A general correlation inequality and the Almost Sure Local Limit Theorem for random sequences in the domain of attraction of a stable law

In the present paper we obtain a new correlation inequality and use it for the purpose of extending the theory of the Almost Sure Local Limit Theorem to the case of lattice random sequences in the domain of attraction of a stable law. In particular, we prove ASLLT in the case of the normal domain of attraction of $\alpha$--stable law, $\alpha\in(1,2)$

Some examples of non-central moderate deviations for sequences of real random variables

The term \emph{moderate deviations} is often used in the literature to mean a class of large deviation principles that, in some sense, fill the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak convergence to a centered Normal distribution. In this paper we present some examples of classes of large deviation principles of this kind, but the involved random variables converge weakly to Gumbel, exponential and Laplace distributions.Comment: 25 page

Asymptotic results for sums and extremes

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability of some random variables to a constant and a weak convergence to a centered Gaussian distribution (when such random variables are properly centered and rescaled). We talk about noncentral moderate deviations when the weak convergence is towards a non-Gaussian distribution. In this paper, we prove a noncentral moderate deviation result for the bivariate sequence of sums and maxima of i.i.d. random variables bounded from above. We also prove a result where the random variables are not bounded from above, and the maxima are suitably normalized. Finally, we prove a moderate deviation result for sums of partial minima of i.i.d. exponential random variables.Comment: 1

Limiting behaviour of moving average processes under ρ\rho-mixing assumption

Let \{Y_i, -\infty<i<\infty\} be a doubly infinite sequence of identically distributed $\rho$-mixing random variables, \{a_i,-\infty<i< \infty\} an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence and Marcinkiewicz-Zygmund strong law of large numbers for the partial sums of the moving average processes $\{\sum\limits^\infty_{i=-\infty}a_i Y_{i+n},n\geq1\}$

Large deviations for some normalized sums of exponentially distributed random variables

We prove large deviation results for sequences of normalized sums which are defined in terms of triangular arrays of exponentially distributed random variables. We also present some examples: one of them might have applications in reliability theory because it concerns the spacings of i.i.d. exponentially distributed random variables; in another one we consider a sequence of logarithmically weighted means

A Digital representation of Euryalus fortress: a historical interpretive study

[EN] It is clear that concepts and cognitive processes aimed at putting forward fortified systems in their relation with the territory and with the surrounding landscape, establish inextricably interwoven “interests” and a consequent osmotic hysteresis between their emergence and disappearance into the deepest part of the earth. The logic behind the defensive structures of Euryalus fortress is particularly interesting. The fortress designed during the Greek period and located on the top of Epipolae hill, represented a strategic fortification for the city’s defence. Therefore, it is reasonable to think about a sequence of emerging or disappearing empty spaces; a semantic vacuum to be filled with logical-subjective interpretations pertaining to those who visit the place. The conceptual framework provides knowledge and documentation meant as indispensable supporting instruments to understand Dionysius I and Archimedes’ thoughts where the integration of people and environment forms the basis of the close iterative connection among nature, artifice and landscape. The research takes this direction implementing innovative technological systems trying to go beyond in order to achieve virtual reconstruction processes, even if partial, of the fortress. Survey, thus, can be applied as an instrument for the knowledge of historical heritage which once converted into digital heritage is a support for the reconstruction of lost ancient scenarios. Actually, the implementation of innovative systems allows an easy-to-use data viewing which supports the interpretive phase, the archiving, consultation and dissemination of survey products. In particular, the survey of the fortress with integrated methodologies (both instrumental and photogrammetric) provides not only a fundamental basis for the documentation of the fortress conditions but also provides a basis for the collection of reconstructive hypotheses formulated by researchers who have been involved with the structure so far. Interactions among archaeology, history, geomorphology and technology make history and a past renowned glory come alive with the common spirit of coming up to a strong synergy between the past and the future destiny of the place.Valenti, R.; Giuliano, S.; Paternò, E. (2020). Una rappresentazione digitale del castello Eurialo per l’indagine storico-interpretativa. Editorial Universitat Politècnica de València. 487-494. https://doi.org/10.4995/FORTMED2020.2020.11526OCS48749

Organic Alternatives to Quantum Dots for Intraoperative Near-Infrared Fluorescent Sentinel Lymph Node Mapping:

Intraoperative near-infrared (NIR) fluorescence imaging provides the surgeon with real-time image guidance during cancer and other surgeries. We have previously reported the use of NIR fluorescent quantum dots (QDs) for sentinel lymph node (SLN) mapping. However, because of concerns over potential toxicity, organic alternatives to QDs will be required for initial clinical studies. We describe a family of 800 nm organic heptamethine indocyanine-based contrast agents for SLN mapping spanning a spectrum from 775 Da small molecules to 7 MDa nanocolloids. We provide a detailed characterization of the optical and physical properties of these contrast agents and discuss the advantages and disadvantages of each. We present robust methods for the covalent conjugation, purification, and characterization of proteins with tetra-sulfonated heptamethine indocyanines, including mass spectroscopic site mapping of highly substituted molecules. One contrast agent, NIR fluorescent human serum albumin (HSA800), emerged as the molecule with the best overall performance with respect to entry to lymphatics, flow to the SLN, retention in the SLN, fluorescence yield and reproducibility. This preclinical study, performed on large animals approaching the size of humans, should serve as a foundation for future clinical studies. Mol Imaging (2005) 4, 172 – 181