3,158 research outputs found
Support code for Bravetti, Seri, Zadra, "New directions for contact integrators"
No full textSupport code for Bravetti, Seri, Zadra, "New directions for contact integrators
Simulation code for Bravetti, Seri, Vermeeren, Zadra: "Numerical integration in celestial mechanics: a case for contact geometry"
No full text<p>Support material for Bravetti, Seri, Vermeeren, Zadra: "Numerical integration in celestial mechanics: a case for contact geometry"</p>
Non-determinism in Probabilistic Timed Systems with General Distributions
No full textAbstractIn this paper we address the problem of adequately handling non-deterministic choices in Generalised Semi-Markov Processes (GSMPs), i.e. probabilistic timed systems where durations of delays are expressed by means of random variables with a general probability distribution. In particular we want the probabilistic duration of a delay not to be decided all at once when the delay starts, but step by step in each system state (in the theory of GSMPs this corresponds to recording spent lifetimes instead of residual lifetimes of delays). In this way an adversary cannot take decisions a priori, based on the knowledge he may get about the future behavior of the system. In order to accomplish this, we consider Interactive Generalised Semi-Markov Processes (IGSMPs). We start by formalizing the class of well-named IGSMP models and the class of Interactive Stochastic Timed Transition Systems (ISTTSs) which are both closed under CSP parallel composition and hiding. Then, we introduce a semantics for IGSMPs which maps well-named IGSMP models onto ISTTSs by recording spent lifetimes of delays. Finally, we show that two weakly bisimilar IGSMPs give rise to two weakly bisimilar semantic models and that our semantic mapping is compositional with respect to both CSP parallel composition and hiding
Discrete Time Generative-Reactive Probabilistic Processes with Different Advancing Speeds
No full textWe present a process algebra expressing probabilistic external/internal choices, multi-way synchronizations, and processes with different advancing speeds in the context of discrete time, i.e. where time is not continuous but is represented by a sequence of discrete steps as in discrete time Markov chains (DTMCs). To this end, we introduce a variant of CSP that employs a probabilistic asynchronous parallel operator whose synchronization mechanism is based on a mixture of the classical generative and reactive models of probability. In particular, differently from existing discrete time process algebras, where parallel processes are executed in synchronous locksteps, the parallel operator that we adopt allows processes with different probabilistic advancing speeds (mean number of actions executed per time unit) to be modeled. Moreover, our generative-reactive synchronization mechanism makes it possible to always derive DTMCs in the case of fully specified systems. We then present a sound and complete axiomatization of probabilistic bisimulation over finite processes of our calculus, that is a smooth extension of the axiom system for a standard process algebra, thus solving the open problem of cleanly axiomatizing action restriction in the generative model. As a further result, we show that, when evaluating steady state based performance measures which are expressible by attaching rewards to actions, our approach provides an exact solution even if the advancing speeds are considered not to be probabilistic, without incurring the state space explosion problem that arises with standard synchronous approaches. We finally present a case study on multi-path routing showing the expressiveness of our calculus and that it makes it particularly easy to produce scalable specifications
Contact Hamiltonian Dynamics: The Concept and Its Use
No full textWe give a short survey on the concept of contact Hamiltonian dynamics and its use in several areas of physics, namely reversible and irreversible thermodynamics, statistical physics and classical mechanics. Some relevant examples are provided along the way. We conclude by giving insights into possible future directions
Expressing Processes with Different Action Durations through Probabilities
No full textWe consider a discrete time process algebra capable of (i) modeling processes with different probabilistic advancing speeds (mean number of actions executed per time unit), and (ii) expressing probabilistic external/internal choices and multiway synchronization. We show that, when evaluating steady state based performance measures expressed by associating rewards with actions, such a probabilistic approach provides an exact solution even if advancing speeds are considered not to be probabilistic (i.e. actions of different processes have a different exact duration), without incurring in the state space explosion problem which arises with an intuitive application of a standard synchronous approach. We then present a case study on multi-path routing showing the expressiveness of our calculus and that it makes it particularly easy to produce scalable specifications
Scaling symmetries, contact reduction and Poincaré’s dream
No full textWe state conditions under which a symplectic Hamiltonian system admitting a certain type of symmetry (a scaling symmetry) may be reduced to a type of contact Hamiltonian system, on a space of one less dimension. We observe that such contact reductions underly the well-known McGehee blow-up process from classical mechanics. As a consequence of this broader perspective, we associate a type of variational Herglotz principle associated to these classical blow-ups. Moreover, we consider some more flexible situations for certain Hamiltonian systems depending on parameters, to which the contact reduction may be applied to yield contact Hamiltonian systems along with their Herglotz variational counterparts as the underlying systems of the associated scale-invariant dynamics. From a philosophical perspective, one obtains an equivalent description for the same physical phenomenon, but with fewer inputs needed, thus realizing Poincare's dream of a scale-invariant description of the Universe
Musical stylistic analysis: a study of intervallic transition graphs via persistent homology
No full textWe develop a novel method to represent a weighted directed graph as a finite metric space and then use persistent homology to extract useful features. We apply this method to weighted directed graphs obtained from pitch transitions information of a given musical fragment and use these techniques to the quantitative study of stylistic trends. As a first illustration, we analyse a selection of string quartets by Haydn, Mozart and Beethoven and discuss possible implications of our results in terms of different approaches by these composers to stylistic exploration and variety. We observe that Haydn is stylistically the most conservative, followed by Mozart, while Beethoven is the most innovative. Finally we also compare the variability of different genres, namely minuets, allegros, prestos, and adagios, by a given composer and conclude that the minuet is the most stable form of the string quartet movements
- …
