Results for "Michael J. Solomon"

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The transition towards immortality: non-linear autocatalytic growth of citations to scientific papersFeb 12 2013We discuss microscopic mechanisms of complex network growth, with the special emphasis of how these mechanisms can be evaluated from the measurements on real networks. As an example we consider the network of citations to scientific papers. Contrary to ... More
Optimal Euclidean spanners: really short, thin and lankyJul 07 2012Nov 27 2012In a seminal STOC'95 paper, titled "Euclidean spanners: short, thin and lanky", Arya et al. devised a construction of Euclidean $(1+\eps)$-spanners that achieves constant degree, diameter $O(\log n)$, and weight $O(\log^2 n) \cdot \omega(MST)$, and has ... More
Uncovering the dynamics of citations of scientific papersOct 01 2014We demonstrate a comprehensive framework that accounts for citation dynamics of scientific papers and for the age distribution of references. We show that citation dynamics of scientific papers is nonlinear and this nonlinearity has far-reaching consequences, ... More
Runaway Events Dominate the Heavy Tail of Citation DistributionsJun 10 2012Statistical distributions with heavy tails are ubiquitous in natural and social phenomena. Since the entries in heavy tail have disproportional significance, the knowledge of its exact shape is very important. Citations of scientific papers form one of ... More
Fast Constructions of Light-Weight Spanners for General GraphsJul 06 2012To our knowledge, there are only two known algorithms for constructing sparse and light spanners for general graphs. One of them is the greedy algorithm of Alth$\ddot{o}$fer et al. \cite{ADDJS93}, analyzed by Chandra et al. in SoCG'92. The greedy algorithm ... More
Balancing Degree, Diameter and Weight in Euclidean SpannersAug 30 2011In this paper we devise a novel \emph{unified} construction of Euclidean spanners that trades between the maximum degree, diameter and weight gracefully. For a positive integer k, our construction provides a (1+eps)-spanner with maximum degree O(k), diameter ... More
Stochastic dynamical model of a growing network based on self-exciting point processOct 02 2012We perform experimental verification of the preferential attachment model that is commonly accepted as a generating mechanism of the scale-free complex networks. To this end we chose citation network of Physics papers and traced citation history of 40,195 ... More
Solar off-limb line widths: Alfven waves, ion-cyclotron waves, and preferential heatingApr 18 2008Alfven waves and ion-cyclotron absorption of high-frequency waves are frequently brought into models devoted to coronal heating and fast solar-wind acceleration. Signatures of ion-cyclotron resonance have already been observed in situ in the solar wind ... More
Spatially Heterogeneous Biofilm Simulations using an Immersed Boundary Method with Lagrangian Nodes Defined by Bacterial LocationsFeb 15 2013In this work we consider how surface-adherent bacterial biofilm communities respond in flowing systems. We simulate the fluid-structure interaction and separation process using the immersed boundary method. In these simulations we model and simulate different ... More
Lasing in localized modes of a slow light photonic crystal waveguideMay 03 2011We demonstrate lasing in GaAs photonic crystal waveguides with InAs quantum dots as gain medium. Structural disorder is present due to fabrication imperfection and causes multiple scat- tering of light and localization of light. Lasing modes with varying ... More
A model colloidal gel for coordinated measurements of force, structure, and rheologyDec 30 2013We introduce a model gel system in which colloidal forces, structure, and rheology are measured by balancing the requirements of rheological and microscopy techniques with those of optical tweezers. Sterically stabilized poly(methyl methacrylate) (PMMA) ... More
Capillary-driven binding of thin triangular prisms at fluid interfacesFeb 08 2018We observe capillary-driven binding between thin, equilateral triangular prisms at a flat air-water interface. The edge length of the equilateral triangle face is 120 $\mu m$, and the thickness of the prism is varied between 2 and 20 $\mu m$. For thickness ... More
Abstract: Probabilistic Prognostic Estimates of Survival in Metastatic Cancer PatientsJan 09 2018Jul 13 2018We propose a deep learning model - Probabilistic Prognostic Estimates of Survival in Metastatic Cancer Patients (PPES-Met) for estimating short-term life expectancy (3 months) of the patients by analyzing free-text clinical notes in the electronic medical ... More
Pair Interaction Potentials of Colloids by Extrapolation of Confocal Microscopy Measurements of Collective StructureMay 14 2010Oct 27 2010A method for measuring the pair interaction potential between colloidal particles by extrapolation measurement of collective structure to infinite dilution is presented and explored using simulation and experiment. The method is particularly well suited ... More
Elasticity of colloidal gels: structural heterogeneity, foppy modes, and rigidityAug 04 2018Rheological measurements of model colloidal gels reveal that large variations in the shear moduli as colloidal volume-fraction changes are not reflected by simple structural parameters such as the coordination number, which remains almost a constant. ... More
Scarcity of cycles for rational functions over a number fieldApr 13 2016Jul 02 2016We provide an explicit bound on the number of periodic points of a rational function defined over a number field, where the bound depends only on the number of primes of bad reduction and the degree of the function, and is linear in the degree. More generally, ... More
Compatibility conditions on local and global spectra for $n$-mode Gaussian statesDec 15 2008Compatibility conditions between the (global) spectrum of an $n$-mode Gaussian state and the spectra of the individual modes are presented, making optimal use of beam splitter and (two-mode) squeezing transformations. An unexpected bye-product of our ... More
Shallow, Low, and Light Trees, and Tight Lower Bounds for Euclidean SpannersJan 23 2008We show that for every $n$-point metric space $M$ there exists a spanning tree $T$ with unweighted diameter $O(\log n)$ and weight $\omega(T) = O(\log n) \cdot \omega(MST(M))$. Moreover, there is a designated point $rt$ such that for every point $v$, ... More
Entanglement of Formation for Gaussian StatesAug 12 2008The entanglement of formation (EOF) is computed for arbitrary two-mode Gaussian states. Apart from a conjecture, our analysis rests on two main ingredients. The first is a four-parameter canonical form we develop for the covariance matrix, one of these ... More
Quadratic maps with a periodic critical point of period 2Oct 15 2015Dec 15 2015We provide a complete classification of possible graphs of rational preperiodic points of endomorphisms of the projective line of degree 2 defined over the rationals with a rational periodic critical point of period 2, under the assumption that these ... More
Scarcity of cycles for rational functions over a number fieldApr 13 2016Feb 22 2017We provide an explicit bound on the number of periodic points of a rational function defined over a number field, where the bound depends only on the number of primes of bad reduction and the degree of the function, and is linear in the degree. More generally, ... More
Can Mean-Curvature Flow Be Made Non-Singular?Mar 30 2012May 14 2012This work considers the question of whether mean-curvature flow can be modified to avoid the formation of singularities. We analyze the finite-elements discretization and demonstrate why the original flow can result in numerical instability due to division ... More
Variable Viscosity and Density Biofilm Simulations using an Immersed Boundary Method, Part II: Experimental Validation and the Heterogeneous Rheology-IBMApr 28 2015Apr 30 2015The goal of this work is to develop a numerical simulation that accurately captures the biomechanical response of bacterial biofilms and their associated extracellular matrix (ECM). In this, the second of a two-part effort, the primary focus is on formally ... More
Light SpannersApr 30 2014A $t$-spanner of a weighted undirected graph $G=(V,E)$, is a subgraph $H$ such that $d_H(u,v)\le t\cdot d_G(u,v)$ for all $u,v\in V$. The sparseness of the spanner can be measured by its size (the number of edges) and weight (the sum of all edge weights), ... More
Ramsey-type theorems for lines in 3-spaceDec 10 2015Sep 15 2016We prove geometric Ramsey-type statements on collections of lines in 3-space. These statements give guarantees on the size of a clique or an independent set in (hyper)graphs induced by incidence relations between lines, points, and reguli in 3-space. ... More
A rheological state diagram for rough colloids in shear flowOct 28 2016The flow of dense suspensions, glasses, and granular materials is heavily influenced by frictional interactions between constituent particles. However, neither hydrodynamics nor friction has successfully explained the full range of flow phenomena in concentrated ... More
Metric Description of Defects in Amorphous MaterialsJun 07 2013Oct 03 2013Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a configuration ... More
Disk enumeration on the quintic 3-foldOct 29 2006May 28 2007Holomorphic disk invariants with boundary in the real Lagrangian of a quintic 3-fold are calculated by localization and proven mirror transforms. A careful discussion of the underlying virtual intersection theory is included. The generating function for ... More
Generation of NPT Entanglement from Nonclassical Photon StatisticsMar 28 2006Apr 05 2006With a product state of the form $\rho_{in} = \rho_a\otimes|0>_b_b< 0|$ as input, the output two-mode state $\rho_{{\rm out}}$, of the beam splitter is shown to be NPT whenever the photon number distribution (PND) statistics $\{p(n_a) \}$ associated with ... More
Operator-sum Representation for Bosonic Gaussian ChannelsDec 20 2010Operator-sum or Kraus representations for single-mode Bosonic Gaussian channels are developed, and several of their consequences explored. Kraus operators are employed to bring out the manner in which the unphysical matrix transposition map when accompanied ... More
Scarcity of finite orbits for rational functions over a number fieldNov 09 2017Let $\phi$ be a an endomorphism of degree $d\geq{2}$ of the projective line, defined over a number field $K$. Let $S$ be a finite set of places of $K$, including the archimedean places, such that $\phi$ has good reduction outside of $S$. The article presents ... More
Active feedback of a Fabry-Perot cavity to the emission of a single InAs/GaAs quantum dotAug 13 2010We present a detailed study of the use of Fabry-Perot (FP) cavities for the spectroscopy of single InAs quantum dots (QDs). We derive optimal cavity characteristics and resolution limits, and measure photoluminescence linewidths as low as 0.9 GHz. By ... More
Multiple-coil k-space interpolation enhances resolution in single-shot spatiotemporal MRIMay 24 2017Purpose: Spatio-temporal encoding (SPEN) experiments can deliver single-scan MR images without folding complications and with robustness to chemical shift and susceptibility artifacts. It is here shown that further resolution improvements can arise by ... More
Informed baseline subtraction of proteomic mass spectrometry data aided by a novel sliding window algorithmMar 23 2016Proteomic matrix-assisted laser desorption/ionisation (MALDI) linear time-of-flight (TOF) mass spectrometry (MS) may be used to produce protein profiles from biological samples with the aim of discovering biomarkers for disease. However, the raw protein ... More
Structure and dynamics of colloidal depletion gels: coincidence of transitions and heterogeneityJun 06 2006Transitions in structural heterogeneity of colloidal depletion gels formed through short-range attractive interactions are correlated with their dynamical arrest. The system is a density and refractive index matched suspension of 0.20 volume fraction ... More
P-values, q-values and posterior probabilities for equivalence in genomics studiesJan 31 2012Equivalence testing is of emerging importance in genomics studies but has hitherto been little studied in this content. In this paper, we define the notion of equivalence of gene expression and determine a `strength of evidence' measure for gene equivalence. ... More
Gene profiling for determining pluripotent genes in a time course microarray experimentMay 23 2008Jul 23 2008In microarray experiments, it is often of interest to identify genes which have a pre-specified gene expression profile with respect to time. Methods available in the literature are, however, typically not stringent enough in identifying such genes, particularly ... More
Invariant theoretic approach to uncertainty relations for quantum systemsMay 23 2012We present a general framework and procedure to derive uncertainty relations for observables of quantum systems in a covariant manner. All such relations are consequences of the positive semidefiniteness of the density matrix of a general quantum state. ... More
Marketing PercolationMay 24 2000A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on differential or ... More
Extended Bell and Stirling numbers from hypergeometric exponentiationJun 14 2001Exponentiating the hypergeometric series gives a recursion relation for integer sequences which are generalizations of conventional Bell numbers. The corresponding associated Stirling numbers of the second kind are also generated and investigated. For ... More
On The Fourier And Wavelet Analysis Of Coronal Time SeriesJun 16 2016Nov 25 2016Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components ... More
Oscillatory motions observed in eruptive filamentsJul 04 2011Context: The origin of the variable component of the solar wind is of great intrinsic interest for heliophysics and space-weather, e.g. the initiation of coronal mass ejections, and the problem of mass loss of all stars. It is also related to the physics ... More
A measure of non-Gaussianity for quantum statesDec 15 2008We propose a measure of non-Gaussianity for quantum states of a system of $n$ oscillator modes. Our measure is based on the quasi-probability $Q(\alpha), \alpha\in{\cal C}^n$. Since any measure of non-Gaussianity is necessarily an attempt at making a ... More
Degrees of controllability for quantum systems and applications to atomic systemsAug 24 2001Mar 20 2002Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions are discussed. The results are applied to determine the degree of controllability for various atomic systems with degenerate ... More
Intersection theory on moduli of disks, open KdV and VirasoroSep 08 2014Aug 19 2015We define a theory of descendent integration on the moduli spaces of stable pointed disks. The descendent integrals are proved to be coefficients of the $\tau$-function of an open KdV heirarchy. A relation between the integrals and a representation of ... More
Reoptimization via Gradual TransformationsMar 15 2018Sep 28 2018This paper introduces a natural "reoptimization" meta-problem, which should be particularly relevant in faulty or dynamic networks. Fix any $\Delta > 0, \epsilon > 0$. Given two "approximate" solutions $M$ and $M'$ to some graph optimization problem, ... More
On The Fourier And Wavelet Analysis Of Coronal Time SeriesJun 16 2016Jun 17 2016Using Fourier and wavelet analysis, we critically re-assess the significance of our detection of periodic pulsations in coronal loops. We show that the proper identification of the frequency dependence and statistical properties of the different components ... More
High Redshift HCN Emission: Dense Star-Forming Molecular Gas in IRAS F10214+4724Sep 09 2004Hydrogen cyanide emission in the J=1-0 transition has been detected at redshift z=2.2858 in IRAS F10214+4724 using the Green Bank Telescope . This is the second detection of HCN emission at high redshift. The large HCN line luminosity in F10214 is similar ... More
Quantum discord plays no distinguished role in characterization of complete positivity: Robustness of the traditional schemeApr 17 2013Apr 18 2013The traditional scheme for realizing open-system quantum dynamics takes the initial state of the system-bath composite as a simple product. Currently, however, the issue of system-bath initial correlations possibly affecting the reduced dynamics of the ... More
Robustness of non-Gaussian entanglement against noisy amplifier and attenuator environmentsMar 07 2011Nov 17 2011The recently developed Kraus representation for bosonic Gaussian channels is employed to study analytically the robustness of non-Gaussian entanglement against evolution under noisy attenuator and amplifier environments, and compare it with the robustness ... More
Transmission of Slow Light through Photonic Crystal Waveguide BendsOct 14 2005The spectral dependence of a bending loss of cascaded 60-degree bends in photonic crystal (PhC) waveguides is explored in a slab-type silicon-on-insulator system. Ultra-low bending loss of (0.05+/-0.03)dB/bend is measured at wavelengths corresponding ... More
Spatial Optical Solitons due to Multistep CascadingApr 29 1999We introduce a novel class of parametric optical solitons supported simultaneously by two second-order nonlinear cascading processes, second-harmonic generation and sum-frequency mixing. We obtain, analytically and numerically, the solutions for three-wave ... More
Thermal Non-Equilibrium Revealed by Periodic Pulses of Random Amplitudes in Solar Coronal LoopsAug 12 2016Aug 19 2016We recently detected variations in extreme ultraviolet intensity in coronal loops repeating with periods of several hours. Models of loops including stratified and quasi-steady heating predict the development of a state of thermal non-equilibrium (TNE): ... More
Is nonclassicality-breaking the same thing as entanglement-breaking?Jun 24 2013Nonclassicality and entanglement are notions fundamental to quantum information processes involving continuous variable systems. That these two notions are intimately related has been intuitively appreciated for quite some time. An aspect of considerable ... More
Criteria for reachability of quantum statesOct 30 2001Nov 15 2002We address the question of which quantum states can be inter-converted under the action of a time-dependent Hamiltonian. In particular, we consider the problem applied to mixed states, and investigate the difference between pure and mixed-state controllability ... More
The Poschl-Teller Like Description of Quantum Mechanical Carnot EngineJun 09 2019In this work an example of a cyclic engine based on a quantum-mechanical properties of the strongly non linear quantum oscillator described by the Poschl-Teller [PT] model is examined. Using the [PT] model as shown in our earlier works [1-4], a quantum-mechanical ... More
Scaling maps of $s$-ordered quasiprobabilities are either nonpositive or completely positiveMay 19 2017Aug 09 2017Continuous-variable systems in quantum theory can be fully described through any one of the ${\rm s}$-ordered family of quasiprobabilities $\Lambda_{\rm s}(\alpha)$, ${\rm s} \in [-1,1]$. We ask for what values of $({\rm s}, a)$ is the scaling map $\Lambda_{\rm ... More
Thermal Non-Equilibrium Revealed by Periodic Pulses of Random Amplitudes in Solar Coronal LoopsAug 12 2016Nov 25 2016We recently detected variations in extreme ultraviolet intensity in coronal loops repeating with periods of several hours. Models of loops including stratified and quasi-steady heating predict the development of a state of thermal non-equilibrium (TNE): ... More
Long-period intensity pulsations in the solar corona during activity cycle 23Dec 13 2013Dec 17 2013We report on the detection (10 \sigma) of 917 events of long-period (3 to 16 hours) intensity pulsations in the 19.5 nm passband of the SOHO Extreme ultraviolet Imaging Telescope. The data set spans from January 1997 to July 2010, i.e the entire solar ... More
Interfacing a quantum dot with a spontaneous parametric down-conversion sourceJun 29 2017Quantum networks require interfacing stationary and flying qubits. These flying qubits are usually nonclassical states of light. Here we consider two of the leading source technologies for nonclassical light, spontaneous parametric down-conversion and ... More
Dynamic Graph CNN for Learning on Point CloudsJan 24 2018Jun 11 2019Point clouds provide a flexible geometric representation suitable for countless applications in computer graphics; they also comprise the raw output of most 3D data acquisition devices. While hand-designed features on point clouds have long been proposed ... More
Tarski's influence on computer scienceAug 15 2006Sep 27 2006The influence of Alfred Tarski on computer science was indirect but significant in a number of directions and was in certain respects fundamental. Here surveyed is the work of Tarski on the decision procedure for algebra and geometry, the method of elimination ... More
Substitution Tilings and Separated Nets with Similarities to the Integer LatticeOct 29 2008Jan 18 2009We show that any primitive substitution tiling of the plane creates a separated net which is biLipschitz to the integer lattice. Then we show that if H is a primitive Pisot substitution in an Euclidean space, for every separated net Y, that corresponds ... More
The net created from the Penrose tiling is biLipschitz to the integer latticeNov 23 2007A separated net is a set of points which is relatively dense and uniformly discrete (another name for a Delone set). We are dealing with tilings and separated nets in Euclidean spaces and with the question whether a given separated net is biLipschitz ... More
The expectation value of the field operatorJul 14 2014Much of the mathematical development of quantum field theory has been in support of determining the S-matrix in order to calculate scattering cross sections. However there is also an interest in determining how expectation values of field operators evolve ... More
Taming the divergent terms that occur during adiabatic switching in perturbation theoryJun 21 2016Aug 30 2016A potential problem with adiabatic switching in perturbation theory is that divergent terms appear in the series solution. An example of this was presented by C. Brouder et al [4] for a simple 2 state system where the evolution of system in the presence ... More
Fully Dynamic Maximal Matching in Constant Update TimeApr 28 2016Baswana, Gupta and Sen [FOCS'11] showed that fully dynamic maximal matching can be maintained in general graphs with logarithmic amortized update time. More specifically, starting from an empty graph on $n$ fixed vertices, they devised a randomized algorithm ... More
Stochastic Lotka-Volterra Systems of Competing Auto-Catalytic Agents Lead Generically to Truncated Pareto Power Wealth Distribution, Truncated Levy Distribution of Market Returns, Clustered Volatility, Booms and CrachesMar 30 1998We give a microscopic representation of the stock-market in which the microscopic agents are the individual traders and their capital. Their basic dynamics consists in the auto-catalysis of the individual capital and in the global competition/cooperation ... More
From Hierarchical Partitions to Hierarchical Covers: Optimal Fault-Tolerant Spanners for Doubling MetricsApr 30 2013May 08 2013In this paper we devise an optimal construction of fault-tolerant spanners for doubling metrics. Specifically, for any $n$-point doubling metric, any $\eps > 0$, and any integer $0 \le k \le n-2$, our construction provides a $k$-fault-tolerant $(1+\eps)$-spanner ... More
Towards Behaviorly Realistic Simulations of the Stock Market (Traders with a Soul)Jan 23 1999The price fluctuations in the financial markets are the result of the individual operations by many individual investors. However for many decades the finacial theory did not use directly this "microscopic representation". The difficulties preventing ... More
PDE Approaches to Graph AnalysisApr 30 2015This paper surveys and discusses recent work adapting partial differential equation (PDE) models to discrete structures.
Stability of Extended Functional Persistence in Dimensions Zero and OneApr 21 2018May 16 2018The stability result, as stated, is incorrect. In particular, the 1-dimensional extended persistence diagrams of a finely-triangulated simplicial complex X equipped with a continuous real-valued function f, and its one-skeleton graph G (also equipped ... More
Resolved Sideband Emission of InAs/GaAs Quantum Dots Strained by Surface Acoustic WavesAug 13 2010The dynamic response of InAs/GaAs self-assembled quantum dots (QDs) to strain is studied experimentally by periodically modulating the QDs with a surface acoustic wave and measuring the QD fluorescence with photoluminescence and resonant spectroscopy. ... More
Dynamic Graph CNN for Learning on Point CloudsJan 24 2018Point clouds provide a flexible and scalable geometric representation suitable for countless applications in computer graphics; they also comprise the raw output of most 3D data acquisition devices. Hence, the design of intelligent computational models ... More
Functional Maps Representation on Product ManifoldsSep 28 2018Jan 09 2019We consider the tasks of representing, analyzing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the ... More
Coupling an epitaxial quantum dot to a fiber-based external-mirror microcavityOct 24 2009We report the coupling of individual InAs quantum dots (QDs) to an external-mirror microcavity. The external mirror is bonded to a fiber and positioned above a semiconductor sample consisting of a QD-containing GaAs layer on top of a distributed Bragg ... More
Odd Order Pandiagonal Latin and Magic Cubes in Three and Four DimensionsOct 17 2002Explicit algorithms are developed for constructing odd order n pandiagonal latin cubes in 3 and 4 dimensions, and these are used to construct pandiagonal magic cubes and 4 dimensional hypercubes, respectively. It is established that these structures exist ... More
Some New Maps and Ideals in Classical Iwasawa Theory with ApplicationsMay 27 2009Aug 03 2010We introduce a new ideal {\mathfrak D} of the p-adic Galois group-ring associated to a real abelian field and a related ideal {\mathfrak J} for imaginary abelian fields. Both result from an equivariant, Kummer-type pairing applied to Stark units in a ... More
Central cross-sections make surfaces of revolution quadricDec 17 2007Jun 06 2008We prove here that when all planes transverse and nearly perpendicular to the axis of a surface of revolution intersect it in loops having central symmetry, the surface must be quadric. It follows that the quadrics are the only surfaces of revolution ... More
A Simple Condition for Bounded DisplacementNov 07 2011Jul 11 2016We study separated nets that correspond to substitution tilings of the Euclidean space. We give a simple condition, in terms of the eigenvalues and eigenspaces of the substitution matrix, to know whether the separated net is a bounded displacement of ... More
Deriving Z[J] from the time evolution operatorMay 30 2014An important quantity in quantum field theory is the vacuum-to-vacuum transition amplitude in the presence of an external source. This quantity is often designated by Z[J] and is the generator for the n-point Greens functions. In textbooks Z[J] is often ... More
Why do non-gauge invariant terms appear in the vacuum polarization tensor?Jul 21 2015It is will known that quantum field theory at the formal level is gauge invariant. However a calculation of the vacuum polarization tensor will include non-gauge invariant terms. These terms must be removed from the calculation in order to get a physically ... More
The MST of Symmetric Disk Graphs (in Arbitrary Metrics) is LightFeb 23 2011Consider an n-point metric M = (V,delta), and a transmission range assignment r: V \rightarrow \mathbb R^+ that maps each point v in V to the disk of radius r(v) around it. The {symmetric disk graph} (henceforth, SDG) that corresponds to M and r is the ... More
Ideal Containments Under Flat ExtensionsDec 25 2015Let $\varphi : S = k[y_0,..., y_n] \to R = k[y_0,...,y_n]$ be given by $y_i \to f_i$ where $f_0,...,f_n$ is an $R$-regular sequence of homogeneous elements of the same degree. A recent paper shows for ideals, $I_\Delta \subseteq S$, of matroids, $\Delta$, ... More
The Heisenberg versus the Schrodinger picture in quantum field theoryAug 18 2003Aug 16 2004The Heisenberg picture and Schrodinger picture are supposed to be equivalent representations of quantum mechanics. However this idea has been challenged by P.A.M. Dirac. Also, it has been recently shown by A. J. Faria et al that this is not necessarily ... More
Surfaces with central cross-sectionsApr 22 2009Apr 23 2009A surface S in R^3 has the central plane oval property (cpo) if (i) S meets at least one affine plane transversally along a strictly convex oval, and (ii) Every such transverse oval on S has central symmetry. We show that a complete, connected C^2 surface ... More
Skew loops in flat toriJan 31 2007Jul 01 2007We produce skew loops -- loops having no pair of parallel tangent lines -- homotopic to any loop in a flat torus or other quotient of R^n. The interesting case here is n=3. More subtly for any n, we characterize the homotopy classes that will contain ... More
Second quantization and gauge invarianceJun 03 2013Jun 30 2013It is well known that the single particle Dirac equation is gauge invariant. This means that observable quantities, such as the current density, are not affected by a gauge transformation. However what happens when the method of second quantization is ... More
Discrete Financial Means: When exception rules, mean means nothing; Auto-catalytic Individuals Survive by all MeansAug 04 2000The origin of macroscopic complexity is traced in a wide range of systems (imunology, ecology, finance, marketing, etc) to the discrete and auto-catalytic (i.e. multiplicative) character of their elementary components. Even in the simplest conditions ... More
Fault-Tolerant Spanners for Doubling Metrics: Better and SimplerJul 30 2012Dec 27 2012In STOC'95 Arya et al. (1995) conjectured that for any constant dimensional $n$-point Euclidean space, a $(1+\eps)$-spanner with constant degree, hop-diameter $O(\log n)$ and weight $O(\log n) \cdot \omega(MST)$ can be built in $O(n \log n)$ time. Recently ... More
Residual periodicity on the Markoff surfaceApr 27 2015Jul 08 2015A case study of arithmetic dynamics over the rationals on the Markoff surface is presented, in particular the local-global dynamical property of strong residual periodicity. The dynamical system induced by the composition of any two of the reflections ... More
X-rays of currents and projections of formsJul 22 2008Aug 21 2009We introduce and study a new Radon-like transform that averages projected differential p-forms in R^n over affine (n-k)-planes. We then prove an explicit inversion formula for our transform on the space of rapidly-decaying smooth p-forms. Our transform ... More
Abelian Conjectures of Stark Type in Z_p Extensions of Totally Real FieldsFeb 21 2003We study the behaviour of the Stark conjecture for an abelian extension K/k of totally real number fields as K varies in a cyclotomic Z_p-tower. We consider possible strengthenings of the natural norm-coherence in the tower of putative solution of the ... More
Central figure-8 cross-cuts make surfaces cylindricalSep 16 2015We prove: If a complete connected smooth surface M in euclidean 3-space has general position, intersects some plane along a clean figure-8 (a loop with total curvature zero) and all compact intersections with planes have central symmetry, then M is a ... More
Ideal Containments under Flat ExtensionsDec 25 2015Jul 18 2017Let $\varphi : S = k[y_0,..., y_n] \to R = k[y_0,...,y_n]$ be given by $y_i \to f_i$ where $f_0,...,f_n$ is an $R$-regular sequence of homogeneous elements of the same degree. A recent paper shows for ideals, $I_\Delta \subseteq S$, of matroids, $\Delta$, ... More
Functions of Substitution Tilings as a JacobianMay 09 2010Jun 05 2012In this paper we show that the function defined by a primitive, star shaped substitu- tion tiling of the plane, can be realized as a Jacobian of a biLipschitz homeomorphism of R^2. In particular it holds for any Penrose tiling.
An Optimal-Time Construction of Euclidean Sparse Spanners with Tiny DiameterMay 22 2010In STOC'95 \cite{ADMSS95} Arya et al.\ showed that for any set of $n$ points in $\mathbb R^d$, a $(1+\epsilon)$-spanner with diameter at most 2 (respectively, 3) and $O(n \log n)$ edges (resp., $O(n \log \log n)$ edges) can be built in $O(n \log n)$ time. ... More
The Microscopic Representation of Complex Macroscopic Phenomena (Critical Slowing Down - A Blessing in Disguise)Nov 29 1994Many complex systems are representable as macroscopic set of elements which interact by simple rules. The complex macroscopically relevant phenomena are then the result of the generic emergence of a space-time multi-scale dynamics. Critical Slowing Down ... More
Generalized Lotka-Volterra (GLV) Models and Generic Emergence of Scaling Laws in Stock MarketsJan 23 1999This is a pedagogical review of the the Generalized Lotka-Volterra (GLV) model: w_i(t+1) = lambda * w_i(t) + a * W (t) - c * W (t) * w_i(t) where i=1, >......, N and W= (w_1 + w_2 + ...w_N)/N is the average of the w_i's. The GLV models provide a generic ... More
Arithmetic dynamics on smooth cubic surfacesJul 11 2013Jan 12 2014We study dynamical systems induced by birational automorphisms on smooth cubic surfaces defined over a number field $K$. In particular we are interested in the product of non-commuting birational Geiser involutions of the cubic surface. We present results ... More