Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial

We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47} (resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <= m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19 Postscript figures. Also included are Mathematica files data_CYL.m and data_FREE.m. Many changes from version 1: new material on series expansions and their analysis, and several proofs of previously conjectured results. Final version to be published in J. Stat. Phy

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

Drawing lines at the sand: evidence for functional vs. visual reef boundaries in temperate Marine Protected Areas.

Marine Protected Areas (MPAs) can either protect all seabed habitats within them or discrete features. If discrete features within the MPA are to be protected humans have to know where the boundaries are. In Lyme Bay, SW England a MPA excluded towed demersal fishing gear from 206 km(2) to protect rocky reef habitats and the associated species. The site comprised a mosaic of sedimentary and reef habitats and so 'non reef' habitat also benefited from the MPA. Following 3 years protection, video data showed that sessile Reef Associated Species (RAS) had colonised sedimentary habitat indicating that 'reef' was present. This suggested that the functional extent of the reef was potentially greater than its visual boundary. Feature based MPA management may not adequately protect targeted features, whereas site based management allows for shifting baselines and will be more effective at delivering ecosystem goods and services

Novel genetic loci associated with hippocampal volume

The hippocampal formation is a brain structure integrally involved in episodic memory, spatial navigation, cognition and stress responsiveness. Structural abnormalities in hippocampal volume and shape are found in several common neuropsychiatric disorders. To identify the genetic underpinnings of hippocampal structure here we perform a genome-wide association study (GWAS) of 33,536 individuals and discover six independent loci significantly associated with hippocampal volume, four of them novel. Of the novel loci, three lie within genes (ASTN2, DPP4 and MAST4) and one is found 200 kb upstream of SHH. A hippocampal subfield analysis shows that a locus within the MSRB3 gene shows evidence of a localized effect along the dentate gyrus, subiculum, CA1 and fissure. Further, we show that genetic variants associated with decreased hippocampal volume are also associated with increased risk for Alzheimer's disease (rg =-0.155). Our findings suggest novel biological pathways through which human genetic variation influences hippocampal volume and risk for neuropsychiatric illness

The artificial intelligence-based model ANORAK improves histopathological grading of lung adenocarcinoma

The introduction of the International Association for the Study of Lung Cancer grading system has furthered interest in histopathological grading for risk stratification in lung adenocarcinoma. Complex morphology and high intratumoral heterogeneity present challenges to pathologists, prompting the development of artificial intelligence (AI) methods. Here we developed ANORAK (pyrAmid pooliNg crOss stReam Attention networK), encoding multiresolution inputs with an attention mechanism, to delineate growth patterns from hematoxylin and eosin-stained slides. In 1,372 lung adenocarcinomas across four independent cohorts, AI-based grading was prognostic of disease-free survival, and further assisted pathologists by consistently improving prognostication in stage I tumors. Tumors with discrepant patterns between AI and pathologists had notably higher intratumoral heterogeneity. Furthermore, ANORAK facilitates the morphological and spatial assessment of the acinar pattern, capturing acinus variations with pattern transition. Collectively, our AI method enabled the precision quantification and morphology investigation of growth patterns, reflecting intratumoral histological transitions in lung adenocarcinoma

Systematic review of oncological outcomes following surgical management of localised renal cancer.

Item does not contain fulltextCONTEXT: Renal cell carcinoma (RCC) accounts for 2-3% of adult malignancies. There remain uncertainties over the oncological outcomes for the surgical management of localised RCC. OBJECTIVE: Systematically review relevant literature comparing oncological outcomes of surgical management of localised RCC (T1-2N0M0). EVIDENCE ACQUISITION: Relevant databases including Medline, Embase, and the Cochrane Library were searched up to October 2010, and an updated scoping search was performed up to January 2012. Randomised controlled trials (RCTs) or quasi-RCTs, prospective observational studies with controls, retrospective matched-pair studies, and comparative studies from well-defined registries/databases were included. The main outcomes were overall survival, cancer-specific survival, recurrence, and metastases. The Cochrane risk of bias tool was used to assess RCTs, and an extended version was used to assess nonrandomised studies (NRSs). The quality of evidence was assessed using Grading of Recommendations Assessment, Development, and Evaluation (GRADE). EVIDENCE SYNTHESIS: A total of 4580 abstracts and 389 full-text articles were assessed. Thirty-four studies met the inclusion criteria (6 RCTs and 28 NRSs). Meta-analyses were planned but were deemed inappropriate due to data heterogeneity. There were high risks of bias and low-quality evidence across the evidence base. Open radical nephrectomy and open partial nephrectomy showed similar cancer-specific and overall survival, but when both open and laparoscopic approaches are considered together, the evidence showed improved survival for partial nephrectomy for tumours </=4cm. The overall evidence suggests either equivalent or better survival with partial nephrectomy. Laparoscopic radical nephrectomy offered equivalent survival to open radical nephrectomy, and all laparoscopic approaches achieved equivalent survival. Open and laparoscopic partial nephrectomy achieved equivalent survival. The issue of ipsilateral adrenalectomy or complete lymph node dissection with radical nephrectomy or partial nephrectomy remains unresolved. CONCLUSIONS: The evidence base suggests localised RCCs are best managed by nephron-sparing surgery where technically feasible. However, the current evidence base has significant limitations due to studies of low methodological quality marked by high risks of bias.1 mei 201