Direct transformations yielding the knight's move pattern in 3x3x3 arrays

Three-way arrays (or tensors) can be regarded as extensions of the traditional two-way data matrices that have a third dimension. Studying algebraic properties of arrays is relevant, for example, for the Tucker three-way PCA method, which generalizes principal component analysis to three-way data. One important algebraic property of arrays is concerned with the possibility of transformations to simplicity. An array is said to be transformed to a simple form when it can be manipulated by a sequence of invertible operations such that a vast majority of its entries become zero. This paper shows how 3 × 3 × 3 arrays, whether symmetric or nonsymmetric, can be transformed to a simple form with 18 out of its 27 entries equal to zero. We call this simple form the “knight's move pattern” due to a loose resemblance to the moves of a knight in a game of chess. The pattern was examined by Kiers, Ten Berge, and Rocci. It will be shown how the knight's move pattern can be found by means of a numeric–algebraic procedure based on the Gröbner basis. This approach seems to work almost surely for randomly generated arrays, whether symmetric or nonsymmetric

First and second-order derivatives for CP and INDSCAL

In this paper we provide the means to analyse the second-order differential structure of optimization functions concerning CANDECOMP/PARAFAC and INDSCAL. Closed-form formulas are given under two types of constraint: unit-length columns or orthonormality of two of the three component matrices. Some numerical problems that might occur during the computation of the Jacobian and Hessian matrices are addressed. The use of these matrices is illustrated in three applications. (C) 2010 Elsevier B.V. All rights reserved

Simplicity transformations for three-way arrays with symmetric slices, and applications to Tucker-3 models with sparse core arrays

AbstractTucker three-way PCA and Candecomp/Parafac are two well-known methods of generalizing principal component analysis to three way data. Candecomp/Parafac yields component matrices A (e.g., for subjects or objects), B (e.g., for variables) and C (e.g., for occasions) that are typically unique up to jointly permuting and rescaling columns. Tucker-3 analysis, on the other hand, has full transformational freedom. That is, the fit does not change when A,B, and C are postmultiplied by nonsingular transformation matrices, provided that the inverse transformations are applied to the so-called core array G̲. This freedom of transformation can be used to create a simple structure in A,B,C, and/or in G̲. This paper deals with the latter possibility exclusively. It revolves around the question of how a core array, or, in fact, any three-way array can be transformed to have a maximum number of zero elements. Direct applications are in Tucker-3 analysis, where simplicity of the core may facilitate the interpretation of a Tucker-3 solution, and in constrained Tucker-3 analysis, where hypotheses involving sparse cores are taken into account. In the latter cases, it is important to know what degree of sparseness can be attained as a tautology, by using the transformational freedom. In addition, simplicity transformations have proven useful as a mathematical tool to examine rank and generic or typical rank of three-way arrays. So far, a number of simplicity results have been attained, pertaining to arrays sampled randomly from continuous distributions. These results do not apply to three-way arrays with symmetric slices in one direction. The present paper offers a number of simplicity results for arrays with symmetric slices of order 2×2,3×3 and 4×4. Some generalizations to higher orders are also discussed. As a mathematical application, the problem of determining the typical rank of 4×3×3 and 5×3×3 arrays with symmetric slices will be revisited, using a sparse form with only 8 out of 36 elements nonzero for the former case and 10 out of 45 elements nonzero for the latter one, that can be attained almost surely for such arrays. The issue of maximal simplicity of the targets to be presented will be addressed, either by formal proofs or by relying on simulation results

Effect of the Vitrification of Human Oocytes on the Binding Capacity and Acrosome Status of Human Sperm

Conocer los aspectos moleculares que acontecen en el proceso de unión de los espermatozoides humanos a la zona pelúcida (ZP) humana es uno de los grandes retos de la biología de la Reproducción. Por otra parte conocer si el proceso de fecundación puede verse afectado por la criopreservación de los gametos femeninos sigue siendo otra cuestión debatida en la literatura. En base a esto, el objetivo principal de este trabajo fue conocer si la vitrificación ovocitaria puede alterar la interacción de los espermatozoides con el glicocáliz de la ZP y demostrar si la ZP de estos ovocitos pierde la capacidad de inducir la reacción acrosómica en los espermatozoides. Según nuestros resultados el método de vitrificación ovocitaria cerrado (S3) no altera la capacidad de unión de los espermatozoides a la zona pelúcida, ni la capacidad de ésta para inducir la reacción acrosómica.To know the molecular aspects that occur in the process of human sperm binding to the human zona pellucida (ZP) is one of the great challenges of reproduction biology. Moreover knowing if the fertilization process may be affected by cryopreservation of female gametes is still another issue discussed in the literature. Based on this, the main objective of this study was to determine whether the oocyte vitrification may alter the interaction of sperm with the glycocalyx of ZP and show whether these oocytes lost the ability to induce the acrosome reaction in sperm. According to our results the oocyte closed vitrification method (S3) does not alter the ability of the sperm binding to the zona pellucida, and their ability to induce the acrosome reaction.Este trabajo fue subvencionado por el Vicerrectorado de Investigación de la Universidad de Alicante (VIGROB-137)

Supramolecularly assisted synthesis of chiral tripodal imidazolium compounds

A strong preference for the formation of tripodal systems over the related monotopic and ditopic compounds is observed for the reaction between tris(halomethyl)benzenes and imidazoles derived from amino acids and containing an amide fragment. This preference allows the formation of the tripodal derivative as the major product even when an equimolar mixture of the tris(halomethyl)benzene and the imidazole is reacted (1 : 1 ratio instead of the stoichiometric 1 : 3 ratio). The reactions were monitored using 1 H NMR spectroscopy and ESI mass spectrometry and kinetically characterized. Computational studies were also performed in order to rationalize the observed preference of the tri-substituted product. The results reveal the existence of well-defined supramolecular interactions between the imidazolium groups and the reacting imidazoles that facilitate the formation of the multitopic systems once the first imidazolium group is formed. Analysis of the different structural components shows that the presence of the amide group from the amino acid moiety is the key structural requirement for such supramolecular assistance to take place. The preorganization of the supramolecular intermediates formed through hydrogen bonding interactions involving amide-NH fragments in imidazoles and bromide anions in imidazolium groups seems to be also present at the corresponding TSs, decreasing the associated energy barriers

Polymeric Ionic Liquids Derived from L-Valine for the Preparation of Highly Selective Silica-Supported Stationary Phases in Gas Chromatography

A series of silica-supported polymeric ionic liquid (PIL)-based stationary phases derived from a vinylic L-valine ionic liquid monomer and divinylbenzene (DVB) as the crosslinking agent have been prepared and studied as gas chromatographic stationary phases. These coated gas chromatographic columns exhibited good thermal stabilities (230–300 ◦C) and high efficiencies (1700–2700 plates/m), and were characterized using a linear solvation parameter model in order to understand the effects of the amount of DVB on the features of the resulting composite systems. Their retention behavior and separation efficiencies were demonstrated using the Grob test. By tuning the crosslinking degree for the IL-derived stationary phase, the separation selectivity and resolution of different compounds were improved. The different retention behaviors observed for many analytes indicate that these stationary phases may be applicable as new types of GC stationary phases

Initiation of ovarian stimulation independent of the menstrual cycle (random-start) in an oocyte donation programme a large, single-center experience

Research Question Do live birth rates differ between recipients matched with donors using conventional ovarian stimulation versus those using random-start protocols? Design Retrospective analysis of 891 ovarian stimulations in egg donors (January-December 2018) and clinical outcomes in matched recipients (n=935). Donors commenced ovarian stimulation on day 1/3 of the menstrual cycle (n=223) or in the mid/late-follicular (n=388) or luteal phase (n=280) under a conventional antagonist protocol. Live birth rate of matched recipients was the main outcome. Results Duration of stimulation and total gonadotropins dose were comparable between conventional versus random-start groups. The number of collected eggs were also similar: 17.6±8.8 vs 17.2±8.5, p=0.6, respectively. Sub-group analysis showed an increased stimulation length (10.2±1.8 vs 9.8±1.7 vs 10.4±1.7, p<0.001) and gonadotropin consumption (2041.5±645.3 vs 2003.2±647.3 vs 2158.2±685.7 IU, p=0.01) in the luteal phase group vs the mid/late follicular and conventional groups; respectively. In matched recipients receiving fresh oocytes and undergoing fresh embryo transfer, the biochemical pregnancy (63.8% and 63.3%; p=0.9), clinical pregnancy (54.6% and 56.1%; p=0.8) and live birth rates (47.7% and 46.6%; p=0.7) per embryo-transfer were similar between conventional versus random groups. Similar results were obtained in recipients receiving vitrified eggs. Euploidy rate was also comparable. Conclusions There were no notable variations in clinical outcomes using oocytes obtained from random-start protocols and those proceeding from conventional ovarian stimulation in oocyte donation treatments. However, luteal-phase stimulation seems to require longer stimulation and higher FSH consumption. Our results indicate that random-start stimulation strategy does not impair the potential of the oocyte yield or clinical outcomes in oocyte donation cycles

Plant feeding by Nesidiocoris tenuis: Quantifying its behavioral and mechanical components

Zoophytophagous predators play an important, though sometimes controversial, role in pest management programs in different crops. In tomato crops, damage caused by phytophagy of the mirid Nesidiocoris tenuis has mainly been reported at high predator population levels or when prey is scarce. Previous research has focused on predator/prey ratios, stylet morphology and saliva composition to explain plant damage by N. tenuis. In this study, we investigated the behavioral and mechanical components of the damage. For this, we compared the feeding behaviors of males, females and fifth-instar nymphs of N. tenuis. Additionally, we investigated the type of stylet activities performed by each stage while probing in plant tissue, using the electrical penetration graph technique (EPG). Furthermore, stylectomy was performed and plant histology studied with the aim to correlate the feeding activities observed in the EPG recordings with stylet tip positions in specific tissues of the leaf petioles. Behavioral observations during a 30-min period showed that nymphs probed more frequently (38.6 ± 1.5 probes) than males and females (25.3 ± 1.1 and 24.3 ± 1.1 probes, respectively). Similarly, nymphs spent a higher proportion of time (656.0 ± 67.6 s) feeding on tomato apical sections compared to males and females (403.0 ± 48.8 s and 356.0 ± 43.7 s, respectively). The EPG recordings during 5 h indicated that cell-rupturing was the main stylet activity for all insect stages, and that fifth-instar nymphs spent a higher proportion of time on cell-rupturing events compared to adults. The histological studies revealed a trend of N. tenuis for the tissues within the vascular semi-ring. The stylet tips were found both in the vascular bundles and in the parenchyma of the interfascicular region. The findings of this study confirm an important role of fifth-instar nymphs feeding behavior in the damage potential of N. tenuis. Moreover, the increased time spent on cell rupturing behaviour suggests that stylet laceration and enzymatic maceration of the saliva occurring during this event might greatly contribute to the inflicted damage. A comprehensive understanding of the interactions of N. tenuis with the plant, at both the behavioral and mechanical levels, might shed light on new approaches to minimize its damage potential to tomato while maintaining its benefits as biocontrol agent

Metabolites involved in cellular communication among human cumulus-oocyte-complex and sperm during in vitro fertilization

Background: Fertilization is a key physiological process for the preservation of the species. Consequently, different mechanisms affecting the sperm and the oocyte have been developed to ensure a successful fertilization. Thus, sperm acrosome reaction is necessary for the egg coat penetration and sperm-oolema fusion. Several molecules are able to induce the sperm acrosome reaction; however, this process should be produced coordinately in time and in the space to allow the success of fertilization between gametes. The goal of this study was to analyze the metabolites secreted by cumulus-oocyte-complex (COC) to find out new components that could contribute to the induction of the human sperm acrosome reaction and other physiological processes at the time of gamete interaction and fertilization. Methods: For the metabolomic analysis, eighteen aliquots of medium were used in each group, containing: a) only COC before insemination and after 3 h of incubation; b) COC and capacitated spermatozoa after insemination and incubated for 16–20 hours; c) only capacitated sperm after 16–20 h in culture and d) only fertilization medium as control. Six patients undergoing assisted reproduction whose male partners provided normozoospermic samples were included in the study. Seventy-two COC were inseminated. Results: The metabolites identified were monoacylglycerol (MAG), lysophosphatidylcholine (LPC) and phytosphingosine (PHS). Analysis by PCR and in silico of the gene expression strongly suggests that the cumulus cells contribute to the formation of the PHS and LPC. Conclusions: LPC and PHS are secreted by cumulus cells during in vitro fertilization and they could be involved in the induction of human acrosome reaction (AR). The identification of new molecules with a paracrine effect on oocytes, cumulus cells and spermatozoa will provide a better understanding of gamete interaction.This study was supported by grant GV/2009/097 from Department of Education, Generalitat Valenciana, Vicerrectorado de Investigación, University of Alicante, Alicante, Spain (Vigrob-137), the Spanish Ministerio de Economía y Competitividad AGL2012-40180-C03-02 and Fundación Seneca (04542/GERM/06)

Reflexiones sobre el aprendizaje de la histología en biología y en ciencias de la salud

El conocimiento de la estructura, composición y función del organismo es fundamental en la formación de los graduados de Ciencias Biomédicas y de Ciencias de la Salud. Las células y los tejidos son los componentes básicos para comprender el normal funcionamiento del organismo y sus procesos patológicos. Por otra parte, la Histología es una de las disciplinas básicas con mayor cantidad de publicaciones sobre temas relacionados con su docencia. Sin embargo, a pesar de la abrumadora literatura existente, todavía no hay criterios claros sobre la pertinencia de los contenidos, los métodos en el aprendizaje y la evaluación de esta materia. En este trabajo; tras una revisión bibliográfica y a partir de la información aportada por profesores de Histología, se lo analizan las principales cuestiones que plantea el proceso de enseñanza aprendizaje de la Histología en el ámbito de Biomedicina (Biología, Medicina, Veterinaria, Enfermería, Nutrición, Fisioterapia, Biotecnología, etc.), a saber: su pertinencia, los contenidos a impartir, las estrategias y los medios didácticos a emplear y los métodos de evaluación. A partir de todos estos datos se describen los principales puntos fuertes y débiles de la Histología con las correspondientes sugerencias de cambio y adaptación al entorno actual