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

Stillbirth should be given greater priority on the global health agenda

Stillbirths are largely excluded from international measures of mortality and morbidity. Zeshan Qureshi and colleagues argue that stillbirth should be higher on the global health agenda

QCD axion and quintessential axion

The axion solution of the strong CP problem is reviewed together with the other strong CP solutions. We also point out the quintessential axion(quintaxion) whose potential can be extremely flat due to the tiny ratio of the hidden sector quark mass and the intermediate hidden sector scale. The quintaxion candidates are supposed to be the string theory axions, the model independent or the model dependent axions.Comment: 15 pages. Talk presented at Castle Ringberg, June 9-14, 200

Computational Complexity of Synchronization under Regular Commutative Constraints

Here we study the computational complexity of the constrained synchronization problem for the class of regular commutative constraint languages. Utilizing a vector representation of regular commutative constraint languages, we give a full classification of the computational complexity of the constraint synchronization problem. Depending on the constraint language, our problem becomes PSPACE-complete, NP-complete or polynomial time solvable. In addition, we derive a polynomial time decision procedure for the complexity of the constraint synchronization problem, given some constraint automaton accepting a commutative language as input.Comment: Published in COCOON 2020 (The 26th International Computing and Combinatorics Conference); 2nd version is update of the published version and 1st version; both contain a minor error, the assumption of maximality in the NP-c and PSPACE-c results (propositions 5 & 6) is missing, and of incomparability of the vectors in main theorem; fixed in this version. See (new) discussion after main theore

Excited exciton and biexciton localised states in a single quantum ring

We observe excited exciton and biexciton states of localised excitons in an anisotropic quantum ring, where large polarisation asymmetry supports the presence of a crescent-like localised structure. We also find that saturation of the localised ground state exciton with increasing excitation can be attributed to relatively fast dissociation of biexcitons (? 430 ps) compared to slow relaxation from the excited state to the ground state (? 1000 ps). As no significant excitonic Aharonov-Bohm oscillations occur up to 14 T, we conclude that phase coherence around the rim is inhibited as a consequence of height anisotropy in the quantum ring.Comment: 4 pages, 4 figure

Comparison of high and low trans-fatty acid consumers: analyses of UK National Diet and Nutrition Surveys before and after product reformulation

Objective: The WHO encourages the virtual elimination of artificial trans-fatty acids (TFA), which increase CHD risk. Our UK analysis explores whether voluntary reformulation results in differential TFA intakes among socio-economic groups by determining characteristics of high TFA consumers before and after product reformulation. Design: Food intake was collected by 7d weighed records pre-reformulation and 4d diaries post-reformulation. Sociodemographic characteristics of TFA consumers above the WHO limit, and of the top 10 % of TFA consumers as a percentage food energy, were compared with those of lower TFA consumers. Multivariate logistic regression determined independent socio-economic predictors of being a top 10 % consumer. Subjects: UK National Diet and Nutrition Surveys (NDNS) for adults aged 19–64 years pre-reformulation (2000/01; N 1724) and post-reformulation (2010/11–2011/12; N 848). Results: Post-reformulation 2·5 % of adults exceeded the WHO limit, v. 57 % pre-reformulation. In unadjusted analyses, high TFA consumption was associated with lower income, lower education and long-term illness/disability pre- but not post-reformulation. In adjusted pre-reformulation analyses, degree holders were half as likely as those without qualifications to be top 10 % consumers (OR=0·51; 95 % CI 0·28, 0·92). In adjusted post-reformulation analyses, those with higher income were 2·5–3·3 times more likely to be top 10 % consumers than lowest income households. Pre-reformulation, high consumers consumed more foods containing artificial TFA, whereas ruminant TFA were more prominent post-reformulation. Conclusions: High TFA consumption was associated with socio-economic disadvantage pre-reformulation, but evidence of this is less clear post-reformulation. Voluntary reformulation appeared effective in reducing TFA content in many UK products with mixed effects on dietary inequalities relating to income and education

Stop, think SCORTCH: rethinking the traditional 'TORCH' screen in an era of re-emerging syphilis

BACKGROUND: The epidemiology of congenital infections is ever changing, with a recent resurgence in syphilis infection rates seen in the UK. Identification of congenital infection is often delayed; early recognition and management of congenital infections is important. Testing modalities and investigations are often limited, leading to missed diagnostic opportunities. METHODS: The SCORTCH (syphilis, cytomegalovirus (CMV), 'other', rubella, toxoplasmosis, chickenpox, herpes simplex virus (HSV) and blood-borne viruses) acronym increases the awareness of clinicians to the increased risk of congenital syphilis, while considering other infectious aetiologies including: zika, malaria, chagas disease, parvovirus, enterovirus, HIV, hepatitis B and C, and human T-lymphotropic virus 1, in addition to the classic congenital infections recognised in the 'TORCH screen' (toxoplasmosis, 'other', rubella, CMV, HSV). The SCORTCH diagnostic approach describes common signs present in infants with congenital infection, details serological testing for mother and infant and important direct diagnostics of the infant. Direct diagnostic investigations include: radiology, ophthalmology, audiology, microbiological and PCR testing for both the infant and placental tissue, the latter also warrants histopathology. CONCLUSION: The traditional 'TORCH screen' focuses on serology-specific investigations, often omits important direct diagnostic testing of the infant, and fails to consider emerging and re-emerging congenital infections. In recognition of syphilis as a re-emerging pathogen and the overlapping clinical presentations of various infectious aetiologies, we advocate for a broader outlook using the SCORTCH diagnostic approach

A particle swarm optimization based memetic algorithm for dynamic optimization problems

Copyright @ Springer Science + Business Media B.V. 2010.Recently, there has been an increasing concern from the evolutionary computation community on dynamic optimization problems since many real-world optimization problems are dynamic. This paper investigates a particle swarm optimization (PSO) based memetic algorithm that hybridizes PSO with a local search technique for dynamic optimization problems. Within the framework of the proposed algorithm, a local version of PSO with a ring-shape topology structure is used as the global search operator and a fuzzy cognition local search method is proposed as the local search technique. In addition, a self-organized random immigrants scheme is extended into our proposed algorithm in order to further enhance its exploration capacity for new peaks in the search space. Experimental study over the moving peaks benchmark problem shows that the proposed PSO-based memetic algorithm is robust and adaptable in dynamic environments.This work was supported by the National Nature Science Foundation of China (NSFC) under Grant No. 70431003 and Grant No. 70671020, the National Innovation Research Community Science Foundation of China under Grant No. 60521003, the National Support Plan of China under Grant No. 2006BAH02A09 and the Ministry of Education, science, and Technology in Korea through the Second-Phase of Brain Korea 21 Project in 2009, the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/01 and the Hong Kong Polytechnic University Research Grants under Grant G-YH60