On totally geodesic submanifolds in the Jacobian locus

We study submanifolds of A_g that are totally geodesic for the locally symmetric metric and which are contained in the closure of the Jacobian locus but not in its boundary. In the first section we recall a formula for the second fundamental form of the period map due to Pirola, Tortora and the first author. We show that this result can be stated quite neatly using a line bundle over the product of the curve with itself. We give an upper bound for the dimension of a germ of a totally geodesic submanifold passing through [C] in M_g in terms of the gonality of C. This yields an upper bound for the dimension of a germ of a totally geodesic submanifold contained in the Jacobian locus, which only depends on the genus. We also study the submanifolds of A_g obtained from cyclic covers of the projective line. These have been studied by various authors. Moonen determined which of them are Shimura varieties using deep results in positive characteristic. Using our methods we show that many of the submanifolds which are not Shimura varieties are not even totally geodesic.Comment: To appear on International Journal of Mathematic

The Conservation of Marcus Aurelius' Monument. Technical studies

The equestrian bronze monument of Marcus Aurelius in Rome has been further investigated, after restoration, mainly to foresee possible damages caused by outdoor exposure. At the same time a copy of it has been cast by following a new original method to obtain the intermediate model. New non-destructive tests have heen carried out to execute the above researches and in the end old and new methodologies can be consldered as a complex experimental tool to study and control outdoor bronze monument

Discrete Approximations of a Controlled Sweeping Process

The paper is devoted to the study of a new class of optimal control problems governed by the classical Moreau sweeping process with the new feature that the polyhe- dral moving set is not fixed while controlled by time-dependent functions. The dynamics of such problems is described by dissipative non-Lipschitzian differential inclusions with state constraints of equality and inequality types. It makes challenging and difficult their anal- ysis and optimization. In this paper we establish some existence results for the sweeping process under consideration and develop the method of discrete approximations that allows us to strongly approximate, in the W^{1,2} topology, optimal solutions of the continuous-type sweeping process by their discrete counterparts

Empirical Tests Of Optimal Cognitive Distance

This article provides empirical tests of the hypothesis of ‘optimal cognitive distance’, proposed by Nooteboom (1999, 2000), in two distinct empirical settings. Variety of cognition, needed for learning, has two dimensions: the number of agents with different cognition, and differences in cognition between them (cognitive distance). The hypothesis is that in interfirm relationships optimal learning entails a trade-off between the advantage of increased cognitive distance for a higher novelty value of a partner’s knowledge, and the disadvantage of less mutual understanding. If the value of learning is the mathematical product of novelty value and understandability, it has an inverse-U shaped relation with cognitive distance, with an optimum level that yields maximal value of learning. With auxiliary hypotheses, the hypothesis is tested on interfirm agreements between pharmaceutical companies and biotech companies, as well as on interfirm agreements in ICT industries.innovation;organizational learning;ICT;biotechnology;alliances

Nonlinear elasticity of monolayer graphene

By combining continuum elasticity theory and tight-binding atomistic simulations, we work out the constitutive nonlinear stress-strain relation for graphene stretching elasticity and we calculate all the corresponding nonlinear elastic moduli. Present results represent a robust picture on elastic behavior of one-atom thick carbon sheets and provide the proper interpretation of recent experiments. In particular, we discuss the physical meaning of the effective nonlinear elastic modulus there introduced and we predict its value in good agreement with available data. Finally, a hyperelastic softening behavior is observed and discussed, so determining the failure properties of graphene.Comment: 4 page

The impact of M&A on the R&D process. An empirical analysis of the role of technological and market relatedness.

While the impact of M&A on R&D and innovation examined at the aggregate level left inconclusive evidence, we find that at the level of the R&D process both the technological and market relatedness between the target and acquirer are helpful dimensions to identify effects. Using information on 31 in-depth cases of individual M&A deals we show that technological relatedness between M&A partners directly affects the inputs and organizational structure of the R&D process. M&A partners that operate in the same technological fields tend to reduce their R&D effort and rationalize the R&D process after the M&A compared to firms active in complementary technological fields that merge. These firms will furthermore face less technological competition in the technology market, but risk creating a more bureaucratic R&D process with a less motivated workforce. Market relatedness between partners, while having comparable aggregate effects on the R&D process, operates on different dimensions of the R&D process. Former rivals that engage in a M&A are significantly less likely to expand into new R&D fields or leverage their technological competences across the products and markets of the new entity. Non-rival firms that join forces, on the contrary, significantly increase R&D output and productivity through these activities.Competition; Effects; Field; Firms; Information; Innovation; International; M&A; Market; Market relatedness; Markets; Organizational structure; Processes; Product; R&D; Risk; Scale and scope; Structure; Subsidiaries; Technolocal relatedness; Technology diffusion;

Shimura varieties in the Torelli locus via Galois coverings of elliptic curves

We study Shimura subvarieties of $\mathsf{A}_g$ obtained from families of Galois coverings $f: C \rightarrow C'$ where $C'$ is a smooth complex projective curve of genus $g' \geq 1$ and $g= g(C)$. We give the complete list of all such families that satisfy a simple sufficient condition that ensures that the closure of the image of the family via the Torelli map yields a Shimura subvariety of $\mathsf{A}_g$ for $g' =1,2$ and for all $g \geq 2,4$ and for $g' > 2$ and $g \leq 9$. In a previous work of the first and second author together with A. Ghigi [FGP] similar computations were done in the case $g'=0$. Here we find 6 families of Galois coverings, all with $g' = 1$ and $g=2,3,4$ and we show that these are the only families with $g'=1$ satisfying this sufficient condition. We show that among these examples two families yield new Shimura subvarieties of $\mathsf{A}_g$, while the other examples arise from certain Shimura subvarieties of $\mathsf{A}_g$ already obtained as families of Galois coverings of $\mathbb{P}^1$ in [FGP]. Finally we prove that if a family satisfies this sufficient condition with $g'\geq 1$, then $g \leq 6g'+1$.Comment: 18 pages, to appear in Geometriae Dedicat

On some differential-geometric aspects of the Torelli map

In this note we survey recent results on the extrinsic geometry of the Jacobian locus inside $\mathsf{A}_g$. We describe the second fundamental form of the Torelli map as a multiplication map, recall the relation between totally geodesic subvarieties and Hodge loci and survey various results related to totally geodesic subvarieties and the Jacobian locus.Comment: To appear on Boll. UMI, special volume in memory of Paolo de Bartolomei

Beyond the cortico-centric models of cognition: the role of subcortical functioning in neurodevelopmental disorders

The main aim of the present opinion article is to discuss and argue how the classic cortico-centricmodel of neurodevelopmental disorders is not exhaustive of the possible explanation of thesedisorders. The alternative proposal presented here is to include the cortico-subcortical networkmodel to explain them

Time-evolving measures and macroscopic modeling of pedestrian flow

This paper deals with the early results of a new model of pedestrian flow, conceived within a measure-theoretical framework. The modeling approach consists in a discrete-time Eulerian macroscopic representation of the system via a family of measures which, pushed forward by some motion mappings, provide an estimate of the space occupancy by pedestrians at successive time steps. From the modeling point of view, this setting is particularly suitable to treat nonlocal interactions among pedestrians, obstacles, and wall boundary conditions. In addition, analysis and numerical approximation of the resulting mathematical structures, which is the main target of this work, follow more easily and straightforwardly than in case of standard hyperbolic conservation laws, also used in the specialized literature by some Authors to address analogous problems.Comment: 27 pages, 6 figures -- Accepted for publication in Arch. Ration. Mech. Anal., 201