981 resultados para Positive Definite Functions
Resumo:
Activated Wnt signaling is critical in the pathogenesis of renal fibrosis, a final common pathway for most forms of chronic kidney disease. Therapeutic intervention by inhibition of individual Wnts or downstream Wnt/β-catenin signaling has been proposed, but these approaches do not interrupt the functions of all Wnts nor block non-canonical Wnt signaling pathways. Alternatively, an orally bioavailable small molecule, Wnt-C59, blocks the catalytic activity of the Wnt-acyl transferase porcupine, and thereby prevents secretion of all Wnt isoforms. We found that inhibiting porcupine dramatically attenuates kidney fibrosis in the murine unilateral ureteral obstruction model. Wnt-C59 treatment similarly blunts collagen mRNA expression in the obstructed kidney. Consistent with its actions to broadly arrest Wnt signaling, porcupine inhibition reduces expression of Wnt target genes and bolsters nuclear exclusion of β-catenin in the kidney following ureteral obstruction. Importantly, prevention of Wnt secretion by Wnt-C59 blunts expression of inflammatory cytokines in the obstructed kidney that otherwise provoke a positive feedback loop of Wnt expression in collagen-producing fibroblasts and epithelial cells. Thus, therapeutic targeting of porcupine abrogates kidney fibrosis not only by overcoming the redundancy of individual Wnt isoforms but also by preventing upstream cytokine-induced Wnt generation. These findings reveal a novel therapeutic maneuver to protect the kidney from fibrosis by interrupting a pathogenic crosstalk loop between locally generated inflammatory cytokines and the Wnt/β-catenin signaling pathway.
Resumo:
Fredholm integral equations of the first kind are the mathematical model common to several electromagnetic, optical and acoustical inverse scattering problems. In most of these problems the solution must be positive in order to satisfy physical plausibility. We consider ill-posed deconvolution problems and investigate several linear regularization algorithms which provide positive approximate solutions at least in the absence of errors on the data.
Resumo:
The paper considers the single machine due date assignment and scheduling problems with n jobs in which the due dates are to be obtained from the processing times by adding a positive slack q. A schedule is feasible if there are no tardy jobs and the job sequence respects given precedence constraints. The value of q is chosen so as to minimize a function ϕ(F,q) which is non-decreasing in each of its arguments, where F is a certain non-decreasing earliness penalty function. Once q is chosen or fixed, the corresponding scheduling problem is to find a feasible schedule with the minimum value of function F. In the case of arbitrary precedence constraints the problems under consideration are shown to be NP-hard in the strong sense even for F being total earliness. If the precedence constraints are defined by a series-parallel graph, both scheduling and due date assignment problems are proved solvable in time, provided that F is either the sum of linear functions or the sum of exponential functions. The running time of the algorithms can be reduced to if the jobs are independent. Scope and purpose We consider the single machine due date assignment and scheduling problems and design fast algorithms for their solution under a wide range of assumptions. The problems under consideration arise in production planning when the management is faced with a problem of setting the realistic due dates for a number of orders. The due dates of the orders are determined by increasing the time needed for their fulfillment by a common positive slack. If the slack is set to be large enough, the due dates can be easily maintained, thereby producing a good image of the firm. This, however, may result in the substantial holding cost of the finished products before they are brought to the customer. The objective is to explore the trade-off between the size of the slack and the arising holding costs for the early orders.
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In this paper we discuss the relationship and characterization of stochastic comparability, duality, and Feller–Reuter–Riley transition functions which are closely linked with each other for continuous time Markov chains. A necessary and sufficient condition for two Feller minimal transition functions to be stochastically comparable is given in terms of their density q-matrices only. Moreover, a necessary and sufficient condition under which a transition function is a dual for some stochastically monotone q-function is given in terms of, again, its density q-matrix. Finally, for a class of q-matrices, the necessary and sufficient condition for a transition function to be a Feller–Reuter–Riley transition function is also given.
Resumo:
Given M(r; f) =maxjzj=r (jf(z)j) , curves belonging to the set of points M = fz : jf(z)j = M(jzj; f)g were de�ned by Hardy to be maximum curves. Clunie asked the question as to whether the set M could also contain isolated points. This paper shows that maximum curves consist of analytic arcs and determines a necessary condition for such curves to intersect. Given two entire functions f1(z) and f2(z), if the maximum curve of f1(z) is the real axis, conditions are found so that the real axis is also a maximum curve for the product function f1(z)f2(z). By means of these results an entire function of in�nite order is constructed for which the set M has an in�nite number of isolated points. A polynomial is also constructed with an isolated point.
Resumo:
A Feller–Reuter–Riley function is a Markov transition function whose corresponding semigroup maps the set of the real-valued continuous functions vanishing at infinity into itself. The aim of this paper is to investigate applications of such functions in the dual problem, Markov branching processes, and the Williams-matrix. The remarkable property of a Feller–Reuter–Riley function is that it is a Feller minimal transition function with a stable q-matrix. By using this property we are able to prove that, in the theory of branching processes, the branching property is equivalent to the requirement that the corresponding transition function satisfies the Kolmogorov forward equations associated with a stable q-matrix. It follows that the probabilistic definition and the analytic definition for Markov branching processes are actually equivalent. Also, by using this property, together with the Resolvent Decomposition Theorem, a simple analytical proof of the Williams' existence theorem with respect to the Williams-matrix is obtained. The close link between the dual problem and the Feller–Reuter–Riley transition functions is revealed. It enables us to prove that a dual transition function must satisfy the Kolmogorov forward equations. A necessary and sufficient condition for a dual transition function satisfying the Kolmogorov backward equations is also provided.
Resumo:
By revealing close links among strong ergodicity, monotone, and the Feller–Reuter–Riley (FRR) transition functions, we prove that a monotone ergodic transition function is strongly ergodic if and only if it is not FRR. An easy to check criterion for a Feller minimal monotone chain to be strongly ergodic is then obtained. We further prove that a non-minimal ergodic monotone chain is always strongly ergodic. The applications of our results are illustrated using birth-and-death processes and branching processes.
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This paper surveys the recent progresses made in the field of unstable denumerable Markov processes. Emphases are laid upon methodology and applications. The important tools of Feller transition functions and Resolvent Decomposition Theorems are highlighted. Their applications particularly in unstable denumerable Markov processes with a single instantaneous state and Markov branching processes are illustrated.
Resumo:
The hemocytes of Mytilus californianus are of three types: small and large basophils and large granular acidophils. The basophils contain lysosomal enzymes and phagocytose colloidal carbon. Agglutinins for yeast and human A Rh+ve erythrocytes are present in plasma, but are not needed for effective phagocytosis; in vitro both acidophilic and basophilic hemocytes rapidly phagocytose these particles. Plasma proteins, analyzed electrophoretically, are under strong homeostatic control. When Mya arenaria mantle is placed orthotopically on M. californianus mantle, the implant is invaded by host hemocytes in a manner consistent with that described in other published reports on molluscan graft rejection. Steady state is achieved by 26 days postimplant. Second- and third-set implants are rejected more rapidly than are first-set implants, but this is not a specific response. Third-set implants elicit a host cellular response that is more localized than the response to first-set implants. These data do not permit conclusions with respect to memory in these molluscan immune responses, but do imply a qualitative “improvement” in this quasi-immune response of M. californianus.
Resumo:
Whilst the biological consequences of long-term, gradual changes in acidity associated with the oceanic uptake of atmospheric carbon dioxide (CO2) are increasingly studied, the potential effects of rapid acidification associated with a failure of sub-seabed carbon storage infrastructure have received less attention. This study investigates the effects of severe short-term (8 days) exposure to acidified seawater on infaunal mediation of ecosystem processes (bioirrigation and sediment particle redistribution) and functioning (nutrient concentrations). Following acidification, individuals of Amphiura filiformis exhibited emergent behaviour typical of a stress response, which resulted in altered bioturbation, but limited changes in nutrient cycling. Under acidified conditions, A. filiformis moved to shallower depths within the sediment and the variability in occupancy depth reduced considerably. This study indicated that rapid acidification events may not be lethal to benthic invertebrates, but may result in behavioural changes that could have longer-term implications for species survival, ecosystem structure and functioning.
Resumo:
There is an increasing demand for environmental assessments of the marine environment to include ecosystem function. However, existing schemes are predominantly based on taxonomic (i.e. structural) measures of biodiversity. Biodiversity and Ecosystem Function (BEF) relationships are suggested to provide a mechanism for converting taxonomic information into surrogates of ecosystem function. This review assesses the evidence for marine BEF relationships and their potential to be used in practical monitoring applications (i.e. operationalized). Five key requirements were identified for the practical application of BEF relationships: (1) a complete understanding of strength, direction and prevalence of marine BEF relationships, (2) an understanding of which biological components are influential within specific BEF relationships, (3) the biodiversity of the selected biological components can be measured easily, (4) the ecological mechanisms that are the most important for generating marine BEF relationships, i.e. identity effects or complementarity, are known and (5) the proportion of the overall functional variance is explained by biodiversity, and hence BEF relationships, has been established. Numerous positive and some negative BEF relationships were found within the literature, although many reproduced poorly the natural species richness, trophic structures or multiple functions of real ecosystems (requirement 1). Null relationships were also reported. The consistency of the positive and negative relationships was often low that compromised the ability to generalize BEF relationships and confident application of BEF within marine monitoring. Equally, some biological components and functions have received little or no investigation. Expert judgement was used to attribute biological components using spatial extent, presence and functional rate criteria (requirement 2). This approach highlighted the main biological components contributing the most to specific ecosystem functions, and that many of the particularly influential components were found to have received the least amount of research attention. The need for biodiversity to be measureable (requirement 3) is possible for most biological components although difficult within the functionally important microbes. Identity effects underpinned most marine BEF relationships (requirement 4). As such, processes that translated structural biodiversity measures into functional diversity were found to generate better BEF relationships. The analysis of the contribution made by biodiversity, over abiotic influences, to the total expression of a particular ecosystem function was rarely measured or considered (requirement 5). Hence it is not possible to determine the overall importance of BEF relationships within the total ecosystem functioning observed. In the few studies where abiotic factors had been considered, it was clear that these modified BEF relationships and have their own direct influence on functional rate. Based on the five requirements, the information required for immediate ‘operationalization’ of BEF relationships within marine functional monitoring is lacking. However, the concept of BEF inclusion within practical monitoring applications, supported by ecological modelling, shows promise for providing surrogate indicators of functioning.