Quantized Nambu-Poisson Manifolds and n-Lie Algebras

We investigate the geometric interpretation of quantized Nambu-Poisson structures in terms of noncommutative geometries. We describe an extension of the usual axioms of quantization in which classical Nambu-Poisson structures are translated to n-Lie algebras at quantum level. We demonstrate that this generalized procedure matches an extension of Berezin-Toeplitz quantization yielding quantized spheres, hyperboloids, and superspheres. The extended Berezin quantization of spheres is closely related to a deformation quantization of n-Lie algebras, as well as the approach based on harmonic analysis. We find an interpretation of Nambu-Heisenberg n-Lie algebras in terms of foliations of R^n by fuzzy spheres, fuzzy hyperboloids, and noncommutative hyperplanes. Some applications to the quantum geometry of branes in M-theory are also briefly discussed.Comment: 43 pages, minor corrections, presentation improved, references adde

Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds

We develop quantization techniques for describing the nonassociative geometry probed by closed strings in flat non-geometric R-flux backgrounds M. Starting from a suitable Courant sigma-model on an open membrane with target space M, regarded as a topological sector of closed string dynamics in R-space, we derive a twisted Poisson sigma-model on the boundary of the membrane whose target space is the cotangent bundle T^*M and whose quasi-Poisson structure coincides with those previously proposed. We argue that from the membrane perspective the path integral over multivalued closed string fields in Q-space is equivalent to integrating over open strings in R-space. The corresponding boundary correlation functions reproduce Kontsevich's deformation quantization formula for the twisted Poisson manifolds. For constant R-flux, we derive closed formulas for the corresponding nonassociative star product and its associator, and compare them with previous proposals for a 3-product of fields on R-space. We develop various versions of the Seiberg-Witten map which relate our nonassociative star products to associative ones and add fluctuations to the R-flux background. We show that the Kontsevich formula coincides with the star product obtained by quantizing the dual of a Lie 2-algebra via convolution in an integrating Lie 2-group associated to the T-dual doubled geometry, and hence clarify the relation to the twisted convolution products for topological nonassociative torus bundles. We further demonstrate how our approach leads to a consistent quantization of Nambu-Poisson 3-brackets.Comment: 52 pages; v2: references adde

Fish as Reservoirs and Vectors of Vibrio cholerae

Vibrio cholerae, the etiologic agent of cholera, is autochthonous to various aquatic environments, but despite intensive efforts its ecology remains an enigma. Recently, it was suggested that copepods and chironomids, both considered as natural reservoirs of V. cholerae, are dispersed by migratory waterbirds, thus possibly distributing the bacteria between water bodies within and between continents. Although fish have been implicated in the scientific literature with cholera cases, as far as we know, no study actually surveyed the presence of the bacteria in the fish. Here we show for the first time that fish of various species and habitats contain V. cholerae in their digestive tract. Fish (n = 110) were randomly sampled from freshwater and marine habitats in Israel. Ten different fish species sampled from freshwater habitats (lake, rivers and fish ponds), and one marine species, were found to carry V. cholerae. The fish intestine of Sarotherodon galilaeus harboured ca. 5×103 V. cholerae cfu per 1 gr intestine content—high rates compared with known V. cholerae cfu numbers in the bacteria's natural reservoirs. Our results, combined with evidence from the literature, suggest that fish are reservoirs of V. cholerae. As fish carrying the bacteria swim from one location to another (some fish species move from rivers to lakes or sea and vice versa), they serve as vectors on a small scale. Nevertheless, fish are consumed by waterbirds, which disseminate the bacteria on a global scale. Moreover, V. cholerae isolates had the ability to degrade chitin, indicating a commensal relationship between V. cholerae and fish. Better understanding of V. cholerae ecology can help reduce the times that human beings come into contact with this pathogen and thus minimize the health risk this poses

Light and tree size influence belowground development in yellow birch and sugar maple

The effects of light and tree size on the root architecture and mycorrhiza of yellow birch (Betula alleghaniensis Britton) and sugar maple (Acer saccharum Marsh) growing in the understory of deciduous forests in southern Qu

D1-Strings in Large RR 3-Form Flux, Quantum Nambu Geometry and M5-Branes in C-Field

We consider D1-branes in a RR flux background and show that there is a low energy - large flux double scaling limit where the D1-branes action is dominated by a Chern-Simons-Myers coupling term. As a classical solution to the matrix model, we find a novel quantized geometry characterized by a quantum Nambu 3-bracket. Infinite dimensional representations of the quantum Nambu geometry are constructed which demonstrate that the quantum Nambu geometry is intrinsically different from the ordinary Lie algebra type noncommutative geometry. Matrix models for the IIB string, IIA string and M-theory in the corresponding backgrounds are constructed. A classical solution of a quantum Nambu geometry in the IIA Matrix string theory gives rise to an expansion of the fundamental strings into a system of multiple D4-branes and the fluctuation is found to describe an action for a non-abelian 3-form field strength which is a natural non-abelian generalization of the PST action for a single D4-brane. In view of the recent proposals of the M5-branes theory in terms of the D4-branes, we suggest a natural way to include all the KK modes and propose an action for the the multiple M5-branes in a constant C-field. The worldvolume of the M5-branes in a C-field is found to be described by a quantum Nambu geometry with self-dual parameters. It is intriguing that our action is naturally formulated in terms of a 1-form gauge field living on a six dimensional quantum Nambu geometry.Comment: 34 pages. LaTe

Capitolo 6 Alimenti del libro dal titolo: Alimentazione Nutrizione e Salute

Leggendo l’indice di quest’opera, si rimane colpiti nel vedere in quanti modi la nutrizione entri, direttamente o indirettamente, nella nostra vita. È un universo che solo da poco tempo la scienza ha cominciato a esplorare, scoprendo molte cose (e sfatandone anche tante altre). È per questa ragione che da più di 20 anni abbiamo creato a SuperQuark la rubrica “Scienza in cucina” (affidata proprio a una co-autrice di questo volume). Si dice spesso che il cibo è il carburante del nostro corpo: in realtà non è solo così. Il cibo “è” il nostro corpo. Noi infatti siamo interamente costruiti con i materiali dei cibi che mangiamo. Le nostre cellule sono come gli individui: nascono, si nutrono, eliminano rifiuti, invecchiano e infine muoiono, mentre altre prendono il loro posto. È come se una casa venisse continuamente demolita, mattone per mattone, e ricostruita con altri nuovi. Questo vale anche per il cervello: è vero che le cellule nervose non si replicano (tranne in alcuni casi) ma ogni singola cellula nervosa ha (a livello molecolare) il suo metabolismo e anch’essa si rinnova con i materiali portati dall’alimentazione. In fondo, anche la stessa lotta per la sopravvivenza in natura, e quindi l’evoluzione, è profondamente legata alla competizione sul cibo. A tutto ciò non pensiamo quando ci mettiamo a tavola, ma all’interno del nostro organismo agisce senza sosta una efficientissima catena di smontaggio e di rimontaggio, che richiede un equilibrio fra i materiali che entrano e quelli che vengono eliminati, in modo che sia assicurato un corretto funzionamento d’insieme. Se la qualità, o la quantità, dei nutrienti è sbagliata, a lungo andare l’organismo ne subisce le conseguenze generando, per esempio, denutrizione, oppure obesità: ma tra questi due estremi esiste una grande varietà di situazioni che spesso possono ridurre l’efficienza del sistema o “ingolfare” la macchina, provocando vari tipi di patologie. Nel campo della nutrizione le ricerche avanzano a ritmo incredibile, e spesso certe conoscenze del passato vanno rivisitate con un’angolazione diversa: come l’interazione personalizzata di ogni organismo con il cibo in funzione del genoma, delle condizioni fisiologiche o patologiche, e anche alla luce delle recenti scoperte nel campo dell’epigenetica. Un altro settore in continua evoluzione è quello riguardante il ruolo del cosiddetto microbiota (cioè dei microrganismi presenti in enorme quantità nell’apparato digerente, e diversi in ogni individuo) nello sviluppo e nel funzionamento dell’intero organismo umano. Insomma, si sta scoprendo sempre più quanto ogni individuo abbia un rapporto particolare con il cibo, al punto di prevedere in futuro dei modelli di alimentazione personalizzati, in funzione delle caratteristiche fisiche, del tipo di attività, ma basandosi anche su elementi finora non presi in considerazione. Questo libro affronta proprio i diversi aspetti del rapporto tra alimentazione, nutrizione e salute, e si propone di aiutare chi studia e lavora in questo campo per meglio orientarsi tra la grande quantità di messaggi che provengono dal mondo della ricerca. Grazie a queste nuove conoscenze, inoltre, diventa anche possibile agire in modo più efficace su due grandi leve che regolano il corretto rapporto tra cibo e salute: la prevenzione e l’educazione alimentare. Piero Angel

Assessment of verbascoside absorption in human colonic tissues using the Ussing chamber model

The intestinal absorption of verbascoside (VB), a phenylpropanoid glycoside, extracted and purified from olive mill waste water (OMWW), was investigated using viable and healthy human colonic tissues, mounted in an Ussing chamber. Additionally, VB absorption and transport through the intestinal mucosa were quantified using permeability coefficients. VB absorption was time-dependent and varied in relation to the specific colonic segments considered. In particular, major uptake/absorption (0.50 μg/cm2) occurred between 5 and 15 min in the proximal tract of the colon, followed by descending colon (0.38 μg/cm2) between 30 and 60 min, and sigmoid–rectum colon (0.34 μg/cm2) at 60 min. Overall, VB was absorbed rapidly, with an average uptake of 0.29 μg VB per cm2, corresponding to a total accumulation efficiency of ~ 0.12%. Moreover, the presence of the VB in the basolateral side supported the hypothesis of its bioavailability in the extent of 0.1%. In addition, the permeability coefficient calculation has contributed in a deeper understanding of VB absorption and transport across the human intestinal barrier and could be utilized for other polyphenols present in food and in dietary supplements

Affect in mathematics education: an introduction

The article presents an introduction to the concept of affect in mathematics education research