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2025 marks the 300th birthday of Father Eliseo della Concezione, professor of Experimental Physics at the Royal Academy of Studies of Palermo. To celebrate this anniversary, the Physics and Chemistry Library of the University Library System and the Department of Physics and Chemistry - Emilio Segre' have organized several cultural activities. In the article, after a brief biographical description of Father Eliseo della Concezione, we will present the activities carried out and discuss the historical and educational aspects of Father Eliseo's work carried out during his stay at the Royal Academy of Palermo at the end of 18th century.
With the proliferation of domain-specific models, model merging has emerged as a set of techniques that combine the capabilities of multiple models into one that can multitask without the cost of additional training. In this paper, we propose a new model merging technique, Drop and rEscaLe via sampLing with mAgnitude (DELLA-Merging), that employs a novel pruning technique, MAGPRUNE, which shows significant advantages over DARE and TIES. MAGPRUNE first ranks the parameters in order of their magnitude and assigns higher dropout probabilities (p) to parameters with lower ranks corresponding to lower magnitudes. To approximate the original embeddings, MAGPRUNE employs a rescaling operation on the parameters that survive the random dropping by 1/(1 - p). On three different expert models considered for merging (LM, Math, Code) and corresponding benchmark datasets (AlpacaEval, GSM8K, MBPP), DELLA shows an average improvement of 2.4 points over baseline methods employing delta parameter pruning (an improvement of 3.6 points over TIES, 1.2 points over DARE), and 11.1 points over the no-pruning baseline (TA). We release the source code at: https://github.com/declare-lab/della.
In the present work it is evaluated the evolutionary state of the Orion Belt stars, an asterism very important for the ancient Egyptians, finding that, when the pyramids were built, the brightness of the three stars of the Belt was practically the same as today. This not trivial result has important implications in the framework of the so-called Orion Correlation Theory, a controversial theory proposed by Bauval and Gilbert (1994), according to which a perfect coincidence would exist between the disposition of the three stars of the Orion Belt and that of the main Giza pyramids, so that the latter would represent the monumental reproduction on the ground of that important asterism. ---- Nel presente lavoro viene determinato lo stato evolutivo delle stelle della Cintura di Orione, ricavando che, all'epoca della costruzione delle piramidi, la luminosita' delle tre stelle della Cintura era di fatto uguale a quella odierna. Tale non banale risultato riveste una importanza fondamentale nell'ambito della verifica della controversa Teoria della Correlazione di Orione proposta da Bauval e Gilbert nel 1994, secondo la quale esisterebbe una perfetta coincidenza tra la disposizione delle tre
In the present thesis we study absorption spectra of spin polarized isolated systems. Thus we introduce the density functional theory (DFT) formalism and its time dependent extension (TDDFT) together with the approximation used. In particula the Casida formulation of TDDFT is described. The equations for the description of open shell systems have been implemented in the abinit code. Then we used the BeH molecule as a test case. Studying the results for this molecule we underline the limits of the commonly used approximations. In particular we discuss why the the spin symmetry of excited states is broken and we propose a rule to find which excitation energies are affected by this problem. Finally, in the last part, we discuss how a better approximation could be obtained starting from the many body perturbation theory. ----- Il lavoro della presente tesi è focalizzato sullo studio dello spettro di eccitazione di sistemi isolati spin polarizzati. Quindi vengono esposte la Density Functional Theory (DFT), la sua estensione al caso dipendente dal tempo (TDDFT) e le approssimazioni utilizzate. In particolare vien esposta la formulazione di Casida della TDDFT. Le equazioni per lo studio d
La teoria di Lagrange per i moti secolari delle eccentricità ed inclinazioni delle orbite planetarie si fondava su un'approssimazione, dettata in larga misura dalla complessità dei calcoli necessari, che consisteva nel considerare solo equazioni lineari. In questa memoria riprendiamo in considerazione i metodi di Lagrange alla luce della teoria della stabilità esponenziale di Nekhoroshev. Grazie agli algoritmi sviluppati negli ultimi anni e alle tecniche di manipolazione algebrica possiamo tener conto anche dei contributi non lineari alle equazioni. Come applicazione cerchiamo di determinare i tempi di stabilità per il problema dei tre corpi nel caso del Sole e dei due pianeti maggiori, Giove e Saturno, mostrando che si possono ottenere risultati realistici, ancorché non ottimali. Lagrange's theory for the secular motion of perihelia and nodes of the planetary orbits was based on consideration of a linear approssimation of the dynamical equations, compatible with the complexity of the calculations. We extend Lagrange's investigations in the light of Nekhoroshev's theory of exponential stability. Using effective algorithms recently developed and computer algebra we investigate the n
We address the phenomenon of reflection in concave spherical mirror in two contrasting approaches to optics. In his Optics (ca.165) Ptolemy applied the cathetus principle as a regulative means for explaining qualitatively effects related to visual perception in concave spherical mirror. By contrast, Della Porta's study of reflection in concave spherical mirror in Bk. 17, Ch. 4 of his Magia naturalis (1589) and De refractione (1593), was based on the assumption that there is a reciprocal relation between reflection in concave spherical mirror and refraction in glass sphere. We juxtapose these two studies and draw several philosophical lessons from the comparison between these two practices with a view to throwing into relief the fundamental differences in their respective conceptions of optics.
In the article, we will report on the recovery of a Melloni's optical bench built at the end of 1800 by the "macchinista" Filippo Caliri in the "belle époque" of Palermo. A scientific instrument of particular historical and didactic interest belonging to the collection of Liceo Classico Statale "Umberto I" of Palermo. In the article, we will discuss the technical aspects of the interventions carried out. In questo articolo discuteremo del recupero di uno strumento scientifico di particolare interesse storico-didattico appartenente alla Collezione del Liceo Classico Statale "Umberto I" di Palermo: un raro banco ottico del Melloni costruito alla fine del 1800 nella Palermo della "belle époque" dal "macchinista" Filippo Caliri. Nell'articolo discuteremo gli aspetti tecnici degli interventi conservativi effettuati.
English: If the current status of theoretical and experimental knowledge in Nuclear Physics could be reduced to a geographical chart or a planisphere, then our epoch would be in some respect comparable to the end of the Medieval age and in other to the beginning of the Reinassance: epochs in which, together with the consolidated knowledge of the Old World, there have been great and revolutionary expeditions as the discovery of America or the periplus of Cape of Good Hope, explorations aimed at reaching the limits that, along the centuries, have lead to more and more engaging scientific discoveries in more and more far away lands, ending only in the twentieth century with the complete mapping of all the continents. Nuclear Physics is living an analogous adventure on the plane of contrast... - Italian: Se lo stato attuale delle conoscenze teoriche e sperimentali della Fisica Nucleare si potesse ridurre a una carta geografica o un mappamondo, allora la nostra epoca si potrebbe paragonare per certi versi alla fine del Medioevo e per altri al Rinascimento: epoche in cui, accanto alla conoscenza consolidata del Vecchio mondo, ci furono grandi e rivoluzionarie spedizioni come la scoperta
Even if laboratory practice is essential for all scientific branches of knowledge, it is often neglected at High School, due to lack of time and/or resources. To establish a closer contact between school and experimental sciences, the University Sapienza of Roma and the Istituto Nazionale di Fisica Nucleare (INFN) launched the Lab2Go project, with the goal of spreading laboratory practice among students and teachers in high schools.
We derive refined entropy upper bounds for $q$-ary $B_2$ codes by exploiting the Fourier structure of the i.i.d. difference distribution $D=X-Y$. Since the pmf of $D$ is an autocorrelation, its Fourier series is a nonnegative trigonometric polynomial of degree at most $q-1$. This leads to a natural convex relaxation over candidate difference distributions, equivalently expressible through an infinite family of positive semidefinite Toeplitz constraints. The resulting formulation admits a simple Gram interpretation and yields certified upper bounds through truncated semidefinite programs. Combined with the prefix-suffix method, this gives improved asymptotic rate upper bounds for $q$-ary $B_2$ codes; in particular, for $q\in\{9,10,11,12,13\}$ the resulting values improve on the best bounds known in the literature. We also study binary constant-weight $B_2$ codes. Extending the distance-distribution method of Cohen, Litsyn, and Zémor to the constant-weight setting, and combining it with Litsyn's asymptotic linear-programming bound for constant-weight codes, we derive a new upper bound on the constant-weight $B_2$ rate.
We discuss implementation details of OSCAR's serialization framework, highlighting the design decisions that allow the fine tuning of serialization methods for specific use cases. In particular, we show how the mrdi file format can be used for distributed computing.
In the last years the attention towards topological dynamical properties of highly discontinuous maps has increased significantly. In [D.Corona, A. Della Corte. The critical exponent functions. Comptes Rendus Mathématique, 360(G4), 315-332, 2022], a class of densely discontinuous interval maps, called "critical exponent maps", was introduced. These maps are defined through the word-combinatorics concept of critical exponent applied to the binary expansion of reals and show highly chaotically properties as well as some challenging problems. In this paper we identify an error in the proof of Theorem 7 in [D.Corona, A. Della Corte. The critical exponent functions. Comptes Rendus Mathématique, 360(G4), 315-332, 2022], a purely combinatorial result which in fact does not hold. We show that most of the results in [D.Corona, A. Della Corte. The critical exponent functions. Comptes Rendus Mathématique, 360(G4), 315-332, 2022], obtained there through Theorem 7, can be recovered. Moreover, we propose as a conjecture a weaker form of Theorem 7.
We study the efficiency of the first Dirichlet eigenfunction $u$ on bounded convex domains $Ω\subset \mathbb{R}^N$, defined as the ratio between the mean value of $u$ on $Ω$ and its maximum value. By exploiting improved log-concavity estimates, we establish new sharp lower bounds for the first eigenvalue $λ_1$ and upper bounds for the efficiency in terms of the geometry of the domain, refining classical inequalities by Payne, Stakgold, and Hersch. Furthermore, we investigate the asymptotic behavior of the efficiency for elongating planar convex domains, making use of 1D limit profiles and Schr{ö}dinger operators with convex potentials. As a main consequence of our analysis, we prove that among all planar convex domains the Payne-Stakgold upper bound is not optimal, and that there exists a maximizer of the efficiency.
Black holes (BHs) play a major role in the structural and dynamical evolutions of Globular Clusters (GCs). Several recent works searched for BHs in Galactic GCs using scaling relations derived from numerical simulations. However, the conclusions drawn by such approaches are strongly dependent on the specific prescriptions adopted in numerical simulations. Therefore, we analyzed a survey of 101 Monte Carlo simulations to identify some observable parameters that allow us to probe the present-day BH population in GCs reliably. We thoroughly show that a single observable is not suited to infer the BH mass fraction in real GCs: similar values could be attained by systems with different BH mass fractions, depending on the specific dynamical evolution of the system. Finally, we present a combination of observable parameters that efficiently breaks this degeneracy. We also compare values from numerical simulations with a sample of Galactic GCs.
In this paper, we bound the rate of linear codes in $\mathbb{F}_q^n$ with the property that any $k\leq q$ codewords are all simultaneously distinct in at least $d_k$ coordinates. For the case of particular interest $q=k=3$ we recover, with a simpler proof, state of the art results in the case $d_3=1$ and new bounds for $d_3>1$. We finally discuss some related open problems on the list-decoding zero-error capacity of discrete memoryless channels.
Practical mechanisms often limit agent reports to constrained formats like trades or orderings, potentially limiting the information agents can express. We propose a novel class of mechanisms that elicit agent reports in natural language and leverage the world-modeling capabilities of large language models (LLMs) to select outcomes and assign payoffs. We identify sufficient conditions for these mechanisms to be incentive-compatible and efficient as the LLM being a good enough world model and a strong inter-agent information over-determination condition. We show situations where these LM-based mechanisms can successfully aggregate information in signal structures on which prediction markets fail.
Even though a variety of methods have been proposed in the literature, efficient and effective latent-space control (i.e., control in a learned low-dimensional space) of physical systems remains an open challenge. We argue that a promising avenue is to leverage powerful and well-understood closed-form strategies from control theory literature in combination with learned dynamics, such as potential-energy shaping. We identify three fundamental shortcomings in existing latent-space models that have so far prevented this powerful combination: (i) they lack the mathematical structure of a physical system, (ii) they do not inherently conserve the stability properties of the real systems, (iii) these methods do not have an invertible mapping between input and latent-space forcing. This work proposes a novel Coupled Oscillator Network (CON) model that simultaneously tackles all these issues. More specifically, (i) we show analytically that CON is a Lagrangian system - i.e., it possesses well-defined potential and kinetic energy terms. Then, (ii) we provide formal proof of global Input-to-State stability using Lyapunov arguments. Moving to the experimental side, we demonstrate that CON rea
The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower bounds on the length of the switching intervals. We adapt and extend the existing theory of multiple Lyapunov functions, providing converse results and thus a complete characterization of uniform stability for this class of systems. We specify our results in the context of switched linear systems, providing the equivalence of exponential stability and the existence of multiple Lyapunov norms. By restricting the class of candidate Lyapunov functions to the set of quadratic functions, we are able to provide semidefinite-optimization-based numerical schemes to check the proposed conditions. We provide numerical examples to illustrate our approach and highlight its advantages over existing methods.
Recent advances in deep reinforcement learning have achieved impressive results in a wide range of complex tasks, but poor sample efficiency remains a major obstacle to real-world deployment. Soft actor-critic (SAC) mitigates this problem by combining stochastic policy optimization and off-policy learning, but its applicability is restricted to distributions whose gradients can be computed through the reparameterization trick. This limitation excludes several important examples such as the beta distribution, which was shown to improve the convergence rate of actor-critic algorithms in high-dimensional continuous control problems thanks to its bounded support. To address this issue, we investigate the use of implicit reparameterization, a powerful technique that extends the class of reparameterizable distributions. In particular, we use implicit reparameterization gradients to train SAC with the beta policy on simulated robot locomotion environments and compare its performance with common baselines. Experimental results show that the beta policy is a viable alternative, as it outperforms the normal policy and is on par with the squashed normal policy, which is the go-to choice for S
In contemporary society, social networks accelerate decision dynamics causing a rapid switch of opinions in a number of fields, including the prevention of infectious diseases by means of vaccines. This means that opinion dynamics can nowadays be much faster than the spread of epidemics. Hence, we propose a Susceptible-Infectious-Removed epidemic model coupled with an evolutionary vaccination game embedding the public health system efforts to increase vaccine uptake. This results in a global system ``epidemic model + evolutionary game''. The epidemiological novelty of this work is that we assume that the switching to the strategy ``pro vaccine'' depends on the incidence of the disease. As a consequence of the above-mentioned accelerated decisions, the dynamics of the system acts on two different scales: a fast scale for the vaccine decisions and a slower scale for the spread of the disease. Another, and more methodological, element of novelty is that we apply Geometrical Singular Perturbation Theory (GSPT) to such a two-scale model and we then compare the geometric analysis with the Quasi-Steady-State Approximation (QSSA) approach, showing a criticality in the latter. Later, we app