DSpace Collection:
http://hdl.handle.net/2445/7508
Thu, 14 Nov 2019 14:06:42 GMT2019-11-14T14:06:42ZInterpolating vector fields for near indentity maps and averaging
http://hdl.handle.net/2445/144297
Title: Interpolating vector fields for near indentity maps and averaging
Author: Gelfreich, V.; Vieiro Yanes, Arturo
Abstract: For a smooth near identity map, we introduce the notion of an interpolating vector field written in terms of iterates of the map. Our construction is based on Lagrangian interpolation and provides an explicit expression for autonomous vector fields which approximately interpolate the map. We study properties of the interpolating vector fields and explore their applications to the study of dynamics. In particular, we construct adiabatic invariants for symplectic near identity maps. We also introduce the notion of a Poincaré section for a near identity map and use it to visualise dynamics of four-dimensional maps. We illustrate our theory with several examples, including the Chirikov standard map, a volume-preserving map and a symplectic map in dimension four. The last example is motivated by the theory of Arnold diffusion.Fri, 08 Nov 2019 14:52:45 GMThttp://hdl.handle.net/2445/1442972019-11-08T14:52:45ZOn the classification of Togliatti systems
http://hdl.handle.net/2445/144240
Title: On the classification of Togliatti systems
Author: Miró-Roig, Rosa M. (Rosa Maria); Salat Moltó, Martí
Abstract: In [MeMR], Mezzetti and Mir\'{o}-Roig proved that the minimal number of generators μ(I) of a minimal (smooth) monomial Togliatti system I⊂k[x0,¿,xn] satisfies 2n+1≤μ(I)≤(n+d−1n−1) and they classify all smooth minimal monomial Togliatti systems I⊂k[x0,¿,xn] with 2n+1≤μ(I)≤2n+2. In this paper, we address the first open case. We classify all smooth monomial Togliatti systems I⊂k[x0,¿,xn] of forms of degree d≥4 with μ(I)=2n+3 and n≥2 and all monomial Togliatti systems I⊂k[x0,x1,x2] of forms of degree d≥6 with μ(I)=7.Thu, 07 Nov 2019 15:27:44 GMThttp://hdl.handle.net/2445/1442402019-11-07T15:27:44ZTowards social pattern characterization in egocentric photo-streams
http://hdl.handle.net/2445/144211
Title: Towards social pattern characterization in egocentric photo-streams
Author: Aghaei, Maedeh; Dimiccoli, Mariella; Canton-Ferrer, Cristian; Radeva, Petia
Abstract: Following the increasingly popular trend of social interaction analysis in egocentric vision, this article presents a comprehensive pipeline for automatic social pattern characterization of a wearable photo-camera user. The proposed framework relies merely on the visual analysis of egocentric photo-streams and consists of three major steps. The first step is to detect social interactions of the user where the impact of several social signals on the task is explored. The detected social events are inspected in the second step for categorization into different social meetings. These two steps act at event-level where each potential social event is modeled as a multi-dimensional time-series, whose dimensions correspond to a set of relevant features for each task; finally, LSTM is employed to classify the time-series. The last step of the framework is to characterize social patterns of the user. Our goal is to quantify the duration, the diversity and the frequency of the user social relations in various social situations. This goal is achieved by the discovery of recurrences of the same people across the whole set of social events related to the user. Experimental evaluation over EgoSocialStyle - the proposed dataset in this work, and EGO-GROUP demonstrates promising results on the task of social pattern characterization from egocentric photo-streams.Thu, 07 Nov 2019 12:44:14 GMThttp://hdl.handle.net/2445/1442112019-11-07T12:44:14ZLefschetz properties for complete intersection ideals generated by products of linear forms
http://hdl.handle.net/2445/144203
Title: Lefschetz properties for complete intersection ideals generated by products of linear forms
Author: Juhnke-Kubitzke, Martina; Miró-Roig, Rosa M. (Rosa Maria); Murai, Satoshi; Wachi, Akihito
Abstract: In this paper, we study the strong Lefschetz property of artinian complete intersection ideals generated by products of linear forms. We prove the strong Lefschetz property for a class of such ideals with binomial generators.Thu, 07 Nov 2019 12:14:20 GMThttp://hdl.handle.net/2445/1442032019-11-07T12:14:20ZHyperelliptic Jacobians and isogenies
http://hdl.handle.net/2445/143342
Title: Hyperelliptic Jacobians and isogenies
Author: Naranjo del Val, Juan Carlos; Pirola, G. P.
Abstract: In this note we mainly consider abelian varieties isogenous to hyperelliptic Jacobians. In the first part we prove that a very general hyperelliptic Jacobian of genus is not isogenous to a non-hyperelliptic Jacobian. As a consequence we obtain that the intermediate Jacobian of a very general cubic threefold is not isogenous to a Jacobian. Another corollary tells that the Jacobian of a very general d-gonal curve of genus is not isogenous to a different Jacobian. In the second part we consider a closed subvariety of the moduli space of principally polarized varieties of dimension . We show that if a very general element of is dominated by the Jacobian of a curve C and , then C is not hyperelliptic. In particular, if the general element in is simple, its Kummer variety does not contain rational curves. Finally we show that a closed subvariety of dimension such that the Jacobian of a very general element of is dominated by a hyperelliptic Jacobian is contained either in the hyperelliptic or in the trigonal locus.Mon, 28 Oct 2019 16:01:53 GMThttp://hdl.handle.net/2445/1433422019-10-28T16:01:53ZEgocentric video description based on temporally-linked sequences
http://hdl.handle.net/2445/143165
Title: Egocentric video description based on temporally-linked sequences
Author: Bolaños Solà, Marc; Peris, Álvaro; Casacuberta, Francisco; Soler, Sergi; Radeva, Petia
Abstract: Egocentric vision consists in acquiring images along the day from a first person point-of-view using wearable cameras. The automatic analysis of this information allows to discover daily patterns for improving the quality of life of the user. A natural topic that arises in egocentric vision is storytelling, that is, how to understand and tell the story relying behind the pictures. In this paper, we tackle storytelling as an egocentric sequences description problem. We propose a novel methodology that exploits information from temporally neighboring events, matching precisely the nature of egocentric sequences. Furthermore, we present a new method for multimodal data fusion consisting on a multi-input attention recurrent network. We also release the EDUB-SegDesc dataset. This is the first dataset for egocentric image sequences description, consisting of 1339 events with 3991 descriptions, from 55 days acquired by 11 people. Finally, we prove that our proposal outperforms classical attentional encoder-decoder methods for video description.Fri, 25 Oct 2019 10:11:47 GMThttp://hdl.handle.net/2445/1431652019-10-25T10:11:47ZOn the Xiao conjecture for plane curves
http://hdl.handle.net/2445/143059
Title: On the Xiao conjecture for plane curves
Author: Favale, F.; Naranjo del Val, Juan Carlos; Pirola, G. P.
Abstract: Let f:S⟶B be a non-trivial fibration from a complex projective smooth surface S to a smooth curve B of genus b. Let cf the Clifford index of the general fibre F of f. In Barja et al. (Journal für die reine und angewandte Mathematik, 2016) it is proved that the relative irregularity of f, qf=h1,0(S)−b is less or equal than or equal to g(F)−cf . In particular this proves the (modified) Xiao's conjecture: qf≤g(F)2+1 for fibrations of general Clifford index. In this short note we assume that the general fiber of f is a plane curve of degree d≥5 and we prove that qf≤g(F)−cf−1 . In particular we obtain the conjecture for families of quintic plane curves. This theorem is implied for the following result on infinitesimal deformations: let F a smooth plane curve of degree d≥5 and let ξ be an infinitesimal deformation of F preserving the planarity of the curve. Then the rank of the cup-product map H0(F,ωF)⟶⋅ξH1(F,OF) is at least d−3 . We also show that this bound is sharp.Thu, 24 Oct 2019 13:09:17 GMThttp://hdl.handle.net/2445/1430592019-10-24T13:09:17ZOn the sharpness of the Rüssmann estimates
http://hdl.handle.net/2445/143058
Title: On the sharpness of the Rüssmann estimates
Author: Figueras, Jordi Lluís; Haro, Àlex; Luque, Alejandro
Abstract: Estimating the norm of the solution of the linear difference equation plays a fundamental role in KAM theory. Optimal (in certain sense) estimates for the solution of this equation were provided by Rüssmann in the mid 70's. The aim of this paper is to compare the sharpness of these classical estimates with more specific estimates obtained with the help of the computer. We perform several experiments to quantify the improvement obtained when using computer assisted estimates. By comparing these estimates with the actual norm of the solution, we can analyze the different sources of overestimation, thus encouraging future improvements.Thu, 24 Oct 2019 11:06:54 GMThttp://hdl.handle.net/2445/1430582019-10-24T11:06:54ZOrbits of polynomial dynamical systems modulo primes
http://hdl.handle.net/2445/142999
Title: Orbits of polynomial dynamical systems modulo primes
Author: Chang, Mei-Chu; D'Andrea, Carlos, 1973-; Ostafe, Alina; Shparlinski, Igor E.; Sombra, Martín
Abstract: We present lower bounds for the orbit length of reduction modulo primes of parametric polynomial dynamical systems defined over the integers, under a suitable hypothesis on its set of preperiodic points over $ \mathbb{C}$. Applying recent results of Baker and DeMarco (2011) and of Ghioca, Krieger, Nguyen and Ye (2017), we obtain explicit families of parametric polynomials and initial points such that the reductions modulo primes have long orbits, for all but a finite number of values of the parameters. This generalizes a previous lower bound due to Chang (2015). As a by-product, we also slightly improve a result of Silverman (2008) and recover a result of Akbary and Ghioca (2009) as special extreme cases of our estimates.Thu, 24 Oct 2019 10:03:46 GMThttp://hdl.handle.net/2445/1429992019-10-24T10:03:46ZSystems of stochastic Poisson equations: Hitting probabilities
http://hdl.handle.net/2445/142997
Title: Systems of stochastic Poisson equations: Hitting probabilities
Author: Sanz, Marta; Viles, Noèlia
Abstract: We consider a -dimensional random field that solves a system of elliptic stochastic equations on a bounded domain , with additive white noise and spatial dimension . Properties of and its probability law are proved. For Gaussian solutions, using results from Dalang and Sanz-Solé (2009), we establish upper and lower bounds on hitting probabilities in terms of the Hausdorff measure and Bessel-Riesz capacity, respectively. This relies on precise estimates of the canonical distance of the process or, equivalently, on estimates of increments of the Green function of the Laplace equation.Thu, 24 Oct 2019 09:39:08 GMThttp://hdl.handle.net/2445/1429972019-10-24T09:39:08Z