EXTENSIONS OF VECTOR BUNDLES WITH APPLICATION TO NOETHER-LEFSCHETZ THEOREMS

Given a smooth, projective variety Y over an algebraically closed field of characteristic zero, and a smooth, ample hyperplane section X subset of Y, we study the question of when a bundle E on X, extends to a bundle epsilon on a Zariski open set U subset of Y containing X. The main ingredients used are explicit descriptions of various obstruction classes in the deformation theory of bundles, together with Grothendieck-Lefschetz theory. As a consequence, we prove a Noether-Lefschetz theorem for higher rank bundles, which recovers and unifies the Noether-Lefschetz theorems of Joshi and Ravindra-Srinivas.

Polynomial time and parameterized approximation algorithms for boxicity

The boxicity (cubicity) of a graph G, denoted by box(G) (respectively cub(G)), is the minimum integer k such that G can be represented as the intersection graph of axis parallel boxes (cubes) in ℝ k . The problem of computing boxicity (cubicity) is known to be inapproximable in polynomial time even for graph classes like bipartite, co-bipartite and split graphs, within an O(n 0.5 − ε ) factor for any ε > 0, unless NP = ZPP. We prove that if a graph G on n vertices has a clique on n − k vertices, then box(G) can be computed in time n22O(k2logk) . Using this fact, various FPT approximation algorithms for boxicity are derived. The parameter used is the vertex (or edge) edit distance of the input graph from certain graph families of bounded boxicity - like interval graphs and planar graphs. Using the same fact, we also derive an O(nloglogn√logn√) factor approximation algorithm for computing boxicity, which, to our knowledge, is the first o(n) factor approximation algorithm for the problem. We also present an FPT approximation algorithm for computing the cubicity of graphs, with vertex cover number as the parameter.

Mechanism design for time critical and cost critical task execution via crowdsourcing

An exciting application of crowdsourcing is to use social networks in complex task execution. In this paper, we address the problem of a planner who needs to incentivize agents within a network in order to seek their help in executing an atomic task as well as in recruiting other agents to execute the task. We study this mechanism design problem under two natural resource optimization settings: (1) cost critical tasks, where the planner's goal is to minimize the total cost, and (2) time critical tasks, where the goal is to minimize the total time elapsed before the task is executed. We identify a set of desirable properties that should ideally be satisfied by a crowdsourcing mechanism. In particular, sybil-proofness and collapse-proofness are two complementary properties in our desiderata. We prove that no mechanism can satisfy all the desirable properties simultaneously. This leads us naturally to explore approximate versions of the critical properties. We focus our attention on approximate sybil-proofness and our exploration leads to a parametrized family of payment mechanisms which satisfy collapse-proofness. We characterize the approximate versions of the desirable properties in cost critical and time critical domain.

Threats and trade-fffs in resource critical crowdsourcing tasks over networks

In recent times, crowdsourcing over social networks has emerged as an active tool for complex task execution. In this paper, we address the problem faced by a planner to incen-tivize agents in the network to execute a task and also help in recruiting other agents for this purpose. We study this mecha-nism design problem under two natural resource optimization settings: (1) cost critical tasks, where the planner’s goal is to minimize the total cost, and (2) time critical tasks, where the goal is to minimize the total time elapsed before the task is executed. We define a set of fairness properties that should beideally satisfied by a crowdsourcing mechanism. We prove that no mechanism can satisfy all these properties simultane-ously. We relax some of these properties and define their ap-proximate counterparts. Under appropriate approximate fair-ness criteria, we obtain a non-trivial family of payment mech-anisms. Moreover, we provide precise characterizations of cost critical and time critical mechanisms.

Interdependent cache analyses for better precision and safety

One of the challenges for accurately estimating Worst Case Execu-tion Time(WCET) of executables is to accurately predict their cache behaviour. Various techniques have been developed to predict the cache contents at different program points to estimate the execution time of memory-accessing instructions. One of the most widely used techniques is Abstract Interpretation based Must Analysis, which de-termines the cache blocks guaranteed to be present in the cache, and hence provides safe estimation of cache hits and misses. However,Must Analysis is highly imprecise, and platforms using Must Analysis have been known to produce blown-up WCET estimates. In our work, we propose to use May Analysis to assist the Must Analysis cache up-date and make it more precise. We prove the safety of our approach as well as provide examples where our Improved Must Analysis provides better precision. Further, we also detect a serious flaw in the original Persistence Analysis, and use Must and May Analysis to assist the Persistence Analysis cache update, to make it safe and more precise than the known solutions to the problem.

Classification calibration dimension for general multiclass losses

We study consistency properties of surrogate loss functions for general multiclass classification problems, defined by a general loss matrix. We extend the notion of classification calibration, which has been studied for binary and multiclass 0-1 classification problems (and for certain other specific learning problems), to the general multiclass setting, and derive necessary and sufficient conditions for a surrogate loss to be classification calibrated with respect to a loss matrix in this setting. We then introduce the notion of \emph{classification calibration dimension} of a multiclass loss matrix, which measures the smallest `size' of a prediction space for which it is possible to design a convex surrogate that is classification calibrated with respect to the loss matrix. We derive both upper and lower bounds on this quantity, and use these results to analyze various loss matrices. In particular, as one application, we provide a different route from the recent result of Duchi et al.\ (2010) for analyzing the difficulty of designing `low-dimensional' convex surrogates that are consistent with respect to pairwise subset ranking losses. We anticipate the classification calibration dimension may prove to be a useful tool in the study and design of surrogate losses for general multiclass learning problems.

Optimal capacity relay node placement in a multi-hop network on a line

We use information theoretic achievable rate formulas for the multi-relay channel to study the problem of optimal placement of relay nodes along the straight line joining a source node and a destination node. The achievable rate formulas that we utilize are for full-duplex radios at the relays and decode-and-forward relaying. For the single relay case, and individual power constraints at the source node and the relay node, we provide explicit formulas for the optimal relay location and the optimal power allocation to the source-relay channel, for the exponential and the power-law path-loss channel models. For the multiple relay case, we consider exponential path-loss and a total power constraint over the source and the relays, and derive an optimization problem, the solution of which provides the optimal relay locations. Numerical results suggest that at low attenuation the relays are mostly clustered close to the source in order to be able to cooperate among themselves, whereas at high attenuation they are uniformly placed and work as repeaters. We also prove that a constant rate independent of the attenuation in the network can be achieved by placing a large enough number of relay nodes uniformly between the source and the destination, under the exponential path-loss model with total power constraint.

Data acquisition and processing at ocean bottom for a Tsunami warning system

The design and development of a Bottom Pressure Recorder for a Tsunami Early Warning System is described here. The special requirements that it should satisfy for the specific application of deployment at ocean bed and pressure monitoring of the water column above are dealt with. A high-resolution data digitization and low circuit power consumption are typical ones. The implementation details of the data sensing and acquisition part to meet these are also brought out. The data processing part typically encompasses a Tsunami detection algorithm that should detect an event of significance in the background of a variety of periodic and aperiodic noise signals. Such an algorithm and its simulation are presented. Further, the results of sea trials carried out on the system off the Chennai coast are presented. The high quality and fidelity of the data prove that the system design is robust despite its low cost and with suitable augmentations, is ready for a full-fledged deployment at ocean bed. (C) 2013 Elsevier Ltd. All rights reserved.

On stellated spheres and a tightness criterion for combinatorial manifolds

We introduce k-stellated spheres and consider the class W-k(d) of triangulated d-manifolds, all of whose vertex links are k-stellated, and its subclass W-k*; (d), consisting of the (k + 1)-neighbourly members of W-k(d). We introduce the mu-vector of any simplicial complex and show that, in the case of 2-neighbourly simplicial complexes, the mu-vector dominates the vector of Betti numbers componentwise; the two vectors are equal precisely for tight simplicial complexes. We are able to estimate/compute certain alternating sums of the components of the mu-vector of any 2-neighbourly member of W-k(d) for d >= 2k. As a consequence of this theory, we prove a lower bound theorem for such triangulated manifolds, and we determine the integral homology type of members of W-k*(d) for d >= 2k + 2. As another application, we prove that, when d not equal 2k + 1, all members of W-k*(d) are tight. We also characterize the tight members of W-k*(2k + 1) in terms of their kth Betti numbers. These results more or less answer a recent question of Effenberger, and also provide a uniform and conceptual tightness proof for all except two of the known tight triangulated manifolds. We also prove a lower bound theorem for homology manifolds in which the members of W-1(d) provide the equality case. This generalizes a result (the d = 4 case) due to Walkup and Kuhnel. As a consequence, it is shown that every tight member of W-1 (d) is strongly minimal, thus providing substantial evidence in favour of a conjecture of Kuhnel and Lutz asserting that tight homology manifolds should be strongly minimal. (C) 2013 Elsevier Ltd. All rights reserved.

Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications

A series expansion for Heckman-Opdam hypergeometric functions phi(lambda) is obtained for all lambda is an element of alpha(C)*. As a consequence, estimates for phi(lambda) away from the walls of a Weyl chamber are established. We also characterize the bounded hypergeometric functions and thus prove an analogue of the celebrated theorem of Helgason and Johnson on the bounded spherical functions on a Riemannian symmetric space of the noncompact type. The L-P-theory for the hypergeometric Fourier transform is developed for 0 < p < 2. In particular, an inversion formula is proved when 1 <= p < 2. (C) 2013 Elsevier Inc. All rights reserved.

Analytical solutions for movement of cold water thermal front in a heterogeneous geothermal reservoir

In the present study an analytical model has been presented to describe the transient temperature distribution and advancement of the thermal front generated due to the reinjection of heat depleted water in a heterogeneous geothermal reservoir. One dimensional heat transport equation in porous media with advection and longitudinal heat conduction has been solved analytically using Laplace transform technique in a semi infinite medium. The heterogeneity of the porous medium is expressed by the spatial variation of the flow velocity and the longitudinal effective thermal conductivity of the medium. A simpler solution is also derived afterwards neglecting the longitudinal conduction depending on the situation where the contribution to the transient heat transport phenomenon in the porous media is negligible. Solution for a homogeneous aquifer with constant values of the rock and fluid parameters is also derived with an aim to compare the results with that of the heterogeneous one. The effect of some of the parameters involved, on the transient heat transport phenomenon is assessed by observing the variation of the results with different magnitudes of those parameters. Results prove the heterogeneity of the medium, the flow velocity and the longitudinal conductivity to have great influence and porosity to have negligible effect on the transient temperature distribution. (C) 2013 Elsevier Inc. All rights reserved.

End point estimates for Radon transform of radial functions on non-Euclidean spaces

We prove end point estimate for Radon transform of radial functions on affine Grasamannian and real hyperbolic space. We also discuss analogs of these results on the sphere.

New luminescent 2-methoxy-6-(4-methoxy-phenyl)-4-p-tolyl-nicotinonitrile: Synthesis, crystal structure, DFT and photophysical studies

In the current communication, we report the synthesis, spectroscopic, crystal structure, DFT and photophysical studies of a new nicotinonitrile derivative, viz. 2-methoxy-6-(4-methoxy-phenyl)-4-p-tolyl-nicotinonitrile (2) as a potential blue light emitting material. The compound 2 was synthesized in good yield via a simple route. The acquired spectral and elemental analysis data were in consistent with the chemical structure of 2. The single crystal study further confirms its three dimensional structure, molecular shape, and nature of short contacts. Its DFT calculations reveal that compound 2 possesses a non-planar structure and its theoretical IR spectral data are found to be in accordance with experimental values. In addition, its UV visible and fluorescence spectral measurements prove that the compound exhibits good absorption and fluorescence properties. Also, it shows positive solvatochromic effect when the solvent polarity was varied from non-polar to polar. (c) 2014 Elsevier B.V. All rights reserved.

Proper holomorphic mappings between hyperbolic product manifolds

We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert and Stein, the proof of the full result relies on the interplay of the latter ideas and a finiteness theorem for Riemann surfaces.

Counterfactual quantum certificate authorization

We present a multipartite protocol in a counterfactual paradigm. In counterfactual quantum cryptography, secure information is transmitted between two spatially separated parties even when there is no physical travel of particles transferring the information between them. We propose here a tripartite counterfactual quantum protocol for the task of certificate authorization. Here a trusted third party, Alice, authenticates an entity Bob (e.g., a bank) that a client Charlie wishes to securely transact with. The protocol is counterfactual with respect to either Bob or Charlie. We prove its security against a general incoherent attack, where Eve attacks single particles.