Related papers: Measure theory through dynamical eyes
The physics of glasses can be studied from many viewpoints, from material scientists interested in the development of new materials to statistical physicists inventing new theoretical tools to deal with disordered systems. In these lectures…
The subject of this thesis is the study of dissipative dynamics and their properties in particle physics, dealing with neutral B-mesons, neutron interferometry and neutrino physics. Modified expressions for the relevant phenomenological…
This is a writeup of lectures on "statistics" that have evolved from the initial version for the 2009 Hadron Collider Physics Summer School at CERN to versions for other venues and, most recently, for the African School of Fundamental…
The term "measurement" in quantum theory (as well as in other physical theories) is ambiguous: It is used to describe both an experience - e.g., an observation in an experiment - and an interaction with the system under scrutiny. If doing…
We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of {\it temporal dynamics} in music. (i) Phase space portraits are…
Measure structured deformations are introduced to present a unified theory of deformations of continua. The energy associated with a measure structured deformation is defined via relaxation departing either from energies associated with…
We discuss a theoretical approach to structural glasses as they happen in real situations. Older ideas based on `configurational entropy', on `fictive temperatures' and on Edwards' `compactivity' are sharpened and unified in an out of…
We analyse the connections between structure and dynamics in two model glass-formers, using the mutual information between an initial configuration and the ensuing dynamics to compare the predictive value of different structural…
Traditional methods in educational research often fail to capture the complex and evolving nature of learning processes. This chapter examines the use of complex systems theory in education to address these limitations. The chapter covers…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
The dynamics of a system, made of a particle interacting with a field mode, thwarted by the action of repeated projective measurements on the particle, is examined. The effect of the partial measurements is discussed by comparing it with…
The dynamical system approach has recently acquired great importance in the investigation on higher order theories of gravity. In this talk I review the main results and I give brief comments on the perspectives for further developments.
This paper is partly an exposition, and partly an extension of our work [1] to the multiparameter case. We consider certain classes of parametrized dynamically defined measures. These are push-forwards, under the natural projection, of…
The purpose of the dynamics of moving systems is to search for the mathematical model that describes the link between the resultant applied force, that is the cause, and the speed of system that is the effect. This mathematical link…
Two-dimensional case in the theory of dynamical systems admitting the normal shift differs crucially from multidimensional case. Features of two-dimensional case are gathered and studied in this thesis.
These are extended notes of the course given by the author at RIMS, Kyoto, in October 2016. The aim is to give a self-contained overview on the recently developed approach to differential calculus on metric measure spaces. The effort is…
While the methodological rigor of computing research has improved considerably in the past two decades, quantitative software engineering research is hampered by immature measures and inattention to theory. Measurement-the principled…
Every physical theory has (at least) two different forms of mathematical equations to represent its target systems: the dynamical (equations of motion) and the kinematical (kinematical constraints). Kinematical constraints are…
It is indicated that the definition of physical measures via ``exponential of minus the action times kinematical measure'' contradicts properties of certain physical models. In particular, theories describing confinement typically cannot be…
In this book, we study Gromov's metric geometric theory on the space of metric measure spaces, based on the idea of concentration of measure phenomenon due to L\'evy and Milman. Although most of the details are omitted in the original…