arXiv subjects

Richard Chow

Publications and source records attributed to Richard Chow.

4 recordsLinked to original sources

arXiv2025

Airy Phase Functions

It is well known that phase function methods allow for the numerical solution of a large class of oscillatory second order linear ordinary differential equations in time independent of frequency. Unfortunately, these methods break down in the commonly-occurring case in which the equation has turning points. Here, we resolve this difficulty by introducing a generalized phase function method designed for the case of second order linear ordinary differential equations with turning points. More explicitly, we prove the existence of a slowly-varying ``Airy phase function'' that efficiently represents a basis in the space of solutions of such an equation, and describe a numerical algorithm for calculating this Airy phase function. The running time of our algorithm is independent of the magnitude of the logarithmic derivatives of the equation's solutions, which is a measure of their rate of variation that generalizes the notion of frequency to functions which are rapidly varying but not necessarily oscillatory. Once the Airy phase function has been constructed, any reasonable initial or boundary value problem for the equation can be readily solved and, unlike step methods which output the values of a rapidly-varying solution on a sparse discretization grid that is insufficient for interpolation, the output of our scheme allows for the rapid evaluation of the obtained solution at any point in its domain. We rigorously justify our approach by proving not only the existence of slowly-varying Airy phase functions, but also the convergence of our numerical method. Moreover, we present the results of extensive numerical experiments demonstrating the efficacy of our algorithm.

math.NA↗

arXiv2020

Democratizing the Edge: A Pervasive Edge Computing Framework

The needs of emerging applications, such as augmented and virtual reality, federated machine learning, and autonomous driving, have motivated edge computing--the push of computation capabilities to the edge. Various edge computing architectures have emerged, including multi-access edge computing and edge-cloud, all with the premise of reducing communication latency and augmenting privacy. However, these architectures rely on static and pre-deployed infrastructure, falling short in harnessing the abundant resources at the network's edge. In this paper, we discuss the design of Pervasive Edge Computing (PEC)--a democratized edge computing framework, which enables end-user devices (e.g., smartphones, IoT devices, and vehicles) to dynamically participate in a large-scale computing ecosystem. Our vision of the democratized edge involves the real-time composition of services using available edge resources like data, software, and compute-hardware from multiple stakeholders. We discuss how the novel Named-Data Networking architecture can facilitate service deployment, discovery, invocation, and migration. We also discuss the economic models critical to the adoption of PEC and the outstanding challenges for its full realization.

cs.NI↗

arXiv2015

Albatross: a Privacy-Preserving Location Sharing System

Social networking services are increasingly accessed through mobile devices. This trend has prompted services such as Facebook and Google+ to incorporate location as a de facto feature of user interaction. At the same time, services based on location such as Foursquare and Shopkick are also growing as smartphone market penetration increases. In fact, this growth is happening despite concerns (growing at a similar pace) about security and third-party use of private location information (e.g., for advertising). Nevertheless, service providers have been unwilling to build truly private systems in which they do not have access to location information. In this paper, we describe an architecture and a trial implementation of a privacy-preserving location sharing system called Albatross. The system protects location information from the service provider and yet enables fine-grained location-sharing. One main feature of the system is to protect an individual's social network structure. The pattern of location sharing preferences towards contacts can reveal this structure without any knowledge of the locations themselves. Albatross protects locations sharing preferences through protocol unification and masking. Albatross has been implemented as a standalone solution, but the technology can also be integrated into location-based services to enhance privacy.

cs.CR↗

arXiv2013

Differential Data Analysis for Recommender Systems

We present techniques to characterize which data is important to a recommender system and which is not. Important data is data that contributes most to the accuracy of the recommendation algorithm, while less important data contributes less to the accuracy or even decreases it. Characterizing the importance of data has two potential direct benefits: (1) increased privacy and (2) reduced data management costs, including storage. For privacy, we enable increased recommendation accuracy for comparable privacy levels using existing data obfuscation techniques. For storage, our results indicate that we can achieve large reductions in recommendation data and yet maintain recommendation accuracy. Our main technique is called differential data analysis. The name is inspired by other sorts of differential analysis, such as differential power analysis and differential cryptanalysis, where insight comes through analysis of slightly differing inputs. In differential data analysis we chunk the data and compare results in the presence or absence of each chunk. We present results applying differential data analysis to two datasets and three different kinds of attributes. The first attribute is called user hardship. This is a novel attribute, particularly relevant to location datasets, that indicates how burdensome a data point was to achieve. The second and third attributes are more standard: timestamp and user rating. For user rating, we confirm previous work concerning the increased importance to the recommender of data corresponding to high and low user ratings.

cs.IR↗