Compact Markov-modulated models for multiclass trace fitting

Markov-modulated Poisson processes (MMPPs) are stochastic models for fitting empirical traces for simulation, workload characterization and queueing analysis purposes. In this paper, we develop the first counting process fitting algorithm for the marked MMPP (M3PP), a generalization of the MMPP for modeling traces with events of multiple types. We initially explain how to fit two-state M3PPs to empirical traces of counts. We then propose a novel form of composition, called interposition, which enables the approximate superposition of several two-state M3PPs without incurring into state space explosion. Compared to exact superposition, where the state space grows exponentially in the number of composed processes, in interposition the state space grows linearly in the number of composed M3PPs. Experimental results indicate that the proposed interposition methodology provides accurate results against artificial and real-world traces, with a significantly smaller state space than superposed processes

On the nonexistence of degenerate phase-shift discrete solitons in a dNLS nonlocal lattice

We consider a one-dimensional discrete nonlinear Schr\uf6dinger (dNLS) model featuring interactions beyond nearest neighbors. We are interested in the existence (or nonexistence) of phase-shift discrete solitons, which correspond to four-sites vortex solutions in the standard two-dimensional dNLS model (square lattice), of which this is a simpler variant. Due to the specific choice of lengths of the inter-site interactions, the vortex configurations considered present a degeneracy which causes the standard continuation techniques to be non-applicable. In the present one-dimensional case, the existence of a conserved quantity for the soliton profile (the so-called density current), together with a perturbative construction, leads to the nonexistence of any phase-shift discrete soliton which is at least C2 with respect to the small coupling \u3f5, in the limit of vanishing \u3f5. If we assume the solution to be only C0 in the same limit of \u3f5, nonexistence is instead proved by studying the bifurcation equation of a Lyapunov-Schmidt reduction, expanded to suitably high orders. Specifically, we produce a nonexistence criterion whose efficiency we reveal in the cases of partial and full degeneracy of approximate solutions obtained via a leading order expansion

Aspects of the planetary Birkhoff normal form

The discovery in [G. Pinzari. PhD thesis. Univ. Roma Tre. 2009], [L. Chierchia and G. Pinzari, Invent. Math. 2011] of the Birkhoff normal form for the planetary many--body problem opened new insights and hopes for the comprehension of the dynamics of this problem. Remarkably, it allowed to give a {\sl direct} proof of the celebrated Arnold's Theorem [V. I. Arnold. Uspehi Math. Nauk. 1963] on the stability of planetary motions. In this paper, using a "ad hoc" set of symplectic variables, we develop an asymptotic formula for this normal form that may turn to be useful in applications. As an example, we provide two very simple applications to the three-body problem: we prove a conjecture by [V. I. Arnold. cit] on the "Kolmogorov set"of this problem and, using Nehoro{\v{s}}ev Theory [Nehoro{\v{s}}ev. Uspehi Math. Nauk. 1977], we prove, in the planar case, stability of all planetary actions over exponentially-long times, provided mean--motion resonances are excluded. We also briefly discuss perspectives and problems for full generalization of the results in the paper.Comment: 44 pages. Keywords: Averaging Theory, Birkhoff normal form, Nehoro{\v{s}}ev Theory, Planetary many--body problem, Arnold's Theorem on the stability of planetary motions, Properly--degenerate kam Theory, steepness. Revised version, including Reviewer's comments. Typos correcte

A Semi-Analytic Algorithm for Constructing Lower Dimensional Elliptic Tori in Planetary Systems

We adapt the Kolmogorov's normalization algorithm (which is the key element of the original proof scheme of the KAM theorem) to the construction of a suitable normal form related to an invariant elliptic torus. As a byproduct, our procedure can also provide some analytic expansions of the motions on elliptic tori. By extensively using algebraic manipulations on a computer, we explicitly apply our method to a planar four-body model not too different with respect to the real Sun--Jupiter--Saturn--Uranus system. The frequency analysis method allows us to check that our location of the initial conditions on an invariant elliptic torus is really accurate.Comment: 31 pages, 4 figure

Back to the Future: Resource Management in Post-Cloud Solutions

The increasing pervasiveness of mobile and embedded devices (IoT/Edge), combined with the access to Cloud infrastructures, makes it possible to build scalable distributed systems, characterized by a multi-dimensional architecture. The overall picture is a massive collection of computing devices, characterized by very heterogeneous levels of performance and power consumption, which we could exploit to reduce the need to access Cloud computing resources. This would play a key role, especially for emerging use cases, where huge amount of data are generated. However, the deployment of distributed applications on such an heterogeneous infrastructures requires suitable management layers. This position paper aims at: (a) proposing a fully-distributed, cooperative, dynamic and multi-layered architecture, capable of integrating different computing paradigms; (b) identifying a possible solution to manage workloads at run-time in a resources continuity perspective, through an analysis of the open research challenges

Enantioselective monoreduction of different 1,2-diaryl-1,2-diketones catalysed by lyophilised whole cells from Pichia glucozyma

In this work we have studied the monoreduction of different 1,2-diaryl-ethanediones (benzils, 1) with lyophilised whole cells from Pichia glucozyma CBS 5766, using the diphenyl compound (benzil, 1a) as model substrate, and extended the enantioselective reduction to structurally different symmetric benzils for producing enantiomerically pure or enriched benzoins (alpha-hydroxyketones 2) in high yields and very short reaction times. In order to study the regio- and stereoselectivity of this biocatalyst, we examined the reduction of diaryldiketones formed from different aryl moieties, to obtain symmetric and asymmetric crossed-benzoins. This methodology is conducted under very mild reaction conditions (aqueous media with small amounts of DMSO for solubilising the substrates, T=28 degrees C), therefore constituting a green alternative compared to other reported procedures for obtaining homochiral benzoins. (C) 2008 Elsevier Ltd. All rights reserved