Topological regulation of activation barriers on fractal substrates

We study phase-ordering dynamics of a ferromagnetic system with a scalar order-parameter on fractal graphs. We propose a scaling approach, inspired by renormalization group ideas, where a crossover between distinct dynamical behaviors is induced by the presence of a length $\lambda$ associated to the topological properties of the graph. The transition between the early and the asymptotic stage is observed when the typical size $L(t)$ of the growing ordered domains reaches the crossover length $\lambda$. We consider two classes of inhomogeneous substrates, with different activated processes, where the effects of the free energy barriers can be analytically controlled during the evolution. On finitely ramified graphs the free energy barriers encountered by domains walls grow logarithmically with $L(t)$ while they increase as a power-law on all the other structures. This produces different asymptotic growth laws (power-laws vs logarithmic) and different dependence of the crossover length $\lambda$ on the model parameters. Our theoretical picture agrees very well with extensive numerical simulations.Comment: 13 pages, 4 figure

Fractal Patterns of Neural Activity Exist within the Suprachiasmatic Nucleus and Require Extrinsic Network Interactions

The mammalian central circadian pacemaker (the suprachiasmatic nucleus, SCN) contains thousands of neurons that are coupled through a complex network of interactions. In addition to the established role of the SCN in generating rhythms of ∼24 hours in many physiological functions, the SCN was recently shown to be necessary for normal self-similar/fractal organization of motor activity and heart rate over a wide range of time scales—from minutes to 24 hours. To test whether the neural network within the SCN is sufficient to generate such fractal patterns, we studied multi-unit neural activity of in vivo and in vitro SCNs in rodents. In vivo SCN-neural activity exhibited fractal patterns that are virtually identical in mice and rats and are similar to those in motor activity at time scales from minutes up to 10 hours. In addition, these patterns remained unchanged when the main afferent signal to the SCN, namely light, was removed. However, the fractal patterns of SCN-neural activity are not autonomous within the SCN as these patterns completely broke down in the isolated in vitro SCN despite persistence of circadian rhythmicity. Thus, SCN-neural activity is fractal in the intact organism and these fractal patterns require network interactions between the SCN and extra-SCN nodes. Such a fractal control network could underlie the fractal regulation observed in many physiological functions that involve the SCN, including motor control and heart rate regulation

Fractal Rigidity in Migraine

We study the middle cerebral artery blood flow velocity (MCAfv) in humans using transcranial Doppler ultrasonography (TCD). Scaling properties of time series of the axial flow velocity averaged over a cardiac beat interval may be characterized by two exponents. The short time scaling exponent (STSE) determines the statistical properties of fluctuations of blood flow velocities in short-time intervals while the Hurst exponent describes the long-term fractal properties. In many migraineurs the value of the STSE is significantly reduced and may approach that of the Hurst exponent. This change in dynamical properties reflects the significant loss of short-term adaptability and the overall hyperexcitability of the underlying cerebral blood flow control system. We call this effect fractal rigidity.Comment: 4 pages, 6 figure

Epigenetic regulation of osteogenesis: human embryonic palatal mesenchymal cells.

Mesenchymal stem cells (MSCs) provide an appropriate model to study epigenetic changes during osteogenesis and bone regeneration due to their differentiation potential. Since there are no unique markers for MSCs, methods of identification are limited. The complex morphology of human embryonic palatal mesenchyme stem cell (HEPM) requires analysis of fractal dimensions to provide an objective quantification of self-similarity, a statistical transformation of cellular shape and border complexity. We propose the hypothesis of a study to compare and contrast sequential steps of osteogenic differentiation in HEPMs both phenotypically using immunocytochemistry, and morphometrically using fractal analysis from undifferentiated passage 1 (P1) to passage 7 (P7) cells. The proof-of-concept is provided by results we present here that identify and compare the modulation of expression of certain epigenetic biomarkers (alkaline phosphatase, ALP; stromal interaction molecule-1, STRO-1; runt-related transcription factor-2, RUNX2), which are established markers of osteogenesis in bone marrow studies, of osteoblastic/skeletal morphogenesis, and of osteoblast maturation. We show that Osteoinductive medium (OIM) modulates the rate of differentiation of HEPM into Run-2+ cells, the most differentiated subpopulation, followed by ALP+ and STRO-1+ cells. Taken together, our phenotypical and morphometric data demonstrate the feasibility of using HEPM to assess osteogenic differentiation from an early undifferentiated to a differentiated stage. This research model may lay the foundation for future studies aimed at characterizing the epigenetic characteristics of osteoimmunological disorders and dysfunctions (e.g., osteoarthritis, temporomandibular joint disorders), so that proteomic profiling can aid the diagnosis and monitor the prognosis of these and other osteoimmunopathologies

Gait variability: methods, modeling and meaning

The study of gait variability, the stride-to-stride fluctuations in walking, offers a complementary way of quantifying locomotion and its changes with aging and disease as well as a means of monitoring the effects of therapeutic interventions and rehabilitation. Previous work has suggested that measures of gait variability may be more closely related to falls, a serious consequence of many gait disorders, than are measures based on the mean values of other walking parameters. The Current JNER series presents nine reports on the results of recent investigations into gait variability. One novel method for collecting unconstrained, ambulatory data is reviewed, and a primer on analysis methods is presented along with a heuristic approach to summarizing variability measures. In addition, the first studies of gait variability in animal models of neurodegenerative disease are described, as is a mathematical model of human walking that characterizes certain complex (multifractal) features of the motor control's pattern generator. Another investigation demonstrates that, whereas both healthy older controls and patients with a higher-level gait disorder walk more slowly in reduced lighting, only the latter's stride variability increases. Studies of the effects of dual tasks suggest that the regulation of the stride-to-stride fluctuations in stride width and stride time may be influenced by attention loading and may require cognitive input. Finally, a report of gait variability in over 500 subjects, probably the largest study of this kind, suggests how step width variability may relate to fall risk. Together, these studies provide new insights into the factors that regulate the stride-to-stride fluctuations in walking and pave the way for expanded research into the control of gait and the practical application of measures of gait variability in the clinical setting