3nj Morphogenesis and Semiclassical Disentangling

Recoupling coefficients (3nj symbols) are unitary transformations between binary coupled eigenstates of N=(n+1) mutually commuting SU(2) angular momentum operators. They have been used in a variety of applications in spectroscopy, quantum chemistry and nuclear physics and quite recently also in quantum gravity and quantum computing. These coefficients, naturally associated to cubic Yutsis graphs, share a number of intriguing combinatorial, algebraic, and analytical features that make them fashinating objects to be studied on their own. In this paper we develop a bottom--up, systematic procedure for the generation of 3nj from 3(n-1)j diagrams by resorting to diagrammatical and algebraic methods. We provide also a novel approach to the problem of classifying various regimes of semiclassical expansions of 3nj coefficients (asymptotic disentangling of 3nj diagrams) for n > 2 by means of combinatorial, analytical and numerical tools

Do Judge a Test by its Cover: Combining Combinatorial and Property-Based Testing

Property-based testing uses randomly generated inputs to validate high-level program specifications. It can be shockingly effective at finding bugs, but it often requires generating a very large number of inputs to do so. In this paper, we apply ideas from combinatorial testing, a powerful and widely studied testing methodology, to modify the distributions of our random generators so as to find bugs with fewer tests. The key concept is combinatorial coverage, which measures the degree to which a given set of tests exercises every possible choice of values for every small combination of input features. In its “classical” form, combinatorial coverage only applies to programs whose inputs have a very particular shape—essentially, a Cartesian product of finite sets. We generalize combinatorial coverage to the richer world of algebraic data types by formalizing a class of sparse test descriptions based on regular tree expressions. This new definition of coverage inspires a novel combinatorial thinning algorithm for improving the coverage of random test generators, requiring many fewer tests to catch bugs. We evaluate this algorithm on two case studies, a typed evaluator for System F terms and a Haskell compiler, showing significant improvements in both

Polynomial tuning of multiparametric combinatorial samplers

Boltzmann samplers and the recursive method are prominent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial structures, such as maps, tilings, RNA sequences or various tree-like structures. In their multiparametric variants, these samplers allow to control the profile of expected values corresponding to multiple combinatorial parameters. One can control, for instance, the number of leaves, profile of node degrees in trees or the number of certain subpatterns in strings. However, such a flexible control requires an additional non-trivial tuning procedure. In this paper, we propose an efficient polynomial-time, with respect to the number of tuned parameters, tuning algorithm based on convex optimisation techniques. Finally, we illustrate the efficiency of our approach using several applications of rational, algebraic and P\'olya structures including polyomino tilings with prescribed tile frequencies, planar trees with a given specific node degree distribution, and weighted partitions.Comment: Extended abstract, accepted to ANALCO2018. 20 pages, 6 figures, colours. Implementation and examples are available at [1] https://github.com/maciej-bendkowski/boltzmann-brain [2] https://github.com/maciej-bendkowski/multiparametric-combinatorial-sampler

Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays

The goal of this paper is to introduce a new method in computer-aided geometry of solid modeling. We put forth a novel algebraic technique to evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with regularized operators of union, intersection, and difference, i.e., any CSG tree. The result is obtained in three steps: first, by computing an independent set of generators for the d-space partition induced by the input; then, by reducing the solid expression to an equivalent logical formula between Boolean terms made by zeros and ones; and, finally, by evaluating this expression using bitwise operators. This method is implemented in Julia using sparse arrays. The computational evaluation of every possible solid expression, usually denoted as CSG (Constructive Solid Geometry), is reduced to an equivalent logical expression of a finite set algebra over the cells of a space partition, and solved by native bitwise operators.Comment: revised version submitted to Computer-Aided Geometric Desig

Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn

Automated blackbox GUI specifications enhancement and test data generation

Applications with a Graphical User Interface (GUI) front-end are ubiquitous nowadays. While automated model-based approaches have been shown to be effective in testing of such applications, most existing techniques produce many infeasible event sequences used as GUI test cases. This happens primarily because the behavioral specifications of the GUI under test are ignored. In this dissertation we present an automated framework that reveals an important set of state-based constraints among GUI events based on infeasible (i.e., unexecutable or partially executable) test cases of a GUI test suite. GUIDiVa, an iterative algorithm at the core of our framework, enumerates all possible constraint violations as potential reasons for test case failure, on the failed event of an infeasible test case. It then selects and adds the most promising constraints of each iteration to a final set based on the Validity Weight of constraints. The results of empirical studies on both seeded and nine non-trivial open-source study subjects show that our framework is capable of capturing important aspects of GUI behavior in the form of state-based event constraints, while considerably reducing the number of insfeasible test cases. The second part of this dissertation deals with the problem of automatic generation of relevant test data for parameterized GUI events (i.e., events associated with widgets that accept user inputs such as textboxes and textareas). Current techniques either manipulate the source code of the application under test (AUT) to generate the test data, or blindly use a set of random string values. We propose a novel way to generate the test data by exploiting the information provided in the GUI structure to extract a set of key identifiers for each parameterized GUI widget. These identifiers are used to compose appropriate online search phrases and collect relevant test data from the Internet. The results of an empirical study on five GUI-based applications show that the proposed approach is applicable and results in execution of some hard-to-cover branches in the subject programs. The proposed technique works from a black-box perspective and is entirely independent from GUI modeling and event sequence generation, thus it does not require source code access and offers the possibility of being integrated with existing GUI testing frameworks

Regulatory motif discovery using a population clustering evolutionary algorithm

This paper describes a novel evolutionary algorithm for regulatory motif discovery in DNA promoter sequences. The algorithm uses data clustering to logically distribute the evolving population across the search space. Mating then takes place within local regions of the population, promoting overall solution diversity and encouraging discovery of multiple solutions. Experiments using synthetic data sets have demonstrated the algorithm's capacity to find position frequency matrix models of known regulatory motifs in relatively long promoter sequences. These experiments have also shown the algorithm's ability to maintain diversity during search and discover multiple motifs within a single population. The utility of the algorithm for discovering motifs in real biological data is demonstrated by its ability to find meaningful motifs within muscle-specific regulatory sequences

Testing embedded system through optimal mining technique (OMT) based on multi-input domain

Testing embedded systems must be done carefully particularly in the significant regions of the embedded systems. Inputs from an embedded system can happen in multiple order and many relationships can exist among the input sequences. Consideration of the sequences and the relationships among the sequences is one of the most important considerations that must be tested to find the expected behavior of the embedded systems. On the other hand combinatorial approaches help determining fewer test cases that are quite enough to test the embedded systems exhaustively. In this paper, an Optimal Mining Technique that considers multi-input domain which is based on built-in combinatorial approaches has been presented. The method exploits multi-input sequences and the relationships that exist among multi-input vectors. The technique has been used for testing an embedded system that monitors and controls the temperature within the Nuclear reactors