1,182 research outputs found

    The Cheeger problem in abstract measure spaces

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    We consider nonnegative (Formula presented.) -finite measure spaces coupled with a proper functional (Formula presented.) that plays the role of a perimeter. We introduce the Cheeger problem in this framework and extend many classical results on the Cheeger constant and on Cheeger sets to this setting, requiring minimal assumptions on the pair measure space perimeter. Throughout the paper, the measure space will never be asked to be metric, at most topological, and this requires the introduction of a suitable notion of Sobolev spaces, induced by the coarea formula with the given perimeter

    Tracking the transfer of antimicrobial resistance genes from raw materials to sourdough breads

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    The present study hypothesizes that raw materials used in bread making can transfer antibiotic resistance genes (ARGs) to processed breads. Four types of flour and four types of semolina were purchased from supermarkets and inoculated with a commercial dried sourdough starter to make breads. The microbiological characteristics of all raw materials and fermented doughs were investigated. The levels of yeasts and lactic acid bacteria (LAB) increased up to 107 CFU/g. The values of pH decreased to 4.54–4.86 while total titratable acidity increased inversely. All unprocessed and processed samples, including breads, were analyzed by a molecular approach to detect bacterial and fungal DNAs and 17 antibiotic resistance genes for penicillins, macrolides, tetracyclines, and chloramphenicol. Illumina technology showed that the operational taxonomy units (OTUs) identified from unprocessed wheat milling products, fermented doughs, and baked products mainly belonged to Acetobacteraceae. Enterococci were present in all doughs. After baking, the relative abundance (RA)% of Enterococcus and Acetobacteraceae decreased. The DNA analyzed for fungal composition showed that Kazachstania humilis dominated dried sourdough starter and doughs, and its OTUs were also detected at high RA% in baked products. The search for ARGs revealed that all samples analyzed did not show resistance to penicillins, chloramphenicol, and macrolides. However, three of the semolinas included in this study (S1, S3 and S4) and the corresponding doughs (SD1, SD3 and SD4) were positive for tet(A) and tet(B) resistance genes. This work indicated that breads have a limited role in the dissemination of ARG

    Tracking the transfer of antimicrobial resistance genes from raw materials to sourdough breads

    Get PDF
    The present study hypothesizes that raw materials used in bread making can transfer antibiotic resistance genes (ARGs) to processed breads. Four types of flour and four types of semolina were purchased from supermarkets and inoculated with a commercial dried sourdough starter to make breads. The microbiological characteristics of all raw materials and fermented doughs were investigated. The levels of yeasts and lactic acid bacteria (LAB) increased up to 107 CFU/g. The values of pH decreased to 4.54–4.86 while total titratable acidity increased inversely. All unprocessed and processed samples, including breads, were analyzed by a molecular approach to detect bacterial and fungal DNAs and 17 antibiotic resistance genes for penicillins, macrolides, tetracyclines, and chloramphenicol. Illumina technology showed that the operational taxonomy units (OTUs) identified from unprocessed wheat milling products, fermented doughs, and baked products mainly belonged to Acetobacteraceae. Enterococci were present in all doughs. After baking, the relative abundance (RA)% of Enterococcus and Acetobacteraceae decreased. The DNA analyzed for fungal composition showed that Kazachstania humilis dominated dried sourdough starter and doughs, and its OTUs were also detected at high RA% in baked products. The search for ARGs revealed that all samples analyzed did not show resistance to penicillins, chloramphenicol, and macrolides. However, three of the semolinas included in this study (S1, S3 and S4) and the corresponding doughs (SD1, SD3 and SD4) were positive for tet(A) and tet(B) resistance genes. This work indicated that breads have a limited role in the dissemination of ARGs

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    Convergence rate of Tsallis entropic regularized optimal transport

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    In this paper, we consider Tsallis entropic regularized optimal transport and discuss the convergence rate as the regularization parameter ε\varepsilon goes to 00. In particular, we establish the convergence rate of the Tsallis entropic regularized optimal transport using the quantization and shadow arguments developed by Eckstein--Nutz. We compare this to the convergence rate of the entropic regularized optimal transport with Kullback--Leibler (KL) divergence and show that KL is the fastest convergence rate in terms of Tsallis relative entropy.Comment: 21 page

    Risposta molecolare ed ecofisiologica del frumento duro a stress abiotici

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    Il frumento duro, Triticum turgidum subsp. durum (Desf.) Husn., è un cereale coltivato in tutto il mondo ed è una delle principali fonti di carboidrati vegetali nell'alimentazione umana. Si tratta di una delle colture più diffuse nei paesi del Mediterraneo, con un ruolo molto importante per la loro economia e tradizione. Queste aree sono caratterizzate da scarsità di piogge, siccità, salinità e basso contenuto di sostanza organica nel suolo, che causano limitazioni alla coltivazione senza apporto di fertilizzanti azotati. Recentemente però, è chiaramente emerso che l'uso massiccio di fertilizzanti a base di azoto (N) può determinare effetti dannosi significativi sul funzionamento degli ecosistemi terrestri e acquatici, sull'inquinamento atmosferico e delle acque e sulla salute umana. Tutte queste preoccupazioni pongono una maggiore enfasi sull'aumento dell'efficienza d'uso dell'azoto (NUE) e più in generale sull’adattamento di queste colture a condizioni di stress abiotico. I fattori di trascrizione (FT) MYB rappresentano una delle più grandi famiglie di FT nelle piante, essendo coinvolti in vari processi vegetali specifici, come le risposte a stress biotici e abiotici. L'implicazione dei FT MYB nei meccanismi di tolleranza allo stress abiotico è particolarmente interessante per il miglioramento genetico delle colture, poiché le condizioni ambientali possono influenzare negativamente la crescita e la produttività. Nel presente studio è stata eseguita un'identificazione dei FT R2R3-MYB nell’intero genoma del grano duro. La ricerca del profilo MYB e le analisi filogenetiche basate sull'omologia con Arabidopsis e riso dei FT MYB hanno portato all'identificazione di 233 R2R3-TdMYB (Triticum durum MYB). Sono stati rilevati tre gruppi MYB specifici per la famiglia delle Poaceae, uno dei quali non era mai stato descritto prima. L’analisi di espressione di otto geni, selezionati in diverse condizioni di stress abiotico, ha rivelato che la maggior parte di essi rispondeva soprattutto allo stress salino e da siccità. Infine, le analisi della rete di regolazione genica hanno portato all'identificazione di 41 bersagli genici per tre R2R3-TdMYB, che rappresentano nuovi candidati per le analisi funzionali. È stata inoltre condotta una sperimentazione su quattro varietà di frumento duro, di cui due moderne, Marco Aurelio e Kanakis; una degli anni Settanta, Svevo, e una antica, Senatore Cappelli. I quattro genotipi sono stati coltivati in due siti sperimentali con caratteristiche pedoclimatiche differenti e alla raccolta sono state valutate la risposta produttiva e qualitativa in relazione al sito e a due diverse condizioni agronomiche: concimazione azotata standard e assenza di concimazione azotata. Complessivamente questo studio fornisce una descrizione dettagliata dei geni R2R3-MYB del grano duro contribuendo ad approfondire la comprensione della risposta molecolare del grano duro a condizioni climatiche sfavorevoli. Fornisce in aggiunta una valutazione della risposta genotipica diversificata allo stress da N sia da un punto di vista quantitativo che qualitativo, gettando le basi per ulteriori studi finalizzati alla selezione di genotipi e caratteri fenotipici di valore per il successo dei futuri programmi di miglioramento genetico del frumento duro

    Stability of Tori under Lower Sectional Curvature

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    Let (Min,gi)GH(X,dX)(M^n_i, g_i)\stackrel{GH}{\longrightarrow} (X,d_X) be a Gromov-Hausdorff converging sequence of Riemannian manifolds with Secgi1{\rm Sec}_{g_i} \ge -1, diam(Mi)D{\rm diam}\, (M_i)\le D, and such that the MinM^n_i are all homeomorphic to tori TnT^n. Then XX is homeomorphic to a kk-dimensional torus TkT^k for some 0kn0\leq k\leq n. This answers a question of Petrunin in the affirmative. In the three dimensional case we prove the same stability under the weaker condition Ricgi2{\rm Ric}_{g_i} \ge -2

    Fast Marching Energy CNN

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    Leveraging geodesic distances and the geometrical information they convey is key for many data-oriented applications in imaging. Geodesic distance computation has been used for long for image segmentation using Image based metrics. We introduce a new method by generating isotropic Riemannian metrics adapted to a problem using CNN and give as illustrations an example of application. We then apply this idea to the segmentation of brain tumours as unit balls for the geodesic distance computed with the metric potential output by a CNN, thus imposing geometrical and topological constraints on the output mask. We show that geodesic distance modules work well in machine learning frameworks and can be used to achieve state-of-the-art performances while ensuring geometrical and/or topological properties

    Lower Ricci Curvature and Nonexistence of Manifold Structure

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    It is known that a limit (Mjn,gj)(Xk,d)(M^n_j,g_j)\to (X^k,d) of manifolds MjM_j with uniform lower bounds on Ricci curvature must be kk-rectifiable for some unique dimX:=kn=dimMj\dim X:= k\leq n = \dim M_j. It is also known that if k=nk=n, then XnX^n is a topological manifold on an open dense subset, and it has been an open question as to whether this holds for k<nk<n. Consider now any smooth complete 44-manifold (X4,h)(X^4,h) with Ric>λ\text{Ric}>\lambda and λR\lambda\in \mathbb{R}. Then for each ϵ>0\epsilon>0 we construct a complete 44-rectifiable metric space (Xϵ4,dϵ)(X^4_\epsilon,d_\epsilon) with dGH(Xϵ4,X4)<ϵd_{GH}(X^4_\epsilon,X^4)<\epsilon such that the following hold. First, Xϵ4X^4_\epsilon is a limit space (Mj6,gj)Xϵ4(M^6_j,g_j)\to X^4_\epsilon where Mj6M^6_j are smooth manifolds with Ricj>λ\text{Ric}_j>\lambda satisfying the same lower Ricci bound. Additionally, Xϵ4X^4_\epsilon has no open subset which is topologically a manifold. Indeed, for any open UXϵ4U\subseteq X^4_\epsilon we have that the second homology H2(U)H_2(U) is infinitely generated. Topologically, Xϵ4X^4_\epsilon is the connect sum of X4X^4 with an infinite number of densely spaced copies of CP2\mathbb{C} P^2 . In this way we see that every 44-manifold X4X^4 may be approximated arbitrarily closely by 44-dimensional limit spaces Xϵ4X^4_\epsilon which are nowhere manifolds. We will see there is an, as now imprecise, sense in which generically one should expect manifold structures to not exist on spaces with higher dimensional Ricci curvature lower bounds
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