Progress in noncommutative function theory

In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of representations. We will show that these spaces of representations can be parameterized as unit balls of certain $W^{*}$-correspondences and the functions can be viewed as Schur class operator functions on these balls. We will provide evidence to show that the elements in these (non commutative) Hardy algebras behave very much like bounded analytic functions and the study of these algebras should be viewed as noncommutative function theory

Strong Shift Equivalence of C∗C^*-correspondences

We define a notion of strong shift equivalence for $C^*$-correspondences and show that strong shift equivalent $C^*$-correspondences have strongly Morita equivalent Cuntz-Pimsner algebras. Our analysis extends the fact that strong shift equivalent square matrices with non-negative integer entries give stably isomorphic Cuntz-Krieger algebras.Comment: 26 pages. Final version to appear in Israel Journal of Mathematic

Groupoids and an index theorem for conical pseudo-manifolds

We define an analytical index map and a topological index map for conical pseudomanifolds. These constructions generalize the analogous constructions used by Atiyah and Singer in the proof of their topological index theorem for a smooth, compact manifold $M$. A main ingredient is a non-commutative algebra that plays in our setting the role of $C_0(T^*M)$. We prove a Thom isomorphism between non-commutative algebras which gives a new example of wrong way functoriality in $K$-theory. We then give a new proof of the Atiyah-Singer index theorem using deformation groupoids and show how it generalizes to conical pseudomanifolds. We thus prove a topological index theorem for conical pseudomanifolds

Operator theory and function theory in Drury-Arveson space and its quotients

The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the structure of a Hilbert module. This survey aims to introduce the Drury-Arveson space, to give a panoramic view of the main operator theoretic and function theoretic aspects of this space, and to describe the universal role that it plays in multivariable operator theory and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page

Quantized reduction as a tensor product

Symplectic reduction is reinterpreted as the composition of arrows in the category of integrable Poisson manifolds, whose arrows are isomorphism classes of dual pairs, with symplectic groupoids as units. Morita equivalence of Poisson manifolds amounts to isomorphism of objects in this category. This description paves the way for the quantization of the classical reduction procedure, which is based on the formal analogy between dual pairs of Poisson manifolds and Hilbert bimodules over C*-algebras, as well as with correspondences between von Neumann algebras. Further analogies are drawn with categories of groupoids (of algebraic, measured, Lie, and symplectic type). In all cases, the arrows are isomorphism classes of appropriate bimodules, and their composition may be seen as a tensor product. Hence in suitable categories reduction is simply composition of arrows, and Morita equivalence is isomorphism of objects.Comment: 44 pages, categorical interpretation adde

Effects of Wolves on Elk and Cattle Behaviors: Implications for Livestock Production and Wolf Conservation

BACKGROUND: In many areas, livestock are grazed within wolf (Canis lupus) range. Predation and harassment of livestock by wolves creates conflict and is a significant challenge for wolf conservation. Wild prey, such as elk (Cervus elaphus), perform anti-predator behaviors. Artificial selection of cattle (Bos taurus) might have resulted in attenuation or absence of anti-predator responses, or in erratic and inconsistent responses. Regardless, such responses might have implications on stress and fitness. METHODOLOGY/PRINCIPAL FINDINGS: We compared elk and cattle anti-predator responses to wolves in southwest Alberta, Canada within home ranges and livestock pastures, respectively. We deployed satellite- and GPS-telemetry collars on wolves, elk, and cattle (n = 16, 10 and 78, respectively) and measured seven prey response variables during periods of wolf presence and absence (speed, path sinuosity, time spent head-up, distance to neighboring animals, terrain ruggedness, slope and distance to forest). During independent periods of wolf presence (n = 72), individual elk increased path sinuosity (Z = -2.720, P = 0.007) and used more rugged terrain (Z = -2.856, P = 0.004) and steeper slopes (Z = -3.065, P = 0.002). For cattle, individual as well as group behavioral analyses were feasible and these indicated increased path sinuosity (Z = -2.720, P = 0.007) and decreased distance to neighbors (Z = -2.551, P = 0.011). In addition, cattle groups showed a number of behavioral changes concomitant to wolf visits, with variable direction in changes. CONCLUSIONS/SIGNIFICANCE: Our results suggest both elk and cattle modify their behavior in relation to wolf presence, with potential energetic costs. Our study does not allow evaluating the efficacy of anti-predator behaviors, but indicates that artificial selection did not result in their absence in cattle. The costs of wolf predation on livestock are often compensated considering just the market value of the animal killed. However, society might consider refunding some additional costs (e.g., weight loss and reduced reproduction) that might be associated with the changes in cattle behaviors that we documented

Post-myocardial infarction heart failure dysregulates the bone vascular niche

The regulation of bone vasculature by chronic diseases, such as heart failure is unknown. Here, we describe the effects of myocardial infarction and post-infarction heart failure on the bone vascular cell composition. We demonstrate an age-independent loss of type H endothelium in heart failure after myocardial infarction in both mice and humans. Using single-cell RNA sequencing, we delineate the transcriptional heterogeneity of human bone marrow endothelium, showing increased expression of inflammatory genes, including IL1B and MYC, in ischemic heart failure. Endothelial-specific overexpression of MYC was sufficient to induce type H bone endothelial cells, whereas inhibition of NLRP3-dependent IL-1β production partially prevented the post-myocardial infarction loss of type H vasculature in mice. These results provide a rationale for using anti-inflammatory therapies to prevent or reverse the deterioration of bone vascular function in ischemic heart disease

Captive-born collared peccary (Pecari tajacu, Tayassuidae) fails to discriminate between predator and non-predator models

Captive animals may lose the ability to recognize their natural predators, making conservation programs more susceptible to failure if such animals are released into the wild. Collared peccaries are American tayassuids that are vulnerable to local extinction in certain areas, and conservation programs are being conducted. Captive-born peccaries are intended for release into the wild in Minas Gerais state, southeastern Brazil. In this study, we tested the ability of two groups of captive-born collared peccaries to recognize their predators and if they were habituated to humans. Recognition tests were performed using models of predators (canids and felids) and non-predators animals, as well as control objects, such as a plastic chair; a human was also presented to the peccaries, and tested as a separate stimulus. Anti-predator defensive responses such as fleeing and threatening displayswere not observed in response to predator models. Predator detection behaviors both from visual and olfactory cues were displayed, although they were not specifically targeted at predator models. These results indicate that collared peccaries were unable to recognize model predators. Habituation effects, particularly on anti-predator behaviors, were observed both with a 1-h model presentation and across testing days. Behavioral responses to humans did not differ from those to other models. Thus, if these animals were to be released into the wild, they should undergo anti-predator training sessions to enhance their chances of survival