相关论文: Mathematical basis for polySAT implication operato…
When formalizing proofs with interactive theorem provers, it often happens that extra background knowledge (declarative or procedural) about mathematical concepts is employed without the formalizer explicitly invoking it, to help the…
The dominant method for defining multivariate operator means is to express them as fix-points under a contraction with respect to the Thompson metric. Although this method is powerful, it crucially depends on monotonicity. We are developing…
This note discusses how an operator analog of the Lagrange polynomial naturally arises in the quantum-mechanical problem of constructing an explicit form of the spin projection operator.
An explicit formula is given for a fundamental solution for a class of semielliptic operators. The fundamental solution is used to investigate properties of these operators as mappings between weighted function spaces. Necessary and…
Mediation analysis breaks down the causal effect of a treatment on an outcome into an indirect effect, acting through a third group of variables called mediators, and a direct effect, operating through other mechanisms. Mediation analysis…
Traditional mathematical notation can lead to confusion. Expressions that appear to define composite functions sometimes do not. A particular example with engineering applications is studied in detail.
The implication relationship between subsystems in Reverse Mathematics has an underlying logic, which can be used to deduce certain new Reverse Mathematics results from existing ones in a routine way. We use techniques of modal logic to…
We present a computable algorithm that assigns probabilities to every logical statement in a given formal language, and refines those probabilities over time. For instance, if the language is Peano arithmetic, it assigns probabilities to…
Lifted probabilistic inference exploits symmetries in a probabilistic model to allow for tractable probabilistic inference with respect to domain sizes. To apply lifted inference, a lifted representation has to be obtained, and to do so,…
We extend the knowledge about so-called structural restrictions of $\mathrm{\#SAT}$ by giving a polynomial time algorithm for $\beta$-acyclic $\mathrm{\#SAT}$. In contrast to previous algorithms in the area, our algorithm does not proceed…
We generalize the construction of multitildes in the aim to provide multitilde operators for regular languages. We show that the underliying algebraic structure involves the action of some operads. An operad is an algebraic structure that…
Adding interpretability to multivariate methods creates a powerful synergy for exploring complex physical systems with higher order correlations while bringing about a degree of clarity in the underlying dynamics of the system.
Economies and societal structures in general are complex stochastic systems which may not lend themselves well to algebraic analysis. An addition of subjective value criteria to the mechanics of interacting agents will further complicate…
The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…
We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…
We review a method for the algebraic treatment of a family of functions which contains the multiple polylogarithms, with applications to the symbolic calculation of Feynman integrals.
The typical mathematical language systematically exploits notational and logical abuses whose resolution requires not just the knowledge of domain specific notation and conventions, but not trivial skills in the given mathematical…
We show that under natural and quite general assumptions, a large part of a matrix for a bounded linear operator on a Hilbert space can be preassigned. The result is obtained in a more general setting of operator tuples leading to…
Recent theoretical work in causal inference has explored an important class of variables which, when conditioned on, may further amplify existing unmeasured confounding bias (bias amplification). Despite this theoretical work, existing…
We show that a symmetric informationally-complete positive operator-valued measure exists in a given dimension $d$ if and only if there exists a $d^2$-dimensional operator system satisfying certain order-theoretic conditions. We also…