Return times for Stochastic processes with power-law scaling

An analytical study of the return time distribution of extreme events for stochastic processes with power-law correlation has been carried on. The calculation is based on an epsilon-expansion in the correlation exponent: C(t)=|t|^{-1+epsilon}. The fixed point of the theory is associated with stretched exponential scaling of the distribution; analytical expressions, valid in the pre-asymptotic regime, have been provided. Also the permanence time distribution appears to be characterized by stretched exponential scaling. The conditions for application of the theory to non-Gaussian processes have been analyzed and the relations with the issue of return times in the case of multifractal measures have been discussed.Comment: 9 pages, 5 figures, revtex

Control of unstable steady states by time-delayed feedback methods

We show that time-delayed feedback methods, which have successfully been used to control unstable periodic ortbits, provide a tool to stabilize unstable steady states. We present an analytical investigation of the feedback scheme using the Lambert function and discuss effects of both a low-pass filter included in the control loop and non-zero latency times associated with the generation and injection of the feedback signal.Comment: 8 pages, 11 figure

Hemispheric competence for auditory spatial representation

Sound localization relies on the analysis of interaural time and intensity differences, as well as attenuation patterns by the outer ear. We investigated the relative contributions of interaural time and intensity difference cues to sound localization by testing 60 healthy subjects: 25 with focal left and 25 with focal right hemispheric brain damage. Group and single-case behavioural analyses, as well as anatomo-clinical correlations, confirmed that deficits were more frequent and much more severe after right than left hemispheric lesions and for the processing of interaural time than intensity difference cues. For spatial processing based on interaural time difference cues, different error types were evident in the individual data. Deficits in discriminating between neighbouring positions occurred in both hemispaces after focal right hemispheric brain damage, but were restricted to the contralesional hemispace after focal left hemispheric brain damage. Alloacusis (perceptual shifts across the midline) occurred only after focal right hemispheric brain damage and was associated with minor or severe deficits in position discrimination. During spatial processing based on interaural intensity cues, deficits were less severe in the right hemispheric brain damage than left hemispheric brain damage group and no alloacusis occurred. These results, matched to anatomical data, suggest the existence of a binaural sound localization system predominantly based on interaural time difference cues and primarily supported by the right hemisphere. More generally, our data suggest that two distinct mechanisms contribute to: (i) the precise computation of spatial coordinates allowing spatial comparison within the contralateral hemispace for the left hemisphere and the whole space for the right hemisphere; and (ii) the building up of global auditory spatial representations in right temporo-parietal cortice

Uncovering convolutional neural network decisions for diagnosing multiple sclerosis on conventional MRI using layer-wise relevance propagation

Machine learning-based imaging diagnostics has recently reached or even superseded the level of clinical experts in several clinical domains. However, classification decisions of a trained machine learning system are typically non-transparent, a major hindrance for clinical integration, error tracking or knowledge discovery. In this study, we present a transparent deep learning framework relying on convolutional neural networks (CNNs) and layer-wise relevance propagation (LRP) for diagnosing multiple sclerosis (MS). MS is commonly diagnosed utilizing a combination of clinical presentation and conventional magnetic resonance imaging (MRI), specifically the occurrence and presentation of white matter lesions in T2-weighted images. We hypothesized that using LRP in a naive predictive model would enable us to uncover relevant image features that a trained CNN uses for decision-making. Since imaging markers in MS are well-established this would enable us to validate the respective CNN model. First, we pre-trained a CNN on MRI data from the Alzheimer's Disease Neuroimaging Initiative (n = 921), afterwards specializing the CNN to discriminate between MS patients and healthy controls (n = 147). Using LRP, we then produced a heatmap for each subject in the holdout set depicting the voxel-wise relevance for a particular classification decision. The resulting CNN model resulted in a balanced accuracy of 87.04% and an area under the curve of 96.08% in a receiver operating characteristic curve. The subsequent LRP visualization revealed that the CNN model focuses indeed on individual lesions, but also incorporates additional information such as lesion location, non-lesional white matter or gray matter areas such as the thalamus, which are established conventional and advanced MRI markers in MS. We conclude that LRP and the proposed framework have the capability to make diagnostic decisions of..

Radiative damping: a case study

We are interested in the motion of a classical charge coupled to the Maxwell self-field and subject to a uniform external magnetic field, B. This is a physically relevant, but difficult dynamical problem, to which contributions range over more than one hundred years. Specifically, we will study the Sommerfeld-Page approximation which assumes an extended charge distribution at small velocities. The memory equation is then linear and many details become available. We discuss how the friction equation arises in the limit of "small" B and contrast this result with the standard Taylor expansion resulting in a second order equation for the velocity of the charge.Comment: 4 figure

Resampling methods for parameter-free and robust feature selection with mutual information

Combining the mutual information criterion with a forward feature selection strategy offers a good trade-off between optimality of the selected feature subset and computation time. However, it requires to set the parameter(s) of the mutual information estimator and to determine when to halt the forward procedure. These two choices are difficult to make because, as the dimensionality of the subset increases, the estimation of the mutual information becomes less and less reliable. This paper proposes to use resampling methods, a K-fold cross-validation and the permutation test, to address both issues. The resampling methods bring information about the variance of the estimator, information which can then be used to automatically set the parameter and to calculate a threshold to stop the forward procedure. The procedure is illustrated on a synthetic dataset as well as on real-world examples

MRI Markers and Functional Performance in Patients With CIS and MS: A Cross-Sectional Study

Introduction: Brain atrophy is a widely accepted marker of disease severity with association to clinical disability in multiple sclerosis (MS). It is unclear to which extent this association reflects common age effects on both atrophy and function. Objective: To explore how functional performance in gait, upper extremities and cognition is associated with brain atrophy in patients with Clinically Isolated Syndrome (CIS) and relapsing-remitting MS (RRMS), controlling for effects of age and sex. Methods: In 27 patients with CIS, 59 with RRMS (EDSS <= 3) and 63 healthy controls (HC), 3T MRI were analyzed for T2 lesion count (T2C), volume (T2V) and brain volumes [normalized brain volume (NBV), gray matter volume (NGMV), white matter volume (NWMV), thalamic volume (NThaIV)]. Functional performance was measured with short maximum walking speed (SMSW speed), 9-hole peg test (9HPT) and symbol digit modalities test (SDMT). Linear regression models were created for functional variables with stepwise inclusion of age, sex and MR imaging markers. Results: CIS differed from HC only in T2C and T2V. RRMS differed from HC in NBV, NGMV and NThaIV, T2C and T2V, but not in NWMV. A strong association with age was seen in HC, CIS and RRMS groups for NBV (r = -0.5 to -0.6) and NGMV (r = -0.6 to -0.8). Associations with age were seen in HC and RRMS but not CIS for NThaIV (r = -0.3; r = -0.5), T2C (r(s) = 0.3; r(s) = 0.2) and T2V (r(s) = 0.3; r(s) = 0.3). No effect of age was seen on NWMV. Correlations of functional performance with age in RRMS were seen for SMSW speed, 9HPTand SDMT (r = -0.27 to -0.46). Regression analyses yielded significant models only in the RRMS group for 9HPT, SMSW speed and EDSS. These included NBV, NGMV, NThaIV, NWMV, logT2V, age and sex as predictors. NThalV was the only MRI variable predicting a functional measure (9HPT(r)) with a higher standardized beta than age and sex (R2 = 0.36, p < 1e-04). Conclusion: Thalamic atrophy was a stronger predictor of hand function (9HPT) in RRMS, than age and sex. This underlines the clinical relevance of thalamic atrophy and the relevance of hand function as a clinical marker even in mildly disabled patients

Topographical anisotropy and wetting of ground stainless steel surfaces

Microscopic and physico-chemical methods were used for a comprehensive surface characterization of different mechanically modified stainless steel surfaces. The surfaces were analyzed using high-resolution confocal microscopy, resulting in detailed information about the topographic properties. In addition, static water contact angle measurements were carried out to characterize the surface heterogeneity of the samples. The effect of morphological anisotropy on water contact angle anisotropy was investigated. The correlation between topography and wetting was studied by means of a model of wetting proposed in the present work, that allows quantifying the air volume of the interface water drop-stainless steel surface