A Tutorial on GrÖbner Bases With Applications in Signals and Systems

This paper is a tutorial on GrÖbner bases and a survey on the applications of GrÖbner bases in the broad field of signals and systems. A reasonably detailed review is given of several fundamental theoretical issues that occur in the use of GrÖbner bases in multidimensional signals and systems applications. These topics include the primeness of multivariate polynomial matrices, multivariate unimodular polynomial matrix completion, and prime factorization of multivariate polynomial matrices. A brief review is also presented on the wide-ranging applications of GrÖbner bases in multidimensional as well as one-dimensional circuits, networks, control, coding, signals, and systems and other related areas like robotics and applied mechanics. The impact and scope of GrÖbner bases in signals and systems are highlighted with respect to what has already been accomplished as a stepping stone to expanding future research.      

AVCOL: Availability-aware information aggregation in large distributed systems under uncollaborative behavior

Aggregation of system-wide information in large-scale distributed systems, such as p2p systems and Grids, can be unfairly influenced by nodes that are selfish, colluding with each other, or are offline most of the time. We present AVCOL, which uses probabilistic and gossip-style techniques to provide availability-aware aggregation. Concretely, AVCOL is the first aggregation system that: (1) implements any (arbitrary) global predicate that explicitly specifies any node’s probability of inclusion in the global aggregate, as a mathematical function of that node’s availability (i.e., percentage time online); (2) probabilistically tolerates large numbers of selfish nodes and large groups of colluders; and (3) scales well with hundreds to thousands of nodes. AVCOL uses several unique design decisions: per-aggregation tree construction where nodes are allowed a limited but flexible probabilistic choice of parents or children, probabilistic aggregation along trees, and auditing of nodes both during aggregation as well as in gossip-style (i.e., periodically). We have implemented AVCOL, and we experimentally evaluated it using real-life churn traces. Our evaluation and our mathematical analysis show that AVCOL satisfies arbitrary predicates, scales well, and withstands a variety of selfish and colluding attacks.     

Plasmon‐Induced Hot Carrier Separation across Dual Interface in Gold–Nickel Phosphide Heterojunction for Photocatalytic Water Splitting

Precise control of the topology of metal nanocrystals and appropriate modulation of the metal–semiconductor heterostructure is an important way to understand the relationship between structure and material properties for plasmon‐induced solar‐to‐chemical energy conversion. Here, a bottom‐up wet chemical approach to synthesize Au/Ni₂P heterostructures via Pt‐catalyzed quasi‐epitaxial overgrowth of Ni on Au nanorods (NR) is presented. The structural motif of the Ni₂P is controlled using the aspect ratio of the Au NR and the effective micelle concentration of the C₁₆TAB capping agent. Highly ordered Au/Pt/Ni₂P nanostructures are employed as the photoelectrocatalytic anode system for water splitting. Electrochemical and ultrafast absorption spectroscopy characterization indicates that the structural motif of the Ni₂P (controlled by the outer‐shell deposition of Ni) helps to manipulate hot electron transfer during surface plasmon decay. With optimized Ni₂P thickness, Pt‐tipped Au NR with an aspect ratio of 5.2 exhibits a geometric current density of 10 mA cm^?2 with an overpotential of 140 mV. The photoanode displays unprecedented long‐term stability with continuous chronoamperometric performance of 50 h at an input potential of 1.5 V with over 30 days. This work provides definitive guidance for designing plasmonic–catalytic nanomaterials for enhanced solar‐to‐chemical energy conversion.     

Fast evaluation of an integral occurring in digital filteringapplications

A fast evaluation procedure for the integral I_m,n,p=1/2πj∯_|z|=1H_m,n(z)H _m,n(z^-1)z^p-1dz for arbitrary nonnegative integer-valued m, n, and p, is presented, where H_m,n (z)=Σ_k=0^mb_m,kz^-k /Σ_l=0ⁿa_n,lz^-1,a _n,0≠0 is the transfer function of an arbitrary digital filter. Evaluation of this integral frequently appears in control, communication, and digital filtering. A notable result is the one-term recursion on p, for arbitrary but fixed nonnegative integers m and n. The computational complexity is analyzed, and two illustrative examples demonstrate some of the advantages of this approach     

Stability of digital filters implemented with two's complementtruncation quantization

The stability of digital filters implemented with two's complement truncation quantization is investigated. Both the direct-form and normal-form realizations are considered and regions in the parameter plane are obtained where the filters are globally asymptotically stable. Regions within the stability triangle of a direct-form digital filter are also studied where limit cycles of period one and two are possible. The results are illustrated with several examples     

Two's complement quantization in two-dimensional state-spacedigital filters

Two-dimensional (2-D) state-space digital filters are investigated for stability with and without quantization. A sufficient condition is obtained for the stability of the linear Fornasini-Marchesini (1976) state-space model. The same model is then studied for stability when implemented using two's complement truncation quantization, and a sufficient condition for asymptotic stability of the nonlinear filter is obtained. In the process, a theorem is proved which gives a sufficient condition for the stability of a one-dimensional (1-D) state-space digital filter under the same type of quantization     

Task allocation and scheduling in wireless distributed computing networks

Wireless distributed computing (WDC) is an enabling technology that allows radio nodes to cooperate in processing complex computational tasks of an application in a distributed manner. WDC research is being driven by the fact that mobile portable computing devices have limitations in executing complex mobile applications, mainly attributed to their limited resource and functionality. This article focuses on resource allocation in WDC networks, specifically on scheduling and task allocation. In WDC, it is important to schedule communications between the nodes in addition to the allocation of computational tasks to nodes. Communication scheduling and heterogeneity in the operating environment make the WDC resource allocation problem challenging to address. This article presents a task allocation and scheduling algorithm that optimizes both energy consumption and makespan in a heuristic manner. The proposed algorithm uses a comprehensive model of the energy consumption for the execution of tasks and communication between tasks assigned to different radio nodes. The algorithm is tested for three objectives, namely, minimization of makespan, minimization of energy consumption, and minimization of both makespan and energy consumption.     

Design of some new efficient balanced codes

A balanced code with r check bits and k information bits is a binary code of length k+r and cardinality 2^k such that each codeword is balanced; that is, it has [(k+r)/2] 1's and [(k+r)/2] 0's. This paper contains new methods to construct efficient balanced codes. To design a balanced code, an information word with a low number of 1's or 0's is compressed and then balanced using the saved space. On the other hand, an information word having almost the same number of 1's and 0's is encoded using the single maps defined by Knuth's (1986) complementation method. Three different constructions are presented. Balanced codes with r check bits and k information bits with k⩽2^r+1-2, k⩽3×2^r-8, and k⩽5×2^r-10r+c(r), c(r)∈{-15, -10, -5, 0, +5}, are given, improving the constructions found in the literature. In some cases, the first two constructions have a parallel coding scheme     

An efficient algorithm for superresolution in medium field imaging

In this paper, we study the problem of reconstruction of a high-resolution (HR) image from several blurred low-resolution (LR) image frames in medium field. The image frames consist of blurred, decimated, and noisy versions of a HR image. The HR image is modeled as a Markov random field (MRF), and a maximum a posteriori (MAP) estimation technique is used for the restoration. We show that with the periodic boundary condition, a HR image can be restored efficiently by using fast Fourier transforms. We also apply the preconditioned conjugate gradient method to restore HR images in the aperiodic boundary condition. Computer simulations are given to illustrate the effectiveness of the proposed approach. This research was conducted with support from the Army Research Office Grant DAAD 19-03-1-0261 and the National Science Foundation Grant CCF-0429481. Research supported in part by RGC Grant Nos. 7130/02P, 7046/03P, 7035/04P and 7035/04P and FRG/04-05/II-51.     

Properties determining choice of mother wavelet

Properties of wavelets with finite as well as infinite support are summarised to facilitate mother wavelet selection in a chosen application. The quantitative guidelines reduce dependence on trial-and-error schemes resorted to for selection and underscore the importance of such selection in any application of interest. In wavelet-based image sequence superresolution, studied during the last four years, the use of a B-spline mother wavelet is justified.