PERFORMANCE OF RISK-INCOME MODELS OUTSIDE THE ORIGINAL DATA SET

Selected risk programming solutions (i.e., profit maximization, Target-MOTAD, and MOTAD) are tested in an economic environment outside the data set from which they were developed. Specifically, solutions are derived from either a longer 10-year (1965-74) or shorter 6-year estimation period (1969-74), and then, they are tested for consistent risk-income characteristics over a later 10-year period (1975-84). Risk solutions estimated from earlier periods perform well in the later test period in spite of different economic conditions between time periods. However, favorable performance may be related to the specific example used in this analysis. Further testing for other farm situations is needed before general conclusions can be reached.Risk and Uncertainty,

Lower Bounds on Complexity of Lyapunov Functions for Switched Linear Systems

We show that for any positive integer $d$, there are families of switched linear systems---in fixed dimension and defined by two matrices only---that are stable under arbitrary switching but do not admit (i) a polynomial Lyapunov function of degree $\leq d$, or (ii) a polytopic Lyapunov function with $\leq d$ facets, or (iii) a piecewise quadratic Lyapunov function with $\leq d$ pieces. This implies that there cannot be an upper bound on the size of the linear and semidefinite programs that search for such stability certificates. Several constructive and non-constructive arguments are presented which connect our problem to known (and rather classical) results in the literature regarding the finiteness conjecture, undecidability, and non-algebraicity of the joint spectral radius. In particular, we show that existence of an extremal piecewise algebraic Lyapunov function implies the finiteness property of the optimal product, generalizing a result of Lagarias and Wang. As a corollary, we prove that the finiteness property holds for sets of matrices with an extremal Lyapunov function belonging to some of the most popular function classes in controls

Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure

Augmenting Biogas Process Modeling by Resolving Intracellular Metabolic Activity

The process of anaerobic digestion in which waste biomass is transformed to methane by complex microbial communities has been modeled for more than 16 years by parametric gray box approaches that simplify process biology and do not resolve intracellular microbial activity. Information on such activity, however, has become available in unprecedented detail by recent experimental advances in metatranscriptomics and metaproteomics. The inclusion of such data could lead to more powerful process models of anaerobic digestion that more faithfully represent the activity of microbial communities. We augmented the Anaerobic Digestion Model No. 1 (ADM1) as the standard kinetic model of anaerobic digestion by coupling it to Flux-Balance-Analysis (FBA) models of methanogenic species. Steady-state results of coupled models are comparable to standard ADM1 simulations if the energy demand for non-growth associated maintenance (NGAM) is chosen adequately. When changing a constant feed of maize silage from continuous to pulsed feeding, the final average methane production remains very similar for both standard and coupled models, while both the initial response of the methanogenic population at the onset of pulsed feeding as well as its dynamics between pulses deviates considerably. In contrast to ADM1, the coupled models deliver predictions of up to 1,000s of intracellular metabolic fluxes per species, describing intracellular metabolic pathway activity in much higher detail. Furthermore, yield coefficients which need to be specified in ADM1 are no longer required as they are implicitly encoded in the topology of the species’ metabolic network. We show the feasibility of augmenting ADM1, an ordinary differential equation-based model for simulating biogas production, by FBA models implementing individual steps of anaerobic digestion. While cellular maintenance is introduced as a new parameter, the total number of parameters is reduced as yield coefficients no longer need to be specified. The coupled models provide detailed predictions on intracellular activity of microbial species which are compatible with experimental data on enzyme synthesis activity or abundance as obtained by metatranscriptomics or metaproteomics. By providing predictions of intracellular fluxes of individual community members, the presented approach advances the simulation of microbial community driven processes and provides a direct link to validation by state-of-the-art experimental techniques

Performance analysis and optimal selection of large mean-variance portfolios under estimation risk

We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of assets remains comparable in magnitude to the sample size, we provide a characterization of the estimation risk by providing deterministic equivalents of the portfolio out-of-sample performance in terms of the underlying investment scenario. The previous estimates represent a means of quantifying the amount of risk underestimation and return overestimation of improved portfolio constructions beyond standard ones. Well-known for the latter, if not corrected, these deviations lead to inaccurate and overly optimistic Sharpe-based investment decisions. Our results are based on recent contributions in the field of random matrix theory. Along with the asymptotic analysis, the analytical framework allows us to find bias corrections improving on the achieved out-of-sample performance of typical portfolio constructions. Some numerical simulations validate our theoretical findings

Bank intermediation and persistent liquidity effects in the presence of a frictionless bond market

An “expansionary” monetary policy that increases the growth rate of bank reserves is generally believed by policy makers to induce a “liquidity effect”, or a persistent decline in short-term nominal interest rates, that stimulates real activity. Christiano, et al. (1991,1995,1997) have incorporated this feature of the economy into equilibrium business cycle models by introducing a commercial bank that acquires deposits from households and channels those funds to firms, which use them to fund their working capital expenses. Bank deposits are the only interest-bearing financial asset available to households, and bank loans are the only source of working capital finance available to firms. To obtain a liquidity effect in response to an unanticipated reserves injection, those models rely on an information friction whereby households precommit to a liquid asset position prior to the monetary shock. In practice, the capital markets are a major source of working capital finance, and U.S. data indicate that bank financing as a share of total short-term working capital finance is countercyclical. This paper extends this literature by introducing a bond market that allows for nonintermediated loans directly from households to firms, and examines the information friction that could induce liquidity effects and countercyclicality in the degree of bank intermediation of working capital finance. The results indicate: (i) “sticky prices” are neither necessary nor sufficient to induce a liquidity effect; (ii) deposit precommitment by households along with a presetting of the deposit rate by banks does induce persistent liquidity effects, but results in excess volatility of consumption and investment; (iii) minimizing the deposit precommitment, while maintaining the preset deposit rate induces a weaker liquidity effect that is more in line with the data, without the excess volatility in consumption and investment; and (iv) the share of bank intermediation in working capital finance is countercyclical in all cases, including the absence of an information friction.Bonds ; Liquidity (Economics) ; Banks and banking