A Match in Time Saves Nine: Deterministic Online Matching With Delays

We consider the problem of online Min-cost Perfect Matching with Delays (MPMD) introduced by Emek et al. (STOC 2016). In this problem, an even number of requests appear in a metric space at different times and the goal of an online algorithm is to match them in pairs. In contrast to traditional online matching problems, in MPMD all requests appear online and an algorithm can match any pair of requests, but such decision may be delayed (e.g., to find a better match). The cost is the sum of matching distances and the introduced delays. We present the first deterministic online algorithm for this problem. Its competitive ratio is $O(m^{\log_2 5.5})$ $= O(m^{2.46})$, where $2 m$ is the number of requests. This is polynomial in the number of metric space points if all requests are given at different points. In particular, the bound does not depend on other parameters of the metric, such as its aspect ratio. Unlike previous (randomized) solutions for the MPMD problem, our algorithm does not need to know the metric space in advance

Relaxing the Irrevocability Requirement for Online Graph Algorithms

Online graph problems are considered in models where the irrevocability requirement is relaxed. Motivated by practical examples where, for example, there is a cost associated with building a facility and no extra cost associated with doing it later, we consider the Late Accept model, where a request can be accepted at a later point, but any acceptance is irrevocable. Similarly, we also consider a Late Reject model, where an accepted request can later be rejected, but any rejection is irrevocable (this is sometimes called preemption). Finally, we consider the Late Accept/Reject model, where late accepts and rejects are both allowed, but any late reject is irrevocable. For Independent Set, the Late Accept/Reject model is necessary to obtain a constant competitive ratio, but for Vertex Cover the Late Accept model is sufficient and for Minimum Spanning Forest the Late Reject model is sufficient. The Matching problem has a competitive ratio of 2, but in the Late Accept/Reject model, its competitive ratio is 3/2

Fluctuating selection models and Mcdonald-Kreitman type analyses

It is likely that the strength of selection acting upon a mutation varies through time due to changes in the environment. However, most population genetic theory assumes that the strength of selection remains constant. Here we investigate the consequences of fluctuating selection pressures on the quantification of adaptive evolution using McDonald-Kreitman (MK) style approaches. In agreement with previous work, we show that fluctuating selection can generate evidence of adaptive evolution even when the expected strength of selection on a mutation is zero. However, we also find that the mutations, which contribute to both polymorphism and divergence tend, on average, to be positively selected during their lifetime, under fluctuating selection models. This is because mutations that fluctuate, by chance, to positive selected values, tend to reach higher frequencies in the population than those that fluctuate towards negative values. Hence the evidence of positive adaptive evolution detected under a fluctuating selection model by MK type approaches is genuine since fixed mutations tend to be advantageous on average during their lifetime. Never-the-less we show that methods tend to underestimate the rate of adaptive evolution when selection fluctuates

Online Multi-Coloring with Advice

We consider the problem of online graph multi-coloring with advice. Multi-coloring is often used to model frequency allocation in cellular networks. We give several nearly tight upper and lower bounds for the most standard topologies of cellular networks, paths and hexagonal graphs. For the path, negative results trivially carry over to bipartite graphs, and our positive results are also valid for bipartite graphs. The advice given represents information that is likely to be available, studying for instance the data from earlier similar periods of time.Comment: IMADA-preprint-c

Large introns in relation to alternative splicing and gene evolution: a case study of Drosophila bruno-3

Background: Alternative splicing (AS) of maturing mRNA can generate structurally and functionally distinct transcripts from the same gene. Recent bioinformatic analyses of available genome databases inferred a positive correlation between intron length and AS. To study the interplay between intron length and AS empirically and in more detail, we analyzed the diversity of alternatively spliced transcripts (ASTs) in the Drosophila RNA-binding Bruno-3 (Bru-3) gene. This gene was known to encode thirteen exons separated by introns of diverse sizes, ranging from 71 to 41,973 nucleotides in D. melanogaster. Although Bru-3's structure is expected to be conducive to AS, only two ASTs of this gene were previously described. Results: Cloning of RT-PCR products of the entire ORF from four species representing three diverged Drosophila lineages provided an evolutionary perspective, high sensitivity, and long-range contiguity of splice choices currently unattainable by high-throughput methods. Consequently, we identified three new exons, a new exon fragment and thirty-three previously unknown ASTs of Bru-3. All exon-skipping events in the gene were mapped to the exons surrounded by introns of at least 800 nucleotides, whereas exons split by introns of less than 250 nucleotides were always spliced contiguously in mRNA. Cases of exon loss and creation during Bru-3 evolution in Drosophila were also localized within large introns. Notably, we identified a true de novo exon gain: exon 8 was created along the lineage of the obscura group from intronic sequence between cryptic splice sites conserved among all Drosophila species surveyed. Exon 8 was included in mature mRNA by the species representing all the major branches of the obscura group. To our knowledge, the origin of exon 8 is the first documented case of exonization of intronic sequence outside vertebrates. Conclusion: We found that large introns can promote AS via exon-skipping and exon turnover during evolution likely due to frequent errors in their removal from maturing mRNA. Large introns could be a reservoir of genetic diversity, because they have a greater number of mutable sites than short introns. Taken together, gene structure can constrain and/or promote gene evolution

Relative amino acid composition signatures of organisms and environments

BACKGROUND: Identifying organism-environment interactions at the molecular level is crucial to understanding how organisms adapt to and change the chemical and molecular landscape of their habitats. In this work we investigated whether relative amino acid compositions could be used as a molecular signature of an environment and whether such a signature could also be observed at the level of the cellular amino acid composition of the microorganisms that inhabit that environment. METHODOLOGIES/PRINCIPAL FINDINGS: To address these questions we collected and analyzed environmental amino acid determinations from the literature, and estimated from complete genomic sequences the global relative amino acid abundances of organisms that are cognate to the different types of environment. Environmental relative amino acid abundances clustered into broad groups (ocean waters, host-associated environments, grass land environments, sandy soils and sediments, and forest soils), indicating the presence of amino acid signatures specific for each environment. These signatures correlate to those found in organisms. Nevertheless, relative amino acid abundance of organisms was more influenced by GC content than habitat or phylogeny. CONCLUSIONS: Our results suggest that relative amino acid composition can be used as a signature of an environment. In addition, we observed that the relative amino acid composition of organisms is not highly determined by environment, reinforcing previous studies that find GC content to be the major factor correlating to amino acid composition in living organisms.AM was supported by Fundação para a Ciência e a Tecnologia, Portugal, through the postdoctoral grant SFRH/BPD/72256/2010. RA was partially supported by the Ministerio de Ciencia e Innovación (Spain) through grant BFU2010-17704, and by the Generalitat de Catalunya through a grant for research group 2009SGR809. MAS was supported in part by a grant from the US Public Health Service (RO1-GM30054). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Authors wish to thank Albert Sorribas, Enrique Herrero and Ester Vilaprinyo for critical reading of the manuscript and Ester Vilaprinyo for assistance with Wolfram Mathematica software.publishe

Stochastic descriptors to study the fate and potential of naive T cell clonotypes in the periphery

The population of naive T cells in the periphery is best described by determining both its T cell receptor diversity, or number of clonotypes, and the sizes of its clonal subsets. In this paper, we make use of a previously introduced mathematical model of naive T cell homeostasis, to study the fate and potential of naive T cell clonotypes in the periphery. This is achieved by the introduction of several new stochastic descriptors for a given naive T cell clonotype, such as its maximum clonal size, the time to reach this maximum, the number of proliferation events required to reach this maximum, the rate of contraction of the clonotype during its way to extinction, as well as the time to a given number of proliferation events. Our results show that two fates can be identified for the dynamics of the clonotype: extinction in the short-term if the clonotype experiences too hostile a peripheral environment, or establishment in the periphery in the long-term. In this second case the probability mass function for the maximum clonal size is bimodal, with one mode near one and the other mode far away from it. Our model also indicates that the fate of a recent thymic emigrant (RTE) during its journey in the periphery has a clear stochastic component, where the probability of extinction cannot be neglected, even in a friendly but competitive environment. On the other hand, a greater deterministic behaviour can be expected in the potential size of the clonotype seeded by the RTE in the long-term, once it escapes extinction

Molecular characterization and genetic mapping of DNA sequences encoding the Type I chlorophyll a/b-binding polypeptide of photosystem I in Lycopersicon esculentum (tomato)

We report the isolation and characterization of a tomato nuclear gene encoding a chlorophyll a/b-binding (CAB) protein of photosystem I (PSI). The coding nucleotide sequence of the gene, designated Cab -6B, is different at eight positions from that of a previously isolated cDNA clone derived from the Cab -6A gene, but the two genes encode identical proteins. Sequence comparison with the cDNA clone revealed the presence of three short introns in Cab -6B. Genetic mapping experiments demonstrate that Cab -6A and Cab -6B are tightly linked and reside on chromosome 5, but the physical distance between the two genes is at least 7 kilobases. Cab -6A and Cab -6B have been designated Type I PSI CAB genes. They are the only two genes of this branch of the CAB gene family in the tomato genome, and they show substantial divergence to the genes encoding CAB polypeptides of photosystem II. The Type I PSI CAB genes, like the genes encoding PSII CAB proteins, are highly expressed in illuminated leaf tissue and to a lesser extent in other green organs.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43459/1/11103_2004_Article_BF00166457.pd

Repetitive Elements May Comprise Over Two-Thirds of the Human Genome

Transposable elements (TEs) are conventionally identified in eukaryotic genomes by alignment to consensus element sequences. Using this approach, about half of the human genome has been previously identified as TEs and low-complexity repeats. We recently developed a highly sensitive alternative de novo strategy, P-clouds, that instead searches for clusters of high-abundance oligonucleotides that are related in sequence space (oligo “clouds”). We show here that P-clouds predicts >840 Mbp of additional repetitive sequences in the human genome, thus suggesting that 66%–69% of the human genome is repetitive or repeat-derived. To investigate this remarkable difference, we conducted detailed analyses of the ability of both P-clouds and a commonly used conventional approach, RepeatMasker (RM), to detect different sized fragments of the highly abundant human Alu and MIR SINEs. RM can have surprisingly low sensitivity for even moderately long fragments, in contrast to P-clouds, which has good sensitivity down to small fragment sizes (∼25 bp). Although short fragments have a high intrinsic probability of being false positives, we performed a probabilistic annotation that reflects this fact. We further developed “element-specific” P-clouds (ESPs) to identify novel Alu and MIR SINE elements, and using it we identified ∼100 Mb of previously unannotated human elements. ESP estimates of new MIR sequences are in good agreement with RM-based predictions of the amount that RM missed. These results highlight the need for combined, probabilistic genome annotation approaches and suggest that the human genome consists of substantially more repetitive sequence than previously believed