An Inverse Problem for Localization Operators

A classical result of time-frequency analysis, obtained by I. Daubechies in 1988, states that the eigenfunctions of a time-frequency localization operator with circular localization domain and Gaussian analysis window are the Hermite functions. In this contribution, a converse of Daubechies' theorem is proved. More precisely, it is shown that, for simply connected localization domains, if one of the eigenfunctions of a time-frequency localization operator with Gaussian window is a Hermite function, then its localization domain is a disc. The general problem of obtaining, from some knowledge of its eigenfunctions, information about the symbol of a time-frequency localization operator, is denoted as the inverse problem, and the problem studied by Daubechies as the direct problem of time-frequency analysis. Here, we also solve the corresponding problem for wavelet localization, providing the inverse problem analogue of the direct problem studied by Daubechies and Paul.Comment: 18 pages, 1 figur

Why Is Change so Slow? Assessing Prospects for United Nations Security Council Reform

The article explores how changed patterns of UN membership affected the prospects for UN Security Council institutional reform. First, we outline a theoretical framework based on path dependency, veto player analysis and social choice theory. Second, we offer calculations of decision probability and show that a higher voting threshold lowers chances of winning coalitions in a non-linear fashion. Third, we explore the specific decision-making procedures for UNSC reform and which actors can block reform. We conclude that not only diverging preferences, but that hurdles established early on combined with membership growth have ‘locked in’ the current institutional arrangement.Security and Global Affair

Rotational state-changing collisions between N2+_2^+ and Rb at low energies

We present a theoretical study of rotationally elastic and inelastic collisions between molecular nitrogen ions and Rb atoms in the sub-Kelvin temperature regime prevalent in ion-atom hybrid trapping experiments. The cross sections for rotational excitation and de-excitation collisions were calculated using quantum-scattering methods on ab-initio potential energy surfaces for the energetically lowest singlet electronic channel of the system. We find that the rotationally inelastic collision rates are at least an order of magnitude smaller than the charge-exchange rates found in this system, rendering inelastic processes a minor channel under the conditions of typical hybrid trapping experiments.Comment: 6 pages, 5 figures, Computational study of rotational state changing collision

In situ Raman spectroscopy on silicon nanowire anodes integrated in lithium ion batteries

Rapid decay of silicon anodes during lithiation poses a significant challenge in application of silicon as an anode material in lithium ion batteries. In situ Raman spectroscopy is a powerful method to study the relationship between structural and electrochemical data during electrode cycling and to allow the observation of amorphous as well as liquid and transient species in a battery cell. Herein, we present in situ Raman spectroscopy on high capacity electrode using uncoated and carbon-coated silicon nanowires during first lithiation and delithiation cycle in an optimized lithium ion battery setup and complement the results with operando X-ray reflection diffraction measurements. During lithiation, we were able to detect a new Raman signal at 1859 cm−1 especially on uncoated silicon nanowires. The detailed in situ Raman measurement of the first lithiation/delithiation cycle allowed to differentiate between morphology changes of the electrode as well as interphase formation from electrolyte components

Neuroanatomic Correlates of Female Sexual Dysfunction in Multiple Sclerosis

OBJECTIVE: This study intended to determine associations between alterations of female sexual arousal as well as vaginal lubrication and the site of cerebral multiple sclerosis (MS) lesions. METHODS: In 44 women with MS (mean age: 36.5 ± 9.9 years), we assessed their medical history and evaluated sexual function using the Female Sexual Function Index scores for arousal and vaginal lubrication. We determined potential confounding factors of sexual dysfunction: age; disease duration; physical disability; depression; bladder or urinary dysfunction; and total volume of cerebral lesions. Arousal and lubrication scores were correlated with one another and with potential confounding factors. Cerebral MS lesions were recorded on imaging scans. A voxel-based lesion symptom mapping (VLSM) analysis adjusted for confounding variables was performed correlating cerebral sites of MS lesions with arousal and lubrication scores. RESULTS: Decreased arousal scores correlated with decreased lubrication scores; decreased lubrication scores were associated with bladder or urinary symptoms. Arousal and lubrication scores were not associated with any other variables. Multivariate VLSM analysis, including arousal and lubrication scores as covariables of interest, showed right occipital lesions associated with impaired arousal and left insular lesions associated with decreased lubrication. Impaired lubrication remained associated with left insular lesions after adjustment for bladder or urinary dysfunction. INTERPRETATION: Our data indicate that impaired female sexual arousal is associated with MS lesions in the occipital region, integrating visual information and modulating attention toward visual input. Impaired lubrication correlated with lesions in the left insular region, contributing to mapping and generating visceral arousal states

Dynamics of fully coupled rotators with unimodal and bimodal frequency distribution

We analyze the synchronization transition of a globally coupled network of N phase oscillators with inertia (rotators) whose natural frequencies are unimodally or bimodally distributed. In the unimodal case, the system exhibits a discontinuous hysteretic transition from an incoherent to a partially synchronized (PS) state. For sufficiently large inertia, the system reveals the coexistence of a PS state and of a standing wave (SW) solution. In the bimodal case, the hysteretic synchronization transition involves several states. Namely, the system becomes coherent passing through traveling waves (TWs), SWs and finally arriving to a PS regime. The transition to the PS state from the SW occurs always at the same coupling, independently of the system size, while its value increases linearly with the inertia. On the other hand the critical coupling required to observe TWs and SWs increases with N suggesting that in the thermodynamic limit the transition from incoherence to PS will occur without any intermediate states. Finally a linear stability analysis reveals that the system is hysteretic not only at the level of macroscopic indicators, but also microscopically as verified by measuring the maximal Lyapunov exponent.Comment: 22 pages, 11 figures, contribution for the book: Control of Self-Organizing Nonlinear Systems, Springer Series in Energetics, eds E. Schoell, S.H.L. Klapp, P. Hoeve

A diagrammatic view of the equals sign: arithmetical equivalence as a means, not an end

It is recommended in the mathematics education literature that pupils be presented with equality statements that can be assessed for numerical balance by attending to notational structure rather than computation. I describe an alternative, diagrammatic approach in which pupils do not assess statements but instead use them to make substitutions of notation. I report on two trials of a computer-based task conducted with pairs of pupils and highlight two findings. First, the pupils found it useful to articulate the distinct substitutive effects of commutative (‘swap’, ‘switch’) and partitional (‘split’, ‘separate’) statements when working on the task. Secondly, the pupils did not notice that some of the statements presented were in fact false, which suggests their substituting activities were independent of numerical equivalence conceptions. This demonstrates that making substitutions offers task designers a mathematical utility for equality statements that is distinct from, but complementary to, assessing numerical balance

Experimental study of the robust global synchronization of Brockett oscillators

International audienceThis article studies the experimental synchronization of a family of a recently proposed oscillator model, i.e. the Brockett oscillator [Brockett, 2013]. Due to its structural property, Brockett oscillator can be considered as a promising benchmark nonlinear model for investigating synchronization and the consensus phenomena. Our experimental setup consists of analog circuit realizations of a network of Brockett oscillators. Experimental results obtained in this work correspond to the prior theoretical findings

Non-Gaussian power grid frequency fluctuations characterized by Levy-stable laws and superstatistics

Multiple types of fluctuations impact the collective dynamics of power grids and thus challenge their robust operation. Fluctuations result from processes as different as dynamically changing demands, energy trading and an increasing share of renewable power feed-in. Here we analyse principles underlying the dynamics and statistics of power grid frequency fluctuations. Considering frequency time series for a range of power grids, including grids in North America, Japan and Europe, we find a strong deviation from Gaussianity best described as Lévy-stable and q-Gaussian distributions. We present a coarse framework to analytically characterize the impact of arbitrary noise distributions, as well as a superstatistical approach that systematically interprets heavy tails and skewed distributions. We identify energy trading as a substantial contribution to today’s frequency fluctuations and effective damping of the grid as a controlling factor enabling reduction of fluctuation risks, with enhanced effects for small power grids