Counting Complex Disordered States by Efficient Pattern Matching: Chromatic Polynomials and Potts Partition Functions

Counting problems, determining the number of possible states of a large system under certain constraints, play an important role in many areas of science. They naturally arise for complex disordered systems in physics and chemistry, in mathematical graph theory, and in computer science. Counting problems, however, are among the hardest problems to access computationally. Here, we suggest a novel method to access a benchmark counting problem, finding chromatic polynomials of graphs. We develop a vertex-oriented symbolic pattern matching algorithm that exploits the equivalence between the chromatic polynomial and the zero-temperature partition function of the Potts antiferromagnet on the same graph. Implementing this bottom-up algorithm using appropriate computer algebra, the new method outperforms standard top-down methods by several orders of magnitude, already for moderately sized graphs. As a first application, we compute chromatic polynomials of samples of the simple cubic lattice, for the first time computationally accessing three-dimensional lattices of physical relevance. The method offers straightforward generalizations to several other counting problems.Comment: 7 pages, 4 figure

Patient perspectives on delays in diagnosis and treatment of cancer: a qualitative analysis of free-text data

Background: Earlier cancer diagnosis is crucial in improving cancer survival. The International Cancer Benchmarking Partnership Module 4 (ICBP4) is a quantitative survey study that explores the reasons for delays in diagnosis and treatment of breast, colorectal, lung, and ovarian cancer. To further understand the associated diagnostic processes, it is also important to explore the patient perspectives expressed in the free-text comments. Aim: To use the free-text data provided by patients completing the ICBP4 survey to augment the understanding of patients’ perspectives of their diagnostic journey. Design and setting: Qualitative analysis of the free-text data collected in Wales between October 2013 and December 2014 as part of the ICBP4 survey. Newly-diagnosed patients with either breast, ovarian, colorectal, or lung cancer were identified from registry data and then invited by their GPs to participate in the survey. Method: A thematic framework was used to analyse the free-text comments provided at the end of the ICBP4 survey. Of the 905 patients who returned a questionnaire, 530 included comments. Results: The free-text data provided information about patients’ perspectives of the diagnostic journey. Analysis identified factors that acted as either barriers or facilitators at different stages of the diagnostic process. Some factors, such as screening, doctor–patient familiarity, and private treatment, acted as both barriers and facilitators depending on the context. Conclusion: Factors identified in this study help to explain how existing models of cancer diagnosis (for example, the Pathways to Treatment Model) work in practice. It is important that clinicians are aware of how these factors may interact with individual clinical cases and either facilitate, or act as a barrier to, subsequent cancer diagnosis. Understanding and implementing this knowledge into clinical practice may result in quicker cancer diagnoses

Assessment of the 2016 National Institute for Health and Care Excellence high-sensitivity troponin rule-out strategy.

OBJECTIVE: We aimed to evaluate the limit of detection of high-sensitivity troponin (hs-cTn) and Thrombolysis In Myocardial Infarction (TIMI) score combination rule-out strategy suggested within the 2016 National Institute for Health and Care Excellence (NICE) Chest Pain of Recent Onset guidelines and establish the optimal TIMI score threshold for clinical use. METHODS: A pooled analysis of adult patients presenting to the emergency department with chest pain and a non-ischaemic ECG, recruited into six prospective studies, from Australia, New Zealand and the UK. We evaluated the sensitivity of TIMI score thresholds from 0 to 2 alongside hs-cTnT or hs-cTnI for the primary outcome of major adverse cardiac events within 30 days. RESULTS: Data were available for 3159 patients for hs-cTnT and 4532 for hs-cTnI, of these 376 (11.9%) and 445 (9.8%) had major adverse cardiac events, respectively. Using a TIMI score of 0, the sensitivity for the primary outcome was 99.5% (95% CI 98.1% to 99.9%) alongside hs-cTnT and 98.9% (97.4% to 99.6%)%) alongside hs-cTnI, identifying 17.9% and 21.0% of patients as low risk, respectively. For a TIMI score ≤1 sensitivity was 98.9% (97.3% to 99.7%)%) alongside hs-cTnT and 98.4% (96.8% to 99.4%)%) alongside hs-cTnI, identifying 28.1% and 35.7% as low risk, respectively. For TIMI≤2, meta-sensitivity was <98% with either assay. CONCLUSIONS: Our findings support the rule-out strategy suggested by NICE. The TIMI score threshold suggested for clinical use is 0. The proportion of patients identified as low risk (18%-21%) and suitable for early discharge using this threshold may be sufficient to encourage change of practice. TRIAL REGISTRATION NUMBERS: ADAPT observational study/IMPACT intervention trial ACTRN12611001069943.ADAPT-ADP randomised controlled trial ACTRN12610000766011.EDACS-ADP randomised controlled trial ACTRN12613000745741.TRUST observational study ISRCTN no. 21109279

Reflecting photonics: reaching new audiences through new partnerships – IYL 2015 and the Royal Horticultural Society Flower Show

The ‘Reflecting Photonics’ show garden was exhibited at the 2015 Royal Horticultural Society (RHS) Flower Show in Tatton Park, UK, to celebrate the International Year of Light and Light-based Technologies. Elks-Smith Garden Design alongside landscapers ‘Turf N’ Earth’ collaborated with researchers, marketing and outreach professionals from the University of Southampton to design, construct and exhibit a photonics-themed garden. The garden and supporting exhibition united science and art to reach new audiences – particularly family groups alongside other key influencers to the young – and showcased the world-leading research in optical fibers at the university in an accessible manner. Researchers and a publicity professional, funded by the EPSRC Centre for Innovative Manufacturing in Photonics, developed an integrated approach to the event’s public engagement and marketing. The overarching aim was to influence a positive change in the attitude of the garden visitors towards physics and photonics, with additional focus on promoting careers for women in STEM. The show garden won an RHS Gold Medal award and the coveted ‘People’s Choice Award’ for the best large garden. The project subsequently won the South East England Physics Network Public Engagement Innovation Project Award. Approximately 80,000 visitors saw the garden, with a further three million television viewers on a popular British gardening show. There were also over 75,400 Tweet impressions on social media. This paper discusses the project aims, explores the design of the garden and its relationship with the research, describes the work of the public engagement team, and outlines the impact of the event

Theory of Distinct Crystal Structures of Polymerized Fullerides AC60, A=K, Rb, Cs: the Specific Role of Alkalis

The polymer phases of AC60 form distinct crystal structures characterized by the mutual orientations of the (C60-)n chains. We show that the direct electric quadrupole interaction between chains always favors the orthorhombic structure Pmnn with alternating chain orientations. However the specific quadrupolar polarizability of the alkali metal ions leads to an indirect interchain coupling which favors the monoclinic structure I2/m with equal chain orientations. The competition between direct and indirect interactions explains the structural difference between KC60 and RbC60, CsC60.Comment: 4 pages, 2 figures, 1 tabl

Lower Bounds and Series for the Ground State Entropy of the Potts Antiferromagnet on Archimedean Lattices and their Duals

We prove a general rigorous lower bound for $W(\Lambda,q)=\exp(S_0(\Lambda,q)/k_B)$, the exponent of the ground state entropy of the $q$-state Potts antiferromagnet, on an arbitrary Archimedean lattice $\Lambda$. We calculate large-$q$ series expansions for the exact $W_r(\Lambda,q)=q^{-1}W(\Lambda,q)$ and compare these with our lower bounds on this function on the various Archimedean lattices. It is shown that the lower bounds coincide with a number of terms in the large-$q$ expansions and hence serve not just as bounds but also as very good approximations to the respective exact functions $W_r(\Lambda,q)$ for large $q$ on the various lattices $\Lambda$. Plots of $W_r(\Lambda,q)$ are given, and the general dependence on lattice coordination number is noted. Lower bounds and series are also presented for the duals of Archimedean lattices. As part of the study, the chromatic number is determined for all Archimedean lattices and their duals. Finally, we report calculations of chromatic zeros for several lattices; these provide further support for our earlier conjecture that a sufficient condition for $W_r(\Lambda,q)$ to be analytic at $1/q=0$ is that $\Lambda$ is a regular lattice.Comment: 39 pages, Revtex, 9 encapsulated postscript figures, to appear in Phys. Rev.

Why does chronic inflammation persist: An unexpected role for fibroblasts

One of the most important but as yet unanswered questions in inflammation research is not why inflammation occurs (we all get episodes of self limiting inflammation during the course of our lives) but why it does not resolve. Current models of inflammation stress the role of antigen-specific lymphocyte responses and attempt to address the causative agent. However, recent studies have begun to challenge the primacy of the leukocyte and have instead focused on an extended immune system in which stromal cells, such as fibroblasts play a role in the persistence of the inflammatory lesion. In this review I will illustrate how fibroblasts help regulate the switch from acute resolving to chronic persistent inflammation and provide positional memory during inflammatory responses. In chronic inflammation the normal physiological process of the removal of unwanted inflammatory effector cells becomes disordered, leading to the accumulation of leucocytes within lymphoid aggregates that resemble those seen in lymphoid tissue. I will describe how fibroblasts provide survival and retention signals for leukocytes leading to their inappropriate and persistent accumulation within inflamed tissue

Exact T=0 Partition Functions for Potts Antiferromagnets on Sections of the Simple Cubic Lattice

We present exact solutions for the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial $P$) on tube sections of the simple cubic lattice of fixed transverse size $L_x \times L_y$ and arbitrarily great length $L_z$, for sizes $L_x \times L_y = 2 \times 3$ and $2 \times 4$ and boundary conditions (a) $(FBC_x,FBC_y,FBC_z)$ and (b) $(PBC_x,FBC_y,FBC_z)$, where $FBC$ ($PBC$) denote free (periodic) boundary conditions. In the limit of infinite-length, $L_z \to \infty$, we calculate the resultant ground state degeneracy per site $W$ (= exponent of the ground-state entropy). Generalizing $q$ from ${\mathbb Z}_+$ to ${\mathbb C}$, we determine the analytic structure of $W$ and the related singular locus ${\cal B}$ which is the continuous accumulation set of zeros of the chromatic polynomial. For the $L_z \to \infty$ limit of a given family of lattice sections, $W$ is analytic for real $q$ down to a value $q_c$. We determine the values of $q_c$ for the lattice sections considered and address the question of the value of $q_c$ for a $d$-dimensional Cartesian lattice. Analogous results are presented for a tube of arbitrarily great length whose transverse cross section is formed from the complete bipartite graph $K_{m,m}$.Comment: 28 pages, latex, six postscript figures, two Mathematica file

Early rheumatoid arthritis is characterized by a distinct and transient synovial fluid cytokine profile of T cell and stromal cell origin

Pathological processes involved in the initiation of rheumatoid synovitis remain unclear. We undertook the present study to identify immune and stromal processes that are present soon after the clinical onset of rheumatoid arthritis ( RA) by assessing a panel of T cell, macrophage, and stromal cell related cytokines and chemokines in the synovial fluid of patients with early synovitis. Synovial fluid was aspirated from inflamed joints of patients with inflammatory arthritis of duration 3 months or less, whose outcomes were subsequently determined by follow up. For comparison, synovial fluid was aspirated from patients with acute crystal arthritis, established RA and osteoarthritis. Rheumatoid factor activity was blocked in the synovial fluid samples, and a panel of 23 cytokines and chemokines measured using a multiplex based system. Patients with early inflammatory arthritis who subsequently developed RA had a distinct but transient synovial fluid cytokine profile. The levels of a range of T cell, macrophage and stromal cell related cytokines ( e. g. IL-2, IL-4, IL-13, IL-17, IL-15, basic fibroblast growth factor and epidermal growth factor) were significantly elevated in these patients within 3 months after symptom onset, as compared with early arthritis patients who did not develop RA. In addition, this profile was no longer present in established RA. In contrast, patients with non-rheumatoid persistent synovitis exhibited elevated levels of interferon-gamma at initiation. Early synovitis destined to develop into RA is thus characterized by a distinct and transient synovial fluid cytokine profile. The cytokines present in the early rheumatoid lesion suggest that this response is likely to influence the microenvironment required for persistent RA

Anterior interosseous nerve syndrome: retrospective analysis of 14 patients

Introduction: The anterior interosseous nerve (AIN) is a only motor nerve innervating the deep muscles of the forearm. Its compression is rare. We present a retrospective analysis of 14 patients with an AIN syndrome with a variety of clinical manifestations who underwent operative and conservative treatment. Patients and methods: Fourteen patients (six female, eight male, mean age 48 ± 9 years) were included. In six patients, the right limb was affected, and in eight patients the left limb. Conservative treatment was started for every patient. If no signs of recovery appeared within 3 months, operative exploration was performed. Final assessment was performed between 2 and 9 years after the onset of paralysis (mean duration of follow-up 46 ± 11 months). Patients were examined clinically for return of power, range of motion, pinch and grip strengths. Also the disability of the arm, shoulder, and hand (DASH) score was calculated. Results: Seven of our 14 patients had incomplete AIN palsy with isolated total loss of function of flexor pollicis longus (FPL), five of FPL and flexor digitorum profundus (FDP)1 simultaneously, and two of FDP1. Weakness of FDP2 could be seen in four patients. Pronator teres was paralysed in two patients. Pain in the forearm was present in nine patients. Four patients had predisposing factors. Eight patients treated conservatively exhibited spontaneous recovery from their paralysis during 3-12 months after the onset. In six patients, the AIN was explored 12 weeks after the initial symptoms and released from compressing structures. Thirteen patients showed good limb function. In one patient with poor result a tendon transfer was necessary. The DASH score of patients treated conservatively and operatively presented no significant difference. Conclusion: AIN syndrome can have different clinical manifestations. If no signs of spontaneous recovery appear within 12 weeks, operative treatment should be performed