New Coins From Old: Computing With Unknown Bias

Suppose that we are given a function f : (0, 1)→(0,1) and, for some unknown p∈(0, 1), a sequence of independent tosses of a p-coin (i.e., a coin with probability p of “heads”). For which functions f is it possible to simulate an f(p)-coin? This question was raised by S. Asmussen and J. Propp. A simple simulation scheme for the constant function f(p)≡1/2 was described by von Neumann (1951); this scheme can be easily implemented using a finite automaton. We prove that in general, an f(p)-coin can be simulated by a finite automaton for all p ∈ (0, 1), if and only if f is a rational function over ℚ. We also show that if an f(p)-coin can be simulated by a pushdown automaton, then f is an algebraic function over ℚ; however, pushdown automata can simulate f(p)-coins for certain nonrational functions such as . These results complement the work of Keane and O’Brien (1994), who determined the functions f for which an f(p)-coin can be simulated when there are no computational restrictions on the simulation scheme. * Supported by a Miller Fellowship. † Supported in part by NSF Grant DMS-0104073 and by a Miller Professorship. ‡ This work is supported under a National Science Foundation Graduate Research Fellowship.     

Nonlinear breakup of an asymmetric electrohydrodynamic jet

Nonlinear asymmetric breakup of a circular capillary jet stressed at the surface by an electrical field is presented. The method of straining of coordinates is used to calculate the cutoff wave number. The numerical results show that an initially sinusoidal wave develops in an asymmetrical form by the nonlinear effect from higher harmonics. It is shown that a linear relation-ship exists between the breakup times and the logarithms of the amplitudes of the wave. The slopes of these lines can be used to calculate the actual growth rates. The effective growth rates are displayed in a graphical form.     

The structural instabilities in ferronematic based on liquid crystal with negative diamagnetic susceptibility anisotropy

The studied ferronematic is a nematic liquid crystal (ZLI1695) of low negative anisotropy of the diamagnetic susceptibility (χ_a<0) doped with the magnetic particles Fe₃O₄. Structural instabilities are interpreted within Burylov and Raikher's theory. The high magnetic fields were oriented perpendicular (Freedericksz transition) or parallel to the initial director. Using capacitance measurements the Freedericksz threshold magnetic field of the ferronematic B_FN, and the critical magnetic field B_max, at which the initial parallel orientation between the director and the magnetic moment of magnetic particles breaks down, have been determined. The values of these quantities have been used to estimate the surface density of the anchoring energy W of liquid crystal molecules on the surface of the magnetic particles. The obtained values indicate a soft anchoring of the liquid crystal on the magnetic particles with a preferred parallel orientation of the magnetic moment of magnetic particles and the director.     

Construction of nonnegative matrices and the inverse eigenvalue problem

This article presents a technique for combining two matrices, an n?×?n matrix M and an m?×?m matrix B, with known spectra to create an (n?+?m???p)?×?(n?+?m???p) matrix N whose spectrum consists of the spectrum of the matrix M and m???p eigenvalues of the matrix B. Conditions are given when the matrix N obtained in this construction is nonnegative. Finally, these observations are used to obtain several results on how to construct a realizable list of n?+?1 complex numbers (λ₁,λ₂,λ₃,σ) from a given realizable list of n complex numbers (c ₁,c ₂,σ), where c ₁ is the Perron eigenvalue, c ₂ is a real number and σ is a list of n???2 complex numbers.     

Cortical disinhibition occurs in chronic neuropathic,but not in chronic nociceptive pain

Background  

The aim of this study was to examine the relationship between chronic neuropathic pain after incomplete peripheral nerve lesion, chronic nociceptive pain due to osteoarthritis, and the excitability of the motor cortex assessed by transcranial magnetic stimulation (TMS). Hence in 26 patients with neuropathic pain resulting from an isolated incomplete lesion of the median or ulnar nerve (neuralgia), 20 patients with painful osteoarthritis of the hand, and 14 healthy control subjects, the excitability of the motor cortex was tested using paired-pulse TMS to assess intracortical inhibition and facilitation. These excitability parameters were compared between groups, and the relationship between excitability parameters and clinical parameters was examined.     

Has the world economy reached its globalization limit?

The economy globalization measure problem is discussed. Four macroeconomic indices of twenty among the “richest” countries are examined. Four types of “distances” are calculated. Two types of networks are next constructed for each distance measure definition. It is shown that the globalization process can be best characterised by an entropy measure, based on entropy Manhattan distance. It is observed that a globalization maximum was reached during the interval 1970-2000. More recently a deglobalization process has been observed.     

Cascades-based synchronization of hyperchaotic systems: Application to Chen systems

We discuss the cascaded-based controlled synchronization method for hyperchaotic systems. The control approach is based on analysis tools for cascaded time-varying systems. That is, the closed-loop system takes the form of two subsystems which are interconnected in a manner that the state of one system enters into another but without feedback loop. The advantage of such construction is that the controller is largely simplified relative to other design methods such as backstepping. We apply the method to Chen’s hyperchaotic system and show that global synchronization is achieved via linear control. Also, we assume that only three instead of four control inputs are available. The method is tested in numerical simulations.     

Comparison of two regulatory results on functional equations with few parameters

Two methods to prove regularity properties of the linear functional equation $$f(x)=h_0(x,y)+\sum_{j=1}^n h_j(x,y)f(x+g_j(y)), $$ where ${(x,y) \in D \subset \mathbb{R}^r \times \mathbb{R}^s}$ , ${x \in \mathbb{R}^r}$ and ${y \in \mathbb{R}^s}$ , with few parameters i.e. allowing 1 ?? s < r are examined. It is proved that??under certain conditions, for some class of equations and in some sense??they are equivalent.