States in Process Calculi

Formal reasoning about distributed algorithms (like Consensus) typically requires to analyze global states in a traditional state-based style. This is in contrast to the traditional action-based reasoning of process calculi. Nevertheless, we use domain-specific variants of the latter, as they are convenient modeling languages in which the local code of processes can be programmed explicitly, with the local state information usually managed via parameter lists of process constants. However, domain-specific process calculi are often equipped with (unlabeled) reduction semantics, building upon a rich and convenient notion of structural congruence. Unfortunately, the price for this convenience is that the analysis is cumbersome: the set of reachable states is modulo structural congruence, and the processes' state information is very hard to identify. We extract from congruence classes of reachable states individual state-informative representatives that we supply with a proper formal semantics. As a result, we can now freely switch between the process calculus terms and their representatives, and we can use the stateful representatives to perform assertional reasoning on process calculus models.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127

Extending Similarity Measures of Interval Type-2 Fuzzy Sets to General Type-2 Fuzzy Sets

Similarity measures provide one of the core tools that enable reasoning about fuzzy sets. While many types of similarity measures exist for type-1 and interval type-2 fuzzy sets, there are very few similarity measures that enable the comparison of general type-2 fuzzy sets. In this paper, we introduce a general method for extending existing interval type-2 similarity measures to similarity measures for general type-2 fuzzy sets. Specifically, we show how similarity measures for interval type-2 fuzzy sets can be employed in conjunction with the zSlices based general type-2 representation for fuzzy sets to provide measures of similarity which preserve all the common properties (i.e. reflexivity, symmetry, transitivity and overlapping) of the original interval type-2 similarity measure. We demonstrate examples of such extended fuzzy measures and provide comparisons between (different types of) interval and general type-2 fuzzy measures.Comment: International Conference on Fuzzy Systems 2013 (Fuzz-IEEE 2013

Encoding CSP into CCS

We study encodings from CSP into asynchronous CCS with name passing and matching, so in fact, the asynchronous pi-calculus. By doing so, we discuss two different ways to map the multi-way synchronisation mechanism of CSP into the two-way synchronisation mechanism of CCS. Both encodings satisfy the criteria of Gorla except for compositionality, as both use an additional top-level context. Following the work of Parrow and Sj\"odin, the first encoding uses a centralised coordinator and establishes a variant of weak bisimilarity between source terms and their translations. The second encoding is decentralised, and thus more efficient, but ensures only a form of coupled similarity between source terms and their translations.Comment: In Proceedings EXPRESS/SOS 2015, arXiv:1508.0634

Relating geometry descriptions to its derivatives on the web

Sharing building information over the Web is becoming more popular, leading to advances in describing building models in a Semantic Web context. However, those descriptions lack unified approaches for linking geometry descriptions to building elements, derived properties and derived other geometry descriptions. To bridge this gap, we analyse the basic characteristics of geometric dependencies and propose the Ontology for Managing Geometry (OMG) based on this analysis. In this paper, we present our results and show how the OMG provides means to link geometric and non-geometric data in meaningful ways. Thus, exchanging building data, including geometry, on the Web becomes more efficient

On the discretization of a bistable cantilever beam with application to energy harvesting

A typical setup for energy harvesting is that of a cantilever beam with piezoceramics excited by ambient base vibrations. In order to get higher energy output for a wide range of excitation frequencies, often a nonlinearity is introduced by intention in that way, that two magnets are fixed close to the free tip of the beam. Depending on strength and position of the magnets, this can either result in a mono-, bi- or tristable system. In our study, we focus on a bistable system. Such systems have been investigated thoroughly in literature while in almost all cases the beam has been discretized by a single shape function, in general the first eigenshape of the linear beam with undeflected stable equilibrium position. There can be some doubts about the suitability of a discretization by a single shape function mainly due to two reasons. First: In case of stochastic broadband excitations a discretization, taking into consideration just the first vibration shape seems not to be reasonable. Second: as the undeflected position of the considered system is unstable and the system significantly nonlinear, the question arises, if using just one eigenshape of the linear beam is a suitable approximation of the operation shapes during excited oscillations even in the case of harmonic excitation. Are there other, e.g. amplitude dependent, possibilities and/or should multiple ansatz functions be considered instead? In this paper, we focus mainly on the second point. Therefore, a bistable cantilever beam with harmonic base excitation is considered and experimental investigations of operation shapes are performed using a high-speed camera. The observed operation shapes are expanded in a similar way as it is done in a theoretical analysis by a corresponding mixed Ritz ansatz. The results show the existence of distinct superharmonics (as one can expect for a nonlinear system) but additionally the necessity to use more than one shape function in the discretization, covering also the amplitude dependence of the observed operation shapes

Measuring the directional distance between fuzzy sets

The measure of distance between two fuzzy sets is a fundamental tool within fuzzy set theory. However, current distance measures within the literature do not account for the direction of change between fuzzy sets; a useful concept in a variety of applications, such as Computing With Words. In this paper, we highlight this utility and introduce a distance measure which takes the direction between sets into account. We provide details of its application for normal and non-normal, as well as convex and non-convex fuzzy sets. We demonstrate the new distance measure using real data from the MovieLens dataset and establish the benefits of measuring the direction between fuzzy sets

Maximal functions and related weight classes

The famous result of Muckenhoupt on the connection between weights $\omega$ in $A_p$-classes and the boundedness of the maximal operator in $L_p(\omega)$ is extended to the case $p=\infty$ by the introduction of the geometrical maximal operator. Estimates of the norm of the maximal operators are given in terms of the $A_p$-constants. The equality of two differently defined $A_{\infty}$-constants is proved. Thereby an answer is given to a question posed by R. Johnson. For non-increasing functions on the positive real line a parallel theory to the $A_p$-theory is established for the connection between weights in $B_p$-classes and maximal functions, thereby extending and developing the recent results of Ari o and Muckenhoupt

Comparison of distance metrics for hierarchical data in medical databases

Distance metrics are broadly used in different research areas and applications, such as bio- informatics, data mining and many other fields. However, there are some metrics, like pq-gram and Edit Distance used specifically for data with a hierarchical structure. Other metrics used for non- hierarchical data are the geometric and Hamming metrics. We have applied these metrics to The Health Improvement Network (THIN) database which has some hierarchical data. The THIN data has to be converted into a tree-like structure for the first group of metrics. For the second group of metrics, the data are converted into a frequency table or matrix, then for all metrics, all distances are found and normalised. Based on this particular data set, our research question: which of these metrics is useful for THIN data? This paper compares the metrics, particularly the pqgram metric on finding the similarities of patients’ data. It also investigates the similar patients who have the same close distances as well as the metrics suitability for clustering the whole patient population. Our results show that the two groups of metrics perform differently as they represent different structures of the data. Nevertheless, all the metrics could represent some similar data of patients as well as discriminate sufficiently well in clustering the patient population using k-means clustering algorithm