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A unified pre-training and adaptation framework for combinatorial optimization on graphs
Combinatorial optimization (CO) on graphs is a classic topic that has been extensively studied across many scientific and industrial fields....
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Loxodromes on Invariant Surfaces in Three-Manifolds
In this paper, we prove some results concerning the loxodromes on an invariant surface in a three-dimensional Riemannian manifold, a part of which...
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Homogeneous Einstein-like metrics on symmetric spaces
In this paper, we study homogeneous Einstein-like metrics on the compact irreducible symmetric space M , which is not isometric to a compact Lie group...
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Diophantine approximation with one prime, two squares of primes and powers of two
In this paper, we prove that, under some conditions, the values taken by certain real linear combinations of one prime, two squares of primes and s ...
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Convex geometries representable with colors, by ellipses on the plane, and impossible by circles
A convex geometry is a closure system satisfying the anti-exchange property. This paper, following the work of Adaricheva and Bolat (Discrete Math...
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An Entropy-Regularized ADMM For Binary Quadratic Programming
We propose an entropy regularized splitting model using low-rank factorization for solving binary quadratic programming with linear inequality...
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Dessins d’Enfants
The Galois group \({\mathbb G}= \mathrm{Aut}_{\mathbb Q}(\overline{{\mathbb Q}})\) , where \(\overline{{\mathbb Q}}\) is an algebraic closure of...
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A group from Hackenbush game
This research presents the reader some algebraic operations related to combinatorial games and gives a detailed outlook of a special game called...
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The Role of Graphlets in Viral Processes on Networks
Predicting the evolution of viral processes on networks is an important problem with applications arising in biology, the social sciences, and the...
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Applications of Affine Surface Theory
In Section 15.1, we present some basic material concerning the Riemannian extension and other notions which we shall need. In Section 15.2, we...
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THE COHEN–MACAULAY PROPERTY OF INVARIANT RINGS OVER THE INTEGERS
We prove various characterisations for the Cohen–Macaulay property for the invariant ring k [ x 1 , …, x n ] G , where k is a PID.We also show that, except...
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Coupled flapwise-chordwise-axial-torsional dynamic responses of rotating pre-twisted and inclined cantilever beams subject to the base excitation
A rotating pre-twisted and inclined cantilever beam model (RPICBM) with the flapwise-chordwise-axial-torsional coupling is established with the...
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SEIDEL’S CONJECTURES IN HYPERBOLIC 3-SPACE
We prove, in the case of hyperbolic 3-space, a couple of conjectures raised by J. J. Seidel in On the volume of a hyperbolic simplex, Stud. Sci....
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On the ∀∃-Theories of Free Projective Planes
Studying the elementary properties of free projective planes of finite rank, we prove that for m > n , an arbitrary ∀∃∀-formula Φ( ȳ ) and a tuple ū of...
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A matrix nonconvex relaxation approach to unconstrained binary polynomial programs
This paper is concerned with a class of unconstrained binary polynomial programs (UBPPs), which covers the classical binary quadratic program and has...
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On the Number of Fixed Points of Automorphisms of Vertex-Transitive Graphs
The main result of this paper is that, if Γ is a finite connected 4-valent vertex- and edge-transitive graph, then either Γ is part of a...
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Managing randomization in the multi-block alternating direction method of multipliers for quadratic optimization
The Alternating Direction Method of Multipliers (ADMM) has gained a lot of attention for solving large-scale and objective-separable constrained...
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Machine Learning Basics
The previous chapters covered some of the key concepts of classical statistics. These include point estimation, confidence intervals, hypothesis...