Engineering a static verification tool for GPU kernels

We report on practical experiences over the last 2.5 years related to the engineering of GPUVerify, a static verification tool for OpenCL and CUDA GPU kernels, plotting the progress of GPUVerify from a prototype to a fully functional and relatively efficient analysis tool. Our hope is that this experience report will serve the verification community by helping to inform future tooling efforts. © 2014 Springer International Publishing

Generating Performance Portable Code using Rewrite Rules: From High-Level Functional Expressions to High-Performance OpenCL Code

Computers have become increasingly complex with the emergence of heterogeneous hardware combining multicore CPUs and GPUs. These parallel systems exhibit tremendous computational power at the cost of increased programming effort resulting in a tension between performance and code portability. Typically, code is either tuned in a low-level imperative language using hardware-specific optimizations to achieve maximum performance or is written in a high-level, possibly functional, language to achieve portability at the expense of performance. We propose a novel approach aiming to combine high-level programming, code portability, and high-performance. Starting from a high-level functional expression we apply a simple set of rewrite rules to transform it into a low-level functional representation, close to the OpenCL programming model, from which OpenCL code is generated. Our rewrite rules define a space of possible implementations which we automatically explore to generate hardware-specific OpenCL implementations. We formalize our system with a core dependently-typed λ-calculus along with a denotational semantics which we use to prove the correctness of the rewrite rules. We test our design in practice by implementing a compiler which generates high performance imperative OpenCL code. Our experiments show that we can automatically derive hardware-specific implementations from simple functional high-level algorithmic expressions offering performance on a par with highly tuned code for multicore CPUs and GPUs written by experts

Slow evolution of sex-biased genes in the reproductive tissue of the dioecious plant Salix viminalis

The relative rate of evolution for sex-biased genes has often been used as a measure of the strength of sex-specific selection. In contrast to studies in a wide variety of animals, far less is known about the molecular evolution of sex-biased genes in plants, particularly in dioecious angiosperms. Here, we investigate the gene expression patterns and evolution of sex-biased genes in the dioecious plant Salix viminalis. We observe lower rates of sequence evolution for male-biased genes expressed in the reproductive tissue compared to unbiased and female-biased genes. These results could be partially explained by the lower codon usage bias for sex-biased genes leading to elevated rates of synonymous substitutions compared to unbiased genes. However, the stronger haploid selection in the reproductive tissue of plants, together with pollen competition, would also lead to higher levels of purifying selection acting to remove deleterious variation. Future work should focus on the differential evolution of haploid- and diploid-specific genes in order to understand the selective dynamics acting on these loci

Analyzing the Impacts of Dams on Riparian Ecosystems: A Review of Research Strategies and Their Relevance to the Snake River Through Hells Canyon

River damming provides a dominant human impact on river environments worldwide, and while local impacts of reservoir flooding are immediate, subsequent ecological impacts downstream can be extensive. In this article, we assess seven research strategies for analyzing the impacts of dams and river flow regulation on riparian ecosystems. These include spatial comparisons of (1) upstream versus downstream reaches, (2) progressive downstream patterns, or (3) the dammed river versus an adjacent free-flowing or differently regulated river(s). Temporal comparisons consider (4) pre- versus post-dam, or (5) sequential post-dam conditions. However, spatial comparisons are complicated by the fact that dams are not randomly located, and temporal comparisons are commonly limited by sparse historic information. As a result, comparative approaches are often correlative and vulnerable to confounding factors. To complement these analyses, (6) flow or sediment modifications can be implemented to test causal associations. Finally, (7) process-based modeling represents a predictive approach incorporating hydrogeomorphic processes and their biological consequences. In a case study of Hells Canyon, the upstream versus downstream comparison is confounded by a dramatic geomorphic transition. Comparison of the multiple reaches below the dams should be useful, and the comparison of Snake River with the adjacent free-flowing Salmon River may provide the strongest spatial comparison. A pre- versus post-dam comparison would provide the most direct study approach, but pre-dam information is limited to historic reports and archival photographs. We conclude that multiple study approaches are essential to provide confident interpretations of ecological impacts downstream from dams, and propose a comprehensive study for Hells Canyon that integrates multiple research strategies

Demographic and Genetic Patterns of Variation among Populations of Arabidopsis thaliana from Contrasting Native Environments

Background: Understanding the relationship between environment and genetics requires the integration of knowledge on the demographic behavior of natural populations. However, the demographic performance and genetic composition of Arabidopsis thaliana populations in the species' native environments remain largely uncharacterized. This information, in combination with the advances on the study of gene function, will improve our understanding on the genetic mechanisms underlying adaptive evolution in A. thaliana. Methodology/Principal Findings: We report the extent of environmental, demographic, and genetic variation among 10 A. thaliana populations from Mediterranean (coastal) and Pyrenean (montane) native environments in northeast Spain. Geographic, climatic, landscape, and soil data were compared. Demographic traits, including the dynamics of the soil seed bank and the attributes of aboveground individuals followed over a complete season, were also analyzed. Genetic data based on genome-wide SNP markers were used to describe genetic diversity, differentiation, and structure. Coastal and montane populations significantly differed in terms of environmental, demographic, and genetic characteristics. Montane populations, at higher altitude and farther from the sea, are exposed to colder winters and prolonged spring moisture compared to coastal populations. Montane populations showed stronger secondary seed dormancy, higher seedling/juvenile mortality in winter, and initiated flowering later than coastal populations. Montane and coastal regions were genetically differentiated, montane populations bearing lower genetic diversity than coastal ones. No significant isolation-by-distance pattern and no shared multilocus genotypes among populations were detected. Conclusions/Significance: Between-region variation in climatic patterns can account for differences in demographic traits, such as secondary seed dormancy, plant mortality, and recruitment, between coastal and montane A. thaliana populations. In addition, differences in plant mortality can partly account for differences in the genetic composition of coastal and montane populations. This study shows how the interplay between variation in environmental, demographic, and genetic parameters may operate in natural A. thaliana populations. © 2009 Montesinos et al

Glacial Refugia in Pathogens: European Genetic Structure of Anther Smut Pathogens on Silene latifolia and Silene dioica

Climate warming is predicted to increase the frequency of invasions by pathogens and to cause the large-scale redistribution of native host species, with dramatic consequences on the health of domesticated and wild populations of plants and animals. The study of historic range shifts in response to climate change, such as during interglacial cycles, can help in the prediction of the routes and dynamics of infectious diseases during the impending ecosystem changes. Here we studied the population structure in Europe of two Microbotryum species causing anther smut disease on the plants Silene latifolia and Silene dioica. Clustering analyses revealed the existence of genetically distinct groups for the pathogen on S. latifolia, providing a clear-cut example of European phylogeography reflecting recolonization from southern refugia after glaciation. The pathogen genetic structure was congruent with the genetic structure of its host species S. latifolia, suggesting dependence of the migration pathway of the anther smut fungus on its host. The fungus, however, appeared to have persisted in more numerous and smaller refugia than its host and to have experienced fewer events of large-scale dispersal. The anther smut pathogen on S. dioica also showed a strong phylogeographic structure that might be related to more northern glacial refugia. Differences in host ecology probably played a role in these differences in the pathogen population structure. Very high selfing rates were inferred in both fungal species, explaining the low levels of admixture between the genetic clusters. The systems studied here indicate that migration patterns caused by climate change can be expected to include pathogen invasions that follow the redistribution of their host species at continental scales, but also that the recolonization by pathogens is not simply a mirror of their hosts, even for obligate biotrophs, and that the ecology of hosts and pathogen mating systems likely affects recolonization patterns

Quantum Information and Variants of Interactive Proof Systems

For nearly three decades, the model of interactive proof systems and its variants have been central to many important and exciting developments in computational complexity theory such as exact characterization of some well known complexity classes, development of probabilistically checkable proof systems and theory of hardness of approximation, and formalization of fundamental cryptographic primitives. On the other hand, the theory of quantum information, which is primarily concerned with harnessing quantum mechanical features for algorithmic, cryptographic, and information processing tasks has found many applications. In the past three decades, quantum information has been used to develop unconditionally secure quantum cryptography protocols, efficient quantum algorithms for certain problems that are believed to be intractable in classical world, and communication efficient protocols. In this thesis, we study the impact of quantum information on the models of interactive proof systems and their multi-prover variants. We study various quantum models and explore two questions. The first question we address pertains to the expressive power of such models with or without resource constraints. The second question is related to error reduction technique of such proof systems via parallel repetition. The question related to the expressive power of models of quantum interactive proof systems and their variants lead us to the following results. (1) We show that the expressive power of quantum interactive proof systems is exactly PSPACE, the class of problems that can be solved by a polynomial-space deterministic Turing machines and that also admit a classical interactive proof systems. This result shows that in terms of complexity-theoretic characterization, both the models are equivalent. The result is obtained using an algorithmic technique known as the matrix multiplicative weights update method to solve a semidefinite program that characterizes the success probability of the quantum prover. (2) We show that polynomially many logarithmic-size unentangled quantum proofs are no more powerful than a classical proof if the verifier has the ability to process quantum information. This result follows from an observation that logarithmic-size quantum states can be efficiently represented classically and such classical representation can be used to efficiently generate the quantum state. (3) We also establish that the model of multi-prover quantum Merlin Arthur proof system, where the verifier is only allowed to apply nonadaptive unentangled measurement on each proof and then a quantum circuit on the classical outcomes, is no more powerful than QMA under the restriction that there are only polynomial number of outcomes per proof. This result follows from showing that such proof systems also admit a QMA verification procedure. The question related to error reduction via parallel repetition lead us to following results on a class of two-prover one-round games with quantum provers and a class of multi-prover QMA proof systems. (1) We establish that for a certain class of two-prover one-round games known as XOR games, admit a perfect parallel repetition theorem in the following sense. When the provers play a collection of XOR games, an optimal strategy of the provers is to play each instance of the collection independently and optimally. In particular, the success probability of the quantum provers in the n-fold repetition of an XOR game G with quantum value w(G) is exactly (w(G))^n. (2) We show a parallel repetition theorem for two-prover one-round unique games. More specifically, we prove that if the quantum value of a unique game is 1-e, then the quantum value of n-fold repetition of the game is at most (1-e^2/49)^n. We also establish that for certain class of unique games, the quantum value of the n-fold repetition of the game is at most (1-e/4)^n. For the special case of XOR games, our proof technique gives an alternate proof of result mentioned above. 3. Our final result on parallel repetition is concerned with SepQMA(m) proof systems, where the verifier receives m unentangled quantum proofs and the measurement operator corresponding to outcome "accept" is a fully separable operator. We give an alternate proof of a result of Harrow and Montanaro [HM10] that states that perfect parallel repetition theorem holds for such proof systems. The first two results follow from the duality of semidefinite programs and the final result follows from cone programming duality

Recombination changes at the boundaries of fully and partially sex-linked regions between closely related Silene species pairs

The establishment of a region of suppressed recombination is a critical change during sex chromosome evolution, leading to such properties as Y (and W) chromosome genetic degeneration, accumulation of repetitive sequences and heteromorphism. Although chromosome inversions can cause large regions to have suppressed recombination, and inversions are sometimes involved in sex chromosome evolution, gradual expansion of the non-recombining region could potentially sometimes occur. We here test whether closer linkage has recently evolved between the sex-determining region and several genes that are partially sex-linked in Silene latifolia, using Silene dioica, a closely related dioecious plants whose XY sex chromosome system is inherited from a common ancestor. The S. latifolia pseudoautosomal region (PAR) includes several genes extremely closely linked to the fully Y-linked region. These genes were added to an ancestral PAR of the sex chromosome pair in two distinct events probably involving translocations of autosomal genome regions causing multiple genes to become partially sex-linked. Close linkage with the PAR boundary must have evolved since these additions, because some genes added in both events now show almost complete sex linkage in S. latifolia. We compared diversity patterns of five such S. latifolia PAR boundary genes with their orthologues in S. dioica, including all three regions of the PAR (one gene that was in the ancestral PAR and two from each of the added regions). The results suggest recent recombination suppression in S. latifolia, since its split from S. dioica