Local Marchenko-Pastur law at the hard edge of the sample covariance ensemble

Consider an N by N matrix X of complex entries with iid real and imaginary parts. We show that the local density of eigenvalues of X*X converges to the Marchenko-Pastur law on the optimal scale with probability 1. We also obtain rigidity of the eigenvalues in the bulk and near both hard and soft edges. Here we avoid logarithmic and polynomial corrections by working directly with high powers of expectation of the Stieltjes transforms. We work under the assumption that the entries have a finite fourth moment and are truncated at N1/4, or alternatively with exploding moments. In this work we simplify and adapt the methods from prior papers of Götze-Tikhomirov [Probab. Relat. Fields 165(1-2), 163-233 (2016)] and Cacciapuoti-Maltsev-Schlein [Probab. Theory Relat. Fields 163(1-2), 1-59 (2015)] to covariance matrices

Spectral properties of random matrices

In the first part of this thesis, we give the theoretical foundations of random matrix theory through the definitions of a random matrix, a random probability measure and the corresponding empirical spectral distribution we will be working with. The main technical tool of the first paper is also defined rigorously and analyzed deeply, which is the Stieltjes transform method. We then use this tool to prove optimal convergence of the empirical spectral distribution of random sample covariance matrices to the deterministic Marchenko-Pastur distribution. We also give new results about the rigidity of the eigenvalues of this random sample covariance matrix as well as about the rate of their convergence. In the second part of this thesis, we define another important and more general technical tool which works additionally well with non-Hermitian random matrices and that is the Dyson equation method which was used in the second paper. Just like the Stieltjes transform method, it is also defined rigorously and analyzed deeply. We then prove new local laws about a random matrix model that interpolates between the Marchenko-Pastur distribution, the elliptical law and the circular law. Through our work these local laws can now be considered universal, which means that they are independent of the initial distribution of the random matrix entries. We finally give an overview of our new results and provide new directions of study

Outcome prediction based on microarray analysis: a critical perspective on methods

<p>Abstract</p> <p>Background</p> <p>Information extraction from microarrays has not yet been widely used in diagnostic or prognostic decision-support systems, due to the diversity of results produced by the available techniques, their instability on different data sets and the inability to relate statistical significance with biological relevance. Thus, there is an urgent need to address the statistical framework of microarray analysis and identify its drawbacks and limitations, which will enable us to thoroughly compare methodologies under the same experimental set-up and associate results with confidence intervals meaningful to clinicians. In this study we consider gene-selection algorithms with the aim to reveal inefficiencies in performance evaluation and address aspects that can reduce uncertainty in algorithmic validation.</p> <p>Results</p> <p>A computational study is performed related to the performance of several gene selection methodologies on publicly available microarray data. Three basic types of experimental scenarios are evaluated, i.e. the independent test-set and the 10-fold cross-validation (CV) using maximum and average performance measures. Feature selection methods behave differently under different validation strategies. The performance results from CV do not mach well those from the independent test-set, except for the support vector machines (SVM) and the least squares SVM methods. However, these wrapper methods achieve variable (often low) performance, whereas the hybrid methods attain consistently higher accuracies. The use of an independent test-set within CV is important for the evaluation of the predictive power of algorithms. The optimal size of the selected gene-set also appears to be dependent on the evaluation scheme. The consistency of selected genes over variation of the training-set is another aspect important in reducing uncertainty in the evaluation of the derived gene signature. In all cases the presence of outlier samples can seriously affect algorithmic performance.</p> <p>Conclusion</p> <p>Multiple parameters can influence the selection of a gene-signature and its predictive power, thus possible biases in validation methods must always be accounted for. This paper illustrates that independent test-set evaluation reduces the bias of CV, and case-specific measures reveal stability characteristics of the gene-signature over changes of the training set. Moreover, frequency measures on gene selection address the algorithmic consistency in selecting the same gene signature under different training conditions. These issues contribute to the development of an objective evaluation framework and aid the derivation of statistically consistent gene signatures that could eventually be correlated with biological relevance. The benefits of the proposed framework are supported by the evaluation results and methodological comparisons performed for several gene-selection algorithms on three publicly available datasets.</p

Investigating the Serially Mediating Mechanisms of Organizational Ambidexterity and the Circular Economy in the Relationship between Ambidextrous Leadership and Sustainability Performance

In this study, based on a resource-based view, we investigate the influence of ambidextrous leadership (reflected in transformational and transactional leadership styles) on sustainability performance (reflected in economic, environmental, and social performance) through the serially mediating mechanisms of organizational ambidexterity (reflected in explorer and exploiter attributes) and the circular economy (reflected in fields of action). By applying structural equation modelling analyses to survey data collected from private and public Greek organizations, which operate in manufacturing, services, and trade sectors, under an externally dynamic environmental context, we found that (a) organizational ambidexterity and the circular economy fields of action positively mediate the relationship between ambidextrous leadership and sustainability performance and (b) the mechanism originating from transformational leadership has a higher impact on sustainability performance compared to the mechanism that originates from transactional leadership. Accordingly, this study addresses the aspect of the special issue that refers to modern approaches to management and leadership for sustainable business performance research and makes several theoretical and practical implications. © 2023 by the authors

Genome-wide single-molecule analysis of long-read DNA methylation reveals heterogeneous patterns at heterochromatin that reflect nucleosome organisation

High-throughput sequencing technology is central to our current understanding of the human methylome. The vast majority of studies use chemical conversion to analyse bulk-level patterns of DNA methylation across the genome from a population of cells. While this technology has been used to probe single-molecule methylation patterns, such analyses are limited to short reads of a few hundred basepairs. DNA methylation can also be directly detected using Nanopore sequencing which can generate reads measuring megabases in length. However, thus far these analyses have largely focused on bulk-level assessment of DNA methylation. Here, we analyse DNA methylation in single Nanopore reads from human lymphoblastoid cells, to show that bulk-level metrics underestimate large-scale heterogeneity in the methylome. We use the correlation in methylation state between neighbouring sites to quantify single-molecule heterogeneity and find that heterogeneity varies significantly across the human genome, with some regions having heterogeneous methylation patterns at the single-molecule level and others possessing more homogeneous methylation patterns. By comparing the genomic distribution of the correlation to epigenomic annotations, we find that the greatest heterogeneity in single-molecule patterns is observed within heterochromatic partially methylated domains (PMDs). In contrast, reads originating from euchromatic regions and gene bodies have more ordered DNA methylation patterns. By analysing the patterns of single molecules in more detail, we show the existence of a nucleosome-scale periodicity in DNA methylation that accounts for some of the heterogeneity we uncover in long single-molecule DNA methylation patterns. We find that this periodic structure is partially masked in bulk data and correlates with DNA accessibility as measured by nanoNOMe-seq, suggesting that it could be generated by nucleosomes. Our findings demonstrate the power of single-molecule analysis of long-read data to understand the structure of the human methylome

Temperature Shifts for Extraction and Purification of Zygomycetes Chitosan with Dilute Sulfuric Acid

The temperature-dependent hydrolysis and solubility of chitosan in sulfuric acid solutions offer the possibility for chitosan extraction from zygomycetes mycelia and separation from other cellular ingredients with high purity and high recovery. In this study, Rhizomucor pusillus biomass was initially extracted with 0.5 M NaOH at 120 °C for 20 min, leaving an alkali insoluble material (AIM) rich in chitosan. Then, the AIM was subjected to two steps treatment with 72 mM sulfuric acid at (i) room temperature for 10 min followed by (ii) 120 °C for 45 min. During the first step, phosphate of the AIM was released into the acid solution and separated from the chitosan-rich residue by centrifugation. In the second step, the residual AIM was re-suspended in fresh 72 mM sulfuric acid, heated at 120 °C and hot filtered, whereby chitosan was extracted and separated from the hot alkali and acid insoluble material (HAAIM). The chitosan was recovered from the acid solution by precipitation at lowered temperature and raised pH to 8–10. The treatment resulted in 0.34 g chitosan and 0.16 g HAAIM from each gram AIM. At the start, the AIM contained at least 17% phosphate, whereas after the purification, the corresponding phosphate content of the obtained chitosan was just 1%. The purity of this chitosan was higher than 83%. The AIM subjected directly to the treatment with hot sulfuric acid (at 120 °C for 45 min) resulted in a chitosan with a phosphate impurity of 18.5%

Chitin Deacetylases: Properties and Applications

Chitin deacetylases, occurring in marine bacteria, several fungi and a few insects, catalyze the deacetylation of chitin, a structural biopolymer found in countless forms of marine life, fungal cell and spore walls as well as insect cuticle and peritrophic matrices. The deacetylases recognize a sequence of four GlcNAc units in the substrate, one of which undergoes deacetylation: the resulting chitosan has a more regular deacetylation pattern than a chitosan treated with hot NaOH. Nevertheless plain chitin is a poor substrate, but glycolated, reprecipitated or depolymerized chitins are good ones. The marine Vibrio sp. colonize the chitin particles and decompose the chitin thanks to the concerted action of chitinases and deacetylases, otherwise they could not tolerate chitosan, a recognized antibacterial biopolymer. In fact, chitosan is used to prevent infections in fishes and crustaceans. Considering that chitin deacetylases play very important roles in the biological attack and defense systems, they may find applications for the biological control of fungal plant pathogens or insect pests in agriculture and for the biocontrol of opportunistic fungal human pathogens