Making up for the deficit in a marathon run

To predict the final result of an athlete in a marathon run thoroughly is the eternal desire of each trainer. Usually, the achieved result is weaker than the predicted one due to the objective (e.g., environmental conditions) as well as subjective factors (e.g., athlete's malaise). Therefore, making up for the deficit between predicted and achieved results is the main ingredient of the analysis performed by trainers after the competition. In the analysis, they search for parts of a marathon course where the athlete lost time. This paper proposes an automatic making up for the deficit by using a Differential Evolution algorithm. In this case study, the results that were obtained by a wearable sports-watch by an athlete in a real marathon are analyzed. The first experiments with Differential Evolution show the possibility of using this method in the future.Comment: ISMSI 201

Cellular decision-making bias: the missing ingredient in cell functional diversity

Cell functional diversity is a significant determinant on how biological processes unfold. Most accounts of diversity involve a search for sequence or expression differences. Perhaps there are more subtle mechanisms at work. Using the metaphor of information processing and decision-making might provide a clearer view of these subtleties. Understanding adaptive and transformative processes (such as cellular reprogramming) as a series of simple decisions allows us to use a technique called cellular signal detection theory (cellular SDT) to detect potential bias in mechanisms that favor one outcome over another. We can apply method of detecting cellular reprogramming bias to cellular reprogramming and other complex molecular processes. To demonstrate scope of this method, we will critically examine differences between cell phenotypes reprogrammed to muscle fiber and neuron phenotypes. In cases where the signature of phenotypic bias is cryptic, signatures of genomic bias (pre-existing and induced) may provide an alternative. The examination of these alternates will be explored using data from a series of fibroblast cell lines before cellular reprogramming (pre-existing) and differences between fractions of cellular RNA for individual genes after drug treatment (induced). In conclusion, the usefulness and limitations of this method and associated analogies will be discussed.Comment: 18 pages; 6 figures, 2 tables, 4 supplemental figure

Relationship Between Quantum Walk and Relativistic Quantum Mechanics

Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This paper revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled form of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schrodinger form. By showing the coin to be a means to make the walk reversible, and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modelled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of quantum walk, maximum speed of the walk propagation and the earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two state system to which the study can be extended.Comment: 12 pages and 1 figure, Published versio

On the Complete Integrability of Nonlinear Dynamical Systems on Discrete Manifolds within the Gradient-Holonomic Approach

A gradient-holonomic approach for the Lax type integrability analysis of differentialdiscrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied, the related gradient identity is stated. The integrability of a discrete nonlinear Schredinger type dynamical system is treated in detail.Comment: 20 page

Open Quantum Systems. An Introduction

We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and methods traditionally employed by different communities. We present in some detail the mathematical structure and the general properties of the dynamical maps underlying open system dynamics. We also discuss the microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions.Comment: 100 pages, 3 figures. Updated version with typos corrected. Preprint version of the published boo

Time-sliced path integrals with stationary states

The path integral approach to the quantization of one degree-of-freedom Newtonian particles is considered within the discrete time-slicing approach, as in Feynman's original development. In the time-slicing approximation the quantum mechanical evolution will generally not have any stationary states. We look for conditions on the potential energy term such that the quantum mechanical evolution may possess stationary states without having to perform a continuum limit. When the stationary states are postulated to be solutions of a second-order ordinary differential equation (ODE) eigenvalue problem it is found that the potential is required to be a solution of a particular first-order ODE. Similarly, when the stationary states are postulated to be solutions of a second-order ordinary difference equation (O$\Delta$E) eigenvalue problem the potential is required to be a solution of a particular first-order O$\Delta$E. The classical limits (which are at times very nontrivial) are integrable maps.Comment: 7 page

Algorithms Applied to Global Optimisation – Visual Evaluation

Evaluation and assessment of various search and optimisation algorithms is subject of large research efforts. Particular interest of this study is global optimisation and presented approach is based on observation and visual evaluation of Real-Coded Genetic Algorithm, Particle Swarm Optimisation, Differential Evolution and Free Search, which are briefly described and used for experiments. 3D graphical views, generated by visualisation tool VOTASA, illustrate essential aspects of global search process such as divergence, convergence, dependence on initialisation and utilisation of accidental events. Discussion on potential benefits of visual analysis, supported with numerical results, which could be used for comparative assessment of other methods and directions for further research conclude presented study