FUZZINESS VS. PROBABILITY

Fuzziness is explored as an alternative to randomness for describing uncertainty. The new sets-as-points geometric view of fuzzy sets is developed. This view identifies a fuzzy set with a point in a unit hypercube and a nonfuzzy set with a vertex of the cube. Paradoxes of two-valued logic and set theory, such as Russell's paradox, correspond to the midpoint of the fuzzy cube. The fundamental questions of fuzzy theory—How fuzzy is a fuzzy set? How much is one fuzzy set a subset of another?—are answered geometrically with the Fuzzy Entropy Theorem, the Fuzzy Subsethood Theorem, and the Entropy-Subsethood Theorem. A new geometric proof of the Subsethood Theorem is given, a corollary of which is that the apparently probabilistic relative frequency n_A /N turns out to be the deterministic subsethood S(X, A), the degree to which the sample space X is contained in its subset A. So the frequency of successful trials is viewed as the degree to which all trials are successful. Recent Bayesian polemics against fuzzy theory are examined in light of the new sets-as-points theorems.     

The law as a dynamic interconnected system of states of affairs: a legal top ontology

In this paper, an abstract model of the law is presented that has three primitives: states of affairs, events and rules. The starting point of the abstract model is that the law is a dynamic system of states of affairs which are connected by means of rules and events. The abstract model can be regarded as a top ontology of the law, that can be applied to legal knowledge representation. After an elaboration of the three primitives, the uses of the abstract model are illustrated by the analysis of central topics of law. Then we discuss heuristic guidelines for legal knowledge representation that are suggested by the abstract model. The paper concludes with a comparison with related work. The appendix contains a formalism for the abstract model.     

Finite element analysis of heat conduction in lasagna during thermal processing

Conductive heat transfer in lasagna during heating was computed by means of the finite element method. the thermophysical properties of the pasta and tomato sauce layers were derived from their chemical composition. Simulation results obtained with an axisymmetric 2D finite element mesh without the typical layer structure differed only slightly from results obtained with a 1D mesh in which the typical layer structure was incorporated. the predicted temperatures at various locations in the lasagna agreed well with experimentally determined temperatures during heating in a commercial medium scale oven under various operating conditions. It is shown that the temperature dependency of the thermophysical parameters has only a minor influence on the temperature near the centre of the lasagna. However, when the lasagna surface is subjected to temperatures above its boiling temperature, incorporation of the water/vapour phase change in the specific heat capacity can avoid over-estimation of the volume averaged temperature and process value.     

OPTIMAL CONTROL OF THE PENICILLIN G FED-BATCH FERMENTATION: AN ANALYSIS OF A MODIFIED UNSTRUCTURED MODEL

This paper presents the application of optimal control theory in determining the optimal glucose feed rate profile for the penicillin G fed-batch fermentation, using a modified unstructured mathematical model based on balancing methods. This updated model allows for a smooth transition between maintenance and endogenous metabolism, while all variables take on physically acceptable values under all conditions

It is illustrated that the resulting computational algorithm is independent of the exact nature of the metabolism (maintenance or endogenous). In this scheme, the unusual optimization of some free initial states is included. However, as shown by simulations, the nature of the metabolism might be a key factor in concluding whether or not altering the substrate feeding strategy has an important influence on the final amount of product

Mathematical and microbial insight leads to the construction of an alternative suboptimal heuristic     

A PLACE FOR AREA‐BASED POLICY? THE SURVIVAL AND GROWTH OF LOCAL FIRMS IN DUTCH RESIDENTIAL NEIGHBORHOODS

ABSTRACT: Although their market scope often exceeds the neighborhood level, for most entrepreneurs of small‐scale firms the neighborhood is the relevant arena for both their professional activities and their personal affairs. Dutch local economic policy aims to stimulate new firm formation and firm survival in (disadvantaged) neighborhoods by conditioning economic, social, and physical aspects of the neighborhood such as economic zoning and clustering, livability, and the quality of the built‐up area. Although substantial differences in firm success exist across neighborhoods, it is not clear whether area‐level factors contribute to these differences, suggesting that area‐level policies are useful, or whether differences are due to either urban effects or to microlevel entrepreneurial and firm composition effects. This article distinguishes neighborhood effects from composition effects on local firm survival and firm growth, thereby also taking into account spatial dependence across neighborhoods. Our results suggest that aspects of the local livability of neighborhoods and of economic agglomeration are significantly related to individual firm survival and firm growth. The models provide proof for spillover effects of livability problems and market potential between adjacent neighborhoods. Neighborhoods and cities are therefore potentially places for area‐based policies, aiming at the survival and growth of local firms.     

DIFFERENCES IN SOCIAL CAPITAL BETWEEN URBAN AND RURAL ENVIRONMENTS

ABSTRACT: In the literature, several contradicting views can be found concerning rural–urban differences in individual social capital. This study combines a literature review with an empirical examination of the different points of view, applying multilevel modeling techniques on data collected from 2,332 students living across 216 municipalities. In general, social capital appears to be higher among students from municipalities in central agglomerations than among those from more rural municipalities. This effect could not be observed with respect to social capital from the family, but was established regarding social capital from friends and acquaintances. In addition, we found that living in an urban environment is associated with more pronounced socioeconomic inequalities in social capital from friends.     

REFERENCE-BASED STOCHASTIC SUBSPACE IDENTIFICATION FOR OUTPUT-ONLY MODAL ANALYSIS

When performing vibration tests on civil engineering structures, it is often unpractical and expensive to use artificial excitation (shakers, drop weights). Ambient excitation on the contrary is freely available (traffic, wind), but it causes other challenges. The ambient input remains unknown and the system identification algorithms have to deal with output-only measurements. For instance, realisation algorithms can be used: originally formulated for impulse responses they were easily extended to output covariances. More recently, data-driven stochastic subspace algorithms which avoid the computation of the output covariances were developed. The key element of these algorithms is the projection of the row space of the future outputs into the row space of the past outputs. Also typical for ambient testing of large structures is that not all degrees of freedom can be measured at once but that they are divided into several set-ups with overlapping reference sensors. These reference sensors are needed to obtain global mode shapes. In this paper, a novel approach of stochastic subspace identification is presented that incorporates the idea of the reference sensors already in the identification step: the row space of future outputs is projected into the row space of past reference outputs. The algorithm is validated with real vibration data from a steel mast excited by wind load. The price paid for the important gain concerning computational efficiency in the new approach is that the prediction errors for the non-reference channels are higher. The estimates of the eigenfrequencies and damping ratios do not suffer from this fact.     

MICROMECHANICS: SIMULATING THE ELASTIC BEHAVIOR OF ONION EPIDERMIS TISSUE

A generic modeling approach is introduced that allows for dynamical simulations of cellular biological tissue. It is derived from the discrete element approach in the sense that the tissue is discretized such that histological aspects like cell geometry and the cellular arrangement within the tissue can be fully incorporated into the model. This makes dynamical simulations of arbitrarily shaped cellular tissues feasible in an elegant and a robust way. The validity of this simulation technique is demonstrated by a case study on the unicellular epidermis layer of onion (Allium cepa). The parameters of a two‐dimensional model are determined using published stress–strain data from a tension test on longitudinal strips. The model is then validated quantitatively against the data for transversal strips.