Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

The existence of periodic solutions of a two dimensional Lattice

We consider a two dimensional lattice coupled with nearest neighbor interaction potential of power type. The existence of infinite many periodic solutions is shown by using minimax methods.

MB-MDR: Model-Based Multifactor Dimensionality Reduction for detecting interactions in high-dimensional genomic data

L’anàlisi de l’efecte dels gens i els factors ambientals en el desenvolupament de malalties complexes és un gran repte estadístic i computacional. Entre les diverses metodologies de mineria de dades que s’han proposat per a l’anàlisi d’interaccions una de les més populars és el mètode Multifactor Dimensionality Reduction, MDR, (Ritchie i al. 2001). L’estratègia d’aquest mètode és reduir la dimensió multifactorial a u mitjançant l’agrupació dels diferents genotips en dos grups de risc: alt i baix. Tot i la seva utilitat demostrada, el mètode MDR té alguns inconvenients entre els quals l’agrupació excessiva de genotips pot fer que algunes interaccions importants no siguin detectades i que no permet ajustar per efectes principals ni per variables confusores. En aquest article il•lustrem les limitacions de l’estratègia MDR i d’altres aproximacions no paramètriques i demostrem la conveniència d’utilitzar metodologies parametriques per analitzar interaccions en estudis cas-control on es requereix l’ajust per variables confusores i per efectes principals. Proposem una nova metodologia, una versió paramètrica del mètode MDR, que anomenem Model-Based Multifactor Dimensionality Reduction (MB-MDR). La metodologia proposada té com a objectiu la identificació de genotips específics que estiguin associats a la malaltia i permet ajustar per efectes marginals i variables confusores. La nova metodologia s’il•lustra amb dades de l’Estudi Espanyol de Cancer de Bufeta.

Desenvolupament d'hidrogels superficials que contenen motius d'adhesió cel·lular

Projecte de recerca elaborat a partir d’una estada al Departament d’Enginyeria Química del Massachusetts Institute of Technology entre abril i octubre del 2006. S’ha dissenyat i sintetitzat uns nous films polimèrics, amb aplicacions en l’àmbit de l’enginyeria de teixits, utilitzant la tècnica anomenada iCVD (initiated Chemical Vapor Deposition), prèviament desenvolupada pel grup receptor. Es tracta d’uns hidrogels superficials de gruix controlable, que incorporen un monòmer fluorat, el qual s’havia estudiat extensament en el grup d’origen. Aquest monòmer es caracteritza per reaccionar molt fàcilment amb pèptids, de manera que aquests queden units covalentment a la superfície. Diferents estratègies pel desenvolupament d’aquests copolímers han estat avaluades, tant des del punt de vista purament sintètic com de la pròpia aplicació. Les condicions de polimerització han estat optimitzades i els hidrogels s’han caracteritzat químicament per tècniques espectroscòpiques (FTIR, XPS), i físicament per angle de contacte i el·lipsometria. D’aquesta manera, s’ha estudiat la capacitat dels hidrogels d’absorbir aigua i alhora augmentar el seu gruix, depenent de la quantitat d’agent reticulant introduït i de la incorporació del nou monòmer. A continuació, s’han optimitzat les condicions de reacció d’aquestes superfícies amb pèptids que incorporen una molècula fluorescent, la qual permet detectar fàcilment per microscòpia de fluorescència si la reacció ha tingut lloc. Una vegada la plataforma ha estat posada a punt, s’han iniciat assajos cel·lulars tant amb fibroblasts embriònics de ratolí com amb cèl·lules humanes umbilicals. Els resultats preliminars suggereixen una morfologia diferent de les cèl·lules segons si es cultiven sobre films modificats amb pèptids que promouen l’adhesió cel·lular o sobre les seves seqüències permutades no actives. Però, el més interessant és que també s’han observat certes diferències depenent si els films contenen el component hidrogel o no, fet que suggeriria un paper actiu d’aquests noves superfícies en el comportament cel·lular.

Hopf bifurcation in higher dimensional differential systems via the averaging method

"vegeu el resum a l'inici del document del fitxer adjunt."

Extracellular matrix components in peripheral nerve repair: how to affect neural cellular response and nerve regeneration?

Peripheral nerve injury is a serious problem affecting significantly patients' life. Autografts are the "gold standard" used to repair the injury gap, however, only 50% of patients fully recover from the trauma. Artificial conduits are a valid alternative to repairing peripheral nerve. They aim at confining the nerve environment throughout the regeneration process, and providing guidance to axon outgrowth. Biocompatible materials have been carefully designed to reduce inflammation and scar tissue formation, but modifications of the inner lumen are still required in order to optimise the scaffolds. Biomicking the native neural tissue with extracellular matrix fillers or coatings showed great promises in repairing longer gaps and extending cell survival. In addition, extracellular matrix molecules provide a platform to further bind growth factors that can be released in the system over time. Alternatively, conduit fillers can be used for cell transplantation at the injury site, reducing the lag time required for endogenous Schwann cells to proliferate and take part in the regeneration process. This review provides an overview on the importance of extracellular matrix molecules in peripheral nerve repair.

Superficial and deep changes of cellular mechanical properties following cytoskeleton disassembly.

The cytoskeleton, composed of actin filaments, intermediate filaments, and microtubules, is a highly dynamic supramolecular network actively involved in many essential biological mechanisms such as cellular structure, transport, movements, differentiation, and signaling. As a first step to characterize the biophysical changes associated with cytoskeleton functions, we have developed finite elements models of the organization of the cell that has allowed us to interpret atomic force microscopy (AFM) data at a higher resolution than that in previous work. Thus, by assuming that living cells behave mechanically as multilayered structures, we have been able to identify superficial and deep effects that could be related to actin and microtubule disassembly, respectively. In Cos-7 cells, actin destabilization with Cytochalasin D induced a decrease of the visco-elasticity close to the membrane surface, while destabilizing microtubules with Nocodazole produced a stiffness decrease only in deeper parts of the cell. In both cases, these effects were reversible. Cell softening was measurable with AFM at concentrations of the destabilizing agents that did not induce detectable effects on the cytoskeleton network when viewing the cells with fluorescent confocal microscopy. All experimental results could be simulated by our models. This technology opens the door to the study of the biophysical properties of signaling domains extending from the cell surface to deeper parts of the cell.

Cellular schwannomas of the intracranial and intraspinal compartment: morphological and immunological characteristics compared with classical benign schwannomas.

The concept of cellular schwannoma as an unusual benign tumor is well established for peripheral nerves but has never been tested in neurosurgical series. In order to test the validity of this concept in cranial nerves and spinal roots we performed an analysis of the clinical and morphological characteristics of 12 cellular and 166 classical benign schwannomas. Immunohistochemical detection of antigen expression in Schwann cells including proliferating cell nuclear antigen (PCNA) was also performed. This study shows that cellular schwannomas in neurosurgical series manifest at a lower age than the classical benign variant and occur mainly in the spinal roots. Mitotic activity and sinusoidal vessels appear more frequently in cellular schwannomas and constitute with high cellularity, the most valuable criteria separating both entities. The postoperative course in both types of tumors was free of metastases or sarcomatous changes. Immunoexpression of S-100 protein, vimentin, epithelial membrane antigen and glial fibrillary acidic protein is not statistically different between the two variants. In contrast, PCNA is more highly expressed in cellular schwannomas. These These results confirm the concept that cellular schwannomas are a clinico-pathological variant of benign schwannomas and provide significant support for the introduction of this entity in neurosurgical oncology.

Tumor necrosis factor (TNF) signaling, but not TWEAK (TNF-like weak inducer of apoptosis)-triggered cIAP1 (cellular inhibitor of apoptosis protein 1) degradation, requires cIAP1 RING dimerization and E2 binding.

Cellular inhibitor of apoptosis (cIAP) proteins, cIAP1 and cIAP2, are important regulators of tumor necrosis factor (TNF) superfamily (SF) signaling and are amplified in a number of tumor types. They are targeted by IAP antagonist compounds that are undergoing clinical trials. IAP antagonist compounds trigger cIAP autoubiquitylation and degradation. The TNFSF member TWEAK induces lysosomal degradation of TRAF2 and cIAPs, leading to elevated NIK levels and activation of non-canonical NF-kappaB. To investigate the role of the ubiquitin ligase RING domain of cIAP1 in these pathways, we used cIAP-deleted cells reconstituted with cIAP1 point mutants designed to interfere with the ability of the RING to dimerize or to interact with E2 enzymes. We show that RING dimerization and E2 binding are required for IAP antagonists to induce cIAP1 degradation and protect cells from TNF-induced cell death. The RING functions of cIAP1 are required for full TNF-induced activation of NF-kappaB, however, delayed activation of NF-kappaB still occurs in cIAP1 and -2 double knock-out cells. The RING functions of cIAP1 are also required to prevent constitutive activation of non-canonical NF-kappaB by targeting NIK for proteasomal degradation. However, in cIAP double knock-out cells TWEAK was still able to increase NIK levels demonstrating that NIK can be regulated by cIAP-independent pathways. Finally we show that, unlike IAP antagonists, TWEAK was able to induce degradation of cIAP1 RING mutants. These results emphasize the critical importance of the RING of cIAP1 in many signaling scenarios, but also demonstrate that in some pathways RING functions are not required.

Bargaining one-dimensional policies and the efficiency of super majority rules

We consider negotiations selecting one-dimensional policies. Individuals have single-peaked preferences, and they are impatient. Decisions arise from a bargaining game with random proposers and (super) majority approval, ranging from the simple majority up to unanimity. The existence and uniqueness of stationary subgame perfect equilibrium is established, and its explicit characterization provided. We supply an explicit formula to determine the unique alternative that prevails, as impatience vanishes, for each majority. As an application, we examine the efficiency of majority rules. For symmetric distributions of peaks unanimity is the unanimously preferred majority rule. For asymmetric populations rules maximizing social surplus are characterized.

Nano-electro-mechanical in dynamical cellular processes

Report for the scientific sojourn carried out at the Department of Structure and Constituents of Matter during 2007.The main focus of the work was on phenomena related to nano-electromechanical processes that take place on a cellular level. Additionally, it has also been performed independent work related to charge and energy transfer in bio molecules, energy transfer in coupled spin systems as well as electrodynamics of nonlinear metamaterials.

Improved temporal resolution for functional studies with reduced number of segments with three-dimensional echo planar imaging.

PURPOSE: To introduce a new k-space traversal strategy for segmented three-dimensional echo planar imaging (3D EPI) that encodes two partitions per radiofrequency excitation, effectively reducing the number excitations used to acquire a 3D EPI dataset by half. METHODS: The strategy was evaluated in the context of functional MRI applications for: image quality compared with segmented 3D EPI, temporal signal-to-noise ratio (tSNR) (the ability to detect resting state networks compared with multislice two-dimensional (2D) EPI and segmented 3D EPI, and temporal resolution (the ability to separate cardiac- and respiration-related fluctuations from the desired blood oxygen level-dependent signal of interest). RESULTS: Whole brain images with a nominal voxel size of 2 mm isotropic could be acquired with a temporal resolution under half a second using traditional parallel imaging acceleration up to 4× in the partition-encode direction and using novel data acquisition speed-up of 2× with a 32-channel coil. With 8× data acquisition speed-up in the partition-encode direction, 3D reduced excitations (RE)-EPI produced acceptable image quality without introduction of noticeable additional artifacts. Due to increased tSNR and better characterization of physiological fluctuations, the new strategy allowed detection of more resting state networks compared with multislice 2D-EPI and segmented 3D EPI. CONCLUSION: 3D RE-EPI resulted in significant increases in temporal resolution for whole brain acquisitions and in improved physiological noise characterization compared with 2D-EPI and segmented 3D EPI. Magn Reson Med 72:786-792, 2014. © 2013 Wiley Periodicals, Inc.