Deep Learning and Mean-Field Games: A Stochastic Optimal Control Perspective

We provide a rigorous mathematical formulation of Deep Learning (DL) methodologies through an in-depth analysis of the learning procedures characterizing Neural Network (NN) models within the theoretical frameworks of Stochastic Optimal Control (SOC) and Mean-Field Games (MFGs). In particular, we show how the supervised learning approach can be translated in terms of a (stochastic) mean-field optimal control problem by applying the Hamilton\u2013Jacobi\u2013Bellman (HJB) approach and the mean-field Pontryagin maximum principle. Our contribution sheds new light on a possible theoretical connection between mean-field problems and DL, melting heterogeneous approaches and reporting the state-of-the-art within such fields to show how the latter different perspectives can be indeed fruitfully unified

Generalized energy equipartition in harmonic oscillators driven by active baths

We study experimentally and numerically the dynamics of colloidal beads confined by a harmonic potential in a bath of swimming E. coli bacteria. The resulting dynamics is well approximated by a Langevin equation for an overdamped oscillator driven by the combination of a white thermal noise and an exponentially correlated active noise. This scenario leads to a simple generalization of the equipartition theorem resulting in the coexistence of two different effective temperatures that govern dynamics along the flat and the curved directions in the potential landscape.Comment: 4 pages, 3 figure

Tau Lepton Identification With Graph Neural Networks at Future Electron–Positron Colliders

Efficient and accurate reconstruction and identification of tau lepton decays plays a crucial role in the program of measurements and searches under the study for the future high-energy particle colliders. Leveraging recent advances in machine learning algorithms, which have dramatically improved the state of the art in visual object recognition, we have developed novel tau identification methods that are able to classify tau decays in leptons and hadrons and to discriminate them against QCD jets. We present the methodology and the results of the application at the interesting use case of the IDEA dual-readout calorimeter detector concept proposed for the future FCC-ee electron–positron collider

Forward-Looking Volatility Estimation for Risk-Managed Investment Strategies during the COVID-19 Crisis

Under the impact of both increasing credit pressure and low economic returns characterizing developed countries, investment levels have decreased over recent years. Moreover, the recent turbulence caused by the COVID-19 crisis has accelerated the latter process. Within this scenario, we consider the so-called Volatility Target (VolTarget) strategy. In particular, we focus our attention on estimating volatility levels of a risky asset to perform a VolTarget simulation over two different time horizons. We first consider a 20 year period, from January 2000 to January 2020, then we analyse the last 12 months to emphasize the effects related to the COVID-19 virus\u2019s diffusion. We propose a hybrid algorithm based on the composition of a GARCH model with a Neural Network (NN) approach. Let us underline that, as an alternative to standard allocation methods based on realized and backward oriented volatilities, we exploited an innovative forward-looking estimation process exploiting a Machine Learning (ML) solution. Our solution provides a more accurate volatility estimation, allowing us to derive an effective investor risk-return profile during market crisis periods. Moreover, we show that, via a forward-looking VolTarget strategy while using an ML-based prediction as the input, the average outcome for an investment in a drawdown plan is more sustainable while representing an efficient risk-control solution for long time period investments

The Epoch of IGM heating by early sources of X-rays

Observations of the 21 cm line from neutral hydrogen indicate that an Epoch of Heating (EoH) might have preceded the later Epoch of Reionization (EoR). Here we study the effects on the ionization state and the thermal history of the Intergalactic Medium (IGM) during the EoH induced by different assumptions on ionizing sources in the high redshift Universe: (i) stars, (ii) X-ray binaries (XRBs), (iii) thermal bremsstrahlung of the hot Interstellar Medium (ISM), and (iv) accreting nuclear black holes (BHs). To this aim, we post-process outputs from the ($100 h^{-1}$ cMpc)$^3$ hydrodynamical simulation MassiveBlack-II with the cosmological 3D radiative transfer code CRASH, which follows the propagation of UV and X-ray photons, computing the thermal and ionization state of hydrogen and helium through the EoH. We find that stars determine the fully ionized morphology of the IGM, while the spectrally hard XRBs pave way for efficient subsequent heating and ionization by the spectrally softer ISM. With the seeding prescription in MassiveBlack-II, BHs do not contribute significantly to either ionization or heating. With only stars, most of the IGM remains in a cold state (with a median $T=11$ K at $z=10$), however, the presence of more energetic sources raises the temperature of regions around the brightest and more clustered sources above that of the CMB, opening the possibility to observing the 21 cm signal in emission.Comment: 18 pages, 9 figures. Accepted for publication in MNRA

Crypto accelerators for power-efficient and realtime on-chip implementation of secure algorithms

The demand for data exchange is ever growing. Internet of Things (IoT), industry 4.0, smart city and next-generation interconnected vehicles are some examples of scenarios in which a high volume of nodes share data across networks. Hence, the data protection plays a fundamental aspect to avoid disclosure or manipulation of sensitive information and disruption of services, particularly in safety critical applications. On the other hand, also the compute power at disposal of possible attackers and hackers is growing, and next-future post-quantum capabilities will require the usage of longer keys, certificates and digital signatures, to preserve the security level offered by cryptographic functions. This will affect not only the amount of exchange data, but also the computational resources to secure data, increasing processing time, latencies and power consumption, and lowering data rates. In this work, we investigate different implementation strategies to overcome such performance limitations. This work provides a comparison among pure software approach (both on 32b and 64b processors) and hardware-based solutions we developed for FPGA and ASIC System-on-Chip platforms, for the most common symmetric-key and public-key cryptographic algorithms. The proposed hardware accelerators feature one order of magnitude higher throughput (and lower latency) and more than two orders lower power consumption than their software counterparts. A highly configurable cryptographic suite is proposed that can be customized according to the application requirements and thus able to increase as much as possible the efficiency in terms of energy per enciphered bits per secon

Maximum Likelihood Approach to Markov Switching Models

The present paper concerns a Maximum Likelihood analysis for the Markov switching approach to the forecasting problem of financial time series. In particular we model the volatility parameter characterizing time series of interest as a state variable of a suitable Markov chain. Latter formulation is based on the idea of describing abrupt changes in the behaviour of studied financial quantities due to, e.g., social or political factors able to substantially change the economic scenarios we are interested in. A case study for the NASDAQ IXIC index in the period 3rd Jan 2007 - 30th Dec 2013 is also provided