82 research outputs found
Quantum Variance and Ergodicity for the baker's map
We prove a Egorov theorem, or quantum-classical correspondence, for the
quantised baker's map, valid up to the Ehrenfest time. This yields a
logarithmic upper bound for the decay of the quantum variance, and, as a
corollary, a quantum ergodic theorem for this map
Follow the fugitive: an application of the method of images to open dynamical systems
Borrowing and extending the method of images we introduce a theoretical
framework that greatly simplifies analytical and numerical investigations of
the escape rate in open dynamical systems. As an example, we explicitly derive
the exact size- and position-dependent escape rate in a Markov case for holes
of finite size. Moreover, a general relation between the transfer operators of
closed and corresponding open systems, together with the generating function of
the probability of return to the hole is derived. This relation is then used to
compute the small hole asymptotic behavior, in terms of readily calculable
quantities. As an example we derive logarithmic corrections in the second order
term. Being valid for Markov systems, our framework can find application in
information theory, network theory, quantum Weyl law and via Ulam's method can
be used as an approximation method in more general dynamical systems.Comment: 9 pages, 1 figur
Exploring TV Seriality and Television Studies through Data-Driven Approaches
The chapter discusses the use of data-driven approaches in television studies, which has become possible due to the increasing availability of digital data. Computational techniques can be used to analyze cultural artifacts, gain insights into audience reactions to specific shows or episodes, and investigate patterns and trends in television programming over time. The chapter also highlights the challenges of analyzing television series, which are complex open systems that interact with external factors such as the production process, audience feedback, and cultural and social context. Content analysis, which involves qualitative and quantitative methods based on the coding process and data collection, can be used to analyze various elements of a TV series.
Generative AI is also discussed, which refers to the use of deep multi-modal algorithms to generate new content such as images, speech, and text. Generative methods like Generative Adversarial Networks (GANs) and Stable Diffusion can create new content that is almost indistinguishable from real data. While generating videos is more challenging, Recurrent Neural Networks (RNNs) like LSTMs can capture the temporal dynamics of the scenes to create interesting and promising applications for complex, but short-duration videos
Entropic measures of individual mobility patterns
Understanding human mobility from a microscopic point of view may represent a
fundamental breakthrough for the development of a statistical physics for
cognitive systems and it can shed light on the applicability of macroscopic
statistical laws for social systems. Even if the complexity of individual
behaviors prevents a true microscopic approach, the introduction of mesoscopic
models allows the study of the dynamical properties for the non-stationary
states of the considered system. We propose to compute various entropy measures
of the individual mobility patterns obtained from GPS data that record the
movements of private vehicles in the Florence district, in order to point out
new features of human mobility related to the use of time and space and to
define the dynamical properties of a stochastic model that could generate
similar patterns. Moreover, we can relate the predictability properties of
human mobility to the distribution of time passed between two successive trips.
Our analysis suggests the existence of a hierarchical structure in the mobility
patterns which divides the performed activities into three different
categories, according to the time cost, with different information contents. We
show that a Markov process defined by using the individual mobility network is
not able to reproduce this hierarchy, which seems the consequence of different
strategies in the activity choice. Our results could contribute to the
development of governance policies for a sustainable mobility in modern cities
Programma del Corso A.A. 14/15
Lista sommaria degli argomenti svolti a lezione. I riferimenti sono alla seconda edizione del libro. A disposizione per chiarimenti o altro
The d'-dibaryon in a colored cluster model
We calculate the mass and structure of a J^P=0^-, T=0 six-quark system using
a colored diquark-tetraquark cluster wave function and a nonrelativistic quark
model Hamiltonian. The calculated mass is some 350 MeV above the empirical
value if the same confinement strength as in the nucleon is used. If the
effective two-body confinement strength is weaker in a compound six-quark
system than in a single baryon, as expected from a simple harmonic oscillator
model, one obtains M_d' = 2092 MeV close to experiment.Comment: 6 pages, Revtex, 2 ps-figures included, to appear in the Proceedings
of the '6th Conference on the Intersections of Particle and Nuclear Physics'
Big Sky, 199
Dynamics of transposable elements generates structure and symmetries in genetic sequences
Genetic sequences are known to possess non-trivial composition together with
symmetries in the frequencies of their components. Recently, it has been shown
that symmetry and structure are hierarchically intertwined in DNA, suggesting a
common origin for both features. However, the mechanism leading to this
relationship is unknown. Here we investigate a biologically motivated dynamics
for the evolution of genetic sequences. We show that a metastable (long-lived)
regime emerges in which sequences have symmetry and structure interlaced in a
way that matches that of extant genomes.Comment: 6 pagesm 4 figure
On a waiting-time result of Kontoyiannis: mixing or decoupling?
We introduce conditions of lower decoupling to the study of waiting-time
estimations of the cross entropy between two mutually independent stationary
stochastic processes. Although similar decoupling conditions have been used in
the literature on large deviations and statistical mechanics, they appear
largely unexplored in information theory. Building on a result of Kontoyiannis,
namely Theorem 4 in [Kontoyiannis, J. Theor. Probab., 1998], and replacing the
-mixing condition in this result with a lower decoupling condition, we
considerably extend the validity of waiting-time estimation of cross entropy
Recurrence times, waiting times and universal entropy production estimators
The universal typical-signal estimators of entropy and cross entropy based on
the asymptotics of recurrence and waiting times play an important role in
information theory. Building on their construction, we introduce and study
universal typical-signal estimators of entropy production in the context of
nonequilibrium statistical mechanics of one-sided shifts over finite alphabets
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