Effects of non-denumerable fixed points in finite dynamical systems

The motion of a spinning football brings forth the possible existence of a whole class of finite dynamical systems where there may be non-denumerably infinite number of fixed points. They defy the very traditional meaning of the fixed point that a point on the fixed point in the phase space should remain there forever, for, a fixed point can evolve as well! Under such considerations one can argue that a free-kicked football should be non-chaotic.Comment: This paper is a replaced version to modify the not-so-true claim, made unknowingly in the earlier version, of being first to propose the peculiar dynamical systems as described in the paper. With respect to the original workers, we present here our original finding

Computing the multifractal spectrum from time series: An algorithmic approach

We show that the existing methods for computing the f(\alpha) spectrum from a time series can be improved by using a new algorithmic scheme. The scheme relies on the basic idea that the smooth convex profile of a typical f(\alpha) spectrum can be fitted with an analytic function involving a set of four independent parameters. While the standard existing schemes [16, 18] generally compute only an incomplete f(\alpha) spectrum (usually the top portion), we show that this can be overcome by an algorithmic approach which is automated to compute the Dq and f(\alpha) spectrum from a time series for any embedding dimension. The scheme is first tested with the logistic attractor with known f(\alpha) curve and subsequently applied to higher dimensional cases. We also show that the scheme can be effectively adapted for analysing practcal time series involving noise, with examples from two widely different real world systems. Moreover, some preliminary results indicating that the set of four independant parameters may be used as diagnostic measures is also included.Comment: 10 pages, 16 figures, submitted to CHAO

Persistent Chaos in High Dimensions

An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter windows with periodic behavior decreases. A subset of parameter space remains in which topological change induced by small parameter variation is very common. It turns out, however, that if the system's dimension is sufficiently high, this inevitable, and expected, topological change is never catastrophic, in the sense chaotic behavior is preserved. One concludes that deterministic chaos is persistent in high dimensions.Comment: 4 pages, 3 figures; Changes in response to referee comment

Pulsive feedback control for stabilizing unstable periodic orbits in a nonlinear oscillator with a non-symmetric potential

We examine a strange chaotic attractor and its unstable periodic orbits in case of one degree of freedom nonlinear oscillator with non symmetric potential. We propose an efficient method of chaos control stabilizing these orbits by a pulsive feedback technique. Discrete set of pulses enable us to transfer the system from one periodic state to another.Comment: 11 pages, 4 figure

Microcirculation abnormalities in patients with fibromyalgia – measured by capillary microscopy and laser fluxmetry

This unblinded preliminary case-control study was done to demonstrate functional and structural changes in the microcirculation of patients with primary fibromyalgia (FM). We studied 10 women (54.0 ± 3.7 years of age) with FM diagnosed in accordance with the classification criteria of the American College of Rheumatology, and controls in three groups (n = 10 in each group) – age-matched women who were healthy or who had rheumatoid arthritis or systemic scleroderma (SSc). All 40 subjects were tested within a 5-week period by the same investigators, using two noninvasive methods, laser fluxmetry and capillary microscopy. The FM patients were compared with the healthy controls (negative controls) and with rheumatoid arthritis patients and SSc patients (positive controls). FM patients had fewer capillaries in the nail fold (P < 0.001) and significantly more capillary dilatations (P < 0.05) and irregular formations (P < 0.01) than the healthy controls. Interestingly, the peripheral blood flow in FM patients was much less (P < 0.001) than in healthy controls but did not differ from that of SSc patients (P = 0.73). The data suggest that functional disturbances of microcirculation are present in FM patients and that morphological abnormalities may also influence their microcirculation

Probability of local bifurcation type from a fixed point: A random matrix perspective

Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties as universal approximators (neural networks). The eigenvalue spectra is considered both numerically and analytically using previous work of Edelman et. al. Based upon the numerical evidence, various conjectures are presented. The conclusion is that in many circumstances, most bifurcations from fixed points of large dynamical systems will be due to complex eigenvalues. Nevertheless, surprising situations are presented for which the aforementioned conclusion is not general, e.g. real random matrices with Gaussian elements with a large positive mean and finite variance.Comment: 21 pages, 19 figure

An Intact Kidney Slice Model to Investigate Vasa Recta Properties and Function in situ

Background: Medullary blood flow is via vasa recta capillaries, which possess contractile pericytes. In vitro studies using isolated descending vasa recta show that pericytes can constrict/dilate descending vasa recta when vasoactive substances are present. We describe a live kidney slice model in which pericyte-mediated vasa recta constriction/dilation can be visualized in situ. Methods: Confocal microscopy was used to image calcein, propidium iodide and Hoechst labelling in ‘live’ kidney slices, to determine tubular and vascular cell viability and morphology. DIC video-imaging of live kidney slices was employed to investigate pericyte-mediated real-time changes in vasa recta diameter. Results: Pericytes were identified on vasa recta and their morphology and density were characterized in the medulla. Pericyte-mediated changes in vasa recta diameter (10–30%) were evoked in response to bath application of vasoactive agents (norepinephrine, endothelin-1, angiotensin-II and prostaglandin E2) or by manipulating endogenous vasoactive signalling pathways (using tyramine, L-NAME, a cyclo-oxygenase (COX-1) inhibitor indomethacin, and ATP release). Conclusions: The live kidney slice model is a valid complementary technique for investigating vasa recta function in situ and the role of pericytes as regulators of vasa recta diameter. This technique may also be useful in exploring the role of tubulovascular crosstalk in regulation of medullary blood flow

A frequentist framework of inductive reasoning

Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly from limiting relative frequencies rather than computed according to the Bayes update rule. The proposal is developed as follows using the confidence measure of a scalar parameter of interest. (With the restriction to one-dimensional parameter space, a confidence measure is essentially a fiducial probability distribution free of complications involving ancillary statistics.) A betting game establishes a sense in which confidence measures are the only reliable inferential probability distributions. The equality between the probabilities encoded in a confidence measure and the coverage rates of the corresponding confidence intervals ensures that the measure's rule for assigning confidence levels to hypotheses is uniquely minimax in the game. Although a confidence measure can be computed without any prior distribution, previous knowledge can be incorporated into confidence-based reasoning. To adjust a p-value or confidence interval for prior information, the confidence measure from the observed data can be combined with one or more independent confidence measures representing previous agent opinion. (The former confidence measure may correspond to a posterior distribution with frequentist matching of coverage probabilities.) The representation of subjective knowledge in terms of confidence measures rather than prior probability distributions preserves approximate frequentist validity.Comment: major revisio

Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics

The atmospheric greenhouse effect, an idea that many authors trace back to the traditional works of Fourier (1824), Tyndall (1861), and Arrhenius (1896), and which is still supported in global climatology, essentially describes a fictitious mechanism, in which a planetary atmosphere acts as a heat pump driven by an environment that is radiatively interacting with but radiatively equilibrated to the atmospheric system. According to the second law of thermodynamics such a planetary machine can never exist. Nevertheless, in almost all texts of global climatology and in a widespread secondary literature it is taken for granted that such mechanism is real and stands on a firm scientific foundation. In this paper the popular conjecture is analyzed and the underlying physical principles are clarified. By showing that (a) there are no common physical laws between the warming phenomenon in glass houses and the fictitious atmospheric greenhouse effects, (b) there are no calculations to determine an average surface temperature of a planet, (c) the frequently mentioned difference of 33 degrees Celsius is a meaningless number calculated wrongly, (d) the formulas of cavity radiation are used inappropriately, (e) the assumption of a radiative balance is unphysical, (f) thermal conductivity and friction must not be set to zero, the atmospheric greenhouse conjecture is falsified.Comment: 115 pages, 32 figures, 13 tables (some typos corrected

Highly-accurate 5-axis flank CNC machining with conical tools

A new method for $5$-axis flank computer numerically controlled (CNC) machining using a predefined set of tappered ball-end-mill tools (aka conical) cutters is proposed. The space of lines that admit tangential motion of an associated truncated cone along a general, doubly curved, free-form surface is explored. These lines serve as discrete positions of conical axes in 3D space. Spline surface fitting is used to generate a ruled surface that represents a single continuous sweep of a rigid conical milling tool. An optimization based approach is then applied to globally minimize the error between the design surface and the conical envelope. Our computer simulation are validated with physical experiments on two benchmark industrial datasets, reducing significantly the execution times while preserving or even reducing the milling error when compared to the state-of-the-art industrial software