相关论文: Standard Lattices of Compatibly Embedded Finite Fi…
Finite automata are used to encode geometric figures, functions and can be used for image compression and processing. The original approach is to represent each point of a figure in $\mathbb{R}^n$ as a convolution of its $n$ coordinates…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
Lattice structures have been widely used in various applications of additive manufacturing due to its superior physical properties. If modeled by triangular meshes, a lattice structure with huge number of struts would consume massive…
We propose a general framework to study constructions of Euclidean lattices from linear codes over finite fields. In particular, we prove general conditions for an ensemble constructed using linear codes to contain dense lattices (i.e.,…
We set up a strategy for studying large families of logarithmic conformal field theories by using the enlarged symmetries and non--semi-simple associative algebras appearing in their lattice regularizations (as discussed in a companion…
We introduce Fermi Sets, a universal and physically interpretable neural architecture for fermionic many-body wavefunctions. Building on a ``parity-graded'' representation [1], we prove that any continuous fermionic wavefunction on a…
Deep learning methods have been shown to be effective in representing ground-state wave functions of quantum many-body systems. Existing methods use convolutional neural networks (CNNs) for square lattices due to their image-like…
Large semantic knowledge bases are grounded in factual knowledge. However, recent approaches to dense text representations (i.e. embeddings) do not efficiently exploit these resources. Dense and robust representations of documents are…
In the last few years there have been rapid developments in SMT solving for finite fields. These include new decision procedures, new implementations of SMT theory solvers, and new software verifiers that rely on SMT solving for finite…
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous…
Slim semimodular lattices (for short, SPS lattices) and slim rectangular lattices (for short, SR lattices) were introduced by G. Gr\"atzer and E. Knapp in 2007 and 2009. These lattices are necessarily finite and planar, and they have been…
It is shown that, given any finite dimensional, split basic algebra $\Lambda = K\Gamma/I$ (where $\Gamma$ is a quiver and $I$ an admissible ideal in the path algebra $K \Gamma$), there is a finite list of affine algebraic varieties, the…
We consider all compatible topologies of an arbitrary finite-dimensional vector space over a non-trivial valuation field whose metric completion is a locally compact space. We construct the canonical lattice isomorphism between the lattice…
Our goal is to develop a more general scheme for constructing integrable lattice regularisations of integrable quantum field theories. Considering the affine Toda theories as examples, we show how to construct such lattice regularisations…
We consider complete lattices equipped with preorderings indexed by the ordinals less than a given (limit) ordinal subject to certain axioms. These structures, called stratified complete lattices, and weakly monotone functions over them,…
Deep neural networks (DNNs) have been deployed in myriad machine learning applications. However, advances in their accuracy are often achieved with increasingly complex and deep network architectures. These large, deep models are often…
An embedding is a function that maps entities from one algebraic structure into another while preserving certain characteristics. Embeddings are being used successfully for mapping relational data or text into vector spaces where they can…
Let K be a number field, let A be a finite dimensional semisimple K-algebra and let Lambda be an O_K-order in A. It was shown in previous work that, under certain hypotheses on A, there exists an algorithm that for a given (left)…
Logarithmic Conformal Field Theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self avoiding walks, etc.), or of critical points in several classes of disordered systems…
Ellipsoids are a common representation for reachability analysis, because they can be transformed efficiently under affine maps, and allow conservative approximation of Minkowski sums, which let one incorporate uncertainty and linearization…