Automorphisms of flag systems

We first discuss the problems in the theory of ordinary differential equations that gave rise to the concept of a flag system and illustrate these with the Cartan criterion for Monge equations (1st order) as well as the Cartan statement concerning the local equivalence of Monge–Ampère type equations (2nd order). Next, we describe a prolongation functor operating on the infinitesimal symmetries (automorphisms) of the Darboux flag and extending these, isomorphically, to all the symmetries of any other flag. Hence, flag systems cannot be distinguished by their symmetry algebras and the local classification of these objects is approached by considering higher order isotropies of these algebras as well as the groupoids of k-th order formal equivalences since the differential equations defining the latter provide precious information for the application of flag systems to differential equations (e.g., Cartan's criterion for non-linear Monge equations). In examining the behavior of the isotropy algebras, that can either diminish or remain the same, when passing from a derived system $S_{\nu }$ to the consecutive system $S_{\nu +1}$, we obtain a full set of numerical invariants for the elementary flag systems that moreover specifies the local models.     

A machine learning efficient frontier

We propose a simple approach to bridge between portfolio theory and machine learning. The outcome is an out-of-sample machine learning efficient frontier based on two assets, high risk and low risk. By rotating between the two assets, we show that the proposed frontier dominates the mean–variance efficient frontier out-of-sample. Our results, therefore, shed important light on the appeal of machine learning into portfolio selection under estimation risk.     

Next-generation NATO reference mobility model complex terramechanics – Part 2: Requirements and prototype

In part 2 of this paper, the Complex Terramechanics (CT) software tools requirements recommended by the NATO research task group RTG-248 are presented along with example simulations from a CT prototype software tool which attempts to satisfy the requirements.     

Computer-aided design of formulated products

Formulated products represent a particular class of complex chemical products, and their design is typically based on experience and extensive experimentation. Although still at an early stage, and despite that their potential is not fully accessed and not fully used by the industry, computer-aided design (CAD) methods and tools offer many possibilities in the design of formulated products. The CAD methodology based on computerized models enables the formulation chemists to speed up the design process, without completely replacing experiments.In this work, we summarize previous studies in the field and present important elements of the CAD framework, emphasizing estimation methods for key target properties, link to specifications, and finally, some case studies will illustrate how the CAD framework can be used in practice for formulated products.     

A stochastic portfolio optimization model with complete memory

In this article, we consider a portfolio optimization problem of the Merton’s type with complete memory over a finite time horizon. The problem is formulated as a stochastic control problem on a finite time horizon and the state evolves according to a process governed by a stochastic process with memory. The goal is to choose investment and consumption controls such that the total expected discounted utility is maximized. Under certain conditions, we derive the explicit solutions for the associated Hamilton–Jacobi–Bellman (HJB) equations in a finite-dimensional space for exponential, logarithmic, and power utility functions. For those utility functions, verification results are established to ensure that the solutions are equal to the value functions, and the optimal controls are also derived.     

Quadratic cone cutting surfaces for quadratic programs with on–off constraints

We study the convex hull of a set arising as a relaxation of difficult convex mixed integer quadratic programs (MIQP). We characterize the extreme points of the convex hull of the set and the extreme points of its continuous relaxation. We derive four quadratic cutting surfaces that improve the strength of the continuous relaxation. Each of the cutting surfaces is second-order-cone representable. Via a shooting experiment, we provide empirical evidence as to the importance of each inequality type in improving the relaxation. Computational results that employ the new cutting surfaces to strengthen the relaxation for MIQPs arising from portfolio optimization applications are promising.     

A New Thiolate-Bound Dimanganese Cluster as a Structural and Functional Model for Class Ib Ribonucleotide Reductases

In class Ib ribonucleotide reductases (RNRs) a dimanganese(II) cluster activates superoxide (O₂⋅⁻) rather than dioxygen (O₂), to access a high valent Mn^III−O₂−Mn^IV species, responsible for the oxidation of tyrosine to tyrosyl radical. In a biomimetic approach, we report the synthesis of a thiolate-bound dimanganese complex [Mn^II₂(BPMT)(OAc)₂](ClO)₄ (BPMT=(2,6-bis{[bis(2-pyridylmethyl)amino]methyl}-4-methylthiophenolate) ( 1 ) and its reaction with O₂⋅⁻ to form a [(BPMT)MnO₂Mn]²⁺ complex 2 . Resonance Raman investigation revealed the presence of an O−O bond in 2 , while EPR analysis displayed a 16-line S_t=1/2 signal at g=2 typically associated with a Mn^IIIMn^IV core, as detected in class Ib RNRs. Unlike all other previously reported Mn−O₂−Mn complexes, generated by O₂⋅⁻ activation at Mn₂ centers, 2 proved to be a capable electrophilic oxidant in aldehyde deformylation and phenol oxidation reactions, rendering it one of the best structural and functional models for class Ib RNRs.     

Multiple Statistical models for simulation and prediction of nonlinear processes

The paper describes a parameterisation procedure for multiple nonlinear equations with intercepts. These equations may consist of numerous members with few practical limitations on their structure. Examples are given on the application of the procedure to simulation in the areas of chemical technology and hydrology. Advantages of the proposed method are simplicity of the fitting procedure, high accuracy of simulations and more reliable simulations beyond the calibration range     

Modeling partial Greeks of variable annuities with dependence

Dynamic hedging used to mitigate the financial risks associated with large portfolios of variable annuities requires calculating partial dollar deltas on major market indices. Metamodeling approaches have been proposed in the past few years to address the computational issues related to the calculation of partial dollar deltas. In this paper, we investigate whether the additional complication of modeling the dependence between the partial dollar deltas improves the accuracy of the metamodeling approaches. We use several copulas to model the dependence structures of the partial dollar deltas and conduct numerical experiments to compare different metamodels. Despite the evidence of strong dependence in the estimated models, our numerical results show that modeling the dependence structures in the metamodels does not improve the accuracy of the estimations at the portfolio level. This is because the dependence between the partial dollar deltas is well captured by the covariates used in the marginal models. This finding suggests that we should focus more on marginal models than specifying the dependence structure explicitly.     

Models of expansions of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb N}$\end{document} with no end extensions

We deal with models of Peano arithmetic (specifically with a question of Ali Enayat). The methods are from creature forcing. We find an expansion of ${\mathbb N}$ such that its theory has models with no (elementary) end extensions. In fact there is a Borel uncountable set of subsets of ${\mathbb N}$ such that expanding ${\mathbb N}$ by any uncountably many of them suffice. Also we find arithmetically closed ${\mathcal A}$ with no ultrafilter on it with suitable definability demand (related to being Ramsey). © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim