KurSL: model of anharmonic coupled oscillations based on Kuramoto coupling and Sturm–Liouville problem

Physiological signaling is often oscillatory and shows nonlinearity due to complex interactions of underlying processes or signal propagation delays. This is particularly evident in case of brain activity which is subject to various feedback loop interactions between different brain structures, that coordinate their activity to support normal function. In order to understand such signaling in health and disease, methods are needed that can deal with such complex oscillatory phenomena. In this paper, a data-driven method for analyzing anharmonic oscillations is introduced. The KurSL model incorporates two well-studied components, which in the past have been used separately to analyze oscillatory behavior. The Sturm–Liouville equations describe a form of a general oscillation, and the Kuramoto coupling model represents a set of oscillators interacting in the phase domain. Integration of these components provides a flexible framework for capturing complex interactions of oscillatory processes of more general form than the most commonly used harmonic oscillators. The paper introduces a mathematical framework of the KurSL model and analyzes its behavior for a variety of parameter ranges. The significance of the model follows from its ability to provide information about coupled oscillators’ phase dynamics directly from the time series. KurSL offers a novel framework for analyzing a wide range of complex oscillatory behaviors, such as the ones encountered in physiological signals

Skew-self-adjoint discrete and continuous Dirac type systems: inverse problems and Borg-Marchenko theorems

New formulas on the inverse problem for the continuous skew-self-adjoint Dirac type system are obtained. For the discrete skew-self-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms of the Weyl functions. The description of the Weyl functions on the interval is given. Borg-Marchenko type uniqueness theorems are derived for both discrete and continuous non-self-adjoint systems too

TrustedPals: Secure Multiparty Computation Implemented with Smart Cards

We study the problem of Secure Multi-party Computation (SMC) in a model where individual processes contain a tamper-proof security module, and introduce the TrustedPals framework, an efficient smart card based implementation of SMC for any number of participating entities in such a model. Security modules can be trusted by other processes and can establish secure channels between each other. However, their availability is restricted by their host, that is, a corrupted party can stop the computation of its own security module as well as drop any message sent by or to its security module. We show that in this model SMC can be implemented by reducing it to a fault-tolerance problem at the level of security modules. Since the critical part of the computation can be executed locally on the smart card, we can compute any function securely with a protocol complexity which is polynomial only in the number of processes (that is, the complexity does not depend on the function which is computed), in contrast to previous approaches

Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds

Measure contraction property is one of the possible generalizations of Ricci curvature bound to more general metric measure spaces. In this paper, we discover sufficient conditions for a three dimensional contact subriemannian manifold to satisfy this property.Comment: 49 page

Die varisierende Femurosteotomie zur Behandlung der lateralen unikompartimentalen Gonarthrose: Neue Implantate, neue Operationstechniken

Jimmy Baxter's ERF box lorry - EVM340D - photographed 1973