Resource
2015 EN
Paolo Nobili · Antonio Sassano
In this paper we show that a connected {claw, net}-free graph $G(V, E)$ with$\alpha(G) \ge 4$ is the union of a strongly bisimplicial clique $Q$ and atmost two clique-strips. A clique is strongly bisimplicial if its neighborhoodis partitioned into two cliques which are mutually non-adjacent and aclique-strip is a sequence of cliques $\{H_0, \dots, H_p\}$ with the propertythat $H_i$ is adjacent only to $H_{i-1}$ and $H_{i+1}$. By exploiting such astructure we show how to solve the Maximum Weight Stable Set Problem in such agraph in time ${\cal O}(|V|\sqrt{|E|})$.
Resource
2015 EN
Michele Benzi · Valeria Simoncini
We present decay bounds for a broad class of Hermitian matrix functions wherethe matrix argument is banded or a Kronecker sum of banded matrices. Besidesbeing significantly tighter than previous estimates, the new bounds closelycapture the actual (non-monotonic) decay behavior of the entries of functionsof matrices with Kronecker sum structure. We also discuss extensions to moregeneral sparse matrices.
Resource
2015 EN
Yongxin Chen · Tryphon Georgiou · Michele Pavon
We consider the problem of steering an initial probability density for thestate vector of a linear system to a final one, in finite time, using minimumenergy control. In the case where the dynamics correspond to an integrator($\dot x(t) = u(t)$) this amounts to a Monge-Kantorovich Optimal Mass Transport(OMT) problem. In general, we show that the problem can again be reduced tosolving an OMT problem and that it has a unique solution. In parallel, we studythe optimal steering of the state-density of a linear stochastic system withwhite noise disturbance; this is known to correspond to a Schr\"odinger bridge.As the white noise intensity tends to zero, the flow of densities converges tothat of the deterministic dynamics and can serve as a way to compute thesolution of its deterministic counterpart. The solution can be expressed inclosed-form for Gaussian initial and final state densities in both cases.
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2015 EN
Michele Pavon
It is observed that for testing between simple hypotheses where the cost ofType I and Type II errors can be quantified, it is better to let theoptimization choose the test size.
Resource
2015 EN
Nicole Berline · Michele Vergne
Consider the Riemann sum of a smooth compactly supported function h(x) on apolyhedron in R^d, sampled at the points of the lattice Z^d/t. We give anasymptotic expansion when t goes to infinity, writing each coefficient of thisexpansion as a sum indexed by the faces f of the polyhedron, where the f-termis the integral over f of a differential operator applied to the function h(x).In particular, if a Euclidean scalar product is chosen, we prove that thedifferential operator for the face f can be chosen (in a unique way) to involveonly normal derivatives to f. Our formulas are valid for a semi-rationalpolyhedron and a real sampling parameter t, if we allow for step-polynomialcoefficients, instead of just constant ones.
Resource
2015 EN
Søren Ulstrup · Jens Christian Johannsen · Federico Cilento
+13 more
In pump-probe time and angle-resolved photoemission spectroscopy (TR-ARPES)experiments the presence of the pump pulse adds a new level of complexity tothe photoemission process in comparison to conventional ARPES. This isevidenced by pump-induced vacuum space-charge effects and surfacephotovoltages, as well as multiple pump excitations due to internal reflectionsin the sample-substrate system. These processes can severely affect a correctinterpretation of the data by masking the out-of-equilibrium electron dynamicsintrinsic to the sample. In this study, we show that such effects indeedinfluence TR-ARPES data of graphene on a silicon carbide (SiC) substrate. Inparticular, we find a time- and laser fluence-dependent spectral shift andbroadening of the acquired spectra, and unambiguously show the presence of adouble pump excitation. The dynamics of these effects is slower than theelectron dynamics in the graphene sample, thereby permitting us to deconvolvethe signals in the time domain. Our results demonstrate that complexpump-related processes should always be considered in the experimental setupand data analysis.
Resource
2015 EN
Michele Fanelli · Alberto Fanelli
The present essay aims at investigating whether and how far an algebraicanalysis of the Zeta Function and of the Riemann Hypothesis can be carried out.Of course the well-established properties of the Zeta Function, explored indepth in over 150 years of world-wide study, are taken for granted. The chosenapproach starts from the recognized necessity of formulating an extension ofthe Zeta Function which is defined for Re(s) = X < 1. A particular form ofextension, based on a Euler-McLaurin integration procedure, is chosen and analgebraic appraisal is made of the conditions required to make the expressionof this extension equal to zero. Imposing the zero-condition on this extensionof the Zeta Function implies the nullity of the sum of three terms withdifferent properties. This can be obtained only if certain compatibilityconditions between the three terms are satisfied. One of the terms is endowedwith a high degree of symmetry with respect to the Critical Line (C.L.) X =1/2, and from the compatibility conditions it follows that either the other twoterms possess the same type of symmetry or any complex-conjugate (c.c.) pair ofzero-points should lie on the C.L. Since the symmetry properties of the firstterm are not shared by the other two terms, it appears that the only allowedc.c. pairs of zero-points must belong to the C.L.
Resource
2015 EN
Michele Conforti · Volker Kaibel · Matthias Walter
+1 more
Given an undirected graph, the non-empty subgraph polytope is the convex hullof the characteristic vectors of pairs (F, S) where S is a non-empty subset ofnodes and F is a subset of the edges with both endnodes in S. We obtain astrong relationship between the non-empty subgraph polytope and the spanningforest polytope. We further show that these polytopes provide polynomial sizeextended formulations for independence polytopes of count matroids, whichgeneralizes recent results obtained by Iwata et al. referring to sparsitymatroids. As a byproduct, we obtain new lower bounds on the extensioncomplexity of the spanning forest polytope in terms of extension complexitiesof independence polytopes of these matroids.
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2015 EN
Michele Matteini
In this paper we will explore different available methodologies toautomatically design controllers for tasks that spans many level ofabstraction, where the gap between primitive behaviours and the task definitionis high. A good understanding of your evolutionary setup is needed to choosethe correct strategy with which to tackle complex tasks thus we'll first reviewthe most used types of each element composing an evolutionary setup(controllers, objective functions, ect.) then we'll move the focus on thebootstrapping problem and on the different strategies used to overcome it.
Resource
2015 EN
Michele Colledanchise · Alejandro Marzinotto · Dimos V. Dimarogonas
+1 more
Multi-robot teams offer possibilities of improved performance and faulttolerance, compared to single robot solutions. In this paper, we show how torealize those possibilities when starting from a single robot system controlledby a Behavior Tree (BT). By extending the single robot BT to a multi-robot BT,we are able to combine the fault tolerant properties of the BT, in terms ofbuilt-in fallbacks, with the fault tolerance inherent in multi-robotapproaches, in terms of a faulty robot being replaced by another one.Furthermore, we improve performance by identifying and taking advantage of theopportunities of parallel task execution, that are present in the single robotBT. Analyzing the proposed approach, we present results regarding how missionperformance is affected by minor faults (a robot losing one capability) as wellas major faults (a robot losing all its capabilities). Finally, a detailedexample is provided to illustrate the approach.