On the Hilbert scheme of curves in higher-dimensional projective space

In this paper we prove that, for any $n\ge 3$, there exist infinitely many $r\in \N$ and for each of them a smooth, connected curve $C_r$ in $\P^r$ such that $C_r$ lies on exactly $n$ irreducible components of the Hilbert scheme \hilb(\P^r). This is proven by reducing the problem to an analogous statement for the moduli of surfaces of general type.Comment: latex, 12 pages, no figure

The Sensoria Approach Applied to the Finance Case Study

This chapter provides an effective implementation of (part of) the Sensoria approach, specifically modelling and formal analysis of service-oriented software based on mathematically founded techniques. The ‘Finance case study’ is used as a test bed for demonstrating the feasibility and effectiveness of the use of the process calculus COWS and some of its related analysis techniques and tools. In particular, we report the results of an application of a temporal logic and its model checker for expressing and checking functional properties of services and a type system for guaranteeing confidentiality properties of services

A Logical Verification Methodology for Service-Oriented Computing

We introduce a logical verification methodology for checking behavioural properties of service-oriented computing systems. Service properties are described by means of SocL, a branching-time temporal logic that we have specifically designed to express in an effective way distinctive aspects of services, such as, e.g., acceptance of a request, provision of a response, and correlation among service requests and responses. Our approach allows service properties to be expressed in such a way that they can be independent of service domains and specifications. We show an instantiation of our general methodology that uses the formal language COWS to conveniently specify services and the expressly developed software tool CMC to assist the user in the task of verifying SocL formulae over service specifications. We demonstrate feasibility and effectiveness of our methodology by means of the specification and the analysis of a case study in the automotive domain

The Drinfel'd Double and Twisting in Stringy Orbifold Theory

This paper exposes the fundamental role that the Drinfel'd double \dkg of the group ring of a finite group $G$ and its twists \dbkg, \beta \in Z^3(G,\uk) as defined by Dijkgraaf--Pasquier--Roche play in stringy orbifold theories and their twistings. The results pertain to three different aspects of the theory. First, we show that $G$--Frobenius algebras arising in global orbifold cohomology or K-theory are most naturally defined as elements in the braided category of \dkg--modules. Secondly, we obtain a geometric realization of the Drinfel'd double as the global orbifold $K$--theory of global quotient given by the inertia variety of a point with a $G$ action on the one hand and more stunningly a geometric realization of its representation ring in the braided category sense as the full $K$--theory of the stack $[pt/G]$. Finally, we show how one can use the co-cycles $\beta$ above to twist a) the global orbifold $K$--theory of the inertia of a global quotient and more importantly b) the stacky $K$--theory of a global quotient $[X/G]$. This corresponds to twistings with a special type of 2--gerbe.Comment: 35 pages, no figure

Specifying and Analysing SOC Applications with COWS

COWS is a recently defined process calculus for specifying and combining service-oriented applications, while modelling their dynamic behaviour. Since its introduction, a number of methods and tools have been devised to analyse COWS specifications, like e.g. a type system to check confidentiality properties, a logic and a model checker to express and check functional properties of services. In this paper, by means of a case study in the area of automotive systems, we demonstrate that COWS, with some mild linguistic additions, can model all the phases of the life cycle of service-oriented applications, such as publication, discovery, negotiation, orchestration, deployment, reconfiguration and execution. We also provide a flavour of the properties that can be analysed by using the tools mentioned above

A prototype large-angle photon veto detector for the P326 experiment at CERN

The P326 experiment at the CERN SPS has been proposed with the purpose of measuring the branching ratio for the decay K^+ \to \pi^+ \nu \bar{\nu} to within 10%. The photon veto system must provide a rejection factor of 10^8 for \pi^0 decays. We have explored two designs for the large-angle veto detectors, one based on scintillating tiles and the other using scintillating fibers. We have constructed a prototype module based on the fiber solution and evaluated its performance using low-energy electron beams from the Frascati Beam-Test Facility. For comparison, we have also tested a tile prototype constructed for the CKM experiment, as well as lead-glass modules from the OPAL electromagnetic barrel calorimeter. We present results on the linearity, energy resolution, and time resolution obtained with the fiber prototype, and compare the detection efficiency for electrons obtained with all three instruments.Comment: 8 pages, 9 figures, 2 tables. Presented at the 2007 IEEE Nuclear Science Symposium, Honolulu HI, USA, 28 October - 3 November 200

Chen-Ruan cohomology of ADE singularities

We study Ruan's \textit{cohomological crepant resolution conjecture} for orbifolds with transversal ADE singularities. In the $A_n$-case we compute both the Chen-Ruan cohomology ring $H^*_{\rm CR}([Y])$ and the quantum corrected cohomology ring $H^*(Z)(q_1,...,q_n)$. The former is achieved in general, the later up to some additional, technical assumptions. We construct an explicit isomorphism between $H^*_{\rm CR}([Y])$ and $H^*(Z)(-1)$ in the $A_1$-case, verifying Ruan's conjecture. In the $A_n$-case, the family $H^*(Z)(q_1,...,q_n)$ is not defined for $q_1=...=q_n=-1$. This implies that the conjecture should be slightly modified. We propose a new conjecture in the $A_n$-case which we prove in the $A_2$-case by constructing an explicit isomorphism.Comment: This is a short version of my Ph.D. Thesis math.AG/0510528. Version 2: chapters 2,3,4 and 5 has been rewritten using the language of groupoids; a link with the classical McKay correpondence is given. International Journal of Mathematics (to appear

GPU-based Real-time Triggering in the NA62 Experiment

Over the last few years the GPGPU (General-Purpose computing on Graphics Processing Units) paradigm represented a remarkable development in the world of computing. Computing for High-Energy Physics is no exception: several works have demonstrated the effectiveness of the integration of GPU-based systems in high level trigger of different experiments. On the other hand the use of GPUs in the low level trigger systems, characterized by stringent real-time constraints, such as tight time budget and high throughput, poses several challenges. In this paper we focus on the low level trigger in the CERN NA62 experiment, investigating the use of real-time computing on GPUs in this synchronous system. Our approach aimed at harvesting the GPU computing power to build in real-time refined physics-related trigger primitives for the RICH detector, as the the knowledge of Cerenkov rings parameters allows to build stringent conditions for data selection at trigger level. Latencies of all components of the trigger chain have been analyzed, pointing out that networking is the most critical one. To keep the latency of data transfer task under control, we devised NaNet, an FPGA-based PCIe Network Interface Card (NIC) with GPUDirect capabilities. For the processing task, we developed specific multiple ring trigger algorithms to leverage the parallel architecture of GPUs and increase the processing throughput to keep up with the high event rate. Results obtained during the first months of 2016 NA62 run are presented and discussed

Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds

We investigate the relationship between the Lagrangian Floer superpotentials for a toric orbifold and its toric crepant resolutions. More specifically, we study an open string version of the crepant resolution conjecture (CRC) which states that the Lagrangian Floer superpotential of a Gorenstein toric orbifold $\mathcal{X}$ and that of its toric crepant resolution $Y$ coincide after analytic continuation of quantum parameters and a change of variables. Relating this conjecture with the closed CRC, we find that the change of variable formula which appears in closed CRC can be explained by relations between open (orbifold) Gromov-Witten invariants. We also discover a geometric explanation (in terms of virtual counting of stable orbi-discs) for the specialization of quantum parameters to roots of unity which appears in Y. Ruan's original CRC ["The cohomology ring of crepant resolutions of orbifolds", Gromov-Witten theory of spin curves and orbifolds, 117-126, Contemp. Math., 403, Amer. Math. Soc., Providence, RI, 2006]. We prove the open CRC for the weighted projective spaces $\mathcal{X}=\mathbb{P}(1,\ldots,1,n)$ using an equality between open and closed orbifold Gromov-Witten invariants. Along the way, we also prove an open mirror theorem for these toric orbifolds.Comment: 48 pages, 1 figure; v2: references added and updated, final version, to appear in CM