Adaptive Data Depth via Multi-Armed Bandits

Data depth, introduced by Tukey (1975), is an important tool in data science, robust statistics, and computational geometry. One chief barrier to its broader practical utility is that many common measures of depth are computationally intensive, requiring on the order of $n^d$ operations to exactly compute the depth of a single point within a data set of $n$ points in $d$-dimensional space. Often however, we are not directly interested in the absolute depths of the points, but rather in their relative ordering. For example, we may want to find the most central point in a data set (a generalized median), or to identify and remove all outliers (points on the fringe of the data set with low depth). With this observation, we develop a novel and instance-adaptive algorithm for adaptive data depth computation by reducing the problem of exactly computing $n$ depths to an $n$-armed stochastic multi-armed bandit problem which we can efficiently solve. We focus our exposition on simplicial depth, developed by Liu (1990), which has emerged as a promising notion of depth due to its interpretability and asymptotic properties. We provide general instance-dependent theoretical guarantees for our proposed algorithms, which readily extend to many other common measures of data depth including majority depth, Oja depth, and likelihood depth. When specialized to the case where the gaps in the data follow a power law distribution with parameter $\alpha<2$, we show that we can reduce the complexity of identifying the deepest point in the data set (the simplicial median) from $O(n^d)$ to $\tilde{O}(n^{d-(d-1)\alpha/2})$, where $\tilde{O}$ suppresses logarithmic factors. We corroborate our theoretical results with numerical experiments on synthetic data, showing the practical utility of our proposed methods.Comment: Keywords: multi-armed bandits, data depth, adaptivity, large-scale computation, simplicial dept

Electrocardiogram derived respiration during sleep

The aim of this study was quantify the ECG Derived Respiration (EDR) in order to extend the capabilities of ECG-based sleep analysis. We examined our results in normal subjects and in patients with Obstructive Sleep Apnea Syndrome (OSAS) or Central Sleep Apnea. Lead 2 ECG and three measures of respiration (thorax and abdominal effort, and oronasal flow signal) were recorded during sleep studies of 12 normal and 12 OSAS patients. Three parameters, the R-wave amplitude (RWA), R-wave duration (RWD), and QRS area, were extracted from the ECG signal, resulting in time series that displayed a behavior similar to that of the respiration signals. EDR frequency was correlated with directly measured respiratory frequency, and averaged over all subjects. The peak-to-peak value of the EDR signals during the apnea event was compared to the average peak-to-peak of the sleep stage, containing the apnea. 1

Allocation Schemes in Analytic Evaluation: Applicant-Centric Holistic or Attribute-Centric Segmented?

Many applications such as hiring and university admissions involve evaluation and selection of applicants. These tasks are fundamentally difficult, and require combining evidence from multiple different aspects (what we term "attributes"). In these applications, the number of applicants is often large, and a common practice is to assign the task to multiple evaluators in a distributed fashion. Specifically, in the often-used holistic allocation, each evaluator is assigned a subset of the applicants, and is asked to assess all relevant information for their assigned applicants. However, such an evaluation process is subject to issues such as miscalibration (evaluators see only a small fraction of the applicants and may not get a good sense of relative quality), and discrimination (evaluators are influenced by irrelevant information about the applicants). We identify that such attribute-based evaluation allows alternative allocation schemes. Specifically, we consider assigning each evaluator more applicants but fewer attributes per applicant, termed segmented allocation. We compare segmented allocation to holistic allocation on several dimensions via theoretical and experimental methods. We establish various tradeoffs between these two approaches, and identify conditions under which one approach results in more accurate evaluation than the other

The PI3K–NF-κB signal transduction pathway is involved in mediating the anti-inflammatory effect of IB-MECA in adjuvant-induced arthritis

The anti-inflammatory effect of adenosine was previously found to be mediated via activation of the A(3 )adenosine receptor (A(3)AR). The aim of the present study was to decipher the molecular mechanism involved with the inhibitory effect of IB-MECA, an A(3)AR agonist, on adjuvant-induced arthritis. The adjuvant-induced arthritis rats responded to IB-MECA treatment with a decrease in the clinical score and the pathological score of the disease. The response to IB-MECA was neutralized by the antagonist MRS 1220, confirming that the efficacy of the synthetic agonist was A(3)AR mediated. The A(3)AR protein expression level was highly expressed in the synovia, in the peripheral blood mononuclear cells and in the drain lymph node (DLN) tissues of adjuvant-induced arthritis rats in comparison with naïve animals. Downregulation of A(3)AR expression was noted upon treatment with IB-MECA. Analysis of synovia and DLN protein extracts revealed a decreased expression level of PI3K, PKB/Akt, IKK, NF-κB and tumor necrosis factor alpha, known to affect survival and apoptosis of inflammatory cells, whereas the caspase-3 level was upregulated. Taken together, high A(3)AR expression is found in the synovia, in the immune cells in the DLN and in peripheral blood mononuclear cells. IB-MECA, an orally bioavailable molecule, activates the A(3)AR, inducing receptor downregulation and the initiation of a molecular mechanism that involves de-regulation of the PI3K–NF-κB signaling pathway. As a result, a potent anti-inflammatory effect manifested in the improvement of the disease clinical score and pathological score occurs. The finding that the A(3)AR expression level in the peripheral blood mononuclear cells and in the DLN reflects the receptor status in the remote inflammatory site suggests use of the A(3)AR as a follow-up biomarker

Modelling of dielectric cavity structures using multiresolution time-domain analysis

Multiresolution time domain (MRTD) analysis is applied directly to Maxwell’s equations to model inhomogeneous dielectric material. In our approach, scaling and wavelet functions are used as a complete basis for the method of moments. The MRTD scheme is used to analyze different types of resonant cavity structures with varying dielectric perturbations in one, two and three dimensions. The results presented here agree very well with those obtained by FDTD, FEM and integral equation methods. MRTD allows for considerable savings in memory and computation time in comparison to FDTD, while maintaining the same accuracy of the results. © 1998 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/35031/1/289_ftp.pd

All-optical silicon simplified passive modulation

In this paper we present an all-optical silicon based modulator suggested also for high power operation and for pulse picker application being used as part of fiber lasers system. The paper theoretically and experimentally investigates several new and important insights involving the dependence of the relative transmission on the pump pulse energy for different finesse values of the constructed cavity as well as the dependence of the response rate of the device to the pump wavelength due to coexistence of two physical recombination processes: fast surface effect and slow bulk recombination. To adapt the constructed silicon based cavity to be used in lasers applications, we aligned the pump and the signal beams to co-propagate through the device while the usage of a cavity allowed a low power pump to yield a significant extinction ratio at the output of the device

Autonomic pain responses during sleep: a study of heart rate variability

The autonomic nervous system (ANS) reacts to nociceptive stimulation during sleep, but whether this reaction is contingent to cortical arousal, and whether one of the autonomic arms (sympathetic/parasympathetic) predominates over the other remains unknown. We assessed ANS reactivity to nociceptive stimulation during all sleep stages through heart rate variability, and correlated the results with the presence of cortical arousal measured in concomitant 32-channel EEG. Fourteen healthy volunteers underwent whole-night polysomnography during which nociceptive laser stimuli were applied over the hand. RR intervals (RR) and spectral analysis by wavelet transform were performed to assess parasympathetic (HF(WV)) and sympathetic (LF(WV) and LF(WV)/HF(WV) ratio) reactivity. During all sleep stages, RR significantly decreased in reaction to nociceptive stimulations, reaching a level similar to that of wakefulness, at the 3rd beat post-stimulus and returning to baseline after seven beats. This RR decrease was associated with an increase in sympathetic LF(WV) and LF(WV)/HF(WV) ratio without any parasympathetic HF(WV) change. Albeit RR decrease existed even in the absence of arousals, it was significantly higher when an arousal followed the noxious stimulus. These results suggest that the sympathetic-dependent cardiac activation induced by nociceptive stimuli is modulated by a sleep dependent phenomenon related to cortical activation and not by sleep itself, since it reaches a same intensity whatever the state of vigilance