Spectra of large diluted but bushy random graphs

We compute an asymptotic expansion in $1/c$ of the limit in $n$ of the empirical spectral measure of the adjacency matrix of an Erd\H{o}s-R\'enyi random graph with $n$ vertices and parameter $c/n$. We present two different methods, one of which is valid for the more general setting of locally tree-like graphs. The second order in the expansion gives some information about the edge.Comment: 24 pages, 5 figure

Global eigenvalue fluctuations of random biregular bipartite graphs

We compute the eigenvalue fluctuations of uniformly distributed random biregular bipartite graphs with fixed and growing degrees for a large class of analytic functions. As a key step in the proof, we obtain a total variation distance bound for the Poisson approximation of the number of cycles and cyclically non-backtracking walks in random biregular bipartite graphs, which might be of independent interest. As an application, we translate the results to adjacency matrices of uniformly distributed random regular hypergraphs.Comment: 45 pages, 5 figure

On the spectrum of Random Simplicial Complexes in Thermodynamic Regime

Linial-Meshulam complex is a random simplicial complex on $n$ vertices with a complete $(d-1)$-dimensional skeleton and $d$-simplices occurring independently with probability p. Linial-Meshulam complex is one of the most studied generalizations of the Erd\H{o}s-R{\'e}nyi random graph in higher dimensions. In this paper, we discuss the spectrum of adjacency matrices of the Linial-Meshulam complex when $np \rightarrow \lambda$. We prove the existence of a non-random limiting spectral distribution(LSD) and show that the LSD of signed and unsigned adjacency matrices of Linial-Meshulam complex are reflections of each other. We also show that the LSD is unsymmetric around zero, unbounded and under the normalization $1/\sqrt{\lambda d}$, converges to standard semicircle law as $\lambda \rightarrow \infty$. In the later part of the paper, we derive the local weak limit of the line graph of the Linial-Meshulam complex and study its consequence on the continuous part of the LSD.Comment: 32 Pages, 7 Figures, 1 Tabl

Neural Circuitry Deficits Associated With Dysfunctional Myelin

In the current study, we have generated mutant mice that lack Claudin 11 (Cldn11) tight junctions in CNS myelin sheaths. In myelin sheaths, Cldn11 forms tight junctions located along the outer and inner edges of the membrane spiral, preventing ions and small molecules from entering the intramyelinic space. The function of Cldn11 tight junctions is to improve the passive properties of the myelin membrane, by increasing membrane resistance and reducing capacitance, thereby improving the speed of saltatory conduction. In the absence of Cldn11, conduction velocity is slowed, most dramatically in small diameter myelinated fibers, somewhat analogous to reducing myelin thickness. Notably, the absence of Cldn11 is without degenerative myelin pathology, enabling direct study on the impact of dysfunctional myelin on neural processing. Undoubtedly, slowed conduction velocity along myelinated axons increases temporal dispersion and, consequently, degrades information transfer between neural circuits. Herein, this dissertation work explores the impact of dysfunctional myelin on neural processing in the conserved integration circuit of the auditory brainstem. We find that dysfunctional myelin alters neural processing, generating an inability to lateralize sound sources on the azimuth plane. Extrapolating this information to higher order circuitry within the cortex, we find that dysfunctional myelin generates a disconnection between brain regions, manifesting in behavioral abnormalities and alteration in neurotransmitter levels. Together, these data demonstrate that non-degenerative changes in myelin membrane passive properties can lead to neurochemistry changes that perturb behavior/perception. Second, they have important implications for the etiology of behavioral disorders in general, and more specifically for the behavioral components of hypomyelinating and demyelinating diseases like multiple sclerosis

Mytilus edulis haemocytes variability : technique, individual and environment

The widely distributed marine bivalve Mytilus edulis is used as a sentinel organism for ecological and toxicological assessments. As a filter feeder, it has the potential to bio-accumulate pollutants. It has been assumed that the cell concentration and cell type ratio of its circulating immune cells, haemocytes, could become complementary sub-lethal indicators of toxicology. These two parameters are respectively referred to as total haemocyte count (THC) and differential cell count (DCC). This study examines these commonly used methods, quantifies their limitations, and develops alternative techniques. The circulating immune cells are investigated to assess their fluctuations. Finally, impacts of environmental challenges on the circulating haemocytes are examined. Despite its importance in the field of Mytilus edulis immunology, THC evaluation is present in only 20% of publications in this field, and DCC in 10%. Ultimately, only 9% of papers consider both THC and DCC before further analyses. The remaining studies disregard THC and DDC, or regard these parameters as being constant and homogenous in M. edulis populations. This study initially quantifies the systematic error induced by sampling, and suggests improvements. For example, a systematic error of 26% is attributed to the use of low precision syringes, and can be reduced with use of higher precision sampling equipment. While the systematic errors in visual count and image analysis of THC and DCC evaluations are equivalent, the computerised methods allow the throughput of larger data sets, reduce workload, and avoid tedious eye counts. Flow cytometry was found to be the most accurate method in THC and DCC evaluation. Furthermore, repeated bleedings influence DCC, triggering the decrease of circulating eosinophils (up to 20%) and the increase of hyaline cells (up to 30%). To mitigate this reaction to sampling, a maximum volume of 50μl using a permanent cannulation is recommended. However, even with improved methods reducing systematic error by half, this study still reports variations as high as 20-fold in the haemocyte concentration in populations of healthy individuals. In addition, over a 2-hour period in a single cannulated individual, fluctuation of the DDC is observed to be as high as 30% for eosinophils, 10% for hyaline cells, and 20% for basophils. These measured variations are explained by haemocyte reservoirs in the tissues. Eosinophils are found in large numbers in epithelial association in the gills, guts and in the mantle, where their numbers have been evaluated at 3x10 7 As a case study, Mytilus edulis challenged with barium sulphate smothering, used by the oil industry in drilling muds, shows gill damage and their subsequent infiltration by eosinophils. In bacterial outbreak, basophilic cells are observed to infiltrate the tissue surrounding the stomach and eosinophils are depleted from the epithelium of the digestive tissues. THC is 10-fold lower than in healthy organisms and eosinophils are depleted from the haemolymph. cells. In conclusion, the THC and DDC methods are shown to be unreliable despite the use of more accurate methods. In addition, Mytilus edulis circulating haemocytes present large variations and the assumption of their homogeneity in terms of time, individuals or methods used cannot be made. These results challenge the conclusions of many past publications regarding causalities established between potential stresses and measured effects. Further research is necessary to understand the mechanisms regulating the circulating haemocytes, the inter-individual variability and to improve investigation methods

Superficies antiadherentes en aplicaciones que requieren contacto prolongado con fluidos

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Químicas, leída el 26-01-2023The aim of this doctoral thesis is to design and develop polymeric surfaces that repel liquids of different nature even in conditions of total and prolonged contact with the fluid, as well as to understand the structural parameters that determine non-stick properties. The objective is to develop a method to generate these surfaces that is easy, fast and scalable at an industrial level. In this doctoral thesis, the obtaining of superhydrophobic, omniphobic and slippery surfaces is explored, using Nature as a source of inspiration for their design.The non-adherence associated with polymeric surfaces is a useful feature to meet technological challenges in many sectors, since it can provide properties such as self-cleaning or low friction, prevent corrosion or surface degradation, ice accumulation, the proliferation of bacteria and biofouling in general. The development of non-stick properties on a surface implies the generation of roughness on a micrometric scale and the use of low surface tension materials. Polymers are presented in this doctoral thesis as materials whose characteristics are favorable for developing roughness generation methodologies in a sustainable, versatile and scalable way. A top-down roughness generation method was developed in two steps: swelling-coagulation, which consists of immersing the polymeric film in a solvent that swells the polymer and subsequent immersion in a coagulant that freeze the swollen state. It is an easy, fast and scalable method with which the inherent roughness of the material was obtained. With the roughness generation method, polymeric surfaces structured at the microscale and hierarchical at the micro and nanoscale were obtained, with properties ranging from hydrophobicity to superhydrophobicity...El objetivo principal de esta tesis doctoral es diseñar y desarrollar superficies poliméricas que repelan líquidos de diferente naturaleza incluso en condiciones de contacto total y prolongado con el fluido, así como comprender los parámetros estructurales que determinan la antiadherencia superficial. Se persigue idear un método para generar estas superficies que sea fácil, rápido y escalable a nivel industrial. En esta tesis doctoral se explora la obtención de superficies superhidrófobas, omnífobas y superdeslizantes, recurriendo a la Naturaleza como fuente de inspiración para su diseño. La antiadherencia asociada a superficies es una característica útil para afrontar retos tecnológicos en multitud de sectores, ya que puede proporcionar propiedades tales como la autolimpieza o la baja fricción, evitar la corrosión o degradación superficial, la acumulación de hielo, la proliferación de bacterias y el bioensuciamiento en general. El desarrollo de propiedades antiadherentes en una superficie implica la generación de rugosidad en escala micrométrica y la utilización de materiales de baja tensión superficial. Los polímeros se presentan en esta tesis doctoral como materiales cuyas características son favorables para desarrollar metodologías de generación de rugosidad de forma sostenible, versátil y escalable. Se desarrolló un método de generación de rugosidad top-down en dos pasos: Hinchamiento-Coagulación, que consiste en la inmersión de la película polimérica en un disolvente que hincha el polímero y la consiguiente inmersión en un coagulante que congela el estado hinchado. Se trata de un método fácil, rápido y escalable con el que se obtuvo rugosidad inherente al material. Con el método de generación de rugosidad se obtuvieron superficies poliméricas estructuradas en la microescala y jerarquizadas en la micro y la nanoescala con propiedades que fueron desde la hidrofobia hasta la superhidrofobia...Fac. de Ciencias QuímicasTRUEunpu