Related papers: On the computation of the M{\"o}bius transform
Deep learning is computationally intensive, with significant efforts focused on reducing arithmetic complexity, particularly regarding energy consumption dominated by data movement. While existing literature emphasizes inference, training…
Recently, a general tool called a holographic transformation, which transforms an expression of the partition function to another form, has been used for polynomial-time algorithms and for improvement and understanding of the belief…
In this paper, we will study the M\"obius polynomial, an invariant of ranked posets that arises in the study of splitting algebras. We will present a formula for the M\"obius polynomial of the direct product of posets in terms of the…
The purpose of this paper is to give some explicit formulas involving M\"obius functions, which may be known under the generalized Riemann Hypothesis, but unconditional in this paper. Concretely, we prove explicit formulas of partial sums…
This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a…
The relationship between quantum physics and discrete mathematics is reviewed in this article. The Boolean functions unitary representation is considered. The relationship between Zhegalkin polynomial, which defines the algebraic normal…
Given an orthogonal polynomial sequence on the real line, another sequence of polynomials can be found by composing these polynomials with a general M\"obius transformation. In this work, we study the properties of such M\"obius-transformed…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
We use M\"obius inversion and the Bernoulli polynomials to prove inequalities between the logarithmic summatory function of the M\"obius function and weighted averages of its ordinary summatory function.
Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…
Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a…
We develop a new way of writing the Lame Hamiltonian in Lie-algebraic form. This yields, in a natural way, an explicit formula for both the Lame polynomials and the classical non-meromorphic Lame functions in terms of Chebyshev polynomials…
We review results of papers written on the topic of polynomial amoebas with an emphasis on computational aspects of the topic. The polynomial amoebas have a lot of applications in various domains of science. Computation of the amoeba for a…
This paper introduces a novel regression model designed for angular response variables with linear predictors, utilizing a generalized M\"{o}bius transformation to define the regression curve. By mapping the real axis to the circle, the…
There are no two identical leaves in the world, so how to find effective markers or features to distinguish them is an important issue. Function transformation, such as f(x,y) and f(x,y,z), can transform two, three, or multiple…
Mapping functions on bits to Hamiltonians acting on qubits has many applications in quantum computing. In particular, Hamiltonians representing Boolean functions are required for applications of quantum annealing or the quantum approximate…
One of the major issues of cryptography is the cryptanalysis of cipher algorithms. Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required.…
This article is a survey on the topic of polynomial amoebas. We review results of papers written on the topic with an emphasis on its computational aspects. Polynomial amoebas have numerous applications in various domains of mathematics and…
We present a new computationally efficient method for multi-beamforming in the broadband setting. Our "fast beamspace transformation" forms $B$ beams from $M$ sensor outputs using a number of operations per sample that scales linearly (to…
A polynomial transformation of the real plane $\Bbb R^2$ is a mapping $\Bbb R^2\to\Bbb R^2$ given by two polynomials of two variables. Such a transformation is called cubic if the degrees of its polynomials are not greater than three. In…