Private Matchings and Allocations

We consider a private variant of the classical allocation problem: given k goods and n agents with individual, private valuation functions over bundles of goods, how can we partition the goods amongst the agents to maximize social welfare? An important special case is when each agent desires at most one good, and specifies her (private) value for each good: in this case, the problem is exactly the maximum-weight matching problem in a bipartite graph. Private matching and allocation problems have not been considered in the differential privacy literature, and for good reason: they are plainly impossible to solve under differential privacy. Informally, the allocation must match agents to their preferred goods in order to maximize social welfare, but this preference is exactly what agents wish to hide. Therefore, we consider the problem under the relaxed constraint of joint differential privacy: for any agent i, no coalition of agents excluding i should be able to learn about the valuation function of agent i. In this setting, the full allocation is no longer published---instead, each agent is told what good to get. We first show that with a small number of identical copies of each good, it is possible to efficiently and accurately solve the maximum weight matching problem while guaranteeing joint differential privacy. We then consider the more general allocation problem, when bidder valuations satisfy the gross substitutes condition. Finally, we prove that the allocation problem cannot be solved to non-trivial accuracy under joint differential privacy without requiring multiple copies of each type of good.Comment: Journal version published in SIAM Journal on Computation; an extended abstract appeared in STOC 201

Attitude Determination and Control System Design for STU-2A CubeSat and In-Orbit Results

STU-2A, a 3U CubeSat developed by Shanghai Engineering Center for Microsatellites, along with the other two 2U CubeSats and one MicroSat, has been sent into a 481km sun-synchronous orbit by CZ-11 launch vehicle with its maiden journey. As the first batch of CubeSats in China that is made in accordance with CubeSat standard, the 2.9kg satellite is featured with the on-board CMOS color camera for taking pictures of polar glacier, Gamalink for Cubesats Networking, MEMS based cold-gas micropropulsion for attitude/orbit maneuver and formation flight and precise ADCS module for technology demonstration. The ADCS module, equipped with two 3-axis magnetometers, 1 fine Sun sensor, five coarse Sun sensors, one three-axis MEMS gyro, one Nano-scaled star tracker, three magnetic coils and three reaction wheels, would provide three-axis stabilization and maneuver capability. Combining the attitude sensors, TRAID and unscented Kalman Filter (UKF) algorithms are adopted to determine the attitude knowledge. Some attitude control modes, such as damping control, Sun-pointing, magnetic-based nadir pointing, momentum-biased stabilization and reaction wheels-based control, are designed to achieve the prefect attitude.In-Orbit data received by ground station verified the performance of ADCS of STU-2A

Online Vertex-Weighted Bipartite Matching: Beating 1-1/e with Random Arrivals

We introduce a weighted version of the ranking algorithm by Karp et al. (STOC 1990), and prove a competitive ratio of 0.6534 for the vertex-weighted online bipartite matching problem when online vertices arrive in random order. Our result shows that random arrivals help beating the 1-1/e barrier even in the vertex-weighted case. We build on the randomized primal-dual framework by Devanur et al. (SODA 2013) and design a two dimensional gain sharing function, which depends not only on the rank of the offline vertex, but also on the arrival time of the online vertex. To our knowledge, this is the first competitive ratio strictly larger than 1-1/e for an online bipartite matching problem achieved under the randomized primal-dual framework. Our algorithm has a natural interpretation that offline vertices offer a larger portion of their weights to the online vertices as time goes by, and each online vertex matches the neighbor with the highest offer at its arrival

Strict Intuitionistic Fuzzy Distance/Similarity Measures Based on Jensen-Shannon Divergence

Being a pair of dual concepts, the normalized distance and similarity measures are very important tools for decision-making and pattern recognition under intuitionistic fuzzy sets framework. To be more effective for decision-making and pattern recognition applications, a good normalized distance measure should ensure that its dual similarity measure satisfies the axiomatic definition. In this paper, we first construct some examples to illustrate that the dual similarity measures of two nonlinear distance measures introduced in [A distance measure for intuitionistic fuzzy sets and its application to pattern classification problems, \emph{IEEE Trans. Syst., Man, Cybern., Syst.}, vol.~51, no.~6, pp. 3980--3992, 2021] and [Intuitionistic fuzzy sets: spherical representation and distances, \emph{Int. J. Intell. Syst.}, vol.~24, no.~4, pp. 399--420, 2009] do not meet the axiomatic definition of intuitionistic fuzzy similarity measure. We show that (1) they cannot effectively distinguish some intuitionistic fuzzy values (IFVs) with obvious size relationship; (2) except for the endpoints, there exist infinitely many pairs of IFVs, where the maximum distance 1 can be achieved under these two distances; leading to counter-intuitive results. To overcome these drawbacks, we introduce the concepts of strict intuitionistic fuzzy distance measure (SIFDisM) and strict intuitionistic fuzzy similarity measure (SIFSimM), and propose an improved intuitionistic fuzzy distance measure based on Jensen-Shannon divergence. We prove that (1) it is a SIFDisM; (2) its dual similarity measure is a SIFSimM; (3) its induced entropy is an intuitionistic fuzzy entropy. Comparative analysis and numerical examples demonstrate that our proposed distance measure is completely superior to the existing ones

DualApp: Tight Over-Approximation for Neural Network Robustness Verification via Under-Approximation

The robustness of neural networks is fundamental to the hosting system's reliability and security. Formal verification has been proven to be effective in providing provable robustness guarantees. To improve the verification scalability, over-approximating the non-linear activation functions in neural networks by linear constraints is widely adopted, which transforms the verification problem into an efficiently solvable linear programming problem. As over-approximations inevitably introduce overestimation, many efforts have been dedicated to defining the tightest possible approximations. Recent studies have however showed that the existing so-called tightest approximations are superior to each other. In this paper we identify and report an crucial factor in defining tight approximations, namely the approximation domains of activation functions. We observe that existing approaches only rely on overestimated domains, while the corresponding tight approximation may not necessarily be tight on its actual domain. We propose a novel under-approximation-guided approach, called dual-approximation, to define tight over-approximations and two complementary under-approximation algorithms based on sampling and gradient descent. The overestimated domain guarantees the soundness while the underestimated one guides the tightness. We implement our approach into a tool called DualApp and extensively evaluate it on a comprehensive benchmark of 84 collected and trained neural networks with different architectures. The experimental results show that DualApp outperforms the state-of-the-art approximation-based approaches, with up to 71.22% improvement to the verification result.Comment: 13 pages, 9 fugures, 3 table

Lasing- Encoded Microsensor Driven by Interfacial Cavity Resonance Energy Transfer

Microlasers are emerging tools for biomedical applications. In particular, whispering- gallery- mode (WGM) microlasers are promising candidates for sensing at the biointerface owing to their high quality- factor and potential in molecular assays, and intracellular and extracellular detection. However, lasing particles with sensing functionality remain challenging since the overlap between the WGM optical mode and external gain medium is much lower compared to internal gain inside the cavity. To overcome this problem, the concept of Förster resonant energy transfer (FRET) is exploited on WGM droplet microlaser by separating donor and acceptor molecules at the cavity- surface interface. It is first discovered that the interfacial FRET laser not only originates from conventional FRET but utilizes coherent radiative energy transfer (CRET) to excite acceptor molecules by inducing light- harvesting effect near the cavity interface. Simulations and experiments have revealed that the absorption spectrum of individual analyte plays a crucial role in interfacial FRET laser. Distinct lasing spectra can therefore distinguish molecules of different absorption properties upon binding. Finally, detection of small fluorescent molecules and photosynthetic protein is performed. The results presented here not only demonstrate the wide- ranging potential of microlaser external cavity implementation in molecular sensing applications, but also provide comprehensive insights into cavity energy transfer in laser physics.A novel concept is proposed to achieve active lasing- encoded biosensors by taking advantage of light- harvesting effect at the cavity interface, where interfacial molecular lasers based on cavity resonant energy transfer are demonstrated. This work marks a critical step of realizing whispering- gallery- mode (WGM) laser probes for biosensing, opening a new avenue in laser- based molecular sensing.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154969/1/adom201901596-sup-0001-SuppMat.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154969/2/adom201901596_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154969/3/adom201901596.pd