On analog quantum algorithms for the mixing of Markov chains

The problem of sampling from the stationary distribution of a Markov chain finds widespread applications in a variety of fields. The time required for a Markov chain to converge to its stationary distribution is known as the classical mixing time. In this article, we deal with analog quantum algorithms for mixing. First, we provide an analog quantum algorithm that given a Markov chain, allows us to sample from its stationary distribution in a time that scales as the sum of the square root of the classical mixing time and the square root of the classical hitting time. Our algorithm makes use of the framework of interpolated quantum walks and relies on Hamiltonian evolution in conjunction with von Neumann measurements. There also exists a different notion for quantum mixing: the problem of sampling from the limiting distribution of quantum walks, defined in a time-averaged sense. In this scenario, the quantum mixing time is defined as the time required to sample from a distribution that is close to this limiting distribution. Recently we provided an upper bound on the quantum mixing time for Erd\"os-Renyi random graphs [Phys. Rev. Lett. 124, 050501 (2020)]. Here, we also extend and expand upon our findings therein. Namely, we provide an intuitive understanding of the state-of-the-art random matrix theory tools used to derive our results. In particular, for our analysis we require information about macroscopic, mesoscopic and microscopic statistics of eigenvalues of random matrices which we highlight here. Furthermore, we provide numerical simulations that corroborate our analytical findings and extend this notion of mixing from simple graphs to any ergodic, reversible, Markov chain.Comment: The section concerning time-averaged mixing (Sec VIII) has been updated: Now contains numerical plots and an intuitive discussion on the random matrix theory results used to derive the results of arXiv:2001.0630

PathGAN: visual scanpath prediction with generative adversarial networks

“This is a post-peer-review, pre-copyedit version of an article published in: Computer Vision – ECCV 2018 Workshops. The final authenticated version is available online at: http://dx.doi.org/10.1007/978-3-030-11021-5_25”.We introduce PathGAN, a deep neural network for visual scanpath prediction trained on adversarial examples. A visual scanpath is defined as the sequence of fixation points over an image defined by a human observer with its gaze. PathGAN is composed of two parts, the generator and the discriminator. Both parts extract features from images using off-the-shelf networks, and train recurrent layers to generate or discriminate scanpaths accordingly. In scanpath prediction, the stochastic nature of the data makes it very difficult to generate realistic predictions using supervised learning strategies, but we adopt adversarial training as a suitable alternative. Our experiments prove how PathGAN improves the state of the art of visual scanpath prediction on the iSUN and Salient360! datasets.Peer ReviewedPostprint (author's final draft

Dynamic instability of the major urinary protein gene family revealed by genomic and phenotypic comparisons between C57 and 129 strain mice

Targeted sequencing, manual genome annotation, phylogenetic analysis and mass spectrometry were used to characterise major urinary proteins (MUPs) and the Mup clusters of two strains of inbred mice

Saliency Benchmarking Made Easy: Separating Models, Maps and Metrics

Dozens of new models on fixation prediction are published every year and compared on open benchmarks such as MIT300 and LSUN. However, progress in the field can be difficult to judge because models are compared using a variety of inconsistent metrics. Here we show that no single saliency map can perform well under all metrics. Instead, we propose a principled approach to solve the benchmarking problem by separating the notions of saliency models, maps and metrics. Inspired by Bayesian decision theory, we define a saliency model to be a probabilistic model of fixation density prediction and a saliency map to be a metric-specific prediction derived from the model density which maximizes the expected performance on that metric given the model density. We derive these optimal saliency maps for the most commonly used saliency metrics (AUC, sAUC, NSS, CC, SIM, KL-Div) and show that they can be computed analytically or approximated with high precision. We show that this leads to consistent rankings in all metrics and avoids the penalties of using one saliency map for all metrics. Our method allows researchers to have their model compete on many different metrics with state-of-the-art in those metrics: "good" models will perform well in all metrics.Comment: published at ECCV 201

The Vertebrate Genome Annotation (Vega) database

The Vertebrate Genome Annotation (Vega) database (http://vega.sanger.ac.uk) has been designed to be a community resource for browsing manual annotation of finished sequences from a variety of vertebrate genomes. Its core database is based on an Ensembl-style schema, extended to incorporate curation-specific metadata. In collaboration with the genome sequencing centres, Vega attempts to present consistent high-quality annotation of the published human chromosome sequences. In addition, it is also possible to view various finished regions from other vertebrates, including mouse and zebrafish. Vega displays only manually annotated gene structures built using transcriptional evidence, which can be examined in the browser. Attempts have been made to standardize the annotation procedure across each vertebrate genome, which should aid comparative analysis of orthologues across the different finished regions

The vertebrate genome annotation (Vega) database

The Vertebrate Genome Annotation (Vega) database (http://vega.sanger.ac.uk) was first made public in 2004 and has been designed to view manual annotation of human, mouse and zebrafish genomic sequences produced at the Wellcome Trust Sanger Institute. Since its initial release, the number of human annotated loci has more than doubled to close to 33 000 and now contains comprehensive annotation on 20 of the 24 human chromosomes, four whole mouse chromosomes and around 40% of the zebrafish Danio rerio genome. In addition, we offer manual annotation of a number of haplotype regions in mouse and human and regions of comparative interest in pig and dog that are unique to Vega

Meeting report: a workshop on Best Practices in Genome Annotation

Efforts to annotate the genomes of a wide variety of model organisms are currently carried out by sequencing centers, model organism databases and academic/institutional laboratories around the world. Different annotation methods and tools have been developed over time to meet the needs of biologists faced with the task of annotating biological data. While standardized methods are essential for consistent curation within each annotation group, methods and tools can differ between groups, especially when the groups are curating different organisms. Biocurators from several institutes met at the Third International Biocuration Conference in Berlin, Germany, April 2009 and hosted the ‘Best Practices in Genome Annotation: Inference from Evidence’ workshop to share their strategies, pipelines, standards and tools. This article documents the material presented in the workshop

Pseudo–Messenger RNA: Phantoms of the Transcriptome

The mammalian transcriptome harbours shadowy entities that resist classification and analysis. In analogy with pseudogenes, we define pseudo–messenger RNA to be RNA molecules that resemble protein-coding mRNA, but cannot encode full-length proteins owing to disruptions of the reading frame. Using a rigorous computational pipeline, which rules out sequencing errors, we identify 10,679 pseudo–messenger RNAs (approximately half of which are transposon-associated) among the 102,801 FANTOM3 mouse cDNAs: just over 10% of the FANTOM3 transcriptome. These comprise not only transcribed pseudogenes, but also disrupted splice variants of otherwise protein-coding genes. Some may encode truncated proteins, only a minority of which appear subject to nonsense-mediated decay. The presence of an excess of transcripts whose only disruptions are opal stop codons suggests that there are more selenoproteins than currently estimated. We also describe compensatory frameshifts, where a segment of the gene has changed frame but remains translatable. In summary, we survey a large class of non-standard but potentially functional transcripts that are likely to encode genetic information and effect biological processes in novel ways. Many of these transcripts do not correspond cleanly to any identifiable object in the genome, implying fundamental limits to the goal of annotating all functional elements at the genome sequence level

Harmonizing model organism data in the Alliance of Genome Resources.

The Alliance of Genome Resources (the Alliance) is a combined effort of 7 knowledgebase projects: Saccharomyces Genome Database, WormBase, FlyBase, Mouse Genome Database, the Zebrafish Information Network, Rat Genome Database, and the Gene Ontology Resource. The Alliance seeks to provide several benefits: better service to the various communities served by these projects; a harmonized view of data for all biomedical researchers, bioinformaticians, clinicians, and students; and a more sustainable infrastructure. The Alliance has harmonized cross-organism data to provide useful comparative views of gene function, gene expression, and human disease relevance. The basis of the comparative views is shared calls of orthology relationships and the use of common ontologies. The key types of data are alleles and variants, gene function based on gene ontology annotations, phenotypes, association to human disease, gene expression, protein-protein and genetic interactions, and participation in pathways. The information is presented on uniform gene pages that allow facile summarization of information about each gene in each of the 7 organisms covered (budding yeast, roundworm Caenorhabditis elegans, fruit fly, house mouse, zebrafish, brown rat, and human). The harmonized knowledge is freely available on the alliancegenome.org portal, as downloadable files, and by APIs. We expect other existing and emerging knowledge bases to join in the effort to provide the union of useful data and features that each knowledge base currently provides

Measures and Limits of Models of Fixation Selection

Models of fixation selection are a central tool in the quest to understand how the human mind selects relevant information. Using this tool in the evaluation of competing claims often requires comparing different models' relative performance in predicting eye movements. However, studies use a wide variety of performance measures with markedly different properties, which makes a comparison difficult. We make three main contributions to this line of research: First we argue for a set of desirable properties, review commonly used measures, and conclude that no single measure unites all desirable properties. However the area under the ROC curve (a classification measure) and the KL-divergence (a distance measure of probability distributions) combine many desirable properties and allow a meaningful comparison of critical model performance. We give an analytical proof of the linearity of the ROC measure with respect to averaging over subjects and demonstrate an appropriate correction of entropy-based measures like KL-divergence for small sample sizes in the context of eye-tracking data. Second, we provide a lower bound and an upper bound of these measures, based on image-independent properties of fixation data and between subject consistency respectively. Based on these bounds it is possible to give a reference frame to judge the predictive power of a model of fixation selection . We provide open-source python code to compute the reference frame. Third, we show that the upper, between subject consistency bound holds only for models that predict averages of subject populations. Departing from this we show that incorporating subject-specific viewing behavior can generate predictions which surpass that upper bound. Taken together, these findings lay out the required information that allow a well-founded judgment of the quality of any model of fixation selection and should therefore be reported when a new model is introduced