Improving the Upper Bound on the Length of the Shortest Reset Word

We improve the best known upper bound on the length of the shortest reset words of synchronizing automata. The new bound is slightly better than 114 n^3 / 685 + O(n^2). The Cerny conjecture states that (n-1)^2 is an upper bound. So far, the best general upper bound was (n^3-n)/6-1 obtained by J.-E. Pin and P. Frankl in 1982. Despite a number of efforts, it remained unchanged for about 35 years. To obtain the new upper bound we utilize avoiding words. A word is avoiding for a state q if after reading the word the automaton cannot be in q. We obtain upper bounds on the length of the shortest avoiding words, and using the approach of Trahtman from 2011 combined with the well-known Frankl theorem from 1982, we improve the general upper bound on the length of the shortest reset words. For all the bounds, there exist polynomial algorithms finding a word of length not exceeding the bound

Complexity of Preimage Problems for Deterministic Finite Automata

Given a subset of states S of a deterministic finite automaton and a word w, the preimage is the subset of all states that are mapped to a state from S by the action of w. We study the computational complexity of three problems related to the existence of words yielding certain preimages, which are especially motivated by the theory of synchronizing automata. The first problem is whether, for a given subset, there exists a word extending the subset (giving a larger preimage). The second problem is whether there exists a word totally extending the subset (giving the whole set of states) - it is equivalent to the problem whether there exists an avoiding word for the complementary subset. The third problem is whether there exists a word resizing the subset (giving a preimage of a different size). We also consider the variants of the problem where an upper bound on the length of the word is given in the input. Because in most cases our problems are computationally hard, we additionally consider parametrized complexity by the size of the given subset. We focus on the most interesting cases that are the subclasses of strongly connected, synchronizing, and binary automata

Attainable Values of Reset Thresholds

An automaton is synchronizing if there exists a word that sends all states of the automaton to a single state. The reset threshold is the length of the shortest such word. We study the set RT_n of attainable reset thresholds by automata with n states. Relying on constructions of digraphs with known local exponents we show that the intervals [1, (n^2-3n+4)/2] and [(p-1)(q-1), p(q-2)+n-q+1], where 2 n, gcd(p,q)=1, belong to RT_n, even if restrict our attention to strongly connected automata. Moreover, we prove that in this case the smallest value that does not belong to RT_n is at least n^2 - O(n^{1.7625} log n / log log n). This value is increased further assuming certain conjectures about the gaps between consecutive prime numbers. We also show that any value smaller than n(n-1)/2 is attainable by an automaton with a sink state and any value smaller than n^2-O(n^{1.5}) is attainable in general case. Furthermore, we solve the problem of existence of slowly synchronizing automata over an arbitrarily large alphabet, by presenting for every fixed size of the alphabet an infinite series of irreducibly synchronizing automata with the reset threshold n^2-O(n)

Combined hydrophilic interaction liquid chromatography-scanning field asymmetric waveform ion mobility spectrometry-time-of-flight mass spectrometry for untargeted metabolomics

Untargeted metabolite profiling of biological samples is a challenge for analytical science due to the high degree of complexity of biofluids. Isobaric species may also not be resolved using mass spectrometry alone. As a result of these factors, many potential biomarkers may not be detected or are masked by co-eluting interferences in conventional LC-MS metabolomic analyses. In this study, a comprehensive liquid chromatography-mass spectrometry workflow incorporating a fast-scanning miniaturised high-field asymmetric waveform ion mobility spectrometry separation (LC-FAIMS-MS) is applied to the untargeted metabolomic analysis of human urine. The time-of-flight mass spectrometer used in the study was scanned at a rate of 20 scans s−1 enabling a FAIMS CF spectrum to be acquired within a 1-s scan time, maintaining an adequate number of data points across each LC peak. The developed method is demonstrated to be able to resolve co-eluting isomeric species and shows good reproducibility (%RSD < 4.9%). The nested datasets obtained for fresh, aged, and QC urine samples were submitted for multivariate statistical analysis. Seventy unique biomarker ions showing a statistically significant difference between fresh and aged urine were identified with optimal transmission CF values obtained across the full CF spectrum. The potential of using FAIMS to select ions for in-source collision-induced dissociation is demonstrated for FAIMS-selected methylxanthine ions yielding characteristic fragment ion species indicative of the precursor

Characterization of crude oil and its saturate, aromatic and resin fractions by high-field asymmetric waveform ion mobility spectrometry – high resolution mass spectrometry

High-field asymmetric waveform ion mobility spectrometry (FAIMS) was coupled to a high-resolution Orbitrap mass spectrometer (MS) with a heated electrospray ionization (HESI) source for the analysis of crude oil and respective saturate, aromatic, and resin fractions. Four classes of compounds N1, N1S1, O1S1, and O2S1 were investigated using FAIMS one-dimensional compensation field scans from −3 to 5 Td for the crude oil and FAIMS static scans from 0.5 to 2.5 Td with 0.5 Td increments for fractions. In all cases, the incorporation of FAIMS into the analysis resulted in an increased number of detected peaks for both the crude oil and fractions. The most significant change was noticed in the aromatic fraction, with an increase of 218% for N1 and up to 514% for the O2S1 class of compounds observed. In addition, pre-analytical fractionation combined with FAIMS–MS enabled a higher number of molecular features to be observed in comparison to whole oil for three classes of compounds N1, O1S1, and O2S1 by 19, 45, and 83%, respectively

Using the Mystery Motivator to Improve Child Bedtime Compliance

Child bedtime problems are commonly reported by parents. A number of behavioral techniques, including extinction of tantrum behaviors, reinforcement of compliant bedtime, and implementation of consistent bedtime routines have been successful in improving bedtime compliance. The present study examined the effects of the Mystery Motivator (MM), a behavioral contract designed to remediate bedtime problems by delivering random reinforcement. Emphasis was placed on the optimal use of clinical intervention by enlisting parents as primary change agents in the home setting. Three adults and their four children, aged 3-5 years, participated. Three of the four children showed substantial changes in both time out of bed and bedtime noncompliance between baseline and treatment phases. A fourth child showed less improvement. Parent participants demonstrated understanding of the materials and successfully implemented the home program. Both parent and child participants rated the Mystery Motivator reinforcement system as an acceptable intervention

The effectiveness, acceptability and cost-effectiveness of psychosocial interventions for maltreated children and adolescents: an evidence synthesis.

BACKGROUND: Child maltreatment is a substantial social problem that affects large numbers of children and young people in the UK, resulting in a range of significant short- and long-term psychosocial problems. OBJECTIVES: To synthesise evidence of the effectiveness, cost-effectiveness and acceptability of interventions addressing the adverse consequences of child maltreatment. STUDY DESIGN: For effectiveness, we included any controlled study. Other study designs were considered for economic decision modelling. For acceptability, we included any study that asked participants for their views. PARTICIPANTS: Children and young people up to 24 years 11 months, who had experienced maltreatment before the age of 17 years 11 months. INTERVENTIONS: Any psychosocial intervention provided in any setting aiming to address the consequences of maltreatment. MAIN OUTCOME MEASURES: Psychological distress [particularly post-traumatic stress disorder (PTSD), depression and anxiety, and self-harm], behaviour, social functioning, quality of life and acceptability. METHODS: Young Persons and Professional Advisory Groups guided the project, which was conducted in accordance with Cochrane Collaboration and NHS Centre for Reviews and Dissemination guidance. Departures from the published protocol were recorded and explained. Meta-analyses and cost-effectiveness analyses of available data were undertaken where possible. RESULTS: We identified 198 effectiveness studies (including 62 randomised trials); six economic evaluations (five using trial data and one decision-analytic model); and 73 studies investigating treatment acceptability. Pooled data on cognitive-behavioural therapy (CBT) for sexual abuse suggested post-treatment reductions in PTSD [standardised mean difference (SMD) -0.44 (95% CI -4.43 to -1.53)], depression [mean difference -2.83 (95% CI -4.53 to -1.13)] and anxiety [SMD -0.23 (95% CI -0.03 to -0.42)]. No differences were observed for post-treatment sexualised behaviour, externalising behaviour, behaviour management skills of parents, or parental support to the child. Findings from attachment-focused interventions suggested improvements in secure attachment [odds ratio 0.14 (95% CI 0.03 to 0.70)] and reductions in disorganised behaviour [SMD 0.23 (95% CI 0.13 to 0.42)], but no differences in avoidant attachment or externalising behaviour. Few studies addressed the role of caregivers, or the impact of the therapist-child relationship. Economic evaluations suffered methodological limitations and provided conflicting results. As a result, decision-analytic modelling was not possible, but cost-effectiveness analysis using effectiveness data from meta-analyses was undertaken for the most promising intervention: CBT for sexual abuse. Analyses of the cost-effectiveness of CBT were limited by the lack of cost data beyond the cost of CBT itself. CONCLUSIONS: It is not possible to draw firm conclusions about which interventions are effective for children with different maltreatment profiles, which are of no benefit or are harmful, and which factors encourage people to seek therapy, accept the offer of therapy and actively engage with therapy. Little is known about the cost-effectiveness of alternative interventions. LIMITATIONS: Studies were largely conducted outside the UK. The heterogeneity of outcomes and measures seriously impacted on the ability to conduct meta-analyses. FUTURE WORK: Studies are needed that assess the effectiveness of interventions within a UK context, which address the wider effects of maltreatment, as well as specific clinical outcomes. STUDY REGISTRATION: This study is registered as PROSPERO CRD42013003889. FUNDING: The National Institute for Health Research Health Technology Assessment programme

Finding Short Synchronizing Words for Prefix Codes

We study the problems of finding a shortest synchronizing word and its length for a given prefix code. This is done in two different settings: when the code is defined by an arbitrary decoder recognizing its star and when the code is defined by its literal decoder (whose size is polynomially equivalent to the total length of all words in the code). For the first case for every epsilon > 0 we prove n^(1 - epsilon)-inapproximability for recognizable binary maximal prefix codes, Theta(log n)-inapproximability for finite binary maximal prefix codes and n^(1/2 - epsilon)-inapproximability for finite binary prefix codes. By c-inapproximability here we mean the non-existence of a c-approximation polynomial time algorithm under the assumption P != NP, and by n the number of states of the decoder in the input. For the second case, we propose approximation and exact algorithms and conjecture that for finite maximal prefix codes the problem can be solved in polynomial time. We also study the related problems of finding a shortest mortal and a shortest avoiding word