Nivat's conjecture holds for sums of two periodic configurations

Nivat's conjecture is a long-standing open combinatorial problem. It concerns two-dimensional configurations, that is, maps $\mathbb Z^2 \rightarrow \mathcal A$ where $\mathcal A$ is a finite set of symbols. Such configurations are often understood as colorings of a two-dimensional square grid. Let $P_c(m,n)$ denote the number of distinct $m \times n$ block patterns occurring in a configuration $c$. Configurations satisfying $P_c(m,n) \leq mn$ for some $m,n \in \mathbb N$ are said to have low rectangular complexity. Nivat conjectured that such configurations are necessarily periodic. Recently, Kari and the author showed that low complexity configurations can be decomposed into a sum of periodic configurations. In this paper we show that if there are at most two components, Nivat's conjecture holds. As a corollary we obtain an alternative proof of a result of Cyr and Kra: If there exist $m,n \in \mathbb N$ such that $P_c(m,n) \leq mn/2$, then $c$ is periodic. The technique used in this paper combines the algebraic approach of Kari and the author with balanced sets of Cyr and Kra.Comment: Accepted for SOFSEM 2018. This version includes an appendix with proofs. 12 pages + references + appendi

Emergency and on-demand health care: modelling a large complex system

This paper describes how system dynamics was used as a central part of a whole-system review of emergency and on-demand health care in Nottingham, England. Based on interviews with 30 key individuals across health and social care, a 'conceptual map' of the system was developed, showing potential patient pathways through the system. This was used to construct a stock-flow model, populated with current activity data, in order to simulate patient flows and to identify system bottle-necks. Without intervention, assuming current trends continue, Nottingham hospitals are unlikely to reach elective admission targets or achieve the government target of 82% bed occupancy. Admissions from general practice had the greatest influence on occupancy rates. Preventing a small number of emergency admissions in elderly patients showed a substantial effect, reducing bed occupancy by 1% per annum over 5 years. Modelling indicated a range of undesirable outcomes associated with continued growth in demand for emergency care, but also considerable potential to intervene to alleviate these problems, in particular by increasing the care options available in the community

Using Linguistic Features to Estimate Suicide Probability of Chinese Microblog Users

If people with high risk of suicide can be identified through social media like microblog, it is possible to implement an active intervention system to save their lives. Based on this motivation, the current study administered the Suicide Probability Scale(SPS) to 1041 weibo users at Sina Weibo, which is a leading microblog service provider in China. Two NLP (Natural Language Processing) methods, the Chinese edition of Linguistic Inquiry and Word Count (LIWC) lexicon and Latent Dirichlet Allocation (LDA), are used to extract linguistic features from the Sina Weibo data. We trained predicting models by machine learning algorithm based on these two types of features, to estimate suicide probability based on linguistic features. The experiment results indicate that LDA can find topics that relate to suicide probability, and improve the performance of prediction. Our study adds value in prediction of suicidal probability of social network users with their behaviors

Bott periodicity and stable quantum classes

We use Bott periodicity to relate previously defined quantum classes to certain "exotic Chern classes" on $BU$. This provides an interesting computational and theoretical framework for some Gromov-Witten invariants connected with cohomological field theories. This framework has applications to study of higher dimensional, Hamiltonian rigidity aspects of Hofer geometry of $\mathbb{CP} ^{n}$, one of which we discuss here.Comment: prepublication versio

Long-term individual retention with cenobamate in adults with focal seizures: Pooled data from the clinical development program

Objective: We determined retention on open-label cenobamate therapy in the clinical development program to assess the long-term efficacy and tolerability of adjunctive cenobamate in individuals with uncontrolled focal seizures. // Methods: Data from two randomized, controlled cenobamate studies and one open-label safety and pharmacokinetic study were pooled. Based on the percentage of participants remaining on treatment, retention rates were estimated using Kaplan-Meier survival analyses. We performed two additional analyses to assess factors contributing to retention, stratifying a robust data set (through 2 years) by cenobamate modal dose and frequently used concomitant anti-seizure medications. Cenobamate discontinuations and treatment-emergent adverse events were summarized. // Results: Data from 1844 participants were pooled: 149 from a single-dose randomized trial, 355 from a multi-dose randomized trial, and 1340 from an open-label safety and pharmacokinetic study. Most participants from randomized trials continued in open-label extensions, and pooled data represent >95% of participants exposed to cenobamate. Baseline characteristics and disease and treatment histories were similar across studies. Median duration of cenobamate exposure was 34 months, with a median modal dose of 200 mg/day. Kaplan-Meier estimates of cumulative cenobamate retention rates were 80% at 1 year and 72% at 2 years. Once participants reached the maintenance phase, retention rates were consistently high in participants receiving ≥100 mg/day cenobamate, and concomitant anti-seizure medications did not affect long-term retention. By 2 years, 535 (29%) had actually discontinued cenobamate; the most common reasons for discontinuation were adverse events (37.6%), withdrawal of consent (21.1%), and other (16.8%). // Significance: Treatment retention rates provide a proxy measure for long-term efficacy, safety, tolerability, and adherence. The consistently high retention rates we found suggest that cenobamate may be an effective and well-tolerated new treatment option for people with drug-resistant focal seizures

Computing Linear Matrix Representations of Helton-Vinnikov Curves

Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron. This leads to the computational problem of explicitly producing a symmetric (positive definite) linear determinantal representation for a given curve. We study three approaches to this problem: an algebraic approach via solving polynomial equations, a geometric approach via contact curves, and an analytic approach via theta functions. These are explained, compared, and tested experimentally for low degree instances.Comment: 19 pages, 3 figures, minor revisions; Mathematical Methods in Systems, Optimization and Control, Birkhauser, Base

Accuracy of five algorithms to diagnose gambiense human African trypanosomiasis.

Algorithms to diagnose gambiense human African trypanosomiasis (HAT, sleeping sickness) are often complex due to the unsatisfactory sensitivity and/or specificity of available tests, and typically include a screening (serological), confirmation (parasitological) and staging component. There is insufficient evidence on the relative accuracy of these algorithms. This paper presents estimates of the accuracy of five algorithms used by past Médecins Sans Frontières programmes in the Republic of Congo, Southern Sudan and Uganda

Impact of proctoring on success rates for percutaneous revascularisation of coronary chronic total occlusions.

OBJECTIVE: To assess the impact of proctoring for chronic total occlusion (CTO) percutaneous coronary intervention (PCI) in six UK centres. METHODS: We retrospectively analysed 587 CTO procedures from six UK centres and compared success rates of operators who had received proctorship with success rates of the same operators before proctorship (pre-proctored) and operators in the same institutions who had not been proctored (non-proctored). There were 232 patients in the pre-proctored/non-proctored group and 355 patients in the post-proctored group. Complexity was assessed by calculating the Japanese CTO (JCTO) score for each case. RESULTS: CTO PCI success was greater in the post-proctored compared with the pre-proctored/non-proctored group (77.5% vs 62.1%, p<0.0001). In more complex cases where JCTO≥2, the difference in success was greater (70.7% vs 49.5%, p=0.0003). After proctoring, there was an increase in CTO PCI activity in centres from 2.5% to 3.5%, p<0.0001 (as a proportion of total PCI), and the proportion of very difficult cases with JCTO score ≥3 increased from 15.3% (35/229) to 29.7% (105/354), p<0.0001. CONCLUSIONS: Proctoring resulted in an increase in procedural success for CTO PCI, an increase in complex CTO PCI and an increase in total CTO PCI activity. Proctoring may be a valuable way to improve access to CTO PCI and the likelihood of procedural success

Exploring the concept of pain of Australian children with and without pain: Qualitative study

© 2019 Author(s). Objective A person's concept of pain can be defined as how they understand what pain actually is, what function it serves and what biological processes are thought to underpin it. This study aimed to explore the concept of pain in children with and without persistent pain. Design In-depth, face-to-face interviews with drawing tasks were conducted with 16 children (aged 8-12 years) in New South Wales, Australia. Thematic analysis was used to analyse and synthesise the data. Setting Children with persistent pain were identified from a pain clinic waiting list in Australia, and children without pain were identified through advertising flyers and email bulletins at a university and hospital. Participants Eight children had persistent pain and eight children were pain free. Results Four themes emerged from the data: â € my pain-related knowledge', â € pain in the world around me', â € pain in me' and â € communicating my concept of pain'. A conceptual framework of the potential interactions between the themes resulting from the analysis is proposed. The concept of pain of Australian children aged 8-12 years varied depending on their knowledge, experiences and literacy levels. For example, when undertaking a drawing task, children with persistent pain tended to draw emotional elements to describe pain, whereas children who were pain free did not. Conclusions Gaining an in-depth understanding of a child's previous pain-related experiences and knowledge is important to facilitate clear and meaningful pain science education. The use of age-appropriate language, in combination with appropriate assessment and education tasks such as drawing and discussing vignettes, allowed children to communicate their individual concept of pain