A statistical approach to persistent homology

Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying space. In this paper we take a statistical approach to this problem. We assume that the data is randomly sampled from an unknown probability distribution. We define two filtered complexes with which we can calculate the persistent homology of a probability distribution. Using statistical estimators for samples from certain families of distributions, we show that we can recover the persistent homology of the underlying distribution.Comment: 30 pages, 2 figures, minor changes, to appear in Homology, Homotopy and Application

Sr0.9_{0.9}K0.1_{0.1}Zn1.8_{1.8}Mn0.2_{0.2}As2_{2}: a ferromagnetic semiconductor with colossal magnetoresistance

A bulk diluted magnetic semiconductor (Sr,K)(Zn,Mn)$_{2}$As$_{2}$ was synthesized with decoupled charge and spin doping. It has a hexagonal CaAl$_{2}$Si$_{2}$-type structure with the (Zn,Mn)$_{2}$As$_{2}$ layer forming a honeycomb-like network. Magnetization measurements show that the sample undergoes a ferromagnetic transition with a Curie temperature of 12 K and \revision{magnetic moment reaches about 1.5 $\mu_{B}$/Mn under $\mu_0H$ = 5 T and $T$ = 2 K}. Surprisingly, a colossal negative magnetoresistance, defined as $[\rho(H)-\rho(0)]/\rho(0)$, up to $-$38\% under a low field of $\mu_0H$ = 0.1 T and to $-$99.8\% under $\mu_0H$ = 5 T, was observed at $T$ = 2 K. The colossal magnetoresistance can be explained based on the Anderson localization theory.Comment: Accepted for publication in EP

A Sec14 domain protein is required for photoautotrophic growth and chloroplast vesicle formation in Arabidopsis thaliana.

In eukaryotic photosynthetic organisms, the conversion of solar into chemical energy occurs in thylakoid membranes in the chloroplast. How thylakoid membranes are formed and maintained is poorly understood. However, previous observations of vesicles adjacent to the stromal side of the inner envelope membrane of the chloroplast suggest a possible role of membrane transport via vesicle trafficking from the inner envelope to the thylakoids. Here we show that the model plant Arabidopsis thaliana has a chloroplast-localized Sec14-like protein (CPSFL1) that is necessary for photoautotrophic growth and vesicle formation at the inner envelope membrane of the chloroplast. The cpsfl1 mutants are seedling lethal, show a defect in thylakoid structure, and lack chloroplast vesicles. Sec14 domain proteins are found only in eukaryotes and have been well characterized in yeast, where they regulate vesicle budding at the trans-Golgi network. Like the yeast Sec14p, CPSFL1 binds phosphatidylinositol phosphates (PIPs) and phosphatidic acid (PA) and acts as a phosphatidylinositol transfer protein in vitro, and expression of Arabidopsis CPSFL1 can complement the yeast sec14 mutation. CPSFL1 can transfer PIP into PA-rich membrane bilayers in vitro, suggesting that CPSFL1 potentially facilitates vesicle formation by trafficking PA and/or PIP, known regulators of membrane trafficking between organellar subcompartments. These results underscore the role of vesicles in thylakoid biogenesis and/or maintenance. CPSFL1 appears to be an example of a eukaryotic cytosolic protein that has been coopted for a function in the chloroplast, an organelle derived from endosymbiosis of a cyanobacterium

Comparing Support Vector Machines with Gaussian Kernels to Radial Basis Function Classifiers

The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights and threshold such as to minimize an upper bound on the expected test error. The present study is devoted to an experimental comparison of these machines with a classical approach, where the centers are determined by $k$--means clustering and the weights are found using error backpropagation. We consider three machines, namely a classical RBF machine, an SV machine with Gaussian kernel, and a hybrid system with the centers determined by the SV method and the weights trained by error backpropagation. Our results show that on the US postal service database of handwritten digits, the SV machine achieves the highest test accuracy, followed by the hybrid approach. The SV approach is thus not only theoretically well--founded, but also superior in a practical application

Improving photosynthesis and crop productivity by accelerating recovery from photoprotection

Crop leaves in full sunlight dissipate damaging excess absorbed light energy as heat. When sunlit leaves are shaded by clouds or other leaves, this protective dissipation continues for many minutes and reduces photosynthesis. Calculations have shown that this could cost field crops up to 20% of their potential yield. Here, we describe the bioengineering of an accelerated response to natural shading events in Nicotiana (tobacco), resulting in increased leaf carbon dioxide uptake and plant dry matter productivity by about 15% in fluctuating light. Because the photoprotective mechanism that has been altered is common to all flowering plants and crops, the findings provide proof of concept for a route to obtaining a sustainable increase in productivity for food crops and a much-needed yield jump

An integrated perspective on assessing agricultural air quality

Abstract: The biogeochemical cycling of trace gases (e.g. nitrogen, sulphur, etc.), and contaminants on local, regional, and global scales is a complex system of emissions, transformations, transport, and deposition. To date, limited, if any, attempt has been made on quantifying and identifying direct emissions of gaseous sulphur compounds from agricultural operations. This represents a major regulatory need for sound and prudent environmental practice. In this paper, we summarise an integrated assessment framework for studying the agricultural air quality issues by discussing the various components of the research, education and outreach involved

Random geometric complexes

We study the expected topological properties of Cech and Vietoris-Rips complexes built on i.i.d. random points in R^d. We find higher dimensional analogues of known results for connectivity and component counts for random geometric graphs. However, higher homology H_k is not monotone when k > 0. In particular for every k > 0 we exhibit two thresholds, one where homology passes from vanishing to nonvanishing, and another where it passes back to vanishing. We give asymptotic formulas for the expectation of the Betti numbers in the sparser regimes, and bounds in the denser regimes. The main technical contribution of the article is in the application of discrete Morse theory in geometric probability.Comment: 26 pages, 3 figures, final revisions, to appear in Discrete & Computational Geometr

Cloudbursts in Indian Himalayas: a review

Cloudbursts in and around the southern rim of the Indian Himalayas are elusive in terms of their position and time of occurrences. Most of the reported cloudbursts are in the interior of the Himalayas and hence their observation itself is limited. Most of these events are reported once their affect in terms of loss to life and property is experienced in the downstream habitats. In addition, they are mostly associated with flash floods as an impact of the torrential precipitation. The principal understanding of the cloudburst is associated with sudden heavy deluge of precipitation in very less time interval over a very small area. Except this understanding and India Meteorology Department (IMD) definition of > 100 mm/h precipitation over a geographical region of approximately 20–30 km2, nothing much else is known about these events. There are a very few studies carried out on understanding of these events. Present paper synthesizes the available information and research on cloudburst events and tries to define it based on associated dynamics, thermodynamics and physical processes leading to a cloudburst event. Thus in the present work, characterizations and impacts of cloudburst leading from precipitation to dynamical to thermodynamical to large scale forcings to orographical forcings to followed geomorphology to impacts are intertwined to present comprehensive portray of it. Most of the cloudburst events are seen occurring in the elevation range of 1000 m to 2500 m within the valley folds of the southern rim of the Indian Himalayas. Apart from some of the large scale flow shown by few of the studies, it is found that cloudburst events are convectively triggered followed by orographically locked systems. These intertwined mechanisms lead cloudburst events to form. Amiss of any one of these mechanisms will not lead the cloudburst mechanism to form. These interactions in the present paper established the vagaries associated with the cloudburst events

Il linguaggio sopra la base magica. Realt\ue0 e scrittura in Nanni Balestrini

Personaggi, fatti ed esperienze collegati con precise realt\ue0 storiche e sociali occupano il piano del contenuto di molte opere in prosa e in versi di Nanni Balestrini. Tuttavia questa semplice constatazione non deve mettere in ombra la complessit\ue0 del rapporto fra realt\ue0 e scrittura nella sua opera, tenacemente irriducibile ad uno schema contenutistico. Non inganni, in casi come il radiodramma Parma 1922, l\u2019apparente trasparenza della prosa: con Balestrini ci si tiene sempre lontano dall\u2019esercizio della scrittura come mimesi realistica. Balestrini \ue8 uno scrittore che, al limite, pu\uf2 non scrivere affatto ma piuttosto riscrivere e - con particolari procedimenti - porre sulla \u201cbase magica\u201d della sua letteratura un dato: il prodotto linguistico di una determinata realt\ue0, che nel caso di Parma 1922 consiste nei discorsi dei protagonisti delle Barricate e di chi li raccont\uf2 negli anni Sessanta (lo storico De Micheli). Come lo spirito epico che anima queste pagine, anche quanto vi si trova di realistico appartiene a quei linguaggi e, in ultima istanza, appartiene a quelle storie. A Balestrini spetta la straordinaria capacit\ue0 di farne letteratura