Manifestation of Chaos in Real Complex Systems: Case of Parkinson's Disease

In this chapter we present a new approach to the study of manifestations of chaos in real complex system. Recently we have achieved the following result. In real complex systems the informational measure of chaotic chatacter (IMC) can serve as a reliable quantitative estimation of the state of a complex system and help to estimate the deviation of this state from its normal condition. As the IMC we suggest the statistical spectrum of the non-Markovity parameter (NMP) and its frequency behavior. Our preliminary studies of real complex systems in cardiology, neurophysiology and seismology have shown that the NMP has diverse frequency dependence. It testifies to the competition between Markovian and non-Markovian, random and regular processes and makes a crossover from one relaxation scenario to the other possible. On this basis we can formulate the new concept in the study of the manifestation of chaoticity. We suggest the statistical theory of discrete non-Markov stochastic processes to calculate the NMP and the quantitative evaluation of the IMC in real complex systems. With the help of the IMC we have found out the evident manifestation of chaosity in a normal (healthy) state of the studied system, its sharp reduction in the period of crises, catastrophes and various human diseases. It means that one can appreciably improve the state of a patient (of any system) by increasing the IMC of the studied live system. The given observation creates a reliable basis for predicting crises and catastrophes, as well as for diagnosing and treating various human diseases, Parkinson's disease in particular.Comment: 20 pages, 8 figures, 3 tables. To be published in "The Logistic Map and the Route to Chaos: From the Beginnings to the Modern Applications", eds. by M. Ausloos, M. Dirickx, pp. 175-196, Springer-Verlag, Berlin (2006

Cohort profile: the Siyakhula cohort, rural South Africa

No abstract available

Child Labour and Its Impact on Children's Access To and Participation in Primary Education: A Case Study from Tanzania

Labor and Human Capital,

A study of the anisotropy of stress in a fluid confined in a nanochannel

We present molecular dynamics simulations of planar Poiseuille flow of a Lennard-Jones fluid at various temperatures and body forces. Local thermostatting is used close to the walls to reach steady-state up to a limit body force. Macroscopic fields are obtained from microscopic data by time- and space-averaging and smoothing the data with a self-consistent coarse-graining method based on kernel interpolation. Two phenomena make the system interesting: (i) strongly confined fluids show layering, i.e., strong oscillations in density near the walls, and (ii) the stress deviates from the Newtonian fluid assumption, not only in the layered regime, but also much further away from the walls. Various scalar, vectorial, and tensorial fields are analyzed and related to each other in order to understand better the effects of both the inhomogeneous density and the anisotropy on the flow behavior and rheology. The eigenvalues and eigendirections of the stress tensor are used to quantify the anisotropy in stress and form the basis of a newly proposed objective, inherently anisotropic constitutive model that allows for non-collinear stress and strain gradient by construction

On the analytical approach to the N-fold B\"acklund transformation of Davey-Stewartson equation

N-fold B\"acklund transformation for the Davey-Stewartson equation is constructed by using the analytic structure of the Lax eigenfunction in the complex eigenvalue plane. Explicit formulae can be obtained for a specified value of N. Lastly it is shown how generalized soliton solutions are generated from the trivial ones

Quantum adiabatic optimization and combinatorial landscapes

In this paper we analyze the performance of the Quantum Adiabatic Evolution algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, $\gamma=M/N$. We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (versus only energy) is used, and are able to show the existence of a dynamic threshold $\gamma=\gamma_d$ starting with some value of K -- the number of variables in each clause. Beyond dynamic threshold, the algorithm should take exponentially long time to find a solution. We compare the results for extended and simplified sets of landscapes and provide numerical evidence in support of our universality ansatz. We have been able to map the ensemble of random graphs onto another ensemble with fluctuations significantly reduced. This enabled us to obtain tight upper bounds on satisfiability transition and to recompute the dynamical transition using the extended set of landscapes.Comment: 41 pages, 10 figures; added a paragraph on paper's organization to the introduction, fixed reference

Lithium in the Symbiotic Mira V407 Cyg

We report an identification of the lithium resonance doublet LiI 6708A in the spectrum of V407 Cyg, a symbiotic Mira with a pulsation period of about 745 days. The resolution of the spectra used was R~18500 and the measured equivalent width of the line is ~0.34A. It is suggested that the lithium enrichment is due to hot bottom burning in the intermediate mass AGB variable, although other possible origins cannot be totally ruled out. In contrast to lithium-rich AGB stars in the Magellanic clouds, ZrO 5551A, 6474A absorption bands were not found in the spectrum of V407Cyg. These are the bands used to classify the S-type stars at low-resolution. Although we identified weak ZrO 5718A, 6412A these are not visible in the low-resolution spectra, and we therefore classify the Mira in V407 Cyg as an M type. This, together with other published work, suggests lithium enrichment can precede the third dredge up of s-process enriched material in galactic AGB stars.Comment: 4 pages, 2 figures, to be published in MNRA

A reactive assimilation model for regional-scale cordierite-bearing granitoids: geochemical evidence from the Late Variscan granites of the Central Iberian Zone, Spain

Regional scale biotite and cordierite-bearing granites (s.l.) in the Variscan of the Central Iberian Zone (CIZ) are spatially closely associated with cordierite-rich nebulites and cordierite-bearing two-mica granites, and with cordierite-rich high grade hornfelses and cordieritites (>60% cordierite) that are relatively common in the aureoles of these granites. Building on published field evidence, petrological data are presented which, combined with new chemical and isotopic (Sr-Nd) modelling, indicate that the cordierite-bearing granites cannot be derived by simple anatexis of regional sedimenatry protoliths; but the data are consistent with a process of reactive assimilation that involves the interaction of biotite granite magma with high-grade host rocks ranging from cordierite nebulites to andalusite-bearing cordieritites. The contribution of the postulated cordierite-rich contaminants to the diversity of cordierite granite compositions is modelled using the compositions of regional Lower Cambrian-Upper Neoproterozoic metasedimentary rocks that are generally chemically mature (CaO very rarely exceeds 1.4%). These rocks include specific horizons in which extreme chemical alteration is attributable to sediment reworking during eustatic falls in sea level. Such compositions may account for the presence of the high concentrations in Al that later produced cordieritites. Fractional crystallisation is also important, particularly in generating the more evolved cordierite granite and cordierite biotite muscovite granite compositions. Although assimilation in situ is normally regarded as a minor contributor volumetrically to evolving plutons, in this instance the emplacement of large volumes of granite magma into a high-T-low-P environment significantly increased the potential for reactive assimilation

Shunting of Passenger Train Units: an Integrated Approach

In this paper, we describe a new model for the Train Unit Shunting Problem. This model is capable of solving the matching and parking subproblems in an integrated manner, usually requiring a reasonable amount of computation time for generating acceptable solutions. Furthermore, the model incorporates complicating details from practice, such as trains composed of several train units and tracks that can be approached from two sides. Computation times are reduced by introducing the concept of virtual shunt tracks. Computational results are presented for real-life cases of NS Reizigers, the main Dutch passenger railway operator.Optimization;Passenger Railways;Shunting

On Randomized Algorithms for Matching in the Online Preemptive Model

We investigate the power of randomized algorithms for the maximum cardinality matching (MCM) and the maximum weight matching (MWM) problems in the online preemptive model. In this model, the edges of a graph are revealed one by one and the algorithm is required to always maintain a valid matching. On seeing an edge, the algorithm has to either accept or reject the edge. If accepted, then the adjacent edges are discarded. The complexity of the problem is settled for deterministic algorithms. Almost nothing is known for randomized algorithms. A lower bound of $1.693$ is known for MCM with a trivial upper bound of $2$. An upper bound of $5.356$ is known for MWM. We initiate a systematic study of the same in this paper with an aim to isolate and understand the difficulty. We begin with a primal-dual analysis of the deterministic algorithm due to McGregor. All deterministic lower bounds are on instances which are trees at every step. For this class of (unweighted) graphs we present a randomized algorithm which is $\frac{28}{15}$-competitive. The analysis is a considerable extension of the (simple) primal-dual analysis for the deterministic case. The key new technique is that the distribution of primal charge to dual variables depends on the "neighborhood" and needs to be done after having seen the entire input. The assignment is asymmetric: in that edges may assign different charges to the two end-points. Also the proof depends on a non-trivial structural statement on the performance of the algorithm on the input tree. The other main result of this paper is an extension of the deterministic lower bound of Varadaraja to a natural class of randomized algorithms which decide whether to accept a new edge or not using independent random choices