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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

Chaos in the mixed even-spin modelsNov 30 2012Nov 11 2013We consider a disordered system obtained by coupling two mixed even-spin models together. The chaos problem is concerned with the behavior of the coupled system when the external parameters in the two models, such as, temperature, disorder, or external ... More

Central Charge and Entangled Gauge FieldsDec 08 2014Feb 01 2016Entanglement entropy of gauge fields is calculated using the partition function in curved spacetime with a boundary. We derive a Gibbons-Hawking-like term from a Becchi-Rouet-Stora-Tyutin (BRST) action and a Wald-entropy-like codimension-2 surface term ... More

Boundary Anomalies and Correlation FunctionsApr 07 2016It was shown recently that boundary terms of conformal anomalies recover the universal contribution to the entanglement entropy and also play an important role in the boundary monotonicity theorem of odd-dimensional quantum field theories. Motivated by ... More

Central Limit Theorems for Cavity and Local Fields of the Sherrington-Kirkpatrick ModelOct 19 2010Jan 17 2011One of the remarkable applications of the cavity method is to prove the Thouless-Anderson-Palmer (TAP) system of equations in the high temperature regime of the Sherrington-Kirkpatrick (SK) model. This naturally leads us to the important study of the ... More

Assessments of Ali, Dome A, and Summit Camp for Mm-wave Observations Using MERRA-2 ReanalysisJul 26 2017The latest MERRA-2 reanalysis of the modern satellite measurements provides unprecedented uniformity and fidelity for the atmospheric data. In this paper, these data are used to evaluate five sites for millimeter-wave (mm-wave) observations. These include ... More

Understanding Convolutional Neural Networks with A Mathematical ModelSep 14 2016Nov 02 2016This work attempts to address two fundamental questions about the structure of the convolutional neural networks (CNN): 1) why a non-linear activation function is essential at the filter output of every convolutional layer? 2) what is the advantage of ... More

Quantum Fluctuations of Scalar Field in Conical SpaceMay 14 1997We consider vacuum polarization effect of a conformally coupled massless scalar field in the background produced by an idealized straight cosmic string. Using previous criterion we show the calculation of back reaction of the field to the metric in the ... 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

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

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

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.

Variational representations for the Parisi functional and the two-dimensional Guerra-Talagrand boundJan 27 2015May 13 2016The validity of the Parisi formula in the Sherrington-Kirkpatrick model (SK) was initially proved by Talagrand [18]. The central argument therein relied on a very dedicated study of the coupled free energy via the two-dimensional Guerra-Talagrand (GT) ... More

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

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

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

Free energy and complexity of spherical bipartite modelsMay 09 2014We investigate both free energy and complexity of the spherical bipartite spin glass model. We first prove a variational formula in high temperature for the limiting free energy based on the well-known Crisanti-Sommers representation of the mixed p-spin ... 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

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

On The Equivalence of Tries and Dendrograms - Efficient Hierarchical Clustering of Traffic DataOct 12 2018The widespread use of GPS-enabled devices generates voluminous and continuous amounts of traffic data but analyzing such data for interpretable and actionable insights poses challenges. A hierarchical clustering of the trips has many uses such as discovering ... 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

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

Universality of chaos and ultrametricity in mixed p-spin modelsOct 29 2014We prove disorder universality of chaos phenomena and ultrametricity in the mixed p-spin model under mild moment assumptions on the environment. This establishes the long-standing belief among physicists that the Parisi solution in mean-field models is ... More

Electromagnetic energy and energy flows in photonic crystals made of arrays of parallel dielectric cylindersMay 01 2004We consider the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel dielectric cylinders embedded a uniform medium. The frequency band structure is computed using the standard plane-wave expansion method, and the corresponding ... More

Renormalization Invariants of the Neutrino Mass MatrixMay 14 2002The renormalization evolution of all parameters in the neutrino mass matrix depends only on one variable, the energy scale. This fact, coupled with rephasing considerations, leads to a set of renormalization invariants, correlating the evolution of physical ... 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

Some examples of quenched self-averaging in models with Gaussian disorderSep 07 2014In this paper we give an elementary approach to several results of Chatterjee in arXiv:0907.3381 and arXiv:1404.7178, as well as some generalizations. First, we prove quenched disorder chaos for the bond overlap in the Edwards-Anderson type models with ... More

On properties of Parisi measuresMar 14 2013We investigate the structure of Parisi measures, the functional order parameters of mixed p-spin models in mean field spin glasses. In the absence of external field, we prove that a Parisi measure satisfies the following properties. First, at all temperatures, ... 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

Light deflection by photonic crystalsNov 26 2003When propagating through periodically structured media, i. e. photonic crystals, optical waves will be modulated with the periodicity. As a result, the dispersion of waves will no longer behave as in a free space, and so called frequency band structures ... More

Band gap or negative refraction effects?Oct 17 2003By a rigorous numerical simulation based on the standard multiple scattering theory, we investigate the optical transmission in photonic crystal structures, formed by dielectric cylinders embedded in parallel in a uniform medium. In contrast to previous ... More

Left-Handed-Material-like behavior revealed by arrays of dielectric cylindersOct 25 2003We investigate the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel dielectric cylinders embedded a uniform medium. The transmission of electromagnetic waves through prism structures are calculated by the standard multiple ... 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.

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

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

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

Depth-resolved resonant inelastic x-ray scattering at a superconductor/half-metallic ferromagnet interface through standing-wave excitationFeb 27 2018Dec 06 2018We demonstrate that combining standing-wave (SW) excitation with resonant inelastic x-ray scattering (RIXS) can lead to depth resolution and interface sensitivity for studying orbital and magnetic excitations in correlated oxide heterostructures. SW-RIXS ... More

Atomic-layer-resolved composition and electronic structure of the cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ from soft x-ray standing-wave photoemissionJan 16 2018Sep 24 2018A major remaining challenge in the superconducting cuprates is the unambiguous differentiation of the composition and electronic structure of the CuO$_2$ layers and those of the intermediate layers. The large c axis for these materials permits employing ... 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

New maximum principles for linear elliptic equationsJul 10 2006We prove extensions of the estimates of Aleksandrov and Bakel$'$man for linear elliptic operators in Euclidean space $\Bbb{R}^{\it n}$ to inhomogeneous terms in $L^q$ spaces for $q < n$. Our estimates depend on restrictions on the ellipticity of the operators ... 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

Stress Tensors from Trace Anomalies in Conformal Field TheoriesJan 21 2013Apr 08 2013Using trace anomalies, we determine the vacuum stress tensors of arbitrary even dimensional conformal field theories in Weyl flat backgrounds. We demonstrate a simple relation between the Casimir energy on the real line times a sphere and the type A anomaly ... 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

On Extended Long Short-term Memory and Dependent Bidirectional Recurrent Neural NetworkFeb 27 2018May 14 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

Quantum interference and spin polarization on Rashba double quantum dotsJul 04 2008We report on the quantum interference and spin accumulation on double quantum dots with Rashba spin-orbit coupling and electron-electron interaction, based on the Keldysh nonequilibrium Green function formalism. It is shown that Rashba spin-orbit interaction ... More

On the Hardnesses of Several Quantum Decoding ProblemsJun 21 2013Jul 11 2013We classify the time complexities of three important decoding problems for quantum stabilizer codes. First, regardless of the channel model, quantum bounded distance decoding is shown to be NP-hard, like what Berlekamp, McEliece and Tilborg did for classical ... More

Studies of $γγ\toΛ\barΛ,Σ^0\bar{Σ^0}$ production at BelleSep 26 2006Cross sections for hyperon pair production from two-photon collisions, $\gamma\gamma\to\Lambda\bar{\Lambda},\Sigma^0\bar{\Sigma^0}$, are measured in the 2-4 GeV energy region at Belle, using 464 fb$^{-1}$ of data. A contribution from the intermediate ... 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

Fluctuations of the free energy in the mixed $p$-spin models with external fieldSep 23 2015Nov 03 2015We show that the free energy in the mixed $p$-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the Poincar\'e inequality. This complements the result of ... 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

Tracking Words in Chinese Poetry of Tang and Song Dynasties with the China Biographical DatabaseNov 19 2016Oct 29 2017Large-scale comparisons between the poetry of Tang and Song dynasties shed light on how words, collocations, and expressions were used and shared among the poets. That some words were used only in the Tang poetry and some only in the Song poetry could ... 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

Extracting entangled qubits from Majorana fermions in quantum dot chains through the measurement of parityMar 30 2014May 27 2015We propose a scheme for extracting entangled charge qubits from quantum-dot chains that support zero-energy edge modes. The edge mode is composed of Majorana fermions localized at the ends of each chain. The qubit, logically encoded in double quantum ... 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

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

Spheroid ages, kinematics and BH relationsOct 27 2006Nov 02 2006I very briefly discuss the ages and kinematics of spheroids as well as the black hole relations, via a few recent and illustrative studies, which include results on the downsizing, scaling laws, angular momentum and central massive objects.

Why (inner) bars are important but not sufficientApr 23 2004I briefly report on the work conducted to probe the gravitational potential of active and non-active disk galaxies using two-dimensional gas and stellar kinematics, first emphasizing the need to make a distinction between ''fuelling the nucleus'' and ... More

The role of inner density waves in fueling galactic nucleiFeb 20 2003I present here an heterogeneous selection of nearby galaxies in which inner density waves (bars, spirals, m=1 modes) have been observed, and which are presumed to host a supermassive black hole, to illustrate the importance of such inner waves in the ... More

Density waves in the central regions of galaxiesJul 17 2001Density waves in the central kpc of galaxies, taking the form of spirals, bars and/or lopsided density distributions are potential actors of the redistribution of angular momentum. They thus play an important role in the overall evolution of the central ... More

Heavy Flavours at CollidersDec 15 1999Jan 21 2000I review some topics in the production and decays of heavy flavours that are relevant for collider physics. In particular, I discuss the present status and some recent progress related to masses, parton densities and fragmentation functions of heavy quarks, ... More

Heat and Moisture Transport in Unsaturated Porous Media -- A Coupled Model in Terms of Chemical PotentialMay 07 2013Transport phenomena in porous media are commonplace in our daily lives. Examples and applications include heat and moisture transport in soils, baking and drying of food stuffs, curing of cement, and evaporation of fuels in wild fires. Of particular interest ... More

Di-Boson production at Hadron Colliders with General 3 Gauge Boson Couplings. Analytic Expressions of Helicity Amplitudes and Cross-SectionOct 10 1996We discuss the tests of general Three Gauge Boson Vertices (TGV) through bosonic pair production at present and future hadron colliders. All bosonic final states are reviewed via the tree level quark-antiquark annihilation sub-process. The full analytic ... More

Generalized Representation Stability and FI_d-modulesJun 08 2016Oct 14 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

Mediation with near insolvent defaulting suppliers: a linear optimisation model to find an optimal outcomeFeb 14 2016This paper presents a model to describe contractual dispute resolution by mediation in situations where a defaulting supplier is near insolvent. While each party has internal constraints, and if alternate performances are available, such as more costly ... More

The Generality of a Section of a CurveMay 20 2016Jun 16 2016Let f: C --> P^3 be a general curve of genus g, mapped to P^3 via a general linear series of degree d; and let Q be a general (and thus smooth) quadric. In this paper, we show that the points of intersection f(C) \cap Q give a general collection of 2d ... More

Stem Cell NetworksJul 11 2016We present a general computational theory of stem cell networks and their developmental dynamics. Stem cell networks are special cases of developmental control networks. Our theory generates a natural classification of all possible stem cell networks ... More