Armando Bazzani

An SVM classifier to separate false signals from microcalcifications in digital mammograms

In this paper we investigate the feasibility of using an SVM (support vector machine) classifier in our automatic system for the detection of clustered microcalcifications in digital mammograms. SVM is a technique for pattern recognition which relies on the statistical learning theory. It minimizes a function of two terms: the number of misclassified vectors of the training set and a term regarding the generalization classifier capability. We compare the SVM classifier with an MLP (multi-layer perceptron) in the false-positive reduction phase of our detection scheme: a detected signal is considered either microcalcification or false signal, according to the value of a set of its features. The SVM classifier gets slightly better results than the MLP one (Az value of 0.963 against 0.958) in the presence of a high number of training data; the improvement becomes much more evident (Az value of 0.952 against 0.918) in training sets of reduced size. Finally, the setting of the SVM classifier is much easier than the MLP one.

Statistical laws in urban mobility from microscopic GPS data in the area of Florence

The application of Statistical Physics to social systems is mainly related to the search for macroscopic laws that can be derived from experimental data averaged in time or space, assuming the system in a steady state. One of the major goals would be to find a connection between the statistical laws and the microscopic properties: for example, to understand the nature of the microscopic interactions or to point out the existence of interaction networks. Probability theory suggests the existence of a few classes of stationary distributions in the thermodynamics limit, so that the question is if a statistical physics approach could be able to enroll the complex nature of the social systems. We have analyzed a large GPS database for single-vehicle mobility in the Florence urban area, obtaining statistical laws for path lengths, for activity downtimes and for activity degrees. We show also that simple generic assumptions on the microscopic behavior could explain the existence of stationary macroscopic laws, with a universal function describing the distribution. Our conclusion is that understanding the system complexity requires a dynamical database for the microscopic evolution, which allows us to solve both small space and time scales in order to study the transients.

Normal forms for Hamiltonian maps and nonlinear effects in a particle accelerator

SummaryWe describe the motion of a particle in the lattice of a hadron accelerator using the formalism of symplectic maps. We revisit the Courant-Snyder’s theory and we stress that the reduction to normal form of a symplectic map is just the natural generalization of the linear theory. We show that a simple FODO cell (formed by linear elements and a sextupole) can be reduced to a quadratic map, for which some results are presented. We show also that it is possible to recover a continuum limit from a discrete description of the lattice. Finally a study of a one-dimensional model for LHC is made. The normal forms are used to compute the tune shifts and smear in various configurations. A comparison is made with the tracking results and an excellent agreement is found in a region whose boundary is close to the dynamical aperture. This suggests that the two-dimensional extension of the method is well suited to treat the coupled betatron nonlinear oscillations.RiassuntoSi descrive il moto di una particella in un acceleratore di adroni, usando il formalismo delle mappe simplettiche. Viene rivista la teoria di Courant-Snyder e si mostra che la riduzione in forma normale di una mappa simplettica è la naturale generalizzazione del caso lineare. Si prova che una cella FODO semplice (composta da elementi lineari e da un sestupolo) può essere ricondotta a una mappa quadratica, per la quale si presentano alcuni risultati e si mostra che è possibile recuperare il limite continuo partendo da una descrizione discreta del sistema. Infine si effettua uno studio di un modello unidimensionale per LHC; si usano le forme normali per calcolare il «tune shift» e lo «smear» in varie configurazioni, si fa un confronto con i risultati del «tracking» e si riscontra un eccellente accordo in una zona il cui limite è non lontano dall’apertura dinamica. Questo suggerisce che l’estensione del metodo a due dimensioni potrà essere un valido strumento per trattare le oscillazioni nonlineari accoppiate di betatrone.РезюмеМы описьваем движение частицы в решетке адронного ускорителя, используя формализм симплексных отображений. В связи с этим мы заново рассматриваем теорию Куранта-Снайдера. Мы подчеркиваем, что преобразование к нормальной форме симплексного отображения, в нерезонансном случае, представляет естественное обобщение теории Куранта-Снайдера, чтобы включить сдвига настройки и для размывания квадратичного обображения. Мы показываем, что можно получить непрерывный предел из дискетного описания решетки. Исследется одномерная модель для большого адронного коллайдера. Мы вычисляем сдвиг настройки и размывание в различных ситуациях, используя метод нормальных сдвиг настройки и размывание в различных ситуациях, используя метод нормальных форм в программе. Мы сравниваем результаты для нормальных форм в различных порядках возмущений с результатами, полученными с использованием модели тонких линз для той же решетки.

Resonant normal forms, interpolating Hamiltonians and stability analysis of area preserving maps

Abstract The geometrical and dynamical properties of area preserving maps in the neighborhood of an elliptic fixed point are analyzed in the framework of resonant normal forms. The interpolating flow is not obtained from a map tangent to the identity, but from the normal form of the given map and a time independent interpolating Hamiltonian H is introduced. On this Hamiltonian the local stability properties of the fixed point and the geometric structure of the orbits are transparent. Numerical agreement between the level lines of H and the orbits of the map suggests that the perturbative expansion of H is asymptotic. This is confirmed by a rigorous error analysis, based on majorant series: the error for the normal form expansion grows as n! while the truncation error for H also has a factorial growth and in a disc of radius r can be made exponentially small with 1/r. The boundary of the global stability domain is considered; for the quadratic map the identification with the inner envelope of the homoclinic tangle of the hyperbolic fixed point is strongly suggested by numerical evidence.

Diffusion and memory effects for stochastic processes and fractional Langevin equations

We consider the diffusion processes defined by stochastic differential equations when the noise is correlated. A functional method based on the Dyson expansion for the evolution operator, associated to the stochastic continuity equation, is proposed to obtain the Fokker–Planck equation, after averaging over the stochastic process. In the white noise limit the standard result, corresponding to the Stratonovich interpretation of the non-linear Langevin equation, is recovered. When the noise is correlated the averaged operator series cannot be summed, unless a family of time-dependent operators commutes. In the case of a linear equation, the constraints are easily worked out. The process defined by a linear Langevin equation with additive noise is Gaussian and the probability density function of its fluctuating component satisfies a Fokker–Planck equation with a time-dependent diffusion coefficient. The same result holds for a linear Langevin equation with a fractional time derivative (defined according to Caputo, Elasticita e Dissipazione, Zanichelli, Bologna, 1969). In the generic linear or non-linear case approximate equations for small noise amplitude are obtained. For small correlation time the evolution equations further simplify in agreement with some previous alternative derivations. The results are illustrated by the linear oscillator with coloured noise and the fractional Wiener process, where the numerical simulation for the probability density and its moments is compared with the analytical solution.

Toward a microscopic model of bidirectional synaptic plasticity

We show that a 2-step phospho/dephosphorylation cycle for the α-amino-3-hydroxy-5-methyl-4-isoxazole proprionic acid receptor (AMPAR), as used in in vivo learning experiments to assess long-term potentiation (LTP) induction and establishment, exhibits bistability for a wide range of parameters, consistent with values derived from biological literature. The AMPAR model we propose, hence, is a candidate for memory storage and switching behavior at a molecular-microscopic level. Furthermore, the stochastic formulation of the deterministic model leads to a mesoscopic interpretation by considering the effect of enzymatic fluctuations on the Michelis–Menten average dynamics. Under suitable hypotheses, this leads to a stochastic dynamical system with multiplicative noise whose probability density evolves according to a Fokker–Planck equation in the Stratonovich sense. In this approach, the probability density associated with each AMPAR phosphorylation state allows one to compute the probability of any concentration value, whereas the Michaelis–Menten equations consider the average concentration dynamics. We show that bistable dynamics are robust for multiplicative stochastic perturbations and that the presence of both noise and bistability simulates LTP and long-term depression (LTD) behavior. Interestingly, the LTP part of this model has been experimentally verified as a result of in vivo, one-trial inhibitory avoidance learning protocol in rats, that produced the same changes in hippocampal AMPARs phosphorylation state as observed with in vitro induction of LTP with high-frequency stimulation (HFS). A consequence of this model is the possibility of characterizing a molecular switch with a defined biochemical set of reactions showing bistability and bidirectionality. Thus, this 3-enzymes-based biophysical model can predict LTP as well as LTD and their transition rates. The theoretical results can be, in principle, validated by in vitro and in vivo experiments, such as fluorescence measurements and electrophysiological recordings at multiple scales, from molecules to neurons. A further consequence is that the bistable regime occurs only within certain parametric windows, which may simulate a “history-dependent threshold”. This effect might be related to the Bienenstock–Cooper–Munro theory of synaptic plasticity.

Nekhoroshev estimate for isochronous non resonant symplectic maps

We prove that non resonant isochronous symplectic maps in a neighborhood of an elliptic fixed point are stable for exponentially long times with the inverse of the distance from the fixed point. In the proof we make use of the majorant series method together with an idea for optimizing remainder estimates first applied to Hamiltonian problems by Nekhoroshev.

A stochastic model of randomly accelerated walkers for human mobility

Recent studies of human mobility largely focus on displacements patterns and power law fits of empirical long-tailed distributions of distances are usually associated to scale-free superdiffusive random walks called Lévy flights. However, drawing conclusions about a complex system from a fit, without any further knowledge of the underlying dynamics, might lead to erroneous interpretations. Here we show, on the basis of a data set describing the trajectories of 780,000 private vehicles in Italy, that the Lévy flight model cannot explain the behaviour of travel times and speeds. We therefore introduce a class of accelerated random walks, validated by empirical observations, where the velocity changes due to acceleration kicks at random times. Combining this mechanism with an exponentially decaying distribution of travel times leads to a short-tailed distribution of distances which could indeed be mistaken with a truncated power law. These results illustrate the limits of purely descriptive models and provide a mechanistic view of mobility.

A novel approach to mass detection in digital mammography based on Support Vector Machines(SVM)

In this paper we present a novel approach to mass detection in digital mammograms. The great variability of the masses appearance is the main obstacle of building a mass detection method. It is indeed demanding to characterize all the varieties of masses with a reduced set of features. Hence, in our approach we decide not to extract any feature, for the detection of the region of interest; on the contrary we exploit all the information available on the image. No a priori knowledge and no appearance model are used. A multiresolution overcomplete wavelet representation is achieved, in order to codify the image with redundancy of information. The vectors of the very-large space obtained are classified by means of an SVM classifier. Training, validation and test are accomplished on images coming from USF DDSM database. The sensitivity of the presented system is 84% with a false-positive rate of 3.1 marks per image.

A chronotopic model of mobility in urban spaces

In this paper, we propose an urban mobility model based on individual stochastic dynamics driven by the chronotopic action with a deterministic public transportation network. Such a model is inspired by a new approach to the problem of urban mobility that focuses the attention to the individuals and considers the presence of random components and attractive areas (chronotopoi), an essential ingredient to understand the citizens dynamics in the modern cities. The computer simulation of the model allows virtual experiments on urban spaces that describe the mobility as the evolution of a non-equilibrium system. In the absence of chronotopoi the relaxation to a stationary state is studied by the mean-field equations. When the chronotopoi are switched on the different classes of people feel an attraction toward the chronotopic areas proportional to a power law of the distance. In such a case, a theoretical description of the average evolution is obtained by using two diffusion equations coupled by local mean-field equations.