li\'{e}nard and Levinson-Smith classes of nonlinear systems. For the Li\'{e}nard type, which has coefficients of odd and odd symmetry, we…
Symmetry-resolved entanglement, capturing the refined structure of quantum entanglement in systems with global symmetries, has attracted a lot of attention recently. In this manuscript, introducing the notion of symmetry-resolved…
Continuing the analysis in a unified scheme for treating generalized superselection sectors based upon the notion of selection criteria for states of relevance in quantum physics, we extend the Doplicher-Roberts superselection theory for…
We consider classical and quantum one and two-dimensional systems with ladder operators that satisfy generalized Heisenberg algebras. In the classical case, this construction is related to the existence of closed trajectories. In…
The symmetry of the generalized Polychronakos-Frahm chain is obtained from the Dunkl-operator deformation of the unitary algebra, which describes the symmetry of the generalized Calogero model.
We find an analog of Zamolodchikov's c-theorem for disordered two dimensional noninteracting systems in their supersymmetric representation. For this purpose we introduce a new parameter b which flows along the renormalization group…
We consider a generalization of the classical Laplace operator, which includes the Laplace-Dunkl operator defined in terms of the differential-difference operators associated with finite reflection groups called Dunkl operators. For this…
A class of decoherence schemes is described for implementing the principles of generalized quantum theory in reparametrization-invariant `hyperbolic' models such as minisuperspace quantum cosmology. The connection with sum-over-histories…
Many efforts have been made to explore systems that show significant deviations from predictions related to the standard statistical mechanics. The present work introduces a unified formalism that connects divergences, generalized free…
The paper contains generalization of the renormgroup algorithm for boundary value problems of mathematical physics and related concept of the renormgroup symmetry, formulated earlier by authors with reference to models based on differential…
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
We introduce N=1 supersymmetric generalization of the mechanical system describing a particle with fractional spin in D=1+2 dimensions and being classically equivalent to the formulation based on the Dirac monopole two-form. The model…
In this paper, we present and analyse a class of "filtered" numerical schemes for second order Hamilton-Jacobi-Bellman equations. Our approach follows the ideas introduced in B.D. Froese and A.M. Oberman, Convergent filtered schemes for the…