k-dimensional Size Functions for shape description and comparison

This paper advises the use of k-dimensional size functions for comparison and retrieval in the context of multidimensional shapes, where by shape we mean something in two or higher dimensions having a visual appearance. The attractive feature of k-dimensional size functions is that they allow to readily establish a similarity measure between shapes of arbitrary dimension, taking into account different properties expressed by a multivalued real function defined on the shape. This task is achieved through a particular projection of k-dimensional size functions into the 1-dimensional case. Therefore, previous results on the stability for matching purposes become applicable to a wider range of data. We outline the potential of our approach in a series of experiments

Keypics: free–hand drawn iconic keywords

We propose an iconic indexing of images to be exposed on the Web. This should be accomplished by “Keypics”, i.e. auxiliary, simplified pictures referring to the geometrical and/or the semantic content of the indexed image. Keypics should not be rigidly standardized; they should be left free to evolve, to express nuances and to stress details. A mathematical tool for dealing with such freedom, in the retrieval task, already exists: Size Functions. An experiment on 494 Keypics with Size Functions based on three measuring functions (distances, projections and jumps) and their combination is presented

Approximating the 2-dimensional matching distance

Some new approximation results about the 2-dimensional matching distance are presented, leading to the formulation of an algorithm for its computation (up to an arbitrary input error)

An Interdisciplinary Approach for the Historical and Technical Characterization of Medieval and Modern Mortars

The study concerns Italian masonries and focuses on historical, medieval and modern mortars. Within the context of the different regions under examination (Piedmont, the Po Valley area, Latium, the Umbria-Marche region, and Apulia and Sardinia) a wide variety of materials with different chemical-physical characteristics were used in masonry work, determining different structural behaviors. The project aims at improving our knowledge about historical mortars in order to further the conservation of Italian built heritage, especially in zones with seismic risk. To achieve these results, we took samples and carried out analyses to investigate the different mechanical and cohesion properties that influence the vulnerability of ruined or collapsed structures. This information has enabled advances to be made in the prevention, maintenance, protection and preservation of historical buildings. Further details will concern the history of construction techniques, with particular regard to the relationship between local resources and construction sites. Another important topic is the role of different components and additives during the preparation of the mortars and their level of hydraulicity.Lo studio riguarda le strutture murarie in Italia e si concentra sulle malte storiche, medievali e moderne. Nei contesti regionali oggetto d’indagine (Piemonte e Pianura Padana, Lazio, Umbria-Marche, Puglia e Sardegna) è stata utilizzata una grande varietà di materiali, con caratteristiche chimico-fisiche diverse, e queste differenze determinano anche comportamenti strutturali diversi. Il progetto mira a migliorare la nostra conoscenza delle malte storiche per approfondire il tema della conservazione del patrimonio edilizio italiano, soprattutto nelle zone a rischio sismico. Per ottenere questi risultati, sono stati prelevati campioni sui quali sono state effettuate analisi per indagare quanto le diverse proprietà meccaniche e di coesione incidano sulla vulnerabilità delle strutture in rovina o collassate. Grazie a queste informazioni è stato possibile contribuire alla prevenzione, manutenzione, protezione e conservazione dell'edilizia storica. Ulteriori conoscenze hanno riguardato la storia delle tecniche di costruzione, con particolare riguardo al rapporto tra risorse locali e i cantieri. Un altro importante tema è stato il ruolo dei diversi componenti e additivi durante la preparazione delle malte e il loro livello di idraulicità

Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learning

The aim of this paper is to provide a general mathematical framework for group equivariance in the machine learning context. The framework builds on a synergy between persistent homology and the theory of group actions. We define group-equivariant non-expansive operators (GENEOs), which are maps between function spaces associated with groups of transformations. We study the topological and metric properties of the space of GENEOs to evaluate their approximating power and set the basis for general strategies to initialise and compose operators. We begin by defining suitable pseudo-metrics for the function spaces, the equivariance groups, and the set of non-expansive operators. Basing on these pseudo-metrics, we prove that the space of GENEOs is compact and convex, under the assumption that the function spaces are compact and convex. These results provide fundamental guarantees in a machine learning perspective. We show examples on the MNIST and fashion-MNIST datasets. By considering isometry-equivariant non-expansive operators, we describe a simple strategy to select and sample operators, and show how the selected and sampled operators can be used to perform both classical metric learning and an effective initialisation of the kernels of a convolutional neural network.Comment: Added references. Extended Section 7. Added 3 figures. Corrected typos. 42 pages, 7 figure

Approximating the 2-dimensional matching distance

Some new approximation results about the 2-dimensional matching distance are presented, leading to the formulation of an algorithm for its computation (up to an arbitrary input error)

Failure of Miltefosine Treatment in Two Dogs with Natural Leishmania infantum Infection

Two dogs, with naturally acquired canine leishmaniasis, were treated orally with miltefosine (2 mg/kg q 24 hr) and allopurinol (10 mg/kg q 12 hr) for 28 days. Both dogs showed good initial response to therapy, with reduction in clinical signs and improvement of clinicopathological changes. However, in both dogs, clinical and clinicopathological abnormalities recurred 150 days after initial treatment and a second course of miltefosine and allopurinol was administered. One dog failed to respond to the 2nd cycle of miltefosine treatment and the other dog responded initially but suffered an early relapse. Treatment with meglumine antimoniate (100 mg/kg q 24 hr for a minimum of 4 weeks) was then started in both dogs. Both dogs showed rapid clinical and clinicopathological improvement and to date they have not received further treatment for 420 and 270 days, respectively. In view of the low number of antileishmanial drugs available and the fact that some of these are used in human as well as veterinary medicine, it is of paramount importance that drug resistance is monitored and documented