A supersymmetric matrix model: II. Exploring higher-fermion-number sectors

Continuing our previous analysis of a supersymmetric quantum-mechanical matrix model, we study in detail the properties of its sectors with fermion number F=2 and 3. We confirm all previous expectations, modulo the appearance, at strong coupling, of {\it two} new bosonic ground states causing a further jump in Witten's index across a previously identified critical 't Hooft coupling $\lambda_c$. We are able to elucidate the origin of these new SUSY vacua by considering the $\lambda \to \infty$ limit and a strong coupling expansion around it.Comment: 14 pages, 4 figure

The emergence of noun and verb categories in the acquisition of French

This paper considers whether the child's early vocabulary shows signs of being organized into word categories. Two main kinds of evidence are looked for: 1. differential production of fillers (referred to here more neutrally as Prefixed Additional Elements); ii. relevant phonomoprhological variation for verb-words, and only in them. Results of analyses of natural speech production provided by the longitudinal studies of two French acquiring children followed between the ages of 1;3 and 2;3, show that there is a first period in which words seem to constitute one, formally undifferentiated, set. Differentiation between noun-words and verb-words appears progressively, as evidenced by the differential occurrence of PAEs in prenominal and in preverbal positions, and in the appearance of phonomorphologically relevant variations only in words that are verbs in the language. Looking at connected aspects of language, other péhenomena are observed to occur at the same time, in particular, a significant increase in the production of multiword speech, that becomes the dominant way of expression

A numerical simulation of pre-big bang cosmology

We analyse numerically the onset of pre-big bang inflation in an inhomogeneous, spherically symmetric Universe. Adding a small dilatonic perturbation to a trivial (Milne) background, we find that suitable regions of space undergo dilaton-driven inflation and quickly become spatially flat ($\Omega \to 1$). Numerical calculations are pushed close enough to the big bang singularity to allow cross checks against previously proposed analytic asymptotic solutions.Comment: 19 pages, revtex, matlab code available at http://www.fis.unipr.it/~onofr

Supersymmetry and Combinatorics

We show how a recently proposed supersymmetric quantum mechanics model leads to non-trivial results/conjectures on the combinatorics of binary necklaces and linear-feedback shift-registers. Pauli's exclusion principle plays a crucial role: by projecting out certain states/necklaces, it allows to represent the supersymmetry algebra in the resulting subspace. Some of our results can be rephrased in terms of generalizations of the well-known Witten index.Comment: 14 pages, 3 figures, text expanded, references adde

A Model for the Big Bounce

I motivate a proposal for modeling, at weak string coupling, the ``Big Bounce" transition from a growing-curvature phase to standard (FRW) cosmology in terms of a pressure-less dense gas of "string-holes" (SH), string states lying on the correspondence curve between strings and black holes. During this phase SH evolve in such a way that temperature and (string-frame) curvature remain $O(M_s)$ and (a cosmological version of) the holographic entropy bound remains saturated. This reasoning also appears to imply a new interpretation of the Hagedorn phase transition in string theory.Comment: 10 pages, 2 figure

Leukocyte telomere shortening in Huntington's disease

Huntington's disease (HD) is an autosomal dominant neurodegenerative disease caused by an expanded CAG repeat. Though symptom onset commonly occurs at midlife and inversely correlates with the CAG repeat expansion, age at clinical onset and progression rate are variable. In the present study we investigated the relationship between leukocyte telomere length (LTL) and HD development. LTL was measured by real-time PCR in manifest HD patients (HD, n = 62), pre-manifest HD patients (pre-HD, n = 38), and age-matched controls (n = 76). Significant LTL differences were observed between the three groups (p < .0001), with LTL values in the order: HD < pre-HD < controls. The relationship between LTL and age was different in the three groups. An inverse relationship between mean LTL and CAG repeat number was found in the pre-HD (p = .03). The overall data seem to indicate that after age 30 years, LT begins to shorten markedly in pre-HD patients according to CAG number and increasing age, up to the values observed in HD. This very suggestive picture allowed us to hypothesize that in pre-manifest HD, LTL could be a measure of time to clinical HD onset. The possible use of LTL as a reliable biomarker to track HD development and progression was evaluated and discussed

N=1 Super Yang-Mills on the Lattice in the Strong Coupling Limit

We study the N=1 supersymmetric SU(N) Yang-Mills theory on the lattice at strong coupling. We analyse and discuss the recent results obtained at strong coupling and large N for the mesonic and fermionic propagators and spectrum.Comment: Latex 3 pages. Contribution to the Lattice99 Proceeding

Microscopic unitary description of tidal excitations in high-energy string-brane collisions

The eikonal operator was originally introduced to describe the effect of tidal excitations on higher-genus elastic string amplitudes at high energy. In this paper we provide a precise interpretation for this operator through the explicit tree-level calculation of generic inelastic transitions between closed strings as they scatter off a stack of parallel Dp-branes. We perform this analysis both in the light-cone gauge, using the Green-Schwarz vertex, and in the covariant formalism, using the Reggeon vertex operator. We also present a detailed discussion of the high energy behaviour of the covariant string amplitudes, showing how to take into account the energy factors that enhance the contribution of the longitudinally polarized massive states in a simple way.Comment: 58 page

The explicit Mordell conjecture for families of curves

In this article we prove the explicit Mordell Conjecture for large families of curves. In addition, we introduce a method, of easy application, to compute all rational points on curves of quite general shape and increasing genus. The method bases on some explicit and sharp estimates for the height of such rational points, and the bounds are small enough to successfully implement a computer search. As an evidence of the simplicity of its application, we present a variety of explicit examples and explain how to produce many others. In the appendix our method is compared in detail to the classical method of Manin-Demjanenko and the analysis of our explicit examples is carried to conclusion

The eta-prime propagator in quenched QCD

The calculation of the eta-prime hairpin diagram is carried out in the modified quenched approximation (MQA) in which the lattice artifact which causes exceptional configurations is removed by shifting observed poles at kappa<kappa_c in the quark propagators to the critical value of hop ping parameter. By this method, the eta-prime propagator can be accurately calculated even for very light quark mass. A determination of the topological susceptibility for quenched QCD is also obtained, using the fermionic method of Smit and Vink to calculate winding numbers.Comment: 3 pages, 3 postscript figure