On the Computation of Clebsch-Gordan Coefficients and the Dilation Effect

We investigate the problem of computing tensor product multiplicities for complex semisimple Lie algebras. Even though computing these numbers is #P-hard in general, we show that if the rank of the Lie algebra is assumed fixed, then there is a polynomial time algorithm, based on counting the lattice points in polytopes. In fact, for Lie algebras of type A_r, there is an algorithm, based on the ellipsoid algorithm, to decide when the coefficients are nonzero in polynomial time for arbitrary rank. Our experiments show that the lattice point algorithm is superior in practice to the standard techniques for computing multiplicities when the weights have large entries but small rank. Using an implementation of this algorithm, we provide experimental evidence for conjectured generalizations of the saturation property of Littlewood--Richardson coefficients. One of these conjectures seems to be valid for types B_n, C_n, and D_n.Comment: 21 pages, 6 table

Vertices of Gelfand-Tsetlin Polytopes

This paper is a study of the polyhedral geometry of Gelfand-Tsetlin patterns arising in the representation theory \mathfrak{gl}_n \C and algebraic combinatorics. We present a combinatorial characterization of the vertices and a method to calculate the dimension of the lowest-dimensional face containing a given Gelfand-Tsetlin pattern. As an application, we disprove a conjecture of Berenstein and Kirillov about the integrality of all vertices of the Gelfand-Tsetlin polytopes. We can construct for each $n\geq5$ a counterexample, with arbitrarily increasing denominators as $n$ grows, of a non-integral vertex. This is the first infinite family of non-integral polyhedra for which the Ehrhart counting function is still a polynomial. We also derive a bound on the denominators for the non-integral vertices when $n$ is fixed.Comment: 14 pages, 3 figures, fixed attribution

Software reliability through fault-avoidance and fault-tolerance

The use of back-to-back, or comparison, testing for regression test or porting is examined. The efficiency and the cost of the strategy is compared with manual and table-driven single version testing. Some of the key parameters that influence the efficiency and the cost of the approach are the failure identification effort during single version program testing, the extent of implemented changes, the nature of the regression test data (e.g., random), and the nature of the inter-version failure correlation and fault-masking. The advantages and disadvantages of the technique are discussed, together with some suggestions concerning its practical use

Experiments in fault tolerant software reliability

Twenty functionally equivalent programs were built and tested in a multiversion software experiment. Following unit testing, all programs were subjected to an extensive system test. In the process sixty-one distinct faults were identified among the versions. Less than 12 percent of the faults exhibited varying degrees of positive correlation. The common-cause (or similar) faults spanned as many as 14 components. However, a majority of these faults were trivial, and easily detected by proper unit and/or system testing. Only two of the seven similar faults were difficult faults, and both were caused by specification ambiguities. One of these faults exhibited variable identical-and-wrong response span, i.e. response span which varied with the testing conditions and input data. Techniques that could have been used to avoid the faults are discussed. For example, it was determined that back-to-back testing of 2-tuples could have been used to eliminate about 90 percent of the faults. In addition, four of the seven similar faults could have been detected by using back-to-back testing of 5-tuples. It is believed that most, if not all, similar faults could have been avoided had the specifications been written using more formal notation, the unit testing phase was subject to more stringent standards and controls, and better tools for measuring the quality and adequacy of the test data (e.g. coverage) were used

Multiversion software reliability through fault-avoidance and fault-tolerance

In this project we have proposed to investigate a number of experimental and theoretical issues associated with the practical use of multi-version software in providing dependable software through fault-avoidance and fault-elimination, as well as run-time tolerance of software faults. In the period reported here we have working on the following: We have continued collection of data on the relationships between software faults and reliability, and the coverage provided by the testing process as measured by different metrics (including data flow metrics). We continued work on software reliability estimation methods based on non-random sampling, and the relationship between software reliability and code coverage provided through testing. We have continued studying back-to-back testing as an efficient mechanism for removal of uncorrelated faults, and common-cause faults of variable span. We have also been studying back-to-back testing as a tool for improvement of the software change process, including regression testing. We continued investigating existing, and worked on formulation of new fault-tolerance models. In particular, we have partly finished evaluation of Consensus Voting in the presence of correlated failures, and are in the process of finishing evaluation of Consensus Recovery Block (CRB) under failure correlation. We find both approaches far superior to commonly employed fixed agreement number voting (usually majority voting). We have also finished a cost analysis of the CRB approach

Software reliability through fault-avoidance and fault-tolerance

Twenty independently developed but functionally equivalent software versions were used to investigate and compare empirically some properties of N-version programming, Recovery Block, and Consensus Recovery Block, using the majority and consensus voting algorithms. This was also compared with another hybrid fault-tolerant scheme called Acceptance Voting, using dynamic versions of consensus and majority voting. Consensus voting provides adaptation of the voting strategy to varying component reliability, failure correlation, and output space characteristics. Since failure correlation among versions effectively reduces the cardinality of the space in which the voter make decisions, consensus voting is usually preferable to simple majority voting in any fault-tolerant system. When versions have considerably different reliabilities, the version with the best reliability will perform better than any of the fault-tolerant techniques

Hematology as Related to Diving Characteristics of Elaphe obsoleta, Nerodia erythrogaster, Nerodia Fasciata and Nerodia rhombifera

The diving capabilities of Nerodia erythrogaster flavigaster and Nerodia fasciata confluens were investigated and the results were compared with similar studies on Nerodia rhombifera rhombifera and Elaphe obsoleta obsoleta (Baeyens et al., 1978). In addition, morphological and hematological parameters contributing to underwater survival were examined. The duration of underwater survival for N. erythrogaster and N. fasciata was approximately one hour with no difference between the species. The lung volumes of the two species were also similar but were significantly less than lung volumes reported for E. obsoleta. There were no significant differences in hemoglobin concentration, red blood cell count or hematocrit between N. rhombifera, N. erythrogaster, N. fasciata, and E. obsoleta. Based on similarities in underwater tolerance, lung morphology and hematology, Nerodia more closely resembles the terrestrial E. obsoleta than those reptiles specifically adapted to an underwater existance

Additional Records of Acanthocephalan Parasites from Arkansas Fishes, with New Records from Missouri Fishes

Over the last decade, our research consortium has provided information on acanthocephalan parasites of Arkansas vertebrates, including records from some of the state’s fishes. Here, we continue to provide data on new geographic and new host records of acanthocephalans from Arkansas fishes. In addition, for the first time, we report records of acanthocephalans for some Missouri fishes. We document 2 new state records as well as 10 new host records for some fish acanthocephalans

An Annotated Checklist of the Crayfishes (Decapoda: Cambaridae) of Arkansas

Prior to the present study, 56 species with 3 additional subspecies for a total of 59 different taxa of crayfishes were recognized from Arkansas. We add a single species (Carmel Crayfish, Fallicambarus schusteri) to that list, subtract a documented synonym (Procambarus ferrugenius = Procambarus liberorum), update the classification to better reflect recent phylogenetic insights, and provide an updated annotated checklist of the 59 crayfish taxa of presently known from the state. There are 8 endemic species in Arkansas, including the Bayou Bodcau Crayfish (Bouchardina robisoni), Boston Mountains Crayfish (Cambarus causeyi), Hell Creek Cave Crayfish (C. zophonastes), Jefferson County Crayfish (Creaserinus gilpini), Ouachita Burrowing Crayfish (Fallicambarus harpi), Slenderwrist Burrowing Crayfish (F. petilicarpus), Saline Burrowing Crayfish (F. strawni), and Redspotted Stream Crayfish (Faxonius acares). There are also 2 federally endangered species, the Benton County Cave Crayfish (Cambarus aculabrum) and the Hell Creek Cave Crayfish (C. zophonastes) that inhabit Arkansas karst habitat. We expect that additional species will be included in the list with further DNA analyses