Related papers: A Note on Kaldi's PLDA Implementation
In this short note, we provide an elementary complex analytic method for converting known real integrals into numerous strange and interesting looking real integrals.
The Palatini formulation has been successful in the development of several alternative theories of gravity. It is well understood that the Palatini and metric formulations are equivalent in minimally coupled scalar-tensor models, but…
Neural networks are increasingly being used to solve partial differential equations (PDEs), replacing slower numerical solvers. However, a critical issue is that neural PDE solvers require high-quality ground truth data, which usually must…
Spreadsheets provide a flexible and easy to use software development environment, but that leads to error proneness. Work has been done to prevent errors in spreadsheets, including using models to specify distinct parts of a spreadsheet as…
The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…
Kleene algebra (KA) is an important tool for reasoning about general program equivalences, with a decidable and complete equational theory. However, KA cannot always prove equivalences between specific programs. For this purpose, one adds…
A new method for continuing the usual Dirichlet series that defines the Riemann zeta function ${\zeta}(s)$ is presented. Numerical experiments demonstrating the computational efficacy of the resulting continuation are discussed.
Many training data attribution (TDA) methods aim to estimate how a model's behavior would change if one or more data points were removed from the training set. Methods based on implicit differentiation, such as influence functions, can be…
The aim of this paper is to present a self contained introduction to the Hubbard model and some of its applications.The paper consists of two parts: the first will introduce the basic notions of the Hubbard model starting from the…
This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more…
We propose an implementation of lambda+, a recently introduced simply typed lambda-calculus with pairs where isomorphic types are made equal. The rewrite system of lambda+ is a rewrite system modulo an equivalence relation, which makes its…
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
In the paper we describe derivations of some classes of Leibniz algebras. It is shown that any derivation of a simple Leibniz algebra can be written as a combination of three derivations. Two of these ingredients are a Lie algebra…
We present some lambda calculus with explicit substitutions and named variables. The characteristic feature of this calculus is as follows: renaming of bound variables when performing substitutions is done using special reductions and may…
Probabilistic linear discriminant analysis (PLDA) is commonly used in speaker verification systems to score the similarity of speaker embeddings. Recent studies improved the performance of PLDA in domain-matched conditions by diagonalizing…
The ideas here are a continuation of a previous article. Some of the applications of the main ideas in the previous article are explained, along with some limitations of the general ideas. There are situations where additional hypotheses…
Advancements in mathematical programming have made it possible to efficiently tackle large-scale real-world problems that were deemed intractable just a few decades ago. However, provably optimal solutions may not be accepted due to the…
In this paper, we derive the quadratic formula as a consequence of constructively proving the existence of standard and factored forms for general form real quadratic functions. Emphasis is put on connections to graphing of corresponding…
Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can exhibit. Inspired by the concept of differential flatness of nonlinear continuous systems and their inherent invertibility property, the…
Making use of inverse Mellin transform techniques for analytical continuation, an elegant proof and an extension of the zeta function regularization theorem is obtained. No series commutations are involved in the procedure; nevertheless the…