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A Generalization Method of Partitioned Activation Function for Complex NumberFeb 08 2018A method to convert real number partitioned activation function into complex number one is provided. The method has 4em variations; 1 has potential to get holomorphic activation, 2 has potential to conserve complex angle, and the last 1 guarantees interaction ... More

Generalizations of the Choe-Hoppe helicoid and Clifford cones in Euclidean spaceOct 13 2014Oct 26 2015Our goal is to generalize the Choe-Hoppe helicoid and Clifford cones in Euclidean space. By sweeping out $L$ indpendent Clifford cones in ${\mathbb{R}}^{2N+2}$ via the multi-screw motion, we construct minimal submanifolds in ${\mathbb{R}}^{L(2N+2)+1}$. ... More

The Three Dimensional Structural Shape of the Gravitational Potential in the Local GroupMay 10 2006Jun 19 2008The Local Group is a small galaxy cluster with the membership of 62 nearby galaxies including the Milky Way and M31. Although the Local Group has yet to be virialized, it interacts with the surrounding matter as one gravitationally bound system. To understand ... More

A New Efficient Key Management Protocol for Wireless Sensor and Actor NetworksDec 03 2009Research on sensor networks has become much more active and is currently being applied to many different fields. However since sensor networks are limited to only collecting and reporting information regarding a certain event, and requires human intervention ... More

On the structure of certain valued fieldsAug 27 2016Sep 19 2016For any two complete discrete valued fields $K_1$ and $K_2$ of mixed characteristic with perfect residue fields, we show that if each pair of $n$-th residue rings is isomorphic for each $n\ge1$, then $K_1$ and $K_2$ are isometric and isomorphic. More ... More

The Variation of Galaxy Morphological Type with the Shear of EnvironmentJan 10 2008Jul 28 2008Recent N-body simulations have shown that the assembly history of galactic halos depend on the density of large-scale environment. It implies that the galaxy properties like age and size of bulge may also vary with the surrounding large-scale structures, ... More

Reconstructing the Intrinsic Triaxial Shape of the Virgo ClusterApr 11 2007To use galaxy clusters as a cosmological probe, it is important to account for their triaxiality. Assuming that the triaxial shapes of galaxy clusters are induced by the tidal interaction with the surrounding matter, Lee and Kang recently developed a ... More

Phonological modeling for continuous speech recognition in KoreanJul 18 1996A new scheme to represent phonological changes during continuous speech recognition is suggested. A phonological tag coupled with its morphological tag is designed to represent the conditions of Korean phonological changes. A pairwise language model of ... More

Chart-driven Connectionist Categorial Parsing of Spoken KoreanNov 29 1995While most of the speech and natural language systems which were developed for English and other Indo-European languages neglect the morphological processing and integrate speech and natural language at the word level, for the agglutinative languages ... More

Unbiased Global Optimization of Lennard-Jones Clusters for N <= 201 by Conformational Space Annealing MethodJul 29 2003We apply the conformational space annealing (CSA) method to the Lennard-Jones clusters and find all known lowest energy configurations up to 201 atoms, without using extra information of the problem such as the structures of the known global energy minima. ... More

A note on the Gunningham's formulaJun 30 2014Gunningham [G] constructed an extended topological quantum field theory (TQFT) to obtain a closed formula for all spin Hurwitz numbers. In this note, we use the gluing theorem in [LP2] to reprove the Gunningham's formula. We also describe a TQFT formalism ... More

Cross correlation of Cosmic Microwave background and Weak LensingOct 16 2015The integrated Sachs-Wolfe (ISW) effect and its non-linear extension Rees-Sciama (RS) effect provide us the information of the time evolution of gravitational potential. The cross-correlation between the cosmic microwave background (CMB) and the large ... More

The thermodynamics of quantum spacetime historiesOct 13 2015We show that the simplicity constraints, which define the dynamics of spin foam models, imply, and are implied by, the first law of thermodynamics, when the latter is applied to causal diamonds in the quantum spacetime. This result reveals an intimate ... More

Non-local beablesJul 30 2015I discuss the idea that the beables underlying quantum physics are non-local and relational, and give an example of a dynamical theory of such beables based on a matrix model, which is the bosonic sector of the BFSS model. Given that the same model has ... More

Dynamics of the cosmological and Newton's constantJul 05 2015A modification of general relativity is presented in which Newton's constant and the cosmological constant become a conjugate pair of dynamical variables.

The case for background independenceJul 25 2005The aim of this paper is to explain carefully the arguments behind the assertion that the correct quantum theory of gravity must be background independent. We begin by recounting how the debate over whether quantum gravity must be background independent ... More

A quantization of topological M theoryMar 17 2005A conjecture is made as to how to quantize topological M theory. We study a Hamiltonian decomposition of Hitchin's 7-dimensional action and propose a formulation for it in terms of 13 first class constraints. The theory has 2 degrees of freedom per point, ... More

The cubic matrix model and a duality between strings and loopsJun 19 2000We find evidence for a duality between the standard matrix formulations of M theory and a background independent theory which extends loop quantum gravity by replacing SU(2) with a supersymmetric and quantum group extension of SU(16). This is deduced ... More

General relativity as the equation of state of spin foamMay 24 2012Building on recent significant results of Frodden, Ghosh and Perez (FGP) and Bianchi, I present a quantum version of Jacobson's argument that the Einstein equations emerge as the equation of state of a quantum gravitational system. I give three criteria ... More

On limitations of the extent of inertial frames in non-commutative relativistic spacetimesJul 05 2010Aug 10 2010We study the interplay of non-locality and Lorentz invariance in a version of deformed or doubly special relativity (DSR) based on kappa-Minkowski spacetime. We find that Einstein's procedure for an inertial observer to assign coordinates to distant events ... More

The status of cosmological natural selectionDec 18 2006The problem of making predictions from theories that have landscapes of possible low energy parameters is reviewed. Conditions for such a theory to yield falsifiable predictions for doable experiments are given. It is shown that the hypothesis of cosmological ... More

The present moment in quantum cosmology: challenges to the arguments for the elimination of timeApr 29 2001Barbour, Hawking, Misner and others have argued that time cannot play an essential role in the formulation of a quantum theory of cosmology. Here we present three challenges to their arguments, taken from works and remarks by Kauffman, Markopoulou and ... More

Finite, diffeomorphism invariant observables in quantum gravityFeb 10 1993Two sets of spatially diffeomorphism invariant operators are constructed in the loop representation formulation of quantum gravity. This is done by coupling general relativity to an anti- symmetric tensor gauge field and using that field to pick out sets ... More

Strings as perturbations of evolving spin-networksJan 06 1998A connection between non-perturbative formulations of quantum gravity and perturbative string theory is exhibited, based on a formulation of the non-perturbative dynamics due to Markopoulou. In this formulation the dynamics of spin network states and ... More

Galactic disks as reaction-diffusion systemsDec 03 1996A model of a galactic disk is presented which extends the homogeneous one zone models by incorporating propagation of material and energy in the disk. For reasonable values of the parameters the homogeneous steady state is unstable to the development ... More

Cosmology as a Problem in Critical PhenomenaMay 16 1995Several problems in cosmology and astrophysics are described in which critical phenomena of various types may play a role. These include the organization of the disks of spiral galaxies, various aspects of the problem of structure formation in icosmology, ... More

A characterization of quasipositive Seifert surfaces (Constructions of quasipositive knots and links, III)Nov 15 2004This article was originally published in Topology 31 (1992). The present hyperTeXed redaction corrects a few typographical errors and updates the references.

Isolated critical points of mappings from $\mathbf{R}^4$ to $\mathbf{R}^2$ and a natural splitting of the Milnor number of a classical fibered link. Part I: Basic theory; examplesMar 04 2002Mar 04 2002From a fibered link in the 3-sphere may be constructed a field of not everywhere tangent 2-planes; when the fibered link is the link of an isolated critical point of a map from 4-space to the plane, the plane field is essentially the field of kernels ... More

Quadratic polynomials of small modulus cannot represent ORSep 29 2015Nov 12 2015An open problem in complexity theory is to find the minimal degree of a polynomial representing the $n$-bit OR function modulo composite $m$. This problem is related to understanding the power of circuits with $\text{MOD}_m$ gates where $m$ is composite. ... More

Pointwise convergence of solutions to Schrödinger equationsNov 05 2007Nov 13 2007We study pointwise convergence of the solutions to Schr\"odinger equations with initial datum $f\in H^s(\mathbb R^n)$. The conjecture is that the solution $e^{it\Delta}f$ converges to $f$ almost everywhere for all $f\in H^s(\mathbb R^n)$ if and only if ... More

An Evolutionary Reduction Principle for Mutation Rates at Multiple LociSep 14 2009Aug 19 2010A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of multilocus event ... More

Cylinders and paths in simplicial categoriesJul 29 2013We prove the uniqueness, the functoriality and the naturality of cylinder objects and path objects in closed simplicial model categories.

Positively curved metrics on symmetric spaces with large symmetry rankSep 20 2012We prove an obstruction at the level of rational cohomology in small degrees to the existence of positively curved metrics with large symmetry rank. The symmetry rank bound is logarithmic in the dimension of the manifold. As an application, we provide ... More

A short note on containment of coresMar 13 2007We show that cores of ideals do not preserve the inclusion.

Quasi-sparse eigenvector diagonalization and stochastic error correctionAug 30 2000We briefly review the diagonalization of quantum Hamiltonians using the quasi-sparse eigenvector (QSE) method. We also introduce the technique of stochastic error correction, which systematically removes the truncation error of the QSE result by stochastically ... More

Superfluidity and excitations at unitarityJun 28 2006Dec 18 2006We present lattice results for spin-1/2 fermions at unitarity, where the effective range of the interaction is zero and the scattering length is infinite. We measure the spatial coherence of difermion pairs for a system of 6, 10, 14, 18, 22, 26 particles ... More

Ground state energy of spin-1/2 fermions in the unitary limitNov 14 2005Jan 06 2006We present lattice results for the ground state energy of a spin-1/2 fermion system in the unitary limit, where the effective range of the interaction is zero and the scattering length is infinite. We compute the ground state energy for a system of 6, ... More

Pressure inequalities for nuclear and neutron matterJul 28 2004Dec 22 2005We prove several inequalities using lowest-order effective field theory for nucleons which give an upper bound on the pressure of asymmetric nuclear matter and neutron matter. We prove two types of inequalities, one based on convexity and another derived ... More

Dynamical Fermions in Hamiltonian Lattice Gauge TheoryOct 24 2001We describe a first attempt to understand dynamical fermions within a Hamiltonian framework. As a testing ground we study compact QED3 which shares some important features of QCD4 such as confinement, glueballs, mesons, and chiral symmetry breaking. We ... More

The role of Monte Carlo within a diagonalization/Monte Carlo schemeOct 31 2000We review the method of stochastic error correction which eliminates the truncation error associated with any subspace diagonalization. Monte Carlo sampling is used to compute the contribution of the remaining basis vectors not included in the initial ... More

Optimal Estimation and Prediction for Dense Signals in High-Dimensional Linear ModelsMar 20 2012Estimation and prediction problems for dense signals are often framed in terms of minimax problems over highly symmetric parameter spaces. In this paper, we study minimax problems over l2-balls for high-dimensional linear models with Gaussian predictors. ... More

Dense Signals, Linear Estimators, and Out-of-Sample Prediction for High-Dimensional Linear ModelsFeb 15 2011Mar 20 2012Motivated by questions about dense (non-sparse) signals in high-dimensional data analysis, we study the unconditional out-of-sample prediction error (predictive risk) associated with three popular linear estimators for high-dimensional linear models: ... More

Transforming floundering into successJul 30 2012We show how logic programs with "delays" can be transformed to programs without delays in a way which preserves information concerning floundering (also known as deadlock). This allows a declarative (model-theoretic), bottom-up or goal independent approach ... More

Practical Multiwriter Lock-Free Queues for "Hard Real-Time" Systems without CASSep 28 2007FIFO queues with a single reader and writer can be insufficient for "hard real-time" systems where interrupt handlers require wait-free guarantees when writing to message queues. We present an algorithm which elegantly and practically solves this problem ... More

Transforming Hidden Vector Encryption Schemes from Composite to Prime Order GroupsNov 09 2016Predicate encryption is a new type of public key encryption that enables searches on encrypted data. By using predicate encryption, we can search keywords or attributes on encrypted data without decrypting ciphertexts. Hidden vector encryption (HVE) is ... More

Amplitudes of low frequency modes in rotating B type starsNov 17 2011Using weakly non-linear theory of oscillation, we estimate the amplitudes of low frequency modes in a slowly pulsating B (SPB) star, taking account of the effects of rotation on the modes. Applying the formulation by Schenk et al (2002), we compute non-linear ... More

Orders of reductions of elliptic curves with many and few prime factorsNov 07 2015In this paper, we investigate extreme values of $\omega(E(\mathbb{F}_p))$, where $E/\mathbb{Q}$ is an elliptic curve with complex multiplication and $\omega$ is the number-of-distinct-prime-divisors function. For fixed $\gamma > 1$, we prove that \[ \#\{p ... More

Some 3-dimensional transverse C-links (Constructions of higher-dimensional C-links, I)Aug 20 2015By use of a variety of techniques (most based on constructions of quasipositive knots and links, some old and others new), many smooth 3-manifolds are realized as transverse intersections of complex surfaces in complex 3-space with strictly pseudoconvex ... More

An alternative proof of the non-Archimedean Montel theorem for polynomial dynamicsMay 21 2015May 22 2015We will see an alternative proof of the non-Archimedean Montel theorem, which is also called Hsia's criterion, for polynomial dynamics.

On computation of morphism spaces and a direct limit of the bordered Floer homology of knot complementsMay 27 2015In the bordered Floer theory, gluing thickened torus of positive meridional Dehn twist to the boundary of a knot complement result in the knot complement of increased framing. For a fixed knot K, we construct a direct system of positively framed knot ... More

Exact Partition Function Zeros of the Wako-Saito-Muñoz-Eaton Protein ModelMay 14 2013I compute exact partition function zeros of the Wako-Saito-Mu\~noz-Eaton model for various secondary structural elements and for two proteins, 1BBL and 1I6C, using both analytic and numerical methods. Two-state and barrierless downhill folding transitions ... More

Analytic Partition Function Zeros of the Wako-Saito-Munoz-Eaton beta-hairpin ModelSep 26 2012Sep 28 2012An analytic formula for the density of states of Wako-Saito-Munoz-Eaton model, for a simple class of beta-hairpins, is obtained. Under certain simplifying assumptions on the structure of the native contacts and the values of local entropy, the partition ... More

Integral matrices as diagonal quadratic formsOct 29 2016In this paper, we investigate the conditions under which a diagonal quadratic form $\sum_{i=1}^{m}a_i X_i^2$ represents every $n \times n$ integral matrix, where $a_i$ ($1 \leq i \leq m$) are integers. For $n=2$, we give a necessary and sufficient condition. ... More

A modular quintic Calabi-Yau threefold of level 55Mar 06 2009In this note we search the parameter space of Horrocks-Mumford quintic threefolds and locate a Calabi-Yau threefold which is modular, in the sense that the L-function of its middle-dimensional cohomology is associated to a classical modular form of weight ... More

Transition Probabilities of the Bethe Ansatz Solvable Interacting Particle SystemsNov 12 2010Oct 04 2011This paper presents the exact expressions of the transition probabilities of some non-determinantal Bethe ansatz solvable interacting particle systems: the two-sided PushASEP, the asymmetric avalanche process and the asymmetric zero range process. The ... More

Distribution of a particle's position in the ASEP with the {alternating} initial conditionApr 09 2010Sep 24 2010In this paper we give the distribution of the position of the particle in the asymmetric simple exclusion process (ASEP) with the alternating initial condition. That is, we find $\mathbb{P}(X_m(t) \leq x)$ where $X_m(t)$ is the position of the particle ... More

Partitioning a Graph into Small Pieces with Applications to Path TransversalJul 18 2016Given a graph $G = (V, E)$ and an integer $k$, we study $k$-Vertex Seperator (resp. $k$-Edge Separator), where the goal is to remove the minimum number of vertices (resp. edges) such that each connected component in the resulting graph has at most $k$ ... More

Hardness of Graph Pricing through Generalized Max-DicutMay 04 2014Nov 05 2014The Graph Pricing problem is among the fundamental problems whose approximability is not well-understood. While there is a simple combinatorial 1/4-approximation algorithm, the best hardness result remains at 1/2 assuming the Unique Games Conjecture (UGC). ... More

Dirac cones for point scatterers on a honeycomb latticeFeb 21 2014Jan 27 2016We investigate the spectrum and the dispersion relation of the Schr\"odinger operator with point scatterers on a triangular lattice and a honeycomb lattice. We prove that the low-level dispersion bands have conic singularities near Dirac points, which ... More

Localization of low-energy eigenfunctions in Seba billiardsJul 26 2014Jan 18 2015We investigate localization of low-energy modes of the Laplacian with a point scatterer on a rectangular plate. We observe that the point scatterer acts as a barrier confining the low-level modes to one side of the plate while assuming the Dirichlet boundary ... More

Dynamics on the PSL(2,C)-character variety of a twisted I-bundleMar 17 2011Let M be a twisted interval bundle over a nonorientable hyperbolizable surface. Let X(M) be the PSL(2,C)-character variety of \pi_1(M). We examine the dynamics of the action of Out(\pi_1(M)) on X(M), and in particular, we find an open set on which the ... More

Homoclinic classes with shadowing propertyJan 07 2011Jan 28 2011We show that for $C^1$ generic diffeomorphisms, an isolated homoclinic class is shadowable if and only if homoclinic class is hyperbolic basic set.

On the Action of the Symmetric Group on the Cohomology of Groups Related to (Virtual) BraidsApr 16 2013Jul 08 2013In this paper we consider the cohomology of four groups related to the virtual braids of [Kauffman] and [Goussarov-Polyak-Viro], namely the pure and non-pure virtual braid groups (PvB_n and vB_n, respectively), and the pure and non-pure flat braid groups ... More

Current status of $\varepsilon_K$ in lattice QCDNov 14 2016We present the current status of $\varepsilon_K$ evaluated directly from the standard model using lattice QCD inputs. The lattice QCD inputs include $\hat{B}_K$, $\xi_0$, $\xi_2$, $|V_{us}|$, $m_c(m_c)$, and $|V_{cb}|$. Recently, FLAG has updated $\hat{B}_K$, ... More

Perturbative improvement of staggered fermions using fat linksAug 21 2002Sep 04 2002We study possibility of improving staggered fermions using various fat links in order to reduce perturbative corrections to the gauge-invariant staggered fermion operators. We prove five theorems on SU(3) projection, triviality in renormalization, multiple ... More

Quark Mass Renormalization on the Lattice with Staggered FermionsOct 18 1993The QCD light quark mass renormalized at a 1 GeV scale in the $ \overline{MS} $ scheme is obtained from the numerical results of the lattice QCD simulation with staggered fermions. The primary emphasis is given to the connection between the lattice and ... More

Asymptotic behavior of the Kobayashi metric on convex domainsNov 11 2009In this paper, we calculate estimates for invariant metrics on a finite type convex domain in $\mathbb C^n$ using the Sibony metric. We also discuss a possible modification of the Sibony metric.

Similarity-Based Approaches to Natural Language ProcessingAug 19 1997This thesis presents two similarity-based approaches to sparse data problems. The first approach is to build soft, hierarchical clusters: soft, because each event belongs to each cluster with some probability; hierarchical, because cluster centroids are ... More

IDF revisited: A simple new derivation within the Robertson-Spärck Jones probabilistic modelMay 08 2007There have been a number of prior attempts to theoretically justify the effectiveness of the inverse document frequency (IDF). Those that take as their starting point Robertson and Sparck Jones's probabilistic model are based on strong or complex assumptions. ... More

"I'm sorry Dave, I'm afraid I can't do that": Linguistics, Statistics, and Natural Language Processing circa 2001Apr 21 2003A brief, general-audience overview of the history of natural language processing, focusing on data-driven approaches.Topics include "Ambiguity and language analysis", "Firth things first", "A 'C' change", and "The empiricists strike back".

Measures of Distributional SimilarityJan 18 2000We study distributional similarity measures for the purpose of improving probability estimation for unseen cooccurrences. Our contributions are three-fold: an empirical comparison of a broad range of measures; a classification of similarity functions ... More

Klein factors and Fermi-Bose EquivalenceDec 21 2015Generalizing the kink operator of the Heisenberg spin 1/2 model, we construct a set of Klein factors explicitly such that $(1+1)$ dimensional fermion theories with arbitrary number of species are mapped onto the corresponding boson theories with the same ... More

Global Exponential Attitude Tracking Controls on SO(3)Sep 13 2012Dec 09 2014This paper presents four types of tracking control systems for the attitude dynamics of a rigid body. First, a smooth control system is constructed to track a given desired attitude trajectory, while guaranteeing almost semi-global exponential stability. ... More

Chiral Vacuum Alignment in Dense QCDMay 31 2000Dec 04 2000We discuss an interesting possibility of nontrivial, quark-mass induced chiral vacuum alignment in color-flavor locking phase of cold, dense QCD. With the simplifying assumption that the gaps for quarks are identical to those of antiquarks and the light ... More

Higher Dimensional Operator Corrections to the Goldstino Goldberger-Treiman VerticesDec 21 1998Oct 02 1999The goldstino-matter interactions given by the Goldberger-Treiman relations can receive higher dimensional operator corrections of $ O(q^{2}/M^{2})$, where $M$ denotes the mass of the mediators through which SUSY breaking is transmitted. These corrections ... More

The Entropy of the BTZ Black Hole and AdS/CFT CorrespondenceJun 15 1998We construct an action, which governs the dynamics of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole and perform the canonical quantization. The quantum action is given by a $SL(2,R)$ Wess-Zumino-Witten model on the boundary coupled to the classical ... More

Chiral radiative corrections in potential model and the P-wave states of heavy-light mesonsMar 05 2008In relativistic potential model of heavy-light mesons it is essential to incorporate the chiral radiative corrections before comparing the model predictions with data. Once the radiative corrections are taken into account the potential model can explain ... More

Applications of Thirring Model to Inhomogenous Rolling Tachyon and Dissipative Quantum MechanicsNov 04 2007We study the rolling tachyon and the dissipative quantum mechanics using the Thirring model with a boundary mass. We construct a boundary state for the dissipative quantum system in one dimension, which describes the system at the off-critical points ... More

Geometric Adaptive Control for Aerial Transportation of a Rigid BodyMar 03 2015This paper is focused on tracking control for a rigid body payload, that is connected to an arbitrary number of quadrotor unmanned aerial vehicles via rigid links. A geometric adaptive controller is constructed such that the payload asymptotically follows ... More

Surviving the renormalon in heavy quark potentialOct 02 2002Dec 02 2002We show that the Borel resummed perturbative static potential at N_f=0 converges well, and is in a remarkable agreement with the quenched lattice calculation at distances 1/r > 660 MeV. This shows that Borel resummation is very good at handling the renormalon ... More

Canonical Quantization of Open String and Noncommutative GeometryNov 18 1999Dec 21 1999We perform canonical quantization of open strings in the $D$-brane background with a $B$-field. Treating the mixed boundary condition as a primary constraint, we get a set of secondary constraints. Then these constraints are shown to be equivalent to ... More

Describing Spin-Selective Reactions of Radical Pairs Using Quantum Jump ApproachesOct 11 2011Recently, spin-selective radical pair reactions have been studied using concepts from quantum measurement theory. In this Article, we show that the approach taken by Kominis (Physical Review E, 83, 2011, 056118) leads to erroneous results due to a problematic ... More

Nondecoupling of Heavy Mirror-FermionMar 11 1994According to one-loop perturbation theory, fermions whose masses are totally generated from Yukawa couplings do not decouple in the heavy mass limit. We investigate this issue nonperturbatively in the strong coupling regime of the chiral $U(1)$ mirror-fermion ... More

On Charge Conservation and The Equivalence Principle in the Noncommutative SpacetimeApr 13 2007Jun 20 2007We investigate one of the consequences of the twisted Poincare symmetry. We derive the charge conservation law and show that the equivalence principle is satisfied in the canonical noncommutative spacetime. We applied the twisted Poincare symmetry to ... More

Every finite acyclic quiver is a full subquiver of a quiver mutation equivalent to a bipartite quiverOct 31 2013Nov 13 2013We give a very short proof of the claim in the title.

On cluster variables of rank two acyclic cluster algebrasAug 11 2010Aug 12 2010In this note, we find an explicit formula for the Laurent expression of cluster variables of coefficient-free rank two cluster algebras associated with the matrix $\left(\begin{array}{cc} 0 & c -c & 0 \end{array}\right)$, and show that a large number ... More

Proof of a Conjectured Formula for the Alexander InvariantSep 04 2012Oct 09 2012In this paper we prove the validity of a formula for computing the Alexander invariant which was originally conjectured by Bar-Natan and Dancso in [BND].

$G$-Frobenius ManifoldsJan 09 2015The goal of this paper is to introduce the notion of $G$-Frobenius manifolds for any finite group $G$. This work is motivated by the fact that any $G$-Frobenius algebra yields an ordinary Frobenius algebra by taking its $G$-invariants. We generalize this ... More

Weierstrass representation for timelike minimal surfaces in Minkowski 3-spaceAug 29 2006Aug 30 2006Using techniques of integrable systems, we study a Weierstrass representation formula for timelike surfaces with prescribed mean curvature in Minkowski 3-space. It is shown that timelike minimal surfaces are obtained by integrating a pair of Lorentz holomorphic ... More

Characteristics of Preferentially Attached Network Grown from Small WorldSep 07 2015We introduce a model for a preferentially attached network which has grown from a small world network. Here, the average path length and the clustering coefficient are estimated, and the topological properties of modeled networks are compared as the initial ... More

Colloidal superlattices for unnaturally high-index metamaterials at broadband optical frequenciesJul 24 2015The recent advance in the assembly of metallic nanoparticles (NPs) has enabled sophisticated engineering of unprecedented light-matter interaction at the optical domain. In this work, I expand the design flexibility of NP optical metamaterial to push ... More

Extending dualities to trialities deepens the foundations of dynamicsMar 04 2015Dualities are often supposed to be foundational, but they may come into conflict with background independence, because a hidden fixed structures is needed to define the duality transformation. This conflict can be eliminated by extending a duality to ... More

Precedence and freedom in quantum physicsMay 16 2012A new interpretation of quantum mechanics is proposed according to which precedence, freedom and novelty play central roles. This is based on a modification of the postulates for quantum theory given by Masanes and Muller. We argue that quantum mechanics ... More

Generic predictions of quantum theories of gravityMay 04 2006I discuss generic consequences (sometimes called "soft predictions") of a class of background independent quantum theories of spacetime called causal spin network theories. These are theories whose kinematics and dynamics is based on the evolution of ... More

A real ensemble interpretation of quantum mechanicsApr 14 2011A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems within the ... More

Newtonian gravity in loop quantum gravityJan 20 2010Feb 22 2010We apply a recent argument of Verlinde to loop quantum gravity, to conclude that Newton's law of gravity emerges in an appropriate limit and setting. This is possible because the relationship between area and entropy is realized in loop quantum gravity ... More

Falsifiable predictions from semiclassical quantum gravityJan 12 2005Apr 18 2005Quantum gravity is studied in a semiclassical approximation and it is found that to first order in the Planck length the effect of quantum gravity is to make the low energy effective spacetime metric energy dependent. The diffeomorphism invariance of ... More

Three Dimensional Strings as Collective Coordinates of Four Dimensional Non-Perturbative Quantum GravitySep 12 1996A string theory in $3$ euclidean spacetime dimensions is found to describe the semiclassical behavior of a certain exact physical state of quantum general relativity in $4$ dimensions. Both the worldsheet and the three dimensional metric emerge as collective ... More

The fate of black hole singularities and the parameters of the standard models of particle physics and cosmologyApr 07 1994A cosmological scenario which explains the values of the parameters of the standard models of elementary particle physics and cosmology is discussed. In this scenario these parameters are set by a process analogous to natural selection which follows naturally ... More

Time, measurement and information loss in quantum cosmologyJan 15 1993Feb 08 1993An error in the gauge fixed quantization of section 3 is corrected. The result is a much simpler treatment of the clock field, leading to a simplification of the gauge fixed quantum theory and the treatment of the semiclassical limit.