Nonnegative integral solution of linear equations

A method to obtain a nonnegative integral solution of a system of linear equations, if such a solution exists is given. The method writes linear equations as an integer programming problem and then solves the problem using a combination of artificial basis technique and a method of integer forms.

2-Dimensional Linear-Stability of Premixed Laminar Flames Under Zero-Gravity

This paper reports on the numerical study of the linear stability of laminar premixed flames under zero gravity. The study specifically addresses the dependence of stability on finite rate chemistry with low activation energy and variable thermodynamic and transport properties. The calculations show that activation energy and details of chemistry play a minor role in altering the linear neutral stability results from asymptotic analysis. Variable specific heat makes a marginal change to the stability. Variable transport properties on the other hand tend to substantially enhance the stability from critical wave number of about 0.5 to 0.20. Also, it appears that the effects of variable properties tend to nullify the effects of non-unity Lewis number. When the Lewis number of a single species is different from unity, as will happen in a hydrogen-air premixed flame, the stability results remain close to that of unity Lewis number.

A note on resolving infeasibility in linear programs by constraint relaxation

We study the problem of finding a set of constraints of minimum cardinality which when relaxed in an infeasible linear program, make it feasible. We show the problem is NP-hard even when the constraint matrix is totally unimodular and prove polynomial-time solvability when the constraint matrix and the right-hand-side together form a totally unimodular matrix.

Field-dependent changeover from current-to voltage-limiting characteristics by non-linear n-type BaTiO3 ceramics

Non-linear resistors having current-limiting capabilities at lower field strengths, and voltage-limiting characteristics (varistors) at higher field strengths, were prepared from sintered polycrystalline ceramics of (Ba0.6Sr0.4)(Ti0.97Zr0.03)O3+0.3 at % La, and reannealed after painting with low-melting mixtures of Bi2O3 + PbO +B2O3. These types of non-linear characteristics were found to depend upon the non-uniform diffusion of lead and the consequent distribution of Curie points (T c) in these perovskites, resulting in diffuse phase transitions. Tunnelling of electrons across the asymmetric barrier at tetragonak-cubic interfaces changes to tunnelling across the symmetric barrier as the cubic phase is fully stabilized through Joule heating at high field strengths. Therefore the current-limiting characteristics switch over to voltage-limiting behaviour because tunnelling to acceptor-type mid-bandgap states gives way to band-to-band tunnelling.

Mobile Base Stations Placement and Energy Aware Routing in Wireless Sensor Networks

Increasing network lifetime is important in wireless sensor/ad-hoc networks. In this paper, we are concerned with algorithms to increase network lifetime and amount of data delivered during the lifetime by deploying multiple mobile base stations in the sensor network field. Specifically, we allow multiple mobile base stations to be deployed along the periphery of the sensor network field and develop algorithms to dynamically choose the locations of these base stations so as to improve network lifetime. We propose energy efficient low-complexity algorithms to determine the locations of the base stations; they include i) Top-K-max algorithm, ii) maximizing the minimum residual energy (Max-Min-RE) algorithm, and iii) minimizing the residual energy difference (MinDiff-RE) algorithm. We show that the proposed base stations placement algorithms provide increased network lifetimes and amount of data delivered during the network lifetime compared to single base station scenario as well as multiple static base stations scenario, and close to those obtained by solving an integer linear program (ILP) to determine the locations of the mobile base stations. We also investigate the lifetime gain when an energy aware routing protocol is employed along with multiple base stations.

Points-to Analysis as a System of Linear Equations

We propose a novel formulation of the points-to analysis as a system of linear equations. With this, the efficiency of the points-to analysis can be significantly improved by leveraging the advances in solution procedures for solving the systems of linear equations. However, such a formulation is non-trivial and becomes challenging due to various facts, namely, multiple pointer indirections, address-of operators and multiple assignments to the same variable. Further, the problem is exacerbated by the need to keep the transformed equations linear. Despite this, we successfully model all the pointer operations. We propose a novel inclusion-based context-sensitive points-to analysis algorithm based on prime factorization, which can model all the pointer operations. Experimental evaluation on SPEC 2000 benchmarks and two large open source programs reveals that our approach is competitive to the state-of-the-art algorithms. With an average memory requirement of mere 21MB, our context-sensitive points-to analysis algorithm analyzes each benchmark in 55 seconds on an average.

Exact-Solutions Of Linear Partial-Differential Equations With Variable-Coefficients

Backlund transformations relating the solutions of linear PDE with variable coefficients to those of PDE with constant coefficients are found, generalizing the study of Varley and Seymour [2]. Auto-Backlund transformations are also determined. To facilitate the generation of new solutions via Backlund transformation, explicit solutions of both classes of the PDE just mentioned are found using invariance properties of these equations and other methods. Some of these solutions are new.

On Computation of Minimum Distance of Linear Block Codes Above 1/2 Rate Coding

The minimum distance of linear block codes is one of the important parameter that indicates the error performance of the code. When the code rate is less than 1/2, efficient algorithms are available for finding minimum distance using the concept of information sets. When the code rate is greater than 1/2, only one information set is available and efficiency suffers. In this paper, we investigate and propose a novel algorithm to find the minimum distance of linear block codes with the code rate greater than 1/2. We propose to reverse the roles of information set and parity set to get virtually another information set to improve the efficiency. This method is 67.7 times faster than the minimum distance algorithm implemented in MAGMA Computational Algebra System for a (80, 45) linear block code.

Reduced ML-Decoding Complexity, Full-Rate STBCs for 4 Transmit Antenna Systems

For an n(t) transmit, n(r) receive antenna system (n(t) x nr system), a full-rate space time block code (STBC) transmits min(n(t), n(r)) complex symbols per channel use. In this paper, a scheme to obtain a full-rate STBC for 4 transmit antennas and any n(r), with reduced ML-decoding complexity is presented. The weight matrices of the proposed STBC are obtained from the unitary matrix representations of a Clifford Algebra. By puncturing the symbols of the STBC, full rate designs can be obtained for n(r) < 4. For any value of n(r), the proposed design offers the least ML-decoding complexity among known codes. The proposed design is comparable in error performance to the well known Perfect code for 4 transmit antennas while offering lower ML-decoding complexity. Further, when n(r) < 4, the proposed design has higher ergodic capacity than the punctured Perfect code. Simulation results which corroborate these claims are presented.

Data compression by linear prediction for storage and transmission of EEG signals

The EEG time series has been subjected to various formalisms of analysis to extract meaningful information regarding the underlying neural events. In this paper the linear prediction (LP) method has been used for analysis and presentation of spectral array data for the better visualisation of background EEG activity. It has also been used for signal generation, efficient data storage and transmission of EEG. The LP method is compared with the standard Fourier method of compressed spectral array (CSA) of the multichannel EEG data. The autocorrelation autoregressive (AR) technique is used for obtaining the LP coefficients with a model order of 15. While the Fourier method reduces the data only by half, the LP method just requires the storage of signal variance and LP coefficients. The signal generated using white Gaussian noise as the input to the LP filter has a high correlation coefficient of 0.97 with that of original signal, thus making LP as a useful tool for storage and transmission of EEG. The biological significance of Fourier method and the LP method in respect to the microstructure of neuronal events in the generation of EEG is discussed.

Positional Consensus of Multi-Agent Systems Using Linear Programming Based Decentralized Control with Rectilinear Decision Domain

In this paper we develop a Linear Programming (LP) based decentralized algorithm for a group of multiple autonomous agents to achieve positional consensus. Each agent is capable of exchanging information about its position and orientation with other agents within their sensing region. The method is computationally feasible and easy to implement. Analytical results are presented. The effectiveness of the approach is illustrated with simulation results.

A Low-Complexity, Full-Rate, Full-Diversity 2 x 2 STBC with Golden Code's Coding Gain

This paper presents a low-ML-decoding-complexity, full-rate, full-diversity space-time block code (STBC) for a 2 transmit antenna, 2 receive antenna multiple-input multiple-output (MIMO) system, with coding gain equal to that of the best and well known Golden code for any QAM constellation. Recently, two codes have been proposed (by Paredes, Gershman and Alkhansari and by Sezginer and Sari), which enjoy a lower decoding complexity relative to the Golden code, but have lesser coding gain. The 2 x 2 STBC presented in this paper has lesser decoding complexity for non-square QAM constellations, compared with that of the Golden code, while having the same decoding complexity for square QAM constellations. Compared with the Paredes-Gershman-Alkhansari and Sezginer-Sari codes, the proposed code has the same decoding complexity for non-rectangular QAM constellations. Simulation results, which compare the codeword error rate (CER) performance, are presented.

High-Rate Space-Time Coded Large MIMO Systems: Low-Complexity Detection and Performance

Large MIMO systems with tens of antennas in each communication terminal using full-rate non-orthogonal space-time block codes (STBC) from Cyclic Division Algebras (CDA) can achieve the benefits of both transmit diversity as well as high spectral efficiencies. Maximum-likelihood (ML) or near-ML decoding of these large-sized STBCs at low complexities, however, has been a challenge. In this paper, we establish that near-ML decoding of these large STBCs is possible at practically affordable low complexities. We show that the likelihood ascent search (LAS) detector, reported earlier by us for V-BLAST, is able to achieve near-ML uncoded BER performance in decoding a 32x32 STBC from CDA, which employs 32 transmit antennas and sends 32(2) = 1024 complex data symbols in 32 time slots in one STBC matrix (i.e., 32 data symbols sent per channel use). In terms of coded BER, with a 16x16 STBC, rate-3/4 turbo code and 4-QAM (i.e., 24 bps/Hz), the LAS detector performs close to within just about 4 dB from the theoretical MIMO capacity. Our results further show that, with LAS detection, information lossless (ILL) STBCs perform almost as good as full-diversity ILL (FD-ILL) STBCs. Such low-complexity detectors can potentially enable implementation of high spectral efficiency large MIMO systems that could be considered in wireless standards.

Linear electro‐optic dispersion in (‐)‐2‐(α‐methylbenzylamino)‐5‐nitropyridine single crystals

The variation of the linear electro-optic effect in (-)-2-(alpha-methylbenzylamino)-5-nitropyridine with the wavelength of the incident light at room temperature has been measured. The reduced half-wave voltages have been found to have the values 2.1, 2.8, and 6.0 kV at 488, 514.5, and 632.8 nm respectively and the corresponding values of the linear electro-optic coefficient have been evaluated.;The interpretation of the results in terms of the structures of the molecule and the crystal is discussed. The thermal variation of the birefringence has also been investigated and the coefficient for the temperature variation of the refractive index difference is found to have the value (d Delta n/dT)=9.3X10(-5) K-1.

Non-Linear effects of membrane fluctuations in the dilute lamellar phase

The static structure factor of the dilute sterically stabilised lamellar phase is calculated and found to have an Ornstein-Zernike form with a correlation length that diverges at infinite dilution. The relaxation time for concentration fluctuations at large wave number q is shown to go as q-3 with a coefficient independent of the membrane bending rigidity. The membrane fluctuations also give rise to strongly frequency-dependent viscosities at high frequencies.