Comparing persistence diagrams through complex vectors

The natural pseudo-distance of spaces endowed with filtering functions is precious for shape classification and retrieval; its optimal estimate coming from persistence diagrams is the bottleneck distance, which unfortunately suffers from combinatorial explosion. A possible algebraic representation of persistence diagrams is offered by complex polynomials; since far polynomials represent far persistence diagrams, a fast comparison of the coefficient vectors can reduce the size of the database to be classified by the bottleneck distance. This article explores experimentally three transformations from diagrams to polynomials and three distances between the complex vectors of coefficients.Comment: 11 pages, 4 figures, 2 table

The Theory of the Interleaving Distance on Multidimensional Persistence Modules

In 2009, Chazal et al. introduced $\epsilon$-interleavings of persistence modules. $\epsilon$-interleavings induce a pseudometric $d_I$ on (isomorphism classes of) persistence modules, the interleaving distance. The definitions of $\epsilon$-interleavings and $d_I$ generalize readily to multidimensional persistence modules. In this paper, we develop the theory of multidimensional interleavings, with a view towards applications to topological data analysis. We present four main results. First, we show that on 1-D persistence modules, $d_I$ is equal to the bottleneck distance $d_B$. This result, which first appeared in an earlier preprint of this paper, has since appeared in several other places, and is now known as the isometry theorem. Second, we present a characterization of the $\epsilon$-interleaving relation on multidimensional persistence modules. This expresses transparently the sense in which two $\epsilon$-interleaved modules are algebraically similar. Third, using this characterization, we show that when we define our persistence modules over a prime field, $d_I$ satisfies a universality property. This universality result is the central result of the paper. It says that $d_I$ satisfies a stability property generalizing one which $d_B$ is known to satisfy, and that in addition, if $d$ is any other pseudometric on multidimensional persistence modules satisfying the same stability property, then $d\leq d_I$. We also show that a variant of this universality result holds for $d_B$, over arbitrary fields. Finally, we show that $d_I$ restricts to a metric on isomorphism classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in Foundations of Computational Mathematics. 36 page

DIVERSITY OF STAPHYLOCOCCAL SPECIES CULTURED FROM CAPTIVE LIVINGSTONE’S FRUIT BATS (PTEROPUS LIVINGSTONII) AND THEIR ENVIRONMENT

Livingstone's fruit bats (Pteropus livingstonii) are critically endangered and a captive population has been established as part of the International Union for Conservation of Nature Species Action Plan. The largest colony, in Jersey Zoo, was sampled for staphylococcal carriage and at infection sites, as disease associated with staphylococci had previously been found. Staphylococci were cultured from swabs from 44 bats (skin, oropharynx, mouth ejecta, skin lesions) and from their enclosure. The isolates were identified by matrix-assisted laser desorption-ionization time of flight mass spectrometry; antimicrobial susceptibility testing was performed by disc diffusion and screening for mecA and mecC. Seventeen species of coagulase-negative staphylococci including Staphylococcus xylosus, S. kloosii, S. nepalensis, and S. simiae were isolated. Staphylococcus aureus was identified from both carriage and lesional sites. These findings suggest S. nepalensis may be part of the normal carriage flora of bats. Antimicrobial resistance rates were low and methicillin-resistant Staphylococcus aureus (MRSA) was not identified. Sampling of mouth ejecta for staphylococci may provide results representative for carriage sites

Graphic-based concept retrieval

Two ways of expressing concepts in the context of image retrieval are presented. One, Keypics, is on the side of an image owner, who wants the image itself to be found on the Web; the second, Trittico, is on the side of the image searcher. Both are based on the paradigm of human intermediation for overcoming the semantic gap. Both require tools capable of qualitative analysis, and have been experimented by using persistent homology

Semiautomated Evaluation of the Primary Motor Cortex in Patients with Amyotrophic Lateral Sclerosis at 3T

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Semiautomated evaluation of the primary motor cortex in patients with amyotrophic lateral sclerosis at 3t

Amyotrophic lateral sclerosis is a neurodegenerative disease involving the upper and lower motor neurons. In amyotrophic lateral sclerosis, pathologic changes in the primary motor cortex include Betz cell depletion and the presence of reactive iron-loaded microglia, detectable on 7T MR images as atrophy and T2*-hypointensity. Our purposes were the following: 1) to investigate the signal hypointensity-to-thickness ratio of the primary motor cortex as a radiologic marker of upper motor neuron involvement in amyotrophic lateral sclerosis with a semiautomated method at 3T, 2) to compare 3T and 7T results, and 3) to evaluate whether semiautomated measurement outperforms visual image assessment

Genetic resistance determinants to fusidic acid and chlorhexidine in variably susceptible staphylococci from dogs

Abstract Background Concern exists that frequent use of topically-applied fusidic acid (FA) and chlorhexidine (CHX) for canine pyoderma is driving clinically relevant resistance, despite rare description of FA and CHX genetic resistance determinants in canine-derived staphylococci. This study aimed to determine minimum inhibitory concentrations (MICs) and investigate presence of putative resistance determinants for FA and CHX in canine-derived methicillin-resistant (MR) and -susceptible (MS) staphylococci. Plasmid-mediated resistance genes (fusB, fusC, fusD, qacA/B, smr; PCR) and MICs (agar dilution) of FA and CHX were investigated in 578 staphylococci (50 MR S. aureus [SA], 50 MSSA, 259 MR S. pseudintermedius [SP], 219 MSSP) from Finland, U.S.A., North (NUK) and South-East U.K. (SEUK) and Germany. In all isolates with FA MIC ≥64 mg/L (n = 27) fusA and fusE were amplified and sequenced. Results FA resistance determinants (fusA mutations n = 24, fusB n = 2, fusC n = 36) were found in isolates from all countries bar U.S.A. and correlated with higher MICs (≥1 mg/L), although 4 SP isolates had MICs of 0.06 mg/L despite carrying fusC. CHX MICs did not correlate with qacA/B (n = 2) and smr (n = 5), which were found in SEUK SA, and SP from NUK and U.S.A. Conclusions Increased FA MICs were frequently associated with fusA mutations and fusC, and this is the first account of fusB in SP. Despite novel description of qacA/B in SP, gene presence did not correlate with CHX MIC. Selection pressure from clinical use might increase prevalence of these genetic determinants, but clinical significance remains uncertain in relation to high skin concentrations achieved by topical therapy

Opportunities for topical antimicrobial therapy: permeation of canine skin by fusidic acid

BACKGROUND: Staphylococcal infection of the canine epidermis and hair follicle is amongst the commonest reasons for antimicrobial prescribing in small animal veterinary practice. Topical therapy with fusidic acid (FA) is an attractive alternative to systemic therapy based on low minimum inhibitory concentrations (MICs, commonly <0.03 mg/l) documented in canine pathogenic staphylococci, including strains of MRSA and MRSP (methicillin-resistant Staphylococcus aureus and S. pseudintermedius). However, permeation of canine skin by FA has not been evaluated in detail. This study aimed to define the degree and extent of FA permeation in canine skin in vitro from two sites with different hair follicle density following application of a licensed ophthalmic formulation that shares the same vehicle as an FA-betamethasone combination product approved for dermal application in dogs. Topical FA application was modelled using skin held in Franz-type diffusion cells. Concentrations of FA in surface swabs, receptor fluid, and transverse skin sections of defined anatomical depth were determined using high-performance liquid chromatography and ultraviolet (HPLC-UV) analysis. RESULTS: The majority of FA was recovered by surface swabs after 24 h, as expected (mean ± SEM: 76.0 ± 17.0%). FA was detected within 424/470 (90%) groups of serial sections of transversely cryotomed skin containing follicular infundibula, but never in 48/48 (100%) groups of sections containing only deeper follicular structures, nor in receptor fluid, suggesting that FA does not permeate beyond the infundibulum. The FA concentration (mean ± SEM) in the most superficial 240 μm of skin was 2000 ± 815 μg/g. CONCLUSIONS: Topically applied FA can greatly exceed MICs for canine pathogenic staphylococci at the most common sites of infection. Topical FA therapy should now be evaluated using available formulations in vivo as an alternative to systemic therapy for canine superficial bacterial folliculitis.Peer reviewedFinal Published versio

Persistent topology for natural data analysis - A survey

Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and classification of cells, lesions, music pieces, gait, oil and gas reservoirs, cyclones, galaxies, bones, brain connections, languages, handwritten and gestured letters are shown