An Abstract Approach to Stratification in Linear Logic

We study the notion of stratification, as used in subsystems of linear logic with low complexity bounds on the cut-elimination procedure (the so-called light logics), from an abstract point of view, introducing a logical system in which stratification is handled by a separate modality. This modality, which is a generalization of the paragraph modality of Girard's light linear logic, arises from a general categorical construction applicable to all models of linear logic. We thus learn that stratification may be formulated independently of exponential modalities; when it is forced to be connected to exponential modalities, it yields interesting complexity properties. In particular, from our analysis stem three alternative reformulations of Baillot and Mazza's linear logic by levels: one geometric, one interactive, and one semantic

The difficulties in geometry: A quantitative analysis based on results of mathematics competitions in Italy

This paper focuses on the difficulties encountered by Italian students in performing geometry tasks. A quantitative analysis, aimed at understanding the extent of the phenomenon, is carried out using the results of district competitions from the year 2018 to 2020, comparing the scores obtained in geometry questions with those in other areas of Olympic mathematics. In addition, the answers given by the students to a questionnaire administered at the end of the 2020 district competition are analyzed in order to better understand possible motivations behind the phenomenon in question. The results obtained need further confirmation through future research on the topic but represent clear trends worthy of further investigation

Asymptotic Quantum Many-Body Scars

We consider a quantum lattice spin model featuring exact quasiparticle towers of eigenstates with low entanglement at finite size, known as quantum many-body scars (QMBS). We show that the states in the neighboring part of the energy spectrum can be superposed to construct entire families of low-entanglement states whose energy variance decreases asymptotically to zero as the lattice size is increased. As a consequence, they have a relaxation time that diverges in the thermodynamic limit, and therefore exhibit the typical behavior of exact QMBS although they are not exact eigenstates of the Hamiltonian for any finite size. We refer to such states as \textit{asymptotic} QMBS. These states are orthogonal to any exact QMBS at any finite size, and their existence shows that the presence of an exact QMBS leaves important signatures of non-thermalness in the rest of the spectrum; therefore, QMBS-like phenomena can hide in what is typically considered the thermal part of the spectrum. We support our study using numerical simulations in the spin-1 XY model, a paradigmatic model for QMBS, and we conclude by presenting a weak perturbation of the model that destroys the exact QMBS while keeping the asymptotic QMBS.Comment: 4.5 pages + supplementary information. 4+3 figure

Gender gap, ansia matematica e difficoltà in geometria dei gifted students in Italia: un'analisi su larga scala

Il presente lavoro affronta alcuni aspetti riguardanti gli studenti italiani che, dal 2017 al 2020, hanno partecipano alle gare matematiche organizzate dall’Unione Matematica Italiana. In particolare, è stato analizzato il fenomeno del gender gap, sia in termini di diversa partecipazione alle competizioni studentesche che in termini di performance. L’analisi combinata dei risultati delle competizioni e di un questionario somministrato al termine della gara di febbraio 2020 ai soli studenti del distretto di Roma ha permesso di evidenziare e approfondire le possibili cause alla base del divario. È stato osservato che le ragazze sottovalutano la loro prestazione, rinunciando talvolta a partecipare alle gare. Inoltre, le stesse hanno un’ansia da prestazione maggiore, dovuta principalmente alla volontà di non deludere le aspettative di famiglie ed insegnanti. Infine, a partire dai dati a disposizione, si è osservato che l’ambito che crea maggiori difficoltà è la geometria, nonostante i quesiti siano i più simili a quelli che gli studenti vedono in classe. Si cercherà quindi di dare una possibile interpretazione del problema e di delineare eventuali sviluppi futuri da portare avanti per una migliore comprensione del fenomeno.This paper addresses some aspects concerning Italian students who, from 2017 to 2020, participated in mathematical competitions organized by the Italian Mathematical Union. In particular, the gender gap phenomenon was analyzed, both in terms of different participation in student competitions and in terms of performance. The combined analysis of the results of the competitions and of a questionnaire administered at the end of the February 2020 competition to students in the Rome district alone allowed us to highlight and investigate the possible causes behind the gap. It was observed that girls underestimate their performance, sometimes giving up participating in competitions. They also have higher performance anxiety, mainly due to their desire not to disappoint the expectations of families and teachers. Finally, from the available data, it was observed that the area that creates the most difficulty is geometry, despite the fact that the questions are the most similar to those that students see in class. Thus, an attempt will be made to give a possible interpretation of the problem and outline possible future developments to be pursued for a better understanding of the phenomenon

Kinetic formation of trimers in a spinless fermionic chain

We show the stabilization of two trimer phases in a chain of spinless fermions with a correlated hopping term. A trimer fluid forms due to a gain in trimer kinetic energy and competes with a fluid of unbound fermions. Furthermore, we observe two intermediate phases where these two fluids coexist and do not spatially separate. Depending on the way trimers are created out of the Fermi sea, hybridization can occur, in which case the onset of correlations between the two fluids is well captured by a generalized BCS ansatz. These results are finally extended to the formation of larger multimers, which highlights the peculiarities of pair and trimer formation.Comment: 5+9 pages, 5+7 figure

Exact many-body scars based on pairs or multimers in a chain of spinless fermions

We construct a 1D model Hamiltonian of spinless fermions for which the spinless analogue of $\eta$-pairing states are quantum many-body scars of the model. These states are excited states and display subvolume entanglement entropy scaling; they form a tower of states that are equally spaced in energy (resulting in periodic oscillations in the Loschmidt echo and in the time evolution of observables for initial states prepared in a superposition of them) and are atypical in the sense that they weakly break the eigenstate thermalization hypothesis, while the other excited states are thermal. We conclude by presenting models with a tower of scar states generated by multimers located at the edge of the Brillouin zone.Comment: 8+9 pages, 4 figures. Extended version with additional results on multimer

Dorsal Prefrontal Cortex Impairment in Methoxetamine-Induced Psychosis: an 18F-FDG PET/CT Case Study

Submitted15 June 2018. Accepted 13 December 2018. Epub ahead of print 13 February 2019Novel psychoactive substances (NPSs) have currently become a major public health concern because of relatively easy accessibility to these compounds and difficulty in identifying them with routine laboratory techniques. Here, we report the 18 F-fluorodeoxyglucose positron emission tomography/computerized tomography ( 18 F-FDG PET/CT) case study of a 23-year-old man who developed a substance-induced psychotic disorder after having intravenously injected himself with an unspecified amount of methoxetamine (MXE), a ketamine derivative hallucinogen. From a clinical perspective, a blunted affective responsiveness with diminished social drive and sense of purpose, along with a profound detachment from the environment, was observed. Psychometric and neuropsychological assessments highlighted severe dissociative symptoms and lack of motivation, along with a mild impairment of verbal fluency, working memory, and attention. Patient’s 18 F-FDG PET/CT scans displayed a significant bilateral deficit of tracer uptake within the dorsolateral prefrontal cortex (DLPFC). DLPFC activity is critical to goal-oriented cognitive functions, including working memory and sustained attention. DLPFC is also involved in both the temporal integration across multiple sensory modes and in the volitional control of actions, leading to the possibility to construct logically coherent temporal configurations of thought, speech, and behavior. This report highlights that a single acute MXE intoxication may produce severe brain impairment.Peer reviewedFinal Accepted Versio