A discrete linearizability test based on multiscale analysis

In this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad-graph by the multiple scale reduction around their harmonic solution. We show that the A_1, A_2 and A_3 linearizability conditions restrain the number of the parameters which enter into the equation. A subclass of the equations which pass the A_3 C-integrability conditions can be linearized by a Mobius transformation

A discrete integrability test based on multiscale analysis

In this article we present the results obtained applying the multiple scale expansion up to the order \epsilon^6 to a dispersive multilinear class of equations on a square lattice depending on 13 parameters. We show that the integrability conditions given by the multiple scale expansion give rise to 4 nonlinear equations, 3 of which are new, depending at most on 2 parameters and containing integrable sub cases. Moreover at least one sub case provides an example of a new integrable system

The Taming of QCD by Fortran 90

We implement lattice QCD using the Fortran 90 language. We have designed machine independent modules that define fields (gauge, fermions, scalars, etc...) and have defined overloaded operators for all possible operations between fields, matrices and numbers. With these modules it is very simple to write QCD programs. We have also created a useful compression standard for storing the lattice configurations, a parallel implementation of the random generators, an assignment that does not require temporaries, and a machine independent precision definition. We have tested our program on parallel and single processor supercomputers obtaining excellent performances.Comment: Talk presented at LATTICE96 (algorithms) 3 pages, no figures, LATEX file with ESPCRC2 style. More information available at: http://hep.bu.edu/~leviar/qcdf90.htm

Multiscale expansion and integrability properties of the lattice potential KdV equation

We apply the discrete multiscale expansion to the Lax pair and to the first few symmetries of the lattice potential Korteweg-de Vries equation. From these calculations we show that, like the lowest order secularity conditions give a nonlinear Schroedinger equation, the Lax pair gives at the same order the Zakharov and Shabat spectral problem and the symmetries the hierarchy of point and generalized symmetries of the nonlinear Schroedinger equation.Comment: 10 pages, contribution to the proceedings of the NEEDS 2007 Conferenc

On the Integrability of the Discrete Nonlinear Schroedinger Equation

In this letter we present an analytic evidence of the non-integrability of the discrete nonlinear Schroedinger equation, a well-known discrete evolution equation which has been obtained in various contexts of physics and biology. We use a reductive perturbation technique to show an obstruction to its integrability.Comment: 4 pages, accepted in EP

An Unknowable Wildness: An Analysis of Cryptids as Queer Cultural Iconography

This essay examines the rise in cryptids – animals whose existence is disputed or unsubstantiated, or creatures who exist on the margins of biological understanding to the point of being mythical – being claimed by younger queer people as symbols of their outsider status and transgression. Beginning with an analysis of the political resistance that the reclamation of monstrosity makes possible for queer subjects, I argue that “cryptid culture” is a refusal of a politics of assimilation that has lately characterized LGBTQ+ communities. I then argue that this attachment to “cryptid culture” is also indicative of shifts in personal queer identity, reinforcing the centrality of individual transgression, post-structural ambiguity, and playful use of symbolism prompted by digital interaction. Ultimately, the adoption of cryptids as the mascots of young queer communities gestures towards an optimistic commitment to political critique, and provides new directions in which for queer theory to proceed

Mind Over Matter: Accounts of Selfhood in an Age of Theoretical Gender

This paper is a reflection on the rapidly shifting social understandings of gender identity. Using a theoretical framework composed of existentialist thought, cultural critique, empirical research, and post-structuralism, I argue that our understandings of gender identity have shifted towards a model which (following decades of theory) takes lived gender to be malleable and constructed. This has caused a movement away from the centrality of the sexed body in determining gender identity – including transgender identities – which in turn has created unresolved tension regarding what constitutes and validates gender identity as “real” in our narratives of selfhood. This movement away from the solidity of the body includes a movement away from Western mind/body dualism, leaving a gap for a new theoretical order to fill. A discussion of what directions may emerge in new thought about gender identity gesture towards future work in the field

A Local Algorithm for the Sparse Spanning Graph Problem

Constructing a sparse \emph{spanning subgraph} is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by examining only a small part of the input; yet, answers must be globally consistent and independent of prior queries. Unfortunately, maximally sparse spanning subgraphs, i.e., spanning trees, cannot be constructed efficiently in this model. Therefore, we settle for a spanning subgraph containing at most $(1+\varepsilon)n$ edges (where $n$ is the number of vertices and $\varepsilon$ is a given approximation/sparsity parameter). We achieve query complexity of $\tilde{O}(poly(\Delta/\varepsilon)n^{2/3})$,\footnote{$\tilde{O}$-notation hides polylogarithmic factors in $n$.} where $\Delta$ is the maximum degree of the input graph. Our algorithm is the first to do so on arbitrary graphs. Moreover, we achieve the additional property that our algorithm outputs a \emph{spanner,} i.e., distances are approximately preserved. With high probability, for each deleted edge there is a path of $O(poly(\Delta/\varepsilon)\log^2 n)$ hops in the output that connects its endpoints

The lattice Schwarzian KdV equation and its symmetries

In this paper we present a set of results on the symmetries of the lattice Schwarzian Korteweg-de Vries (lSKdV) equation. We construct the Lie point symmetries and, using its associated spectral problem, an infinite sequence of generalized symmetries and master symmetries. We finally show that we can use master symmetries of the lSKdV equation to construct non-autonomous non-integrable generalized symmetries.Comment: 11 pages, no figures. Submitted to Jour. Phys. A, Special Issue SIDE VI

The Jacobi last multiplier for difference equations

We present a discretization of the Jacobi last multiplier, with some applications to the computation of solutions of difference equations.Comment: 9 page