Sulla validità del principio di identità degli indiscernibili in meccanica quantistica: verso una nuova discernibilità debole

Lo scopo di questa tesi di dottorato è quello di discutere la controversa questione sulla validità del principio di identità degli indiscernibili di Leibniz in meccanica quantistica. In particolare, si esporrà un anuova relazone di discernibilità debole (WD) per particelle quantistiche, con l'obiettivo di risolvere le critiche sollevate dal Bigaj (2015). Il pioniere della WD è certamente Simon Saunders (2003, 2006) che ha dimostrato come sia possibile distinguere le particelle in meccanica quantistica con metodi basati sull'utilizzo di predicati qualitativi. Egli ha dimostrato che la WD, può essere applicata a fermioni. Il secondo sostenitore della WD è stato F. A. Muller che ha risolto le critiche sollevate contro Saunders (2008). Muller e Saunders (2008) hanno messo a punto la tecnica della distinguibilità dei fermioni con l'uso delle proprietà categoriali (cioè non probabilistici). Muller e Seevinck (2009) hanno esteso la discernibilità debole per tutte le particelle quantistiche. Bigaj (2015) ha sollevato il problema che la proposta di WD di Muller, Saunders, Seevinck è affetta da circolarità, poiché la scelta dell'operatore, su cui si applica la WD, cambia se le particelle sono o meno la stessa. Se si accettano le critiche di Bigaj, sembra opportuno cercare una nuova discernibilità debole, conciliando le posizioni di Muller, Saunders e Seevinck con quella di Bigaj. Secondo Bigaj (2015), quello che sarebbe giusto dire è che, se la relazione R, su cui si basa la WD, contiene l'identità numerica come una componente essenziale, allora la discernibilità diventa banale e l'intera struttura è circolare. Sarebbe desiderabile, invece, avere lo stesso operatore o almeno la stessa operazione sia nel caso in cui le particelle, a e b, sono a priori diverse sia quando sono uguali. Ad esempio una corretta relazione con un unico operatore O sarebbe tale da potersi scrivere: dove xy. Una nuova relazione di discernibilità debole deriva dall' uso della matrice di Gram, seguendo il formalismo della seconda quantizzazione. Se due particelle sono uguali allora la matrice di Gram ha determinante diverso da zero, altrimenti la matrice di Gram ha determinante pari a zero. Indicando con l'operatore G, l’operazione “determinante della matrice di Gram” è possibile definire la relazione R in questo modo: . Questa relazione soddisfa i requisiti di Bigaj (2015). Inoltre, soddisfa anche il requisito di Muller e Saunders (2008) circa l'invarianza per permutazione (dimostrazione banale). L’unico svantaggio è rappresentato dal significativo fisico non particolarmente incisivo di questo particolare operatore. Questa relazione è valida non solo per fermioni, ma anche per qualsiasi tipo di particella quantistica, come i bosoni

Evolutionary Dynamics and Accurate Perception. Critical Realism as an Empirically Testable Hypothesis

none5sìAbstract: Mathematical models can be profitably used to establish whether our perception of the external world is accurate. Donald Hoffman and his collaborators have developed a promising mathematical framework within which this question can be addressed and which is based on an exhaustive taxonomy of the different possible relations between perceptual representations and the external world. After reformulating their framework by means of an improved formal system, we discuss their application of evolutionary game theory, which appears to show that an essentially anti-realistic perceptual strategy would in the long run biologically outcompete its rivals. We argue that their model does not take the crucial biological significance of environmental changes into due consideration and propose alternative models which do. We conclude that a partially realistic representation would be favoured in our models.openVincenzo Fano; Adriano Angelucci; Gabriele Ferretti; Roberto Macrelli; Gino TarozziFano, Vincenzo; Angelucci, Adriano; Ferretti, Gabriele; Macrelli, Roberto; Tarozzi, Gin

Incidence and management of ulcerative keratitis in a pinnipeds population under human care

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A simple problem for simulating demographic noise in biological differential equation models: a discrepancy effect

Dynamical systems described by deterministic differential equations represent idealized situations where random implications are ignored. In the context of biomathematical modeling, the introduction of random noise must be distinguished between environmental (or extrinsic) noise and demographic (or intrinsic) noise. In this last context it is assumed that the variation over time is due to demographic variation of two or more interacting populations, and not to fluctuations in the environment. The modeling and simulation of demographic noise as a stochastic process affecting single units of the populations involved in the model are well known in the literature and they result in discrete stochastic systems. When the population sizes are large, these discrete stochastic processes converge to continuous stochastic processes, giving rise to stochastic differential equations. If noise is ignored, these stochastic differential equations turn to ordinary differential equations. The inverse process, i.e., inferring the effects of demographic noise on a natural system described by a set of ordinary differential equations, is an issue addressed in a recent paper by Carletti M, Banerjee M, A backward technique for demographic noise in biological ordinary differential equation models, Mathematics 7:1204, 2019. In this paper we show an example of how the technique to model and simulate demographic noise going backward from a deterministic continuous differential system to its underlying discrete stochastic process can provide a discrepancy effect, modifying the dynamics of the deterministic model

A First Application of the Backward Technique in Social Sciences: Exploring Demographic Noise in a Model with Three Personality Types

Abstract: In the realm of dynamical systems described by deterministic differential equations used in biomathematical modeling, two types of random events influence the populations involved in the model: the first one is called environmental noise, due to factors external to the system; the second one is called demographic noise, deriving from the inherent randomness of the modeled phenomenon. When the populations are small, only space-discrete stochastic models are capable of describing demographic noise; when the populations are large, these discrete models converge to continuous models described by stochastic ordinary differential systems, maintaining the essence of intrinsic noise. Moving forward again from a continuous stochastic framework, we get to the continuous deterministic setting described by ordinary differential equations if we assume that noise can be neglected. The inverse process has recently been explored in the literature by means of the so-called “backward technique” in a biological context, starting from a system of continuous ordinary differential equations and going “backward” to the reconstruction and numerical simulation of the underlying discrete stochastic process, that models the demographic noise intrinsic to the biological phenomenon. In this study, starting from a predictable, deterministic system, we move beyond biology and explore the effects of demographic noise in a novel model arising from the social sciences. Our field will be psychosocial, that is, the connections and processes that support social relationships between individuals. We consider a group of individuals having three personality types: altruistic, selfish, and susceptible (neutral). Applying the backward technique to this model built on ordinary differential equations, we demonstrate how demographic noise can act as a switching factor, i.e., moving backward from the deterministic continuous model to the discrete stochastic process using the same parameter values, a given equilibrium switches to a different one. This highlights the importance of addressing demographic noise when studying complex social interactions. To our knowledge, this is also the first time that the backward technique has been applied in social contexts

Preliminary Ultrasonographic Study of Healthy California Sea Lion (Zalophus californianus) Pregnancy and Fetal Development

Reproductive success is an important aspect of marine mammals’ population health, as it is an indicator of the trajectory for the population into the future. The aim of this study is to provide additional relevant data on fetus–maternal ultrasonographic monitoring in sea lion species, in order to evaluate possible fetal distress or abnormalities. From 2018 to 2023, serial ultrasonographic scans of two healthy California sea lion females (16 ± 4 years old), kept under human care, were performed over the course of two pregnancies for each female. Animals were monitored from the ovulation to the delivery. Ultrasonography was performed weekly, and, during the last month, daily images were recorded using Logiq Versana Active, General Electric, with a 2–5 MHz curvilinear transducer, and Logiq V2, General Electric, with a 2–5 MHz curvilinear transducer. Right and left lateral recumbencies have been used during the examination. To the author’s knowledge, this is the first study describing in detail the sea lion organogenesis and their correlation with the stage of pregnancy

Hand-Rearing of Three Lesser Flamingo Chicks (Phoeniconaias minor)

There are few published studies regarding lesser flamingo (Phoeniconaias minor) reproduction, crop milk composition, and hand-rearing under human care. Between the end of June and the beginning of August of 2017, three eggs were laid in a group of 29 lesser flamingos kept under human care. Two eggs and one chick were abandoned by the parents, and three chicks were hand-reared. This report describes diet composition, dietary intake, feeding protocols, and growth index, from the first day to 60 days after hatching, for three lesser flamingo chicks.</jats:p