Ferromagnetic phase transitions of inhomogeneous systems modelled by square Ising models with diamond-type bond-decorations

The two-dimensional Ising model defined on square lattices with diamond-type bond-decorations is employed to study the nature of the ferromagnetic phase transitions of inhomogeneous systems. The model is studied analytically under the bond-renormalization scheme. For an $n$-level decorated lattice, the long-range ordering occurs at the critical temperature given by the fitting function as $(k_{B}T_{c}/J)_{n}=1.6410+(0.6281) \exp [ -(0.5857) n]$, and the local ordering inside $n$-level decorated bonds occurs at the temperature given by the fitting function as $(k_{B}T_{m}/J)_{n}=1.6410-(0.8063) \exp [ -(0.7144) n]$. The critical amplitude $A_{\sin g}^{(n)}$ of the logrithmic singularity in specific heat characterizes the width of the critical region, and it varies with the decoration level $n$ as $A_{\sin g}^{(n)}=(0.2473) \exp [ -(0.3018) n]$, obtained by fitting the numerical results. The cross over from a finite-decorated system to an infinite-decorated system is not a smooth continuation. For the case of infinite decorations, the critical specific heat becomes a cusp with the height $c^{(n)}=0.639852$. The results are compared with those obtained in the cell-decorated Ising model.Comment: 18 pages, 7 figure

Conformation-networks of two-dimensional lattice homopolymers

The effect of different Monte Carlo move sets on the the folding kinetics of lattice polymer chains is studied from the geometry of the conformation-network. The networks have the characteristics of small- world. The Monte Carlo move, rigid rotation, has drastic effect on the geometric properties of the network. The move not only change the connections but also reduce greatly the shortest path length between conformations. The networks are as robust as random network

Stroke genetics informs drug discovery and risk prediction across ancestries

Previous genome-wide association studies (GWASs) of stroke — the second leading cause of death worldwide — were conducted predominantly in populations of European ancestry1,2. Here, in cross-ancestry GWAS meta-analyses of 110,182 patients who have had a stroke (five ancestries, 33% non-European) and 1,503,898 control individuals, we identify association signals for stroke and its subtypes at 89 (61 new) independent loci: 60 in primary inverse-variance-weighted analyses and 29 in secondary meta-regression and multitrait analyses. On the basis of internal cross-ancestry validation and an independent follow-up in 89,084 additional cases of stroke (30% non-European) and 1,013,843 control individuals, 87% of the primary stroke risk loci and 60% of the secondary stroke risk loci were replicated (P < 0.05). Effect sizes were highly correlated across ancestries. Cross-ancestry fine-mapping, in silico mutagenesis analysis3, and transcriptome-wide and proteome-wide association analyses revealed putative causal genes (such as SH3PXD2A and FURIN) and variants (such as at GRK5 and NOS3). Using a three-pronged approach4, we provide genetic evidence for putative drug effects, highlighting F11, KLKB1, PROC, GP1BA, LAMC2 and VCAM1 as possible targets, with drugs already under investigation for stroke for F11 and PROC. A polygenic score integrating cross-ancestry and ancestry-specific stroke GWASs with vascular-risk factor GWASs (integrative polygenic scores) strongly predicted ischaemic stroke in populations of European, East Asian and African ancestry5. Stroke genetic risk scores were predictive of ischaemic stroke independent of clinical risk factors in 52,600 clinical-trial participants with cardiometabolic disease. Our results provide insights to inform biology, reveal potential drug targets and derive genetic risk prediction tools across ancestries