Complete positivity on the subsystems level

We consider complete positivity of dynamics regarding subsystems of an open composite quantum system, which is subject of a completely positive dynamics. By "completely positive dynamics", we assume the dynamical maps called the completely positive and trace preserving maps, with the constraint that domain of the map is the whole Banach space of the system's density matrices. We provide a technically simple and conceptually clear proof for the subsystems' completely positive dynamics. Actually, we prove that every subsystem of a composite open system can be subject of a completely positive dynamics if and only if the initial state of the composite open system is tensor-product of the initial states of the subsystems. An algorithm for obtaining the Kraus form for the subsystem's dynamical map is provided. As an illustrative example we consider a pair of mutually interacting qubits. The presentation is performed such that a student with the proper basic knowledge in quantum mechanics should be able to reproduce all the steps of the calculations.Comment: revised ms, improved presentation, 18 pages, no tables or figure

Unraveling the genomic mosaic of a ubiquitous genus of marine cyanobacteria

Background: The picocyanobacterial genus Synechococcus occurs over wide oceanic expanses, having colonized most available niches in the photic zone. Large scale distribution patterns of the different Synechococcus clades (based on 16S rRNA gene markers) suggest the occurrence of two major lifestyles ('opportunists'/'specialists'), corresponding to two distinct broad habitats ('coastal'/'open ocean'). Yet, the genetic basis of niche partitioning is still poorly understood in this ecologically important group. Results: Here, we compare the genomes of 11 marine Synechococcus isolates, representing 10 distinct lineages. Phylogenies inferred from the core genome allowed us to refine the taxonomic relationships between clades by revealing a clear dichotomy within the main subcluster, reminiscent of the two aforementioned lifestyles. Genome size is strongly correlated with the cumulative lengths of hypervariable regions (or 'islands'). One of these, encompassing most genes encoding the light-harvesting phycobilisome rod complexes, is involved in adaptation to changes in light quality and has clearly been transferred between members of different Synechococcus lineages. Furthermore, we observed that two strains (RS9917 and WH5701) that have similar pigmentation and physiology have an unusually high number of genes in common, given their phylogenetic distance. Conclusion: We propose that while members of a given marine Synechococcus lineage may have the same broad geographical distribution, local niche occupancy is facilitated by lateral gene transfers, a process in which genomic islands play a key role as a repository for transferred genes. Our work also highlights the need for developing picocyanobacterial systematics based on genome-derived parameters combined with ecological and physiological data

Faster Shortest Paths in Dense Distance Graphs, with Applications

We show how to combine two techniques for efficiently computing shortest paths in directed planar graphs. The first is the linear-time shortest-path algorithm of Henzinger, Klein, Subramanian, and Rao [STOC'94]. The second is Fakcharoenphol and Rao's algorithm [FOCS'01] for emulating Dijkstra's algorithm on the dense distance graph (DDG). A DDG is defined for a decomposition of a planar graph $G$ into regions of at most $r$ vertices each, for some parameter $r < n$. The vertex set of the DDG is the set of $\Theta(n/\sqrt r)$ vertices of $G$ that belong to more than one region (boundary vertices). The DDG has $\Theta(n)$ arcs, such that distances in the DDG are equal to the distances in $G$. Fakcharoenphol and Rao's implementation of Dijkstra's algorithm on the DDG (nicknamed FR-Dijkstra) runs in $O(n\log(n) r^{-1/2} \log r)$ time, and is a key component in many state-of-the-art planar graph algorithms for shortest paths, minimum cuts, and maximum flows. By combining these two techniques we remove the $\log n$ dependency in the running time of the shortest-path algorithm, making it $O(n r^{-1/2} \log^2r)$. This work is part of a research agenda that aims to develop new techniques that would lead to faster, possibly linear-time, algorithms for problems such as minimum-cut, maximum-flow, and shortest paths with negative arc lengths. As immediate applications, we show how to compute maximum flow in directed weighted planar graphs in $O(n \log p)$ time, where $p$ is the minimum number of edges on any path from the source to the sink. We also show how to compute any part of the DDG that corresponds to a region with $r$ vertices and $k$ boundary vertices in $O(r \log k)$ time, which is faster than has been previously known for small values of $k$

Analytical, computational, and statistical approaches to studying speciation

Two of the most challenging goals of evolutionary biology are to reconstruct the evolutionary relationships among all extant species and to understand the process by which new species form. Accomplishing these goals will require accurate computational methods for reconstructing phylogenetic trees, general analytic models of speciation, and powerful statistical tools for studying the process of speciation in natural systems. In the first chapter, I study the effects of improper model assumption on estimates of phylogeny. Using DNA sequence data simulated under a variety of models of sequence evolution, I demonstrate that use of oversimplified models can result in erroneous phylogeny estimates. This result suggests that if the models currently utilized are oversimplified then current estimates of phylogeny may be inaccurate and more complex models need to be developed and employed. In the second and third chapters, I study one process thought to be important in completing the final stages of speciation: reinforcement. Using simulations of a hybrid zone, I show that the process of reinforcement can result in patterns other than reproductive character displacement. I also show that speciation by reinforcement is more likely when the genes involved in reproductive isolation are sex-linked. In the fourth chapter, I develop a statistical method of quantifying the degree of isolation between species undergoing divergence. Using genotype data obtained from natural hybrid zones, this novel method can be used to estimate the fitness of hybrids during different stages of their life cycle. This approach offers a new approach to empirical biologists studying extrinsic postzygotic isolation in natural systems.Biological Sciences, School o

Identification and assessment of variable single-copy orthologous (SCO) nuclear loci for low-level phylogenomics: a case study in the genus Rosa (Rosaceae)

International audienceBackground: With an ever-growing number of published genomes, many low levels of the Tree of Life now contain several species with enough molecular data to perform shallow-scale phylogenomic studies. Moving away from using just a few universal phylogenetic markers, we can now target thousands of other loci to decipher taxa relationships. Making the best possible selection of informative sequences regarding the taxa studied has emerged as a new issue. Here, we developed a general procedure to mine genomic data, looking for orthologous single-copy loci capable of deciphering phylogenetic relationships below the generic rank. To develop our strategy, we chose the genus Rosa, a rapid-evolving lineage of the Rosaceae family in which several species genomes have recently been sequenced. We also compared our loci to conventional plastid markers, commonly used for phylogenetic inference in this genus

Islands of linkage in an ocean of pervasive recombination reveals two-speed evolution of human cytomegalovirus genomes

Human cytomegalovirus (HCMV) infects most of the population worldwide, persisting throughout the host's life in a latent state with periodic episodes of reactivation. While typically asymptomatic, HCMV can cause fatal disease among congenitally infected infants and immunocompromised patients. These clinical issues are compounded by the emergence of antiviral resistance and the absence of an effective vaccine, the development of which is likely complicated by the numerous immune evasins encoded by HCMV to counter the host's adaptive immune responses, a feature that facilitates frequent super-infections. Understanding the evolutionary dynamics of HCMV is essential for the development of effective new drugs and vaccines. By comparing viral genomes from uncultivated or low-passaged clinical samples of diverse origins, we observe evidence of frequent homologous recombination events, both recent and ancient, and no structure of HCMV genetic diversity at the whole-genome scale. Analysis of individual gene-scale loci reveals a striking dichotomy: while most of the genome is highly conserved, recombines essentially freely and has evolved under purifying selection, 21 genes display extreme diversity, structured into distinct genotypes that do not recombine with each other. Most of these hyper-variable genes encode glycoproteins involved in cell entry or escape of host immunity. Evidence that half of them have diverged through episodes of intense positive selection suggests that rapid evolution of hyper-variable loci is likely driven by interactions with host immunity. It appears that this process is enabled by recombination unlinking hyper-variable loci from strongly constrained neighboring sites. It is conceivable that viral mechanisms facilitating super-infection have evolved to promote recombination between diverged genotypes, allowing the virus to continuously diversify at key loci to escape immune detection, while maintaining a genome optimally adapted to its asymptomatic infectious lifecycle

Study of quantum correlations in LHCb simulated heavy flavour jets

openThe LHCb collaboration has already demonstrated that quantum machine learning can be used to classify jets based on the particles flavor in particular, the so called heavy flavor jets. These studies indicates that improvements on jets classification can arise from the study of the correlation among qubits. The thesis evaluates the possibility to measure qubits correlations and study how to exploit these information for a better data classification