DMT of parallel-path and layered networks under the half-duplex constraint

In this paper, we study the diversity-multiplexing-gain tradeoff (DMT) of wireless relay networks under the half-duplex constraint. It is often unclear what penalty if any, is imposed by the half-duplex constraint on the DMT of such networks. We study two classes of networks; the first class, called KPP(I) networks, is the class of networks with the relays organized in K parallel paths between the source and the destination. While we assume that there is no direct source-destination path, the K relaying paths can interfere with each other. The second class, termed as layered networks, is comprised of relays organized in layers, where links exist only between adjacent layers. We present a communication scheme based on static schedules and amplify-and-forward relaying for these networks. We also show that for KPP(I) networks with K >= 3, the proposed schemes can achieve full-duplex DMT performance, thus demonstrating that there is no performance hit on the DMT due to the half-duplex constraint. We also show that, for layered networks, a linear DMT of d(max)(1 - r)(+) between the maximum diversity d(max) and the maximum MG, r(max) = 1 is achievable. We adapt existing DMT optimal coding schemes to these networks, thus specifying the end-to-end communication strategy explicitly.

Exact internal controllability for a hyperbolic problem in a domain with highly oscillating boundary

In this paper, by using the Hilbert Uniqueness Method (HUM), we study the exact controllability problem described by the wave equation in a three-dimensional horizontal domain bounded at the bottom by a smooth wall and at the top by a rough wall. The latter is assumed to consist in a plane wall covered with periodically distributed asperities whose size depends on a small parameter epsilon > 0, and with a fixed height. Our aim is to obtain the exact controllability for the homogenized equation. In the process, we study the asymptotic analysis of wave equation in two setups, namely solution by standard weak formulation and solution by transposition method.

Analysis of an queue operated under the FCFS policy with exact admission control

In this article, we present an exact theoretical analysis of an system, with arbitrary distribution of relative deadline for the end of service, operated under the first come first served scheduling policy with exact admission control. We provide an explicit solution to the functional equation that must be satisfied by the workload distribution, when the system reaches steady state. We use this solution to derive explicit expressions for the loss ratio and the sojourn time distribution. Finally, we compare this loss ratio with that of a similar system operating without admission control, in the cases of some common distributions of the relative deadline.

A Nearly Exact Reformulation of the Girsanov Linearization for Stochastically Driven Nonlinear Oscillators

The Girsanov linearization method (GLM), proposed earlier in Saha, N., and Roy, D., 2007, ``The Girsanov Linearisation Method for Stochastically Driven Nonlinear Oscillators,'' J. Appl. Mech., 74, pp. 885-897, is reformulated to arrive at a nearly exact, semianalytical, weak and explicit scheme for nonlinear mechanical oscillators under additive stochastic excitations. At the heart of the reformulated linearization is a temporally localized rejection sampling strategy that, combined with a resampling scheme, enables selecting from and appropriately modifying an ensemble of locally linearized trajectories while weakly applying the Girsanov correction (the Radon-Nikodym derivative) for the linearization errors. The semianalyticity is due to an explicit linearization of the nonlinear drift terms and it plays a crucial role in keeping the Radon-Nikodym derivative ``nearly bounded'' above by the inverse of the linearization time step (which means that only a subset of linearized trajectories with low, yet finite, probability exceeds this bound). Drift linearization is conveniently accomplished via the first few (lower order) terms in the associated stochastic (Ito) Taylor expansion to exclude (multiple) stochastic integrals from the numerical treatment. Similarly, the Radon-Nikodym derivative, which is a strictly positive, exponential (super-) martingale, is converted to a canonical form and evaluated over each time step without directly computing the stochastic integrals appearing in its argument. Through their numeric implementations for a few low-dimensional nonlinear oscillators, the proposed variants of the scheme, presently referred to as the Girsanov corrected linearization method (GCLM), are shown to exhibit remarkably higher numerical accuracy over a much larger range of the time step size than is possible with the local drift-linearization schemes on their own.

Transmit power Control with ARQ in energy harvesting sensors: a decision-theoretic approach

This paper addresses the problem of finding optimal power control policies for wireless energy harvesting sensor (EHS) nodes with automatic repeat request (ARQ)-based packet transmissions. The EHS harvests energy from the environment according to a Bernoulli process; and it is required to operate within the constraint of energy neutrality. The EHS obtains partial channel state information (CSI) at the transmitter through the link-layer ARQ protocol, via the ACK/NACK feedback messages, and uses it to adapt the transmission power for the packet (re)transmission attempts. The underlying wireless fading channel is modeled as a finite state Markov chain with known transition probabilities. Thus, the goal of the power management policy is to determine the best power setting for the current packet transmission attempt, so as to maximize a long-run expected reward such as the expected outage probability. The problem is addressed in a decision-theoretic framework by casting it as a partially observable Markov decision process (POMDP). Due to the large size of the state-space, the exact solution to the POMDP is computationally expensive. Hence, two popular approximate solutions are considered, which yield good power management policies for the transmission attempts. Monte Carlo simulation results illustrate the efficacy of the approach and show that the approximate solutions significantly outperform conventional approaches.

Reaction dynamics under confinement: an exact path integral treatment of a two-stage model of stochastic gene expression

Gene expression in living systems is inherently stochastic, and tends to produce varying numbers of proteins over repeated cycles of transcription and translation. In this paper, an expression is derived for the steady-state protein number distribution starting from a two-stage kinetic model of the gene expression process involving p proteins and r mRNAs. The derivation is based on an exact path integral evaluation of the joint distribution, P(p, r, t), of p and r at time t, which can be expressed in terms of the coupled Langevin equations for p and r that represent the two-stage model in continuum form. The steady-state distribution of p alone, P(p), is obtained from P(p, r, t) (a bivariate Gaussian) by integrating out the r degrees of freedom and taking the limit t -> infinity. P(p) is found to be proportional to the product of a Gaussian and a complementary error function. It provides a generally satisfactory fit to simulation data on the same two-stage process when the translational efficiency (a measure of intrinsic noise levels in the system) is relatively low; it is less successful as a model of the data when the translational efficiency (and noise levels) are high.

Impact angle constraint guidance law using cubic splines for intercepting stationary targets

In this paper the cubic spline guidance law is presented for intercepting a stationary target at a desired impact angle. The guidance law is obtained from cubic spline curve based trajectory using an inverse method. The cubic spline t rajectory curve expresses the altitude as a cubic polynomial of the downrange. The guidance law is modified to achieve interception in the cases where impact angle is greater that or equal to 90◦. The guidance law is implemented in a feedback mode to maintain the desired impact angle and to reduce miss distance in the presence of lateral acceleration saturation and atmospheric distur- bances. The simulation results show that the guidance law fulfills all the requirements.

Exact Solution of the PPP Model for Correlated Electronic States of Tetracene and Substituted Tetracene

Tetracene is an important conjugated molecule for device applications. We have used the diagrammatic valence bond method to obtain the desired states, in a Hilbert space of about 450 million singlets and 902 million triplets. We have also studied the donor/acceptor (D/A)-substituted tetracenes with D and A groups placed symmetrically about the long axis of the molecule. In these cases, by exploiting a new symmetry, which is a combination of C-2 symmetry and electron-hole symmetry, we are able to obtain their low-lying states. In the case of substituted tetracene, we find that optically allowed one-photon excitation gaps reduce with increasing D/A strength, while the lowest singlet triplet gap is only wealdy affected. In all the systems we have studied, the excited singlet state, S-i, is at more than twice the energy of the lowest triplet state and the second triplet is very close to the S-1 state. Thus, donor-acceptor-substituted tetracene could be a good candidate in photovoltaic device application as it satisfies energy criteria for singlet fission. We have also obtained the model exact second harmonic generation (SHG) coefficients using the correction vector method, and we find that the SHG responses increase with the increase in D/A strength.

MAXIMUM A-POSTERIORI ESTIMATION OF MISSING SAMPLES WITH CONTINUITY CONSTRAINT IN ELECTROMAGNETIC ARTICULOGRAPHY DATA

Electromagnetic Articulography (EMA) technique is used to record the kinematics of different articulators while one speaks. EMA data often contains missing segments due to sensor failure. In this work, we propose a maximum a-posteriori (MAP) estimation with continuity constraint to recover the missing samples in the articulatory trajectories recorded using EMA. In this approach, we combine the benefits of statistical MAP estimation as well as the temporal continuity of the articulatory trajectories. Experiments on articulatory corpus using different missing segment durations show that the proposed continuity constraint results in a 30% reduction in average root mean squared error in estimation over statistical estimation of missing segments without any continuity constraint.

Solving Dynamic Constraint Single Objective Functions using a Nature Inspired Technique

We present in this paper a new algorithm based on Particle Swarm Optimization (PSO) for solving Dynamic Single Objective Constrained Optimization (DCOP) problems. We have modified several different parameters of the original particle swarm optimization algorithm by introducing new types of particles for local search and to detect changes in the search space. The algorithm is tested with a known benchmark set and compare with the results with other contemporary works. We demonstrate the convergence properties by using convergence graphs and also the illustrate the changes in the current benchmark problems for more realistic correspondence to practical real world problems.

Exact Phase Retrieval for a Class of 2-D Parametric Signals

We address the problem of two-dimensional (2-D) phase retrieval from magnitude of the Fourier spectrum. We consider 2-D signals that are characterized by first-order difference equations, which have a parametric representation in the Fourier domain. We show that, under appropriate stability conditions, such signals can be reconstructed uniquely from the Fourier transform magnitude. We formulate the phase retrieval problem as one of computing the parameters that uniquely determine the signal. We show that the problem can be solved by employing the annihilating filter method, particularly for the case when the parameters are distinct. For the more general case of the repeating parameters, the annihilating filter method is not applicable. We circumvent the problem by employing the algebraically coupled matrix pencil (ACMP) method. In the noiseless measurement setup, exact phase retrieval is possible. We also establish a link between the proposed analysis and 2-D cepstrum. In the noisy case, we derive Cramer-Rao lower bounds (CRLBs) on the estimates of the parameters and present Monte Carlo performance analysis as a function of the noise level. Comparisons with state-of-the-art techniques in terms of signal reconstruction accuracy show that the proposed technique outperforms the Fienup and relaxed averaged alternating reflections (RAAR) algorithms in the presence of noise.

An Improved Outer Bound on the Storage-Repair-Bandwidth Tradeoff of Exact-Repair Regenerating Codes

While the tradeoff between the amount of data stored and the repair bandwidth of an (n, k, d) regenerating code has been characterized under functional repair (FR), the case of exact repair (ER) remains unresolved. It is known that there do not exist ER codes which lie on the FR tradeoff at most of the points. The question as to whether one can asymptotically approach the FR tradeoff was settled recently by Tian who showed that in the (4, 3, 3) case, the ER region is bounded away from the FR region. The FR tradeoff serves as a trivial outer bound on the ER tradeoff. In this paper, we extend Tian's results by establishing an improved outer bound on the ER tradeoff which shows that the ER region is bounded away from the FR region, for any (n; k; d). Our approach is analytical and builds upon the framework introduced earlier by Shah et. al. Interestingly, a recently-constructed, layered regenerating code is shown to achieve a point on this outer bound for the (5, 4, 4) case. This represents the first-known instance of an optimal ER code that does not correspond to a point on the FR tradeoff.

Layered Exact-Repair Regenerating Codes via Embedded Error Correction and Block Designs

A new class of exact-repair regenerating codes is constructed by stitching together shorter erasure correction codes, where the stitching pattern can be viewed as block designs. The proposed codes have the help-by-transfer property where the helper nodes simply transfer part of the stored data directly, without performing any computation. This embedded error correction structure makes the decoding process straightforward, and in some cases the complexity is very low. We show that this construction is able to achieve performance better than space-sharing between the minimum storage regenerating codes and the minimum repair-bandwidth regenerating codes, and it is the first class of codes to achieve this performance. In fact, it is shown that the proposed construction can achieve a nontrivial point on the optimal functional-repair tradeoff, and it is asymptotically optimal at high rate, i.e., it asymptotically approaches the minimum storage and the minimum repair-bandwidth simultaneously.

A Simple Label Switching Algorithm for Semisupervised Structural SVMs

In structured output learning, obtaining labeled data for real-world applications is usually costly, while unlabeled examples are available in abundance. Semisupervised structured classification deals with a small number of labeled examples and a large number of unlabeled structured data. In this work, we consider semisupervised structural support vector machines with domain constraints. The optimization problem, which in general is not convex, contains the loss terms associated with the labeled and unlabeled examples, along with the domain constraints. We propose a simple optimization approach that alternates between solving a supervised learning problem and a constraint matching problem. Solving the constraint matching problem is difficult for structured prediction, and we propose an efficient and effective label switching method to solve it. The alternating optimization is carried out within a deterministic annealing framework, which helps in effective constraint matching and avoiding poor local minima, which are not very useful. The algorithm is simple and easy to implement. Further, it is suitable for any structured output learning problem where exact inference is available. Experiments on benchmark sequence labeling data sets and a natural language parsing data set show that the proposed approach, though simple, achieves comparable generalization performance.

Towards an exact factorization of the molecular wave function

An exact single-product factorisation of the molecular wave function for the timedependent Schrodinger equation is investigated by using an ansatz involving a phasefactor. By using the Frenkel variational method, we obtain the Schrodinger equations for the electronic and nuclear wave functions. The concept of a potential energy surface (PES) is retained by introducing a modified Hamiltonian as suggested earlier by Cederbaum. The parameter in the phase factor is chosen such that the equations of motion retain the physically appealing Born- Oppenheimer-like form, and is therefore unique.