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Network partitioning has gained recent attention as a pathway to enable decentralized operation and control in large-scale systems. This paper addresses the interplay between partitioning, observability, and sensor placement (SP) in dynamic…
The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.
Compressive sensing achieves effective dimensionality reduction of signals, under a sparsity constraint, by means of a small number of random measurements acquired through a sensing matrix. In a signal processing system, the problem arises…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
We discuss here constraint programming (CP) by using a proof-theoretic perspective. To this end we identify three levels of abstraction. Each level sheds light on the essence of CP. In particular, the highest level allows us to bring CP…
We investigate the problem of density estimation on the unit circle and the unit sphere from a computational perspective. Our primary goal is to develop new density estimators that are both rate-optimal and computationally efficient for…
Most existing motion planning algorithms assume that a map (of some quality) is fully determined prior to generating a motion plan. In many emerging applications of robotics, e.g., fast-moving agile aerial robots with constrained embedded…
The multi-user linearly-separable distributed computing problem is considered here, in which $N$ servers help to compute the real-valued functions requested by $K$ users, where each function can be written as a linear combination of up to…
We present an approach to a large class of enumerative problems concerning rational curves in projective spaces. This approach uses analysis to obtain topological information about moduli spaces of stable maps. We demonstrate it by…
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
In this chapter, we present the state of the art of the spectrum sensing techniques for cognitive radio networks as well and their comparisons. The rest of the chapter is organized as below: Section I.1, Section I.2, and Section I.3 present…
In this paper, we develop an approach that enables autonomous robots to build and compress semantic environment representations from point-cloud data. Our approach builds a three-dimensional, semantic tree representation of the environment…
We investigate when a computable automorphism of a computable field can be effectively extended to a computable automorphism of its (computable) algebraic closure. We then apply our results and techniques to study effective embeddings of…
We propose a new class of space-filling designs called rotated sphere packing designs for computer experiments. The approach starts from the asymptotically optimal positioning of identical balls that covers the unit cube. Properly scaled,…
Label assignment problems with large state spaces are important tasks especially in computer vision. Often the pairwise interaction (or smoothness prior) between labels assigned at adjacent nodes (or pixels) can be described as a function…
We show in many cases that there exist rational scrolls which are balanced, i.e. they contain the expected number of general linear spaces as rulings. For example, there exist balanced scrolls of degree $mk+1$ and fibre dimension $k$ in…
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of…
This paper investigates scalable frame in ${\mathbb R}^n$. We define the reduced diagram matrix of a frame and use it to classify scalability of the frame under some conditions. We give a new approach to the scaling problem by breaking the…
Complexity science offers a wide range of measures for quantifying unpredictability, structure, and information. Yet, a systematic conceptual organization of these measures is still missing. We present a unified framework that locates…