Linear Transceiver Design for an Amplify-and-Forward Relay Based on the MBER Criterion

A design methodology based on the Minimum Bit Error Ratio (MBER) framework is proposed for a non-regenerative Multiple-Input Multiple-Output (MIMO) relay-aided system to determine various linear parameters. We consider both the Relay-Destination (RD) as well as the Source-Relay-Destination (SRD) link design based on this MBER framework, including the pre-coder, the Amplify-and-Forward (AF) matrix and the equalizer matrix of our system. It has been shown in the previous literature that MBER based communication systems are capable of reducing the Bit-Error-Ratio (BER) compared to their Linear Minimum Mean Square Error (LMMSE) based counterparts. We design a novel relay-aided system using various signal constellations, ranging from QPSK to the general M-QAM and M-PSK constellations. Finally, we propose its sub-optimal versions for reducing the computational complexity imposed. Our simulation results demonstrate that the proposed scheme indeed achieves a significant BER reduction over the existing LMMSE scheme.

TIME VARYING LINEAR PREDICTION USING SPARSITY CONSTRAINTS

Time-varying linear prediction has been studied in the context of speech signals, in which the auto-regressive (AR) coefficients of the system function are modeled as a linear combination of a set of known bases. Traditionally, least squares minimization is used for the estimation of model parameters of the system. Motivated by the sparse nature of the excitation signal for voiced sounds, we explore the time-varying linear prediction modeling of speech signals using sparsity constraints. Parameter estimation is posed as a 0-norm minimization problem. The re-weighted 1-norm minimization technique is used to estimate the model parameters. We show that for sparsely excited time-varying systems, the formulation models the underlying system function better than the least squares error minimization approach. Evaluation with synthetic and real speech examples show that the estimated model parameters track the formant trajectories closer than the least squares approach.

Linear Index Coding and Representable Discrete Polymatroids

Discrete polymatroids are the multi-set analogue of matroids. In this paper, we explore the connections between linear index coding and representable discrete polymatroids. The index coding problem involves a sender which generates a set of messages X = {x(1), x(2), ... x(k)} and a set of receivers R which demand messages. A receiver R is an element of R is specified by the tuple (x, H) where x. X is the message demanded by R and H subset of X \textbackslash {x} is the side information possessed by R. It is first shown that a linear solution to an index coding problem exists if and only if there exists a representable discrete polymatroid satisfying certain conditions which are determined by the index coding problem considered. El Rouayheb et. al. showed that the problem of finding a multi-linear representation for a matroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that matroid. Multi-linear representation of a matroid can be viewed as a special case of representation of an appropriate discrete polymatroid. We generalize the result of El Rouayheb et. al. by showing that the problem of finding a representation for a discrete polymatroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that discrete polymatroid.

On linear series and a conjecture of D. C. Butler

Let C be a smooth irreducible projective curve of genus g and L a line bundle of degree d generated by a linear subspace V of H-0 (L) of dimension n+1. We prove a conjecture of D. C. Butler on the semistability of the kernel of the evaluation map V circle times O-C -> L and obtain new results on the stability of this kernel. The natural context for this problem is the theory of coherent systems on curves and our techniques involve wall crossing formulae in this theory.

Conservation Properties of the Trapezoidal Rule in Linear Time Domain Analysis of Acoustics and Structures

The trapezoidal rule, which is a special case of the Newmark family of algorithms, is one of the most widely used methods for transient hyperbolic problems. In this work, we show that this rule conserves linear and angular momenta and energy in the case of undamped linear elastodynamics problems, and an ``energy-like measure'' in the case of undamped acoustic problems. These conservation properties, thus, provide a rational basis for using this algorithm. In linear elastodynamics problems, variants of the trapezoidal rule that incorporate ``high-frequency'' dissipation are often used, since the higher frequencies, which are not approximated properly by the standard displacement-based approach, often result in unphysical behavior. Instead of modifying the trapezoidal algorithm, we propose using a hybrid finite element framework for constructing the stiffness matrix. Hybrid finite elements, which are based on a two-field variational formulation involving displacement and stresses, are known to approximate the eigenvalues much more accurately than the standard displacement-based approach, thereby either bypassing or reducing the need for high-frequency dissipation. We show this by means of several examples, where we compare the numerical solutions obtained using the displacement-based and hybrid approaches against analytical solutions.

A micropolar peridynamic theory in linear elasticity

A state-based micropolar peridynamic theory for linear elastic solids is proposed. The main motivation is to introduce additional micro-rotational degrees of freedom to each material point and thus naturally bring in the physically relevant material length scale parameters into peridynamics. Non-ordinary type modeling via constitutive correspondence is adopted here to define the micropolar peridynamic material. Along with a general three dimensional model, homogenized one dimensional Timoshenko type beam models for both the proposed micropolar and the standard non-polar peridynamic variants are derived. The efficacy of the proposed models in analyzing continua with length scale effects is established via numerical simulations of a few beam and plane-stress problems. (C) 2015 Elsevier Ltd. All rights reserved.

Optimal Linear Glauber Model

Contrary to the actual nonlinear Glauber model, the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition rate () in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. The advantage of this work is that, by studying the LGM analytically, we will be able to anticipate how the kinetic properties of an arbitrary Ising system depend on the temperature and the coupling constants. The analytical expressions for the optimal values of the parameters involved in the linear are obtained using a simple Moore-Penrose pseudoinverse matrix. This approach is quite general, in principle applicable to any system and can reproduce the exact results for one dimensional Ising system. In the continuum limit, we get a linear time-dependent Ginzburg-Landau equation from the Glauber's microscopic model of non-conservative dynamics. We analyze the critical and dynamic properties of the model, and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach. We will also show in this paper that the effect of magnetic field can easily be studied within our approach; in particular, we show that the inverse of relaxation time changes quadratically with (weak) magnetic field and that the fluctuation-dissipation theorem is valid for our model.

A Polymatroid Approach to Separable Convex Optimization with Linear Ascending Constraints

We revisit a problem studied by Padakandla and Sundaresan SIAM J. Optim., August 2009] on the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation problems in wireless communication settings. It is also a special case of an optimization of a separable convex function over the bases of a specially structured polymatroid. We give an alternative proof of the correctness of the algorithm of Padakandla and Sundaresan. In the process we relax some of their restrictions placed on the objective function.

Alternative Formulation of the Discrete Linear Quadratic Regulator (DLQR)

In this paper, an alternative apriori and aposteriori formulation has been derived for the discrete linear quadratic regulator (DLQR) in a manner analogous to that used in the discrete Kalman filter. It has been shown that the formulation seamlessly fits into the available formulation of the DLQR and the equivalent terms in the existing formulation and the proposed formulation have been identified. Thereafter, the significance of this alternative formulation has been interpreted in terms of the sensitivity of the controller performances to any changes in the states or to changes in the control inputs. The implications of this alternative formulation to adaptive controller tuning have also been discussed.

On the Bounds of Certain Maximal Linear Codes in a Projective Space

The set of all subspaces of F-q(n) is denoted by P-q(n). The subspace distance d(S)(X, Y) = dim(X) + dim(Y)-2dim(X boolean AND Y) defined on P-q(n) turns it into a natural coding space for error correction in random network coding. A subset of P-q(n) is called a code and the subspaces that belong to the code are called codewords. Motivated by classical coding theory, a linear coding structure can be imposed on a subset of P-q(n). Braun et al. conjectured that the largest cardinality of a linear code, that contains F-q(n), is 2(n). In this paper, we prove this conjecture and characterize the maximal linear codes that contain F-q(n).

Coupling geomorphology parameters with lithology for micro-level groundwater resource assessment: a case study from semi-arid hard rock terrain in Tamil Nadu, India

The standard procedure of groundwater resource estimation in India till date is based on the specific yield parameters of each rock type (lithology) derived through pumping test analysis. Using the change in groundwater level, specific yield, and area of influence, groundwater storage change could be estimated. However, terrain conditions in the form of geomorphological variations have an important bearing on the net groundwater recharge. In this study, an attempt was made to use both lithology and geomorphology as input variables to estimate the recharge from different sources in each lithology unit influenced by the geomorphic conditions (lith-geom), season wise separately. The study provided a methodological approach for an evaluation of groundwater in a semi-arid hard rock terrain in Tirunelveli, Tamil Nadu, India. While characterizing the gneissic rock, it was found that the geomorphologic variations in the gneissic rock due to weathering and deposition behaved differently with respect to aquifer recharge. The three different geomorphic units identified in gneissic rock (pediplain shallow weathered (PPS), pediplain moderate weathered (PPM), and buried pediplain moderate (BPM)) showed a significant variation in recharge conditions among themselves. It was found from the study that Peninsular gneiss gives a net recharge value of 0.13 m/year/unit area when considered as a single unit w.r.t. lithology, whereas the same area considered with lith-geom classes gives recharge values between 0.1 and 0.41 m/year presenting a different assessment. It is also found from this study that the stage of development (SOD) for each lith-geom unit in Peninsular gneiss varies from 168 to 230 %, whereas the SOD is 223 % for the lithology as a single unit.

A new rock dwelling Hemidactylus (Squamata: Gekkonidae) from Chhattisgarh, India

A distinct new species of gecko of the genus Hemidactylus is described from the Kanker district of Chhattisgarh State, east-central India. This large-sized (SVL average 81.33 +/- 13.40 to at least 98.0 mm) Hemidactylus is characterized by a dorsum with small granules, intermixed with 10-12 rows of irregularly arranged, slightly larger, rounded, weakly-keeled tubercles at midbody; 10-12 and 13-15 subdigital lamellae on the first and fourth digits, respectively, of both manus and pes; a single enlarged postcloacal tubercle on either side of the tail; 10-12 femoral pores on each thigh separated by 5-8 poreless scales; 12-14 supralabials and 10-12 infralabials.

A new rock dwelling Hemidactylus (Squamata: Gekkonidae) from Chhattisgarh, India

A distinct new species of gecko of the genus Hemidactylus is described from the Kanker district of Chhattisgarh State, east-central India. This large-sized (SVL average 81.33 +/- 13.40 to at least 98.0 mm) Hemidactylus is characterized by a dorsum with small granules, intermixed with 10-12 rows of irregularly arranged, slightly larger, rounded, weakly-keeled tubercles at midbody; 10-12 and 13-15 subdigital lamellae on the first and fourth digits, respectively, of both manus and pes; a single enlarged postcloacal tubercle on either side of the tail; 10-12 femoral pores on each thigh separated by 5-8 poreless scales; 12-14 supralabials and 10-12 infralabials.

Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis

The ultimate bearing capacity of a circular footing, placed over rock mass, is evaluated by using the lower bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization. The generalized Hoek-Brown (HB) failure criterion, but by keeping a constant value of the exponent, alpha = 0.5, was used. The failure criterion was smoothened both in the meridian and pi planes. The nonlinear optimization was carried out by employing an interior point method based on the logarithmic barrier function. The results for the obtained bearing capacity were presented in a non-dimensional form for different values of GSI, m(i), sigma(ci)/(gamma b) and q/sigma(ci). Failure patterns were also examined for a few cases. For validating the results, computations were also performed for a strip footing as well. The results obtained from the analysis compare well with the data reported in literature. Since the equilibrium conditions are precisely satisfied only at the centroids of the elements, not everywhere in the domain, the obtained lower bound solution will be approximate not true. (C) 2015 Elsevier Ltd. All rights reserved.

Interlaboratory comparison of magnesium isotopic compositions of 12 felsic to ultramafic igneous rock standards analyzed by MC-ICPMS

To evaluate the interlaboratory mass bias for high-precision stable Mg isotopic analysis of natural materials, a suite of silicate standards ranging in composition from felsic to ultramafic were analyzed in five laboratories by using three types of multicollector inductively coupled plasma mass spectrometer (MC-ICPMS). Magnesium isotopic compositions from all labs are in agreement for most rocks within quoted uncertainties but are significantly (up to 0.3 parts per thousand in Mg-26/Mg-24, > 4 times of uncertainties) different for some mafic samples. The interlaboratory mass bias does not correlate with matrix element/Mg ratios, and the mechanism for producing it is uncertain but very likely arises from column chemistry. Our results suggest that standards with different matrices are needed to calibrate the efficiency of column chemistry and caution should be taken when dealing with samples with complicated matrices. Well-calibrated standards with matrix elements matching samples should be used to reduce the interlaboratory mass bias.