Log canonical thresholds of quasi-ordinary hypersurface singularities

The log canonical thresholds of irreducible quasi-ordinary hypersurface singularities are computed, using an explicit list of pole candidates for the motivic zeta function found by the last two authors

The valuative tree is the projective limit of Eggers-Wall trees

Consider a germ $C$ of reduced curve on a smooth germ $S$ of complex analytic surface. Assume that $C$ contains a smooth branch $L$. Using the Newton-Puiseux series of $C$ relative to any coordinate system $(x,y)$ on $S$ such that $L$ is the $y$-axis, one may define the {\em Eggers-Wall tree} $\Theta_L(C)$ of $C$ relative to $L$. Its ends are labeled by the branches of $C$ and it is endowed with three natural functions measuring the characteristic exponents of the previous Newton-Puiseux series, their denominators and contact orders. The main objective of this paper is to embed canonically $\Theta_L(C)$ into Favre and Jonsson's valuative tree $\mathbb{P}(\mathcal{V})$ of real-valued semivaluations of $S$ up to scalar multiplication, and to show that this embedding identifies the three natural functions on $\Theta_L(C)$ as pullbacks of other naturally defined functions on $\mathbb{P}(\mathcal{V})$. As a consequence, we prove an inversion theorem generalizing the well-known Abhyankar-Zariski inversion theorem concerning one branch: if $L'$ is a second smooth branch of $C$, then the valuative embeddings of the Eggers-Wall trees $\Theta_{L'}(C)$ and $\Theta_L(C)$ identify them canonically, their associated triples of functions being easily expressible in terms of each other. We prove also that the space $\mathbb{P}(\mathcal{V})$ is the projective limit of Eggers-Wall trees over all choices of curves $C$. As a supplementary result, we explain how to pass from $\Theta_L(C)$ to an associated splice diagram.Comment: 45 pages, 20 figure

Geometric motivic Poincar\'e series of quasi-ordinary singularities

The geometric motivic Poincar\'e series of a germ $(S,0)$ of complex algebraic variety takes into account the classes in the Grothendieck ring of the jets of arcs through $(S,0)$. Denef and Loeser proved that this series has a rational form. We give an explicit description of this invariant when $(S,0)$ is an irreducible germ of quasi-ordinary hypersurface singularity in terms of the Newton polyhedra of the logarithmic jacobian ideals. These ideals are determined by the characteristic monomials of a quasi-ordinary branch parametrizing $(S,0)$

Expression and characterization of the Trypanosoma cruzi dihydrofolate reductase domain

We have cloned and expressed in Escherichia coli a 702-base pair gene coding for the dihydrofolate reductase (DHFR) domain of the bifunctional dihydrofolate reductase-thymidylate synthase (DHFR-TS) from Trypanosoma cruzi. The DHFR domain was purified to homogeneity by methotrexate-Sepharose chromatography followed by an anion-exchange chromatography step in a mono Q column, and displayed a single 27-kDa band on SDS-PAGE. Gel filtration showed that the catalytic domain was expressed as a monomer. Kinetic parameters were similar to those reported for the wild-type bifunctional enzyme with Km values of 0.75 microM for dihydrofolate and 16 microM for NADPH and a kcat value of 16.5 s-1. T. cruzi DHFR is poorly inhibited by trimethoprim and pyrimethamine and the inhibition constants were always lower for the bifunctional enzyme. The binding of methotrexate was characteristic of a class of inhibitors that form an initial complex which isomerizes slowly to a tighter complex and are referred to as 'slow, tight-binding' inhibitors. While the slow-binding step of inhibition was apparently unaffected in the individually expressed DHFR domain, the overall inhibition constant was two-fold higher as a consequence of the superior inhibition constant value obtained for the initial inhibitory complex

Equilibration of Concentrated Hard Sphere Fluids

We report a systematic molecular dynamics study of the isochoric equilibration of hard-sphere fluids in their metastable regime close to the glass transition. The thermalization process starts with the system prepared in a non-equilibrium state with the desired final volume fraction {\phi} but with a prescribed non-equilibrium static structure factor S_0(k; {\phi}). The evolution of the {\alpha}- relaxation time {\tau}{\alpha} (k) and long-time self-diffusion coefficient DL as a function of the evolution time tw is then monitored for an array of volume fractions. For a given waiting time the plot of {\tau}{\alpha} (k; {\phi}, tw) as a function of {\phi} exhibits two regimes corresponding to samples that have fully equilibrated within this waiting time ({\phi} \leq {\phi}(c) (tw)), and to samples for which equilibration is not yet complete ({\phi} \geq {\phi}(c) (tw)). The crossover volume fraction {\phi}(c) (tw) increases with tw but seems to saturate to a value {\phi}(a) \equiv {\phi}(c) (tw \rightarrow \infty) \approx 0.582. We also find that the waiting time t^(eq)_w({\phi}) required to equilibrate a system grows faster than the corresponding equilibrium relaxation time, t^(eq)({\phi}) \approx 0.27 \times [{\tau}{\alpha} (k; {\phi})]^1.43, and that both characteristic times increase strongly as {\phi} approaches {\phi}^(a), thus suggesting that the measurement of equilibrium properties at and above {\phi}(a) is experimentally impossible

Quantum state of the multiverse

A third quantization formalism is applied to a simplified multiverse scenario. A well defined quantum state of the multiverse is obtained which agrees with standard boundary condition proposals. These states are found to be squeezed, and related to accelerating universes: they share similar properties to those obtained previously by Grishchuk and Siderov. We also comment on related works that have criticized the third quantization approach.Comment: 15 pages, 2 figure

A dark energy multiverse

We present cosmic solutions corresponding to universes filled with dark and phantom energy, all having a negative cosmological constant. All such solutions contain infinite singularities, successively and equally distributed along time, which can be either big bang/crunchs or big rips singularities. Classicaly these solutions can be regarded as associated with multiverse scenarios, being those corresponding to phantom energy that may describe the current accelerating universe

Discovery of New Compounds Active against Plasmodium falciparum by High Throughput Screening of Microbial Natural Products

Due to the low structural diversity within the set of antimalarial drugs currently available in the clinic and the increasing number of cases of resistance, there is an urgent need to find new compounds with novel modes of action to treat the disease. Microbial natural products are characterized by their large diversity provided in terms of the chemical complexity of the compounds and the novelty of structures. Microbial natural products extracts have been underexplored in the search for new antiparasitic drugs and even more so in the discovery of new antimalarials. Our objective was to find new druggable natural products with antimalarial properties from the MEDINA natural products collection, one of the largest natural product libraries harboring more than 130,000 microbial extracts. In this work, we describe the optimization process and the results of a phenotypic high throughput screen (HTS) based on measurements of Plasmodium lactate dehydrogenase. A subset of more than 20,000 extracts from the MEDINA microbial products collection has been explored, leading to the discovery of 3 new compounds with antimalarial activity. In addition, we report on the novel antiplasmodial activity of 4 previously described natural productsThis work was supported by the Junta de Andalucía [BIO-199, P09-CVI- 5367], the VI Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica 2008-2011, Instituto de Salud Carlos III-Subdirección General de Redes y Centros de Investigación Cooperativa-Red de Investigación Cooperativa en Enfermedades Tropicales (RICET FIS Network: RD12/0018/0017),the Plan Nacional (SAF2013-48999-R), the FEDER funds from the EU and the PARAMET network (FP7-PEOPLE-2011-ITN. GA290080) to DG-P. Research of FV and OG was supported by the Instituto de Salud Carlos III-Subdirección General de Redes y Centros de Investigación Cooperativa-Red de Investigación Cooperativa en Enfermedades Tropicales (RICET FIS Network: RD12/0018/0005) and the FEDER funds from the EU and the PARAMET network (FP7-PEOPLE-2011-ITN. GA290080). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewe

Human recombinant glutamate oxaloacetate transaminase 1 (GOT1) supplemented with oxaloacetate induces a protective effect after cerebral ischemia

Blood glutamate scavenging is a novel and attractive protecting strategy to reduce the excitotoxic effect of extracellular glutamate released during ischemic brain injury. Glutamate oxaloacetate transaminase 1 (GOT1) activation by means of oxaloacetate administration has been used to reduce the glutamate concentration in the blood. However, the protective effect of the administration of the recombinant GOT1 (rGOT1) enzyme has not been yet addressed in cerebral ischemia. The aim of this study was to analyze the protective effect of an effective dose of oxaloacetate and the human rGOT1 alone and in combination with a non-effective dose of oxaloacetate in an animal model of ischemic stroke. Sixty rats were subjected to a transient middle cerebral artery occlusion (MCAO). Infarct volumes were assessed by magnetic resonance imaging (MRI) before treatment administration, and 24 h and 7 days after MCAO. Brain glutamate levels were determined by in vivo MR spectroscopy (MRS) during artery occlusion (80 min) and reperfusion (180 min). GOT activity and serum glutamate concentration were analyzed during the occlusion and reperfusion period. Somatosensory test was performed at baseline and 7 days after MCAO. The three treatments tested induced a reduction in serum and brain glutamate levels, resulting in a reduction in infarct volume and sensorimotor deficit. Protective effect of rGOT1 supplemented with oxaloacetate at 7 days persists even when treatment was delayed until at least 2 h after onset of ischemia. In conclusion, our findings indicate that the combination of human rGOT1 with low doses of oxaloacetate seems to be a successful approach for stroke treatment.Ministeiro de Economía y Competitividad de EspañaXunta de Galicia /Consellería Economía IndustriaXunta de Galicia/ Consellería EducaciónInstituto de Salud Carlos IIISpanish Research Network on Cerebrovascular Diseases RETICS-INVICTUSFundación Mútua MadrileñaEuropean Union program FEDEREspaña. Ministerio de Economía y Competitividad/SAF2011-30517Xunta de Galicia /Consellería Economía Industria/10PXIB918282PRXunta de Galicia / Consellería Educación/ CN2011/010Instituto de Salud Carlos III/PI11/00909Instituto de Salud Carlos III/CP12/03121Spanish Research Network on Cerebrovascular Diseases RETICS-INVICTUS /RD12/0014Instituto de Salud Carlos III/PI10/00449Instituto de Salud Carlos III/PI12/0311