Some Positone Problems Suggested by Nonlinear Heat Generation

There is much current interest in boundary value problems containing positive linear differential operators and monotone functions of the dependent variable, see for example, M.A. Krasnosel'ski [1] and H. H. Schaefer [2]. We call such problems "positone" and shall examine here a particular class of them (which have been called non-linear eigenvalue problems in [2])

Overcommitment in Cloud Services -- Bin packing with Chance Constraints

This paper considers a traditional problem of resource allocation, scheduling jobs on machines. One such recent application is cloud computing, where jobs arrive in an online fashion with capacity requirements and need to be immediately scheduled on physical machines in data centers. It is often observed that the requested capacities are not fully utilized, hence offering an opportunity to employ an overcommitment policy, i.e., selling resources beyond capacity. Setting the right overcommitment level can induce a significant cost reduction for the cloud provider, while only inducing a very low risk of violating capacity constraints. We introduce and study a model that quantifies the value of overcommitment by modeling the problem as a bin packing with chance constraints. We then propose an alternative formulation that transforms each chance constraint into a submodular function. We show that our model captures the risk pooling effect and can guide scheduling and overcommitment decisions. We also develop a family of online algorithms that are intuitive, easy to implement and provide a constant factor guarantee from optimal. Finally, we calibrate our model using realistic workload data, and test our approach in a practical setting. Our analysis and experiments illustrate the benefit of overcommitment in cloud services, and suggest a cost reduction of 1.5% to 17% depending on the provider's risk tolerance

A generalization of Gabriel's Galois covering functors and derived equivalences

Let $G$ be a group acting on a category $\mathcal{C}$. We give a definition for a functor $F\colon \mathcal{C} \to \mathcal{C}'$ to be a $G$-covering and three constructions of the orbit category $\mathcal{C}/G$, which generalizes the notion of a Galois covering of locally finite-dimensional categories with group $G$ whose action on $\mathcal{C}$ is free and locally bonded defined by Gabriel. Here $\mathcal{C}/G$ is defined for any category $\mathcal{C}$ and we do not require that the action of $G$ is free or locally bounded. We show that a $G$-covering is a universal "$G$-invariant" functor and is essentially given by the canonical functor $\mathcal{C} \to \mathcal{C}/G$. By using this we improve a covering technique for derived equivalence. Also we prove theorems describing the relationships between smash product construction and the orbit category construction by Cibils and Marcos (2006) without the assumption that the $G$-action is free. The orbit category construction by a cyclic group generated by an auto-equivalence modulo natural isomorphisms (e.g., the construction of cluster categories) is justified by a notion of the "colimit orbit category". In addition, we give a presentation of the orbit category of a category with a monoid action by a quiver with relations, which enables us to calculate many examples.Comment: Title changed. Definitions of $\mathrm{Mod}^G\mathcal{C}$ and $\mathrm{Mod}_G\mathcal{B}$ in section 6 were corrected. Proof of Theorem 8.1 is slightly changed to make it more readable. Other minor change

A generalization of Gabriel's Galois covering functors II: 2-categorical Cohen-Montgomery duality

Given a group $G$, we define suitable 2-categorical structures on the class of all small categories with $G$-actions and on the class of all small $G$-graded categories, and prove that 2-categorical extensions of the orbit category construction and of the smash product construction turn out to be 2-equivalences (2-quasi-inverses to each other), which extends the Cohen-Montgomery duality.Comment: 31 pages. I moved the Sec of G-GrCat into Sec 3, and added Lem 5.6. I added more explanations in the proof of Cor 7.6 with (7.5). I added Def 7.7 and Lem 7.8 with the necessary additional assumptions in Props 7.9 and 7.11. I added Lem 8.8 with a short proof, Rmk 8.9 and the proof of Lem 8.10. The final publication is available at Springer via http://dx.doi.org/10.1007/s10485-015-9416-

Indocyanine green fluorescence imaging in colorectal surgery: overview, applications, and future directions

Indocyanine green fluorescence imaging is a surgical tool with increasing applications in colorectal surgery. This tool has received acceptance in various surgical disciplines as a potential method to enhance surgical field visualisation, improve lymph node retrieval, and decrease the incidence of anastomotic leaks. In colorectal surgery specifically, small studies have shown that intraoperative fluorescence imaging is a safe and feasible method to assess anastomotic perfusion, and its use might affect the incidence of anastomotic leaks. Controlled trials are ongoing to validate these conclusions. The number of new indications for indocyanine green continues to increase, including innovative options for detecting and guiding management of colorectal metastasis to the liver. These advances could offer great value for surgeons and patients, by improving the accuracy and outcomes of oncological resections

Experience with statically-generated proxies for facilitating Java runtime specialisation

Issues pertaining to mechanisms which can be used to change the behaviour of Java classes at runtime are discussed. The proxy mechanism is compared to, and contrasted with other standard approaches to this problem. Some of the problems the proxy mechanism is subject to are expanded upon. The question of whether statically-developed proxies are a viable alternative to bytecode rewriting was investigated by means of the JavaCloak system, which uses statically-generated proxies to alter the runtime behaviour of externally-developed code. The issues addressed include ensuring the type safety, dealing with the self problem, object encapsulation, and issues of object identity and equality. Some performance figures are provided which demonstrate the load the JavaCloak proxy mechanism places on the system

The distribution of Dishevelled in convergently extending mesoderm

Convergent extension (CE) is a conserved morphogenetic movement that drives axial lengthening of the primary body axis and depends on the planar cell polarity (PCP) pathway. In Drosophila epithelia, a polarised subcellular accumulation of PCP core components, such as Dishevelled (Dvl) protein, is associated with PCP function. Dvl has long been thought to accumulate in the mediolateral protrusions in Xenopus chordamesoderm cells undergoing CE. Here we present a quantitative analysis of Dvl intracellular localisation in Xenopus chordamesoderm cells. We find that, surprisingly, accumulations previously observed at mediolateral protrusions of chordamesodermal cells are not protrusion-specific but reflect yolk-free cytoplasm and are quantitatively matched by the distribution of the cytoplasm-filling lineage marker dextran. However, separating cell cortex-associated from bulk Dvl signal reveals a statistical enrichment of Dvl in notochord–somite boundary-(NSB)-directed protrusions, which is dependent upon NSB proximity. Dvl puncta were also observed, but only upon elevated overexpression. These puncta showed no statistically significant spatial bias, in contrast to the strongly posteriorly-enriched GFP-Dvl puncta previously reported in zebrafish. We propose that Dvl distribution is more subtle and dynamic than previously appreciated and that in vertebrate mesoderm it reflects processes other than protrusion as such

Measurement models for time-resolved spectroscopy: a comment

We present an exactly solvable model for photon emission, which allows us to examine the evolution of the photon wavefunction in space and time. We apply this model to coherent phenomena in three-level systems with a special emphasis on the photon detection process.Comment: 14 pages RevTex, 4 figure

Elicited imitation in lexical development: Evidence from a study of temporal reference

This study examined the use of elicited imitation in investigating lexical development within a semantic domain. For this purpose the acquisition of reference to sequence and simultaneity by 3–5 year old children was examined. Three factors were proposed to account for the order in which lexical items within a semantic field are acquired: restrictedness of a lexical item, congruence with perceptual strategies, and conceptual simplicity. A significantly greater number of correct responses was found in sentences describing sequential events than in simultaneous events. Furthermore, imitations of sentences referring to simultaneity were more degraded than imitations of sentences referring to sequence. The children seemed to begin acquiring reference to temporally related events by learning about words describing serially ordered events. A three stage developmental model is proposed to account for the results.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45100/1/10936_2005_Article_BF01067508.pd

Context and strategy in acquiring temporal connectives

There has been considerable debate over the role of comprehension strategies in the acquisition of temporal connectives. This study examined the role of caluse logic and interpretational strategies in the acquisition of temporal words; age-related changes were also considered. Thirty-two children between 3 and 5 years of age served as subjects. Sentences with a variety of temporal words were used to tap children's comprehension of “before,” “after,” “when,” “while,” “just before that,” and “and after that.” Clause logic was found to significantly improve the understanding of these sentences. However, the order of mention and main clause first strategies were used infrequently. Apparently, when children respond to sentences that describe information in a way that is consistent with that they normally hear, these strategies are seldom applied.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45103/1/10936_2005_Article_BF01072000.pd