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.

On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.

The Deleterious Chemical Effects of Concentrated Deicing Solutions on Portland Cement Concrete, TR-480, 2008

This research project investigated the effects of concentrated brines of magnesium chloride, calcium chloride, sodium chloride, and calcium magnesium acetate on portland cement concrete. Although known to be effective at deicing and anti-icing, the deleterious effects these chemicals may have on concrete have not been well documented. As a result of this research, it was determined that there is significant evidence that magnesium chloride and calcium chloride chemically interact with hardened portland cement paste in concrete resulting in expansive cracking, increased permeability, and a significant loss in compressive strength. Although the same effects were not seen with sodium chloride brines, it was shown that sodium chloride brines have the highest rate of ingress into hardened concrete. This latter fact is significant with respect to corrosion of embedded steel. The mechanism for attack of hardened cement paste varies with deicer chemical but in general, a chemical reaction between chlorides and cement hydration products results in the dissolution of the hardened cement paste and formation of oxychloride phases, which are expansive. The chemical attack of the hardened cement paste is significantly reduced if supplementary cementitious materials are included in the concrete mixture. Both coal fly ash and ground granulated blast furnace slag were found to be effective at mitigating the chemical attack caused by the deicers tested. In the tests performed, ground granulated blast furnace slag performed better as a mitigation strategy as compared to coal fly ash. Additionally, siloxane and silane sealants were effective at slowing the ingress of deicing chemicals into the concrete and thereby reducing the observed distress. In general, the siloxane sealant appeared to be more effective than the silane, but both were effective and should be considered as a maintenance strategy.

The Deleterious Chemical Effects of Concentrated Deicing Solutions on Portland Cement Concrete, TR-480, Implementation Guide, 2008

This research project investigated the effects of concentrated brines of magnesium chloride, calcium chloride, sodium chloride, and calcium magnesium acetate on portland cement concrete. Although known to be effective at deicing and anti-icing, the deleterious effects these chemicals may have on concrete have not been well documented. As a result of this research, it was determined that there is significant evidence that magnesium chloride and calcium chloride chemically interact with hardened portland cement paste in concrete resulting in expansive cracking, increased permeability, and a significant loss in compressive strength. Although the same effects were not seen with sodium chloride brines, it was shown that sodium chloride brines have the highest rate of ingress into hardened concrete. This latter fact is significant with respect to corrosion of embedded steel. The mechanism for attack of hardened cement paste varies with deicer chemical but in general, a chemical reaction between chlorides and cement hydration products results in the dissolution of the hardened cement paste and formation of oxychloride phases, which are expansive. The chemical attack of the hardened cement paste is significantly reduced if supplementary cementitious materials are included in the concrete mixture. Both coal fly ash and ground granulated blast furnace slag were found to be effective at mitigating the chemical attack caused by the deicers tested. In the tests performed, ground granulated blast furnace slag performed better as a mitigation strategy as compared to coal fly ash. Additionally, siloxane and silane sealants were effective at slowing the ingress of deicing chemicals into the concrete and thereby reducing the observed distress. In general, the siloxane sealant appeared to be more effective than the silane, but both were effective and should be considered as a maintenance strategy.

The Deleterious Chemical Effects of Concentrated Deicing Solutions on Portland Cement Concrete, TR-480, Executive Summary, 2008

This research project investigated the effects of concentrated brines of magnesium chloride, calcium chloride, sodium chloride, and calcium magnesium acetate on portland cement concrete. Although known to be effective at deicing and anti-icing, the deleterious effects these chemicals may have on concrete have not been well documented. As a result of this research, it was determined that there is significant evidence that magnesium chloride and calcium chloride chemically interact with hardened portland cement paste in concrete resulting in expansive cracking, increased permeability, and a significant loss in compressive strength. Although the same effects were not seen with sodium chloride brines, it was shown that sodium chloride brines have the highest rate of ingress into hardened concrete. This latter fact is significant with respect to corrosion of embedded steel. The mechanism for attack of hardened cement paste varies with deicer chemical but in general, a chemical reaction between chlorides and cement hydration products results in the dissolution of the hardened cement paste and formation of oxychloride phases, which are expansive. The chemical attack of the hardened cement paste is significantly reduced if supplementary cementitious materials are included in the concrete mixture. Both coal fly ash and ground granulated blast furnace slag were found to be effective at mitigating the chemical attack caused by the deicers tested. In the tests performed, ground granulated blast furnace slag performed better as a mitigation strategy as compared to coal fly ash. Additionally, siloxane and silane sealants were effective at slowing the ingress of deicing chemicals into the concrete and thereby reducing the observed distress. In general, the siloxane sealant appeared to be more effective than the silane, but both were effective and should be considered as a maintenance strategy.

The Deleterious Chemical Effects of Concentrated Deicing Solutions on Portland Cement Concrete, Literature Review, TR-480, 2008

This research project investigated the effects of concentrated brines of magnesium chloride, calcium chloride, sodium chloride, and calcium magnesium acetate on portland cement concrete. Although known to be effective at deicing and anti-icing, the deleterious effects these chemicals may have on concrete have not been well documented. As a result of this research, it was determined that there is significant evidence that magnesium chloride and calcium chloride chemically interact with hardened portland cement paste in concrete resulting in expansive cracking, increased permeability, and a significant loss in compressive strength. Although the same effects were not seen with sodium chloride brines, it was shown that sodium chloride brines have the highest rate of ingress into hardened concrete. This latter fact is significant with respect to corrosion of embedded steel. The mechanism for attack of hardened cement paste varies with deicer chemical but in general, a chemical reaction between chlorides and cement hydration products results in the dissolution of the hardened cement paste and formation of oxychloride phases, which are expansive. The chemical attack of the hardened cement paste is significantly reduced if supplementary cementitious materials are included in the concrete mixture. Both coal fly ash and ground granulated blast furnace slag were found to be effective at mitigating the chemical attack caused by the deicers tested. In the tests performed, ground granulated blast furnace slag performed better as a mitigation strategy as compared to coal fly ash. Additionally, siloxane and silane sealants were effective at slowing the ingress of deicing chemicals into the concrete and thereby reducing the observed distress. In general, the siloxane sealant appeared to be more effective than the silane, but both were effective and should be considered as a maintenance strategy.

The Deleterious Chemical Effects of Concentrated Deicing Solutions on Portland Cement Concrete, Technical Appendices, TR-480, 2008

This research project investigated the effects of concentrated brines of magnesium chloride, calcium chloride, sodium chloride, and calcium magnesium acetate on portland cement concrete. Although known to be effective at deicing and anti-icing, the deleterious effects these chemicals may have on concrete have not been well documented. As a result of this research, it was determined that there is significant evidence that magnesium chloride and calcium chloride chemically interact with hardened portland cement paste in concrete resulting in expansive cracking, increased permeability, and a significant loss in compressive strength. Although the same effects were not seen with sodium chloride brines, it was shown that sodium chloride brines have the highest rate of ingress into hardened concrete. This latter fact is significant with respect to corrosion of embedded steel. The mechanism for attack of hardened cement paste varies with deicer chemical but in general, a chemical reaction between chlorides and cement hydration products results in the dissolution of the hardened cement paste and formation of oxychloride phases, which are expansive. The chemical attack of the hardened cement paste is significantly reduced if supplementary cementitious materials are included in the concrete mixture. Both coal fly ash and ground granulated blast furnace slag were found to be effective at mitigating the chemical attack caused by the deicers tested. In the tests performed, ground granulated blast furnace slag performed better as a mitigation strategy as compared to coal fly ash. Additionally, siloxane and silane sealants were effective at slowing the ingress of deicing chemicals into the concrete and thereby reducing the observed distress. In general, the siloxane sealant appeared to be more effective than the silane, but both were effective and should be considered as a maintenance strategy.

Reduced left hemisphere dominance for multiple versus single anagram solutions and its modulation by individuals' schizotypy

Problem solving (including insight, divergent thinking) seems to rely on the right hemisphere (RH). These functions are difficult to assess behaviorally. We propose anagram resolution as a suitable paradigm. University students (n=32) performed three tachistoscopic lateralized visual half-field experiments (stimulus presentation 150ms). In Experiment 1, participants recalled four-letter strings. Subsequently, participants provided solutions for four-letter anagrams (one solution in Experiment 2; two solutions in Experiment 3). Additionally, participants completed a schizotypy questionnaire (O-LIFE). Results showed a right visual field advantage in Experiment 1 and 2, but no visual field advantage in Experiment 3. In Experiment 1, increasing positive schizotypy associated with a RH performance shift. Problem solving seems to require increasingly the RH when facing several rather than one solution. This result supports previous studies on the RH's role in remote associative, metaphor and discourse processing. The more complex language requirements, the less personality traits seem to matter.

EADock : design of a new molecular docking algorithm and some of its applications

3 Summary 3. 1 English The pharmaceutical industry has been facing several challenges during the last years, and the optimization of their drug discovery pipeline is believed to be the only viable solution. High-throughput techniques do participate actively to this optimization, especially when complemented by computational approaches aiming at rationalizing the enormous amount of information that they can produce. In siiico techniques, such as virtual screening or rational drug design, are now routinely used to guide drug discovery. Both heavily rely on the prediction of the molecular interaction (docking) occurring between drug-like molecules and a therapeutically relevant target. Several softwares are available to this end, but despite the very promising picture drawn in most benchmarks, they still hold several hidden weaknesses. As pointed out in several recent reviews, the docking problem is far from being solved, and there is now a need for methods able to identify binding modes with a high accuracy, which is essential to reliably compute the binding free energy of the ligand. This quantity is directly linked to its affinity and can be related to its biological activity. Accurate docking algorithms are thus critical for both the discovery and the rational optimization of new drugs. In this thesis, a new docking software aiming at this goal is presented, EADock. It uses a hybrid evolutionary algorithm with two fitness functions, in combination with a sophisticated management of the diversity. EADock is interfaced with .the CHARMM package for energy calculations and coordinate handling. A validation was carried out on 37 crystallized protein-ligand complexes featuring 11 different proteins. The search space was defined as a sphere of 15 R around the center of mass of the ligand position in the crystal structure, and conversely to other benchmarks, our algorithms was fed with optimized ligand positions up to 10 A root mean square deviation 2MSD) from the crystal structure. This validation illustrates the efficiency of our sampling heuristic, as correct binding modes, defined by a RMSD to the crystal structure lower than 2 A, were identified and ranked first for 68% of the complexes. The success rate increases to 78% when considering the five best-ranked clusters, and 92% when all clusters present in the last generation are taken into account. Most failures in this benchmark could be explained by the presence of crystal contacts in the experimental structure. EADock has been used to understand molecular interactions involved in the regulation of the Na,K ATPase, and in the activation of the nuclear hormone peroxisome proliferatoractivated receptors a (PPARa). It also helped to understand the action of common pollutants (phthalates) on PPARy, and the impact of biotransformations of the anticancer drug Imatinib (Gleevec®) on its binding mode to the Bcr-Abl tyrosine kinase. Finally, a fragment-based rational drug design approach using EADock was developed, and led to the successful design of new peptidic ligands for the a5ß1 integrin, and for the human PPARa. In both cases, the designed peptides presented activities comparable to that of well-established ligands such as the anticancer drug Cilengitide and Wy14,643, respectively. 3.2 French Les récentes difficultés de l'industrie pharmaceutique ne semblent pouvoir se résoudre que par l'optimisation de leur processus de développement de médicaments. Cette dernière implique de plus en plus. de techniques dites "haut-débit", particulièrement efficaces lorsqu'elles sont couplées aux outils informatiques permettant de gérer la masse de données produite. Désormais, les approches in silico telles que le criblage virtuel ou la conception rationnelle de nouvelles molécules sont utilisées couramment. Toutes deux reposent sur la capacité à prédire les détails de l'interaction moléculaire entre une molécule ressemblant à un principe actif (PA) et une protéine cible ayant un intérêt thérapeutique. Les comparatifs de logiciels s'attaquant à cette prédiction sont flatteurs, mais plusieurs problèmes subsistent. La littérature récente tend à remettre en cause leur fiabilité, affirmant l'émergence .d'un besoin pour des approches plus précises du mode d'interaction. Cette précision est essentielle au calcul de l'énergie libre de liaison, qui est directement liée à l'affinité du PA potentiel pour la protéine cible, et indirectement liée à son activité biologique. Une prédiction précise est d'une importance toute particulière pour la découverte et l'optimisation de nouvelles molécules actives. Cette thèse présente un nouveau logiciel, EADock, mettant en avant une telle précision. Cet algorithme évolutionnaire hybride utilise deux pressions de sélections, combinées à une gestion de la diversité sophistiquée. EADock repose sur CHARMM pour les calculs d'énergie et la gestion des coordonnées atomiques. Sa validation a été effectuée sur 37 complexes protéine-ligand cristallisés, incluant 11 protéines différentes. L'espace de recherche a été étendu à une sphère de 151 de rayon autour du centre de masse du ligand cristallisé, et contrairement aux comparatifs habituels, l'algorithme est parti de solutions optimisées présentant un RMSD jusqu'à 10 R par rapport à la structure cristalline. Cette validation a permis de mettre en évidence l'efficacité de notre heuristique de recherche car des modes d'interactions présentant un RMSD inférieur à 2 R par rapport à la structure cristalline ont été classés premier pour 68% des complexes. Lorsque les cinq meilleures solutions sont prises en compte, le taux de succès grimpe à 78%, et 92% lorsque la totalité de la dernière génération est prise en compte. La plupart des erreurs de prédiction sont imputables à la présence de contacts cristallins. Depuis, EADock a été utilisé pour comprendre les mécanismes moléculaires impliqués dans la régulation de la Na,K ATPase et dans l'activation du peroxisome proliferatoractivated receptor a (PPARa). Il a également permis de décrire l'interaction de polluants couramment rencontrés sur PPARy, ainsi que l'influence de la métabolisation de l'Imatinib (PA anticancéreux) sur la fixation à la kinase Bcr-Abl. Une approche basée sur la prédiction des interactions de fragments moléculaires avec protéine cible est également proposée. Elle a permis la découverte de nouveaux ligands peptidiques de PPARa et de l'intégrine a5ß1. Dans les deux cas, l'activité de ces nouveaux peptides est comparable à celles de ligands bien établis, comme le Wy14,643 pour le premier, et le Cilengitide (PA anticancéreux) pour la seconde.

Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

New horizons for black holes and branes

We initiate a systematic scan of the landscape of black holes in any spacetime dimension using the recently proposed blackfold effective worldvolume theory. We focus primarily on asymptotically flat stationary vacuum solutions, where we uncover large classes of new black holes. These include helical black strings and black rings, black odd-spheres, for which the horizon is a product of a large and a small sphere, and non-uniform black cylinders. More exotic possibilities are also outlined. The blackfold description recovers correctly the ultraspinning Myers-Perry black holes as ellipsoidal even-ball configurations where the velocity field approaches the speed of light at the boundary of the ball. Helical black ring solutions provide the first instance of asymptotically flat black holes in more than four dimensions with a single spatial U(1) isometry. They also imply infinite rational non-uniqueness in ultraspinning regimes, where they maximize the entropy among all stationary single-horizon solutions. Moreover, static blackfolds are possible with the geometry of minimal surfaces. The absence of compact embedded minimal surfaces in Euclidean space is consistent with the uniqueness theorem of static black holes

Amlodipine and valsartan as components of a rational and effective fixed-dose combination.

Pharmacological treatment of hypertension is effective in preventing cardiovascular and renal complications. Calcium antagonists and blockers of the renin-angiotensin system are widely used today to initiate antihypertensive therapy but, when given as monotherapy, do not suffice in most patients to normalize blood pressure. Combining the two types of agents considerably increases the antihypertensive efficacy, but not at the expense of a deterioration of tolerability. This is exemplified by the experience accumulated with the recently developed fixed dose combination containing the AT(1)-receptor blocker valsartan (160 mg) and the dihydropyridine amlodipine (5 or 10 mg). In a randomized trial, an 8-week treatment normalized blood pressure (<140/90 mmHg) within 8 weeks in a large fraction of hypertensive patients (78.4% and 85.2% using the 5/160 [n = 371] and 10/160 mg [n = 377] dosage, respectively). Like all AT(1)-receptor blockers valsartan has a placebo-like tolerability. Valsartan prevents to a large extent the occurrence amlodipine-induced peripheral edema. Both amlodipine and valsartan have beneficial effects on cardiovascular morbidity and mortality, as well as protective effects on renal function. The co-administration of these two agents is therefore very attractive, as it enables a rapid and sustained blood pressure control in hypertensive patients. The availability of a fixed-dose combination based on amlodipine and valsartan is expected therefore to facilitate the management of hypertension, to improve long-term adherence with antihypertensive therapy and, ultimately, to have a positive impact on cardiovascular and renal outcomes.

Marinade with alkaline solutions for the improvement of pork quality

The objective of this work was to evaluate the effects of alkaline solution marinades on the characteristics of pork subjected to post-mortem pH decrease in pig muscle. The pH of carcasses was measured in a commercial slaughterhouse (n = 526), 45 min after slaughtering (pH45) and, then, the carcasses were divided into the groups with pH45<5.7 or pH45>5.7. Ten samples of the longissimus dorsi muscles of each group were collected and distributed in an entirely randomized design, in a 2x4 factorial arrangement, with two conditions (pH45<5.7 or pH45>5.7), and four marinade solutions: TC, no marinade; TM1, sodium bicarbonate and sodium chloride; TM2, sodium tripolyphosphate and sodium chloride; TM3, sodium bicarbonate, sodium tripolyphosphate and sodium chloride. There was no interaction between pH45 of the meat and the marinade treatments. Meat with pH45<5.7 showed higher values for lightness, and for purge loss (PL), exudate loss (EL), cooking loss (CL) and shear force (SF). Marinating increased the pH, reduced the lightness, EL, CL and SF, and improved tenderness, juiciness and flavor of meat. Marinades with solutions containing chloride, bicarbonate, and sodium tripolyphosphate are effective in the improvement of pork quality, making physical characteristics of marinated meat similar to those of fresh pork, as a consequence of accelerated postmortem glycolysis.

Safety of a new algorithm for the management of childhood illness (Almanach) to improve quality of care and rational use of drugs

Introduction New evidence from randomized controlled and etiology of fever studies, the availability of reliable RDT for malaria, and novel technologies call for revision of the IMCI strategy. We developed a new algorithm based on (i) a systematic review of published studies assessing the safety and appropriateness of RDT and antibiotic prescription, (ii) results from a clinical and microbiological investigation of febrile children aged <5 years, (iii) international expert IMCI opinions. The aim of this study was to assess the safety of the new algorithm among patients in urban and rural areas of Tanzania.Materials and Methods The design was a controlled noninferiority study. Enrolled children aged 2-59 months with any illness were managed either by a study clinician using the new Almanach algorithm (two intervention health facilities), or clinicians using standard practice, including RDT (two control HF). At day 7 and day 14, all patients were reassessed. Patients who were ill in between or not cured at day 14 were followed until recovery or death. Primary outcome was rate of complications, secondary outcome rate of antibiotic prescriptions.Results 1062 children were recruited. Main diagnoses were URTI 26%, pneumonia 19% and gastroenteritis (9.4%). 98% (531/541) were cured at D14 in the Almanach arm and 99.6% (519/521) in controls. Rate of secondary hospitalization was 0.2% in each. One death occurred in controls. None of the complications was due to withdrawal of antibiotics or antimalarials at day 0. Rate of antibiotic use was 19% in the Almanach arm and 84% in controls.Conclusion Evidence suggests that the new algorithm, primarily aimed at the rational use of drugs, is as safe as standard practice and leads to a drastic reduction of antibiotic use. The Almanach is currently being tested for clinician adherence to proposed procedures when used on paper or a mobile phone

Viability of dourado embryos cooled in different cryoprotectant solutions

The objective of this work was to evaluate the effect of different cryoprotectants on the viability of dourado (Salminus brasiliensis) embryos. Ten cryoprotectant solutions were tested. For each solution, 300 embryos were selected at the closing of the blastopore stage, and 300 more embryos were used as a negative control. After cooling (-8ºC for 6 hours), the embryos were rehydrated directly in the incubator until hatching. The best result is obtained with the cryoprotectant solution containing 9% methanol associated with 17% sucrose, resulting in a larvae hatching rate of 67.06%.