Symmetries and charges of general relativity at null boundaries

We study general relativity at a null boundary using the covariant phase space formalism. We define a covariant phase space and compute the algebra of symmetries at the null boundary by considering the boundary-preserving diffeomorphisms that preserve this phase space. This algebra is the semi-direct sum of diffeomorphisms on the two sphere and a nonabelian algebra of supertranslations that has some similarities to supertranslations at null infinity. By using the general prescription developed by Wald and Zoupas, we derive the localized charges of this algebra at cross sections of the null surface as well as the associated fluxes. Our analysis is covariant and applies to general non-stationary null surfaces. We also derive the global charges that generate the symmetries for event horizons, and show that these obey the same algebra as the linearized diffeomorphisms, without any central extension. Our results show that supertranslations play an important role not just at null infinity but at all null boundaries, including non-stationary event horizons. They should facilitate further investigations of whether horizon symmetries and conservation laws in black hole spacetimes play a role in the information loss problem, as suggested by Hawking, Perry, and Strominger.Comment: v2: added appendices on trivial diffeomorphisms and relation to 1810.01847; v1: 59 pages + appendices, 2 figure

Local Testing for Membership in Lattices

Motivated by the structural analogies between point lattices and linear error-correcting codes, and by the mature theory on locally testable codes, we initiate a systematic study of local testing for membership in lattices. Testing membership in lattices is also motivated in practice, by applications to integer programming, error detection in lattice-based communication, and cryptography. Apart from establishing the conceptual foundations of lattice testing, our results include the following: 1. We demonstrate upper and lower bounds on the query complexity of local testing for the well-known family of code formula lattices. Furthermore, we instantiate our results with code formula lattices constructed from Reed-Muller codes, and obtain nearly-tight bounds. 2. We show that in order to achieve low query complexity, it is sufficient to design one-sided non-adaptive canonical tests. This result is akin to, and based on an analogous result for error-correcting codes due to Ben-Sasson et al. (SIAM J. Computing 35(1) pp1-21)

Polymer compositions suitable for use in enriched oxygen atmospheres

Three organic polymer systems are based on copolymer of chlorotrifluoroethylene, ethylene, and tin-based flame retardants. Fourth system is copolymer of chlorotrifluorethylene and tetrafluoroethylene. This system contains no stabilizers of flame retardant additives

Frequency shifts and depth dependence of premotor beta band activity during perceptual decision-making

Neural activity in the premotor and motor cortices shows prominent structure in the beta frequency range (13–30 Hz). Currently, the behavioral relevance of this beta band activity (BBA) is debated. The underlying source of motor BBA and how it changes as a function of cortical depth are also not completely understood. Here, we addressed these unresolved questions by investigating BBA recorded using laminar electrodes in the dorsal premotor cortex of 2 male rhesus macaques performing a visual reaction time (RT) reach discrimination task. We observed robust BBA before and after the onset of the visual stimulus but not during the arm movement. While poststimulus BBA was positively correlated with RT throughout the beta frequency range, prestimulus correlation varied by frequency. Low beta frequencies (∼12–20 Hz) were positively correlated with RT, and high beta frequencies (∼22–30 Hz) were negatively correlated with RT. Analysis and simulations suggested that these frequency-dependent correlations could emerge due to a shift in the component frequencies of the prestimulus BBA as a function of RT, such that faster RTs are accompanied by greater power in high beta frequencies. We also observed a laminar dependence of BBA, with deeper electrodes demonstrating stronger power in low beta frequencies both prestimulus and poststimulus. The heterogeneous nature of BBA and the changing relationship between BBA and RT in different task epochs may be a sign of the differential network dynamics involved in cue expectation, decision-making, motor preparation, and movement execution.Published versio

Patters of use and key predictors for the use of wearable health care devices by US adults: insights from a national survey

Background: Despite the growing popularity of wearable health care devices (from fitness trackes such as Fitbit to smartwatches such as Apple Watch and more sophisticated devices that can collect information on metrics such as blood pressure, glucose levels, and oxygen levels), we have a limited understanding about the actual use and key factors affecting the use of these devices by US adults. Objective: The main objective of this study was to examine the use of wearable health care devices and the key predictors of wearable use by US adults. Methods: Using a national survey of 4551 respondents, we examined the usage patterns of wearable health care devices (use of wearables, frequency of their use, and willingness to share health data from a wearable with a provider) and a set of predictors that pertain to personal demographics (age, gender, race, education, marital status, and household income), individual health (general health, presence of chronic conditions, weight perceptions, frequency of provider visits, and attitude towards exercise), and technology self-efficacy using logistic regression analysis. Results: About 30% (1266/4551) of US adults use wearable health care devices. Among the users, nearly half (47.33%) use the devices every day, with a majority (82.38% weighted) willing to share the health data from wearables with their care providers. Women (16.25%), White individuals (19.74%), adults aged 18-50 years (19.52%), those with some level of college education or college graduates (25.60%), and those with annual household incomes greater than US $75,000 (17.66report using wearable health care devices. We found that the use of wearables declines with age: Adults aged >50 years were less likely to use wearables compared to those aged 18-34 years (odds ratios [OR] 0.46-0.57). Women (OR 1.26, 95White individuals (OR 1.65, 95incomes greater than US$75,000 (OR 2.6, 95% CI 1.39-4.86) were more likely to use wearables. US adults who reported feeling healthier (OR 1.17, 95% CI 0.98-1.39), were overweight (OR 1.16, 95% CI 1.06-1.27), enjoyed exercise (OR 1.23, 95% CI 1.06-1.43), and reported higher levels of technology self-efficacy (OR 1.33, 95% CI 1.21-1.46) were more likely to adopt and use wearables for tracking or monitoring their health. Conclusions: The potential of wearable health care devices is under-realized, with less than one-third of US adults actively using these devices. With only younger, healthier, wealthier, more educated, technoliterate adults using wearables, other groups have been left behind. More concentrated efforts by clinicians, device makers, and health care policy makers are needed to bridge this divide and improve the use of wearable devices among larger sections of American society [Abstract copyright: ©Ranganathan Chandrasekaran, Vipanchi Katthula, Evangelos Moustakas. Originally published in the Journal of Medical Internet Research (http://www.jmir.org), 16.10.2020.

Too old for technology? Use of wearable healthcare devices by older adults and their willingness to share health data with providers

Wearable healthcare devices offer tremendous promise to effectively track and improve the well-being of older adults. Yet, little is known about the use of wearable devices by older adults. Drawing upon a national survey in US with 1481 older adults, we examine the use of wearable healthcare devices and the key predictors of use viz. sociodemographic factors, health conditions, and technology self-efficacy. We also examine if the predictors are associated with elders’ willingness to share health data from wearable devices with healthcare providers. We find low level of wearable use (17.49%) among US older adults. We find significant positive associations between technology self-efficacy, health conditions, and demographic factors (gender, race, education, and annual household income) and use of wearable devices. Men were less likely (OR = 0.62, 95% CI 0.36–1.04) and Asians were more likely (OR = 2.60, 95% CI 0.89–7.64) to use wearables, as did healthy adults (OR = 1.98, 95% CI 1.37–2.87). Those who electronically communicated with their doctors (OR = 1.86, 95% CI 1.16–2.97), and those who searched online for health information (OR = 1.79, 95% CI 1.03–3.10) were more likely to use wearables. Though 80.15% of wearable users are willing to share health data with providers, those with greater technology self-efficacy and favorable attitudes toward exercise are more willing

Deteriorating Inventory Model For Two Parameter Weibull Demand With Shortages

In this paper a deteriorating inventory model have been developed for two parameter Weibull demand rate. Shortages are allowed and are completely backlogged .This inventory system follows an two-parameter exponnential distribution deterioration rate in which the holding cost is constant .The results are described with the numerical example and sensitivity analysis. Keywords: Deterioration, Exponential distribution, holding cost, Inventory, shortages, Weibull demand rate