Resurgence of inner solutions for perturbations of the McMillan map

A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove here all the results relative to these equations which are necessary to complete the proof of the main result of [MSS09]. The present work relies on ideas from resurgence theory: we describe the formal solutions, study the analyticity of their Borel transforms and use ´Ecalle’s alien derivations to measure the discrepancy between different Borel-Laplace sums.

Estudio prospectivo de eficacia y seguridad de pegaptanib sodio en el tratamiento primario del edema macular secundario a trombosis venosa de la retina

Objectiu:Avaluar l’eficàcia i seguretat de pegaptanib de sodi en el tractament de l’edema macular secundari a obstrucció venosa de la retina (OVR). Mètode: Estudi prospectiu de 16 pacients amb edema macular secundari a OVR tractats mitjançant injeccions intravítrees de pegaptanib de sodi 1mg (0’05ml) a demanda amb un període de seguiment mínim de 6 mesos. Resultat: Millora significativa de l’agudesa visual i del perfil foveal en els nostres pacients. No alarmes de seguretat noves. Conclusions: Pegaptanib de sodi sembla proporcionar beneficis anatòmics i funcionals en el tractament de l’edema macular secundari a trombosis venosa de la retina.

Estudio de la agudeza visual final en correlación con variables anatómicas y funcionales objetivas en pacientes con desprendimiento de retina primario

Estudi de cohort de pacients amb despreniment de retina primaris, intervinguts per vitrectomia posterior i agudesa visual final superior a 0,1. Es recullen 23 pacients i es practica un tall de mesura longitudinal a la cohort, recollint paràmetres demogràfics, agudesa visual final, tomografia de coherència òptica i electrorretinograma multifocal. S'estudien associacions entre l'agudesa visual final i les proves objectives anatòmiques i funcionals.

Factores determinantes del tiempo de demora y resultados funcionales en pacientes con desprendimiento de retina rhegmatógeno primario tratado mediante vitrectomía vía pars plana

Propósito: Determinar, en los pacientes afectados de desprendimiento de retina rhegmatógeno primario que acudieron a nuestro centro, el tiempo de demora entre la aparición de los primeros síntomas y la visita con el cirujano. Los objetivos secundarios son describir los factores que han influido en este tiempo de demora, determinar la relación existente entre el tiempo de evolución del desprendimiento rhegmatógeno de retina primario, el estado de la mácula y el resultado funcional tras la cirugía, y describir la sintomatología referida por los pacientes. Material y Método: Estudio descriptivo prospectivo de 59 ojos de 59 pacientes con desprendimiento de retina rhegmatógeno primario que acudieron al servicio de oftalmología del hospital Vall d’Hebron entre marzo y junio del 2008. Se realizó una anamnesis y exploración oftalmológica detallada a su llegada, fueron sometidos a cirugía mediante vitrectomía vía pars plana y se les realizó un seguimiento mínimo de 6 meses determinando los resultados funcionales de la cirugía. Resultados: El tiempo de demora medio desde la aparición de los síntomas hasta la primera consulta con el facultativo fue de 4,10 días. La media del tiempo de evolución del desprendimiento rhegmatógeno de retina fue de 17,03 días. Un 84,1% de los pacientes con la mácula desprendida tenían un tiempo de evolución menor o igual a 15 días y un 15,9% un tiempo de evolución mayor a 15 días. La agudeza visual media postoperatoria de los pacientes con la mácula aplicada fue de 0,55 en escala decimal, en los pacientes con la mácula afectada de menos de 15 días de evolución fue de 0,41, y en los pacientes con la mácula afectada de más de 15 días de evolución fue de 0,33. El síntoma más frecuente fue la visión borrosa (98,3%), seguido de miodesopsias (28,8%). Conclusiones: El tiempo de demora entre la aparición de los primeros síntomas del DRR y la visita con el cirujano es superior desde la remisión al cirujano por parte del facultativo que desde la aparición de síntomas y consulta con el facultativo por el paciente. La subestimación de la gravedad por parte del paciente es la causa de demora referida más frecuente. Los pacientes con un mayor tiempo de evolución tienen un mayor porcentaje de afectación macular. Los pacientes con la mácula aplicada han tenido un mejor resultado funcional tras la cirugía del DRR que los pacientes con la mácula desprendida.

Biomarcadors oculars en la malaltia d’Alzheimer precoç: Estudi de la capa de fibres nervioses i cèl•lules ganglionars de la retina i alteracions pupil•lars.

Actualment, no existeix un diagnòstic de certesa in vivo per la malaltia d’Alzheimer (MA), i l’ull podria aportar biomarcadors de la malaltia. 15 pacients amb MA i 15 controls es van sotmetre a un test d’hipersensibilitat a la pilocarpina i a OCT de capa de fibres nervioses (CFNR) i de cèl•lules ganglionars retinianes (CCG). Es trobà major hipersensibilitat a la pilocarpina i major gruix de la CCG en el grup de pacients. També una tendència a l’aprimament de la CFNR en estadis avançats de la MA. Aquestes proves representen un camí esperançador per trobar un test diagnòstic de la MA.

Distorted-wave calculation of cross sections for inner-shell ionization by electron and positron impact

The relativistic distorted-wave Born approximation is used to calculate differential and total cross sections for inner shell ionization of neutral atoms by electron and positron impact. The target atom is described within the independent-electron approximation using the self-consistent Dirac-Fock-Slater potential. The distorting potential for the projectile is also set equal to the Dirac-Fock-Slater potential. For electrons, this guarantees orthogonality of all the orbitals involved and simplifies the calculation of exchange T-matrix elements. The interaction between the projectile and the target electrons is assumed to reduce to the instantaneous Coulomb interaction. The adopted numerical algorithm allows the calculation of differential and total cross sections for projectiles with kinetic energies ranging from the ionization threshold up to about ten times this value. Algorithm accuracy and stability are demonstrated by comparing differential cross sections calculated by our code with the distorting potential set to zero with equivalent results generated by a more robust code that uses the conventional plane-wave Born approximation. Sample calculation results are presented for ionization of K- and L-shells of various elements and compared with the available experimental data.

Study of inner ear and lateral line hair cell regeneration

Death of sensory hair cells in the inner ear results in two global health problems that millions of people around the world suffer: hearing loss and balance disorders. Hair cells convert sound vibrations and head movements into electrical signals that are conveyed to the brain, and as a result of aging, exposure to noise, modern drugs or genetic predisposition, hair cells die. In mammals, the great majority of hair cells are produced during embryogenesis, and hair cells that are lost after birth are not replaceable. However, in the last decades, researches have shown some model organisms that retain the ability to regenerate hair cells damaged after embryogenesis, such as Zebrafish and chicken, providing clues as to the cellular and molecular mechanisms that may block hair cell regeneration in mammals. This discovery initiated a search for methods to stimulate regeneration or replacement of hair cells in mammals, a search that, if fruitful, will revolutionize the treatment of hearing loss and balance disorders. One aim of my project is to study the role of retinoic acid in adult Zebrafish and in mice, which is a metabolite of vitamin A known as an essential molecule to activate hair cell regeneration after cells damaged in Zebrafish embryo. We want to study important genes involved in retinoic acid pathway, such as Aldh1a3 and RARs genes, to check what their role is in the inner ear of adult Zebrafish and compare result obtained in the inner ear of mice. On the other hand, Zebrafish lateral line contains neuromast, which are formed by the same structure than the inner ear: hair cells surrounded by supporting cells and neurons. The lateral line is a structure below the skin's surface that makes easier to damage hair cells to study their regeneration. For that reason, another aim of my project is to study how Sox2 and Atoh1, essential genes during the inner ear development, change their expression during hair cell regeneration in the lateral line. In my project, the most important concepts related to Zebrafish world are explained in order to understand why we have studied this animal and these essential genes. Then, techniques that we used are explained, with their protocol attached in the annexes. Finally, results of my project are shown, but many of them were not expected and they would be needed to follow studying.

N-myc controls proliferation, morphogenesis, and patterning of the inner ear

Myc family members play crucial roles in regulating cell proliferation, size, and differentiation during organogenesis. Both N-myc and c-myc are expressed throughout inner ear development. To address their function in the mouse inner ear, we generated mice with conditional deletions in either N-myc or c-myc. Loss of c-myc in the inner ear causes no apparent defects, whereas inactivation of N-myc results in reduced growth caused by a lack of proliferation. Reciprocally, the misexpression of N-myc in the inner ear increases proliferation. Morphogenesis of the inner ear in N-myc mouse mutants is severely disturbed, including loss of the lateral canal, fusion of the cochlea with the sacculus and utriculus, and stunted outgrowth of the cochlea. Mutant cochleas are characterized by an increased number of cells exiting the cell cycle that express the cyclin-dependent kinase inhibitor p27Kip1 and lack cyclin D1, both of which control the postmitotic state of hair cells. Analysis of different molecular markers in N-myc mutant ears reveals the development of a rudimentary organ of Corti containing hair cells and the underlying supporting cells. Differentiated cells, however, fail to form the highly ordered structure characteristic for the organ of Corti but appear as rows or clusters with an excess number of hair cells. The Kölliker's organ, a transient structure neighboring the organ of Corti and a potential source of ectopic hair cells, is absent in the mutant ears. Collectively, our data suggest that N-myc regulates growth, morphogenesis, and pattern formation during the development of the inner ear.

Id Gene regulation and function in the prosensory domains of the chicken inner ear: a link between Bmp Signaling and Atoh1

Bone morphogenetic proteins (Bmps) regulate the expression of the proneural gene Atoh1 and the generation of hair cells in the developing inner ear. The present work explored the role of Inhibitor of Differentiation genes (Id1-3) in this process. The results show that Id genes are expressed in the prosensory domains of the otic vesicle, along with Bmp4 and Bmp7. Those domains exhibit high levels of the phosphorylated form of Bmp-responding R-Smads (P-Smad1,5,8), and of Bmp-dependent Smad transcriptional activity as shown by the BRE-tk-EGFP reporter. Increased Bmp signaling induces the expression of Id1-3 along with the inhibition of Atoh1. Conversely, the Bmp antagonist Noggin or the Bmp-receptor inhibitor Dorsomorphin elicit opposite effects, indicating that Bmp signaling is necessary for Id expression and Atoh1 regulation in the otocyst. The forced expression of Id3 is sufficient to reduce Atoh1 expression and to prevent the expression of hair cell differentiation markers. Together, these results suggest that Ids are part of the machinery that mediates the regulation of hair cell differentiation exerted by Bmps. In agreement with that, during hair cell differentiation Bmp4 expression, P-Smad1,5,8 levels and Id expression are downregulated from hair cells. However, Ids are also downregulated from the supporting cells which contrarily to hair cells exhibit high levels of Bmp4 expression, P-Smad1,5,8, and BRE-tk-EGFP activity, suggesting that in these cells Ids escape from Bmp/Smad signaling. The differential regulation of Ids in time and space may underlie the multiple functions of Bmp signaling during sensory organ development.

A unique role for Kv3 voltage-gated potassium channels in starburst amacrine cell signaling in mouse retina

Direction-selective retinal ganglion cells show an increased activity evoked by light stimuli moving in the preferred direction. This selectivity is governed by direction-selective inhibition from starburst amacrine cells occurring during stimulus movement in the opposite or null direction. To understand the intrinsic membrane properties of starburst cells responsible for direction-selective GABA release, we performed whole-cell recordings from starburst cells in mouse retina. Voltage-clamp recordings revealed prominent voltage-dependent K+ currents. The currents were mostly blocked by 1 mm TEA, activated rapidly at voltages more positive than -20 mV, and deactivated quickly, properties reminiscent of the currents carried by the Kv3 subfamily of K+ channels. Immunoblots confirmed the presence of Kv3.1 and Kv3.2 proteins in retina and immunohistochemistry revealed their expression in starburst cell somata and dendrites. The Kv3-like current in starburst cells was absent in Kv3.1-Kv3.2 knock-out mice. Current-clamp recordings showed that the fast activation of the Kv3 channels provides a voltage-dependent shunt that limits depolarization of the soma to potentials more positive than -20 mV. This provides a mechanism likely to contribute to the electrical isolation of individual starburst cell dendrites, a property thought essential for direction selectivity. This function of Kv3 channels differs from that in other neurons where they facilitate high-frequency repetitive firing. Moreover, we found a gradient in the intensity of Kv3.1b immunolabeling favoring proximal regions of starburst cells. We hypothesize that this Kv3 channel gradient contributes to the preference for centrifugal signal flow in dendrites underlying direction-selective GABA release from starburst amacrine cells.

Insertion of a malE B-Galactosidase fusion protein into the envelope of Escherichia coli disrupts biogenesis of outer membrane proteins and processing of inner membrane proteins

The synthesis of a membrane-bound MalE ,B-galactosidase hybrid protein, when induced by growth of Escherichia coli on maltose, leads to inhibition of cell division and eventually a reduced rate of mass increase. In addition, the relative rate of synthesis of outer membrane proteins, but not that of inner membrane proteins, was reduced by about 50%o. Kinetic experiments demonstrated that this reduction coincided with the period of maximum synthesis of the hybrid protein (and another maltose-inducible protein, LamB). The accumulation of this abnormal protein in the envelope therefore appeared specifically to inhibit the synthesis, the assembly of outer membrane proteins, or both, indicating that the hybrid protein blocks some export site or causes the sequestration of some limiting factor(s) involved in the export process. Since the MalE protein is normally located in the periplasm, the results also suggest that the synthesis of periplasmic and outer membrane proteins may involve some steps in common. The reduced rate of synthesis of outer membrane proteins was also accompanied by the accumulation in the envelope of at least one outer membrane protein and at least two inner membrane proteins as higher-molecular-weight forms, indicating that processing (removal of the N-terminal signal sequence) was also disrupted by the presence of the hybrid protein. These results may indicate that the assembly of these membrane proteins is blocked at a relatively late step rather than at the level of primary recognition of some site by the signal sequence. In addition, the results suggest that some step common to the biogenesis of quite different kinds of envelope protein is blocked by the presence of the hybrid protein.

On the injectivity of the Kudla-Millson lift and surjectivity of the Borcherds lift

We consider the Kudla-Millson lift from elliptic modular forms of weight (p+q)/2 to closed q-forms on locally symmetric spaces corresponding to the orthogonal group O(p,q). We study the L²-norm of the lift following the Rallis inner product formula. We compute the contribution at the Archimedian place. For locally symmetric spaces associated to even unimodular lattices, we obtain an explicit formula for the L²-norm of the lift, which often implies that the lift is injective. For O(p,2) we discuss how such injectivity results imply the surjectivity of the Borcherds lift.

Preparació i caracterització de materials mesoporosos en sistemes tensioactius

Estudi elaborat a partir d’una estada a la Universitat Nacional de Yokohama des de maig fins a mitjans de juny del 2006. S'ha estudiat el comportament fàssic i la preparació de sílica mesoporosa pels nous tensioactius fluorats d'estructura C8F17SO2(C3H7)N(C2H4O)nH (abreujat C8F17(EO)n. El tensioactiu C8F17(EO)n forma micel•les allargades i cristalls líquids en aigua, i per tant pot ser adequat per a la preparació de materials mesoporosos. Sílica mesoestructurada es va preparar pel mètode de precipitació per autoagregació cooperativa. Un estudi sistemàtic es va realitzar, investigant la influència de les concentracions de tensioactiu i precursor (TEOS), l’efecte del pH i de la longitud de cadena de poliòxid d’etilè. Els materials es van caracteritzar per raigs X a angle petit (SAXS), sorció de nitrògen i TEM. Els materials obtinguts presenten diàmetres de por petits i parets de por gruixudes. A més, aquests materials posseeixen altes superfícies específiques, que s’han obtingut emprant concentracions de tensioactiu petites, produint parets de por robustes sense microporositat significativa. La superfície específica es manté durant el procés de calcinació, malgrat un petit encongiment degut a l’entrecreuament de la sílica. Els materials de sílica obtinguts han mostrat ser significativament més robustos que altres materials similars descrits a la bibliografia, com la sílica MCM-41.