Conducting Truthful Surveys, Cheaply

We consider the problem of conducting a survey with the goal of obtaining an unbiased estimator of some population statistic when individuals have unknown costs (drawn from a known prior) for participating in the survey. Individuals must be compensated for their participation and are strategic agents, and so the payment scheme must incentivize truthful behavior. We derive optimal truthful mechanisms for this problem for the two goals of minimizing the variance of the estimator given a fixed budget, and minimizing the expected cost of the survey given a fixed variance goal

Graph Isomorphism and the Lasserre Hierarchy

In this paper we show lower bounds for a certain large class of algorithms solving the Graph Isomorphism problem, even on expander graph instances. Spielman [25] shows an algorithm for isomorphism of strongly regular expander graphs that runs in time exp(O(n^(1/3)) (this bound was recently improved to expf O(n^(1/5) [5]). It has since been an open question to remove the requirement that the graph be strongly regular. Recent algorithmic results show that for many problems the Lasserre hierarchy works surprisingly well when the underlying graph has expansion properties. Moreover, recent work of Atserias and Maneva [3] shows that k rounds of the Lasserre hierarchy is a generalization of the k-dimensional Weisfeiler-Lehman algorithm for Graph Isomorphism. These two facts combined make the Lasserre hierarchy a good candidate for solving graph isomorphism on expander graphs. Our main result rules out this promising direction by showing that even Omega(n) rounds of the Lasserre semidefinite program hierarchy fail to solve the Graph Isomorphism problem even on expander graphs.Comment: 22 pages, 3 figures, submitted to CC

Supersymmetric quantum mechanics and the Korteweg-de Vries hierarchy

The connection between supersymmetric quantum mechanics and the Korteweg- de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the $\tau$-function by means of supersymmetric quantum mechanics is discussed.Comment: 16 pages, latex, EFI 93/2

Precision Tests of Electroweak Physics

We review the current status of precision electroweak measurements and the constraints they impose on new physics. We perform a model independent analysis using the STU-formalism of Ref. 1, and then discuss how the Z-pole data from LEP and SLD can be used to constrain models that are not covered within that framework.Comment: 1 cover page + 8 pages, 8 postscript figures, LaTeX2e, ws-p9-75x6-50.cls, Talk presented at Hadron 13, Mumbai, India, January 14-20, 199

Modeling, Simulation, and Validation of Process-Structure-Property Relationships in Fused Filament Fabrication

As additive manufacturing (AM) grows in popularity, the need for better simulation tools to predict the process-structure-property relationships of AM parts becomes ever more necessary to employ the technology in design of functional parts with varying degrees of complexity and performance requirements. Many simulation tools and techniques have been developed that aim to achieve this goal, and the main purpose of this research is to explore how well different simulation tools and modeling approaches can capture various AM-specific features such as inter-raster and end-of raster voids, and residual stresses induced by dissimilar rates of thermal expansion. Process simulation of fused filament fabrication (FFF) through FEA-based code (ABAQUS) and affiliated programs combined with performance simulation through a nonlinear user-material model (GENOA) to predict the tensile and bending properties of Polylactic Acid (PLA) samples. Following the examination of different process parameters such as rate of extrusion per distance travel, fan speed, and nozzle temperature through a multi-factor design of experiments, an optimal setting was identified and used to explore the effect of raster architecture on tensile response of dog-bone specimens based on ASTM D638 standard, and bending response of rectangular beam specimens based on ASTM D790 standard. Comparison of the experimental data from nearly 300 tests with the simulation-based results indicate that the Young’s modulus, ultimate tensile strength, and bending strength predictions are very sensitive to how FFF-induced voids and temperature effects are modeled, and that it is possible to achieve reasonably good agreements

Buying Private Data without Verification

We consider the problem of designing a survey to aggregate non-verifiable information from a privacy-sensitive population: an analyst wants to compute some aggregate statistic from the private bits held by each member of a population, but cannot verify the correctness of the bits reported by participants in his survey. Individuals in the population are strategic agents with a cost for privacy, \ie, they not only account for the payments they expect to receive from the mechanism, but also their privacy costs from any information revealed about them by the mechanism's outcome---the computed statistic as well as the payments---to determine their utilities. How can the analyst design payments to obtain an accurate estimate of the population statistic when individuals strategically decide both whether to participate and whether to truthfully report their sensitive information? We design a differentially private peer-prediction mechanism that supports accurate estimation of the population statistic as a Bayes-Nash equilibrium in settings where agents have explicit preferences for privacy. The mechanism requires knowledge of the marginal prior distribution on bits $b_i$, but does not need full knowledge of the marginal distribution on the costs $c_i$, instead requiring only an approximate upper bound. Our mechanism guarantees $\epsilon$-differential privacy to each agent $i$ against any adversary who can observe the statistical estimate output by the mechanism, as well as the payments made to the $n-1$ other agents $j\neq i$. Finally, we show that with slightly more structured assumptions on the privacy cost functions of each agent, the cost of running the survey goes to $0$ as the number of agents diverges.Comment: Appears in EC 201