Related papers: Semantics of Division for Polynomial Solvers
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
Call a semantics for a language with variables absolute when variables map to fixed entities in the denotation. That is, a semantics is absolute when the denotation of a variable a is a copy of itself in the denotation. We give a trio of…
A new understanding of the notion of regularizer is proposed. It is argued that this new notion is more realistic than the old one and better fits the practical computational needs. An example of the regularizer in the new sense is given. A…
Developing classification algorithms that are fair with respect to sensitive attributes of the data has become an important problem due to the growing deployment of classification algorithms in various social contexts. Several recent works…
Functional digraphs are unlabelled finite digraphs where each vertex has exactly one out-neighbor. They are isomorphic classes of finite discrete-time dynamical systems. Endowed with the direct sum and product, functional digraphs form a…
For formulas F of propositional calculus I introduce a "metavariable" MF and show how it can be used to define an algorithm for testing satisfiability. MF is a formula which is true/false under all possible truth assignments iff F is…
Scoring systems, as a type of predictive model, have significant advantages in interpretability and transparency and facilitate quick decision-making. As such, scoring systems have been extensively used in a wide variety of industries such…
A challenge in fair algorithm design is that, while there are compelling notions of individual fairness, these notions typically do not satisfy desirable composition properties, and downstream applications based on fair classifiers might…
The satisfiability problem of hybrid logics with the downarrow binder is known to be undecidable. This initiated a research program on decidable and tractable fragments. In this paper, we investigate the effect of restricting the…
We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied…
Existing algorithms for isolating real solutions of zero-dimensional polynomial systems do not compute the multiplicities of the solutions. In this paper, we define in a natural way the multiplicity of solutions of zero-dimensional…
We propose a symbolic-numeric algorithm to count the number of solutions of a polynomial system within a local region. More specifically, given a zero-dimensional system $f_1=\cdots=f_n=0$, with $f_i\in\mathbb{C}[x_1,\ldots,x_n]$, and a…
The analysis of discrimination has long interested economists and lawyers. In recent years, the literature in computer science and machine learning has become interested in the subject, offering an interesting re-reading of the topic. These…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…
This paper analyzes the correctness of the subsumption algorithm used in CLASSIC, a description logic-based knowledge representation system that is being used in practical applications. In order to deal efficiently with individuals in…
In this paper we introduce a new mathematical tool to solve fractional equations representing models of fractional systems : The Ultradistributions. Ultradistributions permit us to unify the notion of integral and derivative in one only…
In the lambda calculus a term is solvable iff it is operationally relevant. Solvable terms are a superset of the terms that convert to a final result called normal form. Unsolvable terms are operationally irrelevant and can be equated…
Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts…
The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that…