On the size of binary decision diagrams representing Boolean functions

AbstractWe consider the size of the representation of Boolean functions by several classes of binary decision diagrams (BDDs) (also called branching programs), namely the classes of arbitrary BDDs of real time BDD (RBDD) (i.e. BDDs where each computation path is limited to the number of variables), of free BDDs (FBDDs) (also called read-once-only branching programs), of ordered BDDs (OBDDS) i.e. FBDDs where variables are tested in the same order along all paths), and binary decision trees (BDTs).Using well-known techniques, we first establish asymptotically sharp bounds as a function of n on the minimum size of arbitrary BDDs representing almost all Boolean functions of n variables and provide asymptotic lower and upper bounds, differing only by a factor of two, on the minimum size OBDDs representing almost all Boolean functions of n variables.We then, using a method to obtain exponential lower bounds on complexity of computation of Boolean functions by RBDD, FBDD and OBDD that originated in (Breitbart, 1968), present the highest such bounds to date and also present improved bounds on the relative economy of description of particular Boolean functions by the above classes of BDDs. For each nontrivial pair of BDD classes considered, we exhibit infinite families of Boolean functions representable much more concisely by BDDs in one class than by BDDs in the other

Parameter Estimation Error Dependency on the Acquisition Protocol in Diffusion Kurtosis Imaging

Mono-exponential kurtosis model is routinely fitted on diffusion weighted, magnetic resonance imaging data to describe non-Gaussian diffusion. Here, the purpose was to optimize acquisitions for this model to minimize the errors in estimating diffusion coefficient and kurtosis. Similar to a previous study, covariance matrix calculations were used, and coefficients of variation in estimating each parameter of this model were calculated. The acquisition parameter, b values, varied in discrete grids to find the optimum ones that minimize the coefficient of variation in estimating the two non-Gaussian parameters. Also, the effect of variation of the target values on the optimized values was investigated. Additionally, the results were benchmarked with Monte Carlo noise simulations. Simple correlations were found between the optimized b values and target values of diffusion and kurtosis. For small target values of the two parameters, there is higher chance of having significant errors; this is caused by maximum b value limits imposed by the scanner than the mathematical bounds. The results here, cover a wide range of parameters D and K so that they could be used in many directionally averaged diffusion weighted cases such as head and neck, prostate, etc

The diagnostic accuracy of high b-value diffusion- and T2-weighted imaging for the detection of prostate cancer: a meta-analysis

Purpose: This study aims to investigate the role of diffusion-weighted imaging (DWI) and T2-weighted imaging (T2WI) in combination for the detection of prostate cancer, specifically assessing the role of high b-values (> 1000 s/mm2), with a systematic review and meta-analysis of the existing published data.  Methods: The electronic databases MEDLINE, EMBASE, and OpenSIGLE were searched between inception and September 1, 2017. Eligible studies were those that reported the sensitivity and specificity of DWI and T2WI for the diagnosis of prostate cancer by visual assessment using a histopathologic reference standard. The QUADAS-2 critical appraisal tool was used to assess the quality of included studies. A meta-analysis with pooling of sensitivity, specificity, likelihood, and diagnostic odds ratios was undertaken, and a summary receiver-operating characteristics (sROC) curve was constructed. Predetermined subgroup analysis was also performed.  Results: Thirty-three studies were included in the final analysis, evaluating 2949 patients. The pooled sensitivity and specificity were 0.69 (95% CI 0.68–0.69) and 0.84 (95% CI 0.83–0.85), respectively, and the sROC AUC was 0.84 (95% CI 0.81–0.87). Subgroup analysis showed significantly better sensitivity with high b-values (> 1000 s/mm2). There was high statistical heterogeneity between studies.  Conclusion: The diagnostic accuracy of combined DWI and T2WI is good with high b-values (> 1000 s/mm2) seeming to improve overall sensitivity while maintaining specificity. However, further large-scale studies specifically looking at b-value choice are required before a categorical recommendation can be made

Non-essential genes form the hubs of genome scale protein function and environmental gene expression networks in Salmonella enterica serovar Typhimurium

Background Salmonella Typhimurium is an important pathogen of human and animals. It shows a broad growth range and survives in harsh conditions. The aim of this study was to analyze transcriptional responses to a number of growth and stress conditions as well as the relationship of metabolic pathways and/or cell functions at the genome-scale-level by network analysis, and further to explore whether highly connected genes (hubs) in these networks were essential for growth, stress adaptation and virulence. Results De novo generated as well as published transcriptional data for 425 selected genes under a number of growth and stress conditions were used to construct a bipartite network connecting culture conditions and significantly regulated genes (transcriptional network). Also, a genome scale network was constructed for strain LT2. The latter connected genes with metabolic pathways and cellular functions. Both networks were shown to belong to the family of scale-free networks characterized by the presence of highly connected nodes or hubs which are genes whose transcription is regulated when responding to many of the assayed culture conditions or genes encoding products involved in a high number of metabolic pathways and cell functions. The five genes with most connections in the transcriptional network (wraB, ygaU, uspA, cbpA and osmC) and in the genome scale network (ychN, siiF (STM4262), yajD, ybeB and dcoC) were selected for mutations, however mutagenesis of ygaU and ybeB proved unsuccessful. No difference between mutants and the wild type strain was observed during growth at unfavorable temperatures, pH values, NaCl concentrations and in the presence of H2O2. Eight mutants were evaluated for virulence in C57/BL6 mice and none differed from the wild type strain. Notably, however, deviations of phenotypes with respect to the wild type were observed when combinations of these genes were deleted. Conclusion Network analysis revealed the presence of hubs in both transcriptional and functional networks of S. Typhimurium. Hubs theoretically confer higher resistance to random mutation but a greater susceptibility to directed attacks, however, we found that genes that formed hubs were dispensable for growth, stress adaptation and virulence, suggesting that evolution favors non-essential genes as main connectors in cellular networks

Approximation algorithms for NEXTtime-hard periodically specified problems and domino problems

We study the efficient approximability of two general class of problems: (1) optimization versions of the domino problems studies in [Ha85, Ha86, vEB83, SB84] and (2) graph and satisfiability problems when specified using various kinds of periodic specifications. Both easiness and hardness results are obtained. Our efficient approximation algorithms and schemes are based on extensions of the ideas. Two of properties of our results obtained here are: (1) For the first time, efficient approximation algorithms and schemes have been developed for natural NEXPTIME-complete problems. (2) Our results are the first polynomial time approximation algorithms with good performance guarantees for `hard` problems specified using various kinds of periodic specifications considered in this paper. Our results significantly extend the results in [HW94, Wa93, MH+94]

Bayes and health care research.

Bayes’ rule shows how one might rationally change one’s beliefs in the light of evidence. It is the foundation of a statistical method called Bayesianism. In health care research, Bayesianism has its advocates but the dominant statistical method is frequentism. There are at least two important philosophical differences between these methods. First, Bayesianism takes a subjectivist view of probability (i.e. that probability scores are statements of subjective belief, not objective fact) whilst frequentism takes an objectivist view. Second, Bayesianism is explicitly inductive (i.e. it shows how we may induce views about the world based on partial data from it) whereas frequentism is at least compatible with non-inductive views of scientific method, particularly the critical realism of Popper. Popper and others detail significant problems with induction. Frequentism’s apparent ability to avoid these, plus its ability to give a seemingly more scientific and objective take on probability, lies behind its philosophical appeal to health care researchers. However, there are also significant problems with frequentism, particularly its inability to assign probability scores to single events. Popper thus proposed an alternative objectivist view of probability, called propensity theory, which he allies to a theory of corroboration; but this too has significant problems, in particular, it may not successfully avoid induction. If this is so then Bayesianism might be philosophically the strongest of the statistical approaches. The article sets out a number of its philosophical and methodological attractions. Finally, it outlines a way in which critical realism and Bayesianism might work together. </p

Periodically specified satisfiability problems with applications: An alternative to domino problems

We characterize the complexities of several basic generalized CNF satisfiability problems SAT(S), when instances are specified using various kinds of 1- and 2-dimensional periodic specifications. We outline how this characterization can be used to prove a number of new hardness results for the complexity classes DSPACE(n), NSPACE(n), DEXPTIME, NEXPTIME, EXPSPACE etc. The hardness results presented significantly extend the known hardness results for periodically specified problems. Several advantages axe outlined of the use of periodically specified satisfiability problems over the use of domino problems in proving both hardness and easiness results. As one corollary, we show that a number of basic NP-hard problems become EXPSPACE hard when inputs axe represented using 1-dimensional infinite periodic wide specifications. This answers a long standing open question posed by Orlin

Data consistency: toward a terminological clarification

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-21413-9_15Consistency is an inconsistency are ubiquitous term in data engineering. Its relevance to quality is obvious, since consistency is a commonplace dimension of data quality. However, connotations are vague or ambiguous. In this paper, we address semantic consistency, transaction consistency, replication consistency, eventual consistency and the new notion of partial consistency in databases. We characterize their distinguishing properties, and also address their differences, interactions and interdependencies. Partial consistency is an entry door to living with inconsistency, which is an ineludible necessity in the age of big data.Decker and F.D. Muñoz—supported by the Spanish MINECO grant TIN 2012-37719-C03-01.Decker, H.; Muñoz Escoí, FD.; Misra, S. (2015). Data consistency: toward a terminological clarification. En Computational Science and Its Applications -- ICCSA 2015: 15th International Conference, Banff, AB, Canada, June 22-25, 2015, Proceedings, Part V. Springer International Publishing. 206-220. https://doi.org/10.1007/978-3-319-21413-9_15S206220Abadi, D.: Consistency tradeoffs in modern distributed database system design: Cap is only part of the story. Computer 45(2), 37–42 (2012)Bailis, P. (2015). http://www.bailis.org/blog/Bailis, P., Ghodsi, A.: Eventual consistency today: limitations, extensions, and beyond. ACM Queue, 11(3) (2013)Balegas, V., Duarte, S., Ferreira, C., Rodrigues, R., Preguica, N., Najafzadeh, M., Shapiro, M.: Putting consistency back into eventual consistency. In: 10th EuroSys. ACM (2015). http://dl.acm.org/citation.cfm?doid=2741948.2741972Beeri, C., Bernstein, P., Goodman, N.: A sophisticate’s introduction to database normalization theory. In: VLDB, pp. 113–124 (1978)Berenson, H., Bernstein, P., Gray, J., Melton, J., O’Neil, E., O’Neil, P.: A critique of ansi sql isolation levels. SIGMoD Record 24(2), 1–10 (1995)Bermbach, D., Tai, S.: Eventual consistency: how soon is eventual? In: 6th MW4SOC. ACM (2011)Bernabé-Gisbert, J., Muñoz-Escoí, F.: Supporting multiple isolation levels in replicated environments. Data & Knowledge Engineering 7980, 1–16 (2012)Bernstein, P., Das, S.. Rethinking eventual consistency. In: SIGMOD 2013, pp. 923–928. ACM (2013)Bernstein, P., Hadzilacos, V., Goodman, N.: Concurrency Control and Recovery in Database Systems. Addison-Wesley (1987)Bertossi, L., Hunter, A., Schaub, T.: Inconsistency Tolerance. In: Bertossi, L., Hunter, A., Schaub, T. (eds.) Inconsistency Tolerance. LNCS, vol. 3300, pp. 1–14. Springer, Heidelberg (2005)Bobenrieth, A.: Inconsistencias por qué no? Un estudio filosófico sobre la lógica paraconsistente. Premios Nacionales Colcultura. Tercer Mundo Editores. Magister Thesis, Universidad de los Andes, Santafé de Bogotá, Columbia (1995)Bosneag, A.-M., Brockmeyer, M.: A formal model for eventual consistency semantics. In: PDCS 2002, pp. 204–209. IASTED (2001)Browne, J.: Brewer’s cap theorem (2009). http://www.julianbrowne.com/article/viewer/brewers-cap-theoremCong, G., Fan, W., Geerts, F., Jia, X., Ma, S.: Improving data quality: consistency and accuracy. In: Proc. 33rd VLDB, pp. 315–326. ACM (2007)Dechter, R., van Beek, P.: Local and global relational consistency. Theor. Comput. Sci. 173(1), 283–308 (1997)Decker, H.: Translating advanced integrity checking technology to SQL. In: Doorn, J., Rivero, L. (eds.) Database integrity: challenges and solutions, pp. 203–249. Idea Group (2002)Decker, H.: Historical and computational aspects of paraconsistency in view of the logic foundation of databases. In: Bertossi, L., Katona, G.O.H., Schewe, K.-D., Thalheim, B. (eds.) Semantics in Databases 2001. LNCS, vol. 2582, pp. 63–81. Springer, Heidelberg (2003)Decker, H.: Answers that have integrity. In: Schewe, K.-D., Thalheim, B. (eds.) SDKB 2010. LNCS, vol. 6834, pp. 54–72. Springer, Heidelberg (2011)Decker, H.: New measures for maintaining the quality of databases. In: Murgante, B., Gervasi, O., Misra, S., Nedjah, N., Rocha, A.M.A.C., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2012, Part IV. LNCS, vol. 7336, pp. 170–185. Springer, Heidelberg (2012)Decker, H.: A pragmatic approach to model, measure and maintain the quality of information in databases (2012). www.iti.upv.es/~hendrik/papers/ahrc-workshop_quality-of-data.pdf , www.iti.upv.es/~hendrik/papers/ahrc-workshop_quality-of-data_comments.pdf . Slides and comments presented at the Workshop on Information Quality. Univ, Hertfordshire, UKDecker, H.: Answers that have quality. In: Murgante, B., Misra, S., Carlini, M., Torre, C.M., Nguyen, H.-Q., Taniar, D., Apduhan, B.O., Gervasi, O. (eds.) ICCSA 2013, Part II. LNCS, vol. 7972, pp. 543–558. Springer, Heidelberg (2013)Decker, H.: Measure-based inconsistency-tolerant maintenance of database integrity. In: Schewe, K.-D., Thalheim, B. (eds.) SDKB 2013. LNCS, vol. 7693, pp. 149–173. Springer, Heidelberg (2013)Decker, H., Martinenghi, D.: Inconsistency-tolerant integrity checking. IEEE Transactions of Knowledge and Data Engineering 23(2), 218–234 (2011)Decker, H., Muñoz-Escoí, F.D.: Revisiting and improving a result on integrity preservation by concurrent transactions. In: Meersman, R., Dillon, T., Herrero, P. (eds.) OTM 2010. LNCS, vol. 6428, pp. 297–306. Springer, Heidelberg (2010)Dong, X.L., Berti-Equille, L., Srivastava, D.: Data fusion: resolving conflicts from multiple sources (2015). http://arxiv.org/abs/1503.00310Eswaran, K., Gray, J., Lorie, R., Traiger, I.: The notions of consistency and predicate locks in a database system. CACM 19(11), 624–633 (1976)Muñoz-Escoí, F.D., Ruiz-Fuertes, M.I., Decker, H., Armendáriz-Íñigo, J.E., de Mendívil, J.R.G.: Extending middleware protocols for database replication with integrity support. In: Meersman, R., Tari, Z. (eds.) OTM 2008, Part I. LNCS, vol. 5331, pp. 607–624. Springer, Heidelberg (2008)Fekete, A.: Consistency models for replicated data. In: Encyclopedia of Database Systems, pp. 450–451. Springer (2009)Fekete, A., Gupta, D., Lynch, V., Luchangco, N., Shvartsman, A.: Eventually-serializable data services. In: 15th PoDC, pp. 300–309. ACM (1996)Gilbert, S., Lynch, N.: Brewer’s conjecture and the feasibility of consistent, available, partition-tolerant web services. SIGACT News 33(2), 51–59 (2002)Golab, W., Rahman, M., Auyoung, A., Keeton, K., Li, X.: Eventually consistent: Not what you were expecting? ACM Queue, 12(1) (2014)Grant, J., Hunter, A.: Measuring inconsistency in knowledgebases. Journal of Intelligent Information Systems 27(2), 159–184 (2006)Gray, J., Lorie, R., Putzolu, G., Traiger, I.: Granularity of locks and degrees of consistency in a shared data base. In: Nijssen, G. (ed.) Modelling in Data Base Management Systems. North Holland (1976)Haerder, T., Reuter, A.: Principles of transaction-oriented database recovery. Computing Surveys 15(4), 287–317 (1983)Herlihy, M., Wing, J.: Linearizability: a correctness condition for concurrent objects. TOPLAS 12(3), 463–492 (1990)R. Ho. Design pattern for eventual consistency (2009). http://horicky.blogspot.com.es/2009/01/design-pattern-for-eventual-consistency.htmlIkeda, R., Park, H., Widom, J.: Provenance for generalized map and reduce workflows. In: CIDR (2011)Kempster, T., Stirling, C., Thanisch, P.: Diluting acid. SIGMoD Record 28(4), 17–23 (1999)Li, X., Dong, X.L., Meng, W., Srivastava, D.: Truth finding on the deep web: Is the problem solved? VLDB Endowment 6(2), 97–108 (2012)Lloyd, W., Freedman, M., Kaminsky, M., Andersen, D.: Don’t settle for eventual: scalable causal consistency for wide-area storage with cops. In: 23rd SOPS, pp. 401–416 (2011)Lomet, D.: Transactions: from local atomicity to atomicity in the cloud. In: Jones, C.B., Lloyd, J.L. (eds.) Dependable and Historic Computing. LNCS, vol. 6875, pp. 38–52. Springer, Heidelberg (2011)Monge, P., Contractor, N.: Theory of Communication Networks. Oxford University Press (2003)Nicolas, J.-M.: Logic for improving integrity checking in relational data bases. Acta Informatica 18, 227–253 (1982)Muñoz-Escoí, F.D., Irún, L., H. Decker: Database replication protocols. In: Encyclopedia of Database Technologies and Applications, pp. 153–157. IGI Global (2005)Oracle: Constraints. http://docs.oracle.com/cd/B19306_01/server.102/b14223/constra.htm (May 1, 2015)Ouzzani, M., Medjahed, B., Elmagarmid, A.: Correctness criteria beyond serializability. In: Encyclopedia of Database Systems, pp. 501–506. Springer (2009)Rosenkrantz, D., Stearns, R., Lewis, P.: Consistency and serializability in concurrent datanbase systems. SIAM J. Comput. 13(3), 508–530 (1984)Saito, Y., Shapiro, M.: Optimistic replication. JACM 37(1), 42–81 (2005)Sandhu, R.: On five definitions of data integrity. In: Proc. IFIP WG11.3 Workshop on Database Security, pp. 257–267. North-Holland (1994)Simmons, G.: Contemporary Cryptology: The Science of Information Integrity. IEEE Press (1992)Sivathanu, G., Wright, C., Zadok, E.: Ensuring data integrity in storage: techniques and applications. In: Proc. 12th Conf. on Computer and Communications Security, p. 26. ACM (2005)Svanks, M.: Integrity analysis: Methods for automating data quality assurance. Information and Software Technology 30(10), 595–605 (1988)Technet, M.: Data integrity. https://technet.microsoft.com/en-us/library/aa933058 (May 1, 2015)Terry, D.: Replicated data consistency explained through baseball. Technical report, Microsoft. MSR Technical Report (2011)Traiger, I., Gray, J., Galtieri, C., Lindsay, B.: Transactions and consistency in distributed database systems. ACM Trans. Database Syst. 7(3), 323–342 (1982)Vidyasankar, K.: Serializability. In: Encyclopedia of Database Systems, pp. 2626–2632. Springer (2009)Vogels, W.: Eventually consistent (2007). http://www.allthingsdistributed.com/2007/12/eventually_consistent.html . Other versions in ACM Queue 6(6), 14–19. http://queue.acm.org/detail.cfm?id=1466448 (2008) and CACM 52(1), 40–44 (2009)Wikipedia: Consistency model. http://en.wikipedia.org/wiki/Consistency_model (May 1, 2015)Wikipedia: Data integrity. http://en.wikipedia.org/wiki/Data_integrity (May 1, 2015)Wikipedia: Data quality. http://en.wikipedia.org/wiki/Data_quality (May 1, 2015)Yin, X., Han, J., Yu, P.: Truth discovery with multiple conflicting information providers on the web. IEEE Transactions of Knowledge and Data Engineering 20(6), 796–808 (2008)Young, G.: Quick thoughts on eventual consistency (2010). http://codebetter.com/gregyoung/2010/04/14/quick-thoughts-on-eventual-consistency/ (May 1, 2015