A note on semi-bent functions with multiple trace terms and hyperelliptic curves

Semi-bent functions with even number of variables are a class of important Boolean functions whose Hadamard transform takes three values. In this note we are interested in the property of semi-bentness of Boolean functions defined on the Galois field $F_{2^n}$ (n even) with multiple trace terms obtained via Niho functions and two Dillon-like functions (the first one has been studied by Mesnager and the second one have been studied very recently by Wang, Tang, Qi, Yang and Xu). We subsequently give a connection between the property of semi-bentness and the number of rational points on some associated hyperelliptic curves. We use the hyperelliptic curve formalism to reduce the computational complexity in order to provide a polynomial time and space test leading to an efficient characterization of semi-bentness of such functions (which includes an efficient characterization of the hyperbent functions proposed by Wang et al.). The idea of this approach goes back to the recent work of Lisonek on the hyperbent functions studied by Charpin and Gong

A new class of hyper-bent functions and Kloosterman sums

This paper is devoted to the characterization of hyper-bent functions. Several classes of hyper-bent functions have been studied, such as Charpin and Gong\u27s $\sum\limits_{r\in R}\mathrm{Tr}_{1}^{n} (a_{r}x^{r(2^m-1)})$ and Mesnager\u27s $\sum\limits_{r\in R}\mathrm{Tr}_{1}^{n}(a_{r}x^{r(2^m-1)}) +\mathrm{Tr}_{1}^{2}(bx^{\frac{2^n-1}{3}})$, where $R$ is a set of representations of the cyclotomic cosets modulo $2^m+1$ of full size $n$ and $a_{r}\in \mathbb{F}_{2^m}$. In this paper, we generalize their results and consider a class of Boolean functions of the form $\sum_{r\in R}\sum_{i=0}^{2}Tr^n_1(a_{r,i}x^{r(2^m-1)+\frac{2^n-1}{3}i}) +Tr^2_1(bx^{\frac{2^n-1}{3}})$, where $n=2m$, $m$ is odd, $b\in\mathbb{F}_4$, and $a_{r,i}\in \mathbb{F}_{2^n}$. With the restriction of $a_{r,i}\in \mathbb{F}_{2^m}$, we present the characterization of hyper-bentness of these functions with character sums. Further, we reformulate this characterization in terms of the number of points on hyper-elliptic curves. For some special cases, with the help of Kloosterman sums and cubic sums, we determine the characterization for some hyper-bent functions including functions with four, six and ten traces terms. Evaluations of Kloosterman sums at three general points are used in the characterization. Actually, our results can generalized to the general case: $a_{r,i}\in \mathbb{F}_{2^n}$. And we explain this for characterizing binomial, trinomial and quadrinomial hyper-bent functions

Desmoglein 2 is less important than desmoglein 3 for keratinocyte cohesion.

Desmosomes provide intercellular adhesive strength required for integrity of epithelial and some non-epithelial tissues. Within the epidermis, the cadherin-type adhesion molecules desmoglein (Dsg) 1-4 and desmocollin (Dsc) 1-3 build the adhesive core of desmosomes. In keratinocytes, several isoforms of these proteins are co-expressed. However, the contribution of specific isoforms to overall cell cohesion is unclear. Therefore, in this study we investigated the roles of Dsg2 and Dsg3, the latter of which is known to be essential for keratinocyte adhesion based on its autoantibody-induced loss of function in the autoimmune blistering skin disease pemphigus vulgaris (PV). The pathogenic PV antibody AK23, targeting the Dsg3 adhesive domain, led to profound loss of cell cohesion in human keratinocytes as revealed by the dispase-based dissociation assays. In contrast, an antibody against Dsg2 had no effect on cell cohesion although the Dsg2 antibody was demonstrated to interfere with Dsg2 transinteraction by single molecule atomic force microscopy and was effective to reduce cell cohesion in intestinal epithelial Caco-2 cells which express Dsg2 as the only Dsg isoform. To substantiate these findings, siRNA-mediated silencing of Dsg2 or Dsg3 was performed in keratinocytes. In contrast to Dsg3-depleted cells, Dsg2 knockdown reduced cell cohesion only under conditions of increased shear. These experiments indicate that specific desmosomal cadherins contribute differently to keratinocyte cohesion and that Dsg2 compared to Dsg3 is less important in this context

Triplicate functions

We define the class of triplicate functions as a generalization of 3-to-1 functions over $\mathbb {F}_{2^{n}}$ for even values of n. We investigate the properties and behavior of triplicate functions, and of 3-to-1 among triplicate functions, with particular attention to the conditions under which such functions can be APN. We compute the exact number of distinct differential sets of power APN functions and quadratic 3-to-1 functions; we show that, in this sense, quadratic 3-to-1 functions are a generalization of quadratic power APN functions for even dimensions, in the same way that quadratic APN permutations are generalizations of quadratic power APN functions for odd dimensions. We show that quadratic 3-to-1 APN functions cannot be CCZ-equivalent to permutations in the case of doubly-even dimensions. We compute a lower bound on the Hamming distance between any two quadratic 3-to-1 APN functions, and give an upper bound on the number of such functions over $\mathbb {F}_{2^{n}}$ for any even n. We survey all known infinite families of APN functions with respect to the presence of 3-to-1 functions among them, and conclude that for even n almost all of the known infinite families contain functions that are quadratic 3-to-1 or are EA-equivalent to quadratic 3-to-1 functions. We also give a simpler univariate representation in the case of singly-even dimensions of the family recently introduced by Göloglu than the ones currently available in the literature. We conduct a computational search for quadratic 3-to-1 functions in even dimensions n ≤ 12. We find six new APN instances for n = 10, and the first sporadic APN instance for n = 12 since 2006. We provide a list of all known 3-to-1 APN functions for n ≤ 12.publishedVersio

Spatial-Longitudinal Bent-Cable Model with an Application to Atmospheric CFC Data

Spatial data (also called georeferenced data) arise in a wide range of scientific studies, including geography, agriculture, criminology, geology, urban and regional economics. The underlying spatial effects – the measurement error caused by any spatial pattern embedded in data – may affect both the validity and robustness of traditional descriptive and inferential techniques. Therefore, it is of paramount importance to take into account spatial effects when analysing spatially dependent data. In particular, addressing the spatial association among attribute values observed at different locations and the systematic variation of phenomena by locations are the two major aspects of modelling spatial data. The bent-cable is a parametric regression model to study data that exhibits a trend change over time. It comprises two linear segments to describe the incoming and outgoing phases, joined by a quadratic bend to model the transition period. For spatial longitudinal data, measurements taken over time are nested within spatially dependent locations. In this thesis, we extend the existing longitudinal bent-cable regression model to handle spatial effects. We do so in a hierarchical Bayesian framework by allowing the error terms to be correlated across space. We illustrate our methodology with an application to atmospheric chlorofluorocarbon (CFC) data. We also present a simulation study to demonstrate the performance of our proposed methodology. Although we have tailored our work for the CFC data, our modelling framework may be applicable to a wide variety of other situations across the range of the econometrics, transportation, social, health and medical sciences. In addition, our methodology can be further extended by taking into account interaction between temporal and spatial effects. With the current model, this could be done with a spatial correlation structure that changes as a function of time

Enhanced clustering analysis pipeline for performance analysis of parallel applications

Clustering analysis is widely used to stratify data in the same cluster when they are similar according to the specific metrics. We can use the cluster analysis to group the CPU burst of a parallel application, and the regions on each process in-between communication calls or calls to the parallel runtime. The resulting clusters obtained are the different computational trends or phases that appear in the application. These clusters are useful to understand the behavior of the computation part of the application and focus the analyses on those that present performance issues. Although density-based clustering algorithms are a powerful and efficient tool to summarize this type of information, their traditional user-guided clustering methodology has many shortcomings and deficiencies in dealing with the complexity of data, the diversity of data structures, high-dimensionality of data, and the dramatic increase in the amount of data. Consequently, the majority of DBSCAN-like algorithms have weaknesses to handle high-dimensionality and/or Multi-density data, and they are sensitive to their hyper-parameter configuration. Furthermore, extracting insight from the obtained clusters is an intuitive and manual task. To mitigate these weaknesses, we have proposed a new unified approach to replace the user-guided clustering with an automated clustering analysis pipeline, called Enhanced Cluster Identification and Interpretation (ECII) pipeline. To build the pipeline, we propose novel techniques including Robust Independent Feature Selection, Feature Space Curvature Map, Organization Component Analysis, and hyper-parameters tuning to feature selection, density homogenization, cluster interpretation, and model selection which are the main components of our machine learning pipeline. This thesis contributes four new techniques to the Machine Learning field with a particular use case in Performance Analytics field. The first contribution is a novel unsupervised approach for feature selection on noisy data, called Robust Independent Feature Selection (RIFS). Specifically, we choose a feature subset that contains most of the underlying information, using the same criteria as the Independent component analysis. Simultaneously, the noise is separated as an independent component. The second contribution of the thesis is a parametric multilinear transformation method to homogenize cluster densities while preserving the topological structure of the dataset, called Feature Space Curvature Map (FSCM). We present a new Gravitational Self-organizing Map to model the feature space curvature by plugging the concepts of gravity and fabric of space into the Self-organizing Map algorithm to mathematically describe the density structure of the data. To homogenize the cluster density, we introduce a novel mapping mechanism to project the data from the non-Euclidean curved space to a new Euclidean flat space. The third contribution is a novel topological-based method to study potentially complex high-dimensional categorized data by quantifying their shapes and extracting fine-grain insights from them to interpret the clustering result. We introduce our Organization Component Analysis (OCA) method for the automatic arbitrary cluster-shape study without an assumption about the data distribution. Finally, to tune the DBSCAN hyper-parameters, we propose a new tuning mechanism by combining techniques from machine learning and optimization domains, and we embed it in the ECII pipeline. Using this cluster analysis pipeline with the CPU burst data of a parallel application, we provide the developer/analyst with a high-quality SPMD computation structure detection with the added value that reflects the fine grain of the computation regions.El análisis de conglomerados se usa ampliamente para estratificar datos en el mismo conglomerado cuando son similares según las métricas específicas. Nosotros puede usar el análisis de clúster para agrupar la ráfaga de CPU de una aplicación paralela y las regiones en cada proceso intermedio llamadas de comunicación o llamadas al tiempo de ejecución paralelo. Los clusters resultantes obtenidos son las diferentes tendencias computacionales o fases que aparecen en la solicitud. Estos clusters son útiles para entender el comportamiento de la parte de computación del aplicación y centrar los análisis en aquellos que presenten problemas de rendimiento. Aunque los algoritmos de agrupamiento basados en la densidad son una herramienta poderosa y eficiente para resumir este tipo de información, su La metodología tradicional de agrupación en clústeres guiada por el usuario tiene muchas deficiencias y deficiencias al tratar con la complejidad de los datos, la diversidad de estructuras de datos, la alta dimensionalidad de los datos y el aumento dramático en la cantidad de datos. En consecuencia, el La mayoría de los algoritmos similares a DBSCAN tienen debilidades para manejar datos de alta dimensionalidad y/o densidad múltiple, y son sensibles a su configuración de hiperparámetros. Además, extraer información de los clústeres obtenidos es una forma intuitiva y tarea manual Para mitigar estas debilidades, hemos propuesto un nuevo enfoque unificado para reemplazar el agrupamiento guiado por el usuario con un canalización de análisis de agrupamiento automatizado, llamada canalización de identificación e interpretación de clúster mejorada (ECII). para construir el tubería, proponemos técnicas novedosas que incluyen la selección robusta de características independientes, el mapa de curvatura del espacio de características, Análisis de componentes de la organización y ajuste de hiperparámetros para la selección de características, homogeneización de densidad, agrupación interpretación y selección de modelos, que son los componentes principales de nuestra canalización de aprendizaje automático. Esta tesis aporta cuatro nuevas técnicas al campo de Machine Learning con un caso de uso particular en el campo de Performance Analytics. La primera contribución es un enfoque novedoso no supervisado para la selección de características en datos ruidosos, llamado Robust Independent Feature. Selección (RIFS).Específicamente, elegimos un subconjunto de funciones que contiene la mayor parte de la información subyacente, utilizando el mismo criterios como el análisis de componentes independientes. Simultáneamente, el ruido se separa como un componente independiente. La segunda contribución de la tesis es un método de transformación multilineal paramétrica para homogeneizar densidades de clústeres mientras preservando la estructura topológica del conjunto de datos, llamado Mapa de Curvatura del Espacio de Características (FSCM). Presentamos un nuevo Gravitacional Mapa autoorganizado para modelar la curvatura del espacio característico conectando los conceptos de gravedad y estructura del espacio en el Algoritmo de mapa autoorganizado para describir matemáticamente la estructura de densidad de los datos. Para homogeneizar la densidad del racimo, introducimos un mecanismo de mapeo novedoso para proyectar los datos del espacio curvo no euclidiano a un nuevo plano euclidiano espacio. La tercera contribución es un nuevo método basado en topología para estudiar datos categorizados de alta dimensión potencialmente complejos mediante cuantificando sus formas y extrayendo información detallada de ellas para interpretar el resultado de la agrupación. presentamos nuestro Método de análisis de componentes de organización (OCA) para el estudio automático de forma arbitraria de conglomerados sin una suposición sobre el distribución de datos.Postprint (published version

Doctor of Philosophy

dissertationCyanobactins are peptide natural products that fall under the broad class of the ribosomally synthesized and posttranslationally modified peptides (RiPPs). Since they are synthesized by the ribosome, the biosynthesis of these peptides is genetically encoded. A precursor peptide gene carries the primary amino acid sequence of the natural product. The precursor peptide is surrounded by other genes, which encode posttranslational enzymes that decorate the primary sequence with elaborate structural motifs. Due to the genetically encoded origins of the cyanobactins, simple manipulations at the peptide sequence level are tolerable and lead to the creation of a diversity of natural products. The roots to this tolerance lie in the innate extreme broad-substrate nature of the posttranslational enzymes. Here, we explore the biochemical basis of this promiscuity and in vitro methodologies to create structurally elaborate peptidic motifs. In addition, the cyanobactin biosynthetic machinery is a rich source of enzymes capable of performing a wide array of intriguing chemistry and here we probe into some of these mechanisms. Put together, the broad-substrate nature coupled with the unique enzymology of the cyanobactin biosynthetic machinery provides a toolkit for the creation of designer peptide motifs. This work holds promise in the field of peptide-based drug discovery

THE ROLE OF THE FLAVODIIRON PROTEINS IN NITRIC OXIDE DETOXIFICATION

"This dissertation portrays recent developments on the knowledge of a protein family whose once elusive role is presently clearer, although still prone to discussion. The family of Flavodiiron Proteins (FDPs), initially thought to protect anaerobes from oxygen exposure, have been proposed to have a role in nitric oxide detoxification. The main object of study of this dissertation, Escherichia coli Flavorubredoxin (FlRd) made a large contribution to establish this role. FlRd was the first member of the FDP family to be assigned as an NO reductase, followed by the demonstration of the same activity in other FDPs, although a role in oxygen scavenging by other FDP family members has to be considered.(...)

Ligand Binding and Activation Properties of the Purified Bacterial Cyclic Nucleotide-Gated Channel SthK

Cyclic nucleotide-modulated ion channels play several essential physiological roles. They are involved in signal transduction in photoreceptors and olfactory sensory neurons as well as pacemaking activity in the heart and brain. Investigations of the molecular mechanism of their actions, including structural and electrophysiological characterization, are restricted by the availability of stable, purified protein obtained from accessible systems. Here, we establish that SthK, a cyclic nucleotide-gated (CNG) channel from Spirochaeta thermophila, is an excellent model for investigating the gating of eukaryotic CNG channels at the molecular level. The channel has high sequence similarity with its eukaryotic counterparts and was previously reported to be activated by cyclic nucleotides in patch-clamp experiments with Xenopus laevis oocytes. We optimized protein expression and purification to obtain large quantities of pure, homogeneous, and active recombinant SthK protein from Escherichia coli A negative-stain electron microscopy (EM) single-particle analysis indicated that this channel is a promising candidate for structural studies with cryo-EM. Using radioactivity and fluorescence flux assays, as well as single-channel recordings in lipid bilayers, we show that the protein is partially activated by micromolar concentrations of cyclic adenosine monophosphate (cAMP) and that channel activity is increased by depolarization. Unlike previous studies, we find that cyclic guanosine monophosphate (cGMP) is also able to activate SthK, but with much lower efficiency than cAMP. The distinct sensitivities to different ligands resemble eukaryotic CNG and hyperpolarization-activated and cyclic nucleotide-modulated channels. Using a fluorescence binding assay, we show that cGMP and cAMP bind to SthK with similar apparent affinities, suggesting that the large difference in channel activation by cAMP or cGMP is caused by the efficacy with which each ligand promotes the conformational changes toward the open state. We conclude that the functional characteristics of SthK reported here will permit future studies to analyze ligand gating and discrimination in CNG channels