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The classical mixture of Gaussians model is related to K-means via small-variance asymptotics: as the covariances of the Gaussians tend to zero, the negative log-likelihood of the mixture of Gaussians model approaches the K-means objective,…
We discuss applications of the perturbative QCD approach in the exclusive non-leptonic two body B-meson decays. We briefly review its ingredients and some important theoretical issues on the factorization approaches. PQCD results are…
We explain how to construct a large class of new quiver gauge theories from branes at singularities by orientifolding and Higgsing old examples. The new models include the MSSM, decoupled from gravity, as well as some classic models of…
Sequential parametrized topological complexity is a numerical homotopy invariant of a fibration, which arose in the robot motion planning problem with external constraints. In this paper, we study sequential parametrized topological…
We consider the Connectivity Augmentation Problem (CAP), a classical problem in the area of Survivable Network Design. It is about increasing the edge-connectivity of a graph by one unit in the cheapest possible way. More precisely, given a…
This work proves an upper bound for the free energy of the Sherrington-Kirkpatrick model and its generalizations in terms of the Thouless-Anderson-Palmer (TAP) energy. The result applies to models with spherical or Ising spins and any mixed…
The Quadratic Assignment Problem (QAP) is a well-known NP-hard problem that is equivalent to optimizing a linear objective function over the QAP polytope. The QAP polytope with parameter $n$ - \qappolytope{n} - is defined as the convex hull…
A novel inner approximation algorithm is proposed for dynamic optimization problems to ensure strict satisfaction of path constraints. Distinct from traditional methods relying on interval analysis, the proposed algorithm leverages the…
We provide string theory examples where a toy model of a SUSY GUT or the MSSM is embedded in a compactification along with a gauge sector which dynamically breaks supersymmetry. We argue that by changing microscopic details of the model…
We consider a system composed by N atoms trapped within a multimode cavity, whose theoretical description is captured by a disordered multimode Dicke model. We show that in the resonant, zero field limit the system exactly realizes the…
The method of squared eigenfunction potentials (SEP) is developed systematically to describe and gain new information about Kadomtsev-Petviashvili (KP) hierarchy and its reductions. Interrelation to the tau-function method is discussed in…
As a step toward clarification of the power of supersymmetry (SUSY) in Matrix theory, a complete calculation, including all the spin effects, is performed of the effective action of a probe D-particle, moving along an arbitrary trajectory…
It has been shown recently that extended supersymmetry in twisted first-order sigma models is related to twisted generalized complex geometry in the target. In the general case there are additional algebraic and differential conditions…
The demand for precision predictions in the field of high energy physics has dramatically increased over recent years. Experiments conducted at the LHC, as well as precision measurements at the intensity frontier such as Belle II require…
We study the computational complexity of one of the particular cases of the knapsack problem: the subset sum problem. For solving this problem we consider one of the basic variants of the Branch-and-Bound method in which any sub-problem is…
In this work, we develop a new complexity metric for an important class of low-rank matrix optimization problems in both symmetric and asymmetric cases, where the metric aims to quantify the complexity of the nonconvex optimization…
Computation fundamentally separates time from space: nondeterministic search is exponential in time but polynomially simulable in space (Savitch's Theorem). We propose that the brain physically instantiates a biological variant of this…
This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several…
Artin Presentation Theory, (AP Theory), is a new, direct infusion, via pure braid theory, of discrete group theory, (i.e., symmetry in its purest form), into the theory of {\it smooth} 4-manifolds, (i.e.,$(3+1)$-Quantum Gravity in its…
Sparsity has been widely recognized as crucial for efficient optimization in graph-based SLAM. Because the sparsity and structure of the SLAM graph reflect the set of incorporated measurements, many methods for sparsification have been…