Time and Energy Complexity of Distributed Computation of a Class of Functions in Wireless Sensor Networks

We consider a scenario in which a wireless sensor network is formed by randomly deploying n sensors to measure some spatial function over a field, with the objective of computing a function of the measurements and communicating it to an operator station. We restrict ourselves to the class of type-threshold functions (as defined in the work of Giridhar and Kumar, 2005), of which max, min, and indicator functions are important examples: our discussions are couched in terms of the max function. We view the problem as one of message-passing distributed computation over a geometric random graph. The network is assumed to be synchronous, and the sensors synchronously measure values and then collaborate to compute and deliver the function computed with these values to the operator station. Computation algorithms differ in (1) the communication topology assumed and (2) the messages that the nodes need to exchange in order to carry out the computation. The focus of our paper is to establish (in probability) scaling laws for the time and energy complexity of the distributed function computation over random wireless networks, under the assumption of centralized contention-free scheduling of packet transmissions. First, without any constraint on the computation algorithm, we establish scaling laws for the computation time and energy expenditure for one-time maximum computation. We show that for an optimal algorithm, the computation time and energy expenditure scale, respectively, as Theta(radicn/log n) and Theta(n) asymptotically as the number of sensors n rarr infin. Second, we analyze the performance of three specific computation algorithms that may be used in specific practical situations, namely, the tree algorithm, multihop transmission, and the Ripple algorithm (a type of gossip algorithm), and obtain scaling laws for the computation time and energy expenditure as n rarr infin. In particular, we show that the computation time for these algorithms scales as Theta(radicn/lo- g n), Theta(n), and Theta(radicn log n), respectively, whereas the energy expended scales as , Theta(n), Theta(radicn/log n), and Theta(radicn log n), respectively. Finally, simulation results are provided to show that our analysis indeed captures the correct scaling. The simulations also yield estimates of the constant multipliers in the scaling laws. Our analyses throughout assume a centralized optimal scheduler, and hence, our results can be viewed as providing bounds for the performance with practical distributed schedulers.

The Structure and Functions of Hantavirus Nucleocapsid Protein

Hantaviruses, members of the genus Hantavirus in the Bunyaviridae family, are enveloped single-stranded RNA viruses with tri-segmented genome of negative polarity. In humans, hantaviruses cause two diseases, hemorrhagic fever with renal syndrome (HFRS) and hantavirus pulmonary syndrome (HPS), which vary in severity depending on the causative agent. Each hantavirus is carried by a specific rodent host and is transmitted to humans through excreta of infected rodents. The genome of hantaviruses encodes four structural proteins: the nucleocapsid protein (N), the glycoproteins (Gn and Gc), and the polymerase (L) and also the nonstructural protein (NSs). This thesis deals with the functional characterization of hantavirus N protein with regard to its structure. Structural studies of the N protein have progressed slowly and the crystal structure of the whole protein is still not available, therefore biochemical assays coupled with bioinformatical modeling proved essential for studying N protein structure and functions. Presumably, during RNA encapsidation, the N protein first forms intermediate trimers and then oligomers. First, we investigated the role of N-terminal domain in the N protein oligomerization. The results suggested that the N-terminal region of the N protein forms a coiled-coil, in which two antiparallel alpha helices interact via their hydrophobic seams. Hydrophobic residues L4, I11, L18, L25 and V32 in the first helix and L44, V51, L58 and L65 in the second helix were crucial for stabilizing the structure. The results were consistent with the head-to-head, tail-to-tail model for hantavirus N protein trimerization. We demonstrated that an intact coiled-coil structure of the N terminus is crucial for the oligomerization capacity of the N protein. We also added new details to the head-to-head, tail-to-tail model of trimerization by suggesting that the initial step is based on interaction(s) between intact intra-molecular coiled-coils of the monomers. We further analyzed the importance of charged aa residues located within the coiled-coil for the N protein oligomerization. To predict the interacting surfaces of the monomers we used an upgraded in silico model of the coiled-coil domain that was docked into a trimer. Next the predicted target residues were mutated. The results obtained using the mammalian two-hybrid assay suggested that conserved charged aa residues within the coiled-coil make a substantial contribution to the N protein oligomerization. This contribution probably involves the formation of interacting surfaces of the N monomers and also stabilization of the coiled-coil via intramolecular ionic bridging. We proposed that the tips of the coiled-coils are the first to come into direct contact and thus initiate tight packing of the three monomers into a compact structure. This was in agreement with the previous results showing that an increase in ionic strength abolished the interaction between N protein molecules. We also showed that residues having the strongest effect on the N protein oligomerization are not scattered randomly throughout the coiled-coil 3D model structure, but form clusters. Next we found evidence for the hantaviral N protein interaction with the cytoplasmic tail of the glycoprotein Gn. In order to study this interaction we used the GST pull-down assay in combination with mutagenesis technique. The results demonstrated that intact, properly folded zinc fingers of the Gn protein cytoplasmic tail as well as the middle domain of the N protein (that includes aa residues 80 248 and supposedly carries the RNA-binding domain) are essential for the interaction. Since hantaviruses do not have a matrix protein that mediates the packaging of the viral RNA in other negatve stranded viruses (NSRV), hantaviral RNPs should be involved in a direct interaction with the intraviral domains of the envelope-embedded glycoproteins. By showing the N-Gn interaction we provided the evidence for one of the crucial steps in the virus replication at which RNPs are directed to the site of the virus assembly. Finally we started analysis of the N protein RNA-binding region, which is supposedly located in the middle domain of the N protein molecule. We developed a model for the initial step of RNA-binding by the hantaviral N protein. We hypothesized that the hantaviral N protein possesses two secondary structure elements that initiate the RNA encapsidation. The results suggest that amino acid residues (172-176) presumably act as a hook to catch vRNA and that the positively charged interaction surface (aa residues 144-160) enhances the initial N-RNA interacation. In conclusion, we elucidated new functions of hantavirus N protein. Using in silico modeling we predicted the domain structure of the protein and using experimental techniques showed that each domain is responsible for executing certain function(s). We showed that intact N terminal coiled-coil domain is crucial for oligomerization and charged residues located on its surface form a interaction surface for the N monomers. The middle domain is essential for interaction with the cytoplasmic tail of the Gn protein and RNA binding.

Functions of human papillomavirus E5 oncogene in epithelial cells and in the onset of cervical cancer

Human papillomaviruses (HPVs) are the causal agents of cervical cancer, which is the second most common cancer among women worldwide. Cellular transformation and carcinogenesis depend on the activities of viral E5, E6 and E7 proteins. Alterations in cell-cell contacts and in communication between epithelial cells take place during cervical carcinogenesis, leading to changes in cell morphology, increased cell motility and finally invasion. The aim of this thesis was to study genome-wide effects of the HPV type 16 (HPV-16) E5 protein on the expression of host cell messenger RNAs (mRNAs) and microRNAs by applying microarray technology. The results showed that the HPV-16 E5 protein alters several cellular pathways involved in cellular adhesion, motility and proliferation as well as in the extracellular matrix. The E5 protein was observed to enhance wound healing of epithelial cell monolayers by increasing cell motility in vivo. HPV-16 E5-induced alterations in the expression of cellular microRNAs and their target genes seem to favour increased proliferation and tumorigenesis. E5 was also shown to affect the expression of adherens junction proteins in HaCaT epithelial keratinocytes. In addition, a study of a membrane cytoskeletal cross-linker protein, ezrin, revealed that when activated, it localizes to adherens junctions. The results suggest that ezrin distribution to forming adherens junctions is due to Rac1 activity in epithelial cells. These studies reveal for the first time the holistic effects of HPV-16 E5 protein in promoting precancerous events in epithelial cells. The results contribute to identifyinging novel markers for cervical precancerous stages and to predicting disease behaviour.

Solution of a hypersingular integral equation of the second kind

A straightforward analysis involving the complex function-theoretic method is employed to determine the closed-form solution of a special hypersingular integral equation of the second kind, and its known solution is recovered.

Novel Functions of (p)ppGpp and Cyclic di-GMP in Mycobacterial Physiology Revealed by Phenotype Microarray Analysis of Wild-Type and Isogenic Strains of Mycobacterium smegmatis

The bacterial second messengers (p)ppGpp and bis-(3'-5')-cyclic dimeric GMP (c-di-GMP) regulate important functions, such as transcription, virulence, biofilm formation, and quorum sensing. In mycobacteria, they regulate long-term survival during starvation, pathogenicity, and dormancy. Recently, a Pseudomonas aeruginosa strain lacking (p) ppGpp was shown to be sensitive to multiple classes of antibiotics and defective in biofilm formation. We were interested to find out whether Mycobacterium smegmatis strains lacking the gene for either (p)ppGpp synthesis (Delta rel(Msm)) or c-di-GMP synthesis (Delta dcpA) would display similar phenotypes. We used phenotype microarray technology to compare the growth of the wild-type and the knockout strains in the presence of several antibiotics. Surprisingly, the Delta rel(Msm) and Delta dcpA strains showed enhanced survival in the presence of many antibiotics, but they were defective in biofilm formation. These strains also displayed altered surface properties, like impaired sliding motility, rough colony morphology, and increased aggregation in liquid cultures. Biofilm formation and surface properties are associated with the presence of glycopeptidolipids (GPLs) in the cell walls of M. smegmatis. Thin-layer chromatography analysis of various cell wall fractions revealed that the levels of GPLs and polar lipids were reduced in the knockout strains. As a result, the cell walls of the knockout strains were significantly more hydrophobic than those of the wild type and the complemented strains. We hypothesize that reduced levels of GPLs and polar lipids may contribute to the antibiotic resistance shown by the knockout strains. Altogether, our data suggest that (p)ppGpp and c-di-GMP may be involved in the metabolism of glycopeptidolipids and polar lipids in M. smegmatis.

A modified approach to numerical solution of Fredholm integral equations of the second kind

A modified approach to obtain approximate numerical solutions of Fredholin integral equations of the second kind is presented. The error bound is explained by the aid of several illustrative examples. In each example, the approximate solution is compared with the exact solution, wherever possible, and an excellent agreement is observed. In addition, the error bound in each example is compared with the one obtained by the Nystrom method. It is found that the error bound of the present method is smaller than the ones obtained by the Nystrom method. Further, the present method is successfully applied to derive the solution of an integral equation arising in a special Dirichlet problem. (C) 2015 Elsevier Inc. All rights reserved.

A C-0 Interior Penalty Method for a Fourth-order Variational Inequality of the Second Kind

In this article, we propose a C-0 interior penalty ((CIP)-I-0) method for the frictional plate contact problem and derive both a priori and a posteriori error estimates. We derive an abstract error estimate in the energy norm without additional regularity assumption on the exact solution. The a priori error estimate is of optimal order whenever the solution is regular. Further, we derive a reliable and efficient a posteriori error estimator. Numerical experiments are presented to illustrate the theoretical results. (c) 2015Wiley Periodicals, Inc.

Regulation of Growth, Cell Shape, Cell Division, and Gene Expression by Second Messengers (p)ppGpp and Cyclic Di-GMP in Mycobacterium smegmatis

The alarmone (p)ppGpp regulates transcription, translation, replication, virulence, lipid synthesis, antibiotic sensitivity, biofilm formation, and other functions in bacteria. Signaling nucleotide cyclic di-GMP (c-di-GMP) regulates biofilm formation, motility, virulence, the cell cycle, and other functions. In Mycobacterium smegmatis, both (p) ppGpp and c-di-GMP are synthesized and degraded by bifunctional proteins Rel(Msm) and DcpA, encoded by rel(Msm) and dcpA genes, respectively. We have previously shown that the Delta rel(Msm) and Delta dcpA knockout strains are antibiotic resistant and defective in biofilm formation, show altered cell surface properties, and have reduced levels of glycopeptidolipids and polar lipids in their cell wall (K. R. Gupta, S. Kasetty, and D. Chatterji, Appl Environ Microbiol 81:2571-2578, 2015, http://dx.doi.org/10.1128/AEM.03999-14). In this work, we have explored the phenotypes that are affected by both (p) ppGpp and c-di-GMP in mycobacteria. We have shown that both (p) ppGpp and c-di-GMP are needed to maintain the proper growth rate under stress conditions such as carbon deprivation and cold shock. Scanning electron microscopy showed that low levels of these second messengers result in elongated cells, while high levels reduce the cell length and embed the cells in a biofilm-like matrix. Fluorescence microscopy revealed that the elongated Delta rel(Msm) and Delta dcpA cells are multinucleate, while transmission electron microscopy showed that the elongated cells are multiseptate. Gene expression analysis also showed that genes belonging to functional categories such as virulence, detoxification, lipid metabolism, and cell-wall-related processes were differentially expressed. Our results suggests that both (p) ppGpp and c-di-GMP affect some common phenotypes in M. smegmatis, thus raising a possibility of cross talk between these two second messengers in mycobacteria. IMPORTANCE Our work has expanded the horizon of (p) ppGpp and c-di-GMP signaling in Gram-positive bacteria. We have come across a novel observation that M. smegmatis needs (p) ppGpp and c-di-GMP for cold tolerance. We had previously shown that the Delta rel(Msm) and Delta dcpA strains are defective in biofilm formation. In this work, the overproduction of (p) ppGpp and c-di-GMP encased M. smegmatis in a biofilm-like matrix, which shows that both (p) ppGpp and c-di-GMP are needed for biofilm formation. The regulation of cell length and cell division by (p) ppGpp was known in mycobacteria, but our work shows that c-di-GMP also affects the cell size and cell division in mycobacteria. This is perhaps the first report of c-di-GMP regulating cell division in mycobacteria.

Nucleon structure functions from ν_µ-Fe interactions and a study of the valence quark distribution

Data were taken in 1979-80 by the CCFRR high energy neutrino experiment at Fermilab. A total of 150,000 neutrino and 23,000 antineutrino charged current events in the approximate energy range 25 < E_v < 250GeV are measured and analyzed. The structure functions F2 and xF_3 are extracted for three assumptions about σ_L/σ_T:R=0., R=0.1 and R= a QCD based expression. Systematic errors are estimated and their significance is discussed. Comparisons or the X and Q^2 behaviour or the structure functions with results from other experiments are made.

We find that statistical errors currently dominate our knowledge of the valence quark distribution, which is studied in this thesis. xF_3 from different experiments has, within errors and apart from level differences, the same dependence on x and Q^2, except for the HPWF results. The CDHS F_2 shows a clear fall-off at low-x from the CCFRR and EMC results, again apart from level differences which are calculable from cross-sections.

The result for the the GLS rule is found to be 2.83±.15±.09±.10 where the first error is statistical, the second is an overall level error and the third covers the rest of the systematic errors. QCD studies of xF_3 to leading and second order have been done. The QCD evolution of xF_3, which is independent of R and the strange sea, does not depend on the gluon distribution and fits yield

ʌ_(LO) = 88^(+163)_(-78) ^(+113)_(-70) MeV

The systematic errors are smaller than the statistical errors. Second order fits give somewhat different values of ʌ, although α_s (at Q^2_0 = 12.6 GeV^2) is not so different.

A fit using the better determined F_2 in place of xF_3 for x > 0.4 i.e., assuming q = 0 in that region, gives

ʌ_(LO) = 266^(+114)_(-104) ^(+85)_(-79) MeV

Again, the statistical errors are larger than the systematic errors. An attempt to measure R was made and the measurements are described. Utilizing the inequality q(x)≥0 we find that in the region x > .4 R is less than 0.55 at the 90% confidence level.

Understanding deep architectures and the effect of unsupervised pre-training

Cette thèse porte sur une classe d'algorithmes d'apprentissage appelés architectures profondes. Il existe des résultats qui indiquent que les représentations peu profondes et locales ne sont pas suffisantes pour la modélisation des fonctions comportant plusieurs facteurs de variation. Nous sommes particulièrement intéressés par ce genre de données car nous espérons qu'un agent intelligent sera en mesure d'apprendre à les modéliser automatiquement; l'hypothèse est que les architectures profondes sont mieux adaptées pour les modéliser. Les travaux de Hinton (2006) furent une véritable percée, car l'idée d'utiliser un algorithme d'apprentissage non-supervisé, les machines de Boltzmann restreintes, pour l'initialisation des poids d'un réseau de neurones supervisé a été cruciale pour entraîner l'architecture profonde la plus populaire, soit les réseaux de neurones artificiels avec des poids totalement connectés. Cette idée a été reprise et reproduite avec succès dans plusieurs contextes et avec une variété de modèles. Dans le cadre de cette thèse, nous considérons les architectures profondes comme des biais inductifs. Ces biais sont représentés non seulement par les modèles eux-mêmes, mais aussi par les méthodes d'entraînement qui sont souvent utilisés en conjonction avec ceux-ci. Nous désirons définir les raisons pour lesquelles cette classe de fonctions généralise bien, les situations auxquelles ces fonctions pourront être appliquées, ainsi que les descriptions qualitatives de telles fonctions. L'objectif de cette thèse est d'obtenir une meilleure compréhension du succès des architectures profondes. Dans le premier article, nous testons la concordance entre nos intuitions---que les réseaux profonds sont nécessaires pour mieux apprendre avec des données comportant plusieurs facteurs de variation---et les résultats empiriques. Le second article est une étude approfondie de la question: pourquoi l'apprentissage non-supervisé aide à mieux généraliser dans un réseau profond? Nous explorons et évaluons plusieurs hypothèses tentant d'élucider le fonctionnement de ces modèles. Finalement, le troisième article cherche à définir de façon qualitative les fonctions modélisées par un réseau profond. Ces visualisations facilitent l'interprétation des représentations et invariances modélisées par une architecture profonde.

Military doctrine, command philosophy and the generation of fighting power: genesis and theory

Military doctrine is one of the conceptual components of war. Its raison d’être is that of a force multiplier. It enables a smaller force to take on and defeat a larger force in battle. This article’s departure point is the aphorism of Sir Julian Corbett, who described doctrine as ‘the soul of warfare’. The second dimension to creating a force multiplier effect is forging doctrine with an appropriate command philosophy. The challenge for commanders is how, in unique circumstances, to formulate, disseminate and apply an appropriate doctrine and combine it with a relevant command philosophy. This can only be achieved by policy-makers and senior commanders successfully answering the Clausewitzian question: what kind of conflict are they involved in? Once an answer has been provided, a synthesis of these two factors can be developed and applied. Doctrine has implications for all three levels of war. Tactically, doctrine does two things: first, it helps to create a tempo of operations; second, it develops a transitory quality that will produce operational effect, and ultimately facilitate the pursuit of strategic objectives. Its function is to provide both training and instruction. At the operational level instruction and understanding are critical functions. Third, at the strategic level it provides understanding and direction. Using John Gooch’s six components of doctrine, it will be argued that there is a lacunae in the theory of doctrine as these components can manifest themselves in very different ways at the three levels of war. They can in turn affect the transitory quality of tactical operations. Doctrine is pivotal to success in war. Without doctrine and the appropriate command philosophy military operations cannot be successfully concluded against an active and determined foe.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

Laguerre polynomials as Jensen polynomials of Laguerre-Polya entire functions

We prove that the only Jensen polynomials associated with an entire function in the Laguerre-Polya class that are orthogonal are the Laguerre polynomials. (C) 2009 Elsevier B.V. All rights reserved.