Related papers: Non-deterministic approximation operators: ultimat…
This paper discusses various theorems on the approximation capabilities of neural networks (NNs), which are known as universal approximation theorems (UATs). The paper gives a systematic overview of UATs starting from the preliminary…
Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial…
The theory of abstract Friedrichs operators was introduced some fifteen years ago with the aim of providing a more comprehensive framework for the study of positive symmetric systems of first-order partial differential equations, nowadays…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…
This article establishes a complete approximate axiomatization for the real-closed field $\mathbb{R}$ expanded with all differentially-defined functions, including special functions such as $\sin(x), \cos(x), e^x, \dots$. Every true…
We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…
Fixed-parameter tractable (FPT) algorithms have been successfully applied to many intractable problems -- with a focus on decision and optimization problems. Their aim is to confine the exponential explosion to some parameter, while the…
In this note, we consider a framework for the analysis of iterative algorithms which can described in terms of a structured set-valued operator. More precisely, at each point in the ambient space, we assume that the value of operator can be…
We study the fixed point problem for a system of multivariate operators that are coordinate-wise monotone (i.e., nondecreasing or nonincreasing in each of the variables, independently), in the setting of quasi-ordered sets. We show that…
We study invariant local expansion operators for conflict-free and admissible sets in Abstract Argumentation Frameworks (AFs). Such operators are directly applied on AFs, and are invariant with respect to a chosen "semantics" (that is…
A large class of non-smooth practical optimization problems can be written as minimization of a sum of smooth and partly smooth functions. We examine such structured problems which also depend on a parameter vector and study the problem of…
We present a logical system CFP (Concurrent Fixed Point Logic) from whose proofs one can extract nondeterministic and concurrent programs that are provably total and correct with respect to the proven formula. CFP is an intuitionistic…
In the setting of modern mathematical logic and model theory, classification theory has been one of the landmark achievements of the field. Likewise, the classification of UHF-algebras and AF-algebras were substantial contributions to the…
The relationship between abstract interpretation and partial deduction has received considerable attention and (partial) integrations have been proposed starting from both the partial deduction and abstract interpretation perspectives. In…
In this paper, we proposed a deep learning-based end-to-end method on the domain specified automatic term extraction (ATE), it considers possible term spans within a fixed length in the sentence and predicts them whether they can be…
In this article the author claims that there is a paradigm shift from ZFC to NFUM and further to NACT - due to philosophical reasons, not mathematical ones. The goal is to construct systems where every "Not-Properclass" is a set! With help…
Nonnegative matrix factorization (NMF), which is the approximation of a data matrix as the product of two nonnegative matrices, is a key issue in machine learning and data analysis. One approach to NMF is to formulate the problem as a…
A general method for estimating the approximation numbers of composition operators on $\Ht$, using finite-dimensional model subspaces, is studied and applied in the case when the symbol of the operator maps the unit disc to a domain whose…
An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…