Phase transition in the three-state Potts antiferromagnet on the diced lattice

We prove that the 3-state Potts antiferromagnet on the diced lattice (dual of the kagome lattice) has entropically driven long-range order at low temperatures (including zero). We then present Monte Carlo simulations, using a cluster algorithm, of the 3-state and 4-state models. The 3-state model has a phase transition to the high-temperature disordered phase at v=e;{J}-1=-0.860 599+/-0.000 004 that appears to be in the universality class of the 3-state Potts ferromagnet. The 4-state model is disordered throughout the physical region, including at zero temperature.     

TIPS: A Framework for Text Summarising with Illustrative Pictures

We propose an algorithm to generate graphical summarising of longer text passages using a set of illustrative pictures (TIPS). TIPS is an algorithm using a voting process that uses results of individual “weak” algorithms. The proposed method includes a summarising algorithm that generates a digest of the input document. Each sentence of the text summary is used as the input for further processing by the sentence transformer separately. A sentence transformer performs text embedding and a group of CLIP similarity-based algorithms trained on different image embedding finds semantic distances between images in the illustration image database and the input text. A voting process extracts the most matching images to the text. The TIPS algorithm allows the integration of the best (highest scored) results of the different recommendation algorithms by diminishing the influence of images that are a disjointed part of the recommendations of the component algorithms. TIPS returns a set of illustrative images that describe each sentence of the text summary. Three human judges found that the use of TIPS resulted in an increase in matching highly relevant images to text, ranging from 5% to 8% and images relevant to text ranging from 3% to 7% compared to the approach based on single-embedding schema.     

Neuropeptide delivery to the brain: a von Willebrand factor signal peptide to direct neuropeptide secretion

Background  

Multiple neuropeptides, sometimes with opposing functions, can be produced from one precursor gene. To study the roles of the different neuropeptides encoded by one large precursor we developed a method to overexpress minigenes and establish local secretion.     

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models

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.     

Correction-to-Scaling Exponents for Two-Dimensional Self-Avoiding Walks

We study the correction-to-scaling exponents for the two-dimensional self-avoiding walk, using a combination of series-extrapolation and Monte Carlo methods. We enumerate all self-avoiding walks up to 59 steps on the square lattice, and up to 40 steps on the triangular lattice, measuring the mean-square end-to-end distance, the mean-square radius of gyration and the mean-square distance of a monomer from the endpoints. The complete endpoint distribution is also calculated for self-avoiding walks up to 32 steps (square) and up to 22 steps (triangular). We also generate self-avoiding walks on the square lattice by Monte Carlo, using the pivot algorithm, obtaining the mean-square radii to ≈ 0.01% accuracy up to N=4000. We give compelling evidence that the first non-analytic correction term for two-dimensional self-avoiding walks is Δ₁=3/2. We compute several moments of the endpoint distribution function, finding good agreement with the field-theoretic predictions. Finally, we study a particular invariant ratio that can be shown, by conformal-field-theory arguments, to vanish asymptotically, and we find the cancellation of the leading analytic correction.     

Join- and-cut algorithm for self-avoiding walks with variable length and free endpoints

We introduce a new Monte Carlo algorithm for generating self-avoiding walks of variable length and free endpoints. The algorithm works in the unorthodox ensemble consisting of all pairs of SAWs such that the total number of stepsN _tot in the two walks is fixed. The elementary moves of the algorithm are fixed-N (e.g., pivot) moves on the individual walks, and a novel join- and-cut move that concatenates the two walks and then cuts them at a random location. We analyze the dynamic critical behavior of the new algorithm, using a combination of rigorous, heuristic, and numerical methods. In two dimensions the autocorrelation time in CPU units grows as N^1.5, and the behavior improves in higher dimensions. This algorithm allows high-precision estimation of the critical exponent.