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The Minimum Covariance Determinant (MCD) approach robustly estimates the location and scatter matrix using the subset of given size with lowest sample covariance determinant. Its main drawback is that it cannot be applied when the dimension…
This paper introduces Relative Predictive Coding (RPC), a new contrastive representation learning objective that maintains a good balance among training stability, minibatch size sensitivity, and downstream task performance. The key to the…
This paper investigates the robust uncertain two-level cooperative set covering problem (RUTLCSCP). Given two types of facilities, which are called y-facility and z-facility. The problem is to decide which facilities of both types to be…
A classical problem in phylogenetic tree analysis is to decide whether there is a phylogenetic tree $T$ that contains all information of a given collection $\cP$ of phylogenetic trees. If the answer is "yes" we say that $\cP$ is compatible…
The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice.…
We study the homographic system u(n+1)u(n)=c+d/v(n), v(n+1)v(n)=c+d/u(n+1) in the positive quadrant. The orbit of a point is contained in an invariant cubic curve, and the restriction to the positive part of this cubic of the associated…
The problem of designing high rate, full diversity noncoherent space-time block codes (STBCs) with low encoding and decoding complexity is addressed. First, the notion of $g$-group encodable and $g$-group decodable linear STBCs is…
Carbon fiber and graphene-based nanostructures such as carbon nanotubes (CNTs) and defective structures have extraordinary potential as strong and lightweight materials. A longstanding bottleneck has been lack of understanding and…
Recently, Convolutional Neural Networks (CNNs) have been widely used to solve the illuminant estimation problem and have often led to state-of-the-art results. Standard approaches operate directly on the input image. In this paper, we argue…
Many artificial intelligence (AI) problems naturally map to NP-hard optimization problems. This has the interesting consequence that enabling human-level capability in machines often requires systems that can handle formally intractable…
We present a new technique called contrastive principal component analysis (cPCA) that is designed to discover low-dimensional structure that is unique to a dataset, or enriched in one dataset relative to other data. The technique is a…
Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by…
A primary problem for perturbative QCD analyses is how to set the renormalization scale of the QCD running coupling in order to achieve maximally precise fixed-order predictions for physical observables. The Principle of Maximum…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
We examine packing of $n$ congruent spheres in a cube when $n$ is close but less than the number of spheres in a regular cubic close-packed (ccp) arrangement of $\lceil p^{3}/2\rceil$ spheres. For this family of packings, the previous…
A conforming partition of a rectilinear n-gon P (possibly with holes) is a partition of P into rectangles without using Steiner points (i.e., all corners of all rectangles must lie on the boundary of P). The stabbing number of such a…
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…
The Quadratic Unconstrained Binary Optimization problem (QUBO) has become a unifying model for representing a wide range of combinatorial optimization problems, and for linking a variety of disciplines that face these problems. A new class…
We address the question of whether a reflecting stationary set may be partitioned into two or more reflecting stationary subsets, providing various affirmative answers in ZFC. As an application to singular cardinals combinatorics, we infer…
Conventional frequentist learning is known to yield poorly calibrated models that fail to reliably quantify the uncertainty of their decisions. Bayesian learning can improve calibration, but formal guarantees apply only under restrictive…