arXiv subjects
Publications and source records attributed to Alessandro Rossi.
This report provides an introduction to some Machine Learning tools within the most common development environments. It mainly focuses on practical problems, skipping any theoretical introduction. It is oriented to both students trying to approach Machine Learning and experts looking for new frameworks.
In this document we shows a first implementation and some preliminary results of a new theory, facing Machine Learning problems in the frameworks of Classical Mechanics and Variational Calculus. We give a general formulation of the problem and then we studies basic behaviors of the model on simple practical implementations.
We analyze a new approach to Machine Learning coming from a modification of classical regularization networks by casting the process in the time dimension, leading to a sort of collapse of dimensionality in the problem of learning the model parameters. This approach allows the definition of a online learning algorithm that progressively accumulates the knowledge provided in the input trajectory. The regularization principle leads to a solution based on a dynamical system that is paired with a procedure to develop a graph structure that stores the input regularities acquired from the temporal evolution. We report an extensive experimental exploration on the behavior of the parameter of the proposed model and an evaluation on artificial dataset.
From the results of a comprehensive asteroid population evolution model, we conclude that the YORP-induced rotational fission hypothesis can be consistent with the observed population statistics of small asteroids in the main belt including binaries and contact binaries. The foundation of this model is the asteroid rotation model of Marzari et al. (2011), which incorporates both the YORP effect and collisional evolution. This work adds to that model the rotational fission hypothesis and the binary evolution model of Jacobson & Scheeres (2011). The asteroid population evolution model is highly constrained by these and other previous works, and therefore it has only two significant free parameters: the ratio of low to high mass ratio binaries formed after rotational fission events and the mean strength of the binary YORP (BYORP) effect. We successfully reproduce characteristic statistics of the small asteroid population: the binary fraction, the fast binary fraction, steady-state mass ratio fraction and the contact binary fraction. We find that in order for the model to best match observations, rotational fission produces high mass ratio ($> 0.2$) binary components with four to eight times the frequency as low mass ratio ($< 0.2$) components, where the mass ratio is the mass of the secondary component divided by the mass of the primary component. This is consistent with post-rotational fission binary system mass ratio being drawn from either a flat or a positive and shallow distribution, since the high mass ratio bin is four times the size of the low mass ratio bin; this is in contrast to the observed steady-state binary mass ratio, which has a negative and steep distribution. This can be understood in the context of the BYORP-tidal equilibrium hypothesis, which predicts that low mass ratio binaries survive for a significantly longer period of time than high mass ratio systems.
Semiconductor-based quantum dot single-electron pumps are currently the most promising candidates for the direct realization of the emerging quantum standard of the ampere in the International System of Units. Here, we discuss a silicon quantum dot single-electron pump with radio frequency control over the transparencies of entrance and exit barriers as well as the dot potential. We show that our driving protocol leads to robust bidirectional pumping: one can conveniently reverse the direction of the quantized current by changing only the phase shift of one driving waveform with respect to the others. We also study the improvement in the robustness of the current quantization owing to the introduction of three control voltages in comparison with the two-waveform driving. We anticipate that this pumping technique may be used in the future to perform error counting experiments by pumping the electrons into and out of a reservoir island monitored by a charge sensor.
Recent studies have shown that the medium-Earth orbit (MEO) region of the Global Navigation Satellite Systems is permeated by a devious network of lunisolar secular resonances, which can interact to produce chaotic and diffusive motions. The precarious state of the four navigation constellations, perched on the threshold of instability, makes it understandable why all past efforts to define stable graveyard orbits, especially in the case of Galileo, were bound to fail; the region is far too complex to allow of an adoption of the simple geosynchronous disposal strategy. We retrace one such recent attempt, funded by ESA's General Studies Programme in the frame of the GreenOPS initiative, that uses a systematic parametric approach and the straightforward maximum-eccentricity method to identify long-term stable regions, suitable for graveyards, as well as large-scale excursions in eccentricity, which can be used for post-mission deorbiting of constellation satellites. We then apply our new results on the stunningly rich dynamical structure of the MEO region toward the analysis of these disposal strategies for Galileo, and discuss the practical implications of resonances and chaos in this regime. We outline how the identification of the hyperbolic and elliptic fixed points of the resonances near Galileo can lead to explicit criteria for defining optimal disposal strategies.
We report electron counting experiments in a silicon metal-oxide-semiconductor quantum dot architecture which has been previously demonstrated to generate a quantized current in excess of 80 pA with uncertainty below 30 parts per million. Single-shot detection of electrons pumped into a reservoir dot is performed using a capacitively coupled single-electron transistor. We extract the full probability distribution of the transfer of n electrons per pumping cycle for n = 0, 1, 2, 3, and 4. We find that the probabilities extracted from the counting experiment are in agreement with direct current measurements in a broad range of dc electrochemical potentials of the pump. The electron counting technique is also used to confirm the improving robustness of the pumping mechanism with increasing electrostatic confinement of the quantum dot.
Schottky Barrier (SB)-MOSFET technology offers intriguing possibilities for cryogenic nano-scale devices, such as Si quantum devices and superconducting devices. We present experimental results on a novel device architecture where the gate electrode is self-aligned with the device channel and overlaps the source and drain electrodes. This facilitates a sub-5 nm gap between the source/drain and channel, and no spacers are required. At cryogenic temperatures, such devices function as p-MOS Tunnel FETs, as determined by the Schottky barrier at the Al-Si interface, and as a further advantage, fabrication processes are compatible with both CMOS and superconducting logic technology.
It has long been suspected that the Global Navigation Satellite Systems exist in a background of complex resonances and chaotic motion; yet, the precise dynamical character of these phenomena remains elusive. Recent studies have shown that the occurrence and nature of the resonances driving these dynamics depend chiefly on the frequencies of nodal and apsidal precession and the rate of regression of the Moon's nodes. Woven throughout the inclination and eccentricity phase space is an exceedingly complicated web-like structure of lunisolar secular resonances, which become particularly dense near the inclinations of the navigation satellite orbits. A clear picture of the physical significance of these resonances is of considerable practical interest for the design of disposal strategies for the four constellations. Here we present analytical and semi-analytical models that accurately reflect the true nature of the resonant interactions, and trace the topological organization of the manifolds on which the chaotic motions take place. We present an atlas of FLI stability maps, showing the extent of the chaotic regions of the phase space, computed through a hierarchy of more realistic, and more complicated, models, and compare the chaotic zones in these charts with the analytical estimation of the width of the chaotic layers from the heuristic Chirikov resonance-overlap criterion. As the semi-major axis of the satellite is receding, we observe a transition from stable Nekhoroshev-like structures at three Earth radii, where regular orbits dominate, to a Chirikov regime where resonances overlap at five Earth radii. From a numerical estimation of the Lyapunov times, we find that many of the inclined, nearly circular orbits of the navigation satellites are strongly chaotic and that their dynamics are unpredictable on decadal timescales.
Numerical simulations carried out over the past decade suggest that the orbits of the Global Navigation Satellite Systems are unstable, resulting in an apparent chaotic growth of the eccentricity. Here we show that the irregular and haphazard character of these orbits reflects a similar irregularity in the orbits of many celestial bodies in our Solar System. We find that secular resonances, involving linear combinations of the frequencies of nodal and apsidal precession and the rate of regression of lunar nodes, occur in profusion so that the phase space is threaded by a devious stochastic web. As in all cases in the Solar System, chaos ensues where resonances overlap. These results may be significant for the analysis of disposal strategies for the four constellations in this precarious region of space.
The size distribution of small asteroids in the Main Belt is assumed to be determined by an equilibrium between the creation of new bodies out of the impact debris of larger asteroids and the destruction of small asteroids by collisions with smaller projectiles. However, for a diameter less than 6 km we find that YORP-induced rotational disruption significantly contributes to the erosion even exceeding the effects of collisional fragmentation. Including this additional grinding mechanism in a collision evolution model for the asteroid belt, we generate size-frequency distributions from either an accretional (Weidenschilling, 2011) or an "Asteroids were born big" (Morbidelli, 2009) initial size-frequency distribution that are consistent with observations reported in Gladman et al. (2009). Rotational disruption is a new mechanism that must be included in all future collisional evolution models of asteroids.
The valley-orbit coupling in a few-electron Si quantum dot is expected to be a function of its occupation number N. We study the spectrum of multivalley Si quantum dots for 2 <= N <= 4, showing that, counterintuitively, electron-electron interaction effects on the valley-orbit coupling are negligible. For N=2 they are suppressed by valley interference, for N=3 they vanish due to spinor overlaps, and for N = 4 they cancel between different pairs of electrons. To corroborate our theoretical findings, we examine the experimental energy spectrum of a few-electron metal-oxide-semiconductor quantum dot. The measured spin-valley state filling sequence in a magnetic field reveals that the valley-orbit coupling is definitively unaffected by the occupation number.
Considerable efforts have been made in recent years to produce detailed topologies of the Internet. Although Internet topology data have been brought to the attention of a wide and somewhat diverse audience of scholars, so far they have been overlooked by economists. In this paper, we suggest that such data could be effectively treated as a proxy to characterize the size of the "digital economy" at country level and outsourcing: thus, we analyse the topological structure of the network of trade in digital services (trade in bits) and compare it with that of the more traditional flow of manufactured goods across countries. To perform meaningful comparisons across networks with different characteristics, we define a stochastic benchmark for the number of connections among each country-pair, based on hypergeometric distribution. Original data are thus filtered by means of different thresholds, so that we only focus on the strongest links, i.e., statistically significant links. We find that trade in bits displays a sparser and less hierarchical network structure, which is more similar to trade in high-skill manufactured goods than total trade. Lastly, distance plays a more prominent role in shaping the network of international trade in physical goods than trade in digital services.
We present the results of a large scale simulation, reproducing the behavior of a data center for the build-up and maintenance of a complete catalog of space debris in the upper part of the low Earth orbits region (LEO). The purpose is to determine the performances of a network of advanced optical sensors, through the use of the newest orbit determination algorithms developed by the Department of Mathematics of Pisa (DM). Such a network has been proposed to ESA in the Space Situational Awareness (SSA) framework by Carlo Gavazzi Space SpA (CGS), Istituto Nazionale di Astrofisica (INAF), DM, and Istituto di Scienza e Tecnologie dell'Informazione (ISTI-CNR). The conclusion is that it is possible to use a network of optical sensors to build up a catalog containing more than 98% of the objects with perigee height between 1100 and 2000 km, which would be observable by a reference radar system selected as comparison. It is also possible to maintain such a catalog within the accuracy requirements motivated by collision avoidance, and to detect catastrophic fragmentation events. However, such results depend upon specific assumptions on the sensor and on the software technologies.
In quantum computation, information is processed by gates that must coherently couple separate qubits. In many systems the qubits are naturally coupled, but such an always-on interaction limits the algorithms that may be implemented. Coupling interactions may also be directed in devices and circuits that are provided with additional control wiring. This can be achieved by adjusting the gate voltage in a semiconductor device or an additional flux in a superconducting device. Such control signals must be applied adiabatically (limiting the speed) and the additional wiring provides pathways for noise, which leads to decoherence. Here we demonstrate an alternative approach to coupling by exploiting the nonlinear behaviour of a degenerately doped silicon transistor. A single transistor can exhibit a large number of individual resonances, which are seen as changes in the source-drain current of a dc-biased device. These resonances may be addressed in frequency space due to their high quality factors. Two widely separated resonances are addressed and coupled in three-frequency spectroscopy by ensuring that the third frequency corresponds to the difference between the two individual resonances. The nonlinearity causes the generation of additional driving signals with appropriate frequency and phase relationships to ensure coupling, resulting in additional spectroscopic features that could be exploited for rapid state manipulation and gate operations.
Franson's Bell experiment with energy-time entanglement [Phys. Rev. Lett. 62, 2205 (1989)] does not rule out all local hidden variable models. This defect can be exploited to compromise the security of Bell inequality-based quantum cryptography. We introduce a novel Bell experiment using genuine energy-time entanglement, based on a novel interferometer, which rules out all local hidden variable models. The scheme is feasible with actual technology.
We report on the implementation of a new interferometric scheme that allows the generation of photon pairs entangled in the time-energy degree of freedom. This scheme does not require any kind of temporal post-selection on the generated pairs and can be used even with lasers with short coherence time.