Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K

We consider systems A_\ell(t) y(q^\ell t) + ... + A_0(t) y(t) = b(t) of higher order q-recurrence equations with rational coefficients. We extend a method for finding a bound on the maximal power of t in the denominator of arbitrary rational solutions y(t) as well as a method for bounding the degree of polynomial solutions from the scalar case to the systems case. The approach is direct and does not rely on uncoupling or reduction to a first order system. Unlike in the scalar case this usually requires an initial transformation of the system.Comment: 8 page

Fast approximate Barnes interpolation: illustrated by Python-Numba implementation fast-barnes-py v1.0

Barnes interpolation is a method that is widely used in geospatial sciences like meteorology to remodel data values recorded at irregularly distributed points into a representative analytical field. When implemented naively, the effort to calculate Barnes interpolation depends on the product of the number of sample points N and the number of grid points W×H, resulting in a computational complexity of O(N⋅W⋅H). In the era of highly resolved grids and overwhelming numbers of sample points, which originate, e.g., from the Internet of Things or crowd-sourced data, this computation can be quite demanding, even on high-performance machines. This paper presents new approaches of how very good approximations of Barnes interpolation can be implemented using fast algorithms that have a computational complexity of O(N+W⋅H). Two use cases in particular are considered, namely (1) where the used grid is embedded in the Euclidean plane and (2) where the grid is located on the unit sphere.</p

The notion of free will and its ethical relevance for decision-making capacity.

Obtaining informed consent from patients is a moral and legal duty and, thus, a key legitimation for medical treatment. The pivotal prerequisite for valid informed consent is decision-making capacity of the patient. Related to the question of whether and when consent should be morally and legally valid, there has been a long-lasting philosophical debate about freedom of will and the connection of freedom and responsibility. The scholarly discussion on decision-making capacity and its clinical evaluation does not sufficiently take into account this fundamental debate. It is contended that the notion of free will must be reflected when evaluating decision-making capacity. Namely, it should be included as a part of the appreciation-criterion for decision-making capacity. The argumentation is mainly drawn on the compatibilism of Harry Frankfurt. A solution is proposed which at the same time takes the notion of free will seriously and enriches the traditional understanding of decision-making capacity, strengthening its justificatory force while remaining clinically applicable

Measuring Optical Properties On Rough And Liquid Metal Surfaces

For understanding and optimizing laser processing of metals and alloys the optical properties, especially the absorption of the work piece in function of the temperature up to the liquid phase have to be known [1]. There are several approaches to extend the Drude-Model [2] for optical properties of metal to temperature dependence [3, 4, 5]. However, a verification of these models is difficult due to the lack of sufficient experimental data. Even though measuring optical properties with ellipsometry is well established, such measurements on metals and alloys at elevated temperatures up to the liquid state are very challenging. To collect the optical properties of different metals and alloys like Al, Ti, Ag, Cu and steel in the solid and liquid state a custom-made high-temperature ellipsometer was used. The instrument is also used to investigate the influence of curved and rough surfaces which may occur due to the heating of the samples during the ellipsometric measurements

A 7 Tesla fMRI Study of Amygdala Responses to Fearful Faces

The amygdalae are involved in the perception of emotions such as happiness, anger and fear. Because of their proximity to the sinuses, the image signal intensity in T2* weighted fMRI data is often affected by signal loss due to through-slice dephasing, especially at high field strength. In this study, the feasibility of fMRI in the amygdalae at 7 Tesla was investigated. A paradigm based on the presentation of fearful faces was used for stimulation. Previously, opposite effects have been found for presentation of averted and direct gaze fearful faces. Here, we show that (1) sufficiently high temporal SNR values are reached in the amygdalae for detection of small BOLD signal changes and (2) that the BOLD signal in the amygdalae for presentation of a direct or averted gaze in a fearful face depends on stimulus duration

Influence of the Barrier Shape on Resonant Activation

The escape of a Brownian particle over a dichotomously fluctuating barrier is investigated for various shapes of the barrier. The problem of resonant activation is revisited with the attention on the effect of the barrier shape on optimal value of the mean escape time in the system. The characteristic features of resonant behavior are analyzed for barriers switching either between different heights, or "on" and "off" positions. PACS number(s): 05.10-a, 02.50.-r, 82.20.-wj.Comment: 7 pages, 8 figures, RevTex4. Manuscript has been revised and enhanced. Pictures have been made more clear and some of them have been cancelled. Additional references have been added. The paper has been submitted to Phys. Rev.

Enhancement of stability in randomly switching potential with metastable state

The overdamped motion of a Brownian particle in randomly switching piece-wise metastable linear potential shows noise enhanced stability (NES): the noise stabilizes the metastable system and the system remains in this state for a longer time than in the absence of white noise. The mean first passage time (MFPT) has a maximum at a finite value of white noise intensity. The analytical expression of MFPT in terms of the white noise intensity, the parameters of the potential barrier, and of the dichotomous noise is derived. The conditions for the NES phenomenon and the parameter region where the effect can be observed are obtained. The mean first passage time behaviours as a function of the mean flipping rate of the potential for unstable and metastable initial configurations are also analyzed. We observe the resonant activation phenomenon for initial metastable configuration of the potential profile.Comment: 9 pages, 5 figures. In press in "European Physical Journal B

A printed transition for matching improvement of SIW horn antennas

The substrate integrated waveguide (SIW) technology allows to construct several types of commonly used antennas in a planar way. However, frequency limitations associated to commercial substrates appear in the implementation of certain types of antennas, e.g., SIW horn antennas are not well matched when the substrate thickness is much smaller than the wavelength. A printed transition is proposed to overcome this problem. Differently from current solutions, no bulky elements are required allowing to maintain the most important features of this technology namely its compactness and ease of manufacturing. In order to quickly analyze and design the transition, both a coupled resonator and a transmission line models are developed, together with design guidelines. The proposed transition is designed to match a H-plane SIW horn antenna built in a thin substrate (thickness < lambda(0)/10) at different frequency bands at the Ku-band. Experimental results for 3 different transitions show that the matching characteristics are efficiently improved compared with the conventional SIW horn antenna and validates the proposed models