Measuring technical efficiency in the presence of pesticide spillovers and production uncertainty: The case of Dutch arable farms

Pesticides’ dynamic effects and production uncertainty play an important role in farmers’ production decisions. Pesticides have a current production impact through reducing crop damage in the current period and a future impact through impacting the farm biodiversity which alters the future production environment. This study presents the difference in inefficiency arising from models that ignore the dynamic effects of pesticides in production decisions and the impact of production uncertainty. A dynamic data envelopment analysis (DEA) model is applied to outputs, inputs, and undesirables of Dutch arable farms over the period 2003–2007. A bootstrap approach is used to explain farmers’ performance, providing empirical representations of the impact of stochastic elements on production. These empirical representations are used to adjust firms’ inefficiency scores to incorporate production uncertainty in efficiency evaluation. We find that efficiency increased dramatically when a production technology representation that considers both pesticides’ dynamic impacts, and production uncertainty is adopted.     

Unifying practical uncertainty representations – I: Generalized p-boxes

There exist several simple representations of uncertainty that are easier to handle than more general ones. Among them are random sets, possibility distributions, probability intervals, and more recently Ferson’s p-boxes and Neumaier’s clouds. Both for theoretical and practical considerations, it is very useful to know whether one representation is equivalent to or can be approximated by other ones. In this paper, we define a generalized form of usual p-boxes. These generalized p-boxes have interesting connections with other previously known representations. In particular, we show that they are equivalent to pairs of possibility distributions, and that they are special kinds of random sets. They are also the missing link between p-boxes and clouds, which are the topic of the second part of this study.     

Hardy-Sobolev Spaces Decomposition in?Signal Analysis

Some fundamental formulas and relations in signal analysis are based on the amplitude-phase representations s(t)=A(t)e ^{i ??(t)} and $\hat{s}(\omega)=B(\omega)e^{i\psi(\omega)}$ , where the amplitude functions A(t) and B(??) and the phase functions ??(t) and ??(??) are assumed to be differentiable. They include the amplitude-phase representations of the first and second order means of the Fourier frequency and time, and the equivalence between two forms of the covariance. A proof of the uncertainty principle is also based on the amplitude-phase representations. In general, however, signals of finite energy do not necessarily have differentiable amplitude-phase representations. The study presented in this paper extends the classical formulas and relations to general signals of finite energy. Under the formulation of the phase and amplitude derivatives based on the Hardy-Sobolev spaces decomposition the extended formulas reveal new features, and contribute to the foundations of time-frequency analysis. The established theory is based on the equivalent classes of the L ² space but not on particular representations of the classes. We also give a proof of the uncertainty principle by using the amplitude-phase representations defined through the Hardy-Sobolev spaces decomposition.     

Uncertainty principles and optimally sparse wavelet transforms

In this paper we introduce a new localization framework for wavelet transforms, such as the 1D wavelet transform and the Shearlet transform. Our goal is to design nonadaptive window functions that promote sparsity in some sense. For that, we introduce a framework for analyzing localization aspects of window functions. Our localization theory diverges from the conventional theory in two ways. First, we distinguish between the group generators, and the operators that measure localization (called observables). Second, we define the uncertainty of a signal transform as a whole, instead of defining the uncertainty of an individual window. We show that the uncertainty of a window function, in the signal space, is closely related to the localization of the reproducing kernel of the wavelet transform, in phase space. As a result, we show that using uncertainty minimizing window functions, results in representations which are optimally sparse in some sense.     

Supports of Representations in the Cohen Class

In this paper we consider a version of the uncertainty principle concerning limitations on the supports of time-frequency representations in the Cohen class. In particular we obtain various classes of kernels with the property that the corresponding representations of non trivial signals cannot be compactly supported. As an application of our results we show that a linear partial differential operator applied to the Wigner distribution of a function f≠0 in the Schwartz class cannot produce a compactly supported function.     

Fuzzy job shop scheduling with lot-sizing

This paper deals with a problem of determining lot-sizes of jobs in a real-world job shop-scheduling in the presence of uncertainty. The main issue discussed in this paper is lot-sizing of jobs. A fuzzy rule-based system is developed which determines the size of lots using the following premise variables: size of the job, the static slack of the job, workload on the shop floor, and the priority of the job. Both premise and conclusion variables are modelled as linguistic variables represented by using fuzzy sets (apart from the priority of the job which is a crisp value). The determined lots’ sizes are input to a fuzzy multi-objective genetic algorithm for job shop scheduling. Imprecise jobs’ processing times and due dates are modelled by using fuzzy sets. The objectives that are used to measure the quality of the generated schedules are average weighted tardiness of jobs, the number of tardy jobs, the total setup time, the total idle time of machines and the total flow time of jobs. The developed algorithm is analysed on real-world data obtained from a printing company.     

Generalizations of expected utility theories: A survey of recent proposals

This paper reviews recently developed theories that generalize the von Neumann — Morgenstern theory of preference under risk and Savage's theory of preference under uncertainty. The new theories are designed to accommodate systematic and predictable violations of previous theories while not giving up too much of the mathematical elegance of their expected utility representations. The material in the paper is adapted from the author's bookNonlinear Preference and Utility Theory.     

Affinely Prime Dynamical Systems(Dedicated to Professor Haim Brezis on the occasion of his 70th birthday)

This paper deals with representations of groups by "affine" automorphisms of compact, convex spaces, with special focus on "irreducible" representations: equivalently"minimal" actions. When the group in question is P SL(2, R), the authors exhibit a oneone correspondence between bounded harmonic functions on the upper half-plane and a certain class of irreducible representations. This analysis shows that, surprisingly, all these representations are equivalent. In fact, it is found that all irreducible affine representations of this group are equivalent. The key to this is a property called "linear Stone-Weierstrass"for group actions on compact spaces. If it holds for the "universal strongly proximal space"of the group(to be defined), then the induced action on the space of probability measures on this space is the unique irreducible affine representation of the group.     

Windowed-Wigner Representations in the Cohen Class and Uncertainty Principles

For representations in the Cohen class, specific Cohen kernels depending only on one half of the variables are showed to produce two types of representations which can in a natural way be associated with time and frequency windows. This leads to the definition of representations with no interference for signals whose time-frequency content is confined in specific zones. We prove the main properties of these representations in the context of the Cohen class. We study then uncertainty principles at first in connection with support compactness and then in the framework of a general concept of duality among representations.     

Affinely Prime Dynamical Systems

This paper deals with representations of groups by "affine" automorphisms of compact,convex spaces,with special focus on "irreducible" representations:equivalently "minimal" actions.When the group in question is PSL(2,R),the authors exhibit a oneone correspondence between bounded harmonic functions on the upper half-plane and a certain class of irreducible representations.This analysis shows that,surprisingly,all these representations are equivalent.In fact,it is found that all irreducible affine representations of this group are equivalent.The key to this is a property called "linear Stone-Weierstrass"for group actions on compact spaces.If it holds for the "universal strongly proximal space"of the group (to be defined),then the induced action on the space of probability measures on this space is the unique irreducible affine representation of the group.     

On solving stochastic production planning problems via scenario modelling

Summary Linear Porgramming models for stochastic planning problems and a methodology for solving them are proposed. A production planning problem with uncertainty in demand is used as a test case, but the methodology presented here is applicable to other types of problems as well. In these models, uncertainty in demand is characterized via scenarios. Solutions are obtained for each scenario and then these individual scenario solutions are aggregated to yield an implementable non-anticipative policy. Such an approach makes it possible to model correlated and nonstationary demand as well as a variety of recourse decision types. For computational purposes, two alternative representations are proposed. A compact approach that is suitable for the Simplex method and a splitting variable approach that is suitable for the Interior Point Methods. A crash procedure that generates an advanced starting solution for the Simplex method is developed. Computational results are reported with both the representations. Although some of the models presented here are very large (over 25000 constraints and 75000 variables), our computational experience with these problems is quite encouraging.     

Capacity augmentation of a supply chain for a short lifecycle product: A system dynamics framework

For an innovative product characterized by short product lifecycle and high demand uncertainty, investment in capacity buildup has to be done cautiously. Otherwise either the product’s market diffusion is impeded or the manufacturer is left with unutilized capacity. Using the right information for making capacity augmentation decisions is critical in facing this challenge. In this paper, we propose a method for identifying critical information flows using the system dynamics model of a two-echelon supply chain. The fundamental premise of system dynamics methodology is that (system) structure determines (its) behavior. Using loop dominance analysis method we study the feedback loop structure of the supply chain system. The outcome is a set of dominant loops that determine the dynamics of capacity growth. It is revealed that the delivery delay information has little effect while the loop that connects retail sales with production order affects the dynamics significantly. Modifying this loop yields appropriate capacity augmentation decisions resulting in higher performance. What-if analyses bring out effects of modifying other structural elements. In conclusion, we claim that the information feedback based methodology is general enough to be useful in designing decision support systems for capacity augmentation. The limitations of the model are also discussed and possible extensions identified.     

Signal representation,uncertainty principles and localization measures

The following collection of articles addresses one of the most basic problems in signal and image processing, namly the search for function systems (basis, frames, dictionaries) which allow efficient representations of certain classes of signals/images. Such representations are essential for decomposition and synthesis of signals, hence they are at the core of almost any application (coding, compression, pattern matching, feature extraction, classification, etc.) in this field. Accordingly, this is one of the best-studied topics in data analysis and a multitude of different concepts also addressing discretization/algorithmic issues has been investigated in this context. The starting point for reviving activities in this field was a recently rediscovered inconsistency in the concept of constructing optimally localized basis functions by minimizing uncertainty principles. In this short introductory note, we shortly sketch the basic dilemma, which was the starting point for this research approximately three years ago. However, the subsequent investigations presented in this collection of papers cover a much wider range of more general localization measures, discretization concepts as well as discussing algorithmic efficiency and stability.     

Confidence models of incomplete preferences

This paper introduces a new class of representations for incomplete preferences called confidence models. Confidence models describe decision makers who behave as if they have probabilistic uncertainty over their true preferences, and are only willing to express a binary preference if it is sufficiently likely to hold. Confidence models provide a natural way to connect incomplete preferences with stochastic choice. This connection is characterized by a simple joint condition on an incomplete preference relation and a random choice rule.     

A new uncertainty analysis for the transformation method

In this paper, a new uncertainty analysis for the transformation method (TM) is proposed. As a practical implementation of fuzzy arithmetic, the TM is a convenient tool for the simulation and analysis of systems with uncertain parameters that are expressed by fuzzy numbers. The proposed uncertainty analysis and the sensitivity analysis of the TM complete each other in providing some quantification of the relationship between the uncertainties of the system input and the system output. The computation of gain factors is proposed, which allows the estimation of the absolute and relative measures of uncertainty. These measures allow the quantification of the influence of the uncertainty of the input on the uncertainty of the output.     

熵在供应链供需不确定性中的应用

从定量和定性的角度分析了供应链系统的不确定性，指出供应链不确定性本质和不确定性产生的因素；本文把熵理论运用到供应链不确定性的研究中，为供应链管理和控制提供了有效的方法。通过实际案例分析，我们可以看出熵理论的运用不但能够对供应链不确定性做出精确的评估，而且能有效地控制整个供应链的运营。     

Orthoscalar quiver representations corresponding to extended Dynkin graphs in the category of Hilbert spaces

It is known that finitely representable quivers correspond to Dynkin graphs and tame quivers correspond to extended Dynkin graphs. In an earlier paper, the authors generalized some of these results to locally scalar (later renamed to orthoscalar) quiver representations in Hilbert spaces; in particular, an analog of the Gabriel theorem was proved. In this paper, we study the relationships between indecomposable representations in the category of orthoscalar representations and indecomposable representations in the category of all quiver representations. For the quivers corresponding to extended Dynkin graphs, the indecomposable orthoscalar representations are classified up to unitary equivalence.     

幂零Lie群上的不定性原理

设N是具有平方可积表示的幂零Lie群,是其Plancherel测度．本文将N上群Fourier变换矩阵化,并由此给出N上不定性原理的一种定量描述．此外,还对N上不定性原理的定性描述（简称QUP）作了讨论,结果显示出N上QUP与P（λ）的零点集之代数、几何性质的一些联系.     

On the calculation of the bounds of probability of events using infinite random sets

This paper presents an extension of the theory of finite random sets to infinite random sets, that is useful for estimating the bounds of probability of events, when there is both aleatory and epistemic uncertainty in the representation of the basic variables. In particular, the basic variables can be modelled as CDFs, probability boxes, possibility distributions or as families of intervals provided by experts. These four representations are special cases of an infinite random set. The method introduces a new geometrical representation of the space of basic variables, where many of the methods for the estimation of probabilities using Monte Carlo simulation can be employed. This method is an appropriate technique to model the bounds of the probability of failure of structural systems when there is parameter uncertainty in the representation of the basic variables. A benchmark example is used to demonstrate the advantages and differences of the proposed method compared with the finite approach.     

Representations Connected with Dixmier Traces and Spaces of Distributions

In this paper we first construct Hilbert spaces related to Dixmier traces. The group representations in these spaces are considered; we refer to authors paper for a detailed exposition of this theme. We show then that this construction is closely related to the representations in the spaces of distributions on a manifold.