Optimisation problems in wireless sensor networks

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating–dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating–dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs – these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating–dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs.

A heuristic clustering algorithm using union of overlapping pattern-cells

Relative geometric arrangements of the sample points, with reference to the structure of the imbedding space, produce clusters. Hence, if each sample point is imagined to acquire a volume of a small M-cube (called pattern-cell), depending on the ranges of its (M) features and number (N) of samples; then overlapping pattern-cells would indicate naturally closer sample-points. A chain or blob of such overlapping cells would mean a cluster and separate clusters would not share a common pattern-cell between them. The conditions and an analytic method to find such an overlap are developed. A simple, intuitive, nonparametric clustering procedure, based on such overlapping pattern-cells is presented. It may be classified as an agglomerative, hierarchical, linkage-type clustering procedure. The algorithm is fast, requires low storage and can identify irregular clusters. Two extensions of the algorithm, to separate overlapping clusters and to estimate the nature of pattern distributions in the sample space, are also indicated.

A knowledge-based approach to pattern generation

Pattern Cognition is looked at from the functional view point. The need for knowledge in synthesizing such patterns is explained and various aspects of knowledge-based pattern generation are highlighted. This approach to the generation of patterns is detailed with a concrete example.

Demixing of severely overlapped H-1 NMR resonances and interpretation of anomalous intensity pattern of dipolar coupled A(3) spins in a weakly aligning medium

We report a single C-13 spin edited selective proton-proton correlation experiment to decipher overcrowded 13C coupled proton NMR spectra of weakly dipolar coupled spin systems. The experiment unravels the masked C-13 satellites in proton spectrum and permits the measurement of one bond carbon-proton residual dipolar couplings in I3S and for each diastereotopic proton in I2S groups. It also provides all the possible homonuclear proton-proton residual couplings which are otherwise difficult to extract from the broad and featureless one dimensional H-1 spectrum, in addition to enantiodifferentiation in a chiral molecule. Employment of heteronuclear (C-13) decoupling in the evolution period results in complete demixing of overlapped signals from enantiomers. The observed anomalous intensity pattern in strongly dipolar coupled methyl protons in methyl selective correlation experiment has been interpreted using polarization operator formalism. (C) 2010 Elsevier Inc. All rights reserved.

Carbon-13 NMR studies of lipid mobilization pattern in germinating groundnut (Arachis hypogaea L.) seeds

The products of lipid mobilization in groundnut (Arachis hypogaea L.) seeds as a function of time immediately after imbibition are monitored by 13C NMR. Different parts of the embryonic axis, namely,the radicle, hypocotyl, and plumule, exhibit characteristic time dependent 13C NMR spectra observed at 24-h intervals after imbibition. The various stages in the transformation of storage lipids present in different parts of the embryonic axis are clearly demonstrated. The transformaton of storage lipids is completed first in the radicle followed by the hypocotyl and finally the plumule. A mechanism of the transformation of the storage lipids is discussed.

The 'neighbour effect' and its role in shaping the positional pattern of seed development in fruits: An illustration from the pods of Erythrina suberosa

Plants exhibit certain intra-fruit positional patterns in the development of seeds. These patterns have been generally interpreted to be a consequence of resource and fertilization gradients. However, such positional patterns might also be shaped by the 'neighbour effect', wherein formation and development of a seed at any position might positively or negatively influence those of other seeds in the neighbourhood. In this article, we examine the role of such neighbour effect in shaping the positional pattern of seeds in the pods of Erythrina suberosa. The results suggest the existence of a positive neighbour effect leading to a higher frequency of seeds in contiguous positions.

Nestedness pattern in stream diatom assemblages of central Western Ghats

Community diversity and the population abundance of a particular group of species are controlled by immediate environment, inter-and intra-species interactions, landscape conditions, historical events and evolutionary processes. Nestedness is a measure of order in an ecological system, referring to the order in which the number of species is related to area or other factors. In this study we have studied the nestedness pattern in stream diatom assemblages in 24 stream sites of central Western Ghats, and report 98 taxa from the streams of central Western Ghats region. The communities show highly significant nested pattern. The Mantel test of matrix revealed a strong relationship between species assemblages and environmental conditions at the sites. A significant relationship between species assemblage and environmental condition was observed. Principal component analysis (PCA) indicated that environmental conditions differed markedly across the sampling sites, with the first three components explaining 78% of variance. Species composition of diatoms is significantly correlated with environmental distance across geographical extent. The current pattern suggests that micro-environment at regional levels influences the species composition of epilithic diatoms in streams. The nestedness shown by the diatom community was highly significant, even though it had a high proportion of idiosyncratic species, characterized with high numbers of cosmopolitan species, whereas the nested species were dominated by endemic species. PCA identifies ionic parameters and nutrients as the major features which determine the characteristics of the sampling sites. Hence the local water quality parameters are the major factors in deciding the diatom species assemblages.

Novel gray coded pattern for unwrapping phase in fringe projection based 3D profiling

A method to reliably extract object profiles even with height discontinuities (that leads to 2n pi phase jumps) is proposed. This method uses Fourier transform profilometry to extract wrapped phase, and an additional image formed by illuminating the object of interest by a novel gray coded pattern for phase unwrapping. Simulation results suggest that the proposed approach not only retains the advantages of the original method, but also contributes significantly in the enhancement of its performance. Fundamental advantage of this method stems from the fact that both extraction of wrapped phase and unwrapping the same were done by gray scale images. Hence, unlike the methods that use colors, proposed method doesn't demand a color CCD camera and is ideal for profiling objects with multiple colors.

Reproductive phenology of a tropical dry forest in Mudumalai, Southern India

1 Flowering and fruiting phenologies of a tropical dry forest in Mudumalai, southern India, were studied between April 1988 and August 1990. Two sites, a wetter site I receiving 1100mm and a drier site II receiving 600mm of rainfall annually, are compared. A total of 286 trees from 38 species at site I and 167 trees from 27 species at site II was marked for phenological observations. There were 11 species common to the two sites. Several hypotheses relating to the evolution of reproductive phenology are tested. 2 Frequency of species flowering attained a peak at site I during the dry season but at site II, where soil moisture may be limiting during the dry months, the peak was during the wet season. At both sites a majority of species flushed leaves and flowered simultaneously. Among various guilds, the bird-pollinated guild showed distinct dry season flowering, which may be related to better advertisement of large flowers to pollinators during the leafless dry phase. The wind-pollinated guild flowered mainly during the wet season, when wind speeds are highest and favourable for pollen transport. The insect-pollinated guild showed no seasonality in flowering in site I but a wet season flowering in site II. 3 Fruiting frequency attained a peak in site I during the late wet season extending into the early dry season; a time-lag correlation showed that fruiting followed rainfall with a lag of about two months. Site II showed a similar fruiting pattern but this was not statistically significant. The dispersal guilds (animal, wind, and explosive passively-dispersed) did not show any clear seasonality in fruiting, except for the animal-dispersed guild which showed wet season fruiting in site I. 4 Hurlbert's overlap index was also calculated in order to look at synchrony in flowering and fruiting irrespective of climatic (dry and wet month) seasonality. In general, overlap in flowering and fruiting guilds was high because of seasonal aggregation. Among the exceptions, at site II the wind-pollinated flowering guild did not show significant overlap between species although flowering aggregated in the wet season. This could be due to the need to avoid heterospecific pollen transfer. 5 Rarer species tended to flower earlier in the dry season and this again could be an adaptation to avoid the risk of heterospecific pollen transfer or competition for pollinators. The more abundant species flowered mainly during the wet season. Species which flower earlier have larger flowers and, having invested more energy in flowers, also have shorter flower to fruit durations.

Inherent structures of phase-separating binary mixtures: Nucleation, spinodal decomposition, and pattern formation

An energy landscape view of phase separation and nonideality in binary mixtures is developed by exploring their potential energy landscape (PEL) as functions of temperature and composition. We employ molecular dynamics simulations to study a model that promotes structure breaking in the solute-solvent parent binary liquid, at low temperatures. The PEL of the system captures the potential energy distribution of the inherent structures (IS) of the system and is obtained by removing the kinetic energy (including that of intermolecular vibrations). The broader distribution of the inherent structure energy for structure breaking liquid than that of the structure making liquid demonstrates the larger role of entropy in stabilizing the parent liquid of the structure breaking type of binary mixtures. At high temperature, although the parent structure of the structure breaking binary mixture is homogenous, the corresponding inherent structure is found to be always phase separated, with a density pattern that exhibits marked correlation with the energy of its inherent structure. Over a broad range of intermediate inherent structure energy, bicontinuous phase separation prevails with interpenetrating stripes as signatures of spinodal decomposition. At low inherent structure energy, the structure is largely phase separated with one interface where as at high inherent structure energy we find nucleation type growth. Interestingly, at low temperature, the average inherent structure energy (< EIS >) exhibits a drop with temperature which signals the onset of crystallization in one of the phases while the other remains in the liquid state. The nonideal composition dependence of viscosity is anticorrelated with average inherent structure energy.

A novel neural network design for long range prediction of rainfall pattern

The importance of long-range prediction of rainfall pattern for devising and planning agricultural strategies cannot be overemphasized. However, the prediction of rainfall pattern remains a difficult problem and the desired level of accuracy has not been reached. The conventional methods for prediction of rainfall use either dynamical or statistical modelling. In this article we report the results of a new modelling technique using artificial neural networks. Artificial neural networks are especially useful where the dynamical processes and their interrelations for a given phenomenon are not known with sufficient accuracy. Since conventional neural networks were found to be unsuitable for simulating and predicting rainfall patterns, a generalized structure of a neural network was then explored and found to provide consistent prediction (hindcast) of all-India annual mean rainfall with good accuracy. Performance and consistency of this network are evaluated and compared with those of other (conventional) neural networks. It is shown that the generalized network can make consistently good prediction of annual mean rainfall. Immediate application and potential of such a prediction system are discussed.

The determination of spatial pattern in Dictyostelium discoideum

Free-living amoebae of the cellular slime mould Dictyostelium discoideum aggregate when starved and give rise to a long and thin multicellular structure, the slug. The slug resembles a metazoan embryo, and as with other embryos it is possible to specify a fate map. In the case of Dictyostelium discoideum the map is especially simple: cells in the anterior fifth of the slug die and form a stalk while the majority of those in the posterior differentiate into spores. The genesis of this anterior-posterior distinction is the subject of our review. In particular, we ask: what are the relative roles of individual pre-aggregative predispositions and post-aggregative position in determining cell fate? We review the literature on the subject and conclude that both factors are important. Variations in nutritional status, or in cell cycle phase at starvation, can bias the probability that an amoeba differentiates into a stalk cell or a spore. On the other hand, isolates, or slug fragments, consisting of only prestalk cells or only prespore cells can regulate so as to result in a normal range of both cell types. We identify three levels of control, each being responsible for guiding patterning in normal development: (i) 'coin tossing', whereby a cell autonomously exhibits a preference for developing along either the stalk or the spore pathway with relative probabilities that can be influenced by the environment; (ii) 'chemical kinetics', whereby prestalk and prespore cells originate from undifferentiated amoebae on a probabilistic basis but, having originated, interact (e.g. via positive and negative feedbacks), and the interaction influences the possibility of conversion of one cell type into the other, and (iii) 'positional information', in which the spatial distribution of morphogens in the slug influences the pathway of differentiation. In the case of possibilities (i) and (ii), sorting out of like cell types leads to the final spatial pattern. In the case of possibility (iii), the pattern arises in situ.

The precision of regulation in Dictyostelium discoideum: implications for cell-type proportioning in the absence of spatial pattern

We have made careful counts of the exact number of spore, stalk and basal disc cells in small fruiting bodies of Dictyostelium discoideum (undifferentiated amoebae are found only rarely and on average their fraction is 4.96 x 10(-4)). (i) Within aggregates of a given size, the relative apportioning of amoebae to the main cell types occurs with a remarkable degree of precision. In most cases the coefficient of variation (c.v.) in the mean fraction of cells that form spores is within 4.86%. The contribution of stalk and basal disc cells is highly variable when considered separately (c.v.'s upto 25% and 100%, respectively), but markedly less so when considered together. Calculations based on theoretical models indicate that purely cell-autonomous specification of cell, fate cannot account for die observed accuracy of proportioning. Cell-autonomous determination to a prestalk or prespore condition followed by cell type interconversion, and stabilised by feedbacks, suffices to explain the measured accuracy. (ii) The fraction of amoebae that differentiates into spores increases monotonically with the total number of cells. This fraction rises from an average of 73.6% for total cell numbers below 30 and reaches 86.0% for cell numbers between 170 and 200 (it remains steady thereafter at around 86%). Correspondingly, the fraction of amoebae differentiating into stalk or basal disc decreases viith total size. These trends are in accordance with evolutionary expectations and imply that a mechanism for sensing the overall size of the aggregate also plays an essential role in the determination of cell-type proportions.