Sublimation‐like behavior of cardiac dynamics in heart failure: A malignant phase transition?

An abrupt transition from sinus rhythm to atrial fibrillation (AF) is common in patients with chronic heart failure (CHF). We propose a conceptual framework for viewing this malignant transition in terms of a type of sublimation marked by the switch from highly periodic sinus interbeat interval dynamics characteristic of CHF to a state of random disorganization with AF. Sublimation of physical substances involves an increase in entropy via heat transfer. In contrast, the disease‐related sublimation‐like behavior involves a loss of information content, associated decreases in cardiac bioenergetic capacity and in multiscale entropy. © 2016 Wiley Periodicals, Inc. Complexity 21: 24–32, 2016     

The Hadamard Product of Circulant Matrices on Three Symbols that are Inverses of M-Matrices

It is shown that the class of all n × n inverse M-matrices A for which both A and A -1 are circulant matrices on three symbols is closed under Hadamard products.     

Towers of gravitational theories

In this essay we introduce a theoretical framework designed to describe black hole dynamics. The difficulties in understanding such dynamics stems from the proliferation of scales involved when one attempts to simultaneously describe all of the relevant dynamical degrees of freedom. These range from the modes that describe the black hole horizon, which are responsible for dissipative effects, to the long wavelength gravitational radiation that drains mechanical energy from macroscopic black hole bound states. We approach the problem from a Wilsonian point of view, by building a tower of theories of gravity each of which is valid at different scales. The methodology leads to multiple new results in diverse topics including phase transitions of Kaluza-Klein black holes and the interactions of spinning black hole in non-relativistic orbits. Moreover, our methods tie together speculative ideas regarding dualities for black hole horizons to real physical measurements in gravitational wave detectors.     

Bemerkung über 4-Azo- und 4-Azoxyphtalsäure

Ohne ZusammenfassungDie Versuche wurden auf Veranlassung von Prof. R. Wegscheider ausgeführt.     

An Improvement of an Inequality of Fiedler Leading to a New Conjecture on Nonnegative Matrices

Suppose that A is an n × n nonnegative matrix whose eigenvalues are = (A), ₂, ..., _n. Fiedler and others have shown that \det( I -A) ⁿ - ⁿ, for all > with equality for any such if and only if A is the simple cycle matrix. Let a _i be the signed sum of the determinants of the principal submatrices of A of order i × i, i=1, ..., n - 1. We use similar techniques to Fiedler to show that Fiedler's inequality can be strengthened to: for all . We use this inequality to derive the inequality that: . In the spirit of a celebrated conjecture due to Boyle-Handelman, this inequality inspires us to conjecture the following inequality on the nonzero eigenvalues of A: If ₁ = (A), ₂,...,_k are (all) the nonzero eigenvalues of A, then . We prove this conjecture for the case when the spectrum of A is real.     

Noise effects on the complex patterns of abnormal heartbeats

Patients at high risk for sudden death often exhibit complex heart rhythms in which abnormal heartbeats are interspersed with normal heartbeats. We analyze such a complex rhythm in a single patient over a 12-h period and show that the rhythm can be described by a theoretical model consisting of two interacting oscillators with stochastic elements. By varying the magnitude of the noise, we show that for an intermediate level of noise, the model gives best agreement with key statistical features of the dynamics.     

Detecting electronic states at stacking faults in magnetic thin films by tunneling spectroscopy

Co islands grown on Cu(111) with a stacking fault at the interface present a conductance in the empty electronic states larger than the Co islands that follow the stacking sequence of the Cu substrate. Electrons can be more easily injected into these faulted interfaces, providing a way to enhance transmission in future spintronic devices. The electronic states associated with the stacking fault are visualized by tunneling spectroscopy, and its origin is identified by band structure calculations.     

Multiscale entropy analysis of complex physiologic time series

There has been considerable interest in quantifying the complexity of physiologic time series, such as heart rate. However, traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long-range correlations. This paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics. We introduce a method to calculate multiscale entropy (MSE) for complex time series. We find that MSE robustly separates healthy and pathologic groups and consistently yields higher values for simulated long-range correlated noise compared to uncorrelated noise.