Location of concentrators in a computer communication network: a stochastic automation search method

The following problem is considered. Given the locations of the Central Processing Unit (ar;the terminals which have to communicate with it, to determine the number and locations of the concentrators and to assign the terminals to the concentrators in such a way that the total cost is minimized. There is alao a fixed cost associated with each concentrator. There is ail upper limit to the number of terminals which can be connected to a concentrator. The terminals can be connected directly to the CPU also In this paper it is assumed that the concentrators can bo located anywhere in the area A containing the CPU and the terminals. Then this becomes a multimodal optimization problem. In the proposed algorithm a stochastic automaton is used as a search device to locate the minimum of the multimodal cost function . The proposed algorithm involves the following. The area A containing the CPU and the terminals is divided into an arbitrary number of regions (say K). An approximate value for the number of concentrators is assumed (say m). The optimum number is determined by iteration later The m concentrators can be assigned to the K regions in (mk) ways (m > K) or (km) ways (K>m).(All possible assignments are feasible, i.e. a region can contain 0,1,…, to concentrators). Each possible assignment is assumed to represent a state of the stochastic variable structure automaton. To start with, all the states are assigned equal probabilities. At each stage of the search the automaton visits a state according to the current probability distribution. At each visit the automaton selects a 'point' inside that state with uniform probability. The cost associated with that point is calculated and the average cost of that state is updated. Then the probabilities of all the states are updated. The probabilities are taken to bo inversely proportional to the average cost of the states After a certain number of searches the search probabilities become stationary and the automaton visits a particular state again and again. Then the automaton is said to have converged to that state Then by conducting a local gradient search within that state the exact locations of the concentrators are determined This algorithm was applied to a set of test problems and the results were compared with those given by Cooper's (1964, 1967) EAC algorithm and on the average it was found that the proposed algorithm performs better.

Distributed nonlinear optimization algorithms for general network problems

There are a number of large networks which occur in many problems dealing with the flow of power, communication signals, water, gas, transportable goods, etc. Both design and planning of these networks involve optimization problems. The first part of this paper introduces the common characteristics of a nonlinear network (the network may be linear, the objective function may be non linear, or both may be nonlinear). The second part develops a mathematical model trying to put together some important constraints based on the abstraction for a general network. The third part deals with solution procedures; it converts the network to a matrix based system of equations, gives the characteristics of the matrix and suggests two solution procedures, one of them being a new one. The fourth part handles spatially distributed networks and evolves a number of decomposition techniques so that we can solve the problem with the help of a distributed computer system. Algorithms for parallel processors and spatially distributed systems have been described.There are a number of common features that pertain to networks. A network consists of a set of nodes and arcs. In addition at every node, there is a possibility of an input (like power, water, message, goods etc) or an output or none. Normally, the network equations describe the flows amoungst nodes through the arcs. These network equations couple variables associated with nodes. Invariably, variables pertaining to arcs are constants; the result required will be flows through the arcs. To solve the normal base problem, we are given input flows at nodes, output flows at nodes and certain physical constraints on other variables at nodes and we should find out the flows through the network (variables at nodes will be referred to as across variables).The optimization problem involves in selecting inputs at nodes so as to optimise an objective function; the objective may be a cost function based on the inputs to be minimised or a loss function or an efficiency function. The above mathematical model can be solved using Lagrange Multiplier technique since the equalities are strong compared to inequalities. The Lagrange multiplier technique divides the solution procedure into two stages per iteration. Stage one calculates the problem variables % and stage two the multipliers lambda. It is shown that the Jacobian matrix used in stage one (for solving a nonlinear system of necessary conditions) occurs in the stage two also.A second solution procedure has also been imbedded into the first one. This is called total residue approach. It changes the equality constraints so that we can get faster convergence of the iterations.Both solution procedures are found to coverge in 3 to 7 iterations for a sample network.The availability of distributed computer systems — both LAN and WAN — suggest the need for algorithms to solve the optimization problems. Two types of algorithms have been proposed — one based on the physics of the network and the other on the property of the Jacobian matrix. Three algorithms have been deviced, one of them for the local area case. These algorithms are called as regional distributed algorithm, hierarchical regional distributed algorithm (both using the physics properties of the network), and locally distributed algorithm (a multiprocessor based approach with a local area network configuration). The approach used was to define an algorithm that is faster and uses minimum communications. These algorithms are found to converge at the same rate as the non distributed (unitary) case.

Minimization Problems Based on Relative alpha-Entropy I: Forward Projection

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative alpha-entropies (denoted I-alpha), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative alpha-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimizers of these relative alpha-entropies on closed and convex sets are shown to exist. Such minimizations generalize the maximum Renyi or Tsallis entropy principle. The minimizing probability distribution (termed forward I-alpha-projection) for a linear family is shown to obey a power-law. Other results in connection with statistical inference, namely subspace transitivity and iterated projections, are also established. In a companion paper, a related minimization problem of interest in robust statistics that leads to a reverse I-alpha-projection is studied.

Minimization Problems Based on Relative alpha-Entropy II: Reverse Projection

In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted I-alpha) were studied. Such minimizers were called forward I-alpha-projections. Here, a complementary class of minimization problems leading to the so-called reverse I-alpha-projections are studied. Reverse I-alpha-projections, particularly on log-convex or power-law families, are of interest in robust estimation problems (alpha > 1) and in constrained compression settings (alpha < 1). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse I-alpha-projection into a forward I-alpha-projection. The transformed problem is a simpler quasi-convex minimization subject to linear constraints.

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.

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.

Leveraging coherent distributed space-time codes for noncoherent communication in relay networks via training

For point to point multiple input multiple output systems, Dayal-Brehler-Varanasi have proved that training codes achieve the same diversity order as that of the underlying coherent space time block code (STBC) if a simple minimum mean squared error estimate of the channel formed using the training part is employed for coherent detection of the underlying STBC. In this letter, a similar strategy involving a combination of training, channel estimation and detection in conjunction with existing coherent distributed STBCs is proposed for noncoherent communication in Amplify-and-Forward (AF) relay networks. Simulation results show that the proposed simple strategy outperforms distributed differential space-time coding for AF relay networks. Finally, the proposed strategy is extended to asynchronous relay networks using orthogonal frequency division multiplexing.

A Quasi-Newton Adaptive Algorithm for Generalized Symmetric Eigenvalue Problem

In this paper, we first recast the generalized symmetric eigenvalue problem, where the underlying matrix pencil consists of symmetric positive definite matrices, into an unconstrained minimization problem by constructing an appropriate cost function, We then extend it to the case of multiple eigenvectors using an inflation technique, Based on this asymptotic formulation, we derive a quasi-Newton-based adaptive algorithm for estimating the required generalized eigenvectors in the data case. The resulting algorithm is modular and parallel, and it is globally convergent with probability one, We also analyze the effect of inexact inflation on the convergence of this algorithm and that of inexact knowledge of one of the matrices (in the pencil) on the resulting eigenstructure. Simulation results demonstrate that the performance of this algorithm is almost identical to that of the rank-one updating algorithm of Karasalo. Further, the performance of the proposed algorithm has been found to remain stable even over 1 million updates without suffering from any error accumulation problems.

The effect of surface tension in porous wave maker problems

Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

Problems with geoengineering schemes to combat climate change

The accelerated rate of increase in atmospheric CO2 concentration in recent years has revived the idea of stabilizing the global climate through geoengineering schemes. Majority of the proposed geoengineering schemes will attempt to reduce the amount of solar radiation absorbed by our planet. Climate modelling studies of these so called 'sunshade geoengineering schemes' show that global warming from increasing concentrations of CO2 can be mitigated by intentionally manipulating the amount of sunlight absorbed by the climate system. These studies also suggest that the residual changes could be large on regional scales, so that climate change may not be mitigated on a local basis. More recent modelling studies have shown that these schemes could lead to a slow-down in the global hydrological cycle. Other problems such as changes in the terrestrial carbon cycle and ocean acidification remain unsolved by sunshade geoengineering schemes. In this article, I review the proposed geoengineering schemes, results from climate models and discuss why geoengineering is not the best option to deal with climate change.

Implementation of Art1 and Art2 Artificial Neural Networks on Ring and Mesh Architectures

The Artificial Neural Networks (ANNs) are being used to solve a variety of problems in pattern recognition, robotic control, VLSI CAD and other areas. In most of these applications, a speedy response from the ANNs is imperative. However, ANNs comprise a large number of artificial neurons, and a massive interconnection network among them. Hence, implementation of these ANNs involves execution of computer-intensive operations. The usage of multiprocessor systems therefore becomes necessary. In this article, we have presented the implementation of ART1 and ART2 ANNs on ring and mesh architectures. The overall system design and implementation aspects are presented. The performance of the algorithm on ring, 2-dimensional mesh and n-dimensional mesh topologies is presented. The parallel algorithm presented for implementation of ART1 is not specific to any particular architecture. The parallel algorithm for ARTE is more suitable for a ring architecture.

Estimation of mineral-adhered biomass of Thiobacillusferrooxidans by protein assay-some problems and remedies

Enumeration of adhered cells of Thiobacillus ferrooxidans on sulphide minerals through protein assay poses problems due to interference from dissolved mineral constituents. The manner in which sulphide minerals such as pyrite, chalcopyrite, sphalerite, arsenopyrite and pyrrhotite interfere with bacterial protein estimation is demonstrated. Such interferences can be minimised either through dilution or addition of H2O2 to the filtrate after hot alkaline digestion of the biotreated mineral samples.

Maximal regularity for second order non-autonomous Cauchy problems

We consider some non-autonomous second order Cauchy problems of the form u + B(t)(u) over dot + A(t)u = f (t is an element of [0, T]), u(0) = (u) over dot(0) = 0. We assume that the first order problem (u) over dot + B(t)u = f (t is an element of [0, T]), u(0) = 0, has L-p-maximal regularity. Then we establish L-p-maximal regularity of the second order problem in situations when the domains of B(t(1)) and A(t(2)) always coincide, or when A(t) = kappa B(t).

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.

Intercellular Communication in the Multicellular Stage of Dictyostelium-Discoideum

The aim of the present study was to draw inferences regarding the properties of single cells responsible for co-operative behaviour in the slug of the soil amoeba Dictyostelium discoideum. The slug is an integrated multicellular mass formed by the aggregation of starved cells. The amoebae comprising the slug differentiate according to their spatial locations relative to one another, implying that, as in the case of other regulative embryos, they must be in mutual communication. We have previously shown that one manifestation of this communication is the time taken for the anteriormost fragment of the slug, the tip, to regenerate from slugs which have been rendered tipless by amputation. We present results of tip-regeneration experiments performed on genetically mosaic slugs. By comparing the mosaics with their component pure genotypes, we were able to discriminate between a set of otherwise equally plausible modes of intercellular signalling. Neither a'pacemaker' model, in which the overall rate of tip regeneration is determined by the cell with the highest frequency of autonomous oscillation, nor an 'independent-particle' model, in which the rate of regeneration is the arithmetical average of independent cell-dependent rates, is in quantitative accord with our findings. Our results are best explained by a form of signalling which operates by means of cell-to-cell relay. Therefore intercellular communication Seems to be essential for tip regeneration.