An extension of a theorem of Schoenberg to products of spheres

We present a characterization for the continuous, isotropic and positive definite kernels on a product of spheres along the lines of a classical result of I. J. Schoenberg on positive definiteness on a single sphere. We also discuss a few issues regarding the characterization, including topics for future investigation

Strictly Positive Definite Kernels on a Product of Spheres II

We present, among other things, a necessary and sufficient condition for the strict positive definiteness of an isotropic and positive definite kernel on the cartesian product of a circle and a higher dimensional sphere. The result complements similar results previously obtained for strict positive definiteness on a product of circles [Positivity, to appear, arXiv:1505.01169] and on a product of high dimensional spheres [J. Math. Anal. Appl. 435 (2016), 286-301, arXiv:1505.03695]

Phytochemical investigations on Artemisia alba Turra growing in the North-East of Italy

Artemisia alba Turra (Asteraceae) is an Euro-Mediterranean plant used in Veneto (North-East of Italy) as traditional medicine for the treatment of various diseases. A. alba is a taxonomically problematic species, characterized by common polymorphism leading to a quite high variability in secondary metabolites content. Nonetheless, the phytochemical knowledge on its phytoconstituents, especially non-volatile components, is limited. In the present paper, the phytochemical composition of a tincture obtained from the aerial parts of A. alba growing in Veneto is presented. Extensive chromatographic separations led to the isolation of three new sesquiterpene derivatives, whose structures were elucidated by 1D and 2D NMR experiments and mass spectrometry. Furthermore, flavonoid composition and volatile constituents of the tincture of A. alba were preliminary studied by HPLC-MSn and GC-MS, respectivel

Spectral Theory of Sparse Non-Hermitian Random Matrices

Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these matrices provide crucial information on system stability and susceptibility, however, their study is greatly complicated by the twin challenges of a lack of symmetry and a sparse interaction structure. In this review we provide a concise and systematic introduction to the main tools and results in this field. We show how the spectra of sparse non-Hermitian matrices can be computed via an analogy with infinite dimensional operators obeying certain recursion relations. With reference to three illustrative examples -- adjacency matrices of regular oriented graphs, adjacency matrices of oriented Erd\H{o}s-R\'{e}nyi graphs, and adjacency matrices of weighted oriented Erd\H{o}s-R\'{e}nyi graphs -- we demonstrate the use of these methods to obtain both analytic and numerical results for the spectrum, the spectral distribution, the location of outlier eigenvalues, and the statistical properties of eigenvectors.Comment: 60 pages, 10 figure

Challenging claims in the study of migratory birds and climate change

Recent shifts in phenology in response to climate change are well established but often poorly understood. Many animals integrate climate change across a spatially and temporally dispersed annual life cycle, and effects are modulated by ecological interactions, evolutionary change and endogenous control mechanisms. Here we assess and discuss key statements emerging from the rapidly developing study of changing spring phenology in migratory birds. These well-studied organisms have been instrumental for understanding climate-change effects, but research is developing rapidly and there is a need to attack the big issues rather than risking affirmative science. Although we agree poorly on the support for most claims, agreement regarding the knowledge basis enables consensus regarding broad patterns and likely causes. Empirical data needed for disentangling mechanisms are still scarce, and consequences at a population level and on community composition remain unclear. With increasing knowledge, the overall support (‘consensus view’) for a claim increased and between-researcher variability in support (‘expert opinions') decreased, indicating the importance of assessing and communicating the knowledge basis. A proper integration across biological disciplines seems essential for the field's transition from affirming patterns to understanding mechanisms and making robust predictions regarding future consequences of shifting phenologies

Capillary rising damp in Venetian context : state of the art and numerical simulation

The fragility of Venice and its buildings are linked to the floods, observed since ancient times and emphasized in recent years: the periodic sea level rise, accompanied by rising damp, are the main causes of the alteration. In particular, the rising damp causes a series of complex diseases in the historic buildings, such as physical decay, chemical or biological, with loss of aesthetic and economic value. In addition, greater heat dispersion and reduced thermal comfort can also occur in interior spaces, with consequent risks for human health. This is a sign of “Sick Building Syndrome”. It is very important to develop models for assessing the vulnerability of assets and to manage sustainable plans related to maintenance processes and activities, satisfying the requirements of effectiveness and compatibility.Basing on numerical models performed with the WUFI 2D software, the paper analyses the different behavior of rising damp in relation to materials or masonry structures. In particular, the construction techniques and typical materials used in Venetian buildings were investigated, such as clay brick walls, lime plaster, Marmorino and Cocciopesto, adopted mainly to limit the capillary rise also caused by the phenomenon of “acqua alta”

PSPACE-completeness of the temporal logic of sub-intervals and suffixes

In this paper, we prove PSPACE-completeness of the finite satisfiability and model checking problems for the fragment of Halpern and Shoham interval logic with modality 〈E〉, for the “suffix” relation on pairs of intervals, and modality 〈D〉, for the “sub-interval” relation, under the homogeneity assumption. The result significantly improves the EXPSPACE upper bound recently established for the same fragment, and proves the rather surprising fact that the complexity of the considered problems does not change when we add either the modality for suffixes (〈E〉) or, symmetrically, the modality for prefixes (〈B〉) to the logic of sub-intervals (featuring only 〈D〉)