On some aspects of mock and quantum modularity in theoretical physics

This thesis explores some aspects of mock and quantum modularity in two different topics arising from String Theory. The first topic is umbral moonshine, a series of surprising relations connecting representations of finite groups, mock modular forms, and K3 sigma models. Chapter 2 presents the construction of vertex algebra modules for some instances of umbral moonshine. This is achieved via the construction of cone vertex algebra modules whose graded traces can be expressed in terms of indefinite theta functions.The second topic concerns a family of three-manifold invariants conjecturally related to Chern-Simons invariants. Chapter 3 explores the connection between mock theta functions and these invariants for Brieskorn spheres and gauge group SU(2). Using a relationship between the latter and mock modular forms obtained by indefinite theta functions, a regularisation procedure is proposed for the expression of the studied invariants under orientation reversal. Chapter 4 explores the connection with quantum modular forms of higher depth, and presents a conjectured recursive relation connecting the invariants for a gauge group of rank n to the invariants for gauge groups of lower ranks. This relation is proven for gauge group SU(3) for the invariants of Brieskorn spheres

A Reinforcement Learning Approach to the Design of Quantum Chains for Optimal Energy Transfer

We propose a bottom-up approach, based on Reinforcement Learning, to the design of a chain achieving efficient excitation-transfer performances. We assume distance-dependent interactions among particles arranged in a chain under tight-binding conditions. Starting from two particles and a localised excitation, we gradually increase the number of constitutents of the system so as to improve the transfer probability. We formulate the problem of finding the optimal locations and numbers of particles as a Markov Decision Process: we use Proximal Policy Optimization to find the optimal chain-building policies and the optimal chain configurations under different scenarios. We consider both the case in which the target is a sink connected to the end of the chain and the case in which the target is the right-most particle in the chain. We address the problem of disorder in the chain induced by particle positioning errors. We are able to achieve extremely high excitation transfer in all cases, with different chain configurations and properties depending on the specific conditions.Comment: 8 pages, 6 figure

Seismic location improvements from an OBS/H temporary network in Southern Tyrrhenian Sea

We present the first investigation performed on the seismicity of Southern Tyrrhenian Sea, off-shore Sicily with the contribution of data from broad-band ocean bottom seismometers and hydrophones (OBS/H). Offshore data were recorded during the TYrrhenian Deep sea Experiment (TYDE) from December 2000 to May 2001 in the Southern Tyrrhenian Sea. Hypocenter locations of a cluster of 53 seismic events occurred in March 2001 in north-eastern Sicily were estimated by the integration of land (permanent network) and offshore (temporary network) data and compared with locations estimated from land data only. The scatter of the cluster was evaluated by dispersion parameters. The off-shore data significantly reduced the scatter of the swarm hypocenters also restricting the depth range of the cluster. Moreover, space trends of the event distribution originally shown by the land data were only partially confirmed by the land-sea joint data. In order to assess the efficiency in terms of hypocenter mislocations in the subject area, of a land-sea integrated network with respect to a land-based network, we performed simulations by assuming a grid distribution of earthquakes and a recent local 3D velocity model, computing synthetic arrival times of body waves to the stations of both network configurations (integrated and land-based) perturbing the computed times and relocating earthquakes by inversion. The results of the synthetic tests demonstrated that the presence of sea bottom stations in the Tyrrhenian basin can reduce the mislocations of large magnitude and/or superficial earthquakes in the southernmost Calabria and Messina Strait and of low magnitude and/or deep earthquakes in north-eastern Sicily. The major accuracy of synthetic earthquake locations obtained including OBS/H data provides an additional support to the interpretation of the cluster occurred in March 2001 and to the opportunity of long-term installation of an off-shore network like TYDE in the study region

Molecular Detection of Babesia spp. (Apicomplexa: Piroplasma) in Free-Ranging Canids and Mustelids From Southern Italy.

Babesiosis is an emerging tick-borne disease caused by apicomplexan parasites with widespread geographical distribution and various wildlife species as reservoir hosts. The aims of this study were to investigate the prevalence and assess the role of free-ranging canids and mustelids in the maintenance of Babesia spp. in southern Italy. PCR analysis of splenic samples targeting the 18S rRNA gene revealed the presence of Babesia spp. in 36 of 82 (43.9%) red foxes (Vulpes vulpes) including 29 (58%) from Campania region and seven (21.8%) from Calabria region, in seven of 13 (53.8%) Eurasian badgers (Meles meles), and in one of 13 (7.7%) gray wolves (Canis lupus). Samples from other host species including 9 Eurasian otters (Lutra lutra), 1 stone marten (Martes foina), 1 least weasel (Mustela nivalis), and 1 European polecat (Mustela putorius) tested Babesia spp. negative. Sequence analysis of the 18S rRNA gene demonstrated the presence of B. vulpes in the red fox and two sequence types of badger-associated Babesia spp. in the Eurasian badger. The Babesia sp. sequence detected in the gray wolf was identical to a badger-associated Babesia sp. This study shows that the number of Babesia spp. infecting free-ranging carnivores in Italy is higher than currently believed, and suggests that these hosts may play an important role in the maintenance of the sylvatic cycle of these parasites. It is the first report of badger-associated Babesia spp. in Italy and in a gray wolf

A tutorial on optimal control and reinforcement learning methods for quantum technologies

Quantum Optimal Control is an established field of research which is necessary for the development of Quantum Technologies. In recent years, Machine Learning techniques have been proved useful to tackle a variety of quantum problems. In particular, Reinforcement Learning has been employed to address typical problems of control of quantum systems. In this tutorial we introduce the methods of Quantum Optimal Control and Reinforcement Learning by applying them to the problem of three-level population transfer. The jupyter notebooks to reproduce some of our results are open-sourced and available on github1

Reinforcement learning-enhanced protocols for coherent population-transfer in three-level quantum systems

We deploy a combination of reinforcement learning-based approaches and more traditional optimization techniques to identify optimal protocols for population transfer in a multi-level system. We constrain our strategy to the case of fixed coupling rates but time-varying detunings, a situation that would simplify considerably the implementation of population transfer in relevant experimental platforms, such as semiconducting and superconducting ones. Our approach is able to explore the space of possible control protocols to reveal the existence of efficient protocols that, remarkably, differ from (and can be superior to) standard Raman, stimulated Raman adiabatic passage or other adiabatic schemes. The new protocols that we identify are robust against both energy losses and dephasing

Analyzing post modern consumer behavior and beef consumption patterns: Insights from Sicilian market

In current events, consumers are subject to various stimuli (advertising campaigns, popular magazines, social) that affect their marginal consumption propensity. However, as Economic Theory teaches us, the marginal propensity to consume does not necessarily translate into consumer spending. This is strongly affected by consumers' eating habits and other variables that determine where the consumption phenomenon occurs. The study aims to analyze post-modern consumer behavior toward beef consumption. An online questionnaire was administered to 535 Sicilian participants to achieve this goal. Statistical analyses were performed by R statistical software, using two-tailed P-values, and setting statistical significance at P <= 0.05. The results show that consumption choices are influenced by beef meat's impact on health. In addition, consumers consider the origin and certifications of the raw material to be extremely crucial

Volcanic tremor at Mt. Etna, Italy, preceding and accompanying the eruption of July-August, 2001

The July 17 – August 9, 2001 flank eruption of Mt. Etna was preceded and accompanied by remarkable changes in volcanic tremor. Based on the records of stations belonging to the permanent seismic network deployed on the volcano, we analyze amplitude and frequency content of the seismic signal. We find considerable changes in the volcanic tremor which mark the transition to different styles of eruptive activity, e.g., lava fountains, phreatomagmatic activity, Strombolian explosions. In particular, the frequency content of the signal decreases from 5 Hz to 3 Hz at our reference station ETF during episodes of lava fountains, and further decreases at about 2 Hz throughout phases of intense lava emission. The frequency content and the ratios of the signal amplitude allow us to distinguish three seismic sources, i.e., the peripheral dike which fed the eruption, the reservoir which fed the lava fountains, and the central conduit. Based on the analysis of the amplitude decay of the signal, we highlight the migration of the dike from a depth of ca. 5 km to about 1 km between July 10 and 12. After the onset of the effusive phase, the distribution of the amplitude decay at our stations can be interpreted as the overall result of sources located within the first half kilometer from the surface. Although on a qualitative basis, our findings shed some light on the complex feeding system of Mt. Etna, and integrate other volcanological and geophysical studies which tackle the problem of magma replenishment for the July–August, 2001 flank eruption. We conclude that volcanic tremor is fundamental in monitoring Mt. Etna, not only as a marker of the different sources which act within the volcano edifice, but also of the diverse styles of eruptive activity