Scalable satisfiability checking and test data generation from modeling diagrams

We explore the automatic generation of test data that respect constraints expressed in the Object-Role Modeling (ORM) language. ORM is a popular conceptual modeling language, primarily targeting database applications, with significant uses in practice. The general problem of even checking whether an ORM diagram is satisfiable is quite hard: restricted forms are easily NP-hard and the problem is undecidable for some expressive formulations of ORM. Brute-force mapping to input for constraint and SAT solvers does not scale: state-of-the-art solvers fail to find data to satisfy uniqueness and mandatory constraints in realistic time even for small examples. We instead define a restricted subset of ORM that allows efficient reasoning yet contains most constraints overwhelmingly used in practice. We show that the problem of deciding whether these constraints are consistent (i.e., whether we can generate appropriate test data) is solvable in polynomial time, and we produce a highly efficient (interactive speed) checker. Additionally, we analyze over 160 ORM diagrams that capture data models from industrial practice and demonstrate that our subset of ORM is expressive enough to handle their vast majority.     

Tight bounds for parallel randomized load balancing

Given a distributed system of \(n\) balls and \(n\) bins, how evenly can we distribute the balls to the bins, minimizing communication? The fastest non-adaptive and symmetric algorithm achieving a constant maximum bin load requires \(\varTheta (\log \log n)\) rounds, and any such algorithm running for \(r\in {\mathcal {O}}(1)\) rounds incurs a bin load of \(\varOmega ((\log n/\log \log n)^{1/r})\). In this work, we explore the fundamental limits of the general problem. We present a simple adaptive symmetric algorithm that achieves a bin load of 2 in \(\log ^* n+{\mathcal {O}}(1)\) communication rounds using \({\mathcal {O}}(n)\) messages in total. Our main result, however, is a matching lower bound of \((1-o(1))\log ^* n\) on the time complexity of symmetric algorithms that guarantee small bin loads. The essential preconditions of the proof are (i) a limit of \({\mathcal {O}}(n)\) on the total number of messages sent by the algorithm and (ii) anonymity of bins, i.e., the port numberings of balls need not be globally consistent. In order to show that our technique yields indeed tight bounds, we provide for each assumption an algorithm violating it, in turn achieving a constant maximum bin load in constant time.     

AR-based serious game framework for post-stroke rehabilitation

Stroke is considered one of the main causes of death around the world. Survivors often suffer different kinds of disabilities in terms of their cognitive and motor capabilities, and are therefore unable to perform their day-to-day activities. To regain some of their cognitive as well as motor abilities, they require rehabilitation. To this end, we present a serious game framework based on augmented reality technology that may motivate the patients’ involvement in the rehabilitation exercise. Additionally, we analyze the requirements for such a framework and describe the concept and implementation of the proposed approach. Furthermore, we designed a wireless vibrotactile output device that is attached to a tangible object. The tangible object that is connected to the framework can give haptic as well as audio-visual feedback to the patient in a more motivating and entertaining environment for rehabilitation exercises. The suitability and utility of the proposed framework was evaluated with real stroke patients and compared against the performance of a healthy control group, thus facilitating occupational therapists in assessing a patient’s progress. Our evaluations show that the serious games with vibrotactile feedback are well accepted by patients.     

Emulation of complex open quantum systems using superconducting qubits

With quantum computers being out of reach for now, quantum simulators are alternative devices for efficient and accurate simulation of problems that are challenging to tackle using conventional computers. Quantum simulators are classified into analog and digital, with the possibility of constructing “hybrid” simulators by combining both techniques. Here we focus on analog quantum simulators of open quantum systems and address the limit that they can beat classical computers. In particular, as an example, we discuss simulation of the chlorosome light-harvesting antenna from green sulfur bacteria with over 250 phonon modes coupled to each electronic state. Furthermore, we propose physical setups that can be used to reproduce the quantum dynamics of a standard and multiple-mode Holstein model. The proposed scheme is based on currently available technology of superconducting circuits consist of flux qubits and quantum oscillators.     

Probabilistic knowledge representation using the principle of maximum entropy and Gröbner basis theory

An often used methodology for reasoning with probabilistic conditional knowledge bases is provided by the principle of maximum entropy (so-called MaxEnt principle) that realises an idea of least amount of assumed information and thus of being as unbiased as possible. In this paper we exploit the fact that MaxEnt distributions can be computed by solving nonlinear equation systems that reflect the conditional logical structure of these distributions. We apply the theory of Gröbner bases that is well known from computational algebra to the polynomial system which is associated with a MaxEnt distribution, in order to obtain results for reasoning with maximum entropy. We develop a three-phase compilation scheme extracting from a knowledge base consisting of probabilistic conditionals the information which is crucial for MaxEnt reasoning and transforming it to a Gröbner basis. Based on this transformation, a necessary condition for knowledge bases to be consistent is derived. Furthermore, approaches to answering MaxEnt queries are presented by demonstrating how inferring the MaxEnt probability of a single conditional from a given knowledge base is possible. Finally, we discuss computational methods to establish general MaxEnt inference rules.     

Computational performance of a parallelized three-dimensional high-order spectral element toolbox

In this paper, a comprehensive performance review of an MPI-based high-order three-dimensional spectral element method C++ toolbox is presented. The focus is put on the performance evaluation of several aspects with a particular emphasis on the parallel efficiency. The performance evaluation is analyzed with the help of a time prediction model based on a parameterization of the application and the hardware resources. Two tailor-made benchmark cases in computational fluid dynamics (CFD) are introduced and used to carry out this review, stressing the particular interest for clusters with up to thousands of cores. Some problems in the parallel implementation have been detected and corrected. The theoretical complexities with respect to the number of elements, to the polynomial degree, and to communication needs are correctly reproduced. It is concluded that this type of code has a nearly perfect speedup on machines with thousands of cores, and is ready to make the step to next-generation petaFLOP machines.     

Multi-class supervised classification of electrical borehole wall images using texture features

Electrical borehole wall images represent micro-resistivity measurements at the borehole wall. The lithology reconstruction is often based on visual interpretation done by geologists. This analysis is very time-consuming and subjective. Different geologists may interpret the data differently. In this work, linear discriminant analysis (LDA) in combination with texture features is used for an automated lithology reconstruction of ODP (Ocean Drilling Program) borehole 1203A drilled during Leg 197. Six rock groups are identified by their textural properties in resistivity data obtained by a Formation MircoScanner (FMS). Although discriminant analysis can be used for multi-class classification, non-optimal decision criteria for certain groups could emerge. For this reason, we use a combination of 2-class (binary) classifiers to increase the overall classification accuracy. The generalization ability of the combined classifiers is evaluated and optimized on a testing dataset where a classification rate of more than 80% for each of the six rock groups is achieved. The combined, trained classifiers are then applied on the whole dataset obtaining a statistical reconstruction of the logged formation. Compared to a single multi-class classifier the combined binary classifiers show better classification results for certain rock groups and more stable results in larger intervals of equal rock type.     

A comparison of local parametric C Bézier interpolants for triangular meshes

Parametric curved shape surface schemes interpolating vertices and normals of a given triangular mesh with arbitrary topology are widely used in computer graphics for gaming and real-time rendering due to their ability to effectively represent any surface of arbitrary genus. In this context, continuous curved shape surface schemes using only the information related to the triangle corresponding to the patch under construction, emerged as attractive solutions responding to the requirements of resource-limited hardware environments. In this paper we provide a unifying comparison of the local parametric C⁰ curved shape schemes we are aware of, based on a reformulation of their original constructions in terms of polynomial Bézier triangles. With this reformulation we find a geometric interpretation of all the schemes that allows us to analyse their strengths and shortcomings from a geometrical point of view. Further, we compare the four schemes with respect to their computational costs, their reproduction capabilities of analytic surfaces and their response to different surface interrogation methods on arbitrary triangle meshes with a low triangle count that actually occur in their real-world use.     

Finding Total Unimodularity in Optimization Problems Solved by Linear Programs

A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally unimodular. Still, sometimes it is possible to build an integer solution with the same cost from the fractional solution. Examples are two scheduling problems (Baptiste and Schieber, J. Sched. 6(4):395–404, 2003; Brucker and Kravchenko, J. Sched. 11(4):229–237, 2008) and the single disk prefetching/caching problem (Albers et al., J. ACM 47:969–986, 2000). We show that problems such as the three previously mentioned can be separated into two subproblems: (1) finding an optimal feasible set of slots, and (2) assigning the jobs or pages to the slots. It is straigthforward to show that the latter can be solved greedily. We are able to solve the former with a totally unimodular linear program, from which we obtain simple combinatorial algorithms with improved worst case running time.