GRB 970228 Revisited: Evidence for a Supernova in the Light Curve and La te Spectral Energy Distribution of the Afterglow

At the time of its discovery, the optical and X-ray afterglow of GRB 970228 appeared to be a ringing endorsement of the previously untried relativistic fireball model of gamma-ray burst (GRB) afterglows, but now that nearly a dozen optical afterglows to GRBs have been observed, the wavering light curve and reddening spectrum of this afterglow make it perhaps the most difficult of the observed afterglows to reconcile with the fireball model. In this Letter, we argue that this afterglow's unusual temporal and spectral properties can be attributed to a supernova that overtook the light curve nearly two weeks after the GRB. This is the strongest case yet for a GRB/supernova connection. It strengthens the case that a supernova also dominated the late afterglow of GRB 980326, and the case that GRB 980425 is related to SN 1998bw.Comment: Accepted to The Astrophysical Journal (Letters), 14 pages, LaTe

A Framework to Assess Social Indicators in a Circular Economy Perspective

The thriving circular economy is expected to contribute to all three dimensions of sustainable development: environmental, economic, and social. This paper aims to propose a framework to assess social indicators to support circular business models. To validate the framework, we conducted a case study in a medium-size Italian footwear luxury industry, using the Value Focused Thinking-VFT. This approach was used to define proper social indicators to measure the perception of the company's managers related to the level of incorporation of social dilemmas in the company. We collect data through interviews, documental analysis and direct observation from October/2019 until August/2020 and apply a questionnaire in 2020/2021. The novelty of this paper lies in the proposition of a framework to assess the social indicators in broad categories, capable of covering all supply chains: Corporation, Community; Consumers; Suppliers; Human Rights and Human Resources. Another novelty is related to the analysis of indicators in terms of strategic, tactical, and operational levels, similarly to the idea of a Balanced Scorecard, which was allowed by applying the VFT approach

A Photometric Investigation of the GRB970228 Afterglow and the Associated Nebulosity

We carefully analyze the WFPC2 and STIS images of GRB970228. We measure magnitudes for the GRB970228 point source component in the WFPC2 images of $V=26.20^{+0.14}_{-0.13}$, $I_c=23.94^{+0.10}_{-0.09}$ and $V=26.52^{+0.16}_{-0.18}$, $I_c=24.31^{+0.15}_{-0.11}$ on March 26 and April 7, respectively; and $R_c=27.09^{+0.14}_{-0.14}$ on September 4 in the STIS image. For the extended component, we measure magnitudes of $R_c=25.48^{+0.22}_{-0.20}$ in the combined WFPC2 images and $R_c=25.54^{+0.33}_{-0.22}$ in the STIS image, which are consistent with no variation. This value is fainter than previously reported (Galama et al. 98) and modifies the previously assumed magnitudes for the optical transient when it faded to a level where the extended source component contribution was not negligible, alleviating the discrepancy to a power-law temporal behavior. We also measure a color of $V_{606}-I_{814}=-0.18^{+0.51}_{-0.61}$ for the extended source component. Taking into account the extinction measured in this field (Castander & Lamb 1998), this color implies that the extended source is most likely a galaxy with ongoing star formation.Comment: 21 pages, including 8 figures. Submitted to Ap

Metal abundances in extremely distant Galactic old open clusters. II. Berkeley 22 and Berkeley 66

We report on high resolution spectroscopy of four giant stars in the Galactic old open clusters Berkeley~22 and Berkeley~66 obtained with HIRES at the Keck telescope. We find that $[Fe/H]=-0.32\pm0.19$ and $[Fe/H]=-0.48\pm0.24$ for Berkeley~22 and Berkeley~66, respectively. Based on these data, we first revise the fundamental parameters of the clusters, and then discuss them in the context of the Galactic disk radial abundance gradient. We found that both clusters nicely obey the most updated estimate of the slope of the gradient from \citet{fri02} and are genuine Galactic disk objects.Comment: 20 pages, 6 eps figures, accepted for publication in the Astronomical Journa

Learning activation functions from data using cubic spline interpolation

Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementations simply select one fixed function from a small set of candidates, which is not adapted during training, and is shared among all neurons throughout the different layers. However, neither two of these assumptions can be supposed optimal in practice. In this paper, we present a principled way to have data-dependent adaptation of the activation functions, which is performed independently for each neuron. This is achieved by leveraging over past and present advances on cubic spline interpolation, allowing for local adaptation of the functions around their regions of use. The resulting algorithm is relatively cheap to implement, and overfitting is counterbalanced by the inclusion of a novel damping criterion, which penalizes unwanted oscillations from a predefined shape. Experimental results validate the proposal over two well-known benchmarks.Comment: Submitted to the 27th Italian Workshop on Neural Networks (WIRN 2017

Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with negative constant drift, described by a Fokker-Planck equation with a potential V(x) = - [b \ln(x) + a\, x], for b>0 and a<0. The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process, that has been extensively studied for its applications in physics, biology and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schroedinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a negative constant drift. We conclude with a comparison with other analytical methods and with numerical solutions.Comment: 21 pages, 8 figure

The Thermodynamic Uncertainty Theorem

Thermodynamic uncertainty relations (TURs) express a fundamental tradeoff between the precision (inverse scaled variance) of any thermodynamic current by functionals of the average entropy production. Relying on purely variational arguments, we significantly extend these inequalities by incorporating and analyzing the impact of higher statistical cumulants of entropy production within a general framework of time-symmetrically controlled computation. This allows us to derive an exact expression for the current that achieves the minimum scaled variance, for which the TUR bound tightens to an equality that we name Thermodynamic Uncertainty Theorem (TUT). Importantly, both the minimum scaled variance current and the TUT are functionals of the stochastic entropy production, thus retaining the impact of its higher moments. In particular, our results show that, beyond the average, the entropy production distribution's higher moments have a significant effect on any current's precision. This is made explicit via a thorough numerical analysis of swap and reset computations that quantitatively compares the TUT against previous generalized TURs. Our results demonstrate how to interpolate between previously-established bounds and how to identify the most relevant TUR bounds in different nonequilibrium regimes