Mind Mapping Technique in Language Learning

The current study aims to describe meaningful, powerful and effective tool, used to encourage technical students to apply mind mapping techniques in the language classroom. For this purpose, we overview the previous and the present studies, concerning the problem and describe the implementation of mind mapping techniques in the learning process. The results of this study showed that mind maps help students solve problems, brainstorm creative ideas, remember new vocabulary, take notes, enhance their reading skills, organize the tasks and prepare presentations. This study concludes that mind mapping technique invented in the XX century is considered to be up-to-date, creative, useful and available tool for students, educators and researchers

The Implementation of the Feedback Principle in Science and Technics

In this study positive and negative influence of the feedback have been examined. A feedback principle in the alternating current amplifier and in the speed regulator of the turbine rotation was described. The main conclusion of the positive and negative effect was obtained. Negative feedback worsens the properties of an object, reducing a strengthening factor, delaying regulatory action. Positive feedback considerably raises device work stability. This research will enable to identify the importance and effectiveness of the feedback principle in science and technics

Markov processes follow from the principle of Maximum Caliber

Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible dynamical trajectories in a time-homogeneous process, then the only type of process that maximizes the path entropy, for any given singlet statistics, is a sequence of identical, independently distributed (i.i.d.) random variables, which is the simplest Markov process. If the data is in the form of sequentially pairwise statistics, then maximizing the caliber dictates that the process is Markovian with a uniform initial distribution. Furthermore, if an initial non-uniform dynamical distribution is known, or multiple trajectories are conditioned on an initial state, then the Markov process is still the only one that maximizes the caliber. Second, given a model, MaxCal can be used to compute the parameters of that model. We show that this procedure is equivalent to the maximum-likelihood method of inference in the theory of statistics.Comment: 4 page

Eisenhart lift for higher derivative systems

The Eisenhart lift provides an elegant geometric description of a dynamical system of second order in terms of null geodesics of the Brinkmann-type metric. In this work, we attempt to generalize the Eisenhart method so as to encompass higher derivative models. The analysis relies upon Ostrogradsky's Hamiltonian. A consistent geometric description seems feasible only for a particular class of potentials. The scheme is exemplified by the Pais-Uhlenbeck oscillator.Comment: V2: 12 pages, minor improvements, references added; the version to appear in PL

A First and Second Law for Nonequilibrium Thermodynamics: Maximum Entropy Derivation of the Fluctuation-Dissipation Theorem and Entropy Production Functionals

A theory for non-equilibrium systems is derived from a maximum entropy approach similar in spirit to the equilibrium theory given by Gibbs. Requiring Hamilton's principle of stationary action to be satisfied on average during a trajectory, we add constraints on the transition probability distribution which lead to a path probability of the Onsager-Machlup form. Additional constraints derived from energy and momentum conservation laws then introduce heat exchange and external driving forces into the system, with Lagrange multipliers related to the temperature and pressure of an external thermostatic system. The result is a fully time-dependent, non-local description of a nonequilibrium ensemble. Detailed accounting of the energy exchange and the change in information entropy of the central system then provides a description of the entropy production which is not dependent on the specification or existence of a steady-state or on any definition of thermostatic variables for the central system. These results are connected to the literature by showing a method for path re-weighting, creation of arbitrary fluctuation theorems, and by providing a simple derivation of Jarzynski relations referencing a steady-state. In addition, we identify path free energy and entropy (caliber) functionals which generate a first law of nonequilibrium thermodynamics by relating changes in the driving forces to changes in path averages. Analogous to the Gibbs relations, the variations in the path averages yield fluctuation-dissipation theorems. The thermodynamic entropy production can also be stated in terms of the caliber functional, resulting in a simple proof of our microscopic form for the Clausius statement. We find that the maximum entropy route provides a clear derivation of the path free energy functional, path-integral, Langevin, Brownian, and Fokker-Planck statements of nonequilibrium processes.Comment: 35 page