Non-exchangeable copulas and multivariate total positivity

Multivariate total positivity of order 2 (MTP2) is a dependence property with a number of applications in statistics and mathematics. Given the theoretical and practical relevance of MTP2, it is important to investigate the conditions under which random vectors have this property. In this paper we contribute to the development of the theory of stochastic dependence by employing the general concept of copula. In particular, we propose a new family of non-exchangeable Archimedean copulas which leads to MTP2. The focus on non-exchangeability allows us to overcome the limitations induced by symmetric dependence, typical of standard Archimedean copulas

Some New Tests of Conformity with Benford's Laws

This paper presents new perspectives and methodological instruments for verifying the validity of Benford’s law for a large given dataset. To this aim, we first propose new general tests for checking the statistical conformity of a given dataset with a generic target distribution; we also provide the explicit representation of the asymptotic distributions of the relevant test statistics. Then, we discuss the applicability of such novel devices to the case of Benford’s law. We implement extensive Monte Carlo simulations to investigate the size and the power of the introduced tests. Finally, we discuss the challenging theme of interpreting, in a statistically reliable way, the conformity between two distributions in the presence of a large number of observations

A network approach to risk theory and portfolio selection

In the context of portfolio theory, the evaluation of risk is of paramount relevance. In this respect, the connections among the risky assets of the portfolio should be carefully explored. This paper elaborates on this topic. We define a portfolio through a network, whose nodes are the assets composing it. The weights on the nodes and the arcs represent the share of capital invested on the assets and the dependence among them, respectively. The risk profile of the portfolio will be given through a suitably defined risk measure on the portfolio-network. The standard Markowitz theory will be rewritten in this particular setting. Surprisingly, we will note that the resulting decision problem is not consistent with an adapted version of the axiomatization of the standard expected utility theory

Risk measures on networks and expected utility

In reliability theory projects are usually evaluated in terms of their riskiness, and often decision under risk is intended as the one-shot-type binary choice of accepting or not accepting the risk. In this paper we elaborate on the concept of risk acceptance, and propose a theoretical framework based on network theory. In doing this, we deal with system reliability, where the interconnections among the random quantities involved in the decision process are explicitly taken into account. Furthermore, we explore the conditions to be satisfied for risk-acceptance criteria to be consistent with the axiomatization of standard expected utility theory within the network framework. In accordance with existing literature, we show that a risk evaluation criterion can be meaningful even if it is not consistent with the standard axiomatization of expected utility, once this is suitably reinterpreted in the light of networks. Finally, we provide some illustrative examples

Determinazione dei tributi, «comunità scientifiche» e «Dialoghi Tributari»

Da quando la determinazione dei tributi dalla tradizionale stima valutativa della ricchezza cui essi fanno riferimento, ma si basa sulla documentazione e la contabilità delle organizzazioni, il bagaglio culturale della classe dirigente e della pubblica opinione non era più sufficiente alla sua comprensione di insieme. Serviva quindi un gruppo omogeneo di «studiosi sociali» dedicati, la cui formazione è stata ostacolata da una serie di circostanze diffuse nelle scienze sociali, e nel diritto in particolare, cioè complessi di inferiorità verso le scienze fisiche, loro imitazioni, ricerche di legittimazione, convenienze e altri fattori indicati nell’articolo. Che cerca di spiegare per quali ragioni la determinazione dei tributi abbia particolarmente risentito del disorientamento generale delle scienze sociali, fino a disperdersi tra particolarità «normativo-professionali» e divagazioni politico sociali sugli effetti dei tributi. Perdendo di vista la centralità della loro determinazione

Long-range properties and data validity for hydrogeological time series: The case of the Paglia river

This paper explores a large collection of about 377,000 observations, spanning more than 20 years with a frequency of 30 min, of the streamflow of the Paglia river, in central Italy. We analyze the long-term persistence properties of the series by computing the Hurst exponent, not only in its original form but also under an evolutionary point of view by analyzing the Hurst exponents over a rolling windows basis. The methodological tool adopted for the persistence is the detrended fluctuation analysis (DFA), which is classically known as suitable for our purpose. As an ancillary exploration, we implement a control on the data validity by assessing if the data exhibit the regularity stated by Benford’s law. Results are interesting under different viewpoints. First, we show that the Paglia river streamflow exhibits periodicities which broadly suggest the existence of some common behavior with El Niño and the North Atlantic Oscillations: this specifically points to a (not necessarily direct) effect of these oceanic phenomena on the hydrogeological equilibria of very far geographical zones: however, such an hypothesis needs further analyses to be validated. Second, the series of streamflows shows an antipersistent behavior. Third, data are not consistent with Benford’s law: this suggests that the measurement criteria should be opportunely revised. Fourth, the streamflow distribution is well approximated by a discrete generalized Beta distribution: this is well in accordance with the measured streamflows being the outcome of a complex system

The birth of a supermassive black hole binary

We study the dynamical evolution of supermassive black holes, in the late stage of galaxy mergers, from kpc to pc scales. In particular, we capture the formation of the binary, a necessary step before the final coalescence, and trace back the main processes causing the decay of the orbit. We use hydrodynamical simulations of galaxy mergers with different resolutions, from $20\,\rm pc$ down to $1\,\rm pc$, in order to study the effects of the resolution on our results, remove numerical effects, and assess that resolving the influence radius of the orbiting black hole is a minimum condition to fully capture the formation of the binary. Our simulations include the relevant physical processes, namely star formation, supernova feedback, accretion onto the black holes and the ensuing feedback. We find that, in these mergers, dynamical friction from the smooth stellar component of the nucleus is the main process that drives black holes from kpc to pc scales. Gas does not play a crucial role and even clumps do not induce scattering or perturb the orbits. We compare the time needed for the formation of the binary to analytical predictions and suggest how to apply such analytical formalism to obtain estimates of binary formation times in lower resolution simulations.Comment: 12 pages, 12 Figures, submitted to MNRA

Chiral spin currents and spectroscopically accessible single merons in quantum dots

We provide unambiguous theoretical evidence for the formation of correlation-induced isolated merons in rotationally-symmetric quantum dots. Our calculations rely on neither the lowest-Landau-level approximation, nor on the maximum-density-droplet approximation, nor on the existence of a spin-polarized state. For experimentally accessible system parameters, unbound merons condense in the ground state at magnetic fields as low as $B^* = 0.2$ T and for as few as N = 3 confined fermions. The four-fold degenerate ground-state at $B^*$ corresponds to four orthogonal merons $\ket{QC}$ characterized by their topological chirality $C$ and charge $Q$. This degeneracy is lifted by the Rashba and Dresselhaus spin-orbit interaction, which we include perturbatively, yielding spectroscopic accessibility to individual merons. We further derive a closed-form expression for the topological chirality in the form of a chiral spin current and use it to both characterize our states and predict the existence of other topological textures in other regions of phase space, for example, at N=5. Finally, we compare the spin textures of our numerically exact meron states to ansatz wave-functions of merons in quantum Hall droplets and find that the ansatz qualitatively describes the meron states.Comment: 4 pages, 5 figures; minor title change, typos fixe

The fine line between total and partial tidal disruption events

Flares from tidal disruption events are unique tracers of quiescent black holes at the centre of galaxies. The appearance of these flares is very sensitive to whether the star is totally or partially disrupted, and in this paper we seek to identify the critical distance of the star from the black hole (r_d) that enables us to distinguish between these two outcomes. We perform here Mesh-free Finite Mass, traditional, and modern Smoothed Particle Hydrodynamical simulations of star-black hole close encounters, with the aim of checking if the value of r_d depends on the simulation technique. We find that the critical distance (or the so-called critical disruption parameter beta_d) depends only weakly on the adopted simulation method, being beta_d=0.92\pm 0.02 for a gamma=5/3 polytrope and beta_d=2.01\pm 0.01 for a gamma=4/3 polytrope.Comment: 8 pages, 8 figures, 2 tables; accepted to A&

Large Polarization and Susceptibilities in Artificial Morphotropic Phase Boundary PbZr1−xTixO3 Superlattices

The ability to produce atomically precise, artificial oxide heterostructures allows for the possibility of producing exotic phases and enhanced susceptibilities not found in parent materials. Typical ferroelectric materials either exhibit large saturation polarization away from a phase boundary or large dielectric susceptibility near a phase boundary. Both large ferroelectric polarization and dielectric permittivity are attained wherein fully epitaxial (PbZr0.8Ti0.2O3)n/(PbZr0.4Ti0.6O3)2n (n = 2, 4, 6, 8, 16 unit cells) superlattices are produced such that the overall film chemistry is at the morphotropic phase boundary, but constitutive layers are not. Long- (n ≥ 6) and short-period (n = 2) superlattices reveal large ferroelectric saturation polarization (Ps = 64 µC cm−2) and small dielectric permittivity (εr ≈ 400 at 10 kHz). Intermediate-period (n = 4) superlattices, however, exhibit both large ferroelectric saturation polarization (Ps = 64 µC cm−2) and dielectric permittivity (εr = 776 at 10 kHz). First-order reversal curve analysis reveals the presence of switching distributions for each parent layer and a third, interfacial layer wherein superlattice periodicity modulates the volume fraction of each switching distribution and thus the overall material response. This reveals that deterministic creation of artificial superlattices is an effective pathway for designing materials with enhanced responses to applied bias