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The increasing prevalence of wearable devices enables low-cost, long-term collection of health relevant data such as heart rate, exercise, and sleep signals. Currently these data are used to monitor short term changes with limited interpretation of their relevance to health. These data provide an untapped resource to monitor daily and long-term activity patterns. Changes and trends identified from such data can provide insights and guidance to the management of many chronic conditions that change over time. In this study we conducted a machine learning based analysis of longitudinal heart rate data collected over multiple years from Fitbit devices. We built a multi-resolutional pipeline for time series analysis, using model-free clustering methods inspired by statistical conformal prediction framework. With this method, we were able to detect health relevant events, their interesting patterns (e.g., daily routines, seasonal differences, and anomalies), and correlations to acute and chronic changes in health conditions. We present the results, lessons, and insights learned, and how to address the challenge of lack of labels. The study confirms the value of long-term heart rate data for health monitoring and surveillance, as complementary to extensive yet intermittent examinations by health care providers.

 

We propose new differential privacy solutions for when external invariants and integer constraints are simultaneously enforced on the data product. These requirements arise in real world applications of private data curation, including the public release of the 2020 U.S. Decennial Census. They pose a great challenge to the production of provably private data products with adequate statistical usability. We propose integer subspace differential privacy to rigorously articulate the privacy guarantee when data products maintain both the invariants and integer characteristics, and demonstrate the composition and post-processing properties of our proposal. To address the challenge of sampling from a potentially highly restricted discrete space, we devise a pair of unbiased additive mechanisms, the generalized Laplace and the generalized Gaussian mechanisms, by solving the Diophantine equations as defined by the constraints. The proposed mechanisms have good accuracy, with errors exhibiting sub-exponential and sub-Gaussian tail probabilities respectively. To implement our proposal, we design an MCMC algorithm and supply empirical convergence assessment using estimated upper bounds on the total variation distance via L-lag coupling. We demonstrate the efficacy of our proposal with applications to a synthetic problem with intersecting invariants, a sensitive contingency table with known margins, and the 2010 Census county-level demonstration data with mandated fixed state population totals. 

Optical phase-change materials exhibit tunable permittivity and switching properties during phase transition, which offers the possibility of dynamic control of optical devices. Here, a wavelength-tunable infrared chiral metasurface integrated with phase-change material GST-225 is demonstrated with the designed unit cell of parallelogram-shaped resonator. By varying the baking time at a temperature above the phase transition temperature of GST-225, the resonance wavelength of the chiral metasurface is tuned in the wavelength range of 2.33 µm to 2.58 µm, while the circular dichroism in absorption is maintained around 0.44. The chiroptical response of the designed metasurface is revealed by analyzing the electromagnetic field and displacement current distributions under left- and right-handed circularly polarized (LCP and RCP) light illumination. Moreover, the photothermal effect is simulated to investigate the large temperature difference in the chiral metasurface under LCP and RCP illumination, which allows for the possibility of circular polarization-controlled phase transition. The presented chiral metasurfaces with phase-change materials offer the potential to facilitate promising applications in the infrared regime, such as chiral thermal switching, infrared imaging, and tunable chiral photonics.

 

Structural balance theory studies stability in networks. Given a n-vertex complete graph G = (V,E) whose edges are labeled positive or negative, the graph is considered balanced if every triangle either consists of three positive edges (three mutual "friends"), or one positive edge and two negative edges (two "friends" with a common "enemy"). From a computational perspective, structural balance turns out to be a special case of correlation clustering with the number of clusters at most two. The two main algorithmic problems of interest are: (i) detecting whether a given graph is balanced, or (ii) finding a partition that approximates the frustration index, i.e., the minimum number of edge flips that turn the graph balanced. We study these problems in the streaming model where edges are given one by one and focus on memory efficiency. We provide randomized single-pass algorithms for: (i) determining whether an input graph is balanced with O(log n) memory, and (ii) finding a partition that induces a (1 + ε)-approximation to the frustration index with O(n ⋅ polylog(n)) memory. We further provide several new lower bounds, complementing different aspects of our algorithms such as the need for randomization or approximation. To obtain our main results, we develop a method using pseudorandom generators (PRGs) to sample edges between independently-chosen vertices in graph streaming. Furthermore, our algorithm that approximates the frustration index improves the running time of the state-of-the-art correlation clustering with two clusters (Giotis-Guruswami algorithm [SODA 2006]) from n^O(1/ε²) to O(n²log³n/ε² + n log n ⋅ (1/ε)^O(1/ε⁴)) time for (1+ε)-approximation. These results may be of independent interest. 

Abstract The design and formation of van der Waals (vdW) heterostructures with different two-dimensional (2D) materials provide an opportunity to create materials with extraordinary physical properties tailored toward specific applications. Mechanical exfoliation of natural vdW materials has been recognized as an effective way for producing high-quality ultrathin vdW heterostructures. Abramovite is one of such naturally occurring vdW materials, where the superlattice is composed of alternating Pb 2 BiS 3 and SnInS 4 2D material lattices. The forced commensuration between the two incommensurate constituent 2D material lattices induces in-plane structural anisotropy in the formed vdW heterostructure of abramovite, even though the individual 2D material lattices are isotropic in nature. Here, we show that ultrathin layers of vdW heterostructures of abramovite can be achieved by mechanical exfoliation of the natural mineral. Furthermore, the structural anisotropy induced highly anisotropic vibrational and optical responses of abramovite thin flakes are demonstrated by angle-resolved polarized Raman scattering, linear dichroism, and polarization-dependent third-harmonic generation. Our results not only establish abramovite as a promising natural vdW material with tailored linear and nonlinear optical properties for building future anisotropic integrated photonic devices, but also provide a deeper understanding of the origin of structural, vibrational and optical anisotropy in vdW heterostructures.