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Mathematical Sensemaking as Seeking Coherence between Calculations and Concepts: Instruction and Assessments for Introductory PhysicsMar 13 2019Mar 18 2019What kind of problem-solving instruction can help students apply what they have learned to solve the new and unfamiliar problems they will encounter in the future? We propose that mathematical sensemaking, the practice of seeking coherence between formal ... More

Graphical Condensation Generalizations Involving Pfaffians and DeterminantsMay 05 2006Graphical condensation is a technique used to prove combinatorial identities among numbers of perfect matchings of plane graphs. Propp and Kuo first applied this technique to prove identities for bipartite graphs. Yan, Yeh, and Zhang later applied graphical ... More

Applications of Graphical Condensation for Enumerating Matchings and TilingsApr 07 2003Sep 11 2003A technique called graphical condensation is used to prove various combinatorial identities among numbers of (perfect) matchings of planar bipartite graphs and tilings of regions. Graphical condensation involves superimposing matchings of a graph onto ... More

Viterbi Sequences and PolytopesJan 24 2004Jan 14 2005A Viterbi path of length n of a discrete Markov chain is a sequence of n+1 states that has the greatest probability of ocurring in the Markov chain. We divide the space of all Markov chains into Viterbi regions in which two Markov chains are in the same ... More

Seeking instructional specificity: an example from analogical instructionApr 24 2015Aug 20 2015Broad instructional methods like interactive engagement have been shown to be effective, but such general characterization provides little guidance on the details of how to structure the instructional materials. In this study, we seek instructional specificity ... More

Language of physics, language of math: Disciplinary culture and dynamic epistemologySep 22 2014Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to effectively ... More

Existence of constant mean curvature foliation in the extended Schwarzschild spacetimeJul 26 2016We construct a $T$-axisymmetric, spacelike, spherically symmetric, constant mean curvature hypersurfaces foliation in the Kruskal extension with properties that the mean curvature varies in each slice and ranges from minus infinity to plus infinity. This ... More

Partial results on the convexity of the Parisi functional with PDE approachAug 29 2013Nov 11 2013We investigate the convexity problem for the Parisi functional defined on the space of the so-called functional ordered parameters in the Sherrington-Kirkpatrick model. In the recent work of Panchenko [3], he proved that this functional is convex along ... More

The Density Functional via Effective ActionSep 21 2009A rigorous derivation of the density functional via the effective action in the Hohenberg-Kohn theory is outlined. Using the auxiliary field method, in which the electric coupling constant $e^2$ need not be small, we show that the loop expansion of the ... More

CNN as Guided Multi-layer RECOS TransformJan 30 2017Feb 19 2017There is a resurging interest in developing a neural-network-based solution to the supervised machine learning problem. The convolutional neural network (CNN) will be studied in this note. To begin with, we introduce a RECOS transform as a basic building ... More

Constant mean curvature foliation properties in the extended Reissner-Nordstrom spacetimesJun 18 2018We solve the spacelike, spherically symmetric, constant mean curvature hypersurfaces in the maximally extended Reissner-Nordstrom spacetime with the charge smaller than the mass. Based on these results, we construct constant mean curvature foliations ... More

Dirichlet problem for the constant mean curvature equation and CMC foliation in the extended Schwarzschild spacetimeJan 15 2016We prove the existence and uniqueness of the Dirichlet problem for spacelike, spherically symmetric, constant mean curvature equation with symmetric boundary data in the extended Schwarzschild spacetime. As an application, we completely solve the CMC ... More

How students blend conceptual and formal mathematical reasoning in solving physics problemsFeb 16 2011Dec 05 2013Current conceptions of expert problem solving depict physical/conceptual reasoning and formal mathematical reasoning as separate steps: a good problem solver first translates a physical Current conceptions of quantitative problem-solving expertise in ... More

Nothing's plenty: The significance of null results in physics education researchOct 23 2018A central aim of physics education research is to understand the processes of learning and use that understanding to inform instruction. To this end, researchers often conduct studies to measure the effect of classroom interventions on student learning ... More

Efficient conversion from rotating matrix to rotation axis and angle by extending Rodrigues' formulaOct 06 2018Oct 09 2018In computational 3D geometric problems involving rotations, it is often that people have to convert back and forth between a rotational matrix and a rotation described by an axis and a corresponding angle. For this purpose, Rodrigues' rotation formula ... More

A Revised Proof of the Existence of Negative Energy Density in Quantum Field TheoryNov 27 1996Jan 07 1997Negative energy density is unavoidable in the quantum theory of field. We give a revised proof of the existence of negative energy density unambiguously for a massless scalar field.

The Aizenman-Sims-Starr scheme and Parisi formula for mixed p-spin spherical modelsApr 23 2012The Parisi formula for the free energy in the spherical models with mixed even p-spin interactions was proven in Michel Talagrand [16]. In this paper we study the general mixed p-spin spherical models including p-spin interactions for odd p. We establish ... More

On the Mixed Even-Spin Sherrington-Kirkpatrick Model with Ferromagnetic InteractionMay 13 2011Nov 30 2012We study a spin system with both mixed even-spin Sherrington-Kirkpatrick (SK) couplings and Curie-Weiss (CW) interaction. Our main results are: (i) The thermodynamic limit of the free energy is given by a variational formula involving the free energy ... More

Limit Theorems in the Imitative Monomer-Dimer Mean-Field Model via Stein's MethodJun 29 2015Jul 23 2015We consider the imitative monomer-dimer model on the complete graph introduced in [1]. It was understood that this model is described by the monomer density and has a phase transition along certain critical line. By reverting the model to a weighted Curie-Weiss ... More

Mathematical Sensemaking as Seeking Coherence between Calculations and Concepts: Instruction and Assessments for Introductory PhysicsMar 13 2019What kind of problem-solving instruction can help students apply what they have learned to solve the new and unfamiliar problems they will encounter in the future? We propose that mathematical sensemaking, the practice of seeking coherence between formal ... More

Application of quasi-Monte Carlo methods to PDEs with random coefficients -- an overview and tutorialOct 26 2017This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an accompanying software ... More

Information Flow in Interaction NetworksDec 16 2011Interaction networks, consisting of agents linked by their interactions, are ubiquitous across many disciplines of modern science. Many methods of analysis of interaction networks have been proposed, mainly concentrating on node degree distribution or ... More

Information flow in interaction networks II: channels, path lengths and potentialsJan 02 2009Apr 19 2012In our previous publication, a framework for information flow in interaction networks based on random walks with damping was formulated with two fundamental modes: emitting and absorbing. While many other network analysis methods based on random walks ... More

Parisi formula, disorder chaos and fluctuation for the ground state energy in the spherical mixed p-spin modelsDec 28 2015Oct 28 2016We show that the limiting ground state energy of the spherical mixed p-spin model can be identified as the infimum of certain variational problem. This complements the well-known Parisi formula for the limiting free energy in the spherical model. As an ... More

The Legendre structure of the Parisi formulaOct 12 2015Oct 26 2015We show that the Parisi formula of the mixed $p$-spin model is a concave function of the squared inverse temperature. This allows us to derive a new expression for the Parisi formula that involves the inverse temperature and the Parisi measure as Legendre ... More

Sonic crystal lenses that obey Lensmaker's formulaDec 11 2003This paper presents a theoretical study of the phenomenon of acoustic imaging by sonic crystals, which are made of two-dimensional regular arrays of rigid cylinders placed in parallel in air. The scattering of acoustic waves is computed using the standard ... More

Flat lens imaging does not need negative refractionDec 11 2003Oct 30 2004In a recent communication, Parimi et al. (Nature 426, 404 (2003)) reported the experimental results on imaging by a flat lens made of photonic crystals. They attributed the observed focusing to the negative refraction expected for the Left-Handed-Materials ... More

Disorder chaos in some diluted spin glass modelsMar 21 2017We prove disorder chaos at zero temperature for three types of diluted models with large connectivity parameter: $K$-spin antiferromagnetic Ising model for even $K\geq 2$, $K$-spin spin glass model for even $K\geq 2$, and random $K$-sat model for all ... More

Temperature chaos in some spherical mixed $p$-spin modelsAug 08 2016Dec 18 2016We give two types of examples of the spherical mixed even-$p$-spin models for which chaos in temperature holds. These complement some known results for the spherical pure $p$-spin models and for models with Ising spins. For example, in contrast to a recent ... More

On concentration properties of disordered HamiltoniansJun 26 2017We present an elementary approach to concentration of disordered Hamiltonians. Assuming differentiability of the limiting free energy $F$ with respect to the inverse temperature $\beta$, we show that the Hamiltonian concentrates around the energy level ... More

ppiTrim: Constructing non-redundant and up-to-date interactomesMar 07 2011Jul 08 2011Robust advances in interactome analysis demand comprehensive, non-redundant and consistently annotated datasets. By non-redundant, we mean that the accounting of evidence for every interaction should be faithful: each independent experimental support ... More

On the TAP free energy in the mixed $p$-spin modelsSep 11 2017Jan 12 2019In [Physical Magazine, 35(3):593-601, 1977], Thouless, Anderson, and Palmer derived a representation for the free energy of the Sherrington-Kirkpatrick model, called the TAP free energy, written as the difference of the energy and entropy on the extended ... More

The Parisi formula has a unique minimizerFeb 20 2014Sep 05 2014In 1979, G. Parisi predicted a variational formula for the thermodynamic limit of the free energy in the Sherrington-Kirkpatrick model and described the role played by its minimizer. This formula was verified in the seminal work of Talagrand and later ... More

An approach to chaos in some mixed p-spin modelsJan 10 2012We consider the problems of chaos in disorder and temperature for coupled copies of the mixed p-spin models. Under certain assumptions on the parameters of the models we will first prove a weak form of chaos by showing that the overlap is concentrated ... More

Parisi formula for the ground state energy in the mixed p-spin modelJun 16 2016Jun 28 2016We show that the thermodynamic limit of the ground state energy in the mixed p-spin model can be identified as a variational problem. This gives a natural generalization of the Parisi formula at zero temperature.

Rapidity Gap of Weakly Coupled Leptoquark Production in ep ColliderMar 06 1997We show that the current bounds on the leptoquark couplings imply that if leptoquarks are produced in e p collisions, a significant fraction of them could form a leptoquark-quark bound state. The decay of the bound state has a distinct event shape with ... More

Asymptotically hyperbolic normalized Ricci flow and rotational symmetryJun 22 2015Sep 27 2016We consider the normalized Ricci flow evolving from an initial metric which is conformally compactifiable and asymptotically hyperbolic. We show that there is a unique evolving metric which remains in this class, and that the flow exists up to the time ... More

Asymptotically hyperbolic normalized Ricci flow and rotational symmetryJun 22 2015Dec 05 2018We consider the normalized Ricci flow evolving from an initial metric which is conformally compactifiable and asymptotically hyperbolic. We show that there is a unique evolving metric which remains in this class, and that the flow exists up to the time ... More

Ununfoldable Polyhedra with Convex FacesAug 03 1999Aug 27 2001Unfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In this paper, we study the limits of unfoldability by studying nonconvex polyhedra with the same combinatorial structure as convex polyhedra. In particular, we give ... More

Interface properties and built-in potential profile of a LaCrO$_3$/SrTiO$_3$ superlattice determined by standing-wave excited photoemission spectroscopyFeb 27 2018Aug 31 2018LaCrO$_3$ (LCO) / SrTiO$_3$ (STO) heterojunctions are intriguing due to a polar discontinuity along (001), two distinct and controllable interface structures [(LaO)$^+$/(TiO$_2$)$^0$ and (SrO)$^0$/(CrO$_2$)$^-$], and interface-induced polarization. In ... More

Mean Curvature flow in Higher Co-dimensionOct 28 2008We make several improvements on the results of M.-T. Wang in [8] and his joint paper with M.-P. Tsui [7] concerning the long time existence and convergence for solutions of mean curvature flow in higher co-dimension. Both the curvature condition and lower ... More

De-Hashing: Server-Side Context-Aware Feature Reconstruction for Mobile Visual SearchJun 29 2016Due to the prevalence of mobile devices, mobile search becomes a more convenient way than desktop search. Different from the traditional desktop search, mobile visual search needs more consideration for the limited resources on mobile devices (e.g., bandwidth, ... More

Conditions of smoothness of moduli spaces of flat connections and of character varietiesOct 31 2016Sep 12 2018We use gauge theoretic and algebraic methods to examine sufficient conditions for smooth points on the moduli space of flat connections on a compact manifold and on the character variety of a finitely generated and presented group. We give a complete ... More

Numerical study of magnetic field induced ordering in BaCuSi$_2$O$_6$ and related systemsJul 28 2005Thermodynamics of spin dimer system BaCuSi_2O_6 is studied using a quantum Monte Carlo calculation (QMC) and a bond-operator mean field theory. We propose that a new type of boson, which, rather than being hard-core, allows up to two occupancy at each ... More

Binding energy of exciton complexes determined by the tunneling current of single electron transistor under optical pumpingApr 22 2005We theoretically study the tunnelling current of a single electron transistor (SET) under optical pumping. It found that holes in the quantum dot(QD) created by optical pumping lead to new channels for the electrons tunnelling from emitter to collector. ... More

Bistable states of quantum dot array junctions for high-density memoryDec 29 2008We demonstrate that two-dimensional (2D) arrays of coupled quantum dots (QDs) with six-fold degenerate p orbitals can display bistable states, suitable for application in high-density memory device with low power consumption. Due to the inter-dot coupling ... More

Thermoelectric Properties of a Semiconductor Quantum Dot Chain Connected to Metallic ElectrodesSep 04 2012Jan 10 2013The thermoelectric properties of a semiconduct quantum dot chain (SQDC) connected to metallic electrodes are theoretically investigated in the Coulomb blockade regime. An extended Hubbard model is employed to simulate the SQDC system consisted of {\color{blue}N=2,3,4, ... More

Effects of interdot hopping and Coulomb blockade on the thermoelectric properties of serially coupled quantum dotsJan 04 2012Dec 15 2012We have theoretically studied the thermoelectric properties of serially coupled quantum dots (SCQD) embedded in an insulator matrix connected to metallic electrodes. In the framework of Keldysh Green's function technique, the Landauer formula of transmission ... More

Evolution of Pairing Orders between Pseudogap and Superconducting Phases of Cuprate SuperconductorsNov 26 2018One of the most puzzling problems of high temperature cuprate superconductor is the pseudogap phase(PG) at temperatures above the superconducting transition temperature in the underdoped regime. The PG phase is found by the angle-resolved photoemission ... More

Effects of electron correlation on the photocurrent in quantum dot infrared photodetectorsOct 16 2002The effect of electron correlation on the photocurrent of self-assembled InAs/InGaAs quantum dot infrared photo-detector (QDIPs) is studied. It is found that Coulomb interaction and level mixing in the many-body open system lead to double peaks associated ... More

Spacelike spherically symmetric CMC foliation in the extended Schwarzschild spacetimeJul 27 2015We first summarize the characterization of smooth spacelike spherically symmetric constant mean curvature (SS-CMC) hypersurfaces in the Schwarzschild spacetime and Kruskal extension. Then use the characterization to prove special SS-CMC foliation property, ... More

Universal Lowest-Twist in CFTs from HolographyMar 13 2019We probe the conformal block structure of a scalar four-point function in $d\geq2$ conformal field theories by including higher-order derivative terms in a bulk gravitational action. We consider a heavy-light four-point function as the boundary correlator ... More

The generalized TAP free energy IIMar 04 2019In a recent paper [14], we developed the generalized TAP approach for mixed $p$-spin models with Ising spins at positive temperature. Here we extend these results in two directions. We find a simplified representation for the energy of the generalized ... More

Refinements of two identities on $(n,m)$-Dyck pathsNov 23 2017Jan 28 2018For integers $n, m$ with $n \geq 1$ and $0 \leq m \leq n$, an $(n,m)$-Dyck path is a lattice path in the integer lattice $\mathbb{Z} \times \mathbb{Z}$ using up steps $(0,1)$ and down steps $(1,0)$ that goes from the origin $(0,0)$ to the point $(n,n)$ ... More

Impact of type ia supernova ejecta on binary companions in the single-degenerate scenarioMar 07 2012Mar 29 2012Type Ia supernovae are thought to be caused by thermonuclear explosions of a carbon-oxygen white dwarf in close binary systems. In the single-degenerate scenario (SDS), the companion star is non-degenerate and can be significantly affected by the explosion. ... More

On the energy landscape of the mixed even $p$-spin modelSep 14 2016Mar 24 2017We investigate the energy landscape of the mixed even $p$-spin model with Ising spin configurations. We show that for any given energy level between zero and the maximal energy, with overwhelming probability there exist exponentially many distinct spin ... More

Tunneling current spectroscopy of a nanostructure junction involving multiple energy levelsFeb 05 2007A multi-level Anderson model is employed to simulate the system of a nanostructure tunnel junction with any number of one-particle energy levels. The tunneling current, including both shell-tunneling and shell-filling cases, is theoretically investigated ... More

Spontaneous spin polarized tunneling current through a quantum dot arraySep 20 2002We show theoretically that a strongly spin-polarized current can be generated in semiconductors by taking advantage of the ferromagnetic phase of a quantum dot array (QDA). A Hubbard model with coupling to leads is used to study the tunneling current ... More

Second-harmonic generation using 4-bar quasi-phasematching in a GaAs microdisk cavityOct 06 2012The 4-bar crystal symmetry in materials such as GaAs can enable quasi-phasematching for efficient frequency conversion without poling, twinning or other engineered domain inversions. 4-bar symmetry means that a 90 degree rotation is equivalent to a crystallographic ... More

Thermal rectification properties of multiple-quantum-dot junctionsJan 08 2010It is illustrated that semiconductor quantum dots (QDs) embedded into an insulating matrix connected with metallic electrodes and some vacuum space can lead to significant thermal rectification effect. A multilevel Anderson model is used to investigate ... More

Light emitting single electron transistorsJun 03 2006Jun 22 2006The dynamic properties of light-emitting single-electron transistors (LESETs) made from quantum dots are theoretically studied by using nonequilibrium Green's function method. Holes residing at QD created by small ac signals added in the base electrode ... More

Stark effect on the exciton complexes of individual quantum dotsOct 17 2005The emission spectrum of exciton complexes formed in individual self-assembled quantum dots (QDs) embedded into a p-n junction is theoretically studied using an effective mass model. We calculate the particle Coulomb interactions, eletron-hole overlaps ... More

Measurement of gamma gamma -> p p-bar production at BelleMar 02 2005Jun 15 2005A high precision study of the process gamma gamma -> p p-bar has been performed using a data sample of 89/fb collected with the Belle detector at the KEKB e+e- collider. The cross section of p p-bar production has been measured at two-photon center-of-mass ... More

Semiclassical Gravity Theory and Quantum FluctuationsApr 06 1993We discuss the limits of validity of the semiclassical theory of gravity in which a classical metric is coupled to the expectation value of the stress tensor. It is argued that this theory is a good approximation only when the fluctuations in the stress ... More

Braiding a novel kind of Majorana-like quasiparticles in nanowire quantum dotsMar 01 2018Mar 04 2018For an electrically driven electron confined in a nanowire quantum dot with spin-orbit coupling (SOC), we find a SOC-magnetism phase-locked condition under which we derive a complete set of Schr\"odinger kitten states which contains some novel degenerate ... More

Can the 750-GeV diphoton resonance be the singlet Higgs boson of custodial Higgs triplet model?Jan 24 2016Jul 20 2016The observation of diphoton excess around the mass of 750 GeV in LHC Run-II motivates us to consider whether the singlet Higgs boson in the custodial Higgs triplet model can serve as a good candidate because an earlier study of comprehensive parameter ... More

Efficient Image Splicing Localization via Contrastive Feature ExtractionJan 22 2019In this work, we propose a new data visualization and clustering technique for discovering discriminative structures in high-dimensional data. This technique, referred to as cPCA++, utilizes the fact that the interesting features of a "target" dataset ... More

On Data-Driven Saak TransformOct 11 2017Oct 14 2017Being motivated by the multilayer RECOS (REctified-COrrelations on a Sphere) transform, we develop a data-driven Saak (Subspace approximation with augmented kernels) transform in this work. The Saak transform consists of three steps: 1) building the optimal ... More

On Extended Long Short-term Memory and Dependent Bidirectional Recurrent Neural NetworkFeb 27 2018Mar 03 2019In this work, we first analyze the memory behavior in three recurrent neural networks (RNN) cells; namely, the simple RNN (SRN), the long short-term memory (LSTM) and the gated recurrent unit (GRU), where the memory is defined as a function that maps ... More

On Greedy Clique Decompositions and Set Representations of GraphsApr 16 2008In 1994 S. McGuinness showed that any greedy clique decompo- sition of an n-vertex graph has at most $\lfloor n^2/4 \rfloor$ cliques (The greedy clique decomposition of a graph, J. Graph Theory 18 (1994) 427-430), where a clique decomposition means a ... More

On Intersection Representations and Clique Partitions of GraphsApr 29 2008A multifamily set representation of a finite simple graph $G$ is a multifamily $\mathcal{F}$ of sets (not necessarily distinct) for which each set represents a vertex in $G$ and two sets in $\mathcal{F}$ intersects if and only if the two corresponding ... More

Angle-Resolved Spectroscopy of Parametric FluorescenceFeb 25 2013The parametric fluorescence from a nonlinear crystal forms a conical radiation pattern. We measure the angular and spectral distributions of parametric fluorescence in a beta-barium borate crystal pumped by a 405-nm diode laser employing angle-resolved ... More

The generalized TAP free energyDec 12 2018In this paper, we define and compute the generalized TAP correction for the energy of the mixed $p$-spin models with Ising spins, and give the corresponding generalized TAP representation for the free energy. We study the generalized TAP states, which ... More

Long distance coherent tunneling effect on the charge and heat currents in serially coupled triple quantum dotsSep 06 2013Mar 12 2014The effect of long distance coherent tunneling (LDCT) on the charge and heat currents in serially coupled triple quantum dots (TQDs) connected to electrodes is illustrated by using a combination of the extended Hurbbard model and Anderson model. The charge ... More

Bipolar thermoelectric effect in a srially coupled quantum dot systemApr 14 2011Nov 01 2011The Seebeck coefficient (S) of a serially coupled quantum dot (SCQD) junction system is theoretically studied via a two-level Anderson model. A change of sign in S with respect to temperature is found, which arises from the competition between tunneling ... More

Thermoelectric and thermal rectification properties of quantum dot junctionsFeb 21 2010The electrical conductance, thermal conductance, thermal power and figure of merit (ZT) of semiconductor quantum dots (QDs) embedded into an insulator matrix connected with metallic electrodes are theoretically investigated in the Coulomb blockade regime. ... More

Tunnelling current and emission spectrum of a single electron transistor under optical pumpingJun 01 2005Theoretical studies of the tunnelling current and emission spectrum of a single electron transistor (SET) under optical pumping are presented. The calculation is performed via Keldysh Green's function method within the Anderson model with two energy levels. ... More

Computing the unique CANDECOMP/PARAFAC decomposition of unbalanced tensors by homotopy methodJul 25 2016The Candecomp/Parafac (CP) decomposition of the tensor whose maximal dimension is greater than its rank is considered. We derive the upper bound of rank under which the generic uniqueness of CP decomposition is guaranteed. The bound only depends on the ... More

Spectral evolution with doping of an antiferromagnetic Mott stateAug 20 2015May 31 2016Since the discovery of half-filled cuprate to be a Mott insulator, the excitation spectra above the chemical potential for the unoccupied states has attracted many research attentions. There were many theoretical works using different numerical techniques ... More

Lifting Tropical Curves in Space and Linear Systems on GraphsSep 09 2010Aug 20 2011Tropicalization is a procedure for associating a polyhedral complex in Euclidean space to a subvariety of an algebraic torus. We study the question of which graphs arise from tropicalizing algebraic curves. By using Baker's specialization of linear systems ... More

An Andreotti-Grauert theorem with $L^r$ estimatesMar 04 2012Apr 16 2014By a theorem of Andreotti and Grauert if $\omega $ is a $(p,q)$ current, $q < n,$ in a Stein manifold $\displaystyle \Omega,\ \bar \partial $ closed and with compact support, then there is a solution $u$ to $\bar \partial u=\omega $ still with compact ... More

The raising steps method. Applications to the $\bar \partial $ equation in Stein manifoldsDec 30 2013Jan 09 2014In order to get estimates on the solutions of the equation $\bar \partial u=\omega $ on Stein manifold, we introduce a new method the "raising steps method", to get global results from local ones. In particular it allows us to transfer results form open ... More

Estimates $ L^{r}-L^{s}$ for solutions of the $\bar \partial $ equation in strictly pseudo convex domains in ${\mathbb{C}}^{n}.$Dec 26 2013Jan 24 2014We prove estimates for solutions of the $\bar \partial u=\omega $ equation in a strictly pseudo convex domain $ \Omega $ in ${\mathbb{C}}^{n}.$ For instance if the $ (p,q)$ current $\omega $ has its coefficients in $L^{r}(\Omega )$ with $1\leq r<2(n+1)$ ... More

Lorentzian Cobordisms, Compact Horizons and the Generic ConditionJun 24 2014We consider the problem of determining which conditions are necessary for cobordisms to admit Lorentzian metrics with certain properties. In particular, we prove a result originally due to Tipler without a smoothness hypothesis necessary in the original ... More

The Semiotic MachineSep 02 2008A semiotic model of the user interface in human-computer interaction. Algorithmic sign, semotics, algorithmic art.

The Stock Market as a Game: An Agent Based Approach to Trading in StocksSep 02 2008Just as war is sometimes fallaciously represented as a zero sum game -- when in fact war is a negative sum game - stock market trading, a positive sum game over time, is often erroneously represented as a zero sum game. This is called the "zero sum fallacy" ... More

Quantum Computing Simulation Optimizations and Operational Errors on Various 2-qubit Multiplier CircuitsAug 15 2002Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates. Additionally, ... More

How to Grow an Organism Inside-Out: Evolution of an internal skeleton from an external skeleton in bilateral organismsJul 16 2012An intriguing unanswered question about the evolution of bilateral animals with internal skeletons is how an internal skeleton evolved in the first place. Computational modeling of the development of bilateral symmetric organisms suggests an answer to ... More

A Density Matrix-based Algorithm for Solving Eigenvalue ProblemsJan 17 2009A new numerical algorithm for solving the symmetric eigenvalue problem is presented. The technique deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques, ... More

Generalized Representation Stability and FI_d-modulesJun 08 2016Oct 04 2016In this note we consider the complex representation theory of FI_d, a natural generalization of the category FI of finite sets and injections. We prove that finitely generated FI_d-modules exhibit behaviors in the spirit of Church-Farb representation ... More

Semi-supervised clustering methodsJul 01 2013Cluster analysis methods seek to partition a data set into homogeneous subgroups. It is useful in a wide variety of applications, including document processing and modern genetics. Conventional clustering methods are unsupervised, meaning that there is ... More

Time Evolution of Entropy of a Charged Domain Wall during Gravitational CollapseFeb 11 2010We study the time evolution of the entropy of a collapsing charged spherical domain wall, from the point of view of an asymptotic observer, by investigating the entropy of the entire system (i.e. charged domain wall and radiation) and induced radiation ... More

Ramanujan's $_{1}ψ_1$ summation, Hecke-type double sums, and Appell-Lerch sumsAug 07 2012We use a specialization of Ramanujan's ${}_1\psi_1$ summation to give a new proof of a recent formula of Hickerson and Mortenson which expands a special family of Hecke-type double sums in terms of Appell-Lerch sums and theta functions.

Graphing and Grafting Graphene: Classifying Finite Topological DefectsJun 30 2011Nov 16 2011The structure of finite-area topological defects in graphene is described in terms of both the direct honeycomb lattice and its dual triangular lattice. Such defects are equivalent to cutting out a patch of graphene and replacing it with a different patch ... More

3+1 Formalism and Bases of Numerical RelativityMar 06 2007These lecture notes provide some introduction to the 3+1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-contained, with detailed calculations and numerous examples. Contents: 1. Introduction, ... More

An introduction to the hydrodynamics of locomotion on small scalesMar 17 2014In these lecture notes, I will briefly review the fundamental physical principles of locomotion in fluids, with a particular emphasis on the low-Reynolds number world.

All roots of unity are detected by the A-polynomialNov 09 2004Mar 30 2005For an arbitrary positive integer n, we construct infinitely many one-cusped hyperbolic 3-manifolds where each manifold's A-polynomial detects every n-th root of unity. This answers a question of Cooper, Culler, Gillet, Long, and Shalen as to which roots ... More

Two remarks on elementary theories of groups obtained by free constructionsFeb 06 2012May 30 2012We give two slight generalizations of results of Poizat about elementary theories of groups obtained by free constructions. The first-one concerns the non-superstability of such groups in most cases, and the second-one concerns the connectedness of most ... More

How far can stochastic and deterministic views be reconciled?May 22 2012In this short note, we try to provide the reader with a brief pedagogical account of some similarities and differences between stochastic and deterministic processes. A short presentation of some basic notions related to the mathematical description of ... More

Candidate Planets in the Habitable Zones of Kepler StarsJan 11 2013May 05 2013A key goal of the Kepler mission is the discovery of Earth-size transiting planets in "habitable zones" where stellar irradiance maintains a temperate climate on an Earth-like planet. Robust estimates of planet radius and irradiance require accurate stellar ... More