Spectral isometries on non-simple C*-algebras

We prove that unital surjective spectral isometries on certain non-simple unital C*-algebras are Jordan isomorphisms. Along the way, we establish several general facts in the setting of semisimple Banach algebras.

C∗-Segal algebras with order unit

We introduce the notion of a (noncommutative) C *-Segal algebra as a Banach algebra (A, {norm of matrix}{dot operator}{norm of matrix} A) which is a dense ideal in a C *-algebra (C, {norm of matrix}{dot operator}{norm of matrix} C), where {norm of matrix}{dot operator}{norm of matrix} A is strictly stronger than {norm of matrix}{dot operator}{norm of matrix} C onA. Several basic properties are investigated and, with the aid of the theory of multiplier modules, the structure of C *-Segal algebras with order unit is determined.

Semiring induced valuation algebras: Exact and approximate local computation algorithms

Local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure, called valuation algebra.There are many models of this algebraic structure ranging from probability theory to numerical analysis, relational databases and various classical and non-classical logics. It turns out that many interesting models of valuation algebras may be derived from semiring valued mappings. In this paper we study how valuation algebras are induced by semirings and how the structure of the valuation algebra is related to the algebraic structure of the semiring. In particular, c-semirings with idempotent multiplication induce idempotent valuation algebras and therefore permit particularly efficient architectures for local computation. Also important are semirings whose multiplicative semigroup is embedded in a union of groups. They induce valuation algebras with a partially defined division. For these valuation algebras, the well-known architectures for Bayesian networks apply. We also extend the general computational framework to allow derivation of bounds and approximations, for when exact computation is not feasible.

Relevance and truthfulness in information correction and fusion

A general approach to information correction and fusion for belief functions is proposed, where not only may the information items be irrelevant, but sources may lie as well. We introduce a new correction scheme, which takes into account uncertain metaknowledge on the source’s relevance and truthfulness and that generalizes Shafer’s discounting operation. We then show how to reinterpret all connectives of Boolean logic in terms of source behavior assumptions with respect to relevance and truthfulness. We are led to generalize the unnormalized Dempster’s rule to all Boolean connectives, while taking into account the uncertainties pertaining to assumptions concerning the behavior of sources. Eventually, we further extend this approach to an even more general setting, where source behavior assumptions do not have to be restricted to relevance and truthfulness.We also establish the commutativity property between correction and fusion processes, when the behaviors of the sources are independent.

The effects of ibuprofen and indomethacin on renal function in the presence and absence of frusemide in healthy volunteers on a restricted sodium diet

1. Since salt depletion stimulates the renal prostaglandin system to maintain renal function, the effects of indomethacin and ibuprofen upon renal haemodynamics, electrolyte excretion and renin release were examined in eight healthy male volunteers on a salt restricted diet, before and after frusemide administration. 2. Neither indomethacin (50 mg) nor ibuprofen (400 mg and 800 mg) affected renal blood flow, glomerular filtration rate or electrolyte excretion before frusemide. 3. Renal blood flow and glomerular filtration rate were significantly increased in the first 20 min after frusemide. These changes were significantly attenuated by indomethacin compared with placebo and ibuprofen 400 mg. Frusemide-induced diuresis but not natriuresis was inhibited by all treatments. 4. Both nonsteroidal agents inhibited equally the rise in renin activity seen after frusemide. 5. In this group of healthy volunteers on a salt restricted diet, ibuprofen and indomethacin had no detrimental effects on renal function in the absence of frusemide. The changes in renal haemodynamics due to frusemide were suppressed more by indomethacin than by ibuprofen, probably reflecting the more potent nature of indomethacin as an inhibitor of prostaglandin synthesis.

Chaotic Banach algebras

We construct an infinite dimensional non-unital Banach algebra $A$ and $a\in A$ such that the sets $\{za^n:z\in\C,\ n\in\N\}$ and $\{({\bf 1}+a)^na:n\in\N\}$ are both dense in $A$, where $\bf 1$ is the unity in the unitalization $A^{\#}=A\oplus \spann\{{\bf 1}\}$ of $A$. As a byproduct, we get a hypercyclic operator $T$ on a Banach space such that $T\oplus T$ is non-cyclic and $\sigma(T)=\{1\}$.

Minimal Hilbert series for quadratic algebras and the Anick conjecture

We study the question on whether the famous Golod–Shafarevich estimate, which gives a lower bound for the Hilbert series of a (noncommutative) algebra, is attained. This question was considered by Anick in his 1983 paper ‘Generic algebras and CW-complexes’, Princeton Univ. Press, where he proved that the estimate is attained for the number of quadratic relations $d\leq n^2/4$
and $d\geq n^2/2$, and conjectured that it is the case for any number of quadratic relations. The particular point where the number of relations is equal to $n(n-1)/2$ was addressed by Vershik. He conjectured that a generic algebra with this number of relations is finite dimensional. We announce here the result that over any infinite field, the Anick conjecture holds for $d \geq 4(n2+n)/9$ and an arbitrary number of generators. We also discuss the result that confirms the Vershik conjecture over any field of characteristic 0, and a series of related
asymptotic results.

Finite dimensional semigroup quadratic algebras with the minimal number of relations

A quadratic semigroup algebra is an algebra over a field given by the generators x_1, . . . , x_n and a finite set of quadratic relations each of which either has the shape x_j x_k = 0 or the shape x_j x_k = x_l x_m . We prove that a quadratic semigroup algebra given by n generators and d=(n^2+n)/4 relations is always infinite dimensional. This strengthens the Golod–Shafarevich estimate for the above class of algebras. Our main result however is that for every n, there is a finite dimensional quadratic semigroup algebra with n generators and d_n relations, where d_n is the first integer greater than (n^2+n)/4 . That is, the above Golod–Shafarevich-type estimate for semigroup algebras is sharp.

Predicting the impacts of climate change on the distribution of threatened forest-restricted birds in Madagascar

The greatest common threat to birds in Madagascar has historically been from anthropogenic deforestation. During recent decades, global climate change is now also regarded as a significant threat to biodiversity. This study uses Maximum Entropy species distribution modeling to explore how potential climate change could affect the distribution of 17 threatened forest endemic bird species, using a range of climate variables from the Hadley Center's HadCM3 climate change model, for IPCC scenario B2a, for 2050. We explore the importance of forest cover as a modeling variable and we test the use of pseudo-presences drawn from extent of occurrence distributions. Inclusion of the forest cover variable improves the models and models derived from real-presence data with forest layer are better predictors than those from pseudo-presence data. Using real-presence data, we analyzed the impacts of climate change on the distribution of nine species. We could not predict the impact of climate change on eight species because of low numbers of occurrences. All nine species were predicted to experience reductions in their total range areas, and their maximum modeled probabilities of occurrence. In general, species range and altitudinal contractions follow the reductive trend of the Maximum presence probability. Only two species (Tyto soumagnei and Newtonia fanovanae) are expected to expand their altitude range. These results indicate that future availability of suitable habitat at different elevations is likely to be critical for species persistence through climate change. Five species (Eutriorchis astur, Neodrepanis hypoxantha, Mesitornis unicolor, Euryceros prevostii, and Oriola bernieri) are probably the most vulnerable to climate change. Four of them (E. astur, M. unicolor, E. prevostii, and O. bernieri) were found vulnerable to the forest fragmentation during previous research. Combination of these two threats in the future could negatively affect these species in a drastic way. Climate change is expected to act differently on each species and it is important to incorporate complex ecological variables into species distribution models.

Display; A Lie

Two original poems

Logics for belief functions on MV-algebras

In this paper we present a generalization of belief functions over fuzzy events. In particular we focus on belief functions defined in the algebraic framework of finite MV-algebras of fuzzy sets. We introduce a fuzzy modal logic to formalize reasoning with belief functions on many-valued events. We prove, among other results, that several different notions of belief functions can be characterized in a quite uniform way, just by slightly modifying the complete axiomatization of one of the modal logics involved in the definition of our formalism. © 2012 Elsevier Inc. All rights reserved.