Machine Learning Models and Statistical Complexity to Analyze the Effects of Posture on Cerebral Hemodynamics

The mechanism of cerebral blood flow autoregulation can be of great importance in diagnosing and controlling a diversity of cerebrovascular pathologies such as vascular dementia, brain injury, and neurodegenerative diseases. To assess it, there are several methods that use changing postures, such as sit-stand or squat-stand maneuvers. However, the evaluation of the dynamic cerebral blood flow autoregulation (dCA) in these postures has not been adequately studied using more complex models, such as non-linear ones. Moreover, dCA can be considered part of a more complex mechanism called cerebral hemodynamics, where others (CO₂ reactivity and neurovascular-coupling) that affect cerebral blood flow (BF) are included. In this work, we analyzed postural influences using non-linear machine learning models of dCA and studied characteristics of cerebral hemodynamics under statistical complexity using eighteen young adult subjects, aged 27 ± 6.29 years, who took the systemic or arterial blood pressure (BP) and cerebral blood flow velocity (BFV) for five minutes in three different postures: stand, sit, and lay. With models of a Support Vector Machine (SVM) through time, we used an AutoRegulatory Index (ARI) to compare the dCA in different postures. Using wavelet entropy, we estimated the statistical complexity of BFV for three postures. Repeated measures ANOVA showed that only the complexity of lay-sit had significant differences.     

Controlling nonlinear waves in excitable media

A new feedback control method is proposed to control the spatio-temporal dynamics in excitable media. Applying suitable external forcing to the system’s slow variable, successful suppression and control of propagating pulses as well as spiral waves can be obtained. The proposed controller is composed by an observer to infer uncertain terms such as diffusive transport and kinetic rates, and an inverse-dynamics feedback function. Numerical simulations shown the effectiveness of the proposed feedback control approach.     

Spatio-temporal characteristics of the Portevin–Le Châtelier effect in austenitic steel with twinning induced plasticity

An experimental investigation of spatio-temporal characteristics of the Portevin–Le Châtelier (PLC) effect in austenitic steel with twinning induced plasticity (TWIP) is presented. Post-processing of high resolution digital images captured from specimens in quasi-static, room temperature tensile tests was conducted with a digital image correlation (DIC) method. This provided direct measurement of strain fields during all stages of the tests. Variable rate digital image capture, enabled with a custom image acquisition algorithm, guaranteed a suitable number of images recorded during serrations in load–time records. Nucleation, propagation, and morphology of individual PLC bands in both straight gage and tapered specimens were quantified with strain rate contours computed with a backward differentiation scheme. Time histories of strain evolution in the PLC band wakes were extracted from cumulative strain contours. Of the three types of PLC bands, only the continuously propagating Type A bands were observed. Band nucleation, which occurred at serration crests in flow curves derived from the DIC results, was not limited to regions of geometry-induced stress concentrations. Due to its importance in finite element springback predictions and to support theoretical model development of inelastic behavior in TWIP steel, we measured Young’s modulus variation with strain in periodic loading–unloading tests. Implications of the experimental results for theoretical modeling of the PLC effect in TWIP steel are discussed.     

Allyl-functionalized hybrid silica monoliths

A hybrid organosilica monolith was synthesized containing an allyl functionality. This provided a viable platform for producing silica-based, chromatographic, monolithic columns with the stationary phase bonded through a surface silicon-carbon bond rather than a conventional siloxane bond.     

Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains

We demonstrate anisotropic enhancement of discrete diffraction and formation of discrete-soliton trains in an optically induced photonic lattice. Such discrete behavior of light propagation was observed when a one-dimensional stripe beam was launched appropriately into a two-dimensional lattice created with partially coherent light. Our experimental results are corroborated with numerical simulations.     

Heteroclinic primary intersections and codimension one Melnikov method for volume-preserving maps

We study families of volume preserving diffeomorphisms in R(3) that have a pair of hyperbolic fixed points with intersecting codimension one stable and unstable manifolds. Our goal is to elucidate the topology of the intersections and how it changes with the parameters of the system. We show that the "primary intersection" of the stable and unstable manifolds is generically a neat submanifold of a "fundamental domain." We compute the intersections perturbatively using a codimension one Melnikov function. Numerical experiments show various bifurcations in the homotopy class of the primary intersections. (c) 2000 American Institute of Physics.     

An Algebraic Version of the Cantor-Bernstein-Schröder Theorem

The Cantor-Bernstein-Schröder theorem of the set theory was generalized by Sikorski and Tarski to -complete boolean algebras, and recently by several authors to other algebraic structures. In this paper we expose an abstract version which is applicable to algebras with an underlying lattice structure and such that the central elements of this lattice determine a direct decomposition of the algebra. Necessary and sufficient conditions for the validity of the Cantor-Bernstein-Schröder theorem for these algebras are given. These results are applied to obtain versions of the Cantor-Bernstein-Schröder theorem for -complete orthomodular lattices, Stone algebras, BL-algebras, MV-algebras, pseudo MV-algebras, ukasiewicz and Post algebras of order n.