AMS Acta
(4.910 recursos)
Repository of the University of Bologna.
Mostrando recursos 1 - 20 de 131
1.
A cortical based model of perceptual completion in the roto-translation space - Citti, G.; Sarti, A.
We present a mathematical model of perceptual completion and formation
of subjective surfaces, which is at the same time inspired by the architecture
of the visual cortex, and is the lifting in the 3-dimensional rototranslation group of
the phenomenological variational models based on elastica functional. The initial
image is lifted by the simple cells to a surface in the rototraslation group and the
completion process is modelled via a diffusion driven motion by curvature. The
convergence of the motion to a minimal surface is proved. Results are presented
both for modal and amodal completion in classic Kanizsa images.
2.
Harnack inequalities and Gaussian estimates for a class of hypoelliptic operators - Pascucci, Andrea; Polidoro, Sergio
We prove a global Harnack inequality for a class of degenerate evolution operators by using repeatedly an invariant local Harnack inequality. As a consequence we obtain an accurate Gaussian lower bound for the fundamental solution for some meaningful families of degenerate operators.
3.
On a class of degenerate parabolic equations of Kolmogorov type - Di Francesco, Marco; Pascucci, Andrea
We adapt the Levi's parametrix method to prove existence, estimates and qualitative properties of a global fundamental solution to ultraparabolic partial differential equations of Kolmogorov type. Existence and uniqueness results for the Cauchy problem are also proved.
4.
Analysis of an uncertain volatility model - Di Francesco, Marco; Foschi, P.; Pascucci, Andrea
We examine, both from an analytical and numerical viewpoint, the uncertain volatility model by Hobson-Rogers in the framework of degenerate parabolic PDEs of Kolmogorov type.
5.
Testing the performance of image
representations for mass classification in
digital mammograms - Angelini, Enrico; Campanini, Renato; Iampieri, Emiro; Lanconelli, Nico; Masotti, Matteo; Roffilli, Matteo
In this paper a two-class classification problem is faced. One class is constituted
by tumoral masses, breast tumors with size ranging from 3 mm to 30 mm. The
other class is constituted by non-masses. A Support Vector Machine (SVM) is used
as a classifier. Both, masses and non-masses, are extracted from the University
of South Florida (USF) mammographic image database and are presented to the
classifier as crops with pixel size 64 x 64. In order to find the optimal solution to
this problem, different featureless crops representations are evaluated. In particular,
a pixel-based representation, a Discrete Wavelet Transform (DWT) representation
and an Overcomplete Wavelet Transform (OWT) representation...
6.
A ranklet–based image representation for
mass classification in digital mammograms - Masotti, Matteo
Ranklets are non–parametric, multi–resolution and orientation selective features
modelled on Haar wavelets. A ranklet–based image representation is proposed in
this paper in order to solve a two–class classification problem. The first class is
constituted by masses, breast tumors with size ranging from 3 mm to 30 mm,
whereas the second class is constituted by non–masses. Masses and non–masses are
both extracted from the University of South Florida (USF) mammographic image
database, submitted to the ranklet transform and finally classified by means of a
Support Vector Machine (SVM). Experiments demonstrate that the proposed image
representation solves succesfully the two–class classification problem. Furthermore,
it achieves an improvement over the pixel–based and...
7.
Analytic smoothing effect for the Schrodinger equation
with long-range perturbation - Martinez, Andre'; Nakamura, Shu; Sordoni, Vania
We study microlocal analytic singularity of solutions to
Schr\"odinger equation with analytic coefficients.
Using microlocal weight estimate developped for estimating
the phase space tunneling, we prove microlocal smoothing
estimates that generalize results by L. Robbiano and C. Zuily.
We suppose the Schr\"odinger operator is a long-range type perturbation of the Laplacian, and we employ positive commutator
type estimates to prove the smoothing property.
8.
Gauge invariance and asymptotic behavior for the Ginzburg-Landau equations of superconductivity - Berti, V.; Fabrizio, M.; Giorgi, C.
In this paper we study the gauge-invariance of the time-dependent Ginzburg Landau equations through the introduction of a model which uses observable variables. Since different choices of gauge lead to a different representation of such variables, the classical formulations of the Ginzburg Landau model do not allow to establish the property of gauge-invariance. With a suitable decomposition of the unknown fields, we write the problem in terms of real variables and deduce some energy estimates which prove the existence of a maximal attractor for the system.
9.
Support vector regression filtering for reduction of false positives in a mass detection cad scheme: preliminary results - Angelini, Enrico; Campanini, Renato; Riccardi, A
Reduction of False Positive signals (FPR) is a fundamental, yet awkward, step in computer aided mass detection schemes.
This paper describes preliminary results of a filtering approach to FPR based on Support Vector Regression (SVR), a machine
learning algorithm arising from a well-founded theoretical framework, the Statistical Learning Theory, which has recently
proved to be superior to the conventional Neural Network framework for both classification and regression tasks: indeed, the
proposed filtering method belongs to the family of neural filters.
The SVR filter is forced to associate subregions extracted from input images, masses and non-masses, to continuous output
values ranging from 0 to 1 representing a...
10.
Calibration of the Hobson&Rogers model: empirical tests - Foschi, P.; Pascucci, A.
The path-dependent volatility model by Hobson and Rogers is considered. It is known that this model can potentially reproduce the observed smile and skew patterns of different directions, while preserving the completeness of the market. In order to quantitatively investigate the pricing performance of the model a calibration procedure is here derived.
Numerical results based on S&P500 option prices give evidence of the effectiveness of the model.
11.
EXPLORING RANKLETS PERFORMANCES IN MAMMOGRAPHIC MASS
CLASSIFICATION USING RECURSIVE FEATURE ELIMINATION - Masotti, Matteo
The ranklet transform is a recent image processing technique
characterized by a multi–resolution and orientation
selective approach similar to that of the wavelet transform.
Yet, differently from the latter, it deals with the ranks of
the pixels rather than with their gray–level intensity values.
In this paper ranklets are used as classification features for a mammographic mass classification problem.
Their performances are explored recursively eliminating some of the less discriminant ranklets coefficients according to the cost function of a Support Vector Machine (SVM) classifier.
Experiments show good classification performances even after
a significant reduction of the number of ranklet coefficients.
12.
Pointwise estimates for a class of non-homogeneous
Kolmogorov equations - Cinti, Chiara; Pascucci, Andrea; Polidoro, Sergio
We consider a class of ultraparabolic differential equations that satisfy the Hörmander's hypoellipticity condition and we prove that the weak solutions to the equation with measurable coe±cients are locally bounded functions. The method extends the Moser's iteration procedure and has previously been employed in the case of operators verifying
a further homogeneity assumption. Here we remove that assumption by proving some potential estimates and some ad hoc Sobolev type inequalities for solutions.
13.
Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term - Polidoro, Sergio; Ragusa, Maria Alessandra
We prove a Harnack inequality for the positive solutions of ultraparabolic equations of the type
L u + V u= 0,
where L is a linear second order hypoelliptic operator and V
belongs to a class of functions of Stummel-Kato type. We also obtain the existence of a Green function and an uniqueness result for the Cauchy-Dirichlet problem.
14.
A PSYCHOGENETIC ALGORITHM FOR BEHAVIORAL SEQUENCE LEARNING - Maniezzo, Vittorio; Roffilli, Matteo
This work presents an original algorithmic model of some essential features of psychogenetic theory, as was proposed by J.Piaget. Specifically, we modeled some elements of cognitive structure learning in children from 0 to 4 months of life. We are in fact convinced that the study of well-established cognitive models of human learning can suggest new, interesting approaches to problem so far not satisfactorily solved in the field of machine learning. Further, we discussed the possible parallels between our model and subsymbolic machine learning and neuroscience. The model was implemented and tested in some simple experimental settings, with reference to the...
15.
Parametrix approximations for option prices - Corielli, Francesco; Pascucci, Andrea
We propose the use of a classical tool in PDE theory, the
parametrix method, to build approximate solutions to generic
parabolic models for pricing and hedging contingent claims. We
obtain an expansion for the price of an option using as starting
point the classical Black&Scholes formula. The approximation can
be truncated to any number of terms and easily computable error
measures are available.
16.
Identifying Multi-Word Units in Context - Philip, Gill
Abstract: Far from being linguistic anomalies, multi-word expressions abound in natural language, yet their identification is surprisingly problematic. The same combination of words can occur as a compositional, fully lexical string or as a delexicalised multi-word unit (MWU). How can these different manifestations of a series of words be distinguished one from the other? To exacerbate the problem, the creativity of language users results in the appearance of non-canonical forms of MWUs. How can these innovative uses be retrieved so that they can be incorporated into a comprehensive analysis of the MWU under study? This paper sets forth procedures for...
17.
Replicating features of natural discourse in the preparation of dialogues for B1 learners - Philip, Gill
There is a considerable difference between the linguistic content of listening exercises and that of natural, spontaneous speech. The discrepancies that exist stem from the pedagogical practice of 'cleaning up' language for classroom use - i.e. ridding it of distracting noise, repetition, irrelevancies, and so on - and also from an unwillingness to expose learners to unfamiliar lexis and grammatical structures ahead of their treatment within the syllabus. Although such an approach is effective in teaching specific language items, it does not prepare learners for the natural discourse that hey will encounter outside the classroom or self-access centre.
Natural, spontaneous speech...
18.
Graphs with prescribed the trace of the Levi form - Martino, Vittorio; Montanari, Annamaria
We prove existence and uniqueness of a viscosity solution of the Dirichlet problem related to the prescribed Levi mean curvature equation, under suitable assumptions on the boundary data and on the Levi curvature of the domain. We also show that such a solution is Lipschitz continuous by proving that it is the uniform limit of a sequence of classical solutions of elliptic problems and by building Lipschitz continuous barriers.
19.
Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov type operators in non-divergence form - Di Francesco, Marco; Polidoro, Sergio
We prove some Schauder type estimates and an invariant Harnack
inequality for a class of degenerate evolution operators of Kolmogorov type. We also prove a Gaussian lower bound for the
fundamental solution of the operator and a uniqueness result for the Cauchy problem. The proof of the lower bound is obtained by solving a suitable optimal control problem and using the invariant Harnack inequality.
20.
Metaphor, the dictionary, and the advanced learner - Philip, Gill
Research into figurative language in foreign language acquisition has primarily focused on the receptive skills, where there is strong evidence to suggest that encouraging students to reflect on the metaphorical origins of figurative expressions makes learning and recall of vocabulary demonstrably more effective. However, very little has been said about the effects of this strategy on students’ productive output. With some advanced learners’ dictionaries now also including information about conceptual metaphor, it is important that the utility of this feature be examined in more detail. This paper examines different types of figurative language produced by advanced learners of English at...
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