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A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
The determination of the pair potential $v({\bf r})$ that accurately yields an equilibrium state at positive temperature $T$ with a prescribed pair correlation function $g_2({\bf r})$ or corresponding structure factor $S({\bf k})$ in…
Classical (maximal) superintegrable systems in $n$ dimensions are Hamiltonian systems with $2n-1$ independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved…
Using the message-passing mechanism in machine learning (ML) instead of self-consistent iterations to directly build the mapping from structures to electronic Hamiltonian matrices will greatly improve the efficiency of density functional…
Realizing a controllable network with multiple degrees of interaction is a challenge to physics and engineering. Here, we experimentally report an on-chip reconfigurable network based on nanoelectromechanical resonators with…
We consider a coupled mode system where the effective propagation constants of localized modes are amenable to modulation. Starting from an unmodulated system where power transfer is heavily suppressed, we demonstrate that small, periodic…
There is a fundamental relationship between belief propagation and maximum a posteriori decoding. A decoding algorithm, which we call the Maxwell decoder, is introduced and provides a constructive description of this relationship. Both, the…
Exact diagonalisations of the extended Hubbard model are performed. In the insulating regime it is shown that the nearest neighbour copper-oxygen repulsion, $V$, leads to Frenkel excitons in the charge transfer gap at values of $V$ of the…
The paper presents a systematic study and implementation of a reconfigurable combinatorial multi-operand adder for use in Deep Learning systems. The size of carry changes with the number of operands and hence a reliable algorithm to…
The bilayer Hubbard model with an intra-layer hopping $t$ and an inter-layer hopping $t_\perp$ provides an interesting testing ground for several aspects of what has been called unconventional superconductivity. One can study the type of…
We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical…
Given a $\mathcal{C}^\infty$ expanding map $T$ of the circle, we construct a Hilbert space $\mathcal{H}$ of smooth functions on which the transfer operator $\mathcal{L}$ associated to $T$ acts as a compact operator. This result is made…
Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing…
We establish the characterizations of commutators of several versions of maximal functions on spaces of homogeneous type. In addition, with the aid of interpolation theory, we provide weighted version of the commutator theorems by…
A recent analysis of optical conductivity data which has provided strong evidence for coupling of the charge carriers to the 41 meV spin resonance, seen in the superconducting state of optimally doped Y123, is extended to other systems. We…
We show that every additive category with kernels and cokernels admits a maximal exact structure. Moreover, we discuss two examples of categories of the latter type arising from functional analysis.
We discuss a class of transfer matrix built by a particular combination of isomorphic and non-isomorphic GL(N) invariant vertex operators. We construct a conformally invariant magnet constituted of an alternating mixture of GL(N) ``spins''…
We present a general (i.e., independent of the underlying model) interpolation technique based on optimal transportation of Gaussian models for parametric advection-dominated problems. The approach relies on a scalar testing function to…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
The Balanced-Pairwise-Affinities (BPA) feature transform is designed to upgrade the features of a set of input items to facilitate downstream matching or grouping related tasks. The transformed set encodes a rich representation of high…