Matrix Cartan superdomains, super Toeplitz operators, and quantization

We present a general theory of non-perturbative quantization of a class of hermitian symmetric supermanifolds. The quantization scheme is based on the notion of a super Toeplitz operator on a suitable Z_2 -graded Hilbert space of superholomorphic functions. The quantized supermanifold arises as the C^* -algebra generated by all such operators. We prove that our quantization framework reproduces the invariant super Poisson structure on the classical supermanifold as Planck's constant tends to zero.Comment: 52

Loop and Path Spaces and Four-Dimensional BF Theories: Connections, Holonomies and Observables

We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures, parallel transports and holonomies are computed and their expressions in local coordinates are exhibited. When the 2-form B is given by the curvature of A, then the so-called non-abelian Stokes formula follows. For a generic 2-form B, we distinguish the cases when the parallel transport depends on the whole path of paths and when it depends only on the spanned surface. In particular we discuss generalizations of the non-abelian Stokes formula. We study also the invariance properties of the (trace of the) holonomy under suitable transformation groups acting on the pairs (A,B). In this way we are able to define observables for both topological and non-topological quantum field theories of the BF type. In the non topological case, the surface terms may be relevant for the understanding of the quark-confinement problem. In the topological case the (perturbative) four-dimensional quantum BF-theory is expected to yield invariants of imbedded (or immersed) surfaces in a 4-manifold M.Comment: TeX, 39 page

Supersymmetry and Fredholm modules over quantized spaces

The purpose of this paper is to apply the framework of non- commutative differential geometry to quantum deformations of a class of Kahler manifolds. For the examples of the Cartan domains of type I and flat space, we construct Fredholm modules over the quantized manifolds using the supercharges which arise in the quantization of supersymmetric generalizations of the manifolds. We compute the explicit formula for the Chern character on generators of the Toeplitz C^* -algebra.Comment: 24

Data and performance of an active-set truncated Newton method with non-monotone line search for bound-constrained optimization

In this data article, we report data and experiments related to the research article entitled “A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization”, by Cristofari et al. (2017). The method proposed in Cristofari et al. (2017), tackles optimization problems with bound constraints by properly combining an active-set estimate with a truncated Newton strategy. Here, we report the detailed numerical experience performed over a commonly used test set, namely CUTEst (Gould et al., 2015). First, the algorithm ASA-BCP proposed in Cristofari et al. (2017) is compared with the related method NMBC (De Santis et al., 2012). Then, a comparison with the renowned methods ALGENCAN (Birgin and Martínez et al., 2002) and LANCELOT B (Gould et al., 2003) is reported

Recurrent and synchronous insect pest outbreaks in forests

The simplest model of plant-insect interactions available in the literature is used to discuss periodicity and synchrony of insect outbreaks in forests. The novelty of the paper is that we present through various formulas and a circular graph a comprehensive theory and show that many, if not all, properties of insect outbreaks pointed out in the past by looking at specific data sets could have been predicted from our theory. In line with the tradition of classical ecology all results are derived without resorting to computer simulation

Laura and Petrarch: An Intriguing Case of Cyclical Love Dynamics

Three ordinary differential equations are proposed to model the dynamics of love between Petrarch, a celebrated Italian poet of the 14th century, and Laura, a beautiful but married lady. The equations are nonlinear but can be studied through the singular perturbation approach if the inspiration of the poet is assumed to have very slow dynamics. In such a case, explicit conditions are found in the appeals of Laura and Petrarch and in their behavioural parameters that guarantee the existence of a globally stable slow-fast limit cycle. These conditions are consistent with the relatively clear portrait of the two personalities one gets while reading the poems addressed to Laura. On the basis of the sparse and only qualitative information available, the calibration of the parameters is also performed; the result is that the calibrated model shows that the poet's emotions have been following for about 20 years a quite regular cyclical pattern ranging from the extremes of ecstasy to despair. All these findings agree with the recent results of Frederic Jones who, through a detailed stylistic and linguistic analysis of the poems inspired by Laura, has discovered Petrarch's emotional cycle in a fully independent way

Synchrony in slow-fast metacommunities

The synchronization of metacommunities due to dispersal among patches is analyzed in the case of slow-fast populations. The analysis is performed by studying a standard model with the fast population dispersing when special meteorological conditions are present. This assumption fits very well with the peculiar nature of slow-fast systems and implies that metacommunities synchronize if the slow population accelerates during the outbreak of the fast population. This result shows great potential in the study of marine and fresh-water plankton communities as well as in the study of synchronization of insect-pest outbreaks in forests

Some Remarks on Periodic Stochastic Linear Reservoirs

Very simple properties of stochastic linear reservoirs are derived for the case of cyclostationary stochastic inflows and seasonally varying operating rules. Although real reservoirs are fairly non-linear, these properties have proved to be helpful in understanding the seasonal pattern of releases and the long-term variations occurring in some of the regulated lakes of Northern Italy