An algebro-geometric proof of Witten's conjecture

We present a new proof of Witten's conjecture. The proof is based on the analysis of the relationship between intersection indices on moduli spaces of complex curves and Hurwitz numbers enumerating ramified coverings of the 2-sphere.Comment: 12 pages, no figure

Towards the Intersection Theory on Hurwitz Spaces

Moduli spaces of algebraic curves and closely related to them Hurwitz spaces, that is, spaces of meromorphic functions on the curves, arise naturally in numerous problems of algebraic geometry and mathematical physics, especially in relationship with the string theory and Gromov--Witten invariants. In particular, the classical Hurwitz problem about enumeration of topologically distinct ramified coverings of the sphere with prescribed ramification type reduces to the study of geometry and topology of these spaces. The cohomology rings of such spaces are complicated even in the simplest cases of rational curves and functions. However, the cohomology classes that are the most important from the point of view of applications (namely, the classes Poincar\'e dual to the strata of functions with given singularities) can be expressed in terms of relatively simple ``basic'' classes (which are, in a sense, tautological). The aim of the present paper is to identify these basic classes, to describe relations among them, and to find expressions for the strata in terms of these classes. Our approach is based on R. Thom's theory of universal polynomials of singularities, which has been extended to the case of multisingularities by the first author. Although the general Hurwitz problem still remains open, our approach allows one to achieve a significant progress in its solution, as well as in the understanding of the geometry and topology of Hurwitz spaces.Comment: 29 pages, AMSTe

Hurwitz numbers and intersections on moduli spaces of curves

This article is an extended version of preprint math.AG/9902104. We find an explicit formula for the number of topologically different ramified coverings of a sphere by a genus g surface with only one complicated branching point in terms of Hodge integrals over the moduli space of genus g curves with marked points.Comment: 30 pages (AMSTeX). Minor typos are correcte

Quantum revival patterns from classical phase-space trajectories

A general semiclassical method in phase space based on the final value representation of the Wigner function is considered that bypasses caustics and the need to root-search for classical trajectories. We demonstrate its potential by applying the method to the Kerr Hamiltonian, for which the exact quantum evolution is punctuated by a sequence of intricate revival patterns. The structure of such revival patterns, lying far beyond the Ehrenfest time, is semiclassically reproduced and revealed as a consequence of constructive and destructive interferences of classical trajectories.Comment: 7 pages, 6 figure

Cyclicality and Firm-size in Private Firm Defaults

The Basel II/III and CRD-IV Accords reduce capital charges on bank loans to smaller firms by assuming that the default probabilities of smaller firms are less sensitive to macroeconomic cycles. We test this assumption in a default intensity framework using a large sample of bank loans to private Danish firms. We find that controlling only for size, the default probabilities of small firms are, in fact, less cyclical than the default probabilities of large firms. However, accounting for firm characteristics other than size, we find that the default probabilities of small firms are equally cyclical or even more cyclical than the default probabilities of large firms. These results hold using a multiplicative Cox model as well as an additive Aalen model with time-varying coefficients

New alphabet-dependent morphological transition in a random RNA alignment

We study the fraction $f$ of nucleotides involved in the formation of a cactus--like secondary structure of random heteropolymer RNA--like molecules. In the low--temperature limit we study this fraction as a function of the number $c$ of different nucleotide species. We show, that with changing $c$, the secondary structures of random RNAs undergo a morphological transition: $f(c)\to 1$ for $c \le c_{\rm cr}$ as the chain length $n$ goes to infinity, signaling the formation of a virtually "perfect" gapless secondary structure; while $f(c)c_{\rm cr}$, what means that a non-perfect structure with gaps is formed. The strict upper and lower bounds $2 \le c_{\rm cr} \le 4$ are proven, and the numerical evidence for $c_{\rm cr}$ is presented. The relevance of the transition from the evolutional point of view is discussed.Comment: 4 pages, 3 figures (title is changed, text is essentially reworked), accepted in PR

La gestione del livello di buffer per la programmazione operativa in processi a ciclo non definito

Viene affrontato il problema della programmazione operativa con riferimento a processi produttivi per i quali non riesce possibile disporre fin dall’inizio di tutte le informazioni al riguardo necessarie. In tali processi (a ciclo non definito) le specifiche del prodotto, non determinate a priori, possono anche mutare in corso di lavorazione, ciò che impedisce l’impiego efficace di sistemi tradizionali di planning. In precedenza, trattando la stessa casistica, si era scelto di utilizzare un modello statistico appositamente sviluppato per determinare la configurazione probabile dei cicli di lavorazione, impiegato per calcolare un valore atteso del grado di utilizzazione delle risorse di produzione ed individuare possibili colli di bottiglia. In questa sede ci proponiamo inoltre di sincronizzare il flusso produttivo agendo sul time buffer posto a protezione della risorsa critica, come sopra individuata. La dimensione ottima del buffer è determinata attraverso il trade-off tra il vantaggio di un’idonea saturazione dell’anzidetta risorsa critica ed il costo alternativo della coda in attesa. Ciò vale a definire efficaci regole di rilascio dei job per le stazioni di lavoro a monte. Il monitoraggio del buffer è necessario inoltre per aggiornare la programmazione al variare delle condizioni operative. L’efficacia del criterio proposto è stata verificata dagli stessi autori attraverso diretta applicazione presso un’azienda operante nel settore della revisione di motori aeronautici. I risultati ottenuti si sono rivelati più che soddisfacenti in ordine al migliore sfruttamento delle risorse produttive nonché in termini di abbattimento del work in process