We give the first algorithm for Matrix Completion that achieves running time and sample complexity that is polynomial in the rank of the unknown target matrix, linear in the dimension of the matrix, and logarithmic in the condition number of the matrix. To the best of our knowledge, all previous algorithms either incurred a quadratic dependence on the condition number of the unknown matrix or a...

abstract. suppose g is an nvertex and medge simple graph with edge set e(g). an integervalued function f: e(g) → z is called a flow. tutte was introduced the flow polynomial f(g, λ) as a polynomial in an indeterminate λ with integer coefficients by f(g,λ) in this paper the flow polynomial of some dendrimers are computed.

To adapt the large number of parameters in a speech recognition acoustic model with a small amount of data, some notion of parameter dependence is needed. We present a dependence model to relate parameters in a parsimonious framework using a Gaussian multiscale process de ned by the evolution of a linear stochastic dynamical system on a tree. To adapt all classes from all adaptation data, we fo...

The construction of a polynomial interpolant to data given at finite pointsets in IR (or, most generally, to data specified by finitely many linear functionals) is considered, with special emphasis on the linear system to be solved. Gauss elimination by segments (i.e., by groups of columns rather than by columns) is proposed as a reasonable means for obtaining a description of all solutions and...

In this paper, we show that there exists a close dependence between the control polygon of a polynomial and the minimum of its blossom under symmetric linear constraints. We consider a given minimization problem P , for which a unique solution will be a point δ on the Bézier curve. For the minimization function f , two sufficient conditions exist that ensure the uniqueness of the solution, name...

Discretizations of the Langevin diffusion have been proven very useful for developing and analyzing algorithms sampling stochastic optimization. We present an improved non-asymptotic analysis Euler-Maruyama discretization diffusion. Our does not require global contractivity, yields polynomial dependence on time horizon. Compared to existing approaches, we make additional smoothness assumption, ...

Over the past two decades, fair resource allocation problems received considerable attention in avariety of application areas. While polynomial time distributed algorithms have been designed formax-min fair resource allocation, the design of distributed algorithms with convergence guarantees forthe more general α−fair allocations received little attention. In this paper, we stud...

We overview numerous algorithms in computational D-module theory together with the theoretical background as well as the implementation in the computer algebra system Singular. We discuss new approaches to the computation of Bernstein operators, of logarithmic annihilator of a polynomial, of annihilators of rational functions as well as complex powers of polynomials. We analyze algorithms for l...

We consider Potts model hypersurfaces defined by the multivariate Tutte polynomial of graphs (Potts model partition function). We focus on the behavior of the number of points over finite fields for these hypersurfaces, in comparison with the graph hypersurfaces of perturbative quantum field theory defined by the Kirchhoff graph polynomial. We give a very simple example of the failure of the “f...

The Omega test is an integer programming algorithm that can determine whether a dependence exists between two array references, and if so, under what conditions. Conventional wisdom holds that integer programming techniques are far too expensive to be used for dependence analysis, except as a method of last resort for situations that cannot be decided by simpler methods. We present evidence tha...