Order-Revealing Encryption and the Hardness of Private Learning

An order-revealing encryption scheme gives a public procedure by which two ciphertexts can be compared to reveal the ordering of their underlying plaintexts. We show how to use order-revealing encryption to separate computationally efficient PAC learning from efficient $(\epsilon, \delta)$-differentially private PAC learning. That is, we construct a concept class that is efficiently PAC learnable, but for which every efficient learner fails to be differentially private. This answers a question of Kasiviswanathan et al. (FOCS '08, SIAM J. Comput. '11). To prove our result, we give a generic transformation from an order-revealing encryption scheme into one with strongly correct comparison, which enables the consistent comparison of ciphertexts that are not obtained as the valid encryption of any message. We believe this construction may be of independent interest.Comment: 28 page

Quantum adiabatic machine learning

We develop an approach to machine learning and anomaly detection via quantum adiabatic evolution. In the training phase we identify an optimal set of weak classifiers, to form a single strong classifier. In the testing phase we adiabatically evolve one or more strong classifiers on a superposition of inputs in order to find certain anomalous elements in the classification space. Both the training and testing phases are executed via quantum adiabatic evolution. We apply and illustrate this approach in detail to the problem of software verification and validation.Comment: 21 pages, 9 figure

Mutual Mate Choice: When it Pays Both Sexes to Avoid Inbreeding

Theoretical models of sexual selection predict that both males and females of many species should benefit by selecting their mating partners. However, empirical evidence testing and validating this prediction is scarce. In particular, whereas inbreeding avoidance is expected to induce sexual conflicts, in some cases both partners could benefit by acting in concert and exerting mutual mate choice for non-assortative pairings. We tested this prediction with the gregarious cockroach Blattella germanica (L.). We demonstrated that males and females base their mate choice on different criteria and that choice occurs at different steps during the mating sequence. Males assess their relatedness to females through antennal contacts before deciding to court preferentially non-siblings. Conversely, females biased their choice towards the most vigorously courting males that happened to be non-siblings. This study is the first to demonstrate mutual mate choice leading to close inbreeding avoidance. The fact that outbred pairs were more fertile than inbred pairs strongly supports the adaptive value of this mating system, which includes no “best phenotype” as the quality of two mating partners is primarily linked to their relatedness. We discuss the implications of our results in the light of inbreeding conflict models

Understanding network concepts in modules

<p>Abstract</p> <p>Background</p> <p>Network concepts are increasingly used in biology and genetics. For example, the clustering coefficient has been used to understand network architecture; the connectivity (also known as degree) has been used to screen for cancer targets; and the topological overlap matrix has been used to define modules and to annotate genes. Dozens of potentially useful network concepts are known from graph theory.</p> <p>Results</p> <p>Here we study network concepts in special types of networks, which we refer to as approximately factorizable networks. In these networks, the pairwise connection strength (adjacency) between 2 network nodes can be factored into node specific contributions, named node 'conformity'. The node conformity turns out to be highly related to the connectivity. To provide a formalism for relating network concepts to each other, we define three types of network concepts: fundamental-, conformity-based-, and approximate conformity-based concepts. Fundamental concepts include the standard definitions of connectivity, density, centralization, heterogeneity, clustering coefficient, and topological overlap. The approximate conformity-based analogs of fundamental network concepts have several theoretical advantages. First, they allow one to derive simple relationships between seemingly disparate networks concepts. For example, we derive simple relationships between the clustering coefficient, the heterogeneity, the density, the centralization, and the topological overlap. The second advantage of approximate conformity-based network concepts is that they allow one to show that fundamental network concepts can be approximated by simple functions of the connectivity in module networks.</p> <p>Conclusion</p> <p>Using protein-protein interaction, gene co-expression, and simulated data, we show that a) many networks comprised of module nodes are approximately factorizable and b) in these types of networks, simple relationships exist between seemingly disparate network concepts. Our results are implemented in freely available R software code, which can be downloaded from the following webpage: <url>http://www.genetics.ucla.edu/labs/horvath/ModuleConformity/ModuleNetworks</url></p

The evolution of postpollination reproductive isolation in Costus

Reproductive isolation is critical to the diversification of species. Postpollination barriers may be important in limiting gene flow between closely related species, but they are relatively cryptic and their evolution is poorly understood. Here, we review the role of postpollination reproductive isolation in plants, including the various stages at which it operates and the hypotheses for how it may evolve. We then review empirical studies in the plant genus Costus, evaluating documented postpollination barriers in light of these hypotheses. We summarize isolation due to parental style length differences and present evidence supporting the hypothesis that the differences are in part a by-product of selection on floral morphology. Additionally, we show that reduced pollen adhesion, germination, and tube growth contribute to reproductive isolation between two closely related sympatric species of Costus. Geographic variation in the strength of these crossing barriers supports the hypothesis that they evolved under reinforcement, or direct natural selection to strengthen isolation

Asymmetric reproductive isolation between terminal forms of the salamander ring species Ensatina eschscholtzii revealed by fine-scale genetic analysis of a hybrid zone

<p>Abstract</p> <p>Background</p> <p>Ring species, exemplified by salamanders of the <it>Ensatina eschscholtzii </it>complex, represent a special window into the speciation process because they allow the history of species formation to be traced back in time through the geographically differentiated forms connecting the two terminal forms of the ring. Of particular interest is the nature and extent of reproductive isolation between the geographically terminal forms, in this case <it>E. e. eschscholtzii </it>and <it>E. e. klauberi</it>. Previous studies have documented infrequent hybridization at the end of the ring. Here, we report the first fine-scale genetic analysis of a hybrid zone between the terminal forms in southern California using individual-based Bayesian analyses of multilocus genetic data to estimate levels and direction of hybridization and maximum-likelihood analysis of linkage disequilibrium and cline shape to make inferences about migration and selection in the hybrid zone.</p> <p>Results</p> <p>The center of the hybrid zone has a high proportion of hybrids, about half of which were classified as F1s. Clines are narrow with respect to dispersal, and there are significant deviations from Hardy-Weinberg equilibrium as well as nonrandom associations (linkage disequilibria) between alleles characteristic of each parental type. There is cytonuclear discordance, both in terms of introgression and the geographic position of mitochondrial versus nuclear clines. Genetic disequilibrium is concentrated on the <it>eschscholtzii </it>side of the zone. Nearly all hybrids possess <it>klauberi </it>mtDNA, indicating that most hybrids are formed from female <it>klauberi </it>mating with male <it>eschscholtzii </it>or male hybrids (but not vice versa).</p> <p>Conclusions</p> <p>Our results are consistent with a tension zone trapped at an ecotone, with gene combinations characteristic of <it>klauberi </it>showing up on the <it>eschscholtzii </it>side of the zone due to asymmetric hybridization. We suggest that the observed asymmetry is best explained by increased discriminatory power of <it>eschscholtzii </it>females, or asymmetric postzygotic isolation. The relatively high frequency of hybrids, particularly F1s, contrasts with other contacts between the terminal forms, and with other contacts between other divergent <it>Ensatina </it>lineages, highlighting the diverse outcomes of secondary contact within a single species complex.</p

Time in a Bottle: The Evolutionary Fate of Species Discrimination in Sibling Drosophila Species

Disadvantageous hybridization favors the evolution of prezygotic isolating behaviors, generating a geographic pattern of interspecific mate discrimination where members of different species drawn from sympatric populations exhibit stronger preference for members of their own species than do individuals drawn from allopatric populations. Geographic shifts in species' boundaries can relax local selection against hybridization; under such scenarios the fate of enhanced species preference is unknown. Lineages established from populations in the region of sympatry that have been maintained as single-species laboratory cultures represent cases where allopatry has been produced experimentally. Using such cultures dating from the 1950s, we assess how Drosophila pseudoobscura and D. persimilis mate preferences respond to relaxed natural selection against hybridization. We found that the propensity to hybridize generally declines with increasing time in experimental allopatry, suggesting that maintaining enhanced preference for conspecifics may be costly. However, our data also suggest a strong role for drift in determining mating preferences once secondary allopatry has been established. Finally, we discuss the interplay between populations in establishing the presence or absence of patterns consistent with reinforcement

Visual mate preference evolution during butterfly speciation is linked to neural processing genes

Abstract: Many animal species remain separate not because their individuals fail to produce viable hybrids but because they “choose” not to mate. However, we still know very little of the genetic mechanisms underlying changes in these mate preference behaviours. Heliconius butterflies display bright warning patterns, which they also use to recognize conspecifics. Here, we couple QTL for divergence in visual preference behaviours with population genomic and gene expression analyses of neural tissue (central brain, optic lobes and ommatidia) across development in two sympatric Heliconius species. Within a region containing 200 genes, we identify five genes that are strongly associated with divergent visual preferences. Three of these have previously been implicated in key components of neural signalling (specifically an ionotropic glutamate receptor and two regucalcins), and overall our candidates suggest shifts in behaviour involve changes in visual integration or processing. This would allow preference evolution without altering perception of the wider environment

Learning k-modal distributions via testing

© 2014 Constantinos Daskalakis, Ilias Diakonikolas, and Rocco A. Servedio. A k-modal probability distribution over the discrete domain {1;……,n} is one whose histogram has at most k “peaks” and “valleys.” Such distributions are natural generalizations of monotone (k = 0) and unimodal (k = 1) probability distributions, which have been intensively studied in probability theory and statistics. In this paper we consider the problem of learning (i. e., performing density estimation of) an unknown k-modal distribution with respect to the L1 distance. The learning algorithm is given access to independent samples drawn from an unknown k-modal distribution p, and it must output a hypothesis distribution bp such that with high probability the total variation distance between p and bp is at most e. Our main goal is to obtain computationally efficient algorithms for this problem that use (close to) an information-theoretically optimal number of samples. We give an efficient algorithm for this problem that runs in time poly(k; log(n),1/ε). For k ≤ Õ(logn), the number of samples used by our algorithm is very close (within an Õ(log(1/ε) factor) to being information-theoretically optimal. Prior to this work computationally efficient algorithms were known only for the cases k = 0;1 (Birgé 1987, 1997). A novel feature of our approach is that our learning algorithm crucially uses a new algorithm for property testing of probability distributions as a key subroutine. The learning algorithm uses the property tester to efficiently decompose the k-modal distribution into k (near-)monotone distributions, which are easier to learn