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

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

On Biomineralization: Enzymes Switch on Mesocrystal Assembly

Cellular machineries guide the bottom-up pathways toward crystal superstructures based on the transport of inorganic precursors and their precise integration with organic frameworks. The biosynthesis of mesocrystalline spines entails concerted interactions between biomolecules and inorganic precursors; however, the bioinorganic interactions and interfaces that regulate material form and growth as well as the selective emergence of structural complexity in the form of nanostructured crystals are not clear. By investigating mineral nucleation under the regulation of recombinant proteins, we show that SpSM50, a matrix protein of the sea urchin spine, stabilizes mineral precursors via vesicle-confinement, a function conferred by a low-complexity, disordered region. Site-specific proteolysis of this domain by a collagenase initiates phase transformation of the confined mineral phase. The residual C-type lectin domain molds the fluidic mineral precursor into hierarchical mesocrystals identical to structural crystal modules constituting the biogenic mineral. Thus, the regulatory functions of proteolytic enzymes can guide biomacromolecular domain constitutions and interfaces, in turn determining inorganic phase transformations toward hybrid materials as well as integrating organic and inorganic components across hierarchical length scales. Bearing striking resemblance to biogenic mineralization, these hybrid materials recruit bioinorganic interactions which elegantly intertwine nucleation and crystallization phenomena with biomolecular structural dynamics, hence elucidating a long-sought key of how nature can orchestrate complex biomineralization processes

Immunological detection of pyrazine-2-carboxylic acid for the detection of pyrazinamide resistance in Mycobacterium tuberculosis.

Pyrazinamide (PZA) susceptibility testing in Mycobacterium tuberculosis (Mtb) is a current area of development and PZA-resistant strains are increasingly prevalent. Previous studies have demonstrated that the detection of pyrazinoic acid (POA), the metabolite produced by the deamidation of PZA, is a good predictor for PZA resistance since a resistant strain would not convert PZA into POA at a critical required rate, whereas a susceptible strain will do, expelling POA to the extracellular environment at a certain rate, and allowing for quantification of this accumulated analyte. In order to quantify POA, an indirect competitive ELISA (icELISA) test using hyperimmune polyclonal rabbit serum against POA was developed: for this purpose, pure POA was first covalently linked to the highly immunogenic Keyhole Limpet Hemocyanine, and inoculated in rabbits. A construct made of bovine serum albumin (BSA) linked to pure POA and fixed at the bottom of wells was used as a competitor against spiked samples and liquid Mtb culture supernatants. When spiked samples (commercial POA alone) were analyzed, the half maximal inhibitory concentration (IC50) was 1.16 mg/mL, the limit of detection 200 μg/mL and the assay was specific (it did not detect PZA, IC50 > 20 mg/mL). However, culture supernatants (7H9-OADC-PANTA medium) disrupted the competition and a proper icELISA curve was not obtainable. We consider that, although we have shown that it is feasible to induce antibodies against POA, matrix effects could damage its analytical usefulness; multiple, upcoming ways to solve this obstacle are suggested