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Incorporating prior knowledge in medical image segmentation: a surveyJul 05 2016Medical image segmentation, the task of partitioning an image into meaningful parts, is an important step toward automating medical image analysis and is at the crux of a variety of medical imaging applications, such as computer aided diagnosis, therapy ... More

Latency Optimization for Resource Allocation in Cloud Computing SystemMay 04 2016Recent studies in different fields of science caused emergence of needs for high performance computing systems like Cloud. A critical issue in design and implementation of such systems is resource allocation which is directly affected by internal and ... More

Practical Issues of Action-conditioned Next Image PredictionFeb 08 2018The problem of action-conditioned image prediction is to predict the expected next frame given the current camera frame the robot observes and an action selected by the robot. We provide the first comparison of two recent popular models, especially for ... More

Language free character recognition using character sketch and center of gravity shiftingAug 03 2016In this research, we present a heuristic method for character recognition. For this purpose, a sketch is constructed from the image that contains the character to be recognized. This sketch contains the most important pixels of image that are representatives ... More

Multi-stage Antenna Selection for Adaptive Beamforming in MIMO ArraysApr 18 2019Increasing the number of transmit and receive elements in multiple-input-multiple-output (MIMO) antenna arrays imposes a substantial increase in hardware and computational costs. We mitigate this problem by employing a reconfigurable MIMO array where ... More

Stabilisers of eigenvectors of finite reflection groupsDec 04 2015Let $x$ be an eigenvector for an element of a finite irreducible reflection group $W$. Let $W_x$ denote the subgroup of $W$ which stabilises $x$. We provide an upper bound for the number of roots in the root system of $W_x$ . This generalises a result ... More

Phase Transition And Hexagonal Patterns In Rich Stimulant Diffusion-Chemotaxis ModelNov 20 2013Dec 18 2013An important component in studying mathematical models in many biochemical systems, such as those found in developmental biology, is phase transition. The purpose of this work is to analyze the phase transition property of a diffusion-chemotaxis model ... More

BRST Quantization of Noncommutative Gauge TheoriesFeb 23 2003Apr 07 2003In this paper, the BRST symmetry transformation is presented for the noncommutative U(N) gauge theory. The nilpotency of the charge associated to this symmetry is then proved. As a consequence for the space-like non-commutativity parameter, the Hilbert ... More

Cyclic Homology of DG Coalgebras and a Kuenneth FormulaJun 19 1998In this note we extend the cyclic homology functor, and in particular the periodic cyclic homology, to the category of DG (= differential graded) coalgebras. We are partly motivated by the question of products and coproducts in the cyclic homology of ... More

Generalized Nonlinear Robust Energy-to-Peak Filtering for Differential Algebraic SystemsFeb 25 2014The problem of robust nonlinear energy-to-peak filtering for nonlinear descriptor systems with model uncertainties is addressed. The system is assumed to have nonlinearities both in the state and output equations as well as norm-bounded time-varying uncertainties ... More

A Generalized Robust Filtering Framework for Nonlinear Differential-Algebraic SystemsFeb 22 2014A generalized dynamical robust nonlinear filtering framework is established for a class of Lipschitz differential algebraic systems, in which the nonlinearities appear both in the state and measured output equations. The system is assumed to be affected ... More

Computer Algebra Methods in Control SystemsDec 26 2017Dec 29 2017As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and design of such ... More

Lectures on Noncommutative GeometryFeb 06 2007Apr 12 2007This text is an introduction to a few selected areas of Alain Connes' noncommutative geometry written for the volume of the school/conference "Noncommutative Geometry 2005" held at IPM Tehran. It is an expanded version of my lectures which was directed ... More

A Short Survey of Cyclic CohomologyAug 06 2010This is a short survey of some aspects of Alain Connes' contributions to cyclic cohomology theory in the course of his work on noncommutative geometry over the past 30 years.

Operations on Cyclic Homology, the X Complex, and a Conjecture of DeligneOct 22 1998Nov 08 1998The goal of this article is to relate recent developments in cyclic homology theory with the theory of operads and homotopical algebra, and hence to provide a general framework to define and study operations in cyclic homology theory.

Worldsheet Interpretation of the Level-Rank DualityJan 26 2015Level-rank duality relates the observables of two different Chern-Simons theories in which the roles of the Chern-Simons level and the rank of the gauge group are exchanged. In this note, we explore the consequences of this duality in the realm of topological ... More

Generalized simplicial chiral modelsMay 27 1999Sep 11 1999Using the auxiliary field representation of the simplicial chiral models on a (d-1)-dimensional simplex, the simplicial chiral models are generalized through replacing the term Tr$(AA^{\d})$ in the Lagrangian of these models by an arbitrary class function ... More

On the maximum conjectureJul 07 2018We verify the maximum conjecture on the rigidity of totally nondegenerate model CR manifolds in the following two cases: (i) for all models of CR dimension one (ii) for the so-called full-models, namely those in which their associated symbol algebras ... More

Biholomorphic equivalence to totally nondegenerate model CR manifolds and Beloshapka's maximum conjectureJan 06 2016May 31 2017Applying Elie Cartan's classical method, we show that the biholomorphic equivalence problem to a totally nondegenerate Beloshapka's model of CR dimension one and codimension $k> 1$, whence of real dimension $2+k$, is reducible to some absolute parallelism, ... More

Optimal subgradient algorithms with application to large-scale linear inverse problemsFeb 28 2014May 27 2014This study addresses some algorithms for solving structured unconstrained convex optimiza- tion problems using first-order information where the underlying function includes high-dimensional data. The primary aim is to develop an implementable algorithmic ... More

Homology of L_{\infty}-Algebras and Cyclic HomologyMay 11 1998A classical result of Loday-Quillen and Tsygan states that the Lie algebra homology of the algebra of stable matrices over an associative algebra is isomorphic, as a Hopf algebra, to the exterior algebra of the cyclic homology of the algebra. In this ... More

Adaptive Model Predictive Control of a Batch Solution Polymerization Process using Trajectory LinearizationOct 12 2015A sequential trajectory linearized adaptive model based predictive controller is designed using the DMC algorithm to control the temperature of a batch MMA polymerization process. Using the mechanistic model of the polymerization, a parametric transfer ... More

Very Basic Noncommutative GeometryAug 30 2004These notes aim to give an introduction to a few aspects of noncommutative geometry.

Is Lipschitz Continuity Preserved under Sampled-Data Discretization?Dec 27 2016Usually, given a continuous-time nonlinear model, a closed form solution for an exact discretization can not be found explicitly, originating the need of approximating discrete-time models. This note studies the preservation of the Lipschitz continuity ... More

Totally nondegenerate models and standard manifolds in CR dimension oneOct 27 2016It is shown that two Levi-Tanaka and infinitesimal CR automorphism algebras, associated with a totally nondegenerate model of CR dimension one are isomorphic. As a result, the model surfaces are maximally homogeneous and standard. This gives an affirmative ... More

Compatibility of the Feigin-Frenkel Isomorphism and the Harish-Chandra Isomorphism for jet algebrasAug 13 2013Let $\fg$ be a simple finite-dimensional complex Lie algebra with a Cartan subalgebra $\fh$ and Weyl group $W$. Let $\fg_n$ denote the Lie algebra of $n$-jets on $\fg$. A theorem of Rais and Tauvel and Geoffriau identifies the centre of the category of ... More

Attractor Bifurcation and Final Patterns of the N-Dimensional and Generalized Swift-Hohenberg EquationsFeb 08 2008In this paper I will investigate the bifurcation and asymptotic behavior of solutions of the Swift-Hohenberg equation and the generalized Swift-Hohenberg equation with the Dirichlet boundary condition on a one- dimensional domain $(0,L)$. I will also ... More

Stacky Abelianization of an Algebraic GroupNov 19 2007Aug 04 2008Let G be a connected algebraic group and let [G,G] be its commutator subgroup. We prove a conjecture of Drinfeld about the existence of a connected etale group cover H of [G,G], characterized by the following properties: every central extension of G, ... More

Constraints on Meta-stable de Sitter Flux VacuaFeb 26 2007Mar 16 2007We consider flux compactification of type IIB string theory as the orientifold limit of an F-theory on a Calabi-Yau fourfold. We show that when supersymmetry is dominantly broken by the axion-dilaton and the contributions of the F-terms associated with ... More

Cusp Annihilation on Ordinary Cosmic StringsJul 16 1993The order of magnitude of energy emission from cusps to light bosons on ordinary cosmic strings is calculated perturbatively. The analysis is applicable to both closed string loops and long cosmic strings. The perturbative result obtained here is much ... More

Some Correlators of $SU(3)_3$ WZW Models on Higher-Genus Riemann SurfacesMay 13 1993Using the conformal embedding on the torus, we can express some characters of $SU(3)_3$ in terms of $SO(8)_1$ characters. Then with the help of crossing symmetry, modular transformation and factorization properties of Green functions, we will calculate ... More

On the notion of conductor in the local geometric Langlands correspondenceJul 09 2015Apr 13 2016Under the local Langlands correspondence, the conductor of an irreducible representation of $\Gl_n(F)$ is greater than the Swan conductor of the corresponding Galois representation. In this paper, we establish the geometric analogue of this statement ... More

Asymptotic behavior of w in general quintom modelJun 10 2007Oct 11 2007For the quintom models with arbitrary potential $V=V(\phi,\sigma)$, the asymptotic value of equation of state parameter w is obtained by a new method. In this method, w of stable attractors are calculated by using the ratio (d ln V)/(d ln a) in asymptotic ... More

Moduli spaces of model real submanifolds: two alternative approachesNov 04 2014Nov 07 2014Instead of the invariant theory approach employed by Beloshaoka and Mamai for constructing the moduli spaces of Beloshapka's universal CR-models, we consider two alternative approaches borrowed from the theories of equivalence problem and Lie symmetries, ... More

The Beloshapka's maximum conjecture is correctJan 06 2016Applying the Elie Cartan's classical method, we show that the biholomorphic equivalence problem to a totally nondegenerate Beloshapka's universal model of CR dimension one and codimension k, whence of real dimension 2+k, is reducible to some absolute ... More

Quantum Chains with $GL_q(2)$ SymmetryMar 03 1994Dec 14 1994Usually quantum chains with quantum group symmetry are associated with representations of quantized universal algebras $U_q(g) $ . Here we propose a method for constructing quantum chains with $C_q(G)$ global symmetry , where $C_q(G)$ is the algebra of ... More

On Cyclic Homology of A_{\infty} AlgebrasMay 11 1998We present an approach to cyclic homology of A_{\infty} algebras. Our main technical tool is the concept of X-complex due to Cuntz and Quillen. This, in particular, enables us to compute the periodic cyclic homology of an A_{\infty} algebra in terms of ... More

Accelerated first-order methods for large-scale convex minimizationApr 29 2016This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with H\"older continuous gradients. ... More

Phase Transition Analysis of the Dynamic Instability of MicrotubulesOct 29 2013This paper provides the phase transition analysis of a reaction diffusion equations system modeling dynamic instability of microtubules. For this purpose we have generalized the macroscopic model studied by Mour\~ao et all [MSS]. This model investigates ... More

Reliable communication over non-binary insertion/deletion channelsApr 15 2012We consider the problem of reliable communication over non-binary insertion/deletion channels where symbols are randomly deleted from or inserted in the transmitted sequence and all symbols are corrupted by additive white Gaussian noise. To this end, ... More

Classical and SUSY solutions of the Boiti-Leon-Manna-Pempinelli equationNov 06 2012Feb 04 2013In this paper, we propose the study of the Boiti-Leon-Manna-Pempinelli equation from two point of views: the classical and supersymmetric cases. In the classical case, we construct new solutions of this equation from Wronskian formalism and Hirota method. ... More

Hopf Modules and Noncommutative Differential GeometryDec 01 2005Dec 07 2005We define a new algebra of noncommutative differential forms for any Hopf algebra with an invertible antipode. We prove that there is a one to one correspondence between anti-Yetter-Drinfeld modules, which serve as coefficients for the Hopf cyclic (co)homology, ... More

Cup Coproducts in Hopf Cyclic CohomologyNov 11 2010Dec 05 2013We define cup coproducts for Hopf cyclic cohomology of Hopf algebras and for its dual theory. We show that for universal enveloping algebras and group algebras our coproduct recovers the standard coproducts on Lie algebra homology and group homology, ... More

Excision in Hopf cyclic homologyNov 01 2005In this paper we show that both variants of the Hopf cyclic homology has excision under some natural homological conditions on the objects and the coefficient module.

A Hybrid, PDE-ODE Control Strategy for Intercepting an Intelligent, well-informed Target in a Stationary, Cluttered EnvironmentAug 20 2016In [1,2] a new class of intelligent controllers that can semantically embed an agent in a spatial context constraining its behavior in a goal-oriented manner was suggested. A controller of such a class can guide an agent in a stationary unknown environment ... More

Managing The Dynamics Of A Harmonic Potential Field-Guided Robot In A Cluttered EnvironmentAug 21 2016This paper demonstrates the ability of the harmonic potential field, HPF, planning method to generate a well-behaved constrained path for a robot with second order dynamics in a cluttered environment. It is shown that HPF-based controllers may be developed ... More

Weyl's Law and Connes' Trace Theorem for Noncommutative Two ToriNov 05 2011Nov 06 2012We prove the analogue of Weyl's law for a noncommutative Riemannian manifold, namely the noncommutative two torus $\mathbb{T}_\theta^2$ equipped with a general translation invariant conformal structure and a Weyl conformal factor. This is achieved by ... More

Issues in Type IIA UpliftingDec 07 2006Jun 09 2007Moduli stabilization in the type IIA massive string theory so far was achieved only in the AdS vacua. The uplifting to dS vacua has not been performed as yet: neither the analogs of type IIB anti-D3 brane at the tip of the conifold, nor the appropriate ... More

Geometrization of continuous characters of $\mathbb{Z}_p^\times$Dec 01 2010Jun 14 2011We define the $p$-adic trace of certain rank-one local systems on the multiplicative group over $p$-adic numbers, using Sekiguchi and Suwa's unification of Kummer and Artin-Schrier-Witt theories. Our main observation is that, for every non-negative integer ... More

On a criterion for local embeddability of 3-dimensional CR-structuresMar 05 2018Mar 11 2018We introduce a CR-invariant class of Lorentzian metrics on a circle bundle over a 3-dimensional CR-structure, which we call quasi-Fefferman metrics. These metrics generalise the Fefferman metric but allow for more control of the Ricci curvature. Our main ... More

Tensor Products of Some Special RingsOct 23 2002Mar 11 2003In this paper we solve a problem, originally raised by Grothendieck, on the properties, i.e. Complete intersection, Gorenstein, Cohen--Macaulay, that are conserved under tensor product of algebras over a field $k$.

An optimal subgradient algorithm for large-scale convex optimization in simple domainsJan 07 2015This paper shows that the optimal subgradient algorithm, OSGA, proposed in \cite{NeuO} can be used for solving structured large-scale convex constrained optimization problems. Only first-order information is required, and the optimal complexity bounds ... More

The homogeneous coordinate ring of the quantum projective planeJul 19 2010Jul 25 2010We define holomorphic structures on canonical line bundles on the quantum projective plane. The space of holomorphic sections of these line bundles will determine the quantum homogeneous coordinate ring of $\qp^2_q$. We also show that the holomorphic ... More

Decentralized, Self-organizing, Potential field-based Control for Individuallymotivated, Mobile Agents in a Cluttered Environment: A Vector-Harmonic Potential Field ApproachJul 09 2016Spatial multi-agency has been receiving growing attention from researchers exploring many of the aspects and modalities of this phenomenon. The aim is to develop the theoretical background needed for a multitude of applications involving the sharing of ... More

Motion Planning With Gamma-Harmonic Potential FieldsJun 29 2016This paper extends the capabilities of the harmonic potential field (HPF) approach to planning. The extension covers the situation where the workspace of a robot cannot be segmented into geometrical subregions where each region has an attribute of its ... More

Studentized Processes of U-statisticsJun 27 2009A uniform in probability approximation is established for Studentized processes of non degenerate U-statistics of order m greater or equal to 2 in terms of a standard Wiener process. The classical condition that the second moment of kernel of the underlying ... More

Relative periods and open-string integer invariants for a compact Calabi-Yau hypersurfaceApr 29 2009In this work we compute relative periods for B-branes, realized in terms of divisors in a compact Calabi-Yau hypersurface, by means of direct integration. Although we exemplify the method of direct integration with a particular Calabi-Yau geometry, the ... More

Computing with hardware neurons: spiking or classical? Perspectives of applied Spiking Neural Networks from the hardware sideFeb 05 2016Apr 06 2016While classical neural networks take a position of a leading method in the machine learning community, spiking neuromorphic systems bring attention and large projects in neuroscience. Spiking neural networks were shown to be able to substitute networks ... More

Cartan equivalences for 5-dimensional CR-manifolds in C^4 belonging to General Class III_1Jan 17 2014We reduce to various absolute parallelisms, namely to certain {e}-structures on manifolds of dimensions 7, 6, 5, the biholomorphic equivalence problem or the intrinsic CR equivalence problem for generic submanifolds M^5 in C^4 of CR dimension 1 and of ... More

Acoustic Nonreciprocity in Coriolis Mean Flow SystemsMay 27 2017One way to break acoustic reciprocity is to have a moving wave propagation medium. If the acoustic wave vector and the moving fluid velocity are collinear we can use the wave vector shift caused by the fluid flow to break reciprocity. In this paper we ... More

Compatible intertwiners for representations of finite nilpotent groupsSep 30 2009Nov 18 2010We sharpen the orbit method for finite groups of small nilpotence class by associating representations to functionals on the corresponding Lie rings. This amounts to describing compatible intertwiners between representations parameterized by an additional ... More

Constrained Nonlinear Model Predictive Control of an MMA Polymerization Process via Evolutionary OptimizationFeb 15 2015In this work, a nonlinear model predictive controller is developed for a batch polymerization process. The physical model of the process is parameterized along a desired trajectory resulting in a trajectory linearized piecewise model (a multiple linear ... More

Hopf cyclic cohomology in braided monoidal categoriesJul 24 2008Nov 21 2009We extend the formalism of Hopf cyclic cohomology to the context of braided categories. For a Hopf algebra in a braided monoidal abelian category we introduce the notion of stable anti-Yetter-Drinfeld module. We associate a para-cocyclic and a cocyclic ... More

Introduction to Hopf-Cyclic CohomologyMar 13 2005We review the recent progress in the study of cyclic cohomology in the presence of Hopf symmetry.

Scalar Curvature for the Noncommutative Two TorusOct 16 2011We give a local expression for the {\it scalar curvature} of the noncommutative two torus $ A_{\theta} = C(\mathbb{T}_{\theta}^2)$ equipped with an arbitrary translation invariant complex structure and Weyl factor. This is achieved by evaluating the value ... More

Geometric measure for two-qubit CS-states: an exactly solvable modelOct 25 2013Oct 24 2018Newly, during an analytical calculation M. A. Yurischev [arXiv: 1302.5239 (2013)] prove that quantum discord (or entanglement) remains unchangeable for any centrosymmetric (CS) states that are converted to their corresponding mode X. In this paper, in ... More

On Certain Spectral Invariants of Dirac Operators on Noncommutative ToriApr 05 2015The spectral eta function for certain families of Dirac operators on noncommutative $3$-torus is considered and the regularity at zero is proved. By using variational techniques, we show that $\eta_{D}(0)$ is a conformal invariant. By studying the Laurent ... More

Optimizing Capacitated Vehicle Scheduling with Time Windows: A Case Study of RMC DeliveryOct 25 2018Ready Mixed Concrete Delivery Problem (RMCDP) is a multi-objective multi-constraint dynamic combinatorial optimization problem. From the operational research prospective, it is a real life logistic problem that is hard to be solved with large instances. ... More

On the image of the parabolic Hitchin mapMar 29 2017We determine the image of the (strongly) parabolic Hitchin map for all parabolics in classical groups and $G_2$. Surprisingly, we find that the image is isomorphic to an affine space in all cases, except for certain "bad parabolics" in type $D$, where ... More

Gauss-Bonnet for matrix conformally rescaled DiracJul 14 2017Jun 19 2018We derive an explicit formula for the scalar curvature over a two-torus with a Dirac operator conformally rescaled by a globally diagonalizable matrix. We show that the Gauss-Bonnet theorem holds and extend the result to all Riemann surfaces with Dirac ... More

On the geometric order of totally nondegenerate CR manifoldsJul 09 2018Jul 13 2018A CR manifold $M$, with CR distribution $\mathcal D^{10}\subset T^\mathbb C M$, is called {\it totally nondegenerate of depth $\mu$} if: (a) the complex tangent space $T^\mathbb C M$ is generated by all complex vector fields that might be determined by ... More

An optimal subgradient algorithm for large-scale bound-constrained convex optimizationJan 07 2015This paper shows that the OSGA algorithm -- which uses first-order information to solve convex optimization problems with optimal complexity -- can be used to efficiently solve arbitrary bound-constrained convex optimization problems. This is done by ... More

Multi-Residual NetworksSep 19 2016Sep 24 2016In this article, we take one step toward understanding the learning behavior of deep residual networks, and supporting the hypothesis that deep residual networks are exponential ensembles by construction. We examine the effective range of ensembles by ... More

N=(4,4) Vector Multiplets on Curved Two-ManifoldsSep 02 2015Mar 24 2016We study the necessary conditions for preserving N=(4,4) supersymmetry on curved 2d backgrounds, following the strategy of Dumitrescu, Festuccia, and Seiberg. We derive the transformation laws and invariant action for off-shell Abelian vector multiplets. ... More

A Harmonic Potential Approach For Simultaneous Planning And Control Of A Generic UAV PlatformJun 29 2016Simultaneous planning and control of a large variety of unmanned aerial vehicles (UAVs) is tackled using the harmonic potential field (HPF) approach. A dense reference velocity field generated from the gradient of an HPF is used to regulate the velocity ... More

Kinodynamic Motion Planning: A Novel Type Of Nonlinear, Passive Damping Forces And AdvantagesJun 29 2016This article extends the capabilities of the harmonic potential field approach to planning to cover both the kinematic and dynamic aspects of a robot motion. The suggested approach converts the gradient guidance field from a harmonic potential to a control ... More

Nearest Neighbor-based Rendezvous for Sparsely Connected Mobile AgentsJul 03 2016In this paper a convergent, nearest-neighbor, control protocol is suggested for agents with nontrivial dynamics. The protocol guarantees convergence to a common point in space even if each agent is restricted to communicate with a single nearest neighbor. ... More

Twisted Spectral Triples and Connes' Character FormulaJun 30 2011We give a proof of an analogue of Connes' Hochschild character theorem for twisted spectral triples obtained from twisting a spectral triple by scaling automorphisms, under some suitable conditions. We also survey some of the properties of twisted spectral ... More

The Gauss-Bonnet Theorem for Noncommutative Two Tori With a General Conformal StructureMay 26 2010Aug 09 2010In this paper we give a proof of the Gauss-Bonnet theorem of Connes and Tretkoff for noncommutative two tori $\mathbb{T}_{\theta}^2$ equipped with an arbitrary translation invariant complex structure. More precisely, we show that for any complex number ... More

Quantum control of topological defects in magnetic systemsJun 05 2017Feb 05 2018Energy-efficient classical information processing and storage based on topological defects in magnetic systems have been studied over past decade. In this work, we introduce a class of macroscopic quantum devices in which a quantum state is stored in ... More

Modules Satisfying the Prime Radical Condition and a Sheaf Construction for Modules IFeb 02 2012The purpose of this paper and its sequel, is to introduce a new class of modules over a commutative ring $R$, called $\mathbb{P}$-radical modules (modules $M$ satisfying the prime radical condition "$(\sqrt[p]{{\cal{P}}M}:M)={\cal{P}}$" for every prime ... More

The Algebra of Formal Twisted Pseudodifferential Symbols and a Noncommutative ResidueOct 02 2008Jan 14 2009We extend the Adler-Manin trace on the algebra of pseudodifferential symbols to a twisted setting.

On Logarithmic Sobolev Inequality for the Noncommutative Two TorusJan 17 2016An analogue of Gross' logarithmic Sobolev inequality for a class of elements of noncommutative two tori is proved.

Fast Encoding and Decoding of Flexible-Rate and Flexible-Length Polar CodesApr 03 2017This work is on fast encoding and decoding of polar codes. We propose and detail 8-bit and 16-bit parallel decoders that can be used to reduce the decoding latency of the successive-cancellation decoder. These decoders are universal and can decode flexible-rate ... More

A Computational Model and Convergence Theorem for Rumor Dissemination in Social NetworksNov 27 2012Oct 21 2014The spread of rumors, which are known as unverified statements of uncertain origin, may cause tremendous number of social problems. If it would be possible to identify factors affecting spreading a rumor (such as agents' desires, trust network, etc.), ... More

Geometrization of principal series representations of reductive groupsNov 19 2010Jul 28 2011In geometric representation theory, one often wishes to describe representations realized on spaces of invariant functions as trace functions of equivariant perverse sheaves. In the case of principal series representations of a connected split reductive ... More

On efficiency of nonmonotone Armijo-type line searchesAug 12 2014Aug 20 2014Monotonicity and nonmonotonicity play a key role in studying the global convergence and the efficiency of iterative schemes employed in the field of nonlinear optimization, where globally convergent and computationally efficient schemes are explored. ... More

Multi-Residual Networks: Improving the Speed and Accuracy of Residual NetworksSep 19 2016Nov 20 2016In this article, we take one step toward understanding the learning behavior of deep residual networks, and supporting the observation that deep residual networks behave like ensembles. We propose a new CNN architecture which builds upon the success of ... More

Scalar Curvature for Noncommutative Four-ToriJan 25 2013In this paper we study the curved geometry of noncommutative 4-tori $\mathbb{T}_\theta^4$. We use a Weyl conformal factor to perturb the standard volume form and obtain the Laplacian that encodes the local geometric information. We use Connes' pseudodifferential ... More

Disjoint LDPC Coding for Gaussian Broadcast ChannelsJun 15 2009Low-density parity-check (LDPC) codes have been used for communication over a two-user Gaussian broadcast channel. It has been shown in the literature that the optimal decoding of such system requires joint decoding of both user messages at each user. ... More

Benefit of Delay on the Diversity-Multiplexing Tradeoffs of MIMO Channels with Partial CSIJul 14 2007This paper re-examines the well-known fundamental tradeoffs between rate and reliability for the multi-antenna, block Rayleigh fading channel in the high signal to noise ratio (SNR) regime when (i) the transmitter has access to (noiseless) one bit per ... More

The Multiplexing Gain of MIMO X-Channels with Partial Transmit Side-InformationJan 15 2007In this paper, we obtain the scaling laws of the sum-rate capacity of a MIMO X-channel, a 2 independent sender, 2 independent receiver channel with messages from each transmitter to each receiver, at high signal to noise ratios (SNR). The X-channel has ... More

A Harmonic Potential Field Approach for Joint Planning & Control of a Rigid, Separable Nonholonomic, Mobile RobotAug 23 2016The main objective of this paper is to provide a tool for performing path planning at the servo level of a mobile robot. The ability to perform, in a provably correct manner, such a complex task at the servo level can lead to a large increase in the speed ... More

Planning With Discrete Harmonic Potential FieldsAug 21 2016In this work a discrete counterpart to the continuous harmonic potential field approach is suggested. The extension to the discrete case makes use of the strong relation HPF-based planning has to connectionist artificial intelligence (AI). Connectionist ... More

Bivariant Hopf cyclic cohomologyJun 14 2006For module algebras and module coalgebras over an arbitrary bialgebra, we define two types of bivariant cyclic cohomology groups called bivariant Hopf cyclic cohomology and bivariant equivariant cyclic cohomology. These groups are defined through an extension ... More

A Riemann-Roch theorem for the noncommutative two torusJul 20 2013We prove the analogue of the Riemann-Roch formula for the noncommutative two torus $ A_{\theta} = C(\mathbb{T}_{\theta}^2)$ equipped with an arbitrary translation invariant complex structure and a Weyl factor represented by a positive element $k\in C^{\infty}(\mathbb{T}_{\theta}^2)$. ... More

Explicit Action of E7(7) on N=8 Supergravity FieldsFeb 28 2008Jun 16 2008We present an explicit, exact to all orders in gravitational coupling E7(7) symmetry transformations of on-shell N=8 supergravity fields in the gauge with 70 scalars in E7(7)/SU(8) coset space, the local SU(8) symmetry being fixed. The non-linear realization ... More

Multi-Residual Networks: Improving the Speed and Accuracy of Residual NetworksSep 19 2016Mar 15 2017In this article, we take one step toward understanding the learning behavior of deep residual networks, and supporting the observation that deep residual networks behave like ensembles. We propose a new convolutional neural network architecture which ... More

Parallelism of the measures in non-Markovian environmentsOct 18 2013Oct 24 2018There are various measures to compute correlation in various conditions, but none of them can be used publicly, because each of them has abnormality in their calculations or behaviors. These abnormalities do not depend on genus of environments. Therefore, ... More

Cohomogeneity one actions on the three-dimensional Einstein universeOct 01 2018The aim of this paper is to classify the cohomogeneity one conformal actions on the 3-dimensional Einstein universe $Ein^{1;2}$ , up to orbit equivalence. In a recent paper [21], we studied the unique (up to conjugacy) irreducible action of $PSL(2; \mathbb{R})$ ... More