Communication Lower Bounds for Statistical Estimation Problems via a Distributed Data Processing Inequality

We study the tradeoff between the statistical error and communication cost of distributed statistical estimation problems in high dimensions. In the distributed sparse Gaussian mean estimation problem, each of the $m$ machines receives $n$ data points from a $d$-dimensional Gaussian distribution with unknown mean $\theta$ which is promised to be $k$-sparse. The machines communicate by message passing and aim to estimate the mean $\theta$. We provide a tight (up to logarithmic factors) tradeoff between the estimation error and the number of bits communicated between the machines. This directly leads to a lower bound for the distributed \textit{sparse linear regression} problem: to achieve the statistical minimax error, the total communication is at least $\Omega(\min\{n,d\}m)$, where $n$ is the number of observations that each machine receives and $d$ is the ambient dimension. These lower results improve upon [Sha14,SD'14] by allowing multi-round iterative communication model. We also give the first optimal simultaneous protocol in the dense case for mean estimation. As our main technique, we prove a \textit{distributed data processing inequality}, as a generalization of usual data processing inequalities, which might be of independent interest and useful for other problems.Comment: To appear at STOC 2016. Fixed typos in theorem 4.5 and incorporated reviewers' suggestion

Some results in the theory of crosstalk-free transmultiplexers

The crosstalk-free transmultiplexer (CF-TMUX) focuses on crosstalk cancellation (CC) rather than on suppressing it. The authors present an analysis of the CF-TMUX based on the polyphase component matrices of the filter banks used in TDM→FDM and FDM→TDM conversions, respectively. Thus a necessary and sufficient condition for complete CC is obtained. It is shown that the filters for a CF-TMUX are the same as the filters for a 1-skewed alias free QMF bank. In addition, if the QMF bank satisfies the perfect reconstruction (PR) property, then the TMUX also satisfies PR. The relation between CF-TMUX filters and alias-free QMF banks is used to obtain a direct design procedure for CF-TMUX filters (both FIR and IIR). It is also shown that approximately crosstalk-free TMUX filters can be obtained from any approximately alias-free QMC bank. Design examples and comparison tables are included

Evolutionary tracks for Betelgeuse

We have constructed a series of non-rotating quasi-hydrostatic evolutionary models for the M2 Iab supergiant Betelgeuse ($\alpha~Orionis$). Our models are constrained by multiple observed values for the temperature, luminosity, surface composition and mass loss for this star, along with the parallax distance and high resolution imagery that determines its radius. We have then applied our best-fit models to analyze the observed variations in surface luminosity and the size of detected surface bright spots as the result of up-flowing convective material from regions of high temperature in the surface convective zone. We also attempt to explain the intermittently observed periodic variability in a simple radial linear adiabatic pulsation model. Based upon the best fit to all observed data, we suggest a best progenitor mass estimate of $20 ^{+5}_{-3} M_\odot$ and a current age from the start of the zero-age main sequence of $8.0 - 8.5$ Myr based upon the observed ejected mass while on the giant branch.Comment: 27 pages, 11 figures, Revised per referee suggestions, Accepted for publication in the Astrophysical Journa

The β-blocker Nebivolol Is a GRK/β-arrestin Biased Agonist

Nebivolol, a third generation β-adrenoceptor (β-AR) antagonist (β-blocker), causes vasodilation by inducing nitric oxide (NO) production. The mechanism via which nebivolol induces NO production remains unknown, resulting in the genesis of much of the controversy regarding the pharmacological action of nebivolol. Carvedilol is another β-blocker that induces NO production. A prominent pharmacological mechanism of carvedilol is biased agonism that is independent of Gαs and involves G protein-coupled receptor kinase (GRK)/β-arrestin signaling with downstream activation of the epidermal growth factor receptor (EGFR) and extracellular signal-regulated kinase (ERK). Due to the pharmacological similarities between nebivolol and carvedilol, we hypothesized that nebivolol is also a GRK/β-arrestin biased agonist. We tested this hypothesis utilizing mouse embryonic fibroblasts (MEFs) that solely express β2-ARs, and HL-1 cardiac myocytes that express β1- and β2-ARs and no detectable β3-ARs. We confirmed previous reports that nebivolol does not significantly alter cAMP levels and thus is not a classical agonist. Moreover, in both cell types, nebivolol induced rapid internalization of β-ARs indicating that nebivolol is also not a classical β-blocker. Furthermore, nebivolol treatment resulted in a time-dependent phosphorylation of ERK that was indistinguishable from carvedilol and similar in duration, but not amplitude, to isoproterenol. Nebivolol-mediated phosphorylation of ERK was sensitive to propranolol (non-selective β-AR-blocker), AG1478 (EGFR inhibitor), indicating that the signaling emanates from β-ARs and involves the EGFR. Furthermore, in MEFs, nebivolol-mediated phosphorylation of ERK was sensitive to pharmacological inhibition of GRK2 as well as siRNA knockdown of β-arrestin 1/2. Additionally, nebivolol induced redistribution of β-arrestin 2 from a diffuse staining pattern into more intense punctate spots. We conclude that nebivolol is a β2-AR, and likely β1-AR, GRK/β-arrestin biased agonist, which suggests that some of the unique clinically beneficial effects of nebivolol may be due to biased agonism at β1- and/or β2-ARs. © 2013 Erickson et al

Physiological mechanisms of hippocampal memory processing : experiments and applied adaptive filtering

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Brain and Cognitive Sciences, 2008.Includes bibliographical references (p. 144-156).The hippocampus is necessary for the formation and storage of episodic memory, however, the computations within and between hippocampal subregions (CA1, CA3, and dentate gyrus) that mediate these memory processing functions are not completely understood. We investigate by recording in the hippocampal subregions as rats execute an augmented linear track task. From these recordings, we construct ensemble rate representations using a point process adaptive filter to characterize single-unit activity from each subregion. We compared the dynamics of these rate representations by computing average max rate and average rate modulation during different experimental epochs and on different segments of the track. We found that the representations in CA3 were modulated most when compared to CAl and DG during the first 5 minutes of experience. With more experience, we found the average rate modulation decreased gradually across all areas and converged to values that were not statistically different. These results suggest a specialized role for CA3 during initial context acquisition, and suggest that rate modulation becomes coherent across HPC subregions after familiarization. Information transfer between the hippocampus and neocortex is important for the consolidation of spatial and episodic memory. This process of information transfer is referred to as memory consolidation and may be mediated by a phenomena called "replay." We know that the process of replay is associated with a rise in multi-unit activity and the presence of ripples (100-250 Hz oscillations lasting from 75ms to 100ms) in CAl. Because ripples result from the same circuits as replay activity, the features of the ripple may allow us to deduce the mechanisms for replay induction and the nature of information transmitted during replay events.(cont.) Because ripples are relatively short events, analytical methods with limited temporal-spectral resolution are unable to fully characterize all the structure of ripples. In the thesis, we develop a framework for characterizing, classifying, and detecting ripples based on instantaneous frequency and instantaneous frequency modulation. The framework uses an autoregressive model for spectral-temporal analysis in combination with a Kalman filter for sample-to-sample estimates of frequency parameters. We show that the filter is flexible in the degree of smoothing as well as robust in the estimation of frequency. We demonstrate that under the proposed framework ripples can be classified based on high or low frequency, and positive or negative frequency modulation; can combine amplitude and frequency information for selective detection of ripple events; and can be used to determine the number of ripples participating in "long ripple" events.by David P. Nguyen.Ph.D

Development of a cost-effective and flexible vibration DAQ system for long-term continuous structural health monitoring

In the structural health monitoring (SHM) field, long-term continuous vibration-based monitoring is becoming increasingly popular as this could keep track of the health status of structures during their service lives. However, implementing such a system is not always feasible due to on-going conflicts between budget constraints and the need of sophisticated systems to monitor real-world structures under their demanding in-service conditions. To address this problem, this paper presents a comprehensive development of a cost-effective and flexible vibration DAQ system for long-term continuous SHM of a newly constructed institutional complex with a special focus on the main building. First, selections of sensor type and sensor positions are scrutinized to overcome adversities such as low-frequency and low-level vibration measurements. In order to economically tackle the sparse measurement problem, a cost-optimized Ethernet-based peripheral DAQ model is first adopted to form the system skeleton. A combination of a high-resolution timing coordination method based on the TCP/IP command communication medium and a periodic system resynchronization strategy is then proposed to synchronize data from multiple distributed DAQ units. The results of both experimental evaluations and experimental-numerical verifications show that the proposed DAQ system in general and the data synchronization solution in particular work well and they can provide a promising cost-effective and flexible alternative for use in real-world SHM projects. Finally, the paper demonstrates simple but effective ways to make use of the developed monitoring system for long-term continuous structural health evaluation as well as to use the instrumented building herein as a multi-purpose benchmark structure for studying not only practical SHM problems but also synchronization related issues

Biological Time Series Analysis Using a Context Free Language: Applicability to Pulsatile Hormone Data

National Space Biomedical Research Institute (NASA NCC 9-58 HFP01603)National Space Biomedical Research Institute (NASA NCC 9-58 HPF00405)National Institutes of Health (U.S.) (NIH NCRR-GCRC-M01-RR-02635)United States. Air Force Office of Scientific Research (AFOSR F49620-95-1-0388)United States. Air Force Office of Scientific Research (AFOSR FA9550-06-0080)National Institutes of Health (U.S.) (NIH P01-AG09975)National Institutes of Health (U.S.) (NIH T32 HL07901-10)National Institutes of Health (U.S.) (NIH F31-GM095340-01)National Institutes of Health (U.S.) (NIH K24-HL105664)National Institutes of Health (U.S.) (NIH K02-HD045459)National Institutes of Health (U.S.) (NIH RC2-HL101340)National Institutes of Health (U.S.) (NIH R01-AR43130)National Institutes of Health (U.S.) (NIH K24-HL103845)National Institutes of Health (U.S.) (NIH R01-MH071847)National Institutes of Health (U.S.) (NIH R01 HL098433)National Institutes of Health (U.S.) (NIH R01 HL098433-02S1

Biological Time Series Analysis Using a Context Free Language: Applicability to Pulsatile Hormone Data

We present a novel approach for analyzing biological time-series data using a context-free language (CFL) representation that allows the extraction and quantification of important features from the time-series. This representation results in Hierarchically AdaPtive (HAP) analysis, a suite of multiple complementary techniques that enable rapid analysis of data and does not require the user to set parameters. HAP analysis generates hierarchically organized parameter distributions that allow multi-scale components of the time-series to be quantified and includes a data analysis pipeline that applies recursive analyses to generate hierarchically organized results that extend traditional outcome measures such as pharmacokinetics and inter-pulse interval. Pulsicons, a novel text-based time-series representation also derived from the CFL approach, are introduced as an objective qualitative comparison nomenclature. We apply HAP to the analysis of 24 hours of frequently sampled pulsatile cortisol hormone data, which has known analysis challenges, from 14 healthy women. HAP analysis generated results in seconds and produced dozens of figures for each participant. The results quantify the observed qualitative features of cortisol data as a series of pulse clusters, each consisting of one or more embedded pulses, and identify two ultradian phenotypes in this dataset. HAP analysis is designed to be robust to individual differences and to missing data and may be applied to other pulsatile hormones. Future work can extend HAP analysis to other time-series data types, including oscillatory and other periodic physiological signals