Hybrid marked point processes: characterisation, existence and uniqueness

We introduce a class of hybrid marked point processes, which encompasses and extends continuous-time Markov chains and Hawkes processes. While this flexible class amalgamates such existing processes, it also contains novel processes with complex dynamics. These processes are defined implicitly via their intensity and are endowed with a state process that interacts with past-dependent events. The key example we entertain is an extension of a Hawkes process, a state-dependent Hawkes process interacting with its state process. We show the existence and uniqueness of hybrid marked point processes under general assumptions, extending the results of Massouli\'e (1998) on interacting point processes.Comment: v6: introduction updated with reference to application of state-dependent Hawkes processe

Ageing, dynamical scaling and its extensions in many-particle systems without detailed balance

Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving branching-annihilating random walk, two exactly solvable particle-reaction models and kinetic growth models. While the generic scaling descriptions known from magnetic system can be taken over, some of the scaling relations between the ageing exponents are no longer valid. In particular, there is no obvious generalization of the universal limit fluctuation-dissipation ratio. The form of the scaling function of the two-time response function is compared with the prediction of the theory of local scale-invariance.Comment: Latex2e with IOP macros, 32 pages; extended discussion on contact process and new section on kinetic growth processe

Justification Of Conditioning Volitional Development Of Children\u27s Mastering Their Language Skills And Functions

The article analyzes the scientific approaches of domestic scientists to understanding the problem of will and the interrelated aspects of its development in ontogenesis. When studying ways of forming volitional behavior at its first stages, special attention is drawn to the fact that the child\u27s volitional behavior arises with the emergence of the skills to build speech utterances, with which he begins to plan his activities and regulate the process of its implementation, that is, the mastering of planning and regulating functions of speech takes place. By analyzing the ways of forming language skills in preschool and early school age, structures for creation a speech utterance, the author clarified the term "expression speech" (stages of its construction) and language skills, provided for the implementation of each stage of verbal expression. Also it is justified the condition of volitional development of children mastering their language skills and functions; relationship stages of planning and regulatory functions of broadcasting in preschool and early school age. The paper presents the author\u27s functional-structural model of the optimization process of development of the planning and regulatory functions in the formation of children\u27s speech in their language skills

The Study of the Level of Artistic Experience Development of Young Teenagers on the Base of Polyart Approach

The aim of this research is the elaboration of diagnostic instruments for revelation of the level of artistic experience development of young teenagers on the base of polyart approach and also analysis of diagnostic arrangements with fifth-year pupils. The criteria, parameters and level of artistic experience development of teenagers were described in the article; the author\u27s diagnostic tasks were elaborated according to the polyart approach. The diagnostic methods (testing, essay, questionnaire, creative tasks) were determined for each parameter. The diagnostic arrangements at institutions of general education allowed make a conclusion about the necessity to raise the level of artistic experience development of pupils and to prognosticate thhe methods that favor it

Time-Optimal Frictionless Atom Cooling in Harmonic Traps

Frictionless atom cooling in harmonic traps is formulated as a time-optimal control problem and a synthesis of optimal controlled trajectories is obtained. This work has already been used to determine the minimum time for transition between two thermal states and to show the emergence of the third law of classical thermodynamics from quantum thermodynamics. It can also find application in the fast adiabatic-like expansion of Bose-Einstein condensates, with possible applications in atom interferometry. This paper is based on our recently published article in SIAM J. Control Optim.Comment: Submitted to 51st IEEE Conference on Decision and Control as a SIAM regular paper, it is a shorter version of our recently published article in SIAM J. Control Optim., vol. 49, pp. 2440-2462, 2011. It contains an elegant proof of the main technical point using the symmetries of the system, and a discussion of the implications of the results on finite time thermodynamic processe

Residual mean first-passage time for jump processes: theory and applications to L\'evy flights and fractional Brownian motion

We derive a functional equation for the mean first-passage time (MFPT) of a generic self-similar Markovian continuous process to a target in a one-dimensional domain and obtain its exact solution. We show that the obtained expression of the MFPT for continuous processes is actually different from the large system size limit of the MFPT for discrete jump processes allowing leapovers. In the case considered here, the asymptotic MFPT admits non-vanishing corrections, which we call residual MFPT. The case of L/'evy flights with diverging variance of jump lengths is investigated in detail, in particular, with respect to the associated leapover behaviour. We also show numerically that our results apply with good accuracy to fractional Brownian motion, despite its non-Markovian nature.Comment: 13 pages, 8 figure