Search results for "Mathematic"

On the continuous and discontinuous maximal operators

2018

Abstract In the first part of this paper we study the regularity properties of a wide class of maximal operators. These results are used to show that the spherical maximal operator is continuous W 1 , p ( R n ) ↦ W 1 , p ( R n ) , when p > n n − 1 . Other given applications include fractional maximal operators and maximal singular integrals. On the other hand, we show that the restricted Hardy–Littlewood maximal operator M λ , where the supremum is taken over the cubes with radii greater than λ > 0 , is bounded from L p ( R n ) to W 1 , p ( R n ) but discontinuous.

Quantum clustering in non-spherical data distributions: Finding a suitable number of clusters

2017

Quantum Clustering (QC) provides an alternative approach to clustering algorithms, several of which are based on geometric relationships between data points. Instead, QC makes use of quantum mechanics concepts to find structures (clusters) in data sets by finding the minima of a quantum potential. The starting point of QC is a Parzen estimator with a fixed length scale, which significantly affects the final cluster allocation. This dependence on an adjustable parameter is common to other methods. We propose a framework to find suitable values of the length parameter σ by optimising twin measures of cluster separation and consistency for a given cluster number. This is an extension of the Se…

Biological investigation of neural circuits in the insect brain

2018

Watching insects thoughtfully one cannot but adore their behavioural capabilities. They have developed amazing reproductive, foraging and orientation strategies and at the same time they followed the evolutionary path of miniaturization and sparseness. Both features together turn them into a role model for autonomous robots. Despite their tiny brains, fruit flies (Drosophila) can orient, walk on uneven terrain, in any orientation to gravity, can fly in adverse winds, find partners, places for egg laying, food and shelter. Drosophila melanogaster is the model animal for geneticists and cutting-edge tools are being continuously developed to study the underpinnings of their behavioural capabil…

Efficient Algorithms for Sequence Analysis with Entropic Profiles

2017

Entropy, being closely related to repetitiveness and compressibility, is a widely used information-related measure to assess the degree of predictability of a sequence. Entropic profiles are based on information theory principles, and can be used to study the under-/over-representation of subwords, by also providing information about the scale of conserved DNA regions. Here, we focus on the algorithmic aspects related to entropic profiles. In particular, we propose linear time algorithms for their computation that rely on suffix-based data structures, more specifically on the truncated suffix tree (TST) and on the enhanced suffix array (ESA). We performed an extensive experimental campaign …

HPG pore: an efficient and scalable framework for nanopore sequencing data.

2016

The use of nanopore technologies is expected to spread in the future because they are portable and can sequence long fragments of DNA molecules without prior amplification. The first nanopore sequencer available, the MinION™ from Oxford Nanopore Technologies, is a USB-connected, portable device that allows real-time DNA analysis. In addition, other new instruments are expected to be released soon, which promise to outperform the current short-read technologies in terms of throughput. Despite the flood of data expected from this technology, the data analysis solutions currently available are only designed to manage small projects and are not scalable. Here we present HPG Pore, a toolkit for …

Deep learning architectures for prediction of nucleosome positioning from sequences data

2018

Abstract Background Nucleosomes are DNA-histone complex, each wrapping about 150 pairs of double-stranded DNA. Their function is fundamental for one of the primary functions of Chromatin i.e. packing the DNA into the nucleus of the Eukaryote cells. Several biological studies have shown that the nucleosome positioning influences the regulation of cell type-specific gene activities. Moreover, computational studies have shown evidence of sequence specificity concerning the DNA fragment wrapped into nucleosomes, clearly underlined by the organization of particular DNA substrings. As the main consequence, the identification of nucleosomes on a genomic scale has been successfully performed by com…

Reducing sample size in experiments with animals: historical controls and related strategies

2015

Reducing the number of animal subjects used in biomedical experiments is desirable for ethical and practical reasons. Previous reviews of the benefits of reducing sample sizes have focused on improving experimental designs and methods of statistical analysis, but reducing the size of control groups has been considered rarely. We discuss how the number of current control animals can be reduced, without loss of statistical power, by incorporating information from historical controls, i.e. subjects used as controls in similar previous experiments. Using example data from published reports, we describe how to incorporate information from historical controls under a range of assumptions that mig…

Network-Wide Adaptive Burst Detection Depicts Neuronal Activity with Improved Accuracy

2017

Neuronal networks are often characterized by their spiking and bursting statistics. Previously, we introducedan adaptive burst analysis methodwhich enhances the analysis power for neuronal networks with highly varying firing dynamics. The adaptation is based on single channels analyzing each element of a network separately. Such kind of analysis was adequate for the assessment of local behavior, where the analysis focuses on the neuronal activity in the vicinity of a single electrode. However, the assessment of the whole network may be hampered, if parts of the network are analyzed using different rules. Here, we test how using multiple channels and measurement time points affect adaptive b…

A new parallel pipeline for DNA methylation analysis of long reads datasets

2017

Background DNA methylation is an important mechanism of epigenetic regulation in development and disease. New generation sequencers allow genome-wide measurements of the methylation status by reading short stretches of the DNA sequence (Methyl-seq). Several software tools for methylation analysis have been proposed over recent years. However, the current trend is that the new sequencers and the ones expected for an upcoming future yield sequences of increasing length, making these software tools inefficient and obsolete. Results In this paper, we propose a new software based on a strategy for methylation analysis of Methyl-seq sequencing data that requires much shorter execution times while…

2019

As rats learn to search for multiple sources of food or water in a complex environment, they generate increasingly efficient trajectories between reward sites. Such spatial navigation capacity involves the replay of hippocampal place-cells during awake states, generating small sequences of spatially related place-cell activity that we call "snippets". These snippets occur primarily during sharp-wave-ripples (SWRs). Here we focus on the role of such replay events, as the animal is learning a traveling salesperson task (TSP) across multiple trials. We hypothesize that snippet replay generates synthetic data that can substantially expand and restructure the experience available and make learni…