A generalized Linear Programming based approach to optimal divisible load scheduling

In this paper we propose a general Linear Programming (LP) based formulation and solution methodology for obtaining optimal solution to the load distribution problem in divisible load scheduling. We exploit the power of the versatile LP formulation to propose algorithms that yield exact solutions to several very general load distribution problems for which either no solutions or only heuristic solutions were available. We consider both star (single-level tree) networks and linear daisy chain networks, having processors equipped with front-ends, that form the generic models for several important network topologies. We consider arbitrary processing node availability or release times and general models for communication delays and computation time that account for constant overheads such as start up times in communication and computation. The optimality of the LP based algorithms is proved rigorously.

Analysis of an LMS linear equalizer for fading channels in decision directed mode

We consider a time varying wireless fading channel, equalized by an LMS linear equalizer in decision directed mode (DD-LMS-LE). We study how well this equalizer tracks the optimal Wiener equalizer. Initially we study a fixed channel.For a fixed channel, we obtain the existence of DD attractors near the Wiener filter at high SNRs using an ODE (Ordinary Differential Equation) approximating the DD-LMS-LE. We also show, via examples, that the DD attractors may not be close to the Wiener filters at low SNRs. Next we study a time varying fading channel modeled by an Auto-regressive (AR) process of order 2. The DD-LMS equalizer and the AR process are jointly approximated by the solution of a system of ODEs. We show via examples that the LMS equalizer ODE show tracks the ODE corresponding to the instantaneous Wiener filter when the SNR is high. This may not happen at low SNRs.

Tracking performance of an LMS-Linear Equalizer for fading channels

We consider a time varying wireless fading channel, equalized by an LMS linear equalizer. We study how well this equalizer tracks the optimal Wiener equalizer. We model the channel by an Auto-regressive (AR) process. Then the LMS equalizer and the AR process are jointly approximated by the solution of a system of ODEs (ordinary differential equations). Using these ODEs, the error between the LMS equalizer and the instantaneous Wiener filter is shown to decay exponentially/polynomially to zero unless the channel is marginally stable in which case the convergence may not hold.Using the same ODEs, we also show that the corresponding Mean Square Error (MSE) converges towards minimum MSE(MMSE) at the same rate for a stable channel. We further show that the difference between the MSE and the MMSE does not explode with time even when the channel is unstable. Finally we obtain an optimum step size for the linear equalizer in terms of the AR parameters, whenever the error decay is exponential.

Information dissemination in socially aware networks under the linear threshold model

We provide new analytical results concerning the spread of information or influence under the linear threshold social network model introduced by Kempe et al. in, in the information dissemination context. The seeder starts by providing the message to a set of initial nodes and is interested in maximizing the number of nodes that will receive the message ultimately. A node's decision to forward the message depends on the set of nodes from which it has received the message. Under the linear threshold model, the decision to forward the information depends on the comparison of the total influence of the nodes from which a node has received the packet with its own threshold of influence. We derive analytical expressions for the expected number of nodes that receive the message ultimately, as a function of the initial set of nodes, for a generic network. We show that the problem can be recast in the framework of Markov chains. We then use the analytical expression to gain insights into information dissemination in some simple network topologies such as the star, ring, mesh and on acyclic graphs. We also derive the optimal initial set in the above networks, and also hint at general heuristics for picking a good initial set.

Generic identity of Camptorrhiza indica (Colchicaceae) based on cytogenetics and molecular phylogenetics

The tribe Iphigenieae (Colchicaceace, Liliales) includes two genera, viz. Camptorrhiza and Iphigenia, which are distributed in Africa, India, and Australasia. Iphigenia is represented by 12 species, of which six occur in India while Camptorrhiza comprises one species each in Africa (C. strumosa) and India (C. indica). The genus Camptorrhiza possesses a knee-shaped tuber attached to the corms, filaments with a thick bulge in the middle and styles with single stigma. Iphigenia on the other hand lacks knee-shaped tuber, bears linear filaments and has styles with three stigmas. Camptorrhiza indica possesses ovoid corms, linear filaments and styles with a single stigma. These characters are intermediate between Iphigenia and Camptorrhiza and hence we studied the cytogenetics and phylogenetic placement of this species to ascertain its generic identity. Somatic chromosome count (2n = 22) and karyotypic features of C. indica are very similar to that of Iphigenia species. Molecular phylogenetic studies based on atpB-rbcL, rps16, trnL, and trnL-F regions showed that C. indica is nested within a lineage of Indian Iphigenia species. Thus, C. indica was reduced to a species of Iphigenia, i.e., I. ratnagirica. Camptorrhiza is now a monotypic genus restricted only to southern Africa. A key to the Indian Iphigenia species is provided. In addition, a new combination Wurmbea novae-zelandiae is proposed for Iphigenia novae-zelandiae.

Constrained Linear Spectral Unmixing Technique for Regional Land Cover Mapping Using MODIS Data

Over the last few decades, there has been a significant land cover (LC) change across the globe due to the increasing demand of the burgeoning population and urban sprawl. In order to take account of the change, there is a need for accurate and up-to-date LC maps. Mapping and monitoring of LC in India is being carried out at national level using multi-temporal IRS AWiFS data. Multispectral data such as IKONOS, Landsat-TM/ETM+, IRS-ICID LISS-III/IV, AWiFS and SPOT-5, etc. have adequate spatial resolution (similar to 1m to 56m) for LC mapping to generate 1:50,000 maps. However, for developing countries and those with large geographical extent, seasonal LC mapping is prohibitive with data from commercial sensors of limited spatial coverage. Superspectral data from the MODIS sensor are freely available, have better temporal (8 day composites) and spectral information. MODIS pixels typically contain a mixture of various LC types (due to coarse spatial resolution of 250, 500 and 1000 in), especially in more fragmented landscapes. In this context, linear spectral unmixing would be useful for mapping patchy land covers, such as those that characterise much of the Indian subcontinent. This work evaluates the existing unmixing technique for LC mapping using MODIS data, using end-members that are extracted through Pixel Purity Index (PPI), Scatter plot and N-dimensional visualisation. The abundance maps were generated for agriculture, built up, forest, plantations, waste land/others and water bodies. The assessment of the results using ground truth and a LISS-III classified map shows 86% overall accuracy, suggesting the potential for broad-scale applicability of the technique with superspectral data for natural resource planning and inventory applications. Index Terms-Remote sensing, digital

A new load distribution strategy for linear network with communication delays

In this paper, we propose a new load distribution strategy called `send-and-receive' for scheduling divisible loads, in a linear network of processors with communication delay. This strategy is designed to optimally utilize the network resources and thereby minimizes the processing time of entire processing load. A closed-form expression for optimal size of load fractions and processing time are derived when the processing load originates at processor located in boundary and interior of the network. A condition on processor and link speed is also derived to ensure that the processors are continuously engaged in load distributions. This paper also presents a parallel implementation of `digital watermarking problem' on a personal computer-based Pentium Linear Network (PLN) topology. Experiments are carried out to study the performance of the proposed strategy and results are compared with other strategies found in literature.

Conformation-activity correlations for chemotactic tripeptide analogs incorporating dialkyl residues with linear and cyclic alkyl sidechains at position 2

Five stereochemically constrained analogs of the chemotactic tripeptide incorporating 1-aminocycloalkane-1-carboxylic acid (Ac(n)c) and alpha,alpha-dialkylglycines (Deg, diethylglycine; Dpg, n,n-dipropylglycine and Dbg, n,n-dibutylglycine) at position 2 have been synthesized. NMR studies of peptides For-Met-Xxx-Phe-OMe (Xxx = Ac(7)c, I; Ac(8)c, II; Deg, III; Dpg, IV and Dbg, V; For, formyl) establish that peptides with cycloalkyl residues, I and II, adopt folded beta-turn conformations in CDCl3 and (CD3)(2)SO. In contrast, analogs with linear alkyl sidechains, III-V, favour fully extended (C-5) conformations in solution. Peptides I-V exhibit high activity in inducing beta-glucosaminidase release from rabbit neutrophils, with ED(50) values ranging from 1.4-8.0 x 10(-11)M. In human neutrophils the Dxg peptides III-V have ED(50) values ranging from 2.3 x 10(-8) to 5.9 x 10(-10) M, with the activity order being V > IV > III. While peptides I-IV are less active than the parent. For-Met-Leu-Phe-OH, in stimulating histamine release from human basophils, the Dbg peptide V is appreciably more potent, suggesting its potential utility as a probe for formyl peptide receptors.

An Efficient Load Distribution Strategy for a Distributed Linear Network of Processors with Communication Delays

In this paper, we present an improved load distribution strategy, for arbitrarily divisible processing loads, to minimize the processing time in a distributed linear network of communicating processors by an efficient utilization of their front-ends. Closed-form solutions are derived, with the processing load originating at the boundary and at the interior of the network, under some important conditions on the arrangement of processors and links in the network. Asymptotic analysis is carried out to explore the ultimate performance limits of such networks. Two important theorems are stated regarding the optimal load sequence and the optimal load origination point. Comparative study of this new strategy with an earlier strategy is also presented.

Non-linear regression model for spatial variation in precipitation chemistry for South India

Chemical composition of rainwater changes from sea to inland under the influence of several major factors - topographic location of area, its distance from sea, annual rainfall. A model is developed here to quantify the variation in precipitation chemistry under the influence of inland distance and rainfall amount. Various sites in India categorized as 'urban', 'suburban' and 'rural' have been considered for model development. pH, HCO3, NO3 and Mg do not change much from coast to inland while, SO4 and Ca change is subjected to local emissions. Cl and Na originate solely from sea salinity and are the chemistry parameters in the model. Non-linear multiple regressions performed for the various categories revealed that both rainfall amount and precipitation chemistry obeyed a power law reduction with distance from sea. Cl and Na decrease rapidly for the first 100 km distance from sea, then decrease marginally for the next 100 km, and later stabilize. Regression parameters estimated for different cases were found to be consistent (R-2 similar to 0.8). Variation in one of the parameters accounted for urbanization. Model was validated using data points from the southern peninsular region of the country. Estimates are found to be within 99.9% confidence interval. Finally, this relationship between the three parameters - rainfall amount, coastline distance, and concentration (in terms of Cl and Na) was validated with experiments conducted in a small experimental watershed in the south-west India. Chemistry estimated using the model was in good correlation with observed values with a relative error of similar to 5%. Monthly variation in the chemistry is predicted from a downscaling model and then compared with the observed data. Hence, the model developed for rain chemistry is useful in estimating the concentrations at different spatio-temporal scales and is especially applicable for south-west region of India. (C) 2008 Elsevier Ltd. All rights reserved.

Stability of a Random Diffusion with Linear Drift

We consider a Linear system with Markovian switching which is perturbed by Gaussian type noise, If the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable, We also shaw that under certain conditions the linear system with Markovian switching can be stabilized by such noisy perturbation.

A linear programming approach for estimating the structure of a sparse linear genetic network from transcript profiling data

Background: A genetic network can be represented as a directed graph in which a node corresponds to a gene and a directed edge specifies the direction of influence of one gene on another. The reconstruction of such networks from transcript profiling data remains an important yet challenging endeavor. A transcript profile specifies the abundances of many genes in a biological sample of interest. Prevailing strategies for learning the structure of a genetic network from high-dimensional transcript profiling data assume sparsity and linearity. Many methods consider relatively small directed graphs, inferring graphs with up to a few hundred nodes. This work examines large undirected graphs representations of genetic networks, graphs with many thousands of nodes where an undirected edge between two nodes does not indicate the direction of influence, and the problem of estimating the structure of such a sparse linear genetic network (SLGN) from transcript profiling data. Results: The structure learning task is cast as a sparse linear regression problem which is then posed as a LASSO (l1-constrained fitting) problem and solved finally by formulating a Linear Program (LP). A bound on the Generalization Error of this approach is given in terms of the Leave-One-Out Error. The accuracy and utility of LP-SLGNs is assessed quantitatively and qualitatively using simulated and real data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) initiative provides gold standard data sets and evaluation metrics that enable and facilitate the comparison of algorithms for deducing the structure of networks. The structures of LP-SLGNs estimated from the INSILICO1, INSILICO2 and INSILICO3 simulated DREAM2 data sets are comparable to those proposed by the first and/or second ranked teams in the DREAM2 competition. The structures of LP-SLGNs estimated from two published Saccharomyces cerevisae cell cycle transcript profiling data sets capture known regulatory associations. In each S. cerevisiae LP-SLGN, the number of nodes with a particular degree follows an approximate power law suggesting that its degree distributions is similar to that observed in real-world networks. Inspection of these LP-SLGNs suggests biological hypotheses amenable to experimental verification. Conclusion: A statistically robust and computationally efficient LP-based method for estimating the topology of a large sparse undirected graph from high-dimensional data yields representations of genetic networks that are biologically plausible and useful abstractions of the structures of real genetic networks. Analysis of the statistical and topological properties of learned LP-SLGNs may have practical value; for example, genes with high random walk betweenness, a measure of the centrality of a node in a graph, are good candidates for intervention studies and hence integrated computational – experimental investigations designed to infer more realistic and sophisticated probabilistic directed graphical model representations of genetic networks. The LP-based solutions of the sparse linear regression problem described here may provide a method for learning the structure of transcription factor networks from transcript profiling and transcription factor binding motif data.

The Linear Tripeptide L-Alanylglyeyl-L- alanine

L-Alanylglycyl-L-alanine, C8H15N3O4, exists as zwitter-ion in the crystal with the N terminus protonated and the C terminus in an ionized form, Both the peptide units are in trans configurations and deviate significantly from planarity. Backbone torsion angles are psi(1)=172.7(2), omega(1)=-178.2(2), phi(2)=91.7(2), phi(2)=-151.9(2), omega(2)=-176.9(2), phi(3)=-71.3(2), phi(31)=-7.0(3) and psi(32) 172.4(2)degrees. The protonated NH3+ group forms three hydrogen bonds with atoms of symmetry-related molecules.

Linear filtering in DCT IV/DST IV and MDCT/MDST domain

In this paper, expressions for convolution multiplication properties of DCT IV and DST IV are derived starting from equivalent DFT representations. Using these expressions methods for implementing linear filtering through block convolution in the DCT IV and DST IV domain are proposed. Techniques developed for DCT IV and DST IV are further extended to MDCT and MDST where the filter implementation is near exact for symmetric filters and approximate for non-symmetric filters. No additional overlapping is required for implementing the symmetric filtering in the MDCT domain and hence the proposed algorithm is computationally competitive with DFT based systems. Moreover, inherent 50% overlap between the adjacent frames used for MDCT/MDST domain reduces the blocking artifacts due to block processing or quantization. The techniques are computationally efficient for symmetric filters and provides a new alternative to DFT based convolution.

A pseudo-dynamical systems approach to a class of inverse problems in engineering

A pseudo-dynamical approach for a class of inverse problems involving static measurements is proposed and explored. Following linearization of the minimizing functional associated with the underlying optimization problem, the new strategy results in a system of linearized ordinary differential equations (ODEs) whose steady-state solutions yield the desired reconstruction. We consider some explicit and implicit schemes for integrating the ODEs and thus establish a deterministic reconstruction strategy without an explicit use of regularization. A stochastic reconstruction strategy is then developed making use of an ensemble Kalman filter wherein these ODEs serve as the measurement model. Finally, we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest.