r-norm bounds and metric properties for zero loci of real analytic functions

We consider the problem of deciding whether or not a zero locus, X, of multivariate real analytic functions crosses a given r-norm ball in the real n-dimensional affine space. We perform a local study of the problem, and we provide both necessary and sufficient conditions to answer the question. Our conditions derive from the analysis of differential geometric properties of X at the center of the ball. An algorithm to evaluate r-norms distances is proposed

The Hough Transform and the Impact of Chronic Leukemia on the Compact Bone Tissue from CT-Images Analysis

Computational analysis of X-ray Computed Tomography (CT) images allows the assessment of alteration of bone structure in adult patients with Advanced Chronic Lymphocytic Leukemia (ACLL), and may even offer a powerful tool to assess the development of the disease (prognostic potential). The crucial requirement for this kind of analysis is the application of a pattern recognition method able to accurately segment the intra-bone space in clinical CT images of the human skeleton. Our purpose is to show how this task can be accomplished by a procedure based on the use of the Hough transform technique for special families of algebraic curves. The dataset used for this study is composed of sixteen subjects including eight control subjects, one ACLL survivor, and seven ACLL victims. We apply the Hough transform approach to the set of CT images of appendicular bones for detecting the compact and trabecular bone contours by using ellipses, and we use the computed semi-axes values to infer information on bone alterations in the population affected by ACLL. The effectiveness of this method is proved against ground truth comparison. We show that features depending on the semi-axes values detect a statistically significant difference between the class of control subjects plus the ACLL survivor and the class of ACLL victims

Informing additive manufacturing technology adoption: total cost and the impact of capacity utilisation

Informing Additive Manufacturing (AM) technology adoption decisions, this paper investigates the relationship between build volume capacity utilisation and efficient technology operation in an inter-process comparison of the costs of manufacturing a complex component used in the packaging industry. Confronting the reported costs of a conventional machining and welding pathway with an estimator of the costs incurred through an AM route utilising Direct Metal Laser Sintering (DMLS), we weave together four aspects: optimised capacity utilisation, ancillary process steps, the effect of build failure and design adaptation. Recognising that AM users can fill unused machine capacity with other, potentially unrelated, geometries, we posit a characteristic of ‘fungible’ build capacity. This aspect is integrated in the cost estimation framework through computational build volume packing, drawing on a basket of sample geometries. We show that the unit cost in mixed builds at full capacity is lower than in builds limited to a single type of geometry; in our study, this results in a mean unit cost overstatement of 157%. The estimated manufacturing cost savings from AM adoption range from 36 to 46%. Additionally, we indicate that operating cost savings resulting from design adaptation are likely to far outweigh the manufacturing cost advantage

Linear Toric Fibrations

These notes are based on three lectures given at the 2013 CIME/CIRM summer school. The purpose of this series of lectures is to introduce the notion of a toric fibration and to give its geometrical and combinatorial characterizations. Polarized toric varieties which are birationally equivalent to projective toric bundles are associated to a class of polytopes called Cayley polytopes. Their geometry and combinatorics have a fruitful interplay leading to fundamental insight in both directions. These notes will illustrate geometrical phenomena, in algebraic geometry and neighboring fields, which are characterized by a Cayley structure. Examples are projective duality of toric varieties and polyhedral adjunction theory

Moore-Penrose approach in the Hough transform framework

Maria-Laura Torrente is a member of GNAMPA - Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni of INDAM. J.R. Sendra is member of the Research Group ASYNACS (Ref.CT-CE2019/683).Let F(x, a) be a real polynomial in two sets of variables, x and a, that is linear with respect to one of the variable sets, say a. In this paper, we deal with two of the main steps of the Hough transform framework for the pattern recognition technique to detect loci in images. More precisely, we present an algorithmic process, based on the Moore–Penrose pseudo-inverse, to provide a region of analysis in the parameter space. In addition, we state an upper bound for the sampling distance of the discretization of the parameter space region.Agencia Estatal de Investigació

Physical propositions and quantum languages

The word \textit{proposition} is used in physics with different meanings, which must be distinguished to avoid interpretational problems. We construct two languages $\mathcal{L}^{\ast}(x)$ and $\mathcal{L}(x)$ with classical set-theoretical semantics which allow us to illustrate those meanings and to show that the non-Boolean lattice of propositions of quantum logic (QL) can be obtained by selecting a subset of \textit{p-testable} propositions within the Boolean lattice of all propositions associated with sentences of $\mathcal{L}(x)$. Yet, the aforesaid semantics is incompatible with the standard interpretation of quantum mechanics (QM) because of known no-go theorems. But if one accepts our criticism of these theorems and the ensuing SR (semantic realism) interpretation of QM, the incompatibility disappears, and the classical and quantum notions of truth can coexist, since they refer to different metalinguistic concepts (\textit{truth} and \textit{verifiability according to QM}, respectively). Moreover one can construct a quantum language $\mathcal{L}_{TQ}(x)$ whose Lindenbaum-Tarski algebra is isomorphic to QL, the sentences of which state (testable) properties of individual samples of physical systems, while standard QL does not bear this interpretation.Comment: 15 pages, no figure, standard Late

On the extreme stationary outflows from super-star clusters: from superwinds to supernebulae and further massive star formation

The properties of star cluster winds in the supercritical, catastrophic cooling regime are discussed. We demonstrate that strong radiative cooling may inhibit superwinds and, after a rapid phase of accumulation of the ejected material within the star-forming volume, a new stationary isothermal regime, supported by the ionizing radiation from the central cluster, is established. The expected appearance of this core/halo supernebula in the visible line regime and possible late evolutionary tracks for super-star cluster winds, in the absence of ionizing radiation, are thoroughly discussed.Comment: 11 pages, 5 figures, accepted for publication by The Astrophysical Journa

The structure of the quantum mechanical state space and induced superselection rules

The role of superselection rules for the derivation of classical probability within quantum mechanics is investigated and examples of superselection rules induced by the environment are discussed.Comment: 11 pages, Standard Latex 2.0

Extended Representations of Observables and States for a Noncontextual Reinterpretation of QM

A crucial and problematical feature of quantum mechanics (QM) is nonobjectivity of properties. The ESR model restores objectivity reinterpreting quantum probabilities as conditional on detection and embodying the mathematical formalism of QM into a broader noncontextual (hence local) framework. We propose here an improved presentation of the ESR model containing a more complete mathematical representation of the basic entities of the model. We also extend the model to mixtures showing that the mathematical representations of proper mixtures does not coincide with the mathematical representation of mixtures provided by QM, while the representation of improper mixtures does. This feature of the ESR model entails that some interpretative problems raising in QM when dealing with mixtures are avoided. From an empirical point of view the predictions of the ESR model depend on some parameters which may be such that they are very close to the predictions of QM in most cases. But the nonstandard representation of proper mixtures allows us to propose the scheme of an experiment that could check whether the predictions of QM or the predictions of the ESR model are correct.Comment: 17 pages, standard latex. Extensively revised versio