pp-adic quotient sets

For $A \subseteq \mathbb{N}$, the question of when $R(A) = \{a/a' : a, a' \in A\}$ is dense in the positive real numbers $\mathbb{R}_+$ has been examined by many authors over the years. In contrast, the $p$-adic setting is largely unexplored. We investigate conditions under which $R(A)$ is dense in the $p$-adic numbers. Techniques from elementary, algebraic, and analytic number theory are employed in this endeavor. We also pose many open questions that should be of general interest.Comment: 24 page

Boundary motion coupled with tensile and compressive deformation: TEM observation of twinning-like lattice reorientation in Mg micropillars

For magnesium and some other hexagonal-close-packed metals, twinning on the plane is a common mode of plastic deformation. Recently, we have used in situ transmission electron microscopy (TEM) to monitor the deformation of submicron-sized single-crystal magnesium, in quantitative compression and tension tests (B-Y. Liu et al., Nature Commun. 2014). We have observed the reorientation of the parent lattice to a “twin” lattice, producing an orientational relationship akin to that of the conventional twinning. However, aberration-corrected TEM observations reveal that the boundary between the parent lattice and the “twin” lattice is composed of many segments of semi-coherent basal-prismatic (B-P) interfaces, instead of the twinning plane. Both TEM and molecular dynamics simulations suggest that the migration of this boundary is accomplished by B-P interfaces undergoing basal-prismatic transformation, in addition to the migration of the boundary of the extension twin. This deformation mode mimics conventional deformation twinning, but is distinct from the latter. It is a form of boundary motion coupled to stresses, but produces plastic strain that is not simple shear. The basal-prismatic transformation appears to be important under deformation conditions when the availability and/or mobility of twinning dislocations/disconnections are limited. As such, this new twist in lattice reorientation accompanying deformation twinning enriches the known repertoire of plasticity mechanisms

Measuring the delay time distribution of binary neutron stars. II. Using the redshift distribution from third-generation gravitational wave detectors network

We investigate the ability of current and third-generation gravitational wave (GW) detectors to determine the delay time distribution (DTD) of binary neutron stars (BNS) through a direct measurement of the BNS merger rate as a function of redshift. We assume that the DTD follows a power law distribution with a slope $\Gamma$ and a minimum merger time $t_{\rm min}$, and also allow the overall BNS formation efficiency per unit stellar mass to vary. By convolving the DTD and mass efficiency with the cosmic star formation history, and then with the GW detector capabilities, we explore two relevant regimes. First, for the current generation of GW detectors, which are only sensitive to the local universe, but can lead to precise redshift determinations via the identification of electromagnetic counterparts and host galaxies, we show that the DTD parameters are strongly degenerate with the unknown mass efficiency and therefore cannot be determined uniquely. Second, for third-generation detectors such as Einstein Telescope (ET) and Cosmic Explorer (CE), which will detect BNS mergers at cosmological distances, but with a redshift uncertainty inherent to GW-only detections ($\delta(z)/z\approx 0.1z$), we show that the DTD and mass efficiency can be well-constrained to better than 10\% with a year of observations. This long-term approach to determining the DTD through a direct mapping of the BNS merger redshift distribution will be supplemented by more near term studies of the DTD through the properties of BNS merger host galaxies at $z\approx 0$ (Safarzadeh & Berger 2019).Comment: 10 pages, Accepted to ApJ Letter

Attracting Investment to REDD+: Capitalizing on Co-Benefits?

At its inception in 2007, the United Nations-sponsored Reducing Emissions from Deforestation and Forest Degradation (REDD+) mechanism had one primary goal: to mitigate carbon dioxide emissions from the global forest sector, which currently account for approximately 10% of global carbon emissions. REDD+ has undergone various modifications to its scope and approach in the succeeding nine years, but little has yet come from subsequent UN climate negotiations in the way of creating an obligatory financing scheme that would require participation from actors in developed countries. Today, dozens of preliminary REDD+ projects are operational across the world, but these projects receive strictly voluntary funding from a suite of public and private actors, including national governments and companies engaged in social responsibility practices. Despite some successes in this voluntary realm and promises of REDD+ advancement at recent negotiations, it has become clear that without assured funding – and pending an international financing mechanism for REDD+ – projects face an increasingly difficult environment for attaining capital resources. Scaling up the mechanism will be virtually impossible without addressing the imbalance between supply and demand for REDD+ credits in the voluntary stage. Code REDD, a San Francisco-based non-governmental organization whose mission is to support and scale the REDD+ mechanism, is attempting to discover whether untapped opportunities exist for sustaining REDD+ before the commencement of an international financing scheme, specifically by capitalizing on the co-benefits of REDD+ projects: the social and environmental outcomes that inherently accompany responsibly designed carbon offset projects. These co-benefits can include biodiversity benefits, freshwater provision, community economic development, and women’s empowerment. This question of the potential for co-benefit quantification and sale as a means to sustain REDD+ in the voluntary phase was the foundation of the research we undertook here. We aimed to determine how REDD+ stakeholders envisioned the role of co-benefits within the financing of REDD+, and if further efforts to quantify and sell them could bear meaningful results for the future of the mechanism. Splitting the REDD+ community into two distinct categories – practitioners (those who design, implement, and monitor REDD+ projects) and investors (both those who purchase REDD+ credits and those who invest in REDD+ projects) – we held more than twenty interviews to determine the answer to the above question. We found that, though co-benefits were considered an important – even indispensable – part of REDD+ success, few practitioners or investors were interested in their further quantification or expected that voluntary REDD+ could be sustained based on such action. That said, many current and potential investors offered insight into how the business case for REDD+ could be better articulated in order to attract more investment. Also, in speaking with practitioners, we identified ways that the mechanism could be better integrated with other contemporary environmental efforts, including biodiversity offsetting and water funds, offering what we believe could represent partial solutions to the REDD+ demand shortfall

Cheating off your neighbors: Improving activity recognition through corroboration

Understanding the complexity of human activities solely through an individual's data can be challenging. However, in many situations, surrounding individuals are likely performing similar activities, while existing human activity recognition approaches focus almost exclusively on individual measurements and largely ignore the context of the activity. Consider two activities: attending a small group meeting and working at an office desk. From solely an individual's perspective, it can be difficult to differentiate between these activities as they may appear very similar, even though they are markedly different. Yet, by observing others nearby, it can be possible to distinguish between these activities. In this paper, we propose an approach to enhance the prediction accuracy of an individual's activities by incorporating insights from surrounding individuals. We have collected a real-world dataset from 20 participants with over 58 hours of data including activities such as attending lectures, having meetings, working in the office, and eating together. Compared to observing a single person in isolation, our proposed approach significantly improves accuracy. We regard this work as a first step in collaborative activity recognition, opening new possibilities for understanding human activity in group settings

Selective Differential Privacy for Language Modeling

With the increasing applications of language models, it has become crucial to protect these models from leaking private information. Previous work has attempted to tackle this challenge by training RNN-based language models with differential privacy guarantees. However, applying classical differential privacy to language models leads to poor model performance as the underlying privacy notion is over-pessimistic and provides undifferentiated protection for all tokens in the data. Given that the private information in natural language is sparse (for example, the bulk of an email might not carry personally identifiable information), we propose a new privacy notion, selective differential privacy, to provide rigorous privacy guarantees on the sensitive portion of the data to improve model utility. To realize such a new notion, we develop a corresponding privacy mechanism, Selective-DPSGD, for RNN-based language models. Besides language modeling, we also apply the method to a more concrete application--dialog systems. Experiments on both language modeling and dialog system building show that the proposed privacy-preserving mechanism achieves better utilities while remaining safe under various privacy attacks compared to the baselines. The data and code are released at https://github.com/wyshi/lm_privacy to facilitate future research .Comment: NAACL 202

RadCool: a Web-enabled Simulation Tool for Radiative Cooling

Thermophotovoltaic (TPV) systems can generate electricity from high-temperature heat sources via thermal radiation. However, the intense heating of a photovoltaic (PV) cell can greatly reduce the overall efficiency of the system. Therefore, it is critical to develop techniques to keep the PV cells close to ambient temperature without consuming energy. Radiative cooling is a passive technique that dissipates heat into remote space via thermal radiation. A simulation tool to predict the performance of radiative cooling systems would be particularly helpful in designing new experiments. The current TPV model simulation tool, TPVexpt, can calculate the theoretical performance of the TPV system. However, it does not consider the thermal management of the PV cell. A new tool, Radcool, is created to complement TPVexpt as well as to predict the performance of a radiative cooling system in general. The main design considerations of Radcool include: (1) the area ratio between the PV cell and the cooling emitter, and (2) the cooling emitter materials. The cooling performance is evaluated by equilibrium heat transfer analysis. Radcool has been validated with the existing experiment, but more experiments need to be done to confirm the generality of the system and modeling approach. In the future, this radiative cooling model can be connected directly with the existing TPV model, so that TPV systems will become more efficient for real world applications. The radiative cooling technique is not limited to TPV systems; other potential applications include solar cell cooling, infrared detectors, and sensitive electronic devices that are used outdoors