Jones index theory for Hilbert C*-bimodules and its equivalence with conjugation theory

We introduce the notion of finite right (respectively left) numerical index on a bimodule $X$ over C*-algebras A and B with a bi-Hilbertian structure. This notion is based on a Pimsner-Popa type inequality. The right (respectively left) index element of X can be constructed in the centre of the enveloping von Neumann algebra of A (respectively B). X is called of finite right index if the right index element lies in the multiplier algebra of A. In this case we can perform the Jones basic construction. Furthermore the C*--algebra of bimodule mappings with a right adjoint is a continuous field of finite dimensional C*-algebras over the spectrum of Z(M(A)), whose fiber dimensions are bounded above by the index. We show that if A is unital, the right index element belongs to A if and only if X is finitely generated as a right module. We show that bi-Hilbertian, finite (right and left) index C*-bimodules are precisely those objects of the tensor 2-C*-category of right Hilbertian C*-bimodules with a conjugate object, in the sense of Longo and Roberts, in the same category.Comment: 59 pages, amste

KMS States, Entropy and the Variational Principle in full C*-dynamical systems

To any periodic, unital and full C*-dynamical system (A, \alpha, R) an invertible operator s acting on the Banach space of trace functionals of the fixed point algebra is canonically associated. KMS states correspond to positive eigenvectors of s. A Perron-Frobenius type theorem asserts the existence of KMS states at inverse temperatures equal the logarithms of the inner and outer spectral radii of s (extremal KMS states). Examples arising from subshifts in symbolic dynamics, self-similar sets in fractal geometry and noncommutative metric spaces are discussed. Certain subshifts are naturally associated to the system and the relationship between their topological entropy and inverse temperatures of extremal KMS states are given. Noncommutative shift maps are considered. It is shown that their entropy is bounded by the sum of the entropy of the associated subshift and a suitable entropy computed in the homogeneous subalgebra. Examples are discussed among Matsumoto algebras associated to certain non finite type subshifts. The CNT entropy is compared to the classical measure-theoretic entropy of the subshift. A noncommutative analogue of the classical variational principle for the entropy of subshifts is obtained for the noncommutative shift of certain Matsumoto algebras. More generally, a necessary condition is discussed. In the case of Cuntz-Krieger algebras an explicit construction of the state with maximal entropy from the unique KMS state is done.Comment: 52 pages, AMSTeX. An error in Prop. 7.3 v1 has been corrected, and related text in sections 7-9 has been modified. References added. Abstract modifie

An Algebraic Duality Theory for Multiplicative Unitaries

Multiplicative Unitaries are described in terms of a pair of commuting shifts of relative depth two. They can be generated from ambidextrous Hilbert spaces in a tensor C*-category. The algebraic analogue of the Takesaki-Tatsuuma Duality Theorem characterizes abstractly C*-algebras acted on by unital endomorphisms that are intrinsically related to the regular representation of a multiplicative unitary. The relevant C*-algebras turn out to be simple and indeed separable if the corresponding multiplicative unitaries act on a separable Hilbert space. A categorical analogue provides internal characterizations of minimal representation categories of a multiplicative unitary. Endomorphisms of the Cuntz algebra related algebraically to the grading are discussed as is the notion of braided symmetry in a tensor C*-category.Comment: one reference adde

Distribution patterns of fungi and bacteria in saline soils

Saline soils are environments characterized by uneven temporal and spatial water distribution and localized high concentrations of salts. Spatial distribution patterns of fungi and bacteria in saline soils, and the link between microbial community dynamics and salts accumulation are critical issues throughout the world (Ettema, Wardle 2002). This study was focused on spatial distribution patterns of soil fungi and bacteria in a saline soil located in Piana del Signore (Gela, Italy) where some ecological variables acted as shaping factors in aboveground and belowground communities distribution. Bacterial, archaeal, and fungal communities diversity and distribution in ten soil sites (A horizons, 0-10cm), were characterized by 16S rDNA genes with T-RFLP method. Pyrosequencing-based analysis of the V2-V3 16S rRNA gene region was performed to characterize the sites on the basis of bacterial groups distribution, diversity and assemblage. To better investigate the ecological niches of some of the main culturable species of this environment, it was carried out the isolation and identification of the fungal flora from soil, using Warcup plating within two different salt concentrations (NaCl 5% and 15%), combined with a metabolic screening of some representative isolates (Di Lonardo et al., 2013). A natural gradient of soil salinity shaped the distribution of microbial species in the environment. The different concentration of salt (NaCl), and calcium sulfate (Ca2SO4) in soil influenced the structure and distribution of the microbial communities even when comparing neighboring areas within a 50 m scale. Some bacterial phyla, together with some fungal species, appeared spread in the whole area, independently of the salinity gradient, thus highlighting the presence of organisms with a very different survival strategy in such an extreme environment. In conclusion, the organization and diversity of microbial taxa at a spatial scale reflected the scales of heterogeneity of physical and chemical properties of the habitat under investigation

Salinity and Bacterial Diversity: To What Extent Does the Concentration of Salt Affect the Bacterial Community in a Saline Soil?

In this study, the evaluation of soil characteristics was coupled with a pyrosequencing analysis of the V2-V3 16S rRNA gene region in order to investigate the bacterial community structure and diversity in the A horizon of a natural saline soil located in Sicily (Italy). The main aim of the research was to assess the organisation and diversity of microbial taxa using a spatial scale that revealed physical and chemical heterogeneity of the habitat under investigation. The results provided information on the type of distribution of different bacterial groups as a function of spatial gradients of soil salinity and pH. The analysis of bacterial 16S rRNA showed differences in bacterial composition and diversity due to a variable salt oncentration in the soil. The bacterial community showed a statistically significant spatial variability. Some bacterial phyla appeared spread in the whole area, whatever the salinity gradient. It emerged therefore that a patchy saline soil can not contain just a single microbial community selected to withstand extreme osmotic phenomena, but many communities that can be variously correlated to one or more environmental parameters. Sequences have been deposited to the SRA database and can be accessed on ID Project PRJNA241061

A natural saline soil as a model for understanding to what extent the concentration of salt affects the distribution of microorganisms

Soils preserve and sustain life. Their health and functioning are crucial for crop production and for the maintenance of major ecosystem services. Human induced salinity is one of the main soil threats that reduces soil fertility and affect crop yields. In recent times, great attention has been paid to the general shortage of arable land and to the increasing demand for ecological restoration of areas affected by salinization processes. Despite the diffuse interest on the effects of salinization on plants\u2019 growth, and all the derived socioeconomic issues, very few studies analyzed the ecology of the microbial species in naturally saline soils and the resilience of biological fertility in these extreme habitats. Microorganisms inhabiting such environments may share a strategy, may have developed multiple adaptations for maintaining their populations, and cope eventually to extreme conditions by altruistic or cooperative behaviors for maintaining their metabolism active. The understanding and the knowledge of the composition and distribution of microbial communities in natural hypersaline soils can be interesting for ecological reasons but also to develop new restoration strategy where soil fertility was compromised by natural accidents or human mismanagement. The aim of this research was to provide specific information on saline soils in Italy, stressing mainly their distribution, the socioeconomic issues and the understanding of the characterizing ecological processes. Moreover, natural saline soils were used as a model for understanding to what extent the concentration of salt can affect some basic microbial processes. In the present study, physical, chemical and microbiological soil properties were investigated in the shallower horizons of natural salt affected soils in Sicily (Italy), where some ecological contrasting variables acted as strong drivers in fungal and bacterial spatial distribution. Furthermore, the interface between biological and geochemical components in the surface of that peculiar habitat was investigated to evaluate the organization and diversity of the phototrophic and heterotrophic microorganisms. Sixteen soil samples from A horizons were collected according to a random sampling scheme. Bacterial and archaeal communities were characterized by their 16S rDNA genes with T-RFLP method. A total of 92 genera were identified from the 16S pyrosequencing analysis suggesting that cyanobacteria and communities of sulfur bacteria might directly or indirectly promote the formation of protective envelope. Some bacterial phyla appeared spread in the whole area, whatever the salinity gradient, while other groups showed a distribution linked to very compartmentalised soil properties, such as the presence of saline crusts in the soil surface. Results show that saline soils couldn\u2019t contain just one single microbial community selected to withstand extreme osmotic phenomena, but many communities that can be variously correlated to one or more environmental parameters having great importance for the maintenance of the overall homeostasis

Metabolic synergies in the biotransformation of organic and metallic toxic compounds by a saprotrophic soil fungus

The saprotrophic fungus Penicillium griseofulvum was chosen as model organism to study responses to a mixture of hexachlorocyclohexane (HCH) isomers (α-HCH, β-HCH, γ-HCH, δ-HCH) and of potentially toxic metals (vanadium, lead) in solid and liquid media. The P. griseofulvum FBL 500 strain was isolated from polluted soil containing high concentrations of HCH isomers and potentially toxic elements (Pb, V). Experiments were performed in order to analyse the tolerance/resistance of this fungus to xenobiotics, and to shed further light on fungal potential in inorganic and organic biotransformations. The aim was to examine the ecological and bioremedial potential of this fungus verifying the presence of mechanisms that allow it to transform HCH isomers and metals under different, extreme, test conditions. To our knowledge, this work is the first to provide evidence on the biotransformation of HCH mixtures, in combination with toxic metals, by a saprotrophic non-white-rot fungus and on the metabolic synergies involved

Wettability Modification of Nanomaterials by Low-Energy Electron Flux

Controllable modification of surface free energy and related properties (wettability, hygroscopicity, agglomeration, etc.) of powders allows both understanding of fine physical mechanism acting on nanoparticle surfaces and improvement of their key characteristics in a number of nanotechnology applications. In this work, we report on the method we developed for electron-induced surface energy and modification of basic, related properties of powders of quite different physical origins such as diamond and ZnO. The applied technique has afforded gradual tuning of the surface free energy, resulting in a wide range of wettability modulation. In ZnO nanomaterial, the wettability has been strongly modified, while for the diamond particles identical electron treatment leads to a weak variation of the same property. Detailed investigation into electron-modified wettability properties has been performed by the use of capillary rise method using a few probing liquids. Basic thermodynamic approaches have been applied to calculations of components of solid–liquid interaction energy. We show that defect-free, low-energy electron treatment technique strongly varies elementary interface interactions and may be used for the development of new technology in the field of nanomaterials