4,661 research outputs found
On a symmetric space attached to polyzeta values
Quickly convergent series are given to compute polyzeta numbers. The formula
involves an intricate combination of (generalized) polylogarithms at 1/2.
However, the combinatorics has a very simple geometric interpretation: it
corresponds with the square map on some symmetric space P.Comment: 18 page
Evolution of sparsity and modularity in a model of protein allostery
The sequence of a protein is not only constrained by its physical and
biochemical properties under current selection, but also by features of its
past evolutionary history. Understanding the extent and the form that these
evolutionary constraints may take is important to interpret the information in
protein sequences. To study this problem, we introduce a simple but physical
model of protein evolution where selection targets allostery, the functional
coupling of distal sites on protein surfaces. This model shows how the
geometrical organization of couplings between amino acids within a protein
structure can depend crucially on its evolutionary history. In particular, two
scenarios are found to generate a spatial concentration of functional
constraints: high mutation rates and fluctuating selective pressures. This
second scenario offers a plausible explanation for the high tolerance of
natural proteins to mutations and for the spatial organization of their least
tolerant amino acids, as revealed by sequence analyses and mutagenesis
experiments. It also implies a faculty to adapt to new selective pressures that
is consistent with observations. Besides, the model illustrates how several
independent functional modules may emerge within a same protein structure,
depending on the nature of past environmental fluctuations. Our model thus
relates the evolutionary history and evolutionary potential of proteins to the
geometry of their functional constraints, with implications for decoding and
engineering protein sequences
Schur Superpolynomials: Combinatorial Definition and Pieri Rule
Schur superpolynomials have been introduced recently as limiting cases of the
Macdonald superpolynomials. It turns out that there are two natural
super-extensions of the Schur polynomials: in the limit and
, corresponding respectively to the Schur
superpolynomials and their dual. However, a direct definition is missing. Here,
we present a conjectural combinatorial definition for both of them, each being
formulated in terms of a distinct extension of semi-standard tableaux. These
two formulations are linked by another conjectural result, the Pieri rule for
the Schur superpolynomials. Indeed, and this is an interesting novelty of the
super case, the successive insertions of rows governed by this Pieri rule do
not generate the tableaux underlying the Schur superpolynomials combinatorial
construction, but rather those pertaining to their dual versions. As an aside,
we present various extensions of the Schur bilinear identity
A Broad-Spectrum Computational Approach for Market Efficiency
The Efficient Market Hypothesis (EMH) is one of the most investigated questions in Finance. Nevertheless, it is still a puzzle, despite the enormous amount of research it has provoked. For instance, it is still discussed that market cannot be outperformed in the long run (Detry and Gregoire, 2001), persistent market anomalies cannot be easily explained in this theoretical framework (Shiller, 2003) and some talented hedge-fund managers keep earning excess risk-adjusted rates of returns regularly. We concentrate in this paper on the weak form of efficiency(Fama, 1970). We focus on the efficacity of simple technical trading rules, following a large research stream presented in Park and Irwin (2004). Nevertheless, we depart from previous works in many ways : we first have a large population of technical investment rules (more than 260.000) exploiting real-world data to manage a financial portfolio. Very few researches have used such a large amount of calculus to examine the EMH. Our experimental design allows for strategy selection based on past absolute performance. We take into account the data-snooping risk, which is an unavoidable problem in such broad-spectrum researches, using a rigorous Bootstrap Reality Check procedure. While market inefficiencies, after including transaction costs, cannot clearly be successfully exploited, our experiments present troubling outcomes inviting close re-consideration of the weak-form EMH.efficient market hypothesis, large scale simulations, bootstrap
Algebraic Renormalization of Supersymmetric Yang-Mills Chern-Simons Theory in the Wess-Zumino Gauge
We consider a N=2 supersymmetric Yang-Mills-Chern-Simons model, coupled to
matter, in the Wess-Zumino gauge. The theory is characterized by a superalgebra
which displays two kinds of obstructions to the closure on the translations:
field dependent gauge transformations, which give rise to an infinite algebra,
and equations of motion. The aim is to put the formalism in a closed form,
off-shell, without introducing auxiliary fields. In order to perform that, we
collect all the symmetries of the model into a unique nilpotent Slavnov-Taylor
operator. Furthermore, we prove the renormalizability of the model through the
analysis of the cohomology arising from the generalized Slavnov-Taylor
operator. In particular, we show that the model is free of anomaly.Comment: 17 pages, latex, no figures. Computation of the cohomology corrected.
Appendix adde
The supersymmetric Ruijsenaars-Schneider model
An integrable supersymmetric generalization of the trigonometric
Ruijsenaars-Schneider model is presented whose symmetry algebra includes the
super Poincar\'e algebra. Moreover, its Hamiltonian is showed to be
diagonalized by the recently introduced Macdonald superpolynomials. Somewhat
surprisingly, the consistency of the scalar product forces the discreteness of
the Hilbert space.Comment: v1: 11 pages, 1 figure. v2: new format, 5 pages, short section added
at the end of the article addressing the problem of consistency of the scalar
product (e.g., positivity of the weight functions and the normalization of
the ground state wave function). To appear in Physical Review Letter
Estimating the dimension of Thurston spine
For g at least 2, the Thurston spine Pg is the subspace of Teichmueller space
Tg , consisting of the marked surfaces for which the set of shortest curves,
the systoles, cuts the surface into polygons. Our main result is the existence
of an infinite set A of integers such that codim Pg is a o(g/ log g), when g
varies over A.
This proves the recent conjecture of M. Fortier Bourque.Comment: 27 pages, 7 figure
A quartet of fermionic expressions for Virasoro characters via half-lattice paths
We derive new fermionic expressions for the characters of the Virasoro
minimal models by analysing the recently introduced half-lattice
paths. These fermionic expressions display a quasiparticle formulation
characteristic of the and integrable perturbations.
We find that they arise by imposing a simple restriction on the RSOS
quasiparticle states of the unitary models . In fact, four fermionic
expressions are obtained for each generating function of half-lattice paths of
finite length , and these lead to four distinct expressions for most
characters . These are direct analogues of Melzer's
expressions for , and their proof entails revisiting, reworking and
refining a proof of Melzer's identities which used combinatorial transforms on
lattice paths.
We also derive a bosonic version of the generating functions of length
half-lattice paths, this expression being notable in that it involves
-trinomial coefficients. Taking the limit shows that the
generating functions for infinite length half-lattice paths are indeed the
Virasoro characters .Comment: 29 pages. v2: minor improvements, references adde
Linearity and Nonlinearity of Groups of Polynomial Automorphisms of the Plane
Given a field K, we investigate which subgroups of the group Aut A 2 K of
polynomial automorphisms of the plane are linear or not. The results are
contrasted. The group Aut A 2 K itself is nonlinear, except if K is finite, but
it contains some large ''finite-codimensional'' subgroups which are linear.
This phenomenon is specific to dimension two: it is easy to prove that any
''finite-codimensional'' subgroup of Aut A 3 K is nonlinear, even for a finite
field K. When ch K = 0, we also look at a similar questions for f.g. subgroups,
and the results are also contrasted. Some ''finite-codimensional'' subgroups
are locally linear but not linear. This paper is respectfully dedicated to the
memory of Jacques Tits
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