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We propose a deep learning framework for modeling complex high-dimensional densities called Non-linear Independent Component Estimation (NICE). It is based on the idea that a good representation is one in which the data has a distribution…

In this work we develop a discrete trace theory that spans non-conforming hybrid discretization methods and holds on polytopal meshes. A notion of a discrete trace seminorm is defined, and trace and lifting results with respect to a…

An $N$-tiling of triangle $ABC$ by triangle $T$ (the `tile') is a way of writing $ABC$ as a union of $N$ copies of $T$ overlapping only at their boundaries. Let the tile $T$ have angles $(\alpha,\beta,\gamma)$, and sides $(a,b,c)$. This…

This paper introduces PyDCI, a new implementation of Distributional Correspondence Indexing (DCI) written in Python. DCI is a transfer learning method for cross-domain and cross-lingual text classification for which we had provided an…

This paper presents a probabilistic approach for DNA sequence analysis. A DNA sequence consists of an arrangement of the four nucleotides A, C, T and G and different representation schemes are presented according to a probability measure…

Using the slow triangle map (a type of multi-dimensional continued fraction algorithm), we exhibit a method for generating any number of new identities for subsets of integer partitions.

Choice correspondences are crucial in decision-making, especially when faced with indifferences or ties. While tie-breaking can transform a choice correspondence into a choice function, it often introduces inefficiencies. This paper…

The combination of nondeterminism and probability in concurrent systems lead to the development of several interpretations of process behavior. If we restrict our attention to linear properties only, we can identify three main approaches to…

Two of the most studied extensions of trace and testing equivalences to nondeterministic and probabilistic processes induce distinctions that have been questioned and lack properties that are desirable. Probabilistic trace-distribution…

In this paper is proposed the method of the identification of complex dynamic systems. Method can be used for the identification of linear and nonlinear complex dynamic systems for the determined or stochastic signals at the inputs and the…

We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies in its use of Picard iteration to reformulate the typically…

Nonlinear system identification often involves a fundamental trade-off between interpretability and flexibility, often requiring the incorporation of physical constraints. We propose a unified data-driven framework that combines the…

This paper discusses a practical approach that combines synthetic control with triple difference to address violations of the parallel trends assumption. By transforming triple difference into a DID structure, we can apply synthetic control…

For nearly a century, mathematicians have been developing techniques for constructing abelian automorphism groups of combinatorial objects, and, conversely, constructing combinatorial objects from abelian groups. While abelian groups are a…

Our focus is upon {\it irreducible} nonnegative $n$-by-$n$ matrix realizations of nonnegatively realizable spectra or, equivalently, characteristic polynomials. After giving some general background, we make some useful new observations and…

Authentication is a process by which an entity,which could be a person or intended computer,establishes its identity to another entity.In private and public computer networks including the Internet,authentication is commonly done through…

This paper proposes that common measures for network transitivity, based on the enumeration of transitive triples, do not reflect the theoretical statements about transitivity they aim to describe. These statements are often formulated as…

There exists an apparent negative correlation between performance and interpretability of deep learning models. In an effort to reduce this negative correlation, we propose a Born Identity Network (BIN), which is a post-hoc approach for…

Using techniques from calculus, we combine classical identities for $\pi$, $\operatorname{ln}2$, and harmonic numbers, to arrive at a nice infinite series formula for $\pi/3$ that does not appear to be well known. In addition, we give…

In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…