Analogues of the Wiener-Tauberian and Schwartz theorems for radial functions on symmetric spaces

We prove a Wiener Tauberian theorem for the L-1 spherical functions on a semisimple Lie group of arbitrary real rank. We also establish a Schwartz-type theorem for complex groups. As a corollary we obtain a Wiener Tauberian type result for compactly supported distributions.

Guessers for Finite-State Transducer Lexicons

Language software applications encounter new words, e.g., acronyms, technical terminology, names or compounds of such words. In order to add new words to a lexicon, we need to indicate their inflectional paradigm. We present a new generally applicable method for creating an entry generator, i.e. a paradigm guesser, for finite-state transducer lexicons. As a guesser tends to produce numerous suggestions, it is important that the correct suggestions be among the first few candidates. We prove some formal properties of the method and evaluate it on Finnish, English and Swedish full-scale transducer lexicons. We use the open-source Helsinki Finite-State Technology to create finitestate transducer lexicons from existing lexical resources and automatically derive guessers for unknown words. The method has a recall of 82-87 % and a precision of 71-76 % for the three test languages. The model needs no external corpus and can therefore serve as a baseline.

Transformation formula for exponential sums involving fourier coefficients of modular forms

In 1984 Jutila [5] obtained a transformation formula for certain exponential sums involving the Fourier coefficients of a holomorphic cusp form for the full modular group SL(2, Z). With the help of the transformation formula he obtained good estimates for the distance between consecutive zeros on the critical line of the Dirichlet series associated with the cusp form and for the order of the Dirichlet series on the critical line, [7]. In this paper we follow Jutila to obtain a transformation formula for exponential sums involving the Fourier coefficients of either holomorphic cusp forms or certain Maass forms for congruence subgroups of SL(2, Z) and prove similar estimates for the corresponding Dirichlet series.

Stochastic Approximation Algorithms for Constrained Optimization via Simulation

We develop four algorithms for simulation-based optimization under multiple inequality constraints. Both the cost and the constraint functions are considered to be long-run averages of certain state-dependent single-stage functions. We pose the problem in the simulation optimization framework by using the Lagrange multiplier method. Two of our algorithms estimate only the gradient of the Lagrangian, while the other two estimate both the gradient and the Hessian of it. In the process, we also develop various new estimators for the gradient and Hessian. All our algorithms use two simulations each. Two of these algorithms are based on the smoothed functional (SF) technique, while the other two are based on the simultaneous perturbation stochastic approximation (SPSA) method. We prove the convergence of our algorithms and show numerical experiments on a setting involving an open Jackson network. The Newton-based SF algorithm is seen to show the best overall performance.

An actor-critic algorithm with function approximation for discounted cost constrained Markov decision processes

We develop in this article the first actor-critic reinforcement learning algorithm with function approximation for a problem of control under multiple inequality constraints. We consider the infinite horizon discounted cost framework in which both the objective and the constraint functions are suitable expected policy-dependent discounted sums of certain sample path functions. We apply the Lagrange multiplier method to handle the inequality constraints. Our algorithm makes use of multi-timescale stochastic approximation and incorporates a temporal difference (TD) critic and an actor that makes a gradient search in the space of policy parameters using efficient simultaneous perturbation stochastic approximation (SPSA) gradient estimates. We prove the asymptotic almost sure convergence of our algorithm to a locally optimal policy. (C) 2010 Elsevier B.V. All rights reserved.

Past Queue Length Based Low-Overhead Link Scheduling in Multi-beam Wireless Mesh Networks

Wireless mesh networks with multi-beam capability at each node through the use of multi-antenna beamforming are becoming practical and attracting increased research attention. Increased capacity due to spatial reuse and increased transmission range are potential benefits in using multiple directional beams in each node. In this paper, we are interested in low-complexity scheduling algorithms in such multi-beam wireless networks. In particular, we present a scheduling algorithm based on queue length information of the past slots in multi-beam networks, and prove its stability. We present a distributed implementation of this proposed algorithm. Numerical results show that significant improvement in delay performance is achieved using the proposed multi-beam scheduling compared to omni-beam scheduling. In addition, the proposed algorithm is shown to achieve a significant reduction in the signaling overhead compared to a current slot queue length approach.

Multi-Agent Rendezvous Algorithm with Rectilinear Decision Domain

The aim of this paper is to develop a computationally efficient decentralized rendezvous algorithm for a group of autonomous agents. The algorithm generalizes the notion of sensor domain and decision domain of agents to enable implementation of simple computational algorithms. Specifically, the algorithm proposed in this paper uses a rectilinear decision domain (RDD) as against the circular decision domain assumed in earlier work. Because of this, the computational complexity of the algorithm reduces considerably and, when compared to the standard Ando's algorithm available in the literature, the RDD algorithm shows very significant improvement in convergence time performance. Analytical results to prove convergence and supporting simulation results are presented in the paper.

Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f is an element of L-1 (G) has lacunary Fourier series and f vanishes on a non empty open subset of G, then we prove that f vanishes identically. This result can be viewed as a qualitative uncertainty principle.

CM defect and Hilbert functions of monomial curves

In this article we consider a semigroup ring R = KGamma] of a numerical semigroup Gamma and study the Cohen- Macaulayness of the associated graded ring G(Gamma) := gr(m), (R) := circle plus(n is an element of N) m(n)/m(n+1) and the behaviour of the Hilbert function H-R of R. We define a certain (finite) subset B(Gamma) subset of F and prove that G(Gamma) is Cohen-Macaulay if and only if B(Gamma) = empty set. Therefore the subset B(Gamma) is called the Cohen-Macaulay defect of G(Gamma). Further, we prove that if the degree sequence of elements of the standard basis of is non-decreasing, then B(F) = empty set and hence G(Gamma) is Cohen-Macaulay. We consider a class of numerical semigroups Gamma = Sigma(3)(i=0) Nm(i) generated by 4 elements m(0), m(1), m(2), m(3) such that m(1) + m(2) = mo m3-so called ``balanced semigroups''. We study the structure of the Cohen-Macaulay defect B(Gamma) of Gamma and particularly we give an estimate on the cardinality |B(Gamma, r)| for every r is an element of N. We use these estimates to prove that the Hilbert function of R is non-decreasing. Further, we prove that every balanced ``unitary'' semigroup Gamma is ``2-good'' and is not ``1-good'', in particular, in this case, c(r) is not Cohen-Macaulay. We consider a certain special subclass of balanced semigroups Gamma. For this subclass we try to determine the Cohen-Macaulay defect B(Gamma) using the explicit description of the standard basis of Gamma; in particular, we prove that these balanced semigroups are 2-good and determine when exactly G(Gamma) is Cohen-Macaulay. (C) 2011 Published by Elsevier B.V.

Low-Complexity Detection and Performance in Multi-Gigabit High Spectral Efficiency Wireless Systems

Recently, we reported a low-complexity likelihood ascent search (LAS) detection algorithm for large MIMO systems with several tens of antennas that can achieve high spectral efficiencies of the order of tens to hundreds of bps/Hz. Through simulations, we showed that this algorithm achieves increasingly near SISO AWGN performance for increasing number of antennas in Lid. Rayleigh fading. However, no bit error performance analysis of the algorithm was reported. In this paper, we extend our work on this low-complexity large MIMO detector in two directions: i) We report an asymptotic bit error probability analysis of the LAS algorithm in the large system limit, where N-t, N-r -> infinity keeping N-t = N-r, where N-t and N-r are the number of transmit and receive antennas, respectively. Specifically, we prove that the error performance of the LAS detector for V-BLAST with 4-QAM in i.i.d. Rayleigh fading converges to that of the maximum-likelihood (ML) detector as N-t, N-r -> infinity keeping N-t = N-r ii) We present simulated BER and nearness to capacity results for V-BLAST as well as high-rate non-orthogonal STBC from Division Algebras (DA), in a more realistic spatially correlated MIMO channel model. Our simulation results show that a) at an uncoded BER of 10(-3), the performance of the LAS detector in decoding 16 x 16 STBC from DA with N-t = = 16 and 16-QAM degrades in spatially correlated fading by about 7 dB compared to that in i.i.d. fading, and 19) with a rate-3/4 outer turbo code and 48 bps/Hz spectral efficiency, the performance degrades by about 6 dB at a coded BER of 10(-4). Our results further show that providing asymmetry in number of antennas such that N-r > N-t keeping the total receiver array length same as that for N-r = N-t, the detector is able to pick up the extra receive diversity thereby significantly improving the BER performance.

Some results and approaches for reconstruction conjectures

Tutte (1979) proved that the disconnected spanning subgraphs of a graph can be reconstructed from its vertex deck. This result is used to prove that if we can reconstruct a set of connected graphs from the shuffled edge deck (SED) then the vertex reconstruction conjecture is true. It is proved that a set of connected graphs can be reconstructed from the SED when all the graphs in the set are claw-free or all are P-4-free. Such a problem is also solved for a large subclass of the class of chordal graphs. This subclass contains maximal outerplanar graphs. Finally, two new conjectures, which imply the edge reconstruction conjecture, are presented. Conjecture 1 demands a construction of a stronger k-edge hypomorphism (to be defined later) from the edge hypomorphism. It is well known that the Nash-Williams' theorem applies to a variety of structures. To prove Conjecture 2, we need to incorporate more graph theoretic information in the Nash-Williams' theorem.

Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. (C) 2010 Elsevier Inc. All rights reserved.

An optimal dynamic inversion approach for controlling a class of one-dimensional nonlinear distributed parameter systems

Combining the principles of dynamic inversion and optimization theory, a new approach is presented for stable control of a class of one-dimensional nonlinear distributed parameter systems, assuming the availability a continuous actuator in the spatial domain. Unlike the existing approximate-then-design and design-then-approximate techniques, here there is no need of any approximation either of the system dynamics or of the resulting controller. Rather, the control synthesis approach is fairly straight-forward and simple. The controller formulation has more elegance because we can prove the convergence of the controller to its steady state value. To demonstrate the potential of the proposed technique, a real-life temperature control problem for a heat transfer application is solved. It has been demonstrated that a desired temperature profile can be achieved starting from any arbitrary initial temperature profile.

Design issues and caching strategies for CD-ROM based multimedia storage

CD-ROMs have proliferated as a distribution media for desktop machines for a large variety of multimedia applications (targeted for a single-user environment) like encyclopedias, magazines and games. With CD-ROM capacities up to 3 GB being available in the near future, they will form an integral part of Video on Demand (VoD) servers to store full-length movies and multimedia. In the first section of this paper we look at issues related to the single- user desktop environment. Since these multimedia applications are highly interactive in nature, we take a pragmatic approach, and have made a detailed study of the multimedia application behavior in terms of the I/O request patterns generated to the CD-ROM subsystem by tracing these patterns. We discuss prefetch buffer design and seek time characteristics in the context of the analysis of these traces. We also propose an adaptive main-memory hosted cache that receives caching hints from the application to reduce the latency when the user moves from one node of the hyper graph to another. In the second section we look at the use of CD-ROM in a VoD server and discuss the problem of scheduling multiple request streams and buffer management in this scenario. We adapt the C-SCAN (Circular SCAN) algorithm to suit the CD-ROM drive characteristics and prove that it is optimal in terms of buffer size management. We provide computationally inexpensive relations by which this algorithm can be implemented. We then propose an admission control algorithm which admits new request streams without disrupting the continuity of playback of the previous request streams. The algorithm also supports operations such as fast forward and replay. Finally, we discuss the problem of optimal placement of MPEG streams on CD-ROMs in the third section.

Crystal Structure Engineering by Fine-Tuning the Surface Energy: The Case of CdE (E = S/Se) Nanocrystals

We prove that CdS nanocrystals can be thermodynamically stabilized in both wurtzite and zinc-blende crystallographic phases at will, just by the proper choice of the capping ligand. As a striking demonstration of this, the largest CdS nanocrystals (similar to 15 nm diameter) ever formed with the zinc-blende structure have been synthesized at a high reaction temperature of 310 degrees C, in contrast to previous reports suggesting the formation of zinc-blende CdS only in the small size limit (< 4.5 nm) or at a lower reaction temperature (<= 240 degrees C). Theoretical analysis establishes that the binding energy of trioctylphosphine molecules on the (001) surface of zinc-blende CdS is significantly larger than that for any of the wurtzite planes. Consequently, trioctylphosphine as a capping agent stabilizes the zinc-blende phase via influencing the surface energy that plays an important role in the overall energetics of a nanocrystal. Besides achieving giant zinc-blende CdS nanocrystals, this new understanding allows us to prepare CdSe and CdSe/CdS core/shell nanocrystals in the zinc-blende structure.