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Normalisation and subformula property for a system of classical logic with Tarski’s rule
This paper considers a formalisation of classical logic using general introduction rules and general elimination rules. It proposes a definition of...
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The Complexity of the Hausdorff Distance
We investigate the computational complexity of computing the Hausdorff distance. Specifically, we show that the decision problem of whether the...
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Nonsmooth rank-one matrix factorization landscape
We provide the first positive result on the nonsmooth optimization landscape of robust principal component analysis, to the best of our knowledge. It...
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A Tiny Bit of Informal Logic
Although we have already used quantifiers, \(\exists \) and...
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The additive structure of integers with the lower Wythoff sequence
We have provided a model-theoretic proof for the decidability of the additive structure of integers together with the function f map** x to
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Tropical Spectrahedra
We introduce tropical spectrahedra, defined as the images by the nonarchimedean valuation of spectrahedra over the field of real Puiseux series. We...
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Corcoran the Mathematician
The aim of this chapter is to sketch John Corcoran’s mathematical contributions and to relate them to his (and others’) philosophical interests.
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Symbolic computation for the qualitative theory of differential equations
This paper provides a survey on symbolic computational approaches for the analysis of qualitative behaviors of systems of ordinary differential...
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VerifyRealRoots: A Matlab Package for Computing Verified Real Solutions of Polynomials Systems of Equations and Inequalities
VerifyRealRoots is a Matlab package for computing and verifying real solutions of polynomial systems of equations and inequalities. It calls Bertini...
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Complexity of linear relaxations in integer programming
For a set X of integer points in a polyhedron, the smallest number of facets of any polyhedron whose set of integer points coincides with X is called...
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Elementary Equivalence
The \(\tau \) -type structures...
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Conormal Spaces and Whitney Stratifications
We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic...
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Positive indiscernibles
We generalise various theorems for finding indiscernible trees and arrays to positive logic: based on an existing modelling theorem for s-trees, we...
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Decidability of Logical Theories and Their Combination
This textbook provides a self-contained introduction to decidability of first-order theories and their combination. The technical material is...
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Embeddings and Substructures
We study embeddings of structures and how the truth of formulas is preserved under embeddings. Elementary embeddings are introduced and the...
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On Types of Isolated KKT Points in Polynomial Optimization
Let f be a real polynomial function with n variables and S be a basic closed semialgebraic set in ℝ n . In this paper, the authors are interested in...
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Nyāyasūtra Proof Pattern: An Interpretation of Similarity as the Fact of Sharing Two Properties
In the book Nyāyasūtra, there is an inference that Schayer related to first-order predicate logic. The relation was challenged, because it seemed to...