Periodic Sequences of Arbitrage: A Tale of Four Currencies

This paper investigates arbitrage chains involving four currencies and four foreign exchange trader-arbitrageurs. In contrast with the three-currency case, we fi nd that arbitrage operations when four currencies are present may appear periodic in nature, and not involve smooth convergence to a \balanced" ensemble of exchange rates in which the law of one price holds. The goal of this article is to understand some interesting features of sequences of arbitrage operations, features which might well be relevant in other contexts in finance and economics.

Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

Fine structural variations of alphabetaTCRs selected by vaccination with natural versus altered self-antigen in melanoma patients.

Immunotherapy of cancer is often performed with altered "analog" peptide Ags optimized for HLA class I binding, resulting in enhanced immunogenicity, but the induced T cell responses require further evaluation. Recently, we demonstrated fine specificity differences and enhanced recognition of naturally presented Ag by T cells after vaccination with natural Melan-A/MART-1 peptide, as compared with analog peptide. In this study, we compared the TCR primary structures of 1489 HLA-A*0201/Melan-A(26-35)-specific CD8 T cells derived from both cohorts of patients. Although a strong preference for TRAV12-2 segment usage was present in nearly all patients, usage of particular TRAJ gene segments and CDR3alpha composition differed slightly after vaccination with natural vs analog peptide. Moreover, TCR beta-chain repertoires were broader after natural than analog peptide vaccination. In all patients, we observed a marked conservation of the CDR3beta amino acid composition with recurrent sequences centered on a glycyl-leucyl/valyl/alanyl-glycyl motif. In contrast to viral-specific TCR repertoires, such "public" motifs were primarily expressed by nondominant T cell clonotypes, which contrasted with "private" CDR3beta signatures frequently found in T cell clonotypes that dominated repertoires of individual patients. Interestingly, no differences in functional avidity were observed between public and private T cell clonotypes. Collectively, our data indicate that T cell repertoires generated against natural or analog Melan-A peptide exhibited slightly distinct but otherwise overlapping and structurally conserved TCR features, suggesting that the differences in binding affinity/avidity of TCRs toward pMHC observed in the two cohorts of patients are caused by subtle structural TCR variations.

Fine structural variations of alphabeta TCRs selected by vaccination with natural versus altered self-antigen in melanoma patients

Immunotherapy of cancer is often performed with altered "analog" peptide Ags optimized for HLA class I binding, resulting in enhanced immunogenicity, but the induced T cell responses require further evaluation. Recently, we demonstrated fine specificity differences and enhanced recognition of naturally presented Ag by T cells after vaccination with natural Melan-A/MART-1 peptide, as compared with analog peptide. In this study, we compared the TCR primary structures of 1489 HLA-A*0201/Melan-A26-35-specific CD8 T cells derived from both cohorts of patients. Although a strong preference for TRAV12-2 segment usage was present in nearly all patients, usage of particular TRAJ gene segments and CDR3 composition differed slightly after vaccination with natural vs analog peptide. Moreover, TCR β-chain repertoires were broader after natural than analog peptide vaccination. In all patients, we observed a marked conservation of the CDR3β amino acid composition with recurrent sequences centered on a glycyl-leucyl/valyl/alanyl-glycyl motif. In contrast to viral-specific TCR repertoires, such "public" motifs were primarily expressed by nondominant T cell clonotypes, which contrasted with "private" CDR3β signatures frequently found in T cell clonotypes that dominated repertoires of individual patients. Interestingly, no differences in functional avidity were observed between public and private T cell clonotypes. Collectively, our data indicate that T cell repertoires generated against natural or analog Melan-A peptide exhibited slightly distinct but otherwise overlapping and structurally conserved TCR features, suggesting that the differences in binding affinity/avidity of TCRs toward pMHC observed in the two cohorts of patients are caused by subtle structural TCR variations.

STOCHASTIC ADDING MACHINE AND 2-DIMENSIONAL JULIA SETS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Modeling High-Dimensional Audio Sequences with Recurrent Neural Networks

Cette thèse étudie des modèles de séquences de haute dimension basés sur des réseaux de neurones récurrents (RNN) et leur application à la musique et à la parole. Bien qu'en principe les RNN puissent représenter les dépendances à long terme et la dynamique temporelle complexe propres aux séquences d'intérêt comme la vidéo, l'audio et la langue naturelle, ceux-ci n'ont pas été utilisés à leur plein potentiel depuis leur introduction par Rumelhart et al. (1986a) en raison de la difficulté de les entraîner efficacement par descente de gradient. Récemment, l'application fructueuse de l'optimisation Hessian-free et d'autres techniques d'entraînement avancées ont entraîné la recrudescence de leur utilisation dans plusieurs systèmes de l'état de l'art. Le travail de cette thèse prend part à ce développement. L'idée centrale consiste à exploiter la flexibilité des RNN pour apprendre une description probabiliste de séquences de symboles, c'est-à-dire une information de haut niveau associée aux signaux observés, qui en retour pourra servir d'à priori pour améliorer la précision de la recherche d'information. Par exemple, en modélisant l'évolution de groupes de notes dans la musique polyphonique, d'accords dans une progression harmonique, de phonèmes dans un énoncé oral ou encore de sources individuelles dans un mélange audio, nous pouvons améliorer significativement les méthodes de transcription polyphonique, de reconnaissance d'accords, de reconnaissance de la parole et de séparation de sources audio respectivement. L'application pratique de nos modèles à ces tâches est détaillée dans les quatre derniers articles présentés dans cette thèse. Dans le premier article, nous remplaçons la couche de sortie d'un RNN par des machines de Boltzmann restreintes conditionnelles pour décrire des distributions de sortie multimodales beaucoup plus riches. Dans le deuxième article, nous évaluons et proposons des méthodes avancées pour entraîner les RNN. Dans les quatre derniers articles, nous examinons différentes façons de combiner nos modèles symboliques à des réseaux profonds et à la factorisation matricielle non-négative, notamment par des produits d'experts, des architectures entrée/sortie et des cadres génératifs généralisant les modèles de Markov cachés. Nous proposons et analysons également des méthodes d'inférence efficaces pour ces modèles, telles la recherche vorace chronologique, la recherche en faisceau à haute dimension, la recherche en faisceau élagué et la descente de gradient. Finalement, nous abordons les questions de l'étiquette biaisée, du maître imposant, du lissage temporel, de la régularisation et du pré-entraînement.

Study of spontaneous recurrent seizures and morphological alterations after status epilepticus induced by intrahippocampal injection of pilocarpine

Epileptic seizures are clinical manifestations of neuronal discharges characterized by hyperexcitability and/or hypersynchrony in the cortex and other subcortical regions. The pilocarpine (PILO) model of epilepsy mimics temporal lobe epilepsy (TLE) in humans. In the present study, we used a more selective approach: microinjection of PILO into the hilus of the dentate gyrus (H-PILO). Our main goal was to evaluate the behavioral and morphological alterations present in this model of TLE. Seventy-six percent of all animals receiving H-PILO injections had continuous seizures called status epilepticus (SE). A typical pattern of evolution of limbic seizures during the SE with a latency of 29.3 +/- 16.3 minutes was observed using an analysis of behavioral sequences. During the subsequent 30 days, 71% of all animals exhibited spontaneous recurrent seizures (SRSs) during a daily 8-hour videotaping session. These SRSs had a very conspicuous and characteristic pattern detected by behavioral sequences or neuroethological analysis. Only the animals that had SE showed positive Neo-Timm staining in the inner molecular layer of the dentate gyrus (sprouting) and reduced cell density in Ammon`s horn pyramidal cell subfield CA1. However, no correlation between the intensity of sprouting and the mean number and total number of SRSs was found. Additionally, using Fluoro-Jade staining, we observed neurodegeration in the hilus and pyramidal cell subfields CA3 and CM 24 hours after SE. These data indicate that H-PILO is a reliable, selective, efficient, low-mortality model that mimics the acute and chronic behavioral and morphological aspects of TLE. (C) 2010 Elsevier Inc. All rights reserved.

Recurrent gains and losses of large (84-109 bp) repeats in the rDNA internal transcribed spacer 2 (ITS2) of rhipicephaline ticks

We studied the internal transcribed spacer 2 (ITS2) in twenty-two spp. of ticks from the subfamily Rhipicephalinae. A 104-109 base pair (bp) region was Imperfectly repeated In most ticks studied. Mapping the number of repeat copies on to a phylogeny from the ITS2 showed that there have been many Independent gains and losses of repeats. Comparison of the sequences of the repeat copies Indicated that in most taxa concerted evolution had played little if any role in the evolution of these regions, as the copies clustered by sequence position rather than species, In our putative secondary structure, each repeat copy can fold into a distinct and almost identical stem-loop complex; a gain or loss of a repeat copy apparently does not impair the function of the ITS2 in these ticks.

Nucleotide and phylogenetic analysis of human papillomavirus types 6 and 11 isolated from recurrent respiratory papillomatosis in Brazil

There are few studies about the distribution of natural molecular variants of low-risk HPVs. Our aim was to evaluate the E6 early gene variability among HPV-6 and HPV-11 isolates detected in recurrent respiratory papillomatosis (RRP) samples obtained in a cohort of Brazilian patients. We also performed a phylogenetic analysis in order to compare nucleotide sequences identified in our study with previously reported isolates from different anatomic sites (laryngeal papillomas, genital warts, cervical cancer and anal swabs) obtained from other parts of the world to determine the phylogenetic relationships of variants detected in Brazil. The complete coding region of the E6 gene of 25 samples was cloned and sequenced: 18 isolates of HPV-6 (72%) and 7 isolates of HPV-11 (28%). A total of four different HPV-6 genomic variants and two HPV-11 genomic variants was identified. It was not possible to correlate specific variants with disease severity. Phylogenetic trees for both HPV types were constructed enclosing both E6 sequences detected in our study and formerly published sequences. In both phylogenetic trees, the sequences from Brazil did not group together. We could not establish a geographical association between HPV-6 or HPV-11 variants, unlike HPV-16 and HPV-18. © 2013 Elsevier B.V.

Analysis of eruptive and seismic sequences to improve the short-and long-term eruption forecasting

Forecasting the time, location, nature, and scale of volcanic eruptions is one of the most urgent aspects of modern applied volcanology. The reliability of probabilistic forecasting procedures is strongly related to the reliability of the input information provided, implying objective criteria for interpreting the historical and monitoring data. For this reason both, detailed analysis of past data and more basic research into the processes of volcanism, are fundamental tasks of a continuous information-gain process; in this way the precursor events of eruptions can be better interpreted in terms of their physical meanings with correlated uncertainties. This should lead to better predictions of the nature of eruptive events. In this work we have studied different problems associated with the long- and short-term eruption forecasting assessment. First, we discuss different approaches for the analysis of the eruptive history of a volcano, most of them generally applied for long-term eruption forecasting purposes; furthermore, we present a model based on the characteristics of a Brownian passage-time process to describe recurrent eruptive activity, and apply it for long-term, time-dependent, eruption forecasting (Chapter 1). Conversely, in an effort to define further monitoring parameters as input data for short-term eruption forecasting in probabilistic models (as for example, the Bayesian Event Tree for eruption forecasting -BET_EF-), we analyze some characteristics of typical seismic activity recorded in active volcanoes; in particular, we use some methodologies that may be applied to analyze long-period (LP) events (Chapter 2) and volcano-tectonic (VT) seismic swarms (Chapter 3); our analysis in general are oriented toward the tracking of phenomena that can provide information about magmatic processes. Finally, we discuss some possible ways to integrate the results presented in Chapters 1 (for long-term EF), 2 and 3 (for short-term EF) in the BET_EF model (Chapter 4).

Integrated pararetroviral sequences define a unique class of dispersed repetitive DNA in plants

Although integration of viral DNA into host chromosomes occurs regularly in bacteria and animals, there are few reported cases in plants, and these involve insertion at only one or a few sites. Here, we report that pararetrovirus-like sequences have integrated repeatedly into tobacco chromosomes, attaining a copy number of ≈103. Insertion apparently occurred by illegitimate recombination. From the sequences of 22 independent insertions recovered from a healthy plant, an 8-kilobase genome encoding a previously uncharacterized pararetrovirus that does not contain an integrase function could be assembled. Preferred boundaries of the viral inserts may correspond to recombinogenic gaps in open circular viral DNA. An unusual feature of the integrated viral sequences is a variable tandem repeat cluster, which might reflect defective genomes that preferentially recombine into plant DNA. The recurrent invasion of pararetroviral DNA into tobacco chromosomes demonstrates that viral sequences can contribute significantly to plant genome evolution.

Recurrent invasion and extinction of a selfish gene

Homing endonuclease genes show super-Mendelian inheritance, which allows them to spread in populations even when they are of no benefit to the host organism. To test the idea that regular horizontal transmission is necessary for the long-term persistence of these genes, we surveyed 20 species of yeasts for the ω-homing endonuclease gene and associated group I intron. The status of ω could be categorized into three states (functional, nonfunctional, or absent), and status was not clustered on the host phylogeny. Moreover, the phylogeny of ω differed significantly from that of the host, strong evidence of horizontal transmission. Further analyses indicate that horizontal transmission is more common than transposition, and that it occurs preferentially between closely related species. Parsimony analysis and coalescent theory suggest that there have been 15 horizontal transmission events in the ancestry of our yeast species, through simulations indicate that this value is probably an underestimate. Overall, the data support a cyclical model of invasion, degeneration, and loss, followed by reinvasion, and each of these transitions is estimated to occur about once every 2 million years. The data are thus consistent with the idea that frequent horizontal transmission is necessary for the long-term persistence of homing endonuclease genes, and further, that this requirement limits these genes to organisms with easily accessible germ lines. The data also show that mitochondrial DNA sequences are transferred intact between yeast species; if other genes do not show such high levels of horizontal transmission, it would be due to lack of selection, rather than lack of opportunity.

Involvement of a human gene related to the Drosophila spen gene in the recurrent t(1;22) translocation of acute megakaryocytic leukemia

The recurrent t(1;22)(p13;q13) translocation is exclusively associated with infant acute megakaryoblastic leukemia. We have identified the two genes involved in this translocation. Both genes possess related sequences in the Drosophila genome. The chromosome 22 gene (megakaryocytic acute leukemia, MAL) product is predicted to be involved in chromatin organization, and the chromosome 1 gene (one twenty-two, OTT) product is related to the Drosophila split-end (spen) family of proteins. Drosophila genetic experiments identified spen as involved in connecting the Raf and Hox pathways. Because almost all of the sequences and all of the identified domains of both OTT and MAL proteins are included in the predicted fusion protein, the OTT-MAL fusion could aberrantly modulate chromatin organization, Hox differentiation pathways, or extracellular signaling.

Expansion of a recurrent V beta 5.3+ T-cell population in newly diagnosed and untreated HLA-DR2 multiple sclerosis patients.

We have used a PCR-based technology to study the V beta 5 and V beta 17 repertoire of T-cell populations in HLA-DR2 multiple sclerosis (MS) patients. We have found that the five MS DR2 patients studied present, at the moment of diagnosis and prior to any treatment, a marked expansion of a CD4+ T-cell population bearing V beta 5-J beta 1.4 beta chains. The sequences of the complementarity-determining region 3 of the expanded T cells are highly homologous. One shares structural features with that of the T cells infiltrating the central nervous system and of myelin basic protein-reactive T cells found in HLA-DR2 MS patients. An homologous sequence was not detectable in MS patients expressing DR alleles other than DR2. However, it is detectable but not expanded in healthy DR2 individuals. The possible mechanisms leading to its in vivo proliferation at the onset of MS are discussed.

Prediction of subcellular localization using sequence-biased recurrent networks

Motivation: Targeting peptides direct nascent proteins to their specific subcellular compartment. Knowledge of targeting signals enables informed drug design and reliable annotation of gene products. However, due to the low similarity of such sequences and the dynamical nature of the sorting process, the computational prediction of subcellular localization of proteins is challenging. Results: We contrast the use of feed forward models as employed by the popular TargetP/SignalP predictors with a sequence-biased recurrent network model. The models are evaluated in terms of performance at the residue level and at the sequence level, and demonstrate that recurrent networks improve the overall prediction performance. Compared to the original results reported for TargetP, an ensemble of the tested models increases the accuracy by 6 and 5% on non-plant and plant data, respectively.