Non-Stationary Semi-Markov Decision Processes on a Finite Horizon

We introduce and study a class of non-stationary semi-Markov decision processes on a finite horizon. By constructing an equivalent Markov decision process, we establish the existence of a piecewise open loop relaxed control which is optimal for the finite horizon problem.

Rainbow connectivity: hardness and tractability

A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices. The (strong) rainbow connectivity of a graph G, denoted by (src(G), respectively) rc(G) is the smallest number of colors required to edge color the graph such that G is (strongly) rainbow connected. In this paper we study the rainbow connectivity problem and the strong rainbow connectivity problem from a computational point of view. Our main results can be summarised as below: 1) For every fixed k >= 3, it is NP-Complete to decide whether src(G) <= k even when the graph G is bipartite. 2) For every fixed odd k >= 3, it is NP-Complete to decide whether rc(G) <= k. This resolves one of the open problems posed by Chakraborty et al. (J. Comb. Opt., 2011) where they prove the hardness for the even case. 3) The following problem is fixed parameter tractable: Given a graph G, determine the maximum number of pairs of vertices that can be rainbow connected using two colors. 4) For a directed graph G, it is NP-Complete to decide whether rc(G) <= 2.

Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems

An operator-splitting finite element method for solving high-dimensional parabolic equations is presented. The stability and the error estimates are derived for the proposed numerical scheme. Furthermore, two variants of fully-practical operator-splitting finite element algorithms based on the quadrature points and the nodal points, respectively, are presented. Both the quadrature and the nodal point based operator-splitting algorithms are validated using a three-dimensional (3D) test problem. The numerical results obtained with the full 3D computations and the operator-split 2D + 1D computations are found to be in a good agreement with the analytical solution. Further, the optimal order of convergence is obtained in both variants of the operator-splitting algorithms. (C) 2012 Elsevier Inc. All rights reserved.

A method of designing seamless connectivity algorithm in ubiquitous networks

The b-phase of polyvinylidene fluoride (PVDF) is well known for its piezoelectric properties. PVDF films have been developed using solvent cast method. The films thus produced are in a-phase. The a-phase is transformed to piezoelectric b-phase when the film is hotstretched with various different stretching factors at various different temperatures. The films are then characterized in terms of their mechanical properties and surface morphological changes during the transformation from a- to b-phases by using X-ray diffraction, differential scanning calorimeter, Raman spectra, Infrared spectra, tensile testing, and scanning electron microscopy. The films showed increased crystallinity with stretching at temperature up to 808C. The optimum conditions to achieve b-phase have been discussed in detail. The fabricated PVDF sensors have been tested for free vibration and impact on plate structure, and its response is compared with conventional piezoelectric wafer type sensor. The resonant and antiresonant peaks in the frequency response of PVDF sensor match well with that of lead zirconate titanate wafer sensors. Effective piezoelectric properties and the variations in the frequency response spectra due to free vibration and impact loading conditions are reported. POLYM. ENG. SCI., 00:000–000, 2012. ª2012 Society of Plastics Engineers

On the capacity of quantized gaussian MAC channels with finite input alphabet

In this paper, we investigate the achievable rate region of Gaussian multiple access channels (MAC) with finite input alphabet and quantized output. With finite input alphabet and an unquantized receiver, the two-user Gaussian MAC rate region was studied. In most high throughput communication systems based on digital signal processing, the analog received signal is quantized using a low precision quantizer. In this paper, we first derive the expressions for the achievable rate region of a two-user Gaussian MAC with finite input alphabet and quantized output. We show that, with finite input alphabet, the achievable rate region with the commonly used uniform receiver quantizer has a significant loss in the rate region compared. It is observed that this degradation is due to the fact that the received analog signal is densely distributed around the origin, and is therefore not efficiently quantized with a uniform quantizer which has equally spaced quantization intervals. It is also observed that the density of the received analog signal around the origin increases with increasing number of users. Hence, the loss in the achievable rate region due to uniform receiver quantization is expected to increase with increasing number of users. We, therefore, propose a novel non-uniform quantizer with finely spaced quantization intervals near the origin. For a two-user Gaussian MAC with a given finite input alphabet and low precision receiver quantization, we show that the proposed non-uniform quantizer has a significantly larger rate region compared to what is achieved with a uniform quantizer.

Optimal forwarding in delay tolerant networks with multiple destinations

We study the trade-off between delivery delay and energy consumption in a delay tolerant network in which a message (or a file) has to be delivered to each of several destinations by epidemic relaying. In addition to the destinations, there are several other nodes in the network that can assist in relaying the message. We first assume that, at every instant, all the nodes know the number of relays carrying the packet and the number of destinations that have received the packet. We formulate the problem as a controlled continuous time Markov chain and derive the optimal closed loop control (i.e., forwarding policy). However, in practice, the intermittent connectivity in the network implies that the nodes may not have the required perfect knowledge of the system state. To address this issue, we obtain an ODE (i.e., fluid) approximation for the optimally controlled Markov chain. This fluid approximation also yields an asymptotically optimal open loop policy. Finally, we evaluate the performance of the deterministic policy over finite networks. Numerical results show that this policy performs close to the optimal closed loop policy.

A finite-rate-of-innovation signal sampling perspective of the source-filter model of speech production

We consider the speech production mechanism and the asso- ciated linear source-filter model. For voiced speech sounds in particular, the source/glottal excitation is modeled as a stream of impulses and the filter as a cascade of second-order resonators. We show that the process of sampling speech signals can be modeled as filtering a stream of Dirac impulses (a model for the excitation) with a kernel function (the vocal tract response),and then sampling uniformly. We show that the problem of esti- mating the excitation is equivalent to the problem of recovering a stream of Dirac impulses from samples of a filtered version. We present associated algorithms based on the annihilating filter and also make a comparison with the classical linear prediction technique, which is well known in speech analysis. Results on synthesized as well as natural speech data are presented.

A Novel Power Allocation Scheme for Two-User GMAC with Finite Input Constellations

Constellation Constrained (CC) capacity regions of two-user Gaussian Multiple Access Channels (GMAC) have been recently reported, wherein an appropriate angle of rotation between the constellations of the two users is shown to enlarge the CC capacity region. We refer to such a scheme as the Constellation Rotation (CR) scheme. In this paper, we propose a novel scheme called the Constellation Power Allocation (CPA) scheme, wherein the instantaneous transmit power of the two users are varied by maintaining their average power constraints. We show that the CPA scheme offers CC sum capacities equal (at low SNR values) or close (at high SNR values) to those offered by the CR scheme with reduced decoding complexity for QAM constellations. We study the robustness of the CPA scheme for random phase offsets in the channel and unequal average power constraints for the two users. With random phase offsets in the channel, we show that the CC sum capacity offered by the CPA scheme is more than the CR scheme at high SNR values. With unequal average power constraints, we show that the CPA scheme provides maximum gain when the power levels are close, and the advantage diminishes with the increase in the power difference.

A Finite Element Method Based Approach for Evaluating the Sensitivity of Faraday-Type Electromagnetic Flow Meter for Liquid Sodium Flow

Faraday-type electromagnetic flow meters are employed for measuring the flow rate of liquid sodium in fast breeder reactors. The calibration of such flow meters, owing to the required elaborative arrangements is rather difficult. On the other hand, theoretical approach requires solution of two coupled electromagnetic partial differential equation with profile of the flow and applied magnetic field as the inputs. This is also quite involved due to the 3D nature of the problem. Alternatively, Galerkin finite element method based numerical solution is suggested in the literature as an attractive option for the required calibration. Based on the same, a computer code in Matlab platform has been developed in this work with both 20 and 27 node brick elements. The boundary conditions are correctly defined and several intermediate validation exercises are carried out. Finally it is shown that the sensitivities predicted by the code for flow meters of four different dimensions agrees well with the results given by analytical expression, thereby providing strong validation. Sensitivity for higher flow rates, for which analytical approach does not exist, is shown to decrease with increase in flow velocity.

Bearing capacity of two interfering strip footings from lower bound finite elements limit analysis

A rigorous lower bound solution, with the usage of the finite elements limit analysis, has been obtained for finding the ultimate bearing capacity of two interfering strip footings placed on a sandy medium. Smooth as well as rough footingsoil interfaces are considered in the analysis. The failure load for an interfering footing becomes always greater than that for a single isolated footing. The effect of the interference on the failure load (i) for rough footings becomes greater than that for smooth footings, (ii) increases with an increase in phi, and (iii) becomes almost negligible beyond S/B>3. Compared with various theoretical and experimental results reported in literature, the present analysis generally provides the lowest magnitude of the collapse load. Copyright (c) 2011 John Wiley & Sons, Ltd.

An Outward-Wave-Favouring Finite Element-Based Strategy for Exterior Acoustical Problems

This work presents a finite element-based strategy for exterior acoustical problems based on an assumed pressure form that favours outgoing waves. The resulting governing equation, weak formulation, and finite element formulation are developed both for coupled and uncoupled problems. The developed elements are very similar to conventional elements in that they are based on the standard Galerkin variational formulation and use standard Lagrange interpolation functions and standard Gaussian quadrature. In addition and in contrast to wave envelope formulations and their extensions, the developed elements can be used in the immediate vicinity of the radiator/scatterer. The method is similar to the perfectly matched layer (PML) method in the sense that each layer of elements added around the radiator absorbs acoustical waves so that no boundary condition needs to be applied at the outermost boundary where the domain is truncated. By comparing against strategies such as the PML and wave-envelope methods, we show that the relative accuracy, both in the near and far-field results, is considerably higher.

Chapman-Enskog analysis for finite-volume formulation of lattice Boltzmann equation

The classical Chapman-Enskog expansion is performed for the recently proposed finite-volume formulation of lattice Boltzmann equation (LBE) method D.V. Patil, K.N. Lakshmisha, Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh, J. Comput. Phys. 228 (2009) 5262-5279]. First, a modified partial differential equation is derived from a numerical approximation of the discrete Boltzmann equation. Then, the multi-scale, small parameter expansion is followed to recover the continuity and the Navier-Stokes (NS) equations with additional error terms. The expression for apparent value of the kinematic viscosity is derived for finite-volume formulation under certain assumptions. The attenuation of a shear wave, Taylor-Green vortex flow and driven channel flow are studied to analyze the apparent viscosity relation.

Rapid mass spectrometric determination of disulfide connectivity in peptides and proteins

Disulfide crosslinks are ubiquitous in natural peptides and proteins, providing rigidity to polypeptide scaffolds. The assignment of disulfide connectivity in multiple crosslinked systems is often difficult to achieve. Here, we show that rapid unambiguous characterisation of disulfide connectivity can be achieved through direct mass spectrometric CID fragmentation of the disulfide intact polypeptides. The method requires a direct mass spectrometric fragmentation of the native disulfide bonded polypeptides and subsequent analysis using a newly developed program, DisConnect. Technical difficulties involving direct fragmentation of proteins are surmounted by an initial proteolytic nick and subsequent determination of the structures of these proteolytic peptides through DisConnect. While the connectivity in proteolytic fragments containing one cystine is evident from the MS profile alone, those with multiple cystines are subjected to subsequent mass spectrometric fragmentation. The wide applicability of this method is illustrated using examples of peptide hormones, peptide toxins, proteins, and disulfide foldamers of a synthetic analogue of a marine peptide toxin. The method, coupled with DisConnect, provides an unambiguous, straightforward approach, especially useful for the rapid screening of the disulfide crosslink fidelity in recombinant proteins, determination of disulfide linkages in natural peptide toxins and characterization of folding intermediates encountered in oxidative folding pathways.

A multichannel sampling method for 2-D finite-rate-of-innovation signals

We address the problem of sampling and reconstruction of two-dimensional (2-D) finite-rate-of-innovation (FRI) signals. We propose a three-channel sampling method for efficiently solving the problem. We consider the sampling of a stream of 2-D Dirac impulses and a sum of 2-D unit-step functions. We propose a 2-D causal exponential function as the sampling kernel. By causality in 2-D, we mean that the function has its support restricted to the first quadrant. The advantage of using a multichannel sampling method with causal exponential sampling kernel is that standard annihilating filter or root-finding algorithms are not required. Further, the proposed method has inexpensive hardware implementation and is numerically stable as the number of Dirac impulses increases.

Wave propagation in stiffened structures using spectrally formulated finite element

In this work, the wave propagation analysis of built-up composite structures is performed using frequency domain spectral finite elements, to study the high frequency wave responses. The paper discusses basically two methods for modeling stiffened structures. In the first method, the concept of assembly of 2D spectral plate elements is used to model a built-up structure. In the second approach, spectral finite element method (SFEM) model is developed to model skin-stiffener structures, where the skin is considered as plate element and the stiffener as beam element. The SFEM model developed using the plate-beam coupling approach is then used to model wave propagation in a multiple stiffened structure and also extended to model the stiffened structures with different cross sections such as T-section, I-section and hat section. A number of parametric studies are performed to capture the mode coupling, that is, the flexural-axial coupling present in the wave responses.