Combinatorial lemmas and applications to dynamics

The well-known combinatorial lemma of Karpovsky, Milman and Alon and a very recent one of Kerr and Li are extended. The obtained lemmas are applied to study the maximal pattern entropy introduced in the paper. It turns out that the maximal pattern entropy is equal to the supremum of sequence entropies over all sequences both in topological and measure-theoretical settings. Moreover, it is shown the maximal pattern entropy of any topological system is logk for some with k the maximal length of intrinsic sequence entropy tuples; and a zero-dimensional system has zero sequence entropy for any sequence if and only if the maximal pattern with respect to any open cover is of polynomial order.     

Price dynamics in the European Union Emissions Trading System and evaluation of its ability to boost emission-related investment decisions

The price of permits in the European Union Emissions Trading System (EU ETS) has historically been highly sensitive and prone to jumps. We consider different stochastic processes to model the price of permits, and show that the Variance Gamma (VG) model provides the best fit for the price distribution, among a selection of infinite activity processes. Using this result as a starting point, we assess the effects of the EU ETS in delivering low-carbon investments at the firm level, by modeling a price taker electricity producer subject to the EU ETS jurisdiction. We compute, via Least Squares Monte Carlo, the value of the real option the greenhouse gas emitter has, consisting in the opportunity to switch from its current high-carbon technology to a cleaner one. We use a VG specification for carbon prices, and a mean-reverting (Brennan–Schwartz) process for the price of fuel. Moreover, we further analyze the investment decision problem, in case of a CO₂ price stabilization mechanism in the form of a price floor, by explicitly computing the expected value of the investment project by means of Fourier methods. Our results show that the introduction of the price stabilization mechanism significantly affects the timing of the investment decision, and supports emission-related investments.     

Hypocoercivity for degenerate Kolmogorov equations and applications to the Langevin dynamics

We present an extension of the powerful Hilbert space hypocoercivity method that was developed originally by Dolbeault, Mouhot and Schmeiser. We focus attention on including important domain issues that have not been considered before. The setting can be used to provide a complete elaboration of the hypocoercivity theorem for the degenerate Langevin dynamics. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Perturbed iterative solution of nonlinear equations with applications to fluid dynamics

In this work a technique has been developed to solve a set of nonlinear equations with the assumption that a solution exists. The algorithm involves nonlinear Gauss-Seidel iteractions and at each iteration the value of the iterate is added to a predetermined perturbation parameter which is computed in terms of quantities already known. This perturbation parameter has two properties: (i) it determines the mode of convergence, that means it shows how many more computations are required so that convergence may be achieved, and (ii) it accelerates the rate of convergence. The algorithm is computationally simple. Several nonlinear equations have been studied. The results seem to be encouraging.     

A class of Furstenberg families and their applications to chaotic dynamics

For each sequence of positive real numbers,tending to positive infinity,a Furstenberg family is defined.All these Furstenberg families are compatible with dynamical systems.Then,chaos with respect to such Furstenberg families are intently discussed.This greatly improves some classical results of distributional chaos.To confirm the effectiveness of these improvements,the relevant examples are provided finally.     

Generalized convex relations with applications to optimization and models of economic dynamics

We examine a notion of generalized convex set-valued mapping, extending the notions of a convex relation and a convex process. Under general conditions, we establish duality results for composite set-valued mappings and for convex programming problems involving convex set-valued mappings. We also present applications to the study of economic dynamical systems, by obtaining the characteristics of optimal paths generated by convex processes, and to optimization problems of a certain class of positively homogeneous increasing functions.     

Group actions on chains of Banach manifolds and applications to fluid dynamics

This paper presents the theory of non-smooth Lie group actions on chains of Banach manifolds. The rigorous functional analytic spaces are given to deal with quotients of such actions. A hydrodynamical example is studied in detail.      

Tree-valued resampling dynamics Martingale problems and applications

The measure-valued Fleming–Viot process is a diffusion which models the evolution of allele frequencies in a multi-type population. In the neutral setting the Kingman coalescent is known to generate the genealogies of the “individuals” in the population at a fixed time. The goal of the present paper is to replace this static point of view on the genealogies by an analysis of the evolution of genealogies. We encode the genealogy of the population as an (isometry class of an) ultra-metric space which is equipped with a probability measure. The space of ultra-metric measure spaces together with the Gromov-weak topology serves as state space for tree-valued processes. We use well-posed martingale problems to construct the tree-valued resampling dynamics of the evolving genealogies for both the finite population Moran model and the infinite population Fleming–Viot diffusion. We show that sufficient information about any ultra-metric measure space is contained in the distribution of the vector of subtree lengths obtained by sequentially sampled “individuals”. We give explicit formulas for the evolution of the Laplace transform of the distribution of finite subtrees under the tree-valued Fleming–Viot dynamics.     

Partial functional differential equation with an integral condition and applications to population dynamics

In this work we consider a semilinear functional partial differential equation with an integral condition. We apply the method of semidiscretization in time, to establish the existence and uniqueness of solutions. We also study the continuation of the solution to the maximal interval of existence. Finally we give examples to demonstrate the applications of our results.     

Data envelopment analysis applied to quality in primary health care

The performance of primary care should ultimately be judged on its effect on the health outcome of individual patients. However, for the foreseeable future, it is inconceivable that the outcome data necessary to come to a judgement on performance will be available. And in any case, specification of the statistical model necessary to analyze outcome is fraught with difficulty. This paper therefore sets out a model of primary care performance which is based on the premise that certain measurable quality indicators can act as proxies for outcome. This being the case, a model of performance can be deduced which takes into account the effect of resources and patient characteristics on outcome. The most appropriate analytic technique to make this model operational is data envelopment analysis (DEA). It is argued that DEA can handle multiple dimensions of performance more comfortably, and is less vulnerable to the misspecification bias that afflicts statistically based models. The issues are illustrated with an example from English Family Health Service Authorities.     

Gas dynamics applications of a characteristic Cauchy problem

Some initial-boundary-value problems for a system of quasilinear partial differential equations of gas dynamics with the initial data prescribed on the characteristic surface (characteristic Cauchy problem) are considered. The following three-dimensional flow problems are investigated: the flow produced by a motion of an impermeable piston; the flow produced by a permeable piston with a given pressure; and the flow produced by the moving free boundary. In the first two problems, the piston motion is prescribed; in the last problem, the free boundary motion cannot be prescribed in advance and must be determined as a part of the problem. It is shown that those problems can be reduced to a characteristic Cauchy problem of a certain standard type that satisfies the analog of Cauchy-Kowalewski's existence theorem in the class of analytical functions (Differential Equations 12 (1977) 1438-1444). Thus, it is proved that, in the case of the analyticity of the input data, the considered problems have unique piecewise analytic solutions which may be expressed by infinite power series (the procedure of constructing the power series solution is described in Differential Equations 12 (1977) 1438-1444 as a part of the proof of the theorem).     

Global dynamics of Nicholson-type delay systems with applications

Models of marine protected areas and B-cell chronic lymphocytic leukemia dynamics that belong to the Nicholson-type delay differential systems are proposed. To study the global stability of the Nicholson-type models we construct an exponentially stable linear system such that its solution is a solution of the nonlinear model. Explicit conditions of the existence of positive global solutions, lower and upper estimations of solutions, and the existence and uniqueness of a positive equilibrium were obtained. New results, obtained for the global stability and instability of equilibria solutions, extend known results for the scalar Nicholson models. The conditions for the stability test are quite practical, and the methods developed are applicable to the modeling of a broad spectrum of biological processes. To illustrate our finding, we study the dynamics of the fish populations in Marine Protected Areas.     

Spectral projectors and their applications in structural dynamics

Spectral projectors exhibit some powerful properties. For example, the trace of a spectral projector can be used to determine the number of eigenvalues enclosed by a curve. Here some other nice features of spectral projectors are investigated. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling toolkit to assist with introducing a stepped care system design in mental health care

We describe a modelling toolkit that was developed with the aim of assisting those responsible for introducing stepped care systems to local mental health services in the UK. The toolkit was pre-populated with real patient flow data collected from four sites that piloted the stepped care system design. Two analytical models were developed and coded as part of the toolkit to provide insights concerning workload, patient throughput, and changes in waiting times and waiting list size. An interface was built to allow users to specify their own stepped care system and input their own estimates or data of service demands and capacities at different steps. Despite the challenges and limitations, the use of modelling to inform the design of new service configurations is an important step in the right direction and we would recommend this as a reasonable way forward.     

Weighted multiple majority games with unions: Generating functions and applications to the European Union

An a priori system of unions or coalition structure is a partition of a finite set of players into disjoint coalitions which have made a prior commitment to cooperate in playing a game. This paper provides “ready-to-apply” procedures based on generating functions that are easily implementable to compute coalitional power indices in weighted multiple majority games. As an application of the proposed procedures, we calculate and compare coalitional power indices under the decision rules prescribed by the Treaty of Nice and the new rules proposed by the Council of the European Union.     

Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds

We assign to each nondegenerate Hamiltonian on a closed symplectic manifold a Floer-theoretic quantity called its “boundary depth,” and establish basic results about how the boundary depths of different Hamiltonians are related. As applications, we prove that certain Hamiltonian symplectomorphisms supported in displaceable subsets have infinitely many nontrivial geometrically distinct periodic points, and we also significantly expand the class of coisotropic submanifolds which are known to have positive displacement energy. For instance, any coisotropic submanifold of contact type (in the sense of Bolle) in any closed symplectic manifold has positive displacement energy, as does any stable coisotropic submanifold of a Stein manifold. We also show that any stable coisotropic submanifold admits a Riemannian metric that makes its characteristic foliation totally geodesic, and that this latter, weaker, condition is enough to imply positive displacement energy under certain topological hypotheses.     

A non random walk theory of exchange rate dynamics with applications to option pricing

A two dimensional stochastic process is developed to model exchange rate dynamics. We incorporate the non random walk influence of pur–chasing power parity, to synthesise the theories of international trade and foreign currency options. Our results, which include a closed form expression for the transition density function of the exchange rate and an exact formula to price currency options, offer a theoretical framework for further study of foreign exchange markets