DP-SIPS: A simpler, more scalable mechanism for differentially private partition selection

Partition selection, or set union, is an important primitive in differentially private mechanism design: in a database where each user contributes a list of items, the goal is to publish as many of these items as possible under differential privacy. In this work, we present a novel mechanism for differentially private partition selection. This mechanism, which we call DP-SIPS, is very simple: it consists of iterating the naive algorithm over the data set multiple times, removing the released partitions from the data set while increasing the privacy budget at each step. This approach preserves the scalability benefits of the naive mechanism, yet its utility compares favorably to more complex approaches developed in prior work

Utility Cost of Formal Privacy for Releasing National Employer-Employee Statistics

National statistical agencies around the world publish tabular summaries based on combined employer-employee (ER-EE) data. The privacy of both individuals and business establishments that feature in these data are protected by law in most countries. These data are currently released using a variety of statistical disclosure limitation (SDL) techniques that do not reveal the exact characteristics of particular employers and employees, but lack provable privacy guarantees limiting inferential disclosures. In this work, we present novel algorithms for releasing tabular summaries of linked ER-EE data with formal, provable guarantees of privacy. We show that state-of-the-art differentially private algorithms add too much noise for the output to be useful. Instead, we identify the privacy requirements mandated by current interpretations of the relevant laws, and formalize them using the Pufferfish framework. We then develop new privacy definitions that are customized to ER-EE data and satisfy the statutory privacy requirements. We implement the experiments in this paper on production data gathered by the U.S. Census Bureau. An empirical evaluation of utility for these data shows that for reasonable values of the privacy-loss parameter ϵ≥1, the additive error introduced by our provably private algorithms is comparable, and in some cases better, than the error introduced by existing SDL techniques that have no provable privacy guarantees. For some complex queries currently published, however, our algorithms do not have utility comparable to the existing traditiona

Symmetric Interdiction for Matching Problems

Motivated by denial-of-service network attacks, we introduce the symmetric interdiction model, where both the interdictor and the optimizer are subject to the same constraints of the underlying optimization problem. We give a general framework that relates optimization to symmetric interdiction for a broad class of optimization problems. We then study the symmetric matching interdiction problem - with applications in traffic engineering - in more detail. This problem can be simply stated as follows: find a matching whose removal minimizes the size of the maximum matching in the remaining graph. We show that this problem is APX-hard, and obtain a 3/2-approximation algorithm that improves on the approximation guarantee provided by the general framework

Retracting Graphs to Cycles

We initiate the algorithmic study of retracting a graph into a cycle in the graph, which seeks a mapping of the graph vertices to the cycle vertices so as to minimize the maximum stretch of any edge, subject to the constraint that the restriction of the mapping to the cycle is the identity map. This problem has its roots in the rich theory of retraction of topological spaces, and has strong ties to well-studied metric embedding problems such as minimum bandwidth and 0-extension. Our first result is an O(min{k, sqrt{n}})-approximation for retracting any graph on n nodes to a cycle with k nodes. We also show a surprising connection to Sperner\u27s Lemma that rules out the possibility of improving this result using certain natural convex relaxations of the problem. Nevertheless, if the problem is restricted to planar graphs, we show that we can overcome these integrality gaps by giving an optimal combinatorial algorithm, which is the technical centerpiece of the paper. Building on our planar graph algorithm, we also obtain a constant-factor approximation algorithm for retraction of points in the Euclidean plane to a uniform cycle

Human Astrocytes Exhibit Tumor Microenvironment-, Age-, and Sex-Related Transcriptomic Signatures

: Astrocytes are critical for the development and function of synapses. There are notable species differences between human astrocytes and commonly used animal models. Yet, it is unclear whether astrocytic genes involved in synaptic function are stable or exhibit dynamic changes associated with disease states and age in humans, which is a barrier in understanding human astrocyte biology and its potential involvement in neurological diseases. To better understand the properties of human astrocytes, we acutely purified astrocytes from the cerebral cortices of over 40 humans across various ages, sexes, and disease states. We performed RNA sequencing to generate transcriptomic profiles of these astrocytes and identified genes associated with these biological variables. We found that human astrocytes in tumor-surrounding regions downregulate genes involved in synaptic function and sensing of signals in the microenvironment, suggesting involvement of peri-tumor astrocytes in tumor-associated neural circuit dysfunction. In aging, we also found downregulation of synaptic regulators and upregulation of markers of cytokine signaling, while in maturation we identified changes in ionic transport with implications for calcium signaling. In addition, we identified subtle sexual dimorphism in human cortical astrocytes, which has implications for observed sex differences across many neurological disorders. Overall, genes involved in synaptic function exhibit dynamic changes in the peritumor microenvironment and aging. This data provides powerful new insights into human astrocyte biology in several biologically relevant states, that will aid in generating novel testable hypotheses about homeostatic and reactive astrocytes in humans.SIGNIFICANCE STATEMENTAstrocytes are an abundant class of cells playing integral roles at synapses. Astrocyte dysfunction is implicated in a variety of human neurological diseases. Yet our knowledge of astrocytes is largely based on mouse studies. Direct knowledge of human astrocyte biology remains limited. Here, we present transcriptomic profiles of human cortical astrocytes, and we identified molecular differences associated with age, sex, and disease state. We found that peritumor and aging astrocytes downregulate genes involved in astrocyte-synapse interactions. These data provide necessary insight into human astrocyte biology that will improve our understanding of human disease

Revisiting the Myths of Protein Interior: Studying Proteins with Mass-Fractal Hydrophobicity-Fractal and Polarizability-Fractal Dimensions

A robust marker to describe mass, hydrophobicity and polarizability distribution holds the key to deciphering structural and folding constraints within proteins. Since each of these distributions is inhomogeneous in nature, the construct should be sensitive in describing the patterns therein. We show, for the first time, that the hydrophobicity and polarizability distributions in protein interior follow fractal scaling. It is found that (barring ‘all-α’) all the major structural classes of proteins have an amount of unused hydrophobicity left in them. This amount of untapped hydrophobicity is observed to be greater in thermophilic proteins, than that in their (structurally aligned) mesophilic counterparts. ‘All-β’(thermophilic, mesophilic alike) proteins are found to have maximum amount of unused hydrophobicity, while ‘all-α’ proteins have been found to have minimum polarizability. A non-trivial dependency is observed between dielectric constant and hydrophobicity distributions within (α+β) and ‘all-α’ proteins, whereas absolutely no dependency is found between them in the ‘all-β’ class. This study proves that proteins are not as optimally packed as they are supposed to be. It is also proved that origin of α-helices are possibly not hydrophobic but electrostatic; whereas β-sheets are predominantly hydrophobic in nature. Significance of this study lies in protein engineering studies; because it quantifies the extent of packing that ensures protein functionality. It shows that myths regarding protein interior organization might obfuscate our knowledge of actual reality. However, if the later is studied with a robust marker of strong mathematical basis, unknown correlations can still be unearthed; which help us to understand the nature of hydrophobicity, causality behind protein folding, and the importance of anisotropic electrostatics in stabilizing a highly complex structure named ‘proteins’