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Intervention Pathway Discovery via Context-Dependent Dynamic Sensitivity AnalysisFeb 08 2019The sensitivity analysis of biological system models can significantly contribute to identifying and explaining influences of internal or external changes on model and its elements. We propose here a comprehensive framework to study sensitivity of intra-cellular ... More

DiSH Simulator: Capturing Dynamics of Cellular Signaling with Heterogeneous KnowledgeMay 07 2017We present DiSH-Sim, a simulator for large discrete models of biological signal transduction pathways, capable of simulating networks with multi-valued elements in both deterministic and stochastic manner. We focus on order of update and thus incorporate ... More

Formal Modeling and Analysis of Pancreatic Cancer MicroenvironmentJun 09 2016The focus of pancreatic cancer research has been shifted from pancreatic cancer cells towards their microenvironment, involving pancreatic stellate cells that interact with cancer cells and influence tumor progression. To quantitatively understand the ... More

Recipes for Translating Big Data Machine Reading to Executable Cellular Signaling ModelsJun 13 2017With the tremendous increase in the amount of biological literature, developing automated methods for extracting big data from papers, building models and explaining big mechanisms becomes a necessity. We describe here our approach to translating machine ... More

Methods to Expand Cell Signaling Models using Automated Reading and Model CheckingJun 15 2017Biomedical research results are being published at a high rate, and with existing search engines, the vast amount of published work is usually easily accessible. However, reproducing published results, either experimental data or observations is often ... More

A Faster DiSH: Hardware Implementation of a Discrete Cell Signaling Network SimulatorNov 19 2018Development of fast methods to conduct in silico experiments using computational models of cellular signaling is a promising approach toward advances in personalized medicine. However, software-based cellular network simulation has run-times plagued by ... More

Iterative method for improvement of coding and decryptionApr 05 2010Cryptographic check values (digital signatures, MACs and H-MACs) are useful only if they are free of errors. For that reason all of errors in cryptographic check values should be corrected after the transmission over a noisy channel before their verification ... More

Limiting behaviour of the Ricci flowFeb 12 2004May 20 2004We will consider a {\it $\tau$-flow}, given by the equation $\frac{d}{dt}g_{ij} = -2R_{ij} + \frac{1}{\tau}g_{ij}$ on a closed manifold $M$, for all times $t\in [0,\infty)$. We will prove that if the curvature operator and the diameter of $(M,g(t))$ are ... More

Biological network comparison using graphlet degree distributionJan 29 2009Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally infeasible, ... More

Curvature tensor under the Ricci flowNov 22 2003Feb 10 2004Consider the unnormalized Ricci flow $(g_{ij})_t = -2R_{ij}$ for $t\in [0,T)$, where $T < \infty$. Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times $t\in [0,T)$ then the solution can be extended ... More

Convergence of Kahler-Einstein orbifoldsJun 25 2003Jul 09 2003We proved the convergence of a sequence of 2 dimensional comapct Kahler-Einstein orbifolds with rational quotient singularities and with some uniform bounds on the volumes and on the Euler characteristics of our orbifods to a Kahler-Einstein 2-dimensional ... More

A case study of conspiracy theories about Charlie Hebdo terrorist attackSep 30 2015The results of the public opinion poll performed in January 2015, just after the terrorist attack on the French satirical weekly magazine Charlie Hebdo and the kosher supermarket in Paris, when 17 people were killed, showed that a significant number of ... More

Actuality and Future of Optical SystemsDec 11 2009Today's high-capacity telecommunication systems are unimaginable without the use of optical fibres and accompanying optical components which are briefly presented in this paper with an accent on the receivers of optical signal. An overview of main characteristics ... More

Strategies and performances of Soft Input DecryptionJul 26 2009Sep 17 2009This paper analyzes performance aspects of Soft Input Decryption and L values. Soft Input Decryption is a novel method which uses L values (soft output) of a SISO channel decoder for the correction of input of Soft Input Decryption (SID blocks) which ... More

Rotation of 10 Be stars through Fourier transform analysisFeb 28 2006Here we determine the projected rotational velocity of 10 Be stars using Fourier Transform Method. Also, we discuss the gravity darkening and extend of deviation from solid body rotation for our sample of stars. We found that 7 of considered stars are ... More

Linear and dynamical stability of Ricci flat metricsOct 04 2004Oct 05 2004We can talk about two kinds of stability of the Ricci flow at Ricci flat metrics. One of them is a linear stability, defined with respect to Perelman's functional $\mathcal{F}$. The other one is a dynamical stability and it refers to a convergence of ... More

Convergence of a Kähler-Ricci flowFeb 14 2004In this paper we prove that for a given K\"ahler-Ricci flow with uniformly bounded Ricci curvatures in an arbitrary dimension, for every sequence of times $t_i$ converging to infinity, there exists a subsequence such that $(M,g(t_i + t))\to (Y,\bar{g}(t))$ ... More

The Precise and Powerful Chaos of the 5:2 Mean Motion Resonance with JupiterDec 01 2016This work reexamines the dynamics of the 5:2 mean motion resonance with Jupiter located in the Outer Belt at $a\sim 2.82$ AU. First, we compute dynamical maps revealing the precise structure of chaos inside the resonance. Being interested to verify the ... More

CAT(0) spaces with polynomial divergence of geodesicsJan 17 2011May 21 2012We construct a family of finite 2-complexes whose universal covers are CAT(0) and have polynomial divergence of desired degree. This answers a question of Gersten, namely whether such CAT(0) complexes exist.

Compactness results for the Kähler-Ricci flowJul 19 2007Sep 23 2007We consider the K\"ahler-Ricci flow $\frac{\partial}{\partial t}g_{i\bar{j}} = g_{i\bar{j}} - R_{i\bar{j}}$ on a compact K\"ahler manifold $M$ with $c_1(M) > 0$, of complex dimension $k$. We prove the $\epsilon$-regularity lemma for the K\"ahler-Ricci ... More

Convergence of the Ricci flow toward a unique solitonMay 20 2004We will consider a {\it $\tau$-flow}, given by the equation $\frac{d}{dt}g_{ij} = -2R_{ij} + \frac{1}{\tau}g_{ij}$ on a closed manifold $M$, for all times $t\in [0,\infty)$. We will prove that if the curvature operator and the diameter of $(M,g(t))$ are ... More

Subsampled Inexact Newton methods for minimizing large sums of convex functionsNov 14 2018This paper deals with the minimization of large sum of convex functions by Inexact Newton (IN) methods employing subsampled functions, gradients and Hessian approximations. The Conjugate Gradient method is used to compute the inexact Newton step and global ... More

Conspiratorial beliefs observed through entropy principlesJun 02 2015We propose a novel approach framed in terms of information theory and entropy to tackle the issue of conspiracy theories propagation. We start with the report of an event (such as 9/11 terroristic attack) represented as a series of individual strings ... More

Field theoretic description of charge regulation interactionMar 16 2014May 15 2014In order to find the exact form of the electrostatic interaction between two proteins with dissociable charge groups in aqueous solution, we have studied a model system composed of two macroscopic surfaces with charge dissociation sites immersed in a ... More

Kirkwood-Shumaker interactions and general thermal fluctuation forcesJan 21 2014We present an extension of the Kirkwood-Shumaker (KS) theory of proton-fluctuation interactions to situations where the perturbation theory, usually invoked to derive these interactions, fails. In order to do that we formulate a generalized theory of ... More

Titratable Macroions in Multivalent Electrolyte Solutions: Strong Coupling Dressed Ion ApproachApr 08 2016We present a theoretical description of the effect of polyvalent ions on the interaction between titratable macro-ions. The model system consists of two point-like macro-ions with dissociable sites, immersed in an asymmetric ionic mixture of monovalent ... More

Asymptotic behavior of Type III mean curvature flow on noncompact hypersurfacesMar 02 2014Nov 06 2014In this paper, we introduce a monotonicity formula for the mean curvature flow which is related to self-expanders. Then we use the monotonicity to study the asymptotic behavior of Type III mean curvature flow on noncompact hypersurfaces.

Exact Spectral-Like Gradient Method for Distributed OptimizationJan 17 2019Since the initial proposal in the late 80s, spectral gradient methods continue to receive significant attention, especially due to their excellent numerical performance on various large scale applications. However, to date, they have not been sufficiently ... More

Uncovering Biological Network Function via Graphlet Degree SignaturesFeb 05 2008Proteins are essential macromolecules of life and thus understanding their function is of great importance. The number of functionally unclassified proteins is large even for simple and well studied organisms such as baker's yeast. Methods for determining ... More

Effect of optical purity on phase sequence in antiferroelectric liquid crystalsSep 29 2004We use the discrete phenomenological model to study theoretically the phase diagrams in antiferroelectric liquid crystals (AFLCs) as a function of optical purity and temperature. Recent experiments have shown that in some systems the number of phases ... More

Eternal Solutions to the Ricci Flow on $\R^2$Mar 22 2006Mar 23 2006We provide the classification of eternal (or ancient) solutions of the two-dimensional Ricci flow, which is equivalent to the fast diffusion equation $ \frac{\partial u}{\partial t} = \Delta \log u $ on $ \R^2 \times \R.$ We show that, under the necessary ... More

The harmonic mean curvature flow of nonconvex surfaces in $\mathbb{R}^3$Jun 10 2008Sep 03 2008We consider a compact, star-shaped, mean convex hypersurface $\Sigma^2\subset \mathbb{R}^3$. We prove that in some cases the flow exists until it shrinks to a point in a spherical manner, which is very typical for convex surfaces as well (see \cite{An1}). ... More

Dynamic instability of $\mathbb{CP}^N$ under Ricci flowSep 04 2017Apr 06 2018The intent of this short note is to provide context for and an independent proof of the discovery of Klaus Kroencke that complex projective space with its canonical Fubini--Study metric is dynamically unstable under Ricci flow in all complex dimensions ... More

Microeconomic Structure determines Macroeconomic Dynamics. Aoki defeats the Representative AgentJan 29 2014Masanao Aoki developed a new methodology for a basic problem of economics: deducing rigorously the macroeconomic dynamics as emerging from the interactions of many individual agents. This includes deduction of the fractal / intermittent fluctuations of ... More

Classification of singularities in the complete conformally flat Yamabe flowMay 24 2007Mar 05 2012We show that an eternal solution to a complete, locally conformally flat Yamabe flow, $\frac{\partial}{\partial t} g = -Rg$, with uniformly bounded scalar curvature and positive Ricci curvature at $t = 0$, where the scalar curvature assumes its maximum ... More

On gradient Ricci solitonsOct 06 2009Sep 06 2011In the first part of the paper we derive integral curvature estimates for complete gradient shrinking Ricci solitons. Our results and the recent work of Lopez-Rio imply rigidity of gradient shrinking Ricci solitons with harmonic Weyl tensor. In the second ... More

Improve Positioning Accuracy in WCDMA/FDD Networks Utilizing Adaptive Threshold for Direct Component DetectionJan 07 2016In NLOS propagation conditions power of direct component can be attenuated significantly. Therefore detection of direct component is aggravated which can degrades accuracy of Time of Arrival mobile positioning. The goal of this paper is to determine possibilities ... More

Surface stress of Ni adlayers on W(110): the critical role of the surface atomic structureMar 15 2012Puzzling trends in surface stress were reported experimentally for Ni/W(110) as a function of Ni coverage. In order to explain this behavior, we have performed a density-functional-theory study of the surface stress and atomic structure of the pseudomorphic ... More

A rigorous derivation of a ternary Boltzmann equation for a classical system of particlesMar 11 2019In this paper we present a rigorous derivation of a new kinetic equation describing the limiting behavior of a classical system of particles with three particle instantaneous interactions. The equation, which we call ternary Boltzmann equation, can be ... More

Ricci flow on three-dimensional manifolds with symmetryFeb 22 2011Oct 07 2011We describe the Ricci flow on two classes of compact three-dimensional manifolds: 1. Warped products with a circle fiber over a two-dimensional base. 2. Manifolds with a free local isometric U(1) x U(1) action.

Polarization modulation instability in liquid crystals with spontaneous chiral symmetry breakingMar 11 2005We present a theoretical model which describes the polarization modulated and layer undulated structure of the B7 phase and gives the phase transition from the synclinic ferroelectric B2 phase to the B7 phase as observed experimentally. The system is ... More

On the extinction profile of solutions to fast-diffusionSep 19 2006May 02 2007We study the extinction behavior of solutions to the fast diffusion equation $u_t = \Delta u^m$ on $\R^N\times (0,T)$, in the range of exponents $m \in (0, \frac{N-2}{N})$, $N > 2$. We show that if the initial data $u_0$ is trapped in between two Barenblatt ... More

The rate of convergence of the mean curvature flowFeb 25 2005May 16 2005We study the flow $M_t$ of a smooth, strictly convex hypersurface by its mean curvature in $\mathrm{R}^{n+1}$. The surface remains smooth and convex, shrinking monotonically until it disappears at a critical time $T$ and point $x^*$ (which is due to Huisken). ... More

An ab-initio investigation of magnetism in two-dimensional uranium systemsSep 14 2004The orbital and spin magnetic moments, and the X-ray-magnetic circular-dichroism (XMCD) spectra at the $M_{4,5}$ edges of the U atoms in a UAs/Co multilayer and in an $\alpha$-U film are calculated within the framework of the density-functional theory ... More

A regularity criterion for the dissipative quasi-geostrophic equationsOct 27 2007We establish a regularity criterion for weak solutions of the dissipative quasi-geostrophic equations in mixed time-space Besov spaces.

The classification of locally conformally flat Yamabe solitonsApr 12 2011Mar 05 2012We provide the classification of locally conformally flat gradient Yamabe solitons with positive sectional curvature. We first show that locally conformally flat gradient Yamabe solitons with positive sectional curvature have to be rotationally symmetric ... More

The mean curvature at the first singular time of the mean curvature flowJan 20 2010Consider a family of smooth immersions $F(\cdot,t): M^n\to \mathbb{R}^{n+1}$ of closed hypersurfaces in $\mathbb{R}^{n+1}$ moving by the mean curvature flow $\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot \nu(p,t)$, for $t\in [0,T)$. We prove that ... More

The Poisson equation on complete manifolds with positive spectrum and applicationsNov 07 2008Dec 02 2008In this paper we investigate the existence of a solution to the Poisson equation on complete manifolds with positive spectrum and Ricci curvature bounded from below. We show that if a function $f$ has decay $f=O(r^{-1-\varepsilon}) $ for some $\varepsilon ... More

Minsky Financial Instability, Interscale Feedback, Percolation and Marshall-Walras DisequilibriumFeb 02 2014We study analytically and numerically Minsky instability as a combination of top-down, bottom-up and peer-to-peer positive feedback loops. The peer-to-peer interactions are represented by the links of a network formed by the connections between firms, ... More

How do life, economy and other complex systems escape the heat death?Feb 02 2014The primordial confrontation underlying the existence of our universe can be conceived as the battle between entropy and complexity. The law of ever-increasing entropy (Boltzmann H-theorem) evokes an irreversible, one-directional evolution (or rather ... More

Charge regulation in ionic solutions: thermal fluctuations and Kirkwood-Schumaker interactionDec 21 2014We study the behavior of two macroions with dissociable charge groups, regulated by local variables such as pH and electrostatic potential, immersed in a mono-valent salt solution, considering cases where the net charge can either change sign or remain ... More

Properties of the solutions of the conjugate heat equationJan 17 2006In this paper we consider the class $\mathcal{A}$ of those solutions $u(x,t)$ to the conjugate heat equation $\frac{d}{dt}u = -\Delta u + Ru$ on compact K\"ahler manifolds $M$ with $c_1 > 0$ (where $g(t)$ changes by the unnormalized K\"ahler Ricci flow, ... More

Blow-up of the mean curvature at the first singular time of the mean curvature flowFeb 05 2013It is conjectured that the mean curvature blows up at the first singular time of the mean curvature flow in Euclidean space, at least in dimensions less or equal to 7. We show that the mean curvature blows up at the singularities of the mean curvature ... More

Uniqueness of ancient compact non-collapsed solutions to the 3-dimensional Ricci flowJul 02 2019In this paper we study the classification of compact $\kappa$-noncollapsed ancient solutions to the 3-dimensional Ricci flow which are rotationally and reflection symmetric. We prove that any such solution is isometric to the sphere or the type II ancient ... More

Type II extinction profile of maximal solutions to the Ricci flow in $\R^2$Jun 12 2006We consider the initial value problem $u_t = \Delta \log u$, $u(x,0) = u_0(x)\ge 0$ in $\R^2$, corresponding to the Ricci flow, namely conformal evolution of the metric $u (dx_1^2 + dx_2^2)$ by Ricci curvature. It is well known that the maximal (complete) ... More

Crossover exponent for piecewise directed walk adsorption on Sierpinski fractalsDec 07 1998We study the problem of critical adsorption of piecewise directed random walks on a boundary of fractal lattices that belong to the Sierpinski gasket family. By applying the exact real space renormalization group method, we calculate the crossover exponent ... More

Blow-up rate of the mean curvature during the mean curvature flow and a gap theorem for self-shrinkersNov 23 2010In this paper, we prove that the mean curvature blows up at the same rate as the second fundamental form at the first singular time $T$ of any compact, Type I mean curvature flow. For the mean curvature flow of surfaces, we obtain similar result provided ... More

Remarks on curvature behavior at the first singular time of the Ricci flowMay 07 2010May 28 2010In this paper, we study curvature behavior at the first singular time of solution to the Ricci flow on a smooth, compact n-dimensional Riemannian manifold $M$, $\frac{\partial}{\partial t}g_{ij} = -2R_{ij}$ for $t\in [0,T)$. If the flow has uniformly ... More

On the extension of the mean curvature flowMay 07 2009May 08 2009Consider a family of smooth immersions $F(\cdot,t): M^n\to \mathbb{R}^{n+1}$ of closed hypersurfaces in $\mathbb{R}^{n+1}$ moving by the mean curvature flow $\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot \nu(p,t)$, for $t\in [0,T)$. In \cite{Cooper} ... More

Analysis of Vel$\acute{a}$zquez's solution to the mean curvature flow with a type $\mathrm{II}$ singularityJan 07 2017Jul 12 2017J.J.L. Vel$\acute{a}$zquez in 1994 used the degree theory to show that there is a perturbation of Simons' cone, starting from which the mean curvature flow develops a type $\mathrm{II}$ singularity at the origin. He also showed that under a proper time-dependent ... More

Distributed Gradient Methods with Variable Number of Working NodesApr 15 2015Mar 10 2016We consider distributed optimization where $N$ nodes in a connected network minimize the sum of their local costs subject to a common constraint set. We propose a distributed projected gradient method where each node, at each iteration $k$, performs an ... More

Frequentist uncertainty estimates for deep learningNov 02 2018Feb 11 2019We provide frequentist estimates of aleatoric and epistemic uncertainty for deep neural networks. To estimate aleatoric uncertainty we propose simultaneous quantile regression, a loss function to learn all the conditional quantiles of a given target variable. ... More

The compactness result for Kähler Ricci solitonsApr 26 2005Sep 21 2005In this paper we prove the compactness result for compact K\"ahler Ricci gradient shrinking solitons. If $(M_i,g_i)$ is a sequence of K\"ahler Ricci solitons of real dimension $n \ge 4$, whose curvatures have uniformly bounded $L^{n/2}$ norms, whose Ricci ... More

Newton-like method with diagonal correction for distributed optimizationSep 05 2015We consider distributed optimization problems where networked nodes cooperatively minimize the sum of their locally known convex costs. A popular class of methods to solve these problems are the distributed gradient methods, which are attractive due to ... More

Newton-like method with diagonal correction for distributed optimizationSep 05 2015Feb 20 2017We consider distributed optimization problems where networked nodes cooperatively minimize the sum of their locally known convex costs. A popular class of methods to solve these problems are the distributed gradient methods, which are attractive due to ... More

Functional geometry of protein-protein interaction networksApr 12 2018Motivation: Protein-protein interactions (PPIs) are usually modelled as networks. These networks have extensively been studied using graphlets, small induced subgraphs capturing the local wiring patterns around nodes in networks. They revealed that proteins ... More

Distributed second order methods with increasing number of working nodesSep 05 2017Sep 20 2018Recently, an idling mechanism has been introduced in the context of distributed \emph{first order} methods for minimization of a sum of nodes' local convex costs over a generic, connected network. With the idling mechanism, each node $i$, at each iteration ... More

p-Adic Invariant Summation of Some p-Adic Functional SeriesNov 15 2014We consider summation of some finite and infinite functional p-adic series with factorials. In particular, we are interested in the infinite series which are convergent for all primes p, and have the same integer value for an integer argument. In this ... More

Line Patterns in Free GroupsJun 10 2010Jul 19 2010We study line patterns in a free group by considering the topology of the decomposition space, a quotient of the boundary at infinity of the free group related to the line pattern. We show that the group of quasi-isometries preserving a line pattern in ... More

Direction dependency of extraordinary refraction index in uniaxial nematic liquid crystalsAug 15 2012Nov 06 2012The article presents a straightforward experiment that directly and illustratively demonstrates double refraction. For this purpose, two liquid crystalline cells were designed, which enable qualitative and quantitative measurements of the extraordinary ... More

An integrative approach to modeling biological networksMay 31 2009Sep 24 2009Since proteins carry out biological processes by interacting with other proteins, analyzing the structure of protein-protein interaction (PPI) networks could explain complex biological mechanisms, evolution, and disease. Similarly, studying protein structure ... More

An inviscid dyadic model of turbulence: the fixed point and Onsager's conjectureOct 26 2006Dec 31 2006Properties of an infinite system of nonlinearly coupled ordinary differential equations are discussed. This system models some properties present in the equations of motion for an inviscid fluid such as the skew symmetry and the 3-dimensional scaling ... More

Extinction profile of complete non-compact solutions to the Yamabe flowJun 04 2013This work addresses the {\em singularity formation} of complete non-compact solutions to the conformally flat Yamabe flow whose conformal factors have {\em cylindrical behavior at infinity}. Their singularity profiles happen to be {\em Yamabe solitons}, ... More

Ricci flow neckpinches without rotational symmetryDec 10 2013Oct 21 2014We study "warped Berger" solutions $\big(\mc S^1\times\mc S^3,G(t)\big)$ of Ricci flow: generalized warped products with the metric induced on each fiber $\{s\}\times\mathrm{SU}(2)$ a left-invariant Berger metric. We prove that this structure is preserved ... More

Type II ancient compact solutions to the Yamabe flowSep 25 2012Oct 22 2012We construct new type II ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as $t \to -\infty$, to a tower of two spheres. Their curvature operator changes sign. We allow two time-dependent parameters ... More

Uniqueness of two-convex closed ancient solutions to the mean curvature flowApr 19 2018In this paper we consider closed non-collapsed ancient solutions to the mean curvature flow ($n \ge 2$) which are uniformly two-convex. We prove that any two such ancient solutions are the same up to translations and scaling. In particular, they must ... More

Inexact restoration with subsampled trust-region methods for finite-sum minimizationFeb 05 2019Convex and nonconvex finite-sum minimization arises in many scientific computing and machine learning applications. Recently, first-order and second-order methods where objective functions, gradients and Hessians are approximated by randomly sampling ... More

Higher order molecular organisation as a source of biological functionApr 13 2018Sep 20 2018Molecular interactions have widely been modelled as networks. The local wiring patterns around molecules in molecular networks are linked with their biological functions. However, networks model only pairwise interactions between molecules and cannot ... More

Improving the Secrecy of Distributed Storage Systems using Interference AlignmentJan 05 2018Regenerating codes based on the approach of interference alignment for wireless interference channel achieve the cut-set bound for distributed storage systems. These codes provide data reliability, and perform efficient exact node repair when some node ... More

Moments and Regularity for a Boltzmann Equation via Wigner TransformApr 11 2018In this paper, we continue our study of the Boltzmann equation by use of tools originating from the analysis of dispersive equations in quantum dynamics. Specifically, we focus on properties of solutions to the Boltzmann equation with collision kernel ... More

Non-Kahler Ricci flow singularities modeled on Kahler-Ricci solitonsMar 08 2017Mar 05 2019We investigate Riemannian (non-Kahler) Ricci flow solutions that develop finite-time Type-I singularities and present evidence in favor of a conjecture that parabolic rescalings at the singularities converge to singularity models that are shrinking Kahler-Ricci ... More

Nonparametric Quantile-Based Causal DiscoveryJan 31 2018Oct 07 2018Distinguishing cause from effect using observational data is a challenging problem, especially in the bivariate case. Contemporary methods often assume an independence between the cause and the generating mechanism of the effect given the cause. From ... More

Ricci flow on surfaces with cuspsMar 12 2007May 11 2009We consider the normalized Ricci flow $\del_t g = (\rho - R)g$ with initial condition a complete metric $g_0$ on an open surface $M$ where $M$ is conformal to a punctured compact Riemann surface and $g_0$ has ends which are asymptotic to hyperbolic cusps. ... More

Liquid crystals: a new topic in physics for undergraduatesNov 06 2012The paper presents a teaching module about liquid crystals. Since liquid crystals are linked to everyday student experiences and are also a topic of a current scientific research, they are an excellent candidate of a modern topic to be introduced into ... More

Modeling Interactome: Scale-Free or Geometric?Apr 17 2004Networks have been used to model many real-world phenomena to better understand the phenomena and to guide experiments in order to predict their behavior. Since incorrect models lead to incorrect predictions, it is vital to have a correct model. As a ... More

Copulas as High-Dimensional Generative Models: Vine Copula AutoencodersJun 12 2019We propose a vine copula autoencoder to construct flexible generative models for high-dimensional distributions in a straightforward three-step procedure. First, an autoencoder compresses the data using a lower dimensional representation. Second, the ... More

Classification of compact ancient solutions to the Ricci flow on surfacesFeb 06 2009Mar 05 2012We consider an ancient solution $g(\cdot,t)$ of the Ricci flow on a compact surface that exists for $t\in (-\infty,T)$ and becomes spherical at time $t=T$. We prove that the metric $g(\cdot,t)$ is either a family of contracting spheres, which is a type ... More

Non-Kahler Ricci flow singularities that converge to Kahler-Ricci solitonsMar 08 2017May 15 2018We investigate Riemannian (non-Kahler) Ricci flow solutions that develop finite-time Type-I singularities with the property that parabolic rescalings at the singularities converge to singularity models taking the form of shrinking Kahler-Ricci solitons. ... More

Efficient distribution and improved security for reliable cloud storage systemFeb 05 2016The distributed data storage systems are constructed by large number of nodes which are interconnected over a network. Each node in such peer-to-peer network is vulnerable and at a potential risk for attack. The attackers can eavesdrop the nodes and possibly ... More

Ricci flow on asymptotically conical surfaces with nontrivial topologyMar 26 2010As part of the general investigation of Ricci flow on complete surfaces with finite total curvature, we study this flow for surfaces with asymptotically conical (which includes as a special case asymptotically Euclidean) geometries. After establishing ... More

Multiplier Ideal Sheaves and the Kähler-Ricci FlowNov 27 2006Jan 10 2007Multiplier ideal sheaves are constructed as obstructions to the convergence of the K\"ahler-Ricci flow on Fano manifolds, following earlier constructions of Kohn, Siu, and Nadel, and using the recent estimates of Kolodziej and Perelman

Ricci flow on surfaces with conic singularitiesJun 28 2013Mar 11 2015We establish the short-time existence of the Ricci flow on surfaces with a finite number of conic points, all with cone angle between 0 and $2\pi$, where the cone angles remain fixed or change in some smooth prescribed way. For the angle-preserving flow ... More

Ricci Flow in Two DimensionsMar 24 2011Ricci flow on two dimensional surfaces is far simpler than in the higher dimensional cases. This presents an opportunity to obtain much more detailed and comprehensive results. We review the basic facts about this flow, including the original results ... More

On the evolution of convex hypersurfaces by the $Q_k$ flowApr 03 2009We prove the existence and uniqueness of a $C^{1,1}$ solution of the $Q_k$ flow in the viscosity sense for compact convex hypersurfaces $\Sigma_t$ embedded in $R^{n+1}$ ($n \geq 2$) . In particular, for compact convex hypersurfaces with flat sides we ... More

An inviscid dyadic model of turbulence: the global attractorOct 26 2006Properties of an infinite system of nonlinearly coupled ordinary differential equations are discussed. This system models some properties present in the equations of motion for an inviscid fluid such as the skew symmetry and the 3-dimensional scaling ... More

Unique asymptotics of ancient convex mean curvature flow solutionsMar 04 2015Sep 23 2015We study the compact noncollapsed ancient convex solutions to Mean Curvature Flow in $\mathbb{R}^{n+1}$ with $O(1)\times O(n)$ symmetry. We show they all have unique asymptotics as $t\to -\infty$ and we give precise asymptotic description of these solutions. ... More

Classification of compact ancient solutions to the curve shortening flowJun 10 2008We consider an embedded convex ancient solution $\Gamma_t$ to the curve shortening flow in $\mathbb{R}^2$. We prove that there are only two possibilities: the family $\Gamma_t$ is either the family of contracting circles, which is a type I ancient solution, ... More

Deep Smoothing of the Implied Volatility SurfaceJun 12 2019We present an artificial neural network (ANN) approach to value financial derivatives. Atypically to standard ANN applications, practitioners equally use option pricing models to validate market prices and to infer unobserved prices. Importantly, models ... More

Unique asymptotics of ancient compact non-collapsed solutions to the 3-dimensional Ricci flowJun 27 2019We consider compact noncollapsed ancient solutions to the 3-dimensional Ricci flow that are rotationally and reflection symmetric. We prove that these solutions are either the spheres or they all have unique asymptotic behavior as $t\to-\infty$ and we ... More

Modularity of Directed Networks: Cycle Decomposition ApproachJul 30 2014Jul 31 2014The problem of decomposing networks into modules (or clusters) has gained much attention in recent years, as it can account for a coarse-grained description of complex systems, often revealing functional subunits of these systems. A variety of module ... More