DFAs and PFAs with Long Shortest Synchronizing Word Length

It was conjectured by \v{C}ern\'y in 1964, that a synchronizing DFA on $n$ states always has a shortest synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all DFAs reaching this bound was only given for $n \leq 4$, and with bounds on the number of symbols for $n \leq 10$. Here we give the full analysis for $n \leq 6$, without bounds on the number of symbols. For PFAs the bound is much higher. For $n \leq 6$ we do a similar analysis as for DFAs and find the maximal shortest synchronizing word lengths, exceeding $(n-1)^2$ for $n =4,5,6$. For arbitrary n we give a construction of a PFA on three symbols with exponential shortest synchronizing word length, giving significantly better bounds than earlier exponential constructions. We give a transformation of this PFA to a PFA on two symbols keeping exponential shortest synchronizing word length, yielding a better bound than applying a similar known transformation.Comment: 16 pages, 2 figures source code adde

Most Complex Non-Returning Regular Languages

A regular language $L$ is non-returning if in the minimal deterministic finite automaton accepting it there are no transitions into the initial state. Eom, Han and Jir\'askov\'a derived upper bounds on the state complexity of boolean operations and Kleene star, and proved that these bounds are tight using two different binary witnesses. They derived upper bounds for concatenation and reversal using three different ternary witnesses. These five witnesses use a total of six different transformations. We show that for each $n\ge 4$ there exists a ternary witness of state complexity $n$ that meets the bound for reversal and that at least three letters are needed to meet this bound. Moreover, the restrictions of this witness to binary alphabets meet the bounds for product, star, and boolean operations. We also derive tight upper bounds on the state complexity of binary operations that take arguments with different alphabets. We prove that the maximal syntactic semigroup of a non-returning language has $(n-1)^n$ elements and requires at least $\binom{n}{2}$ generators. We find the maximal state complexities of atoms of non-returning languages. Finally, we show that there exists a most complex non-returning language that meets the bounds for all these complexity measures.Comment: 22 pages, 6 figure

Commutative positive varieties of languages

We study the commutative positive varieties of languages closed under various operations: Shuffle, renaming and product over one-letter alphabets

Vectorial Languages and Linear Temporal Logic

International audienceDetermining for a given deterministic complete automaton the sequence of visited states while reading a given word is the core of important problems with automata-based solutions, such as approximate string matching. The main difficulty is to do this computation efficiently, especially when dealing with very large texts. Considering words as vectors and working on them using vectorial (parallel) operations allows to solve the problem faster than in linear time using sequential computations. In this paper, we show first that the set of vectorial operations needed by an algorithm representing a given automaton depends only on the language accepted by the automaton. We give precise characterizations of vectorial algorithms for star-free, solvable and regular languages in terms of the vectorial operations allowed. We also consider classes of languages associated with restricted sets of vectorial operations and relate them with languages defined by fragments of linear temporal logic. Finally, we consider the converse problem of constructing an automaton from a given vectorial algorithm. As a byproduct, we show that the satisfiability problem for some extensions of linear-time temporal logic characterizing solvable and regular languages is PSPACE-complete

Composition and screening of antifungal activity against Cladosporium sphaerospermum and Cladosporium cladosporioides of essential oils of leaves and fruits of Piper species

This study investigated the composition and antifungal activity against Cladosporium sphaerospermum and Cladosporium cladosporioides of essential oils of leaves of Piper cernuum, Piper diospyrifolium, Piper crassinervium, Piper solmsianum and Piper umbelata and fruits of P. cernuum and P. diospyrifolium. The essentials oils were analyzed by GC-MS and submitted of the antifungal activity tests. The essential oils of fruits from P. cernuum and leaves of P. crassinervium and P. solmsianum showed potential antifungal activity against C. sphaerospermum and C. cladosporioides. In addition, this is the first report of the composition of essential oils of fruits of P. cernuum and P. diospyrifolium.Key words: Piperaceae, Piper; essential oil composition, antifungal activity, GC-MS

Nutritional and ameliorative effects of dietary curcumin and its nano-silica and nano-zeolite encapsulated forms on growth, biochemical and fatty acid profile of common carp (Cyprinus carpio)

The present study aimed to examine individual nutritional and ameliorative effects of silica nanoparticles (SiO(2)NPs) and natural zeolite nanoparticles (ZeNPs) and their potential role as carriers to alter the bioavailability of curcumin. Common carps (Cyprinus carpio) were fed during 60 days with a control diet, and curcumin, turmeric, SiO(2)NPs, curcumin-loaded SiO(2)NPs, ZeNPs, and curcumin-loaded ZeNPs each at 1, 50, 6.15, 7.15, 39, and 40 g/kg diet, respectively. The highest weight gain (WG) and specific growth rate (SGR) were observed in fish fed with turmeric (P < 0.05). Moreover, dietary curcumin and ZeNPs increased the content of monounsaturated fatty acids (P < 0.05). After exposure to silver nanoparticles (AgNPs), the lowest amount of aspartate aminotransferase (AST) was obtained in fish fed with curcumin (P < 0.05). In addition, alanine aminotransferase (ALT) decreased significantly in the negative control, curcumin, and curcumin-loaded SiO(2)NPs treatments in comparison to the positive control group (P < 0.05). The lowest silver accumulation was observed in the negative control and SiO(2)NPs groups (P < 0.05). This experiment demonstrated that while the nanoencapsulation of curcumin on SiO(2)NPs and ZeNPs did not enhanced the impact of curcumin on the growth and biochemical factors of carps, it can still be considered a potential dietary supplement for enhancing growth and antioxidant indices when added individually to the diet.GRC97-06503-1info:eu-repo/semantics/publishedVersio

Complexity of Left-Ideal, Suffix-Closed and Suffix-Free Regular Languages

A language $L$ over an alphabet $\Sigma$ is suffix-convex if, for any words $x,y,z\in\Sigma^*$, whenever $z$ and $xyz$ are in $L$, then so is $yz$. Suffix-convex languages include three special cases: left-ideal, suffix-closed, and suffix-free languages. We examine complexity properties of these three special classes of suffix-convex regular languages. In particular, we study the quotient/state complexity of boolean operations, product (concatenation), star, and reversal on these languages, as well as the size of their syntactic semigroups, and the quotient complexity of their atoms.Comment: 20 pages, 11 figures, 1 table. arXiv admin note: text overlap with arXiv:1605.0669

Nanofluidic Refractive-Index Sensors Formed by Nanocavity Resonators in Metals without Plasmons

Nanocavity resonators in metals acting as nanofluidic refractive-index sensors were analyzed theoretically. With the illumination of transverse electric polarized light, the proposed refractive index sensor structure acts as a pure electromagnetic resonator without the excitation of surface plasmons. The reflected signal from the nanocavity resonators can be very sensitive to the refractive index of the fluids inside the nanocavities due to the enhancement of the electric field of the resonant mode inside the cavities. Such a sensor configuration can be a useful tool for probing the refractive index change of the fluid inside the nanocavities using the spectral, angular or intensity interrogation schemes. The wavelength sensitivity of 430 nm/RIU, angular sensitivity of 200–1,000 deg/RIU and intensity sensitivity of 25.5 RIU−1 can be achieved in the proposed sensor configuration

Algebraic synchronization criterion and computing reset words

We refine a uniform algebraic approach for deriving upper bounds on reset thresholds of synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain upper bounds for the reset thresholds of automata with a short word of a small rank. The results are applied to make several improvements in the area. We improve the best general upper bound for reset thresholds of finite prefix codes (Huffman codes): we show that an $n$-state synchronizing decoder has a reset word of length at most $O(n \log^3 n)$. In addition to that, we prove that the expected reset threshold of a uniformly random synchronizing binary $n$-state decoder is at most $O(n \log n)$. We also show that for any non-unary alphabet there exist decoders whose reset threshold is in $\varTheta(n)$. We prove the \v{C}ern\'{y} conjecture for $n$-state automata with a letter of rank at most $\sqrt[3]{6n-6}$. In another corollary, based on the recent results of Nicaud, we show that the probability that the \v{C}ern\'y conjecture does not hold for a random synchronizing binary automaton is exponentially small in terms of the number of states, and also that the expected value of the reset threshold of an $n$-state random synchronizing binary automaton is at most $n^{3/2+o(1)}$. Moreover, reset words of lengths within all of our bounds are computable in polynomial time. We present suitable algorithms for this task for various classes of automata, such as (quasi-)one-cluster and (quasi-)Eulerian automata, for which our results can be applied.Comment: 18 pages, 2 figure

Replication of Association between ADAM33 Polymorphisms and Psoriasis

Polymorphisms in ADAM33, the first gene identified in asthma by positional cloning, have been recently associated with psoriasis. No replication study of this association has been published so far. Data available in the French EGEA study (Epidemiological study on Genetics and Environment of Asthma, bronchial hyperresponsivensess and Atopy) give the opportunity to attempt to replicate the association between ADAM33 and psoriasis in 2002 individuals. Psoriasis (n = 150) has been assessed by questionnaire administered by an interviewer and a sub-sample of subjects with early-onset psoriasis (n = 74) has been identified based on the age of the subjects at time of interview (<40 years). Nine SNPs in ADAM33 and 11 SNPs in PSORS1 were genotyped. Association analysis was conducted by using two methods, GEE regression-based method and a likelihood-based method (LAMP program). The rs512625 SNP in ADAM33 was found associated with psoriasis at p = 0.01, the usual threshold required for replication (OR [95% CI] for heterozygotes compared to the reference group of homozygotes for the most frequent allele = 0.61 [0.42;0.89]). The rs628977 SNP, which was not in linkage disequilibrium with rs512625, was significantly associated with early-onset psoriasis (p = 0.01, OR [95% CI] for homozygotes for the minor allele compared to the reference group = 2.52 [1.31;4.86]). Adjustment for age, sex, asthma and a PSORS1 SNP associated with psoriasis in the EGEA data did not change the significance of these associations. This suggests independent effects of ADAM33 and PSORS1 on psoriasis. This is the first study that replicates an association between genetic variants in ADAM33 and psoriasis. Interestingly, the 2 ADAM33 SNPs associated with psoriasis in the present analysis were part of the 3-SNPs haplotypes showing the strongest associations in the initial study. The identification of a pleiotropic effect of ADAM33 on asthma and psoriasis may contribute to the understanding of these common immune-mediated diseases