Families of periodic orbits for the spatial isosceles 3-body problem

We study the families of periodic orbits of the spatial isosceles 3-body problem (for small enough values of the mass lying on the symmetry axis) coming via the analytic continuation method from periodic orbits of the circular Sitnikov problem. Using the first integral of the angular momentum, we reduce the dimension of the phase space of the problem by two units. Since periodic orbits of the reduced isosceles problem generate invariant two-dimensional tori of the nonreduced problem, the analytic continuation of periodic orbits of the (reduced) circular Sitnikov problem at this level becomes the continuation of invariant two-dimensional tori from the circular Sitnikov problem to the nonreduced isosceles problem, each one filled with periodic or quasi-periodic orbits. These tori are not KAM tori but just isotropic, since we are dealing with a three-degrees-of-freedom system. The continuation of periodic orbits is done in two different ways, the first going directly from the reduced circular Sitnikov problem to the reduced isosceles problem, and the second one using two steps: first we continue the periodic orbits from the reduced circular Sitnikov problem to the reduced elliptic Sitnikov problem, and then we continue those periodic orbits of the reduced elliptic Sitnikov problem to the reduced isosceles problem. The continuation in one or two steps produces different results. This work is merely analytic and uses the variational equations in order to apply Poincar´e’s continuation method.

Equilibrium points and central configurations for the Lennard-Jones 2-and 3-body problems

Abstract. In this paper we study the relative equilibria and their stability for a system of three point particles moving under the action of a Lennard{Jones potential. A central con guration is a special position of the particles where the position and acceleration vectors of each particle are proportional, and the constant of proportionality is the same for all particles. Since the Lennard{Jones potential depends only on the mutual distances among the particles, it is invariant under rotations. In a rotating frame the orbits coming from central con gurations become equilibrium points, the relative equilibria. Due to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum of inertia I. In this work we characterize the relative equilibria, we nd the bifurcation values of I for which the number of relative equilibria is changing, we also analyze the stability of the relative equilibria.

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.

UVB-Induced Skin Inflammation and Cutaneous Tissue Injury Is Dependent on the MHC Class I-Like Protein, CD1d.

CD1d is a major histocompatibility complex class 1-like molecule that regulates the function and development of natural killer T (NKT) cells. Previously, we identified a critical role for the CD1d-NKT cell arm of innate immunity in promoting the development of UVB-induced p53 mutations, immune suppression, and skin tumors. Sunburn, an acute inflammatory response to UVB-induced cutaneous tissue injury, represents a clinical marker for non-melanoma skin cancer (NMSC) risk. However, the innate immune mechanisms controlling sunburn development are not considered relevant in NMSC etiology, and remain poorly investigated. Here we found that CD1d knockout (CD1d(-/-)) mice resist UVB-induced cutaneous tissue injury and inflammation compared with wild-type (WT) mice. This resistance was coupled with a faster epithelial tissue healing response. In contrast, the skins of UVB-irradiated invariant NKT cell-knockout (Jα18(-/-)) and NKT cell-deficient (TCRα(-/-)) mice, which express CD1d but are deficient in CD1d-dependent NKT cells, exhibited as much cutaneous tissue injury and inflammation as WT mice. In the absence of NKT cells, CD1d-deficient keratinocytes, dendritic cells, and macrophages exhibited diminished basal and stress-induced levels of pro-inflammatory mediators. Thus, our findings identify an essential role for CD1d in promoting UVB-induced cutaneous tissue injury and inflammation. They also suggest sunburn and NMSC etiologies are immunologically linked.

Site quality curves for birch stands in north-western Spain

Abstract

CD1d-antibody fusion proteins target iNKT cells to the tumor and trigger long-term therapeutic responses.

Despite the well-established antitumor activity of CD1d-restricted invariant natural killer T lymphocytes (iNKT), their use for cancer therapy has remained challenging. This appears to be due to their strong but short-lived activation followed by long-term anergy after a single administration of the CD1d agonist ligand alpha-galactosylceramide (αGC). As a promising alternative, we obtained sustained mouse iNKT cell responses associated with prolonged antitumor effects through repeated administrations of tumor-targeted recombinant sCD1d-antitumor scFv fusion proteins loaded with αGC. Here, we demonstrate that CD1d fusion proteins bound to tumor cells via the antibody fragment specific for a tumor-associated antigen, efficiently activate human iNKT cell lines leading to potent tumor cell lysis. The importance of CD1d tumor targeting was confirmed in tumor-bearing mice in which only the specific tumor-targeted CD1d fusion protein resulted in tumor inhibition of well-established aggressive tumor grafts. The therapeutic efficacy correlated with the repeated activation of iNKT and natural killer cells marked by their release of TH1 cytokines, despite the up-regulation of the co-inhibitory receptor PD-1. Our results demonstrate the superiority of providing the superagonist αGC loaded on recombinant CD1d proteins and support the use of αGC/sCD1d-antitumor fusion proteins to secure a sustained human and mouse iNKT cell activation, while targeting their cytotoxic activity and cytokine release to the tumor site.

High capacity robust audio watermarking scheme based on FFT and linear regression

Peer-reviewed

A game theoretical approach to the algebraic counterpart of the Wagner hierarchy

La hiérarchie de Wagner constitue à ce jour la plus fine classification des langages ω-réguliers. Par ailleurs, l'approche algébrique de la théorie de langages formels montre que ces ensembles ω-réguliers correspondent précisément aux langages reconnaissables par des ω-semigroupes finis pointés. Ce travail s'inscrit dans ce contexte en fournissant une description complète de la contrepartie algébrique de la hiérarchie de Wagner, et ce par le biais de la théorie descriptive des jeux de Wadge. Plus précisément, nous montrons d'abord que le degré de Wagner d'un langage ω-régulier est effectivement un invariant syntaxique. Nous définissons ensuite une relation de réduction entre ω-semigroupes pointés par le biais d'un jeu infini de type Wadge. La collection de ces structures algébriques ordonnée par cette relation apparaît alors comme étant isomorphe à la hiérarchie de Wagner, soit un quasi bon ordre décidable de largeur 2 et de hauteur ω. Nous exposons par la suite une procédure de décidabilité de cette hiérarchie algébrique : on décrit une représentation graphique des ω-semigroupes finis pointés, puis un algorithme sur ces structures graphiques qui calcule le degré de Wagner de n'importe quel élément. Ainsi le degré de Wagner de tout langage ω-régulier peut être calculé de manière effective directement sur son image syntaxique. Nous montrons ensuite comment construire directement et inductivement une structure de n''importe quel degré. Nous terminons par une description détaillée des invariants algébriques qui caractérisent tous les degrés de cette hiérarchie. Abstract The Wagner hierarchy is known so far to be the most refined topological classification of ω-rational languages. Also, the algebraic study of formal languages shows that these ω-rational sets correspond precisely to the languages recognizable by finite pointed ω-semigroups. Within this framework, we provide a construction of the algebraic counterpart of the Wagner hierarchy. We adopt a hierarchical game approach, by translating the Wadge theory from the ω-rational language to the ω-semigroup context. More precisely, we first show that the Wagner degree is indeed a syntactic invariant. We then define a reduction relation on finite pointed ω-semigroups by means of a Wadge-like infinite two-player game. The collection of these algebraic structures ordered by this reduction is then proven to be isomorphic to the Wagner hierarchy, namely a well-founded and decidable partial ordering of width 2 and height $\omega^\omega$. We also describe a decidability procedure of this hierarchy: we introduce a graph representation of finite pointed ω-semigroups allowing to compute their precise Wagner degrees. The Wagner degree of every ω-rational language can therefore be computed directly on its syntactic image. We then show how to build a finite pointed ω-semigroup of any given Wagner degree. We finally describe the algebraic invariants characterizing every Wagner degree of this hierarchy.

Adaptations of Natural Killer Cells to Self-MHC Class I.

Natural Killer (NK) cells use germ line encoded receptors to detect diseased host cells. Despite the invariant recognition structures, NK cells have a significant ability to adapt to their surroundings, such as the presence or absence of MHC class I molecules. It has been assumed that this adaptation occurs during NK cell development, but recent findings show that mature NK cells can also adapt to the presence or absence of MHC class I molecules. Here, we summarize how NK cells adjust to changes in the expression of MHC class I molecules. We propose an extension of existing models, in which MHC class I recognition during NK cell development sequentially instructs and maintains NK cell function. The elucidation of the molecular basis of the two effects may identify ways to improve the fitness of NK cells and to prevent the loss of NK cell function due to persistent alterations in their environment.

Normaalijakaumaan perustuva mutaatio-operaatio differentiaalievoluutioalgoritmiin

Evoluutioalgoritmit ovat viime vuosina osoittautuneet tehokkaiksi menetelmiksi globaalien optimointitehtävien ratkaisuun. Niiden vahvuutena on etenkin yleiskäyttöisyys ja kyky löytää globaali ratkaisu juuttumatta optimoitavan tavoitefunktion paikallisiin optimikohtiin. Tässä työssä on tavoitteena kehittää uusi, normaalijakaumaan perustuva mutaatio-operaatio differentiaalievoluutioalgoritmiin, joka on eräs uusimmista evoluutiopohjaisista optimointialgoritmeista. Menetelmän oletetaan vähentävän entisestään sekä populaation ennenaikaisen suppenemisen, että algoritmin tilojen juuttumisen riskiä ja se on teoreettisesti osoitettavissa suppenevaksi. Tämä ei päde alkuperäisen differentiaalievoluution tapauksessa, koska on voitu osoittaa, että sen tilanmuutokset voivat pienellä todennäköisyydellä juuttua. Työssä uuden menetelmän toimintaa tarkastellaan kokeellisesti käyttäen testiongelmina monirajoiteongelmia. Rajoitefunktioiden käsittelyyn käytetään Jouni Lampisen kehittämää, Pareto-optimaalisuuden periaatteeseen perustuvaa menetelmää. Samalla saadaan kerättyä lisää kokeellista näyttöä myös tämän menetelmän toiminnasta. Kaikki käytetyt testiongelmat kyettiin ratkaisemaan sekä alkuperäisellä differentiaalievoluutiolla, että uutta mutaatio-operaatiota käyttävällä versiolla. Uusi menetelmä osoittautui kuitenkin luotettavammaksi sellaisissa tapauksissa, joissa alkuperäisellä algoritmilla oli vaikeuksia. Lisäksi useimmat ongelmat kyettiin ratkaisemaan luotettavasti pienemmällä populaation koolla kuin alkuperäistä differentiaalievoluutiota käytettäessä. Uuden menetelmän käyttö myös mahdollistaa paremmin sellaisten kontrolliparametrien käytön, joilla hausta saadaan rotaatioinvariantti. Laskennallisesti uusi menetelmä on hieman alkuperäistä differentiaalievoluutiota raskaampi ja se tarvitsee yhden kontrolliparametrin enemmän. Uusille kontrolliparametreille määritettiin kuitenkin mahdollisimman yleiskäyttöiset arvot, joita käyttämällä on mahdollista ratkaista suuri joukko erilaisia ongelmia.

From Full stopping to transparency in a holographic model of heavy ion collisions

We numerically simulate planar shock wave collisions in anti-de Sitter space as a model for heavy ion collisions of large nuclei. We uncover a crossover between two different dynamical regimes as a function of the collision energy. At low energies the shocks first stop and then explode in a manner approximately described by hydrodynamics, in close similarity with the Landau model. At high energies the receding fragments move outwards at the speed of light, with a region of negative energy density and negative longitudinal pressure trailing behind them. The rapidity distribution of the energy density at late times around midrapidity is not approximately boost invariant but Gaussian, albeit with a width that increases with the collision energy.

A Gradient based algorithm for blind inversion of Wiener System using multi-variate score functions

A Wiener system is a linear time-invariant filter, followed by an invertible nonlinear distortion. Assuming that the input signal is an independent and identically distributed (iid) sequence, we propose an algorithm for estimating the input signal only by observing the output of the Wiener system. The algorithm is based on minimizing the mutual information of the output samples, by means of a steepest descent gradient approach.

Reliable computation of robust response tori on the verge of breakdown

We prove the existence and local uniqueness of invariant tori on the verge of breakdown for two systems: the quasi-periodically driven logistic map and the quasi-periodically forced standard map. These systems exemplify two scenarios: the Heagy-Hammel route for the creation of strange non- chaotic attractors and the nonsmooth bifurcation of saddle invariant tori. Our proofs are computer- assisted and are based on a tailored version of the Newton-Kantorovich theorem. The proofs cannot be performed using classical perturbation theory because the two scenarios are very far from the perturbative regime, and fundamental hypotheses such as reducibility or hyperbolicity either do not hold or are very close to failing. Our proofs are based on a reliable computation of the invariant tori and a careful study of their dynamical properties, leading to the rigorous validation of the numerical results with our novel computational techniques.

Mechanisms of OGT-mediated HCF-1 protein maturation

Post-translational protein modifications are crucial for many fundamental cellular and extracellular processes and greatly contribute to the complexity of organisms. Human HCF-1 is a transcriptional co-regulator that undergoes complex protein maturation involving reversible and irreversible post-translational modifications. Upon synthesis as a large precursor protein, HCF-1 undergoes extensive reversible glycosylation with β-N-acetylglucosamine giving rise to O-linked-β-N-acetylglucosamine (O-GlcNAc) modified serines and threonines. HCF-1 also undergoes irreversible site-specific proteolysis, which is important for one of HCF-1's major functions - the regulation of the cell-division cycle. HCF-1 O-GlcNAcylation and site-specific proteolysis are both catalyzed by a single enzyme with an unusual dual enzymatic activity, the O-GlcNAc transferase (OGT). HCF-1 is cleaved by OGT at any of six highly conserved 26 amino acid repeated sequences (HCF-1PRO repeats), but the mechanisms and the substrate requirements for OGT-mediated cleavage are not understood. In the present work, I characterized substrate requirements for OGT-mediated cleavage and O-GlcNAcylation of HCF-1. I identified key elements within the HCF-1PRO-repeat sequence that are important for proteolysis. Remarkably, an invariant single amino acid side-chain within the HCF-1PRO-repeat sequence displays particular OGT-binding properties and is essential for proteolysis. Additionally, I characterized substrate requirements for proteolysis outside of the HCF-1PRO repeat and identified a novel, highly O-GlcNAcylated OGT-binding sequence that enhances cleavage of the first HCF-1PRO repeat. These results link OGT association and its O-GlcNAcylation activities to HCF-1PRO-repeat proteolysis.

The Measurement Invariance of Schizotypy in Europe

The short version of the Oxford-Liverpool Inventory of Feelings and Experiences (sO-LIFE) is a widely used measure assessing schizotypy. There is limited information, however, on how sO-LIFE scores compare across different countries. The main goal of the present study is to test the measurement invariance of the sO-LIFE scores in a large sample of non-clinical adolescents and young adults from four European countries (UK, Switzerland, Italy, and Spain). The scores were obtained from validated versions of the sO-LIFE in their respective languages. The sample comprised 4190 participants (M = 20.87 years; SD = 3.71 years). The study of the internal structure, using confirmatory factor analysis, revealed that both three (i.e., positive schizotypy, cognitive disorganisation, and introvertive anhedonia) and four-factor (i.e., positive schizotypy, cognitive disorganisation, introvertive anhedonia, and impulsive nonconformity) models fitted the data moderately well. Multi-group confirmatory factor analysis showed that the three-factor model had partial strong measurement invariance across countries. Eight items were non-invariant across samples. Significant statistical differences in the mean scores of the s-OLIFE were found by country. Reliability scores, estimated with Ordinal alpha ranged from 0.75 to 0.87. Using the Item Response Theory framework, the sO-LIFE provides more accuracy information at the medium and high end of the latent trait. The current results show further evidence in support of the psychometric proprieties of the sO-LIFE, provide new information about the cross-cultural equivalence of schizotypy and support the use of this measure to screen for psychotic-like features and liability to psychosis in general population samples from different European countries.