Secure Computation in a Bidirectional Relay

Bidirectional relaying, where a relay helps two user nodes to exchange equal length binary messages, has been an active area of recent research. A popular strategy involves a modified Gaussian MAC, where the relay decodes the XOR of the two messages using the naturally-occurring sum of symbols simultaneously transmitted by user nodes. In this work, we consider the Gaussian MAC in bidirectional relaying with an additional secrecy constraint for protection against a honest but curious relay. The constraint is that, while the relay should decode the XOR, it should be fully ignorant of the individual messages of the users. We exploit the symbol addition that occurs in a Gaussian MAC to design explicit strategies that achieve perfect independence between the received symbols and individual transmitted messages. Our results actually hold for a more general scenario where the messages at the two user nodes come from a finite Abelian group G, and the relay must decode the sum within G of the two messages. We provide a lattice coding strategy and study optimal rate versus average power trade-offs for asymptotically large dimensions.

Wave propagation in a porous composite beam: Porosity determination, location and quantification

A wave-based method is developed to quantify the defect due to porosity and also to locate the porous regions, in a composite beam-type structure. Wave propagation problem for a porous laminated composite beam is modeled using spectral finite element method (SFEM), based on the modified rule of mixture approach, which is used to include the effect of porosity on the stiffness and density of the composite beam structure. The material properties are obtained from the modified rule of mixture model, which are used in a conventional SFEM to develop a new model for solving wave propagation problems in porous laminated composite beam. The influence of the porosity content on the group speed and also the effect of variation in theses parameters on the time responses are studied first, in the forward problem. The change in the time responses with the change in the porosity of the structure is used as a parameter to find the porosity content in a composite beam. The actual measured response from a structure and the numerically obtained time responses are used for the estimation of porosity, by solving a nonlinear optimization problem. The effect of the length of the porous region (in the propagation direction), on the time responses, is studied. The damage force indicator technique is used to locate the porous region in a beam and also to find its length, using the measured wave propagation responses. (C) 2012 Elsevier Ltd. All rights reserved.

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.

Engagement of CF3 Group in N-H center dot center dot center dot F-C Hydrogen Bond in the Solution State: NMR Spectroscopy and MD Simulation Studies

Unambiguous evidence for the engagement of CF3 group in N-H center dot center dot center dot F-C hydrogen bond in a low polarity solvent, the first observation of its kind, is reported. The presence of such weak molecular interactions in the solution state is convincingly established by one and two-dimensional H-1, F-19, and natural abundant N-15 NMR spectroscopic studies. The strong and direct evidence is derived by the observation of through-space couplings, such as, (1h)J(FH), (1h)J(FN), and (2h)J(FF), where the spin polarization is transmitted through hydrogen bond. In an interesting example of a molecule containing two CF3 groups getting simultaneously involved in hydrogen bond, where hydrogen bond mediated couplings are not reflected in the NMR spectrum, F-19-F-19 NOESY experiment yielded confirmatory evidence. Significant deviations in the strengths of (1)J(NH), variable temperature, and the solvent induced perturbations yielded additional support. The NMR results are corroborated by both DFT calculations and MD simulations, where the quantitative information on different ways of involvement of fluorine in two and three centered hydrogen bonds, their percentage of occurrences, and geometries have been obtained. The hydrogen bond interaction energies have also been calculated.

Selective excitation and detection of maximum quantum coherence of a group of scalar coupled protons in chiral molecules: an NMR experiment for enantiodiscrimination

The H-1 NMR spectroscopic discrimination of enantiomers in the solution state and the measurement of enantiomeric composition is most often hindered due to either very small chemical shift differences between the discriminated peaks or severe overlap of transitions from other chemically non-equivalent protons. In addition the use of chiral auxiliaries such as, crown ether and chiral lanthanide shift reagent may often cause enormous line broadening or give little degree of discrimination beyond the crown ether substrate ratio, hampering the discrimination. In circumventing such problems we are proposing the utilization of the difference in the additive values of all the chemical shifts of a scalar coupled spin system. The excitation and detection of appropriate highest quantum coherence yields the measurable difference in the frequencies between two transitions, one pertaining to each enantiomer in the maximum quantum dimension permitting their discrimination and the F-2 cross section at each of these frequencies yields an enantiopure spectrum. The advantage of the utility of the proposed method is demonstrated on several chiral compounds where the conventional one dimensional H-1 NMR spectra fail to differentiate the enantiomers.

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.

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.

Spectral-envelope and group-delay models for transient signals—applications to castanets and stop consonants

We present a novel approach to represent transients using spectral-domain amplitude-modulated/frequency -modulated (AM-FM) functions. The model is applied to the real and imaginary parts of the Fourier transform (FT) of the transient. The suitability of the model lies in the observation that since transients are well-localized in time, the real and imaginary parts of the Fourier spectrum have a modulation structure. The spectral AM is the envelope and the spectral FM is the group delay function. The group delay is estimated using spectral zero-crossings and the spectral envelope is estimated using a coherent demodulator. We show that the proposed technique is robust to additive noise. We present applications of the proposed technique to castanets and stop-consonants in speech.

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.

Spectral-envelope-group-delay models for transients

Transient signals such as plosives in speech or Castanets in audio do not have a specific modulation or periodic structure in time domain. However, in the spectral domain they exhibit a prominent modulation structure, which is a direct consequence of their narrow time localization. Based on this observation, a spectral-domain AM-FM model for transients is proposed. The spectral AM-FM model is built starting from real spectral zero-crossings. The AM and FM correspond to the spectral envelope (SE) and group delay (GD), respectively. Taking into account the modulation structure and spectral continuity, a local polynomial regression technique is proposed to estimate the GD function from the real spectral zeros. The SE is estimated based on the phase function computed from the estimated GD. Since the GD estimation is parametric, the degree of smoothness can be controlled directly. Simulation results based on synthetic transient signals generated using a beta density function are presented to analyze the noise-robustness of the SEGD model. Three specific applications are considered: (1) SEGD based modeling of Castanet sounds; (2) appropriateness of the model for transient compression; and (3) determining glottal closure instants in speech using a short-time SEGD model of the linear prediction residue.