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

Enhanced thermoelectric figure of merit in vertical graphene junctions

In this work, we investigate thermoelectric properties of junctions consisting of two partially overlapped graphene sheets coupled to each other in the cross-plane direction. It is shown that because of the weak van-der Waals interactions between graphene layers, the phonon conductance in these junctions is strongly reduced, compared to that of single graphene layer structures, while their electrical performance is weakly affected. By exploiting this effect, we demonstrate that the thermoelectric figure of merit can reach values higher than 1 at room temperature in junctions made of gapped graphene materials, for instance, graphene nanoribbons and graphene nanomeshes. The dependence of thermoelectric properties on the junction length is also discussed. This theoretical study hence suggests an efficient way to enhance thermoelectric efficiency of graphene devices.Comment: 6 pages, 4 figures, submitte

Multiple regression analysis of epistemological beliefs, learning approaches, and self-regulated learning.

Abstract Introduction. Recent research in educational psychology has explored student approaches t

Pressure-temperature phase diagram of ferromagnetic superconductors

The symmetry approach to the description of the (P,T) phase diagram of ferromagnet superconductors with triplet pairing is developed. Taking into account the recent experimental observations made on UCoGe it is considered the case of a crystal with orthorhombic structure and strong spin-orbital coupling. It is shown that formation of ferromagnet superconducting state from a superconducting state is inevitably accompanied by the first order type transition.Comment: 4 pages, 1 figur

Positive Psychology: The Use of the Framework of Achievement Bests to Facilitate Personal Flourishing

The Framework of Achievement Bests, which was recently published in Educational Psychology Review, makes a theoretical contribution to the study of positive psychology. The Framework of Achievement Bests provides an explanatory account of a person’s optimal best practice from his/her actual best. Another aspect emphasizes on the saliency of the psychological process of optimization, which is central to our understanding of person’s optimal functioning in a subject matter. Achieving an exceptional level of best practice (e.g. achieving excellent grades in mathematics) does not exist in isolation, but rather depends on the potent impact of optimization. This chapter, theoretical in nature, focuses on an in‐depth examination of the expansion of the Framework of Achievement Bests. Our discussion of the Framework of Achievement Bests, reflecting a methodical conceptualization, is benchmarked against another notable theory for understanding, namely: Martin Seligman’s PERMA theory. For example, for consideration, one aspect that we examine entails the extent to which the Framework of Achievement Bests could explain the optimization of each of the five components of PERMA (e.g. how does the Framework of Achievement Bests explain the optimization of engagement?)

Achievement Bests Framework, Cognitive Load Theory, and Equation Solving

The Framework of Achievement Bests provides an explanatory account into the process of optimization, which details how a person reaches from one level of best practice to that of a more optimal level. This framework, we contend, is significant in its explanatory account of personal growth, an internal state of flourishing, and the achievement of exceptionality. This chapter conceptualizes the applicability of the Framework of Achievement Bests to the context of instructional designs. We highlight the tenet of element interactivity, which is integral to the design of a particular mathematics instruction and its potential effectiveness. Element interactivity entails the interaction between elements within a learning material. Owing to the limited working memory capacity, an instruction that incurs high level of element interactivity would impose high cognitive load leading to reduced learning. Our conceptualization postulates the possible alignment between suboptimal and optimal instructional designs with realistic and optimal levels of best practice, respectively. This postulation (e.g., suboptimal instructional design → realistic level of best practice), which recognizes the importance of cognitive load imposition, is significant from a practical point of view. By focusing on instructional designs, it is possible to assist individuals to achieve optimal best practice in learning

On Deterministic Sketching and Streaming for Sparse Recovery and Norm Estimation

We study classic streaming and sparse recovery problems using deterministic linear sketches, including $\ell_1/\ell_1$ and $\ell_{\infty}/\ell_1$ sparse recovery problems (the latter also being known as ℓ1ℓ1-heavy hitters), norm estimation, and approximate inner product. We focus on devising a fixed matrix $A \epsilon \mathbb{R}^{m \times n}$ and a deterministic recovery/estimation procedure which work for all possible input vectors simultaneously. Our results improve upon existing work, the following being our main contributions: • A proof that $\ell_{\infty}/\ell_1$ sparse recovery and inner product estimation are equivalent, and that incoherent matrices can be used to solve both problems. Our upper bound for the number of measurements is $m=O(\varepsilon^{-2}min\{log n,(log n/log(1/\varepsilon))^2\})$. We can also obtain fast sketching and recovery algorithms by making use of the Fast Johnson–Lindenstrauss transform. Both our running times and number of measurements improve upon previous work. We can also obtain better error guarantees than previous work in terms of a smaller tail of the input vector. • A new lower bound for the number of linear measurements required to solve $\ell_1/\ell_1$ sparse recovery. We show $\Omega(k/\varepsilon^2+k log(n/k)/\varepsilon)$ measurements are required to recover an x′ with $‖x-x′‖_1\leq(1+\varepsilon)‖x_{tail(k)}‖_1$, where $x_{tail(k)}$ is x projected onto all but its largest k coordinates in magnitude. • A tight bound of $m=\theta(\varepsilon^{-2}log(\varepsilon^2n))$ on the number of measurements required to solve deterministic norm estimation, i.e., to recover $‖x‖_2\pm\varepsilon‖x‖_1$. For all the problems we study, tight bounds are already known for the randomized complexity from previous work, except in the case of $\ell_1/\ell_1$ sparse recovery, where a nearly tight bound is known. Our work thus aims to study the deterministic complexities of these problems. We remark that some of the matrices used in our algorithms, although known to exist, currently are not yet explicit in the sense that deterministic polynomial time constructions are not yet known, although in all cases polynomial time Monte Carlo algorithms are known.Engineering and Applied Science

Frequency Bin Entangled Photons

A monochromatic laser pumping a parametric down conversion crystal generates frequency entangled photon pairs. We study this experimentally by addressing such frequency entangled photons at telecommunication wavelengths (around 1550 nm) with fiber optics components such as electro-optic phase modulators and narrow band frequency filters. The theory underlying our approach is developed by introducing the notion of frequency bin entanglement. Our results show that the phase modulators address coherently up to eleven frequency bins, leading to an interference pattern which can violate a Bell inequality adapted to our setup by more than five standard deviations.Comment: 10 pages, 4 figures (extended version

Metabolic syndrome does not affect sustained virologic response of direct-acting antivirals while hepatitis C clearance improves hemoglobin A1c.

AimTo determine whether successful treatment with directacting antivirals (DAA) is associated with improvements in hemoglobin A1c (HbA1c) and if type 2 diabetes mellitus (T2DM) or metabolic syndrome affects sustained virologic response (SVR).MethodsWe performed a retrospective analysis of all hepatitis C virus (HCV) patients at the VA Greater Los Angeles Healthcare System treated with varying DAA therapy between 2014-2016. Separate multivariable logistic regression was performed to determine predictors of HbA1c decrease ≥ 0.5 after DAA treatment and predictors of SVR 12-wk post treatment (SVR12).ResultsA total of 1068 patients were treated with DAA therapy between 2014-2016. The presence of T2DM or metabolic syndrome did not adversely affect SVR12. 106 patients had both HCV and T2DM. Within that cohort, patients who achieved SVR12 had lower mean HbA1c pre treatment (7.35 vs 8.60, P = 0.02), and lower mean HbA1c post-treatment compared to non-responders (6.55 vs 8.61, P = 0.01). The mean reduction in HbA1c after treatment was greater for those who achieved SVR12 than for non-responders (0.79 vs 0.01, P = 0.03). In adjusted models, patients that achieved SVR12 were more likely to have a HbA1c decrease of ≥ 0.5 than those that did not achieve SVR12 (adjusted OR = 7.24, 95%CI: 1.22-42.94).ConclusionIn HCV patients with T2DM, successful treatment with DAA was associated with a significant reduction in HbA1c suggesting that DAA may have a role in improving insulin sensitivity. Furthermore, the presence of T2DM or metabolic syndrome does not adversely affect SVR12 rates in patients treated with DAA

Modeling predictors of risky drug use behavior among male street laborers in urban Vietnam

BACKGROUND: The application of theoretical frameworks for modeling predictors of drug risk among male street laborers remains limited. The objective of this study was to test a modified version of the IMB (Information-Motivation-Behavioral Skills Model), which includes psychosocial stress, and compare this modified version with the original IMB model in terms of goodness-of-fit to predict risky drug use behavior among this population. METHODS: In a cross-sectional study, social mapping technique was conducted to recruit 450 male street laborers from 135 street venues across 13 districts of Hanoi city, Vietnam, for face-to-face interviews. Structural equation modeling (SEM) was used to analyze data from interviews. RESULTS: Overall measures of fit via SEM indicated that the original IMB model provided a better fit to the data than the modified version. Although the former model was able to predict a lesser variance than the latter (55% vs. 62%), it was of better fit. The findings suggest that men who are better informed and motivated for HIV prevention are more likely to report higher behavioral skills, which, in turn, are less likely to be engaged in risky drug use behavior. CONCLUSIONS: This was the first application of the modified IMB model for drug use in men who were unskilled, unregistered laborers in urban settings. An AIDS prevention program for these men should not only distribute information and enhance motivations for HIV prevention, but consider interventions that could improve self-efficacy for preventing HIV infection. Future public health research and action may also consider broader factors such as structural social capital and social policy to alter the conditions that drive risky drug use among these men