Simultaneous Confidence Bands for Functional Data Using the Gaussian Kinematic Formula

This article constructs simultaneous confidence bands (SCBs) for functional parameters using the Gaussian Kinematic formula of $t$-processes (tGKF). Although the tGKF relies on Gaussianity, we show that a central limit theorem (CLT) for the parameter of interest is enough to obtain asymptotically precise covering rates even for non-Gaussian processes. As a proof of concept we study the functional signal-plus-noise model and derive a CLT for an estimator of the Lipschitz-Killing curvatures, the only data dependent quantities in the tGKF SCBs. Extensions to discrete sampling with additive observation noise are discussed using scale space ideas from regression analysis. Here we provide sufficient conditions on the processes and kernels to obtain convergence of the functional scale space surface. The theoretical work is accompanied by a simulation study comparing different methods to construct SCBs for the population mean. We show that the tGKF works well even for small sample sizes and only a Rademacher multiplier-$t$ bootstrap performs similarily well. For larger sample sizes the tGKF often outperforms the bootstrap methods and is computational faster. We apply the method to diffusion tensor imaging (DTI) fibers using a scale space approach for the difference of population means. R code is available in our Rpackage SCBfda

Multiple testing of local maxima for detection of peaks in 1D

A topological multiple testing scheme for one-dimensional domains is proposed where, rather than testing every spatial or temporal location for the presence of a signal, tests are performed only at the local maxima of the smoothed observed sequence. Assuming unimodal true peaks with finite support and Gaussian stationary ergodic noise, it is shown that the algorithm with Bonferroni or Benjamini--Hochberg correction provides asymptotic strong control of the family wise error rate and false discovery rate, and is power consistent, as the search space and the signal strength get large, where the search space may grow exponentially faster than the signal strength. Simulations show that error levels are maintained for nonasymptotic conditions, and that power is maximized when the smoothing kernel is close in shape and bandwidth to the signal peaks, akin to the matched filter theorem in signal processing. The methods are illustrated in an analysis of electrical recordings of neuronal cell activity.Comment: Published in at http://dx.doi.org/10.1214/11-AOS943 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Peak Detection as Multiple Testing

This paper considers the problem of detecting equal-shaped non-overlapping unimodal peaks in the presence of Gaussian ergodic stationary noise, where the number, location and heights of the peaks are unknown. A multiple testing approach is proposed in which, after kernel smoothing, the presence of a peak is tested at each observed local maximum. The procedure provides strong control of the family wise error rate and the false discovery rate asymptotically as both the signal-to-noise ratio (SNR) and the search space get large, where the search space may grow exponentially as a function of SNR. Simulations assuming a Gaussian peak shape and a Gaussian autocorrelation function show that desired error levels are achieved for relatively low SNR and are robust to partial peak overlap. Simulations also show that detection power is maximized when the smoothing bandwidth is close to the bandwidth of the signal peaks, akin to the well-known matched filter theorem in signal processing. The procedure is illustrated in an analysis of electrical recordings of neuronal cell activity.Comment: 37 pages, 8 figure

Functional delta residuals and applications to functional effect sizes

Given a functional central limit (fCLT) and a parameter transformation, we use the functional delta method to construct random processes, called functional delta residuals, which asymptotically have the same covariance structure as the transformed limit process. Moreover, we prove a multiplier bootstrap fCLT theorem for these transformed residuals and show how this can be used to construct simultaneous confidence bands for transformed functional parameters. As motivation for this methodology, we provide the formal application of these residuals to a functional version of the effect size parameter Cohen's $d$, a problem appearing in current brain imaging applications. The performance and necessity of such residuals is illustrated in a simulation experiment for the covering rate of simultaneous confidence bands for the functional Cohen's $d$ parameter

Adults can be trained to acquire synesthetic experiences

Synesthesia is a condition where presentation of one perceptual class consistently evokes additional experiences in different perceptual categories. Synesthesia is widely considered a congenital condition, although an alternative view is that it is underpinned by repeated exposure to combined perceptual features at key developmental stages. Here we explore the potential for repeated associative learning to shape and engender synesthetic experiences. Non-synesthetic adult participants engaged in an extensive training regime that involved adaptive memory and reading tasks, designed to reinforce 13 specific letter-color associations. Following training, subjects exhibited a range of standard behavioral and physiological markers for grapheme-color synesthesia; crucially, most also described perceiving color experiences for achromatic letters, inside and outside the lab, where such experiences are usually considered the hallmark of genuine synesthetes. Collectively our results are consistent with developmental accounts of synesthesia and illuminate a previously unsuspected potential for new learning to shape perceptual experience, even in adulthood

New directions in EEG measurement: an investigation into the fidelity of electrical potential sensor signals

Low frequency noise performance is the key indicator in determining the signal to noise ratio of a capacitively coupled sensor when used to acquire electroencephalogram signals. For this reason, a prototype Electric Potential Sensor device based on an auto-zero operational amplifier has been developed and evaluated. The absence of 1/f noise in these devices makes them ideal for use with signal frequencies ~10 Hz or less. The active electrodes are designed to be physically and electrically robust and chemically and biochemically inert. They are electrically insulated (anodized) and have diameters of 12 mm or 18 mm. In both cases, the sensors are housed in inert stainless steel machined housings with the electronics fabricated in surface mount components on a printed circuit board compatible with epoxy potting compounds. Potted sensors are designed to be immersed in alcohol for sterilization purposes. A comparative study was conducted with a commercial wet gel electrode system. These studies comprised measurements of both free running electroencephalogram and Event Related Potentials. Quality of the recorded electroencephalogram was assessed using three methods of inspection of raw signal, comparing signal to noise ratios, and Event Related Potentials noise analysis. A strictly comparable signal to noise ratio was observed and the overall conclusion from these comparative studies is that the noise performance of the new sensor is appropriate

Complex regional pain syndrome with associated chest wall dystonia: a case report

Patients with complex regional pain syndrome (CRPS) often suffer from an array of associated movement disorders, including dystonia of an affected limb. We present a case of a patient with long standing CRPS after a brachial plexus injury, who after displaying several features of the movement disorder previously, developed painful dystonia of chest wall musculature. Detailed neurologic examination found palpable sustained contractions of the pectoral and intercostal muscles in addition to surface allodynia. Needle electromyography of the intercostal and paraspinal muscles supported the diagnosis of dystonia. In addition, pulmonary function testing showed both restrictive and obstructive features in the absence of a clear cardiopulmonary etiology. Treatment was initiated with intrathecal baclofen and the patient had symptomatic relief and improvement of dystonia. This case illustrates a novel form of the movement disorder associated with CRPS with response to intrathecal baclofen treatment

Impact of DM direct searches and the LHC analyses on branon phenomenology

Dark Matter direct detection experiments are able to exclude interesting parameter space regions of particle models which predict an important amount of thermal relics. We use recent data to constrain the branon model and to compute the region that is favored by CDMS measurements. Within this work, we also update present colliders constraints with new studies coming from the LHC. Despite the present low luminosity, it is remarkable that for heavy branons, CMS and ATLAS measurements are already more constraining than previous analyses performed with TEVATRON and LEP data.Comment: 17 pages, 2 figure

On a problem of A. Weil

A topological invariant of the geodesic laminations on a modular surface is constructed. The invariant has a continuous part (the tail of a continued fraction) and a combinatorial part (the singularity data). It is shown, that the invariant is complete, i.e. the geodesic lamination can be recovered from the invariant. The continuous part of the invariant has geometric meaning of a slope of lamination on the surface.Comment: to appear Beitr\"age zur Algebra und Geometri

Role of PknB Kinase in Antibiotic Resistance and Virulence in Community-Acquired Methicillin-Resistant Staphylococcus aureus Strain USA300

The regulation of cellular processes by eukaryote-like serine/threonine kinases is widespread in bacteria. In the last 2 years, several studies have examined the role of serine/threonine kinases in Staphylococcus aureus on cell wall metabolism, autolysis, and virulence, mostly in S. aureus laboratory isolates in the 8325-4 lineage. In this study, we showed that the pknB gene (also called stk1) of methicillin-resistant S. aureus (MRSA) strain COL and the community-acquired MRSA (CA-MRSA) strain USA300 is involved in cell wall metabolism, with the pknB mutant exhibiting enhanced sensitivity to β-lactam antibiotics but not to other classes of antibiotics, including aminoglycosides, ciprofloxacin, bactrim, and other types of cell wall-active agents (e.g., vancomycin and bacitracin). Additionally, the pknB mutant of USA300 was found to be more resistant to Triton X-100-induced autolysis and also to lysis by lysostaphin. We also showed that pknB is a positive regulator of sigB activity, resulting in compromise in its response to heat and oxidative stresses. In association with reduced sigB activity, the expression levels of RNAII and RNAIII of agr and the downstream effector hla are upregulated while spa expression is downmodulated in the pknB mutant compared to the level in the parent. Consistent with an enhanced agr response in vitro, virulence studies of the pknB mutant of USA300 in a murine cutaneous model of infection showed that the mutant was more virulent than the parental strain. Collectively, our results have linked the pknB gene in CA-MRSA to antibiotic resistance, sigB activity, and virulence and have highlighted important differences in pknB phenotypes (virulence and sigB activity) between laboratory isolates and the prototypic CA-MRSA strain USA300