32 research outputs found
Levy-Student Distributions for Halos in Accelerator Beams
We describe the transverse beam distribution in particle accelerators within
the controlled, stochastic dynamical scheme of the Stochastic Mechanics (SM)
which produces time reversal invariant diffusion processes. This leads to a
linearized theory summarized in a Shchr\"odinger--like (\Sl) equation. The
space charge effects have been introduced in a recent paper~\cite{prstab} by
coupling this \Sl equation with the Maxwell equations. We analyze the space
charge effects to understand how the dynamics produces the actual beam
distributions, and in particular we show how the stationary, self--consistent
solutions are related to the (external, and space--charge) potentials both when
we suppose that the external field is harmonic (\emph{constant focusing}), and
when we \emph{a priori} prescribe the shape of the stationary solution. We then
proceed to discuss a few new ideas~\cite{epac04} by introducing the generalized
Student distributions, namely non--Gaussian, L\'evy \emph{infinitely divisible}
(but not \emph{stable}) distributions. We will discuss this idea from two
different standpoints: (a) first by supposing that the stationary distribution
of our (Wiener powered) SM model is a Student distribution; (b) by supposing
that our model is based on a (non--Gaussian) L\'evy process whose increments
are Student distributed. We show that in the case (a) the longer tails of the
power decay of the Student laws, and in the case (b) the discontinuities of the
L\'evy--Student process can well account for the rare escape of particles from
the beam core, and hence for the formation of a halo in intense beams.Comment: revtex4, 18 pages, 12 figure
L\'evy-Schr\"odinger wave packets
We analyze the time--dependent solutions of the pseudo--differential
L\'evy--Schr\"odinger wave equation in the free case, and we compare them with
the associated L\'evy processes. We list the principal laws used to describe
the time evolutions of both the L\'evy process densities, and the
L\'evy--Schr\"odinger wave packets. To have self--adjoint generators and
unitary evolutions we will consider only absolutely continuous, infinitely
divisible L\'evy noises with laws symmetric under change of sign of the
independent variable. We then show several examples of the characteristic
behavior of the L\'evy--Schr\"odinger wave packets, and in particular of the
bi-modality arising in their evolutions: a feature at variance with the typical
diffusive uni--modality of both the L\'evy process densities, and the usual
Schr\"odinger wave functions.Comment: 41 pages, 13 figures; paper substantially shortened, while keeping
intact examples and results; changed format from "report" to "article";
eliminated Appendices B, C, F (old names); shifted Chapters 4 and 5 (old
numbers) from text to Appendices C, D (new names); introduced connection
between Relativistic q.m. laws and Generalized Hyperbolic law
Quantum Mechanical Interaction-Free Measurements
A novel manifestation of nonlocality of quantum mechanics is presented. It is
shown that it is possible to ascertain the existence of an object in a given
region of space without interacting with it. The method might have practical
applications for delicate quantum experiments.Comment: (revised file with no need for macro), 12, TAUP 1865-91
Mixtures in non stable Levy processes
We analyze the Levy processes produced by means of two interconnected classes
of non stable, infinitely divisible distribution: the Variance Gamma and the
Student laws. While the Variance Gamma family is closed under convolution, the
Student one is not: this makes its time evolution more complicated. We prove
that -- at least for one particular type of Student processes suggested by
recent empirical results, and for integral times -- the distribution of the
process is a mixture of other types of Student distributions, randomized by
means of a new probability distribution. The mixture is such that along the
time the asymptotic behavior of the probability density functions always
coincide with that of the generating Student law. We put forward the conjecture
that this can be a general feature of the Student processes. We finally analyze
the Ornstein--Uhlenbeck process driven by our Levy noises and show a few
simulation of it.Comment: 28 pages, 3 figures, to be published in J. Phys. A: Math. Ge
Renormalization of the QED of self-interacting second order spin 1/2 fermions
We study the one-loop level renormalization of the electrodynamics of spin
1/2 fermions in the Poincar\'e projector formalism, in arbitrary covariant
gauge and including fermion self-interactions, which are dimension four
operators in this framework. We show that the model is renormalizable for
arbitrary values of the tree level gyromagnetic factor g within the validity
region of the perturbative expansion, \alpha g^2 << 1. In the absence of tree
level fermion self-interactions, we recover the pure QED of second order
fermions, which is renormalizable only for |g|=2. Turning off the
electromagnetic interaction we obtain a renormalizable Nambu-Jona-Lasinio-like
model with second order fermions in four space-time dimensions.Comment: 32 pages, 9 figures. Published versio
Levy flights and Levy -Schroedinger semigroups
We analyze two different confining mechanisms for L\'{e}vy flights in the
presence of external potentials. One of them is due to a conservative force in
the corresponding Langevin equation. Another is implemented by
Levy-Schroedinger semigroups which induce so-called topological Levy processes
(Levy flights with locally modified jump rates in the master equation). Given a
stationary probability function (pdf) associated with the Langevin-based
fractional Fokker-Planck equation, we demonstrate that generically there exists
a topological L\'{e}vy process with the very same invariant pdf and in the
reverse.Comment: To appear in Cent. Eur. J. Phys. (2010
Corrigendum to “Circulating Cancer Stem Cell-Derived Extracellular Vesicles as a Novel Biomarker for Clinical Outcome Evaluation”
[This corrects the article DOI: 10.1155/2019/5879616.].Peer Reviewe
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Circulating Cancer Stem Cell-Derived Extracellular Vesicles as a Novel Biomarker for Clinical Outcome Evaluation.
The recent introduction of the "precision medicine" concept in oncology pushed cancer research to focus on dynamic measurable biomarkers able to predict responses to novel anticancer therapies in order to improve clinical outcomes. Recently, the involvement of extracellular vesicles (EVs) in cancer pathophysiology has been described, and given their release from all cell types under specific stimuli, EVs have also been proposed as potential biomarkers in cancer. Among the techniques used to study EVs, flow cytometry has a high clinical potential. Here, we have applied a recently developed and simplified flow cytometry method for circulating EV enumeration, subtyping, and isolation from a large cohort of metastatic and locally advanced nonhaematological cancer patients (N = 106); samples from gender- and age-matched healthy volunteers were also analysed. A large spectrum of cancer-related markers was used to analyse differences in terms of peripheral blood circulating EV phenotypes between patients and healthy volunteers, as well as their correlation to clinical outcomes. Finally, EVs from patients and controls were isolated by fluorescence-activated cell sorting, and their protein cargoes were analysed by proteomics. Results demonstrated that EV counts were significantly higher in cancer patients than in healthy volunteers, as previously reported. More interestingly, results also demonstrated that cancer patients presented higher concentrations of circulating CD31+ endothelial-derived and tumour cancer stem cell-derived CD133 + CD326- EVs, when compared to healthy volunteers. Furthermore, higher levels of CD133 + CD326- EVs showed a significant correlation with a poor overall survival. Additionally, proteomics analysis of EV cargoes demonstrated disparities in terms of protein content and function between circulating EVs in cancer patients and healthy controls. Overall, our data strongly suggest that blood circulating cancer stem cell-derived EVs may have a role as a diagnostic and prognostic biomarker in cancer
The Schroedinger Problem, Levy Processes Noise in Relativistic Quantum Mechanics
The main purpose of the paper is an essentially probabilistic analysis of
relativistic quantum mechanics. It is based on the assumption that whenever
probability distributions arise, there exists a stochastic process that is
either responsible for temporal evolution of a given measure or preserves the
measure in the stationary case. Our departure point is the so-called
Schr\"{o}dinger problem of probabilistic evolution, which provides for a unique
Markov stochastic interpolation between any given pair of boundary probability
densities for a process covering a fixed, finite duration of time, provided we
have decided a priori what kind of primordial dynamical semigroup transition
mechanism is involved. In the nonrelativistic theory, including quantum
mechanics, Feyman-Kac-like kernels are the building blocks for suitable
transition probability densities of the process. In the standard "free" case
(Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered.
In the framework of the Schr\"{o}dinger problem, the "free noise" can also be
extended to any infinitely divisible probability law, as covered by the
L\'{e}vy-Khintchine formula. Since the relativistic Hamiltonians
and are known to generate such laws, we focus on
them for the analysis of probabilistic phenomena, which are shown to be
associated with the relativistic wave (D'Alembert) and matter-wave
(Klein-Gordon) equations, respectively. We show that such stochastic processes
exist and are spatial jump processes. In general, in the presence of external
potentials, they do not share the Markov property, except for stationary
situations. A concrete example of the pseudodifferential Cauchy-Schr\"{o}dinger
evolution is analyzed in detail. The relativistic covariance of related waveComment: Latex fil
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Corrigendum to "Circulating Cancer Stem Cell-Derived Extracellular Vesicles as a Novel Biomarker for Clinical Outcome Evaluation".
[This corrects the article DOI: 10.1155/2019/5879616.]