Energy spectra of quasiperiodic systems via information entropy

Periodic, quasiperiodic, fractal, Kolakoski, and random binary polymers: Energy structure and carrier transport

We study periodic, quasiperiodic (Thue-Morse, Fibonacci, period doubling, Rudin-Shapiro), fractal (Cantor, generalized Cantor), Kolakoski, and random binary sequences using a tight-binding wire model, where a site is a monomer (e.g., in DNA, a base pair). We use B-DNA as our prototype system. All sequences have purines, guanine (G) or adenine (A), on the same strand, i.e., our prototype binary alphabet is {G,A}. Our aim is to examine the influence of sequence intricacy and magnitude of parameters on energy structure, localization, and charge transport. We study quantities such as autocorrelation function, eigenspectra, density of states, Lyapunov exponents, transmission coefficients, and current-voltage curves. We show that the degree of sequence intricacy and the presence of correlations decisively affect the aforementioned physical properties. Periodic segments have enhanced transport properties. Specifically, in homogeneous sequences transport efficiency is maximum. There are several deterministic aperiodic sequences that can support significant currents, depending on the Fermi level of the leads. Random sequences is the less efficient category.

Recurrence Quantification Analysis at work: Quasi-periodicity based interpretation of gait force profiles for patients with Parkinson disease

In this letter, making use of real gait force profiles of healthy and patient groups with Parkinson disease which have different disease severity in terms of Hoehn-Yahr stage, we calculate various heuristic complexity measures of the recurrence quantification analysis (RQA). Using this technique, we are able to evince that entropy, determinism and average diagonal line length (divergence) measures decrease (increases) with increasing disease severity. We also explain these tendencies using a theoretical model (based on the sine-circle map), so that we clearly relate them to decreasing degree of irrationality of the system as a course of gait’s nature. This enables us to interpret the dynamics of normal/pathological gait and is expected to increase further applications of this technique on gait timings, gait force profiles and combinations of them with various physiological signals.

The possibilities of modeling neural networks in the framework of the thermodynamics of genetically disordered systems (glasses)

Non-spin glasses possess a number of specific features which, in structural and dynamic aspects, are close to conditions necessary for neural networks to function. In a disordered network there exists a plurality of structural parameters and a number of two-level states defined by double-well potentials. Their characteristics are specified by the conditions of glass formation, i.e. by genesis. The thermodynamic description of glass as a self-organizing system (that does not require introducing an interacting potential model) leads to an unambiguous conclusion that its frequency spectrum is predetermined by the structure, which is characterized by zero-point entropy. Glass is a natural system of oscillators which form a disordered network. In this sense, glass conforms to a known model of a disordered neural network formed by interconnected oscillators. If one assumes that in living organisms the structure of a neural network (the brain) is inherited according to a genetic mechanism, the quickness of learning and recognition of patterns, the stability of associative memory and other capabilities have to be inherited genetically. The more ordered a neural network formed by distinguishable neurons, the better its capabilities.