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

The Index of (White) Noises and their Product Systems

(See detailed abstract in the article.) We single out the correct class of spatial product systems (and the spatial endomorphism semigroups with which the product systems are associated) that allows the most far reaching analogy in their classifiaction when compared with Arveson systems. The main differences are that mere existence of a unit is not it sufficient: The unit must be CENTRAL. And the tensor product under which the index is additive is not available for product systems of Hilbert modules. It must be replaced by a new product that even for Arveson systems need not coincide with the tensor product

Nevanlinna-Pick interpolation on distinguished varieties in the bidisk

This article treats Nevanlinna-Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of reproducing kernels naturally associated to the variety. The examples of the Neil parabola and doubly connected domains are discussed.Comment: 31 pages. The question left open at the end of version 1 has been answered in the affirmative; see Theorem 1.12 and Corollary 1.13 in version

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

Testing umbrella species and food-web properties of large carnivores in the Rocky Mountains

Despite criticisms, the umbrella species concept remains a fundamental conservation tool for protecting biodiversity in the face of global change, yet it is rarely tested. Food web theory provides a tool to test both umbrella-species' suitability and their ecological function, which we investigate in a large-mammal food web. Using data from 698 camera trap locations in the Canadian Rockies, we develop hierarchical occupancy models to predict the co-occurrence of 16 large mammal species. We draw upon previous diet studies in the Canadian Rockies to describe the meta food-web (meta-web) for these species. Next, we filtered the meta-web using predicted occupancy to estimate realized food webs at each camera location. We tested the umbrella species concept using predicted occupancy across all 698 camera sites. We then tested for carnivore effects using realized food webs on 5 food-web properties: species richness, links, connectance, nestedness and modularity using generalized linear models while accounting for landscape covariates known to affect food web dynamics. Our multispecies occupancy models reflected factors previously demonstrated to affect large mammal occurrence. Our results also demonstrated that grizzly bear (Ursus horribilis), a generalist carnivore, was the best umbrella carivore species, and explained species richness the best. When considering food web properties, however, wolves (Canis lupus) and cougars (Felis concolor) served as better umbrellas that also captured food web properties such as connectance, links and nestedness that better reflect ecological interactions. Our results support the role of large carnivores as umbrella and ecologically interactive species in conservation planning

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

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

A systematic review of outcomes reported inpediatric perioperative research: A report from the Pediatric Perioperative Outcomes Group

The Pediatric Perioperative Outcomes Group (PPOG) is an international collaborative of clinical investigators and clinicians within the subspecialty of pediatric anesthesiology and perioperative care which aims to use COMET (Core Outcomes Measures in Effectiveness Trials) methodology to develop core outcome sets for infants, children, and young people that are tailored to the priorities of the pediatric surgical population. Focusing on four age‐dependent patient subpopulations determined a priori for core outcome set development: (a) neonates and former preterm infants (up to 60 weeks postmenstrual age); (b) infants (>60 weeks postmenstrual age—1‐13‐<18 years), we conducted a systematic review of outcomes reported in perioperative studies that include participants within age‐dependent pediatric subpopulations. Our review of pediatric perioperative controlled trials published from 2008 to 2018 identified 724 articles reporting 3192 outcome measures. The proportion of published trials and the most frequently reported outcomes varied across predetermined age‐groups. Outcomes related to patient comfort, particularly pain and analgesic requirement, were the most frequent domain for infants, children, and adolescents. Clinical indicators, particularly cardiorespiratory or medication‐related adverse events, were the most common outcomes for neonates and infants <60 weeks and were the second most frequent domain at all other ages. Neonates and infants <60 weeks of age were significantly under‐represented in perioperative trials. Patient‐centered outcomes, healthcare utilization, and bleeding/transfusion‐related outcomes were less often reported. In most studies, outcomes were measured in the immediate perioperative period, with the duration often restricted to the postanesthesia care unit or the first 24 postoperative hours. The outcomes identified with this systematic review will be combined with patient‐centered outcomes identified through a subsequent stakeholder engagement study to arrive at a core outcome set for each age‐specific group