On the Maximal Invariant Statistic for Adaptive Radar Detection in Partially-Homogeneous Disturbance with Persymmetric Covariance

This letter deals with the problem of adaptive signal detection in partially-homogeneous and persymmetric Gaussian disturbance within the framework of invariance theory. First, a suitable group of transformations leaving the problem invariant is introduced and the Maximal Invariant Statistic (MIS) is derived. Then, it is shown that the (Two-step) Generalized-Likelihood Ratio test, Rao and Wald tests can be all expressed in terms of the MIS, thus proving that they all ensure a Constant False-Alarm Rate (CFAR).Comment: submitted for journal publicatio

Rational approximations of f(R)f(R) cosmography through Pad\'e polynomials

We consider high-redshift $f(R)$ cosmography adopting the technique of polynomial reconstruction. In lieu of considering Taylor treatments, which turn out to be non-predictive as soon as $z>1$, we take into account the Pad\'e rational approximations which consist in performing expansions converging at high redshift domains. Particularly, our strategy is to reconstruct $f(z)$ functions first, assuming the Ricci scalar to be invertible with respect to the redshift $z$. Having the thus-obtained $f(z)$ functions, we invert them and we easily obtain the corresponding $f(R)$ terms. We minimize error propagation, assuming no errors upon redshift data. The treatment we follow naturally leads to evaluating curvature pressure, density and equation of state, characterizing the universe evolution at redshift much higher than standard cosmographic approaches. We therefore match these outcomes with small redshift constraints got by framing the $f(R)$ cosmology through Taylor series around $z\simeq 0$. This gives rise to a calibration procedure with small redshift that enables the definitions of polynomial approximations up to $z\simeq 10$. Last but not least, we show discrepancies with the standard cosmological model which go towards an extension of the $\Lambda$CDM paradigm, indicating an effective dark energy term evolving in time. We finally describe the evolution of our effective dark energy term by means of basic techniques of data mining.Comment: 11 pages, 14 figures, accepted for publication in JCA

High-energy γ\gamma-ray emission from GRBs

GRBs are nowadays a rather well understood phenomenon in the soft (KeV-MeV) $\gamma$-ray energy band, while only a few GRBs have been observed at high photon energies (E_{\gamma} \ut > 1 GeV). It is also widely recognized that GRBs accelerate protons to relativistic energies and that dense media are often present nearby the sources. Within this framework we compute in detail the high-energy $\gamma$-ray flux from the decay of neutral pions produced through the interaction of accelerate protons with nucleons in the surrounding medium. We also take into account the local and intergalactic $\gamma$-ray absorption. The presence of magnetic fields around the GRB sources causes the deflection of the accelerated protons and so a temporal spread of the produced high-energy $\gamma$-rays with respect to the signal in the soft $\gamma$-ray band. Moreover, we analyze the possibility to detect the $\gamma$-ray signal in the GeV-TeV energy range by the ARGO detector under construction in Tibet.Comment: 9 pages, 7 figures, abstract shortened, to appear in Astronomy and Astrophysic

Model Order Selection Rules For Covariance Structure Classification

The adaptive classification of the interference covariance matrix structure for radar signal processing applications is addressed in this paper. This represents a key issue because many detection architectures are synthesized assuming a specific covariance structure which may not necessarily coincide with the actual one due to the joint action of the system and environment uncertainties. The considered classification problem is cast in terms of a multiple hypotheses test with some nested alternatives and the theory of Model Order Selection (MOS) is exploited to devise suitable decision rules. Several MOS techniques, such as the Akaike, Takeuchi, and Bayesian information criteria are adopted and the corresponding merits and drawbacks are discussed. At the analysis stage, illustrating examples for the probability of correct model selection are presented showing the effectiveness of the proposed rules

The Gauge-Bethe Correspondence and Geometric Representation Theory

The Gauge/Bethe correspondence of Nekrasov and Shatashvili relates the spectrum of integrable spin chains to the ground states of supersymmetric gauge theories. Up to now, this correspondence has been an observation; the underlying reason for its existence remaining elusive. We argue here that geometrical representation theory is the mathematical foundation of the Gauge/Bethe correspondence, and it provides a framework to study families of gauge theories in a unified way.Comment: 8 page