Consistent Approximations for the Optimal Control of Constrained Switched Systems

Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In this paper, we devise an algorithm for the computation of an optimal control of constrained nonlinear switched dynamical systems. The control parameter for such systems include a continuous-valued input and discrete-valued input, where the latter corresponds to the mode of the switched system that is active at a particular instance in time. Our approach, which we prove converges to local minimizers of the constrained optimal control problem, first relaxes the discrete-valued input, then performs traditional optimal control, and then projects the constructed relaxed discrete-valued input back to a pure discrete-valued input by employing an extension to the classical Chattering Lemma that we prove. We extend this algorithm by formulating a computationally implementable algorithm which works by discretizing the time interval over which the switched dynamical system is defined. Importantly, we prove that this implementable algorithm constructs a sequence of points by recursive application that converge to the local minimizers of the original constrained optimal control problem. Four simulation experiments are included to validate the theoretical developments

Physical constraints on interacting dark energy models

Physical limits on the equation-of-state (EoS) parameter of a dark energy component non-minimally coupled with the dark matter field are examined in light of the second law of thermodynamics and the positiveness of entropy. Such constraints are combined with observational data sets of type Ia supernovae, baryon acoustic oscillations and the angular acoustic scale of the cosmic microwave background to impose restrictions on the behaviour of the dark matter/dark energy interaction. Considering two EoS parameterisations of the type $w = w_0 + w_a\zeta(z)$, we derive a general expression for the evolution of the dark energy density and show that the combination of thermodynamic limits and observational data provide tight bounds on the $w_0 - w_a$ parameter space.Comment: 7 pages, 4 figures. Accepted for publication in European Physical Journal

Is there a place for love in early childhood education and care in England? Early years educators’ beliefs

The importance of love for young children is well documented. Increasing numbers of young children are spending time in early years settings. The recent Government policy announcement of free childcare for children from nine months is likely to increase the number of babies attending early years settings, so the concept of love within early years education and childcare has never been more important. However, the qualifications that enable someone to work within an early years setting in England do not mention love. Similarly, love does not feature within the Statutory Framework for the Early Years Foundation Stage, which those working with our youngest children must follow. This research identified polarised opinions regarding the place of love within early childhood education and care, with some practitioners clearly uncomfortable with the idea of loving children who are not their own, whilst others believing that loving the children you work with is vital

Geometry of fully coordinated, two-dimensional percolation

We study the geometry of the critical clusters in fully coordinated percolation on the square lattice. By Monte Carlo simulations (static exponents) and normal mode analysis (dynamic exponents), we find that this problem is in the same universality class with ordinary percolation statically but not so dynamically. We show that there are large differences in the number and distribution of the interior sites between the two problems which may account for the different dynamic nature.Comment: ReVTeX, 5 pages, 6 figure

Adaptive statistical pattern classifiers for remotely sensed data

A technique for the adaptive estimation of nonstationary statistics necessary for Bayesian classification is developed. The basic approach to the adaptive estimation procedure consists of two steps: (1) an optimal stochastic approximation of the parameters of interest and (2) a projection of the parameters in time or position. A divergence criterion is developed to monitor algorithm performance. Comparative results of adaptive and nonadaptive classifier tests are presented for simulated four dimensional spectral scan data

Unpolarised Transverse Momentum Dependent Distribution and Fragmentation Functions from SIDIS Multiplicities

The unpolarised transverse momentum dependent distribution and fragmentation functions are extracted from HERMES and COMPASS experimental measurements of SIDIS multiplicities for charged hadron production. The data are grouped into independent bins of the kinematical variables, in which the TMD factorisation is expected to hold. A simple factorised functional form of the TMDs is adopted, with a Gaussian dependence on the intrinsic transverse momentum, which turns out to be quite adequate in shape. HERMES data do not need any normalisation correction, while fits of the COMPASS data much improve with a $y$-dependent overall normalisation factor. A comparison of the extracted TMDs with previous EMC and JLab data confirms the adequacy of the simple Gaussian distributions. The possible role of the TMD evolution is briefly considered.Comment: 21 pages, 16 figure

Malmquist Bias and the Distance to the Virgo Cluster

This paper investigates the impact of Malmquist bias on the distance to the Virgo cluster determined by the H_0 Key Project using M100, and consequently on the derived value of H_0. Malmquist bias is a volume-induced statistical effect which causes the most probable distance to be different from the raw distance measured. Consideration of the bias in the distance to the Virgo cluster raises this distance and lowers the calculated value of H_0. Monte Carlo simulations of the cluster have been run for several possible distributions of spirals within the cluster and of clusters in the local universe. Simulations consistent with known information regarding the cluster and the errors of measurement result in a bias of about 6.5%-8.5%. This corresponds to an unbiased distance of 17.2-17.4 Mpc and a value of H_0 in the range 80-82 km/s/Mpc. The problem of determining the bias to Virgo illustrates several key points regarding Malmquist bias. Essentially all conventional astronomical distance measurements are subject to this bias. In addition, the bias accumulates when an attempt is made to construct "distance ladders" from measurements which are individually biased. As will be shown in the case of Virgo, the magnitude and direction of the bias are sensitive to the spatial distribution of the parent poputation from which the observed object is drawn - a distribution which is often poorly known. This leads to uncertainty in the magnitude of the bias, and adds to the importance of minimizing the number of steps in "distance ladders".Comment: 19 pages, 3 figures, Latex, To appear in Ap

THE DIFFERENTIAL IMPACT OF CORRUPTION ON MICROENTERPRISES IN RUSSIA

Over the past decade, the repressive legal and regulatory environment in transition economies has received considerable attention in the literature. In Russia, this framework has resulted in an environment in which rules and regulations govern almost all aspects of economic activity. The elaborate system of regulations with which firms must comply, in combination with a lack of accountability for regulatory enforcers, has created a corrupt cadre of government officials who frequently engage in rent-seeking behavior while monitoring and enforcing firm compliance. The objective of this paper is to investigate the manner in which corruption affects micro and small enterprises in Russia. Empirical evidence suggests that micro and small enterprises vary substantially in reporting how problematic corruption is for their enterprise. A theoretical model explores why extortion from regulators may occur in a non-uniform manner across firms. The theoretical model postulates that government regulators customize the nature of their rent-seeking activities towards, similar to a price-discriminating monopolist facing hidden information. The model shows that production technologies, input choices, and other firm characteristics such as location play a role in determining the bribe price that a regulator will charge a firm, as well as the number of times he will return to collect it. Supportive evidence comes from survey data collected on Russian microenterprises. The model described above is tested using econometrics, and numerical simulations.Political Economy,