Related papers: Rational sphere maps, linear programming, and comp…
We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a connected graph. It is motivated by a particular problem in epidemiology, and may be useful in studies of various dynamical processes in…
In 'An asymptotic result on compressed sensing matrices', a new construction for compressed sensing matrices using combinatorial design theory was introduced. In this paper, we use deterministic and probabilistic methods to analyse the…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
This paper studies a class of so-called linear semi-infinite polynomial programming (LSIPP) problems. It is a subclass of linear semi-infinite programming problems whose constraint functions are polynomials in parameters and index sets are…
Many packing, scheduling and covering problems that were previously considered by computer science literature in the context of various transportation and production problems, appear also suitable for describing and modeling various…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
The Macaulay2 package Cremona performs some computations on rational and birational maps between irreducible projective varieties. For instance, it provides methods to compute degrees and projective degrees of rational maps without any…
What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections.…
Iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems. In this paper we extend the scope of the iterative relaxation method in two directions: (1)…
This letter proposes a novel distributed compressed estimation scheme for sparse signals and systems based on compressive sensing techniques. The proposed scheme consists of compression and decompression modules inspired by compressive…
We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of…
Compressed sensing is the art of reconstructing a sparse vector from its inner products with respect to a small set of randomly chosen measurement vectors. It is usually assumed that the ensemble of measurement vectors is in isotropic…
This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing…
Mixture of linear regressions is a popular learning theoretic model that is used widely to represent heterogeneous data. In the simplest form, this model assumes that the labels are generated from either of two different linear models and…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
We consider the problem of inference in higher-order undirected graphical models with binary labels. We formulate this problem as a binary polynomial optimization problem and propose several linear programming relaxations for it. We compare…
Graph is a useful data structure to model various real life aspects like email communications, co-authorship among researchers, interactions among chemical compounds, and so on. Supporting such real life interactions produce a knowledge…
This chapter summarizes several approaches combining theory, simulation and experiment that aim for a better understanding of phenomena in lipid bilayers and membrane protein systems, covering topics such as lipid rafts, membrane mediated…
For a finite dimensional vector space equipped with a $\mathbb C$-algebra structure, one can define rational maps using the algebraic structure. In this paper, we describe the growth of the degree sequences for this type of rational maps.
Modern data acquisition routinely produces massive amounts of network data. Though many methods and models have been proposed to analyze such data, the research of network data is largely disconnected with the classical theory of…