A Decomposition of Calderón–Zygmund Type and Some Observations on Differentiation of Integrals on the Infinite-Dimensional Torus

In this note we will show a Calder\'on--Zygmund decomposition associated with a function $f\in L^1(\mathbb{T}^{\omega})$. The idea relies on an adaptation of a more general result by J. L. Rubio de Francia in the setting of locally compact groups. Some related results about differentiation of integrals on the infinite-dimensional torus are also discussed.2017 Leonardo grant for Researchers and Cultural Creators, BBVA Foundatio

On the absolute divergence of Fourier series in the infinite dimensional torus

In this note we present some simple counterexamples, based on quadratic forms in infinitely many variables, showing that the implication $f\in C^{(\infty}(\mathbb{T}^\omega)\Longrightarrow\sum_{\bar{p}\in\mathbb{Z}^\infty}|\widehat{f}(\bar{p})|<\infty$ is false. There are functions of the class $C^{(\infty}(\mathbb{T}^\omega)$ (depending on an infinite number of variables) whose Fourier series diverges absolutely. This fact establishes a significant difference to what happens in the finite dimensional case.BCAM Severo Ochoa excellence accreditation SEV-2013-0323 MTM2015-65888-C04-4-P 2017 Leonardo grant for Researchers and Cultural Creators, BBVA Foundatio

Computing Scalable Multivariate Glocal Invariants of Large (Brain-) Graphs

Graphs are quickly emerging as a leading abstraction for the representation of data. One important application domain originates from an emerging discipline called "connectomics". Connectomics studies the brain as a graph; vertices correspond to neurons (or collections thereof) and edges correspond to structural or functional connections between them. To explore the variability of connectomes---to address both basic science questions regarding the structure of the brain, and medical health questions about psychiatry and neurology---one can study the topological properties of these brain-graphs. We define multivariate glocal graph invariants: these are features of the graph that capture various local and global topological properties of the graphs. We show that the collection of features can collectively be computed via a combination of daisy-chaining, sparse matrix representation and computations, and efficient approximations. Our custom open-source Python package serves as a back-end to a Web-service that we have created to enable researchers to upload graphs, and download the corresponding invariants in a number of different formats. Moreover, we built this package to support distributed processing on multicore machines. This is therefore an enabling technology for network science, lowering the barrier of entry by providing tools to biologists and analysts who otherwise lack these capabilities. As a demonstration, we run our code on 120 brain-graphs, each with approximately 16M vertices and up to 90M edges.Comment: Published as part of 2013 IEEE GlobalSIP conferenc

MAXIMAL OPERATORS ON THE INFINITE-DIMENSIONAL TORUS

We study maximal operators related to bases on the infinite- dimensional torus Tω. For the normalized Haar measure dx on Tω it is known that MR0, the maximal operator associated with the dyadic basis R0, is of weak type (1,1), but MR, the operator associated with the natural general basis R, is not. We extend the latter result to all q ∈ [1, ∞). Then we find a wide class of intermediate bases R0 ⊂ R′ ⊂ R, for which maximal functions have controlled, but sometimes very peculiar behavior. Precisely, for given q0 ∈ [1, ∞) we construct R′ such that M R′ is of restricted weak type (q, q) if and only if q belongs to a predetermined range of the form (q0,∞] or [q0,∞]. Finally, we study the weighted setting, considering the Muckenhoupt ARp (Tω) and reverse Hölder RHRr (Tω) classes of weights associated with R. For each p ∈ (1,∞) and each w ∈ ARp (Tω) we obtain that MR is not bounded on Lq(w) in the whole range q ∈ [1, ∞). Since we are able to show that ARp (Tω)= RHRr (Tω), p∈(1,∞) r∈(1,∞) the unboundedness result applies also to all reverse Hölder weights

STATISTICAL ANALYSIS OF THE EFFECTS OF MIXING POTATO VARIETIES ON LATE BLIGHT

A field study in two regions of Peru was conducted to determine how host-diversity effects on potato late blight varied geographically. Foliar disease severity was evaluated separately for the potato varieties in mixtures as well as in the single-variety plots. The TAUDPC (truncated area under the disease progress curve) and RMR (relative mixture response) for each site were analyzed separately using SAS mixed effects model procedures. While there was little difference between the sites in the 1997-1998 season, host-diversity effects were generally greater near Huancayo than near Cajamarca in the 1998-1999 season. Estimates of host-diversity effects from studies in Oregon and Ecuador were also compared with results for Peru. Host-diversity effects for reduced disease were generally greater for sites where we predicted lower levels of outside inoculum

An Automated Images-to-Graphs Framework for High Resolution Connectomics

Reconstructing a map of neuronal connectivity is a critical challenge in contemporary neuroscience. Recent advances in high-throughput serial section electron microscopy (EM) have produced massive 3D image volumes of nanoscale brain tissue for the first time. The resolution of EM allows for individual neurons and their synaptic connections to be directly observed. Recovering neuronal networks by manually tracing each neuronal process at this scale is unmanageable, and therefore researchers are developing automated image processing modules. Thus far, state-of-the-art algorithms focus only on the solution to a particular task (e.g., neuron segmentation or synapse identification). In this manuscript we present the first fully automated images-to-graphs pipeline (i.e., a pipeline that begins with an imaged volume of neural tissue and produces a brain graph without any human interaction). To evaluate overall performance and select the best parameters and methods, we also develop a metric to assess the quality of the output graphs. We evaluate a set of algorithms and parameters, searching possible operating points to identify the best available brain graph for our assessment metric. Finally, we deploy a reference end-to-end version of the pipeline on a large, publicly available data set. This provides a baseline result and framework for community analysis and future algorithm development and testing. All code and data derivatives have been made publicly available toward eventually unlocking new biofidelic computational primitives and understanding of neuropathologies.Comment: 13 pages, first two authors contributed equally V2: Added additional experiments and clarifications; added information on infrastructure and pipeline environmen

In situ electron microscopy techniques for nanoparticle dispersion analysis of commercial sunscreen

Nanoparticles are common active ingredients within many commercial products including sunscreen. Consequently, accurate characterisation of nanoparticles in these products is vital to enhance product design, whilst also understanding the toxicological implications of these nanoparticles. Whilst bulk techniques are useful in providing some information, they often cannot resolve individual particles, and therefore electron microscopy can be used for high-resolution nanoparticle characterisation. However, conventional high vacuum dry TEM does not accurately represent nanoparticle dispersions and other in situ methods must be used. Here, we use a combination of techniques including liquid cell transmission electron microscopy (LCTEM), cryogenic (cryo)-TEM and cryo-scanning electron microscopy (SEM) to characterise a commercial sunscreen containing titanium dioxide (TiO2) and zinc oxide (ZnO) nanoparticles. Our work illustrates that whilst LCTEM does not require any sample preparation more beam artefacts can occur causing ZnO dissolution with only TiO2 nanoparticles visualised. Comparatively, cryo-TEM allows characterisation of both ZnO and TiO2, yet only cryo-SEM could be used to analyse the pure product (without dilution) but biased the characterisation to the larger fraction of nanoparticles and agglomerates. Ultimately, only with a combination of different in situ EM techniques can an accurate characterisation of commercial products be achieved in order to ensure effective and safe product design and manufacture

EM and XRM Connectomics Imaging and Experimental Metadata Standards

High resolution volumetric neuroimaging datasets from electron microscopy (EM) and x-ray micro and holographic-nano tomography (XRM/XHN) are being generated at an increasing rate and by a growing number of research teams. These datasets are derived from an increasing number of species, in an increasing number of brain regions, and with an increasing number of techniques. Each of these large-scale datasets, often surpassing petascale levels, is typically accompanied by a unique and varied set of metadata. These datasets can be used to derive connectomes, or neuron-synapse level connectivity diagrams, to investigate the fundamental organization of neural circuitry, neuronal development, and neurodegenerative disease. Standardization is essential to facilitate comparative connectomics analysis and enhance data utilization. Although the neuroinformatics community has successfully established and adopted data standards for many modalities, this effort has not yet encompassed EM and XRM/ XHN connectomics data. This lack of standardization isolates these datasets, hindering their integration and comparison with other research performed in the field. Towards this end, our team formed a working group consisting of community stakeholders to develop Image and Experimental Metadata Standards for EM and XRM/XHN data to ensure the scientific impact and further motivate the generation and sharing of these data. This document addresses version 1.1 of these standards, aiming to support metadata services and future software designs for community collaboration. Standards for derived annotations are described in a companion document. Standards definitions are available on a community github page. We hope these standards will enable comparative analysis, improve interoperability between connectomics software tools, and continue to be refined and improved by the neuroinformatics community.Comment: 15 Pages, 3 figures, 2 table