Percolation and connectivity in AB random geometric graphs

Given two independent Poisson point processes Phi((1)), Phi((2)) in R-d, the AB Poisson Boolean model is the graph with the points of Phi((1)) as vertices and with edges between any pair of points for which the intersection of balls of radius 2r centered at these points contains at least one point of Phi((2)). This is a generalization of the AB percolation model on discrete lattices. We show the existence of percolation for all d >= 2 and derive bounds fora critical intensity. We also provide a characterization for this critical intensity when d = 2. To study the connectivity problem, we consider independent Poisson point processes of intensities n and tau n in the unit cube. The AB random geometric graph is defined as above but with balls of radius r. We derive a weak law result for the largest nearest-neighbor distance and almost-sure asymptotic bounds for the connectivity threshold.

Distinct and Contrasting Transcription Initiation Patterns at Mycobacterium tuberculosis Promoters

Although sequencing of Mycobacterium tuberculosis genome lead to better understanding of transcription units and gene functions, interactions occurring during transcription initiation between RNA polymerase and promoters is yet to be elucidated. Different stages of transcription initiation include promoter specific binding of RNAP, isomerization, abortive initiation and promoter clearance. We have now analyzed these events with four promoters of M. tuberculosis viz. P-gyrB1, P-gyrR, P-rrnPCL1 and P-metU. The promoters differed from each other in their rates of open complex formation, decay, promoter clearance and abortive transcription. The equilibrium binding and kinetic studies of various steps revealed distinct rate limiting events for each of the promoter, which also differed markedly in their characteristics from the respective promoters of Mycobacterium smegmatis. Surprisingly, the transcription at gyr promoter was enhanced in the presence of initiating nucleotides and decreased in the presence of alarmone, pppGpp, a pattern typically seen with rRNA promoters studied so far. The gyr promoter of M. smegmatis, on the other hand, was not subjected to pppGpp mediated regulation. The marked differences in the transcription initiation pathway seen with rrn and gyr promoters of M. smegmatis and M. tuberculosis suggest that such species specific differences in the regulation of expression of the crucial housekeeping genes could be one of the key determinants contributing to the differences in growth rate and lifestyle of the two organisms. Moreover, the distinct rate limiting steps during transcription initiation of each one of the promoters studied point at variations in their intracellular regulation.

Rainbow connectivity: hardness and tractability

A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices. The (strong) rainbow connectivity of a graph G, denoted by (src(G), respectively) rc(G) is the smallest number of colors required to edge color the graph such that G is (strongly) rainbow connected. In this paper we study the rainbow connectivity problem and the strong rainbow connectivity problem from a computational point of view. Our main results can be summarised as below: 1) For every fixed k >= 3, it is NP-Complete to decide whether src(G) <= k even when the graph G is bipartite. 2) For every fixed odd k >= 3, it is NP-Complete to decide whether rc(G) <= k. This resolves one of the open problems posed by Chakraborty et al. (J. Comb. Opt., 2011) where they prove the hardness for the even case. 3) The following problem is fixed parameter tractable: Given a graph G, determine the maximum number of pairs of vertices that can be rainbow connected using two colors. 4) For a directed graph G, it is NP-Complete to decide whether rc(G) <= 2.

A method of designing seamless connectivity algorithm in ubiquitous networks

The b-phase of polyvinylidene fluoride (PVDF) is well known for its piezoelectric properties. PVDF films have been developed using solvent cast method. The films thus produced are in a-phase. The a-phase is transformed to piezoelectric b-phase when the film is hotstretched with various different stretching factors at various different temperatures. The films are then characterized in terms of their mechanical properties and surface morphological changes during the transformation from a- to b-phases by using X-ray diffraction, differential scanning calorimeter, Raman spectra, Infrared spectra, tensile testing, and scanning electron microscopy. The films showed increased crystallinity with stretching at temperature up to 808C. The optimum conditions to achieve b-phase have been discussed in detail. The fabricated PVDF sensors have been tested for free vibration and impact on plate structure, and its response is compared with conventional piezoelectric wafer type sensor. The resonant and antiresonant peaks in the frequency response of PVDF sensor match well with that of lead zirconate titanate wafer sensors. Effective piezoelectric properties and the variations in the frequency response spectra due to free vibration and impact loading conditions are reported. POLYM. ENG. SCI., 00:000–000, 2012. ª2012 Society of Plastics Engineers

Rapid mass spectrometric determination of disulfide connectivity in peptides and proteins

Disulfide crosslinks are ubiquitous in natural peptides and proteins, providing rigidity to polypeptide scaffolds. The assignment of disulfide connectivity in multiple crosslinked systems is often difficult to achieve. Here, we show that rapid unambiguous characterisation of disulfide connectivity can be achieved through direct mass spectrometric CID fragmentation of the disulfide intact polypeptides. The method requires a direct mass spectrometric fragmentation of the native disulfide bonded polypeptides and subsequent analysis using a newly developed program, DisConnect. Technical difficulties involving direct fragmentation of proteins are surmounted by an initial proteolytic nick and subsequent determination of the structures of these proteolytic peptides through DisConnect. While the connectivity in proteolytic fragments containing one cystine is evident from the MS profile alone, those with multiple cystines are subjected to subsequent mass spectrometric fragmentation. The wide applicability of this method is illustrated using examples of peptide hormones, peptide toxins, proteins, and disulfide foldamers of a synthetic analogue of a marine peptide toxin. The method, coupled with DisConnect, provides an unambiguous, straightforward approach, especially useful for the rapid screening of the disulfide crosslink fidelity in recombinant proteins, determination of disulfide linkages in natural peptide toxins and characterization of folding intermediates encountered in oxidative folding pathways.

Stochastic analysis of epidemics on adaptive time varying networks

Many studies investigating the effect of human social connectivity structures (networks) and human behavioral adaptations on the spread of infectious diseases have assumed either a static connectivity structure or a network which adapts itself in response to the epidemic (adaptive networks). However, human social connections are inherently dynamic or time varying. Furthermore, the spread of many infectious diseases occur on a time scale comparable to the time scale of the evolving network structure. Here we aim to quantify the effect of human behavioral adaptations on the spread of asymptomatic infectious diseases on time varying networks. We perform a full stochastic analysis using a continuous time Markov chain approach for calculating the outbreak probability, mean epidemic duration, epidemic reemergence probability, etc. Additionally, we use mean-field theory for calculating epidemic thresholds. Theoretical predictions are verified using extensive simulations. Our studies have uncovered the existence of an ``adaptive threshold,'' i.e., when the ratio of susceptibility (or infectivity) rate to recovery rate is below the threshold value, adaptive behavior can prevent the epidemic. However, if it is above the threshold, no amount of behavioral adaptations can prevent the epidemic. Our analyses suggest that the interaction patterns of the infected population play a major role in sustaining the epidemic. Our results have implications on epidemic containment policies, as awareness campaigns and human behavioral responses can be effective only if the interaction levels of the infected populace are kept in check.

Algebraic characterization of rainbow connectivity

The use of algebraic techniques to solve combinatorial problems is studied in this paper. We formulate the rainbow connectivity problem as a system of polynomial equations. We first consider the case of two colors for which the problem is known to be hard and we then extend the approach to the general case. We also present a formulation of the rainbow connectivity problem as an ideal membership problem.

Using intra-flock association patterns to understand why birds participate in mixed-species foraging flocks in terrestrial habitats

Bird species are hypothesized to join mixed-species flocks (flocks hereon) either for direct foraging or anti-predation-related benefits. In this study, conducted in a tropical evergreen forest in the Western Ghats of India, we used intra-flock association patterns to generate a community-wide assessment of flocking benefits for different species. We assumed that individuals needed to be physically proximate to particular heterospecific individuals within flocks to obtain any direct foraging benefit (flushed prey, kleptoparasitism, copying foraging locations). Alternatively, for anti-predation benefits, physical proximity to particular heterospecifics is not required, i.e. just being in the flock vicinity can suffice. Therefore, we used choice of locations within flocks to infer whether individual species are obtaining direct foraging or anti-predation benefits. A small subset of the bird community (5/29 species), composed of all members of the sallying guild, showed non-random physical proximity to heterospecifics within flocks. All preferred associates were from non-sallying guilds, suggesting that the sallying species were likely obtaining direct foraging benefits either in the form of flushed or kleptoparasitized prey. The majority of the species (24/29) chose locations randomly with respect to heterospecifics within flocks and, thus, were likely obtaining antipredation benefits. In summary, our study indicates that direct foraging benefits are important for only a small proportion of species in flocks and that predation is likely to be the main driver of flocking for most participants. Our findings apart, our study provides methodological advances that might be useful in understanding asymmetric interactions in social groups of single and multiple species.

Variation at Diabetes- and Obesity-Associated Loci May Mirror Neutral Patterns of Human Population Diversity and Diabetes Prevalence in India

South Asian populations harbor a high degree of genetic diversity, due in part to demographic history. Two studies on genome-wide variation in Indian populations have shown that most Indian populations show varying degrees of admixture between ancestral north Indian and ancestral south Indian components. As a result of this structure, genetic variation in India appears to follow a geographic cline. Similarly, Indian populations seem to show detectable differences in diabetes and obesity prevalence between different geographic regions of the country. We tested the hypothesis that genetic variation at diabetes-and obesity-associated loci may be potentially related to different genetic ancestries. We genotyped 2977 individuals from 61 populations across India for 18 SNPs in genes implicated in T2D and obesity. We examined patterns of variation in allele frequency across different geographical gradients and considered state of origin and language affiliation. Our results show that most of the 18 SNPs show no significant correlation with latitude, the geographic cline reported in previous studies, or by language family. Exceptions include KCNQ1 with latitude and THADA and JAK1 with language, which suggests that genetic variation at previously ascertained diabetes-associated loci may only partly mirror geographic patterns of genome-wide diversity in Indian populations.

Connectivity analysis of multichannel EEG signals using recurrence based phase synchronization technique

Real world biological systems such as the human brain are inherently nonlinear and difficult to model. However, most of the previous studies have either employed linear models or parametric nonlinear models for investigating brain function. In this paper, a novel application of a nonlinear measure of phase synchronization based on recurrences, correlation between probabilities of recurrence (CPR), to study connectivity in the brain has been proposed. Being non-parametric, this method makes very few assumptions, making it suitable for investigating brain function in a data-driven way. CPR's utility with application to multichannel electroencephalographic (EEG) signals has been demonstrated. Brain connectivity obtained using thresholded CPR matrix of multichannel EEG signals showed clear differences in the number and pattern of connections in brain connectivity between (a) epileptic seizure and pre-seizure and (b) eyes open and eyes closed states. Corresponding brain headmaps provide meaningful insights about synchronization in the brain in those states. K-means clustering of connectivity parameters of CPR and linear correlation obtained from global epileptic seizure and pre-seizure showed significantly larger cluster centroid distances for CPR as opposed to linear correlation, thereby demonstrating the superior ability of CPR for discriminating seizure from pre-seizure. The headmap in the case of focal epilepsy clearly enables us to identify the focus of the epilepsy which provides certain diagnostic value. (C) 2013 Elsevier Ltd. All rights reserved.

Early Warning Signals of Ecological Transitions: Methods for Spatial Patterns

A number of ecosystems can exhibit abrupt shifts between alternative stable states. Because of their important ecological and economic consequences, recent research has focused on devising early warning signals for anticipating such abrupt ecological transitions. In particular, theoretical studies show that changes in spatial characteristics of the system could provide early warnings of approaching transitions. However, the empirical validation of these indicators lag behind their theoretical developments. Here, we summarize a range of currently available spatial early warning signals, suggest potential null models to interpret their trends, and apply them to three simulated spatial data sets of systems undergoing an abrupt transition. In addition to providing a step-by-step methodology for applying these signals to spatial data sets, we propose a statistical toolbox that may be used to help detect approaching transitions in a wide range of spatial data. We hope that our methodology together with the computer codes will stimulate the application and testing of spatial early warning signals on real spatial data.

Characterising weather patterns associated with fire in a seasonally dry tropical forest in southern India

Anthropogenic fires in seasonally dry tropical forests are a regular occurrence during the dry season. Forest managers in India, who presently follow a fire suppression policy in such forests, would benefit from a system of assessing the potential risk to fire on a particular day. We examined the relationship between weather variables (seasonal rainfall, relative humidity, temperature) and days of fire during the dry seasons of 2004-2010, based on MODIS fire incident data in the seasonally dry tropical forests of Mudumalai in the Western Ghats, southern India. Logistic regression analysis showed that high probabilities of a fire day, indicating successful ignition of litter and grass fuel on the forest floor, were associated with low levels of early dry season rainfall, low daily average relative humidity and high daily average temperatures. These weather conditions are representative of low moisture levels of fine fuels, suggesting that the occurrence of fire is moderated by environmental conditions that reduce the flammability of fine fuels in the dry tropics. We propose a quantitative framework for assessing risk of a fire day to assist forest managers in anticipating fire occurrences in this seasonally dry tropical forest, and possibly for those across South Asia.

Turing and animal coat patterns

The present article describes a beautiful contribution of Alan Turing to our understanding of how animal coat patterns form. The question that Turing posed was the following. A collection of identical cells (or processors for that matter), all running the exact same program, and all communicating with each other in the exact same way, should always be in the same state. Yet they produce nonhomogeneous periodic patterns, like those seen on animal coats. How does this happen? Turing gave an elegant explanation for this phenomenon, namely that differences between the cells due to small amounts of random noise can actually be amplified into structured periodic patterns. We attempt to describe his core conceptual contribution below.

Monitoring urbanization and its implications in a mega city from space: Spatiotemporal patterns and its indicators

Rapid and invasive urbanization has been associated with depletion of natural resources (vegetation and water resources), which in turn deteriorates the landscape structure and conditions in the local environment. Rapid increase in population due to the migration from rural areas is one of the critical issues of the urban growth. Urbanisation in India is drastically changing the land cover and often resulting in the sprawl. The sprawl regions often lack basic amenities such as treated water supply, sanitation, etc. This necessitates regular monitoring and understanding of the rate of urban development in order to ensure the sustenance of natural resources. Urban sprawl is the extent of urbanization which leads to the development of urban forms with the destruction of ecology and natural landforms. The rate of change of land use and extent of urban sprawl can be efficiently visualized and modelled with the help of geo-informatics. The knowledge of urban area, especially the growth magnitude, shape geometry, and spatial pattern is essential to understand the growth and characteristics of urbanization process. Urban pattern, shape and growth can be quantified using spatial metrics. This communication quantifies the urbanisation and associated growth pattern in Delhi. Spatial data of four decades were analysed to understand land over and land use dynamics. Further the region was divided into 4 zones and into circles of 1 km incrementing radius to understand and quantify the local spatial changes. Results of the landscape metrics indicate that the urban center was highly aggregated and the outskirts and the buffer regions were in the verge of aggregating urban patches. Shannon's Entropy index clearly depicted the outgrowth of sprawl areas in different zones of Delhi. (C) 2014 Elsevier Ltd. All rights reserved.

Simultaneously Uncovering the Patterns of Brain Regions Involved in Different Story Reading Subprocesses

Story understanding involves many perceptual and cognitive subprocesses, from perceiving individual words, to parsing sentences, to understanding the relationships among the story characters. We present an integrated computational model of reading that incorporates these and additional subprocesses, simultaneously discovering their fMRI signatures. Our model predicts the fMRI activity associated with reading arbitrary text passages, well enough to distinguish which of two story segments is being read with 74% accuracy. This approach is the first to simultaneously track diverse reading subprocesses during complex story processing and predict the detailed neural representation of diverse story features, ranging from visual word properties to the mention of different story characters and different actions they perform. We construct brain representation maps that replicate many results from a wide range of classical studies that focus each on one aspect of language processing and offer new insights on which type of information is processed by different areas involved in language processing. Additionally, this approach is promising for studying individual differences: it can be used to create single subject maps that may potentially be used to measure reading comprehension and diagnose reading disorders.