On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection

Extended regular expressions (with complement and intersection) are used in many applications due to their succinctness. In particular, regular expressions extended with intersection only (also called semi-extended) can already be exponentially smaller than standard regular expressions or equivalent nondeterministic finite automata (NFA). For practical purposes it is important to study the average behaviour of conversions between these models. In this paper, we focus on the conversion of regular expressions with intersection to nondeterministic finite automata, using partial derivatives and the notion of support. First, we give a tight upper bound of 2O(n) for the worst-case number of states of the resulting partial derivative automaton, where n is the size of the expression. Using the framework of analytic combinatorics, we then establish an upper bound of (1.056 + o(1))n for its asymptotic average-state complexity, which is significantly smaller than the one for the worst case. (c) IFIP International Federation for Information Processing 2016

Optimization of ATM filling-in with cash

This report presents an approach for modeling daily cash demand for all ATMs in the Credit Agricole Bank network in Serbia. The approach is based on time series and regression methods for forecasting an optimal amount of money that should be placed daily in the ATMs in order to meet customers’ demands and mimimize costs of the bank. Three different types of costs were considered: cash freezing costs, transportation costs and insurance costs. The performance of the resulting forecasts were compared with results of the application that bank uses for prediciton of the time and the amount of filling-in for each ATM based on historical data

Whole Genome Sequence Analysis of a Large Isoniazid-Resistant Tuberculosis Outbreak in London: A Retrospective Observational Study

BACKGROUND: A large isoniazid-resistant tuberculosis outbreak centred on London, United Kingdom, has been ongoing since 1995. The aim of this study was to investigate the power and value of whole genome sequencing (WGS) to resolve the transmission network compared to current molecular strain typing approaches, including analysis of intra-host diversity within a specimen, across body sites, and over time, with identification of genetic factors underlying the epidemiological success of this cluster. METHODS AND FINDINGS: We sequenced 344 outbreak isolates from individual patients collected over 14 y (2 February 1998-22 June 2012). This demonstrated that 96 (27.9%) were indistinguishable, and only one differed from this major clone by more than five single nucleotide polymorphisms (SNPs). The maximum number of SNPs between any pair of isolates was nine SNPs, and the modal distance between isolates was two SNPs. WGS was able to reveal the direction of transmission of tuberculosis in 16 cases within the outbreak (4.7%), including within a multidrug-resistant cluster that carried a rare rpoB mutation associated with rifampicin resistance. Eleven longitudinal pairs of patient pulmonary isolates collected up to 48 mo apart differed from each other by between zero and four SNPs. Extrapulmonary dissemination resulted in acquisition of a SNP in two of five cases. WGS analysis of 27 individual colonies cultured from a single patient specimen revealed ten loci differed amongst them, with a maximum distance between any pair of six SNPs. A limitation of this study, as in previous studies, is that indels and SNPs in repetitive regions were not assessed due to the difficulty in reliably determining this variation. CONCLUSIONS: Our study suggests that (1) certain paradigms need to be revised, such as the 12 SNP distance as the gold standard upper threshold to identify plausible transmissions; (2) WGS technology is helpful to rule out the possibility of direct transmission when isolates are separated by a substantial number of SNPs; (3) the concept of a transmission chain or network may not be useful in institutional or household settings; (4) the practice of isolating single colonies prior to sequencing is likely to lead to an overestimation of the number of SNPs between cases resulting from direct transmission; and (5) despite appreciable genomic diversity within a host, transmission of tuberculosis rarely results in minority variants becoming dominant. Thus, whilst WGS provided some increased resolution over variable number tandem repeat (VNTR)-based clustering, it was insufficient for inferring transmission in the majority of cases

Cross-shell excitation in two-proton knockout: Structure of 52^{52}Ca

The two-proton knockout reaction $^9$Be($^{54}$Ti,$^{52}$Ca$+ \gamma$) has been studied at 72 MeV/nucleon. Besides the strong feeding of the $^{52}$Ca ground state, the only other sizeable cross section proceeds to a 3$^-$ level at 3.9 MeV. There is no measurable direct yield to the first excited 2$^+$ state at 2.6 MeV. The results illustrate the potential of such direct reactions for exploring cross-shell proton excitations in neutron-rich nuclei and confirms the doubly-magic nature of $^{52}$Ca

Nature of yrast excitations near N=40: Level structure of Ni-67

Excited states in Ni-67 were populated in deep-inelastic reactions of a Ni-64 beam at 430 MeV on a thick U-238 target. A level scheme built on the previously known 13 micro-s isomer has been delineated up to an excitation energy of ~5.3 MeV and a tentative spin and parity of (21/2-). Shell model calculations have been carried out using two effective interactions in the f5/2pg9/2 model space with a Ni-56 core. Satisfactory agreement between experiment and theory is achieved for the measured transition energies and branching ratios. The calculations indicate that the yrast states are associated with rather complex configurations, herewith demonstrating the relative weakness of the N=40 subshell gap and the importance of multi particle-hole excitations involving the g9/2 neutron orbital.Comment: Accepted by Physical Review

Effective interactions and shell model studies of heavy tin isotopes

We calculate the low-lying spectra of heavy tin isotopes from A=120 to A=130 using the 2s1d0g_{7/2}0h_{11/2} shell to define the model space. An effective interaction has been derived using 132Sn as closed core employing perturbative many-body techniques. We start from a nucleon-nucleon potential derived from modern meson exchange models. This potential is in turn renormalized for the given medium, 132Sn, yielding the nuclear reaction matrix, which is then used in perturbation theory to obtain the shell model effective interaction.Comment: 19 pages, Elsevier latex style espart.sty, submitted to Nuclear Physics

Deciding synchronous Kleene algebra with derivatives

Synchronous Kleene algebra (SKA) is a decidable framework that combines Kleene algebra (KA) with a synchrony model of concurrency. Elements of SKA can be seen as processes taking place within a fixed discrete time frame and that, at each time step, may execute one or more basic actions or then come to a halt. The synchronous Kleene algebra with tests (SKAT) combines SKA with a Boolean algebra. Both algebras were introduced by Prisacariu, who proved the decidability of the equational theory, through a Kleene theorem based on the classical Thompson -NFA construction. Using the notion of partial derivatives, we present a new decision procedure for equivalence between SKA terms. The results are extended for SKAT considering automata with transitions labeled by Boolean expressions instead of atoms. This work continous previous research done for KA and KAT, where derivative based methods were used in feasible algorithms for testing terms equivalence. (c) Springer International Publishing Switzerland 2015

Optimization of the MALDIxin test for the rapid identification of colistin resistance in Klebsiella pneumoniae using MALDI-TOF-MS

Background. With the dissemination of carbapenemase producers, a revival of colistin was observed for the treatment of infections caused by multidrug-resistant Gram-negatives. Unfortunately, the increasing usage of colistin led to the emergence of resistance. In Klebsiella pneumoniae, colistin resistance arises through addition of L-arabinose-4N (L-Ara4N) or phosphoethanolamine (pEtN) on the native lipid A. The underlying mechanisms involve numerous chromosome-encoded genes or the plasmid-encoded phosphoethanolamine transferase MCR. Currently, detection of colistin resistance is time consuming since it still relies on MIC determination by broth microdilution. Recently, a rapid diagnostic test based on MALDI-TOF detection of modified lipid A was developed (the MALDIxin test) and tested on Escherichia coli and Acinetobacter baumannii. Objectives. Optimize the MALDIxin test for the rapid detection of colistin resistance in Klebsiella pneumoniae. Methods. This optimization consists on an additional mild-acid hydrolysis of 15 min in 1% acetic acid. The optimized method was tested on a collection of 81 clinical K. pneumoniae isolates including 49 colistin resistant strains among which 45 correspond to chromosome-encoded resistance, 3 MCR-related resistance and one isolate harbouring both mechanisms. Results. The optimized method allowed the rapid (< 30 min) identification of L-Ara4N and pEtN modified lipid A of K. pneumoniae which are known to be the real triggers of polymyxin resistance. In the same time, it discriminates between chromosome-encoded and MCR-related polymyxin resistance. Conclusions. The MALDIxin test has the potential to become an accurate tool for the rapid diagnostic of colistin resistance in clinically-relevant Gram negative bacteria

Completeness and Incompleteness of Synchronous Kleene Algebra

Synchronous Kleene algebra (SKA), an extension of Kleene algebra (KA), was proposed by Prisacariu as a tool for reasoning about programs that may execute synchronously, i.e., in lock-step. We provide a countermodel witnessing that the axioms of SKA are incomplete w.r.t. its language semantics, by exploiting a lack of interaction between the synchronous product operator and the Kleene star. We then propose an alternative set of axioms for SKA, based on Salomaa's axiomatisation of regular languages, and show that these provide a sound and complete characterisation w.r.t. the original language semantics.Comment: Accepted at MPC 201