Motivic Zeta Functions of the Quartic and its Mirror Dual

We use a formula of Bultot to compute the motivic zeta function for the toric degeneration of the quartic K3 and its Gross-Siebert mirror dual degeneration. We check for this explicit example that the identification of the logarithm of the monodromy and the mirror dual Lefschetz operator works at an integral level

The motivic nearby fiber and degeneration of stable rationality

We prove that stable rationality specializes in regular families whose fibers are integral and have at most ordinary double points as singularities. Our proof is based on motivic specialization techniques and the criterion of Larsen and Lunts for stable rationality in the Grothendieck ring of varieties

Some multilevel methods on graded meshes

AbstractWe consider Yserentant's hierarchical basis method and multilevel diagonal scaling method on a class of refined meshes used in the numerical approximation of boundary value problems on polygonal domains in the presence of singularities. We show, as in the uniform case, that the stiffness matrix of the first method has a condition number bounded by (ln(1/h))2, where h is the meshsize of the triangulation. For the second method, we show that the condition number of the iteration operator is bounded by ln(1/h), which is worse than in the uniform case but better than the hierarchical basis method. As usual, we deduce that the condition number of the BPX iteration operator is bounded by ln(1/h). Finally, graded meshes fulfilling the general conditions are presented and numerical tests are given which confirm the theoretical bounds

Localization effects in a periodic quantum graph with magnetic field and spin-orbit interaction

A general technique for the study of embedded quantum graphs with magnetic fields and spin-orbit interaction is presented. The analysis is used to understand the contribution of Rashba constant to the extreme localization induced by magnetic field in the T3 shaped quantum graph. We show that this effect is destroyed at generic values of the Rashba constant. On the other hand, for certain combinations of the Rashba constant and the magnetic parameters another series of infinitely degenerate eigenvalues appears.Comment: 25 pages, typos corrected, references extende

Motivic Serre invariants, ramification, and the analytic Milnor fiber

We show how formal and rigid geometry can be used in the theory of complex singularities, and in particular in the study of the Milnor fibration and the motivic zeta function. We introduce the so-called analytic Milnor fiber associated to the germ of a morphism f from a smooth complex algebraic variety X to the affine line. This analytic Milnor fiber is a smooth rigid variety over the field of Laurent series C((t)). Its etale cohomology coincides with the singular cohomology of the classical topological Milnor fiber of f; the monodromy transformation is given by the Galois action. Moreover, the points on the analytic Milnor fiber are closely related to the motivic zeta function of f, and the arc space of X. We show how the motivic zeta function can be recovered as some kind of Weil zeta function of the formal completion of X along the special fiber of f, and we establish a corresponding Grothendieck trace formula, which relates, in particular, the rational points on the analytic Milnor fiber over finite extensions of C((t)), to the Galois action on its etale cohomology. The general observation is that the arithmetic properties of the analytic Milnor fiber reflect the structure of the singularity of the germ f.Comment: Some minor errors corrected. The original publication is available at http://www.springerlink.co

X-Ray Microanalysis of Calcium Containing Organelles in Resin Embedded Tissue

The localization of calcium in cell organelles at the electron microscope level is often achieved through cytochemical techniques, and verified by X-ray microanalysis. Various methods have been used to cytochemically detect calcium or calcium-binding sites : calcium loading, calcium substitution by strontium, barium, or even lead, and calcium precipitation by oxalate, phosphate, fluoride, or pyroantimonate. Their results may have heuristic value, particularly in preliminary studies of poorly known cell types. A complementary and more physiological approach is offered by quantitative measurement of the total calcium content of organelles after cryofixation. Resin embedding is less demanding than cryomicrotomy and gives better images : it can be used after cryosubstitution in the presence of oxalic acid. This technique was tested, and applied to several cell types

Early phrenic motor neuron loss and transient respiratory abnormalities following unilateral cervical spinal cord contusion

Contusion-type cervical spinal cord injury (SCI) is one of the most common forms of SCI observed in patients. In particular, injuries targeting the C3-C5 region affect the pool of phrenic motor neurons (PhMNs) that innervates the diaphragm, resulting in significant and often chronic respiratory dysfunction. Using a previously described rat model of unilateral midcervical C4 contusion with the Infinite Horizon Impactor, we have characterized the early time course of PhMN degeneration and consequent respiratory deficits following injury, as this knowledge is important for designing relevant treatment strategies targeting protection and plasticity of PhMN circuitry. PhMN loss (48% of the ipsilateral pool) occurred almost entirely during the first 24 h post-injury, resulting in persistent phrenic nerve axonal degeneration and denervation at the diaphragm neuromuscular junction (NMJ). Reduced diaphragm compound muscle action potential amplitudes following phrenic nerve stimulation were observed as early as the first day post-injury (30% of pre-injury maximum amplitude), with slow functional improvement over time that was associated with partial reinnervation at the diaphragm NMJ. Consistent with ipsilateral diaphragmatic compromise, the injury resulted in rapid, yet only transient, changes in overall ventilatory parameters measured via whole-body plethysmography, including increased respiratory rate, decreased tidal volume, and decreased peak inspiratory flow. Despite significant ipsilateral PhMN loss, the respiratory system has the capacity to quickly compensate for partially impaired hemidiaphragm function, suggesting that C4 hemicontusion in rats is a model of SCI that manifests subacute respiratory abnormalities. Collectively, these findings demonstrate significant and persistent diaphragm compromise in a clinically relevant model of midcervical contusion SCI; however, the therapeutic window for PhMN protection is restricted to early time points post-injury. On the contrary, preventing loss of innervation by PhMNs and/or inducing plasticity in spared PhMN axons at the diaphragm NMJ are relevant long-term targets

Stem Cells of the Aging Brain.

The adult central nervous system (CNS) contains resident stem cells within specific niches that maintain a self-renewal and proliferative capacity to generate new neurons, astrocytes, and oligodendrocytes throughout adulthood. Physiological aging is associated with a progressive loss of function and a decline in the self-renewal and regenerative capacities of CNS stem cells. Also, the biggest risk factor for neurodegenerative diseases is age, and current in vivo and in vitro models of neurodegenerative diseases rarely consider this. Therefore, combining both aging research and appropriate interrogation of animal disease models towards the understanding of the disease and age-related stem cell failure is imperative to the discovery of new therapies. This review article will highlight the main intrinsic and extrinsic regulators of neural stem cell (NSC) aging and discuss how these factors impact normal homeostatic functions within the adult brain. We will consider established in vivo animal and in vitro human disease model systems, and then discuss the current and future trajectories of novel senotherapeutics that target aging NSCs to ameliorate brain disease

Constructible motivic functions and motivic integration

We introduce a direct image formalism for constructible motivic functions. One deduces a very general version of motivic integration for which a change of variables theorem is proved. These constructions are generalized to the relative framework, in which we develop a relative version of motivic integration. These results have been announced in math.AG/0403349 and math.AG/0403350. Main results and statements unchanged. Many minor slips corrected and some details added.Comment: Final versio

Pathophysiological changes occurring during Escherichia coli endotoxin and Pasteurella multocida challenge in piglets: relationship with cough and temperature and predicitive value for intensity of lesions.

The aims of this study were (1) to correlate cough and body temperature (BT) with the severity of bronchopneumonia in pigs, (2) to determine whether these clinical signs can be used to early diagnose bronchopneumonia and (3) to assess the predictive values of cough and BT regarding lung lesions. Bronchopneumonia was induced by administering E. coli endotoxin (LPS) combined with Pasteurella multocida type A (PmA) in the trachea of 13 piglets. Saline-instilled negative controls (n = 8), PmA inoculated (n = 6) and LPS instilled (n = 5) groups were also constituted. Cough and BT were recorded daily while the bronchopneumonia severity was assessed using bronchoalveolar lavage fluid (BALF) cytology, cytokines and measurement of lung lesion volume. Changes in expiratory breathing pattern were also measured (Penh). The combination of LPS and PmA induced a subacute bronchopneumonia characterised by macrophage, neutrophil, and lymphocyte infiltration, changes in Penh and an increase in the mRNA level of IFN-gamma while IL8, IL-18 and TNF-alpha mRNA levels remained unchanged. The daily body weight gain of infected animals was significantly reduced. Cough and BT changes were proportional to the intensity of the lung inflammatory process, functional respiratory changes and to the extent of macroscopic lesions. When comparing the individual values of cough and BT to thresholds defined for both parameters, an early diagnosis of pneumonia was possible. Considering the pooled data of each group, it was possible to define thresholds allowing an early segregation between the groups of diseased and healthy piglets. The daily values of cough and BT were predictive for the volume of lung lesions recorded at the end of the trial. In conclusion, cough and BT appear as potential indicators for the intensity and the evolution of the respiratory disease. They also seem to be good predictors for the magnitude of lung lesions and weight gain recorded at the study endpoint