For object classification and detection, the algorithm pipeline often involves classifying feature vectors extracted from image patches. Existing features such as HOG, fail to map the image patches into a space where a linear hyperplane is suitable for separating the classes, while many non-linear classification methods are too expensive for many tasks. We propose a sparse tree-based mapping me...

This paper studies the effect of flexible linear torso on the dynamics of passive quadruped bounding. A reduced-order passive and conservative model with linear flexible torso and springy legs is introduced. The model features extensive spine deformation during high-speed bounding, resembling those observed in a cheetah. Fixed points corresponding to cyclic bounding motions are found and calcul...

Let R be a commutative ring. Unless indicated otherwise, all modules are R-modules and all tensor products are taken over R, so we abbreviate ⊗R to ⊗. A bilinear function out of M1 × M2 turns into a linear function out of the tensor product M1 ⊗ M2. In a similar way, a multilinear function out of M1 × · · · ×Mk turns into a linear function out of the k-fold tensor product M1 ⊗ · · · ⊗Mk. We wil...

A family of subsets of [n] is positive linear combination free if the characteristic vector of neither edge is the positive linear combination of the characteristic vectors of some other ones. We construct a positive linear combination free family which contains (1−o(1))2 subsets of [n] and we give tight bounds on the o(1)2 term. The problem was posed by the late Levon Khachatrian and the resul...

Positive linear systems are frequently used as mathematical models in research areas like biology and economics. The problem to classify all minimal realizations of these systems is treated in this paper. Extensive use is made of the theory of polyhedral cones. Suucient and necessary conditions for the existence of a positive realization are given, but the problem of minimality leads to the fac...

The most general evolution of the density matrix of a quantum system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear convex set that may be viewed as supermatrices. The property of hermiticity of density matrices renders an associated supermatrix hermitian and hence d...

Let $X$ be a Banach space of $dim X > 2$ and $B(X)$ be the space of bounded linear operators on X. If $L : B(X)to B(X)$ be a Lie higher derivation on $B(X)$, then there exists an additive higher derivation $D$ and a linear map $tau : B(X)to FI$ vanishing at commutators $[A, B]$ for all $A, Bin B(X)$ such that $L = D + tau$.

Maximum a posteriori (MAP) inference is one of the fundamental inference tasks in graphical models. MAP inference is in general NP-hard, making approximate methods of interest for many problems. One successful class of approximate inference algorithms is based on linear programming (LP) relaxations. The augmented Lagrangian method can be used to overcome a lack of strict convexity in LP relaxat...

Let M be a von Neumann algebra with a faithful normal trace τ , and let H∞ be a finite, maximal, subdiagonal algebra of M. Fundamental theorems on conjugate functions for weak∗-Dirichlet algebras are shown to be valid for non-commutative H∞. In particular the Hilbert transform is shown to be a bounded linear map from Lp(M, τ) into Lp(M, τ) for 1 < p < ∞, and to be a continuous map from L1(M, τ)...