Promoting environmentally sustainable enterprises: some policy options

Governments around the world are taking an increasing interest in promoting environmentally-sustainable economic activity. They have developed a variety of policy approaches in an effort to address environmental issues that range from localised pollution incidents to global climate change. This chapter examines the kinds of intervention tools that are being used to improve the environmental performance of SMEs, and to guide entrepreneurial energies towards more environmentally-benign goals. The chapter aims to: (1) outline the main options available to policy-makers; (2) compare specific intervention tools, noting their strengths and limitations; and (3) discuss the case for adopting more holistic approaches to address the pervasive, complex and often deeply-rooted challenges of sustainable development. Key lessons are that policy makers need to select appropriate combinations of tools based on careful reviews of the evidence, and that well-integrated, context-sensitive policies are likely to prove the most effective

On the construction of probabilistic Newton-type algorithms

It has recently been shown that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Importantly, this understanding allows us to safely start assembling probabilistic Newton-type algorithms, applicable in situations where we only have access to noisy observations of the cost function and its derivatives. This is where our interest lies. We make contributions to the use of the non-parametric and probabilistic Gaussian process models in solving these stochastic optimisation problems. Specifically, we present a new algorithm that unites these approximations together with recent probabilistic line search routines to deliver a probabilistic quasi-Newton approach. We also show that the probabilistic optimisation algorithms deliver promising results on challenging nonlinear system identification problems where the very nature of the problem is such that we can only access the cost function and its derivative via noisy observations, since there are no closed-form expressions available

Combinatorial Hopf algebraic description of the multiscale renormalization in quantum field theory

We define in this paper several Hopf algebras describing the combinatorics of the so-called multi-scale renormalization in quantum field theory. After a brief recall of the main mathematical features of multi-scale renormalization, we define assigned graphs, that are graphs with appropriate decorations for the multi-scale framework. We then define Hopf algebras on these assigned graphs and on the Gallavotti-Nicol\`o trees, particular class of trees encoding the supplementary informations of the assigned graphs. Several morphisms between these combinatorial Hopf algebras and the Connes-Kreimer algebra are given. Finally, scale dependent couplings are analyzed via this combinatorial algebraic setting.Comment: 26 pages, 3 figures; the presentation of the results has been reorganized. Several details of various proofs are given and some references have been adde

Complex Master Slave Interferometry

A general theoretical model is developed to improve the novel Spectral Domain Interferometry method denoted as Master/Slave (MS) Interferometry. In this model, two functions, g and h are introduced to describe the modulation chirp of the channeled spectrum signal due to nonlinearities in the decoding process from wavenumber to time and due to dispersion in the interferometer. The utilization of these two functions brings two major improvements to previous implementations of the MS method. A first improvement consists in reducing the number of channeled spectra necessary to be collected at Master stage. In previous MSI implementation, the number of channeled spectra at the Master stage equated the number of depths where information was selected from at the Slave stage. The paper demonstrates that two experimental channeled spectra only acquired at Master stage suffice to produce A-scans from any number of resolved depths at the Slave stage. A second improvement is the utilization of complex signal processing. Previous MSI implementations discarded the phase. Complex processing of the electrical signal determined by the channeled spectrum allows phase processing that opens several novel avenues. A first consequence of such signal processing is reduction in the random component of the phase without affecting the axial resolution. In previous MSI implementations, phase instabilities were reduced by an average over the wavenumber that led to reduction in the axial resolution

Purity results for pp-divisible groups and abelian schemes over regular bases of mixed characteristic

Let $p$ be a prime. Let (R,\ideal{m}) be a regular local ring of mixed characteristic $(0,p)$ and absolute index of ramification $e$. We provide general criteria of when each abelian scheme over \Spec R\setminus\{\ideal{m}\} extends to an abelian scheme over \Spec R. We show that such extensions always exist if $e\le p-1$, exist in most cases if $p\le e\le 2p-3$, and do not exist in general if $e\ge 2p-2$. The case $e\le p-1$ implies the uniqueness of integral canonical models of Shimura varieties over a discrete valuation ring $O$ of mixed characteristic $(0,p)$ and index of ramification at most $p-1$. This leads to large classes of examples of N\'eron models over $O$. If $p>2$ and index $p-1$, the examples are new.Comment: 28 pages. Final version identical (modulo style) to the galley proofs. To appear in Doc. Mat