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Embedded Index CodingApr 03 2019Apr 24 2019Motivated by applications in distributed storage and distributed computation, we introduce embedded index coding (EIC). EIC is a type of distributed index coding in which nodes in a distributed system act as both senders and receivers of information. ... More

Competitive binding of transcription factors drives Mendelian dominance in regulatory genetic pathwaysJun 21 2016Aug 27 2016We report a new mechanism for allelic dominance in regulatory genetic interactions that we call binding dominance. We investigated a biophysical model of gene regulation, where the fractional occupancy of a transcription factor (TF) on the cis-regulated ... More

Laboratory Measurements of X-Ray Emission from Highly Charged Argon IonsMar 09 2018Nov 03 2018Uncertainties in atomic models will introduce noticeable additional systematics in calculating the flux of weak dielectronic recombination (DR) satellite lines, affecting the detection and flux measurements of other weak spectral lines. One important ... More

Collaborative Computation in Self-Organizing Particle SystemsOct 22 2017Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and coating materials ... More

Models of Continuous-Time Networks with Tie Decay, Diffusion, and ConvectionJun 22 2019The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. For many complex systems, however, it is useful to develop continuous-time models of networks and to ... More

iGen: Dynamic Interaction Inference for Configurable SoftwareMar 28 2019To develop, analyze, and evolve today's highly configurable software systems, developers need deep knowledge of a system's configuration options, e.g., how options need to be set to reach certain locations, what configurations to use for testing, etc. ... More

The unreasonable effectiveness of tree-based theory for networks with clusteringJan 09 2010We demonstrate that a tree-based theory for various dynamical processes yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance $\ell$ is sufficiently ... More

Metamorphic Detection of Adversarial Examples in Deep Learning Models With Affine TransformationsJul 10 2019Adversarial attacks are small, carefully crafted perturbations, imperceptible to the naked eye; that when added to an image cause deep learning models to misclassify the image with potentially detrimental outcomes. With the rise of artificial intelligence ... More

Contragenic Functions of Three VariablesJul 06 2012It is shown that harmonic functions from a simply connected domain in R^3 to R^3 cannot always be expressed as a sum of a monogenic (hyperholomorphic) function and an antimonogenic function, in contrast to the situation for complex numbers or quaternions. ... More

Faster and better: a machine learning approach to corner detectionOct 14 2008The repeatability and efficiency of a corner detector determines how likely it is to be useful in a real-world application. The repeatability is importand because the same scene viewed from different positions should yield features which correspond to ... More

Correlations from p-p collisions at $\sqrt{s} = 200$ GeVJun 17 2005We describe a comprehensive survey of two-particle correlations from p-p collisions at $\sqrt{s} = 200$ GeV. Correlations on transverse rapidity $y_t$ are separated into a soft component (string fragments) and a hard component (parton fragments). Fragment ... More

Mixed linear-nonlinear least squares regressionMar 12 2017The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of discrepancy by ... More

Conformal Mapping of Right Circular QuadrilateralsApr 23 2009We study conformal mappings from the unit disk to circular-arc quadrilaterals with four right angles. The problem is reduced to a Sturm-Liouville boundary value problem on a real interval, with a nonlinear boundary condition, in which the coefficient ... More

General solution of the inhomogenous div-curl system and consequencesMay 30 2017We consider the inhomogeneous div-curl system (i.e.\ to find a vector field with prescribed div and curl) in a bounded star-shaped domain in $\mathbb{R}^3$. An explicit general solution is given in terms of classical integral operators, completing previously ... More

Monotone Covering Properties defined by Closure-Preserving OperatorsOct 28 2017We continue Gartside, Moody, and Stares' study of versions of monotone paracompactness. We show that the class of spaces with a monotone closure-preserving open operator is strictly larger than those with a monotone open locally-finite operator. We prove ... More

Load-Balanced Fractional Repetition CodesFeb 02 2018We introduce load-balanced fractional repetition (LBFR) codes, which are a strengthening of fractional repetition (FR) codes. LBFR codes have the additional property that multiple node failures can be sequentially repaired by downloading no more than ... More

Desargues maps and the Hirota-Miwa equationJun 04 2009Sep 28 2009We study the Desargues maps $\phi:\ZZ^N\to\PP^M$, which generate lattices whose points are collinear with all their nearest (in positive directions) neighbours. The multidimensional compatibility of the map is equivalent to the Desargues theorem and its ... More

Geometric algebra and quadrilateral latticesJan 03 2008Motivated by the fundamental results of the geometric algebra we study quadrilateral lattices in projective spaces over division rings. After giving the noncommutative discrete Darboux equations we discuss differences and similarities with the commutative ... More

Geometric discretization of the Koenigs netsMar 07 2002Apr 26 2002We introduce the Koenigs lattice, which is a new integrable reduction of the quadrilateral lattice (discrete conjugate net) and provides natural integrable discrete analogue of the Koenigs net. We construct the Darboux-type transformations of the Koenigs ... More

Holomorphic Curves and Toda SystemsJul 03 1995Jul 04 1995Geometry of holomorphic curves from point of view of open Toda systems is discussed. Parametrization of curves related this way to non-exceptional simple Lie algebras is given. This gives rise to explicit formulas for minimal surfaces in real, complex ... More

Asymptotically periodic L^2 minimizers in strongly segregating diblock copolymersJan 07 2009Using the delta correction to the standard free energy \cite{bc} in the elastic setting with a quadratic foundation term and some parameters, we introduce a one dimension only model for strong segregation in diblock copolymers, whose sharp interface periodic ... More

Topological Triviality of $μ$-constant Deformations of Type f(x) + tg(x)Nov 11 1997We show that every $\mu$-constant family of isolated hypersurface singularities of type f(x) + tg(x), where t is a parameter, is topologically trivial. In the proof we construct explicitely a vector field trivializing the family. The proof uses only the ... More

Blow-analytic retraction onto the central fibreJan 26 1997Let X be a complex analytic space and let f:X -> C be a proper complex analytic function with nonsingular generic fibres. By adapting the blowanalytic methods of Kuo we construct a retraction of a neighbourhood of the central fibre f^{-1}(0) onto f^{-1}(0). ... More

Distinct Distances: Open Problems and Current BoundsJun 08 2014May 19 2015We survey the variants of Erd\H{o}s' distinct distances problem and the current best bounds for each of those.

Additivity of the ideal of microscopic setsMay 25 2015A set $M\subset\mathbb{R}$ is microscopic if for each $\varepsilon>0$ there is a sequence of intervals $(J_n)_{n\in\omega}$ covering $M$ and such that $|J_n|\leq \varepsilon^{n+1}$ for each $n\in\omega$. We show that there is a microscopic set which cannot ... More

YSO Jets and Molecular Outflows: Tracing the History of Star FormationApr 29 1998Collimated outflows from Young Stellar Objects (YSOs) can be seen as tracers of the accretion powered systems which drive them. In this paper I review some theoretical and observational aspects of YSO outflows through the prism of questions relating to ... More

Towards a Synthesis of Core-Collapse Supernova TheoryJun 06 1996New insights into the mechanism and character of core--collapse supernova explosions are transforming the approach of theorists to their subject. The universal realization that the direct hydrodynamic mechanism does not work and that a variety of hydrodynamic ... More

Consistent and covariant commutator anomalies in the chiral Schwinger modelOct 06 1997We derive all covariant and consistent divergence and commutator anomalies of chiral QED$_2$ within the framework of canonical quantization of the fermions. Further, we compute the time evolution of all occurring operators and find that all commutators ... More

Decay widths in the massive Schwinger modelSep 18 1996By a closer inspection of the massive Schwinger model within mass perturbation theory we find that, in addition to the $n$-boson bound states, a further type of hybrid bound states has to be included into the model. Further we explicitly compute the decay ... More

General bound-state structure of the massive Schwinger modelFeb 29 1996Within the Euclidean path integral and mass perturbation theory we derive, from the Dyson-Schwinger equations of the massive Schwinger model, a general formula that incorporates, for sufficiently small fermion mass, all the bound-state mass poles of the ... More

Nonstandard transition GUE-GOE for random matrices and spectral statistics of graphene nanoflakesApr 13 2016Jun 21 2016Spectral statistics of weakly-disordered triangular graphene flakes with zigzag edges are revisited. Earlier, we have found numerically that such systems may shown spectral fluctuations of GUE, signalling the time-reversal symmetry breaking at zero magnetic ... More

The concept of duality for automata over a changing alphabet and generation of a free group by such automataJul 26 2016In the paper, we deal with the notion of an automaton over a changing alphabet, which generalizes the concept of a Mealy-type automaton. We modify the methods based on the idea of a dual automaton and its action used by B. Steinberg et al. (2011) and ... More

Characterization of Parity-Time Symmetry in Photonic Lattices Using Heesh-Shubnikov Group TheoryJun 16 2016We investigate the properties of parity-time symmetric periodic photonic structures using Heesh-Shubnikov group theory. Classical group theory cannot be used to categorize the symmetry of the eigenmodes because the time-inversion operator is antiunitary. ... More

On geometry of congruences of null strings in 4-dimensional complex and real pseudo-Riemannian spacesOct 08 20164-dimensional spaces equipped with 2-dimensional (complex holomorphic or real smooth) completely integrable distributions are considered. The integral manifolds of such distributions are totally null and totally geodesics 2-dimensional surfaces which ... More

Generic freeness in frame bundle prolongations of $C^\infty$ actionsMay 20 2016Let a real Lie group $G$ act on a $C^\infty$ real manifold~$M$. Assume that the action is $C^\infty$ and that every nontrivial element of~$G$ has a nowhere dense fixpoint set in $M$. We show that, in some higher order frame bundle $F$ of~$M$, there exist ... More

Strange anti-particle to particle ratios at mid-rapidity in sqrt(s_NN)= 130 GeV Au+Au CollisionsNov 22 2002Jul 15 2003Values of the ratios in the mid-rapidity yields of anti-Lambda/Lambda = 0.71 +/- 0.01(stat.) +/- 0.04(sys.), anti-Xi+/Xi- = 0.83 +/- 0.04(stat.) +/- 0.05 (sys.), anti-Omega+/Omega- = 0.95 +/- 0.15(stat) +/- 0.05(sys.) and K+/K- 1.092 +/- 0.023(combined) ... More

Search for the decay K_L-> pi^0 nu nubarJun 08 1998Jun 10 1998We report on a search for the rare decay K_L -> pi^0 nu nubar in the KTeV experiment at Fermilab. We searched for two-photon events whose kinematics were consistent with an isolated pi^0 coming from the decay K_L -> pi^0 nu nubar. One candidate event ... More

Efficient, Differentially Private Point EstimatorsSep 27 2008Differential privacy is a recent notion of privacy for statistical databases that provides rigorous, meaningful confidentiality guarantees, even in the presence of an attacker with access to arbitrary side information. We show that for a large class of ... More

Pseudo-goldstone higgs from five dimensionsOct 22 2007Oct 27 2007I discuss radiative generation of the higgs potential in 5D models of gauge-higgs unification.

Lambda-Free Logical FrameworksApr 11 2008Nov 18 2008We present the definition of the logical framework TF, the Type Framework. TF is a lambda-free logical framework; it does not include lambda-abstraction or product kinds. We give formal proofs of several results in the metatheory of TF, and show how it ... More

The Generic Critical Behaviour for 2D Polymer CollapseOct 30 2015Dec 01 2015The nature of the theta point for a polymer in two dimensions has long been debated, with a variety of candidates put forward for the critical exponents. This includes those derived by Duplantier and Saleur (DS) for an exactly solvable model. We use a ... More

Searches for Long-lived Particles at the Tevatron ColliderFeb 07 2008Several searches for long-lived particles have been performed using data from p-pbar collisions from Run II at the Tevatron. In most cases, new analysis techniques have been developed to carry out each search and/or estimate the backgrounds. These searches ... More

Young Physicists' ForumOct 15 2001The Young Physicists' Forum was an opportunity for the younger members of the particle-physics community to gather at Snowmass 2001 and to study and debate major issues that face the field over the next twenty years. Discussions were organized around ... More

Weight reduction for cohomological mod $p$ modular forms over imaginary quadratic fieldsAug 23 2011Let $ F$ be an imaginary quadratic field and $\mathcal{O}$ its ring of integers. Let $ \mathfrak{n} \subset \mathcal{O} $ be a non-zero ideal and let $ p> 5$ be a rational inert prime in $F$ and coprime with $\mathfrak{n}$. Let $ V$ be an irreducible ... More

The Next U.S. Astronomy Decadal SurveyAug 01 2017The U.S. astronomy decadal surveys have been models for advice to government on how to apportion resources to optimise the scientific return on national investments in facilities and manpower. The U.S. is now gearing up to conduct its 2020 survey and ... More

Point Leaf Maximal Singular Riemannian Foliations in Positive CurvatureApr 25 2018May 02 2018We generalize the notion of fixed point homogeneous isometric group actions to the context of singular Riemannian foliations. We find that in some cases, positively curved manifolds admitting these so-called point leaf maximal SRF's are diffeo/homeomorphic ... More

Exploring phase transitions by finite-entanglement scaling of MPS in the 1D ANNNI modelFeb 21 2011We use the finite-entanglement scaling of infinite matrix product states (iMPS) to explore supposedly infinite order transitions. This universal method may have lower computational costs than finite-size scaling. To this end, we study possible MPS-based ... More

Making the coherent state path integral great again: insights from stochastic calculusJun 06 2019Recently, doubts have been cast on the validity of the continuous-time coherent state path integral. This has led to controversies regarding the correct way of performing calculations with path integrals, and to several alternative definitions of what ... More

Non-commutative double-sided continued fractionsMay 24 2019We study double-sided continued fractions whose coefficients are non-commuting symbols. We work within the formal approach of the Mal'cev-Neumann series and free division rings. We start with presenting the analogs of the standard results from the theory ... More

Improved Photometric Classification of Supernovae using Deep LearningOct 15 2018We present improved photometric supernovae classification using deep recurrent neural networks. The main improvements over previous work are (i) the introduction of a time gate in the recurrent cell that uses the observational time as an input; (ii) greatly ... More

A new reduction strategy for special negative sectors of planar two-loop integrals without Laporta algorithmDec 13 2018In planar two-loop integrals there is a dedicated sector such that when its index is zero, the two-loop integral decomposes into the product of two one-loop integrals. We show an alternative reduction strategy for these sectors when their index is negative ... More

Auditory information loss in real-world listening environmentsFeb 20 2019Whether animal or speech communication, environmental sounds, or music -- all sounds carry some information. Sound sources are embedded in acoustic environments that contain any number of additional sources that emit sounds that reach the listener's ears ... More

Asymptotic Solutions of Polynomial Equations with Exp-Log CoefficientsApr 15 2019We present an algorithm for computing asymptotic approximations of roots of polynomials with exp-log function coefficients. The real and imaginary parts of the approximations are given as explicit exp-log expressions. We provide a method for deciding ... More

A Brief History of the Co-evolution of Supernova Theory with Neutrino PhysicsDec 13 2018The histories of core-collapse supernova theory and of neutrino physics have paralleled one another for more than seventy years. Almost every development in neutrino physics necessitated modifications in supernova models. What has emerged is a complex ... More

Bernoulli property for homogeneous systemsDec 07 2018Let $G$ be a semisimple Lie group with Haar measure $\mu$ and let $\Gamma$ be an irreducible lattice in $G$. For $g\in G$, we consider left translation $L_g$ acting on $(G\backslash\Gamma,\mu)$. We show that if $L_g$ is $K$ (which is equivalent to positive ... More

Generalizations of the Burns-Hale TheoremNov 26 2018The Burns-Hale theorem states that a group G is left-orderable if and only if G is locally projectable onto the class of left-orderable groups. Similar results have appeared in the literature in the case of UPP groups and Conradian left-orderable groups, ... More

The Real Chevalley InvolutionMar 08 2012Feb 13 2014We consider the Chevalley involution in the context of real reductive groups. We show that if G(R) is the real points of a connected reductive group, there is an involution, unique up to conjugacy by G(R), taking any semisimple element to a conjugate ... More

The Kodaira dimension of moduli spaces of curves with marked points, IIOct 29 2001We sharpen our previous results on the g and n such that the moduli space of curves of genus g with n marked points is of general type.

Eigenvalues of Toeplitz Operators on the Annulus and Neil AlgebraMar 13 2013Aug 27 2013By working with all collection of all the Sarason Hilbert Hardy spaces for the annulus algebra an improvement to the results of Aryana and Clancey on eigenvalues of self adjoint Toeplitz operators on an annulus is obtained. The ideas are applied to Toeplitz ... More

Multivariable spectral multipliers and quasielliptic operatorsJul 28 2008We study multivariable spectral multipliers $F(L_1,L_2)$ acting on Cartesian product of ambient spaces of two self-adjoint operators $L_1$ and $L_2$. We prove that if $F$ satisfies H\"ormander type differentiability condition then the operator $F(L_1,L_2)$ ... More

Bondary-connectivity via graph theoryNov 12 2007Sep 27 2011We generalize theorems of Kesten and Deuschel-Pisztora about the connectedness of the exterior boundary of a connected subset of $\Z^d$, where "connectedness" and "boundary" are understood with respect to various graphs on the vertices of $\Z^d$. We provide ... More

Kummer Subspaces of Tensor Products of Cyclic AlgebrasMay 01 2014We discuss the Kummer subspaces of tensor products of cyclic algebras, focusing mainly on the case of cyclic algebras of degree 3. We present a family of maximal spaces in the general case, classify all the monomial spaces in the case of tensor products ... More

Categoricity and covering spacesDec 10 2014This thesis develops some of the basic model theory of covers of algebraic curves. In particular, an equivalence between the good model-theoretic behaviour of the modular j-function, and the openness of certain Galois representations in the Tate-modules ... More

Slow recurrent regimes for a class of one-dimensional stochastic growth modelsMar 31 2016Apr 07 2016We classify the possible behaviors of a class of one-dimensional stochastic recurrent growth models. In our main result, we obtain nearly optimal bounds for the tail of hitting times of some compact sets. If the process is an aperiodic irreducible Markov ... More

Criterion of unlimited growth of critical multidimensional stochastic modelsFeb 13 2015Apr 07 2016We give a criterion for unlimited growth with positive probability for a large class of multidimensional stochastic models. As a by-product, we recover the necessary and sufficient conditions for recurrence and transience for critical multitype Galton-Watson ... More

On groups generated by bi-reversible automata: the two-state case over a changing alphabetFeb 01 2017The notion of an automaton over a changing alphabet $X=(X_i)_{i\geq 1}$ is used to define and study automorphism groups of the tree $X^*$ of finite words over $X$. The concept of bi-reversibility for Mealy-type automata is extended to automata over a ... More

The Ozsváth-Szabó spectral sequence and combinatorial link homologyOct 09 2015Jul 13 2017The Khovanov homology of a link in $S^3$ and the Heegaard Floer homology of its branched double cover are related through a spectral sequence constructed by Ozsv\'ath and Szab\'o. This spectral sequence has topological applications but is difficult to ... More

Mutation-invariance of Khovanov-Floer theoriesJun 14 2018Khovanov-Floer theories are a class of homological link invariants which admit spectral sequences from Khovanov homology. They include Khovanov homology, Szab{\'o}'s geometric link homology, singular instanton homology, and various Floer theories applied ... More

Invariants of knotted surfaces from link homology and bridge trisectionsSep 17 2018Jan 16 2019Meier and Zupan showed that every surface in the four-sphere admits a bridge trisection and can therefore be represented by three simple tangles. This raises the possibility of applying methods from link homology to knotted surfaces. We use link homology ... More

The $r$-matching sequencibility of complete multi-$k$-partite $k$-graphsMay 10 2019Alspach [{\sl Bull. Inst. Combin. Appl.}~{\bf 52} (2008), 7--20] defined the maximal matching sequencibility of a graph $G$, denoted~$ms(G)$, to be the largest integer $s$ for which there is an ordering of the edges of $G$ such that every $s$ consecutive ... More

On g-functions for countable state subshiftsDec 27 2016This note revisits the problem of finding necessary and sufficient conditions for a subshift to have a continuous g-function. Results obtained by Krieger (IMS Lecture Notes-Monograph Series, 48, 306--316, 2006) on finite alphabet subshifts are generalized ... More

Approximating Cayley diagrams versus Cayley graphsMar 25 2011Nov 15 2011We construct a sequence of finite graphs that weakly converge to a Cayley graph, but there is no labelling of the edges that would converge to the corresponding Cayley diagram. A similar construction is used to give graph sequences that converge to the ... More

Can all muscular load sharing patterns be regarded as optimal in some sense?Nov 16 2006Muscles crossing a joint usually outnumber its degrees of freedom, which renders the motor system underdetermined. Typically, optimization laws are postulated to cope with this redundancy. A natural question then arises whether all muscular load sharing ... More

Non-commutative rational Yang-Baxter mapsAug 13 2013Aug 14 2013Starting from multidimensional consistency of non-commutative lattice modified Gel'fand-Dikii systems we present the corresponding solutions of the functional (set-theoretic) Yang-Baxter equation, which are non-commutative versions of the maps arising ... More

On $τ$-function of the quadrilateral latticeDec 31 2008We investigate the $\tau$-function of the quadrilateral lattice using the nonlocal $\bar\partial$-dressing method, and we show that it can be identified with the Fredholm determinant of the integral equation which naturally appears within that approach. ... More

The normal dual congruences and the dual Bianchi latticeDec 15 2003The main goal of this paper is to find the discrete analogue of the Bianchi system in spaces of arbitrary dimesion together with its geometric interpretation. We show that the proper geometric framework of such generalization is the language of dual quadrilateral ... More

The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa systemJun 17 2010We study recently introduced Desargues maps, which provide simple geometric interpretation of the non-commutative Hirota--Miwa system. We characterize them as maps of the A-type root lattice into a projective space such that images of vertices of any ... More

Quadratic reductions of quadrilateral latticesFeb 13 1998It is shown that quadratic constraints are compatible with the geometric integrability scheme of the multidimensional quadrilateral lattice equation. The corresponding Ribaucour reduction of the fundamental transformation of quadrilateral lattices is ... More

Vector boson scattering at high mass with ATLASOct 14 2008In the absence of a light Higgs boson, the mechanism of electroweak symmetry breaking will be best studied in processes of vector boson scattering at high mass. Various models predict resonances in this channel. Scalar and vector resonances have been ... More

Existence of traveling waves for the nonlocal Burgers equationMar 27 2006We study the equation $u_t +uu_x +u-K*u=0$ in the case of an arbitrary $K \geq 0$, which is a generalization of a model for radiating gas, in which $K(y)={1/2}e^{-|y|}$. Using a monotone iteration scheme argument we establish the existence of traveling ... More

Divide-And-Conquer Computation of Cylindrical Algebraic DecompositionFeb 04 2014We present a divide-and-conquer version of the Cylindrical Algebraic Decomposition (CAD) algorithm. The algorithm represents the input as a Boolean combination of subformulas, computes cylindrical algebraic decompositions of solution sets of the subformulas, ... More

Scientific Return of Coronagraphic Exoplanet Imaging and Spectroscopy Using WFIRSTDec 18 2014In this study, we explore and review the scientific potential for exoplanet characterization by a high-contrast optical coronagraph on WFIRST/AFTA. We suggest that the heterogeneity in albedo spectra and planet/star flux ratios as a function of orbital ... More

Highlights in the Study of Exoplanet AtmospheresSep 25 2014Exoplanets are now being discovered in profusion. However, to understand their character requires spectral models and data. These elements of remote sensing can yield temperatures, compositions, and even weather patterns, but only if significant improvements ... More

Spectra as Windows into Exoplanet AtmospheresDec 06 2013Understanding a planet's atmosphere is a necessary condition for understanding not only the planet itself, but also its formation, structure, evolution, and habitability, This puts a premium on obtaining spectra, and developing credible interpretative ... More

The Role of Dust Clouds in the Atmospheres of Brown DwarfsFeb 10 2009The new spectroscopic classes, L and T, are defined by the role of dust clouds in their atmospheres, the former by their presence and the latter by their removal and near absence. Moreover, the M to L and L to T transitions are intimately tied to the ... More

A Critique of Core--Collapse Supernova Theory Circa 1997Mar 02 1997There has been a new infusion of ideas in the study of the mechanism and early character of core--collapse supernovae. However, despite recent conceptual and computational progress, fundamental questions remain. Some are summarize herein.

Classification of the Killing Vectors in Nonexpanding HH-Spaces with LambdaNov 11 2011Conformal Killing equations and their integrability conditions for nonexpanding hyperheavenly spaces with Lambda are studied. Reduction of ten Killing equations to one master equation is presented. Classification of homothetic and isometric Killing vectors ... More

A Paradigm Lost: New Theories for Aspherical PNeDec 09 1999Theoretical Models for the shaping of PNe are reviewed in light of new high resolution images. The new data indicate the purely hydrodynamic interacting stellar winds model can not recover the full variety of shapes and kinematics. New models, some speculative, ... More

Comment on covariant Stora--Zumino chain termsMar 23 1999In a recent paper, Ekstrand proposed a simple expression from which covariant anomaly, covariant Schwinger term and higher covariant chain terms may be computed. We comment on the relation of his result to the earlier work of Tsutsui.

Massive Schwinger model within mass perturbation theoryApr 08 1997In this article we give a detailed discussion of the mass perturbation theory of the massive Schwinger model. After discussing some general features and briefly reviewing the exact solution of the massless case, we compute the vacuum energy density of ... More

Decay widths and scattering processes in massive QED$_2$Oct 06 1997Using mass perturbation theory, we infer the bound-state spectrum of massive QED$_2$ and compute some decay widths of unstable bound states. Further, we discuss scattering processes, where all the resonances and particle production thresholds are properly ... More

Vacuum Functional and Fermion Condensate in the Massive Schwinger ModelJul 11 1995We derive a systematic procedure of computing the vacuum functional and fermion condensate of the massive Schwinger model via a perturbative expansion in the fermion mass. We compute numerical results for the first nontrivial order.

Oscillatory behaviour in a lattice prey-predator systemOct 07 1999Using Monte Carlo simulations we study a lattice model of a prey-predator system. We show that in the three-dimensional model populations of preys and predators exhibit coherent periodic oscillations but such a behaviour is absent in lower-dimensional ... More

Dimensional reduction in a model with infinitely many absorbing statesOct 04 1999Using Monte Carlo method we study a two-dimensional model with infinitely many absorbing states. Our estimation of the critical exponent beta=0.273(5) suggests that the model belongs to the (1+1) rather than (2+1) directed-percolation universality class. ... More

All ASD complex and real 4-dimensional Einstein spaces with $Λ\ne 0$ admitting a nonnull Killing vectorDec 16 2013Feb 02 2015Anti-self-dual (ASD) 4-dimensional complex Einstein spaces with nonzero cosmological constant $\Lambda$ equipped with a nonnul Killing vector are considered. It is shown, that any conformally nonflat metric of such spaces can be always brought to a special ... More

A Hasse Principle for Periodic PointsSep 11 2012May 06 2013Let $F$ be a global field, let $\vp \in \Fx$ be a rational map of degree at least 2, and let $\a \in F$. We say that $\a $ is periodic if $\vpn (\a) = \a$ for some $n \geq 1$. A Hasse principle is the idea, or hope, that a phenomenon which happens everywhere ... More

Subset Space Public Announcement Logic RevisitedFeb 16 2013By a modification of the central definition given in [W\'ang and {\AA}gotnes, 2013], we provide semantics for public annoucements in subset spaces. We argue that these revised semantics improve on the original, and we provide a simple sound and complete ... More

Infinitesimal Thurston Rigidity and the Fatou-Shishikura InequalityFeb 26 1999We prove a refinement of the Fatou-Shishikura Inequality - that the total count of nonrepelling cycles of a rational map is less than or equal to the number of independent infinite forward critical orbits - from a suitable application of Thurston's Rigidity ... More

Multiple fundamental strings and waves to non-linear order in the background fieldsMay 23 2006Mar 30 2007The Chern-Simons actions of the multiple fundamental string and the multiple gravitational wave are established to full order in the background fields. Gauge invariance is checked. Special attention is drawn to the non-Abelian gauge transformations of ... More

On some examples of para-Hermite and para-Kähler Einstein spaces with $Λ\ne 0$Feb 09 2016Nov 14 2016Spaces equipped with two complementary (distinct) congruences of self-dual null strings and at least one congruence of anti-self-dual null strings are considered. It is shown that if such spaces are Einsteinian then the vacuum Einstein field equations ... More