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Financial series prediction using Attention LSTMFeb 28 2019Financial time series prediction, especially with machine learning techniques, is an extensive field of study. In recent times, deep learning methods (especially time series analysis) have performed outstandingly for various industrial problems, with ... More

A short proof of rigidity of convex polytopesFeb 25 2006We present a much simplified proof of Dehn's theorem on the infinitesimal rigidity of convex polytopes. Our approach is based on the ideas of Trushkina and Schramm.

Recent Results from PHOBOS at RHICFeb 28 2003The PHOBOS experiment at RHIC has recorded measurements for Au-Au collisions spanning nucleon-nucleon center-of-mass energies from 19.6 GeV to 200 GeV. Global observables such as elliptic flow and charged particle multiplicity provide important constraints ... More

The toolbox of modern multi-loop calculations: novel analytic and semi-analytic techniquesNov 03 2011We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate their identification. ... More

The discrete square peg problemApr 04 2008The square peg problem asks whether every Jordan curve in the plane has four points which form a square. The problem has been resolved (positively) for various classes of curves, but remains open in full generality. We present two new direct proofs for ... More

Combinatorial inequalitiesApr 02 2019This is an expanded version of the Notices of the AMS column with the same title. The text is unchanged, but we added acknowledgements and a large number of endnotes which provide the context and the references.

Inflating the cube without stretchingJul 28 2006We give a simple proof of the following result: There exists a non-convex polyhedron whose surface is isometric to the surface of a cube of smaller volume.

Complexity problems in enumerative combinatoricsMar 18 2018Mar 31 2018We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.

The area of cyclic polygons: Recent progress on Robbins' ConjecturesAug 09 2004In his works [R1,R2] David Robbins proposed several interrelated conjectures on the area of the polygons inscribed in a circle as an algebraic function of its sides. Most recently, these conjectures have been established in the course of several independent ... More

History of Catalan numbersAug 25 2014Aug 27 2014We give a brief history of Catalan numbers, from their first discovery in the 18th century to modern times. This note will appear as an appendix in Richard Stanley's forthcoming book on Catalan numbers.

Imaging of interlayer coupling in van der Waals heterostructures using a bright-field optical microscopeDec 23 2016May 01 2017Vertically stacked atomic layers from different layered crystals can be held together by van der Waals forces, which can be used for building novel heterostructures, offering a platform for developing a new generation of atomically thin, transparent and ... More

A combinatorial proof of the Rogers-Ramanujan and Schur identitiesNov 03 2004Sep 19 2005We give a combinatorial proof of the first Rogers-Ramanujan identity by using two symmetries of a new generalization of Dyson's rank. These symmetries are established by direct bijections.

Differential Calculi on the Quantum Group $SU_q(2)$ and Global $U(1)$-covarianceOct 26 1995A variety of three-dimensional left-covariant differential calculi on the quantum group $SU_q(2)$ is considered using an approach based on global $ U(1) $ -covariance. Explicit representations of possible $q $-Lie algebras are constructed in terms of ... More

Heavy-to-heavy quark decays at NNLOAug 26 2008Details of a recent calculation of O(alpha_s^2) corrections to the decay b -> c,l,nu_l, taking into account the c-quark mass, are described. Construction of the expansion in the mass ratio m_c/m_b as well as the evaluation of new four-loop master integrals ... More

New overlap construction of Weyl fermionsFeb 18 2008Mar 28 2008In a recent article Hasenfratz and von Allmen have suggested a fixed point action for two flavors of Weyl fermions on the lattice with gauge group SU(2). The block-spin transformation they use maps the chiral and vector symmetries of the underlying vector ... More

Chiral symmetry breaking in Hamiltonian QCD in Coulomb gaugeJul 26 2011Spontaneous breaking of chiral symmetry is investigated in the Hamiltonian approach to QCD in Coulomb gauge. The quark wave functional is determined by the variational principle using an ansatz which goes beyond the commonly used BCS-type of wave functionals ... More

The Webster scalar curvature flow on CR sphere. Part IIOct 21 2014This is the second of two papers, in which we study the problem of prescribing Webster scalar curvature on the CR sphere as a given function f. Using the Webster scalar curvature flow, we prove an existence result under suitable assumptions on the Morse ... More

On the crossing number of some complete multipartite graphsOct 16 2013In this paper, we find the crossing number of the complete multipartite graphs $K_{1,1,1,1,n}$, $K_{1,2,2,n}$, $K_{1,1,1,2,n}$ and $K_{1,4,n}$.

Enumerating projections of integer points in unbounded polyhedraDec 23 2016Mar 04 2018We extend the Barvinok-Woods algorithm for enumerating projections of integer points in polytopes to unbounded polyhedra. For this, we obtain a new structural result on projections of semilinear subsets of the integer lattice. We extend the results to ... More

Redesigning the urban design studio: Two learning experimentsSep 07 2015The main aim of this paper is to discuss how the combination of Web 2.0, social media and geographic technologies can provide opportunities for learning and new forms of participation in an urban design studio. This discussion is mainly based on our recent ... More

Bijections for refined restricted permutationsDec 23 2002We present a bijection between 321- and 132-avoiding permutations that preserves the number of fixed points and the number of excedances. This gives a simple combinatorial proof of recent results of Robertson, Saracino and Zeilberger, and the first author. ... More

Geometry and complexity of O'Hara's algorithmOct 08 2007Oct 08 2007In this paper we analyze O'Hara's partition bijection. We present three type of results. First, we show that O'Hara's bijection can be viewed geometrically as a certain scissor congruence type result. Second, we obtain a number of new complexity bounds, ... More

A Hopf Algebra from Preprojective ModulesApr 17 2019Let $Q$ be a finite type quiver i.e. ADE Dynkin quiver. Denote by $\Lambda$ its preprojective algebra. It is known that there are finitely many indecomposable $\Lambda$-modules if and only if $Q$ is of type $A_1,A_2,A_3,A_4$. In this paper, extending ... More

Non-commutative extensions of the MacMahon Master TheoremJul 28 2006We present several non-commutative extensions of the MacMahon Master Theorem, further extending the results of Cartier-Foata and Garoufalidis-Le-Zeilberger. The proofs are combinatorial and new even in the classical cases. We also give applications to ... More

Combinatorics and geometry of Littlewood-Richardson conesJul 09 2004We present several direct bijections between different combinatorial interpretations of the Littlewood-Richardson coefficients. The bijections are defined by explicit linear maps which have other applications.

The Kauffman bracket of virtual links and the Bollobás-Riordan polynomialSep 01 2006We show that the Kauffman bracket $[L]$ of a checkerboard colorable virtual link $L$ is an evaluation of the Bollob\'as-Riordan polynomial $R_{G_L}$ of a ribbon graph associated with $L$. This result generalizes Thistlethwaite's celebrated theorem relating ... More

The complexity of generalized domino tilingsMay 09 2013Tiling planar regions with dominoes is a classical problem in which the decision and counting problems are polynomial. We prove a variety of hardness results (both NP- and #P-completeness) for different generalizations of dominoes in three and higher ... More

Triangulations of Cayley and Tutte polytopesAug 09 2011Cayley polytopes were defined recently as convex hulls of Cayley compositions introduced by Cayley in 1857. In this paper we resolve Braun's conjecture, which expresses the volume of Cayley polytopes in terms of the number of connected graphs. We extend ... More

Limit shapes via bijectionsNov 18 2016We compute the limit shape for several classes of restricted integer partitions, where the restrictions are placed on the part sizes rather than the multiplicities. Our approach utilizes certain classes of bijections which map limit shapes continuously ... More

On the complexity of computing Kronecker coefficientsApr 02 2014Feb 24 2015We study the complexity of computing Kronecker coefficients $g(\lambda,\mu,\nu)$. We give explicit bounds in terms of the number of parts $\ell$ in the partitions, their largest part size $N$ and the smallest second part $M$ of the three partitions. When ... More

Three Dimensional Differential Calculus on the Quantum Group SU_q(2) and Minimal Gauge TheoryDec 20 1999Three-dimensional bicovariant differential calculus on the quantum group SU_q(2) is constructed using the approach based on global covariance under the action of the stabilizing subgroup U(1). Explicit representations of possible q-deformed Lie algebras ... More

Bounds on Kronecker and $q$-binomial coefficientsOct 26 2014May 02 2016We present a lower bound on the Kronecker coefficients for tensor squares of the symmetric group via the characters of~$S_n$, which we apply to obtain various explicit estimates. Notably, we extend Sylvester's unimodality of $q$-binomial coefficients ... More

Pattern avoidance is not P-recursiveMay 25 2015Let $F \subset S_k$ be a finite set of permutations and let $C_n(F)$ denote the number of permutations $\sigma$ in $S_n$ avoiding the set of patterns $F$. The Noonan-Zeilberger conjecture states that the sequence ${C_n(F)}$ is P-recursive. We use Computability ... More

Words in Linear Groups, Random Walks, Automata and P-RecursivenessFeb 23 2015Fix a finite set $S \subset {GL}(k,\mathbb{Z})$. Denote by $a_n$ the number of products of matrices in $S$ of length $n$ that are equal to 1. We show that the sequence $\{a_n\}$ is not always P-recursive. This answers a question of Kontsevich.

On Higman's $k(U_n(\mathbb{F}_q))$ conjectureJul 02 2015A classical conjecture by Graham Higman states that the number of conjugacy classes of $U_n(q)$, the group of upper triangular $n\times n$ matrices over $\mathbb{F}_q$, is polynomial in $q$, for all $n$. In this paper we present both positive and negative ... More

Complexity of short Presburger arithmeticApr 02 2017Apr 28 2017We study complexity of short sentences in Presburger arithmetic (Short-PA). Here by "short" we mean sentences with a bounded number of variables, quantifiers, inequalities and Boolean operations; the input consists only of the integers involved in the ... More

Incidence coloring of Regular graphs and Complement graphsMar 28 2012Apr 30 2012Using a relation between domination number and incidence chromatic number, we obtain necessary and sufficient conditions for $r$-regular graphs to be $(r+1)$-incidence colorable. Also, we determine the optimal Nordhaus-Gaddum inequality for the incidence ... More

Groups of Intermediate Growth: an Introduction for BeginnersJul 17 2006We present an accessible introduction to basic results on groups of intermediate growth.

Existence and Uniqueness of the Solution to a Nonlinear Differential Equation with Caputo Fractional Derivative in the Space of Continuously Differentiable FunctionsAug 10 2012Apr 08 2013In the paper, we considered the existence and uniqueness of the global solution in the space of continuously differentiable functions for a nonlinear differential equation with the Caputo fractional derivative of general form. Our main method is to derive ... More

Reductions of Young tableau bijectionsAug 12 2004We introduce notions of linear reduction and linear equivalence of bijections for the purposes of study bijections between Young tableaux. Originating in Theoretical Computer Science, these notions allow us to give a unified view of a number of classical ... More

The Kauffman bracket and the Bollobas-Riordan polynomial of ribbon graphsApr 27 2004Jun 02 2004For a ribbon graph $G$ we consider an alternating link $L_G$ in the 3-manifold $G\times I$ represented as the product of the oriented surface $G$ and the unit interval $I$. We show that the Kauffman bracket $[L_G]$ is an evaluation of the recently introduced ... More

Groups of Oscillating Intermediate GrowthAug 01 2011We construct an uncountable family of finitely generated groups of intermediate growth, with growth functions of new type. These functions can have large oscillations between lower and upper bounds, both of which come from a wide class of functions. In ... More

Massive c-quark contributions to semileptonic b-quark decay near thresholdNov 03 2006The decay width of b to c,c,c,l,nu has been computed as an expansion in limit (1- 3*(m_c/m_b)) << 1 with zero lepton invariant mass. Considering O(alpha_s^2) corrections to b to c,l,nu with zero invariant lepton mass, inclusion of our result is shown ... More

Mass effects in muon and semileptonic b -> c decaysMar 06 2008Quantum chromodynamics (QCD) effects in the semileptonic decay b -> c l nu are evaluated to the second order in the coupling constant, O(alpha_s^2), and to several orders in the expansion in quark masses, m_c/m_b. Corrections are calculated for the total ... More

Phrase database Approach to structural and semantic disambiguation in English-Korean Machine TranslationMar 19 2015In machine translation it is common phenomenon that machine-readable dictionaries and standard parsing rules are not enough to ensure accuracy in parsing and translating English phrases into Korean language, which is revealed in misleading translation ... More

A note on compact CR Yamabe solitonDec 14 2014In this paper, we show that the Webster scalar curvature of any compact CR Yamabe soliton must be constant.

Large mass expansion in two-loop QCD corrections of para-charmonium decayOct 30 2006Jan 16 2008We calculate the two-loop QCD corrections to paracharmonium decays $eta_{c} rightarrow gamma gamma$ and $eta_{c} rightarrow g g$ involving light-by-light scattering diagrams with light quark loops. Artificial large mass expansion and convergence improvement ... More

Complexity of short generating functionsFeb 28 2017Oct 11 2017We give complexity analysis of the class of short generating functions (GF). Assuming $\#P \not\subseteq FP/poly$, we show that this class is not closed under taking many intersections, unions or projections of GFs, in the sense that these operations ... More

On the number of integer points in translated and expanded polyhedraMay 09 2018We prove that the problem of minimizing the number of integer points inparallel translations of a rational convex polytope in $\mathbb{R}^6$ is NP-hard. We apply this result to show that given a rational convex polytope $P \subset \mathbb{R}^6$, finding ... More

A Compactness Theorem for Homogenization of Parabolic Partial Differential EquationsJun 30 2003In order to have a better description of homogenization for parabolic partial differential equations with periodic coefficients, we define the notion of parametric two-scale convergence. A compactness theorem is proved to justify this notion.

On the longest k-alternating subsequenceJun 19 2014We show that the longest k-alternating substring of a random permutation has length asymptotic to 2 (n-k) / 3.

Log-Concavity of the Partition FunctionOct 29 2013Jul 04 2014We prove that the partition function $p(n)$ is log-concave for all $n>25$. We then extend the results to resolve two related conjectures by Chen. The proofs are based on Lehmer's estimates on the remainders of the Hardy--Ramanujan and the Rademacher series ... More

The Very Bright and Nearby GRB 130427A: The Extra Hard Spectral Component and Implications for Very High-energy Gamma-ray Observations of Gamma-ray BurstsJan 08 2014The extended high-energy gamma-ray (>100 MeV) emission occurring after the prompt gamma-ray bursts (GRBs) is usually characterized by a single power-law spectrum, which has been explained as the afterglow synchrotron radiation. We report on the Fermi ... More

The Expected Shape of Random Doubly Alternating Baxter PermutationsJan 04 2014Guibert and Linusson introduced the family of doubly alternating Baxter permutations, i.e. Baxter permutations $\sigma \in S_n$, such that $\sigma$ and $\sigma^{-1}$ are alternating. They proved that the number of such permutations in $S_{2n}$ and $S_{2n+1}$ ... More

Unimodality via Kronecker productsApr 18 2013Mar 11 2014We present new proofs and generalizations of unimodality of the q-binomial coefficients \binom{n}{k}_q as polynomials in q. We use an algebraic approach by interpreting the differences between numbers of certain partitions as Kronecker coefficients of ... More

Strict unimodality of q-binomial coefficientsJun 21 2013Nov 10 2013We prove strict unimodality of the q-binomial coefficients \binom{n}{k}_q as polynomials in q. The proof is based on the combinatorics of certain Young tableaux and the semigroup property of Kronecker coefficients of S_n representations.

On P_T-distribution of gluon production rate in constant chromoelectric fieldFeb 13 2007Feb 22 2007A complete expression for the p_T-distribution of the gluon production rate in the homogeneous chromoelectric field has been obtained. Our result contains a new additional term proportional to the singular function \delta(p_T^2). We demonstrate that the ... More

Representation of $SU_q(2)$-covariant $q$-Lie Algebra in Terms of Differential OperatorsOct 19 1995A three-dimensional $q$-Lie algebra of $SU_q(2)$ is realized in terms of first- and second-order differential operators. Starting from the $q$-Lie algebra one has constructed a left-covariant differential calculus on the quantum group. The proposed construction ... More

Reply to the Comment by U. Jentschura and E. WenigerOct 27 2000Dec 12 2000It is shown that the criticism (revised version) made in hep-th/0007108 (by Jentschura and Weniger) on hep-th/0006057 has no valid ground. Furthemore we emphasize that the concept of the electric-magnetic duality used in the analysis of QED one-loop effective ... More

Overlap Quark Propagator in Coulomb Gauge QCD and the Interrelation of Confinement and Chiral Symmetry BreakingFeb 26 2015Apr 06 2015The chirally symmetric overlap quark propagator is explored in Coulomb gauge for the first time. This gauge is especially well suited for studying the interrelation between confinement and chiral symmetry breaking, since confinement can be attributed ... More

Quark Sector of the QCD Groundstate in Coulomb GaugeOct 07 2013The variational approach to Yang-Mills theory in Coulomb gauge is extended to full QCD. For the quark sector we use a trial wave functional, which goes beyond the previously used BCS-type state and which explicitly contains the coupling of the quarks ... More

Remarks on left-handed lattice fermionsOct 29 2007We study whether applying lattice projectors on a vector-like Ginsparg-Wilson Dirac operator is the only way to construct left-handed lattice fermions. Using RG transformations we derive an equation for the generating functional on the lattice, obtained ... More

The Webster scalar curvature flow on CR sphere. Part IOct 21 2014This is the first of two papers, in which we prove some properties of the Webster scalar curvature flow. More precisely, we establish the long-time existence, L^p convergence and the blow-up analysis for the solution of the flow. As a by-product, we prove ... More

Geometric approach to asymptotic expansion of Feynman integralsNov 22 2010We present an algorithm that reveals relevant contributions in non-threshold-type asymptotic expansion of Feynman integrals about a small parameter. It is shown that the problem reduces to finding a convex hull of a set of points in a multidimensional ... More

Geoweb 2.0 for Participatory Urban Design: Affordances and Critical Success FactorsSep 07 2015In this paper, we discuss the affordances of open-source Geoweb 2.0 platforms to support the participatory design of urban projects in real-world practices.We first introduce the two open-source platforms used in our study for testing purposes. Then, ... More

Design Studio 2.0: Augmenting Reflective Architectural Design LearningSep 07 2015Web 2.0 is beyond a jargon describing technological transformation: it refers to new strategies, tools and techniques that encourage and augment informed, creative and social inter(actions). When considered in an educational context, Web 2.0 provides ... More

The computational complexity of integer programming with alternationsFeb 28 2017May 03 2017We prove that integer programming with three quantifier alternations is $NP$-complete, even for a fixed number of variables. This complements earlier results by Lenstra and Kannan, which together say that integer programming with at most two quantifier ... More

VC-dimension of short Presburger formulasOct 11 2017We study VC-dimension of short formulas in Presburger Arithmetic, defined to have a bounded number of variables, quantifiers and atoms. We give both lower and upper bounds, which are tight up to a polynomial factor in the bit length of the formula.

An algebraic extension of the MacMahon Master TheoremJul 31 2006We present a new algebraic extension of the classical MacMahon Master Theorem. The basis of our extension is the Koszul duality for non-quadratic algebras defined by Berger. Combinatorial implications are also discussed.

A Quantitative Steinitz Theorem for Plane TriangulationsNov 04 2013We give a new proof of Steinitz's classical theorem in the case of plane triangulations, which allows us to obtain a new general bound on the grid size of the simplicial polytope realizing a given triangulation, subexponential in a number of special cases. ... More

Proof of Lemma 6.3 in ``The crossing number of $K_{4,n}$ on the torus and the Klein bottle"Aug 27 2007Mar 01 2008We found that Lemma 6.3 in the paper ``The crossing number of $K_{4,n}$ on the torus and the Klein bottle" is wrong.

Counting linear extensions of restricted posetsFeb 17 2018The classical 1991 result by Brightwell and Winkler states that the number of linear extensions of a poset is #P-complete. We extend this result to posets with certain restrictions. First, we prove that the number of linear extension for posets of height ... More

Bounds on the Kronecker coefficientsJun 11 2014Jun 16 2014We present several upper and lower bounds on the Kronecker coefficients of the symmetric group. We prove $k$-stability of the Kronecker coefficients generalizing the (usual) stability, and giving a new upper bound. We prove a lower bound via the characters ... More

Confinement, Vacuum Structure: from QCD to Quantum GravityMay 01 2010A minimal Lorentz gauge gravity model with R^2-type Lagrangian is proposed. In the absence of torsion the model admits a topological phase with unfixed metric. The model possesses a minimal set of dynamical degrees of freedom for the torsion. Remarkably, ... More

The Shape of Random Pattern-Avoiding PermutationsMar 29 2013Nov 28 2013We initiate the study of limit shapes for random permutations avoiding a given pattern. Specifically, for patterns of length 3, we obtain delicate results on the asymptotics of distributions of positions of numbers in the permutations. We view the permutations ... More

Counting With Irrational TilesJul 30 2014We introduce and study the number of tilings of unit height rectangles with irrational tiles. We prove that the class of sequences of these numbers coincides with the class of diagonals of N-rational generating functions and a class of certain binomial ... More

The Wilson loop from a Dyson equationOct 15 2009The Dyson equation proposed for planar temporal Wilson loops in the context of supersymmetric gauge theories is critically analysed thereby exhibiting its ingredients and approximations involved. We reveal its limitations and identify its range of applicability ... More

Growth in product replacement graphsApr 19 2013Aug 01 2014We prove the exponential growth of product replacement graphs for a large class of groups. Much of our effort is dedicated to the study of product replacement graphs of Grigorchuk groups, where the problem is most difficult.

Lifts, derandomization, and diameters of Schreier graphs of Mealy automataJul 17 2014It is known that random 2-lifts of graphs give rise to expander graphs. We present a new conjectured derandomization of this construction based on certain Mealy automata. We verify that these graphs have polylogarithmic diameter, and present a class of ... More

Tiling simply connected regions with rectanglesMay 13 2013In [BNRR], it was shown that tiling of general regions with two rectangles is NP-complete, except for a few trivial special cases. In a different direction, R\'emila showed that for simply connected regions by two rectangles, the tileability can be solved ... More

Metric combinatorics of convex polyhedra: cut loci and nonoverlapping unfoldingsDec 12 2003This paper is a study of the interaction between the combinatorics of boundaries of convex polytopes in arbitrary dimension and their metric geometry. Let S be the boundary of a convex polytope of dimension d+1, or more generally let S be a `convex polyhedral ... More

Reconstruction of potential energy profiles from multiple rupture time distributionsFeb 16 2010We explore the mathematical and numerical aspects of reconstructing a potential energy profile of a molecular bond from its rupture time distribution. While reliable reconstruction of gross attributes, such as the height and the width of an energy barrier, ... More

Improved IKE Protocol Design Based On PKI/ECCApr 29 2016This Paper proposes an ECDH key exchange method and an ECsig Digital Signature Authentication method based on group with Koblits curve, man-in-the-middle attack prevention method for SA payload and initiator identification payload to design high intensity ... More

A method to Implement the Kerberos User Authentication and the secured Internet ServiceApr 29 2016This paper proposes a PKINIT_AS Kerberos V5 authentication system to use public key cryptography and a method to implement the gssapi_krb authentication method and secured Internet service using it in IPSec VPN

Generalized squirming motion of a sphereFeb 05 2014A number of swimming microorganisms such as ciliates ($\textit{Opalina}$) and multicellular colonies of flagellates ($\textit{Volvox}$) are approximately spherical in shape and swim using beating arrays of cilia or short flagella covering their surfaces. ... More

Non-Topological Gauss-Bonnet type model of gravity with torsionSep 13 2007Mar 06 2008A non-topological Lorentz gauge model of gravity with torsion based on Gauss-Bonnet type Lagrangian is considered. The Lagrangian differs from the Lovelock term in four-dimensional space-time and has a number of interesting features. We demonstrate that ... More

Dipole coefficients in B -> X_s gamma in supersymmetry with large \tanβand explicit CP violationJan 22 2002Jan 31 2002We perform a detailed study of the electric and chromoelectric dipole coefficients in B -> X_s \gamma decay in a supersymmetric scheme with explicit CP violation. In our analysis, we adopt the minimal flavor violation scheme by taking into account the ... More

Effect of Transverse Gluons on Chiral Restoration in Excited MesonsJul 16 2013The effect of transverse gluons on the chiral symmetry patterns of excited mesons is studied in a Coulomb gauge QCD model. The linear rising static quark-antiquark potential and the transverse gluon propagator known from lattice studies are input into ... More

Steady states and linear stability analysis of precipitation pattern formation at geothermal hot springsJun 21 2007Aug 22 2007A dynamical theory of geophysical precipitation pattern formation is presented and applied to irreversible calcium carbonate (travertine) deposition. Specific systems studied here are the terraces and domes observed at geothermal hot springs, such as ... More

Nonlinear Elasticity of the Phase Field Crystal Model from the Renormalization GroupOct 15 2009Dec 23 2009The rotationally-covariant renormalization group equations of motion for the density wave amplitudes in the phase field crystal model are shown to follow from a dynamical equation driven by an effective free energy density that we derive. We show that ... More

Resonantly hybridised excitons in moiré superlattices in van der Waals heterostructuresApr 12 2019Atomically-thin layers of two-dimensional materials can be assembled in vertical stacks held together by relatively weak van der Waals forces, allowing for coupling between monolayer crystals with incommensurate lattices and arbitrary mutual rotation. ... More

Effects of Fermion Masses and Twisting on Non-Integrable Phases on Compact Extra DimensionsFeb 23 2004Aug 17 2004The effective potential for the Wilson loop in the SU(2) gauge theory with N_f massive fundamental and N_a massive adjoint fermions on S^1 x M^4 is computed at the one-loop level, assuming periodic boundary conditions for the gauge field and general boundary ... More

Correlating the Higgs and Kaon Sector CP ViolationsAug 10 2000Taking the most general two-doublet models with explicit CP violation in the Higgs sector but no phase in the CKM matrix, we determine the correlation between the Higgs and Kaon sectors using the experimental values of $\Delta M_K$ and $\epsilon_K$. It ... More

Consistency of the Born Approximation for the spin-1/2 Aharonov-Bohm ScatteringApr 24 2000The relativistic scattering of a spin-1/2 particle from an infinitely long solenoid is considered in the framework of covariant perturbation theory. The first order term agrees with the corresponding term in the series expansion of the exact amplitude, ... More

Theoretical models in low-Reynolds-number locomotionOct 16 2014The locomotion of microorganisms in fluids is ubiquitous and plays an important role in numerous biological processes. In this chapter we present an overview of theoretical modeling for low-Reynolds-number locomotion.

Extensibility enables locomotion under isotropic dragAug 31 2011Anisotropic viscous drag is usually believed to be a requirement for the low Reynolds number locomotion of slender bodies such as flagella and cilia. Here we show that locomotion under isotropic drag is possible for extensible slender bodies. After general ... More

Pumping by flapping in a viscoelastic fluidFeb 25 2010In a world without inertia, Purcell's scallop theorem states that in a Newtonian fluid a time-reversible motion cannot produce any net force or net flow. Here we consider the extent to which the nonlinear rheological behavior of viscoelastic fluids can ... More

Accelerated search kinetics mediated by redox reactions of DNA repair enzymesMay 20 2009A Charge Transport (CT) mechanism has been proposed in several papers (e.g., Yavin, et al. PNAS, v102 3546 (2005)) to explain the localization of Base Excision Repair (BER) enzymes to lesions on DNA. The CT mechanism relies on redox reactions of iron-sulfur ... More

The effect of Magnetic Field on Spin Injection of DMS/FM HeterostructureSep 12 2012We discuss spin injection efficiency as a function of Fermi energy in DMS/FM heterostructures by spin injection efficiency equation and Landauer formula. The higher electric field, the stronger spin injection efficiency, and its velocity of increase gets ... More

Profiles of inflated surfacesJul 29 2009We study the shape of inflated surfaces introduced in \cite{B1} and \cite{P1}. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more generally an almost everywhere flat surface, with a symmetry plane. We show ... More