qq-Stability conditions on Calabi-Yau-X\mathbb{X} categories and twisted periods

We introduce q-stability conditions $(\sigma,s)$ on Calabi-Yau-$\mathbb{X}$ categories $\mathcal{D}_\mathbb{X}$, where $\sigma$ is a stability condition on $\mathcal{D}_\mathbb{X}$ and $s$ a complex number. Sufficient and necessary conditions are given, for a stability condition on an $\mathbb{X}$-baric heart $\mathcal{D}_\infty$ of $\mathcal{D}_\mathbb{X}$ to $q$-stability conditions on $\mathcal{D}_\mathbb{X}$. As a consequence, we show that the space $\operatorname{QStab}^\oplus\mathcal{D}_\mathbb{X}$ of (induced) open $q$-stability conditions is a complex manifold, whose fibers (fixing $s$) give usual type of spaces of stability conditions. Our motivating examples for $\mathcal{D}_\mathbb{X}$ are coming from Calabi-Yau-$\mathbb{X}$ completions of dg algebras. A geometric application is that, for type $A$ quiver $Q$, the corresponding space $\operatorname{QStab}^\circ_s\mathcal{D}_\mathbb{X}(Q)$ of $q$-stability conditions admits almost Frobenius structure while the central charge $Z_s$ corresponds to the twisted period $P_\nu$, for $\nu=(s-2)/2$, where $s\in\mathbb{C}$ with $\operatorname{Re}(s)\ge2$. A categorical application is that we realize perfect derived categories as cluster(-$\mathbb{X}$) categories for acyclic quiver $Q$. In the sequel, we construct quivers with superpotential from flat surfaces with the corresponding Calabi-Yau-$\mathbb{X}$ categories and realize open/closed $q$-stability conditions as $q$-quadratic differentials.Comment: Updated semistable version, 43 pages, 3 figures. Comments are welcome

qq-Stability conditions via qq-quadratic differentials for Calabi-Yau-X\mathbb{X} categories

We construct a quiver with superpotential $(Q_\mathbf{T},W_\mathbf{T})$ from a marked surface $\mathbf{S}$ with full formal arc system $\mathbf{T}$. Categorically, we show that the associated cluster-$\mathbb{X}$ category is Haiden-Katzarkov-Kontsevich's topological Fukaya category $\mathcal{D}_{\infty}(\mathbf{T})$ of $\mathbf{S}$, which is also an $\mathbb{X}$-baric heart of the Calabi-Yau-$\mathbb{X}$ category $\mathcal{D}_{\mathbb{X}}(\mathbf{T})$ of $(Q_\mathbf{T},W_\mathbf{T})$. Thus stability conditions on $\mathcal{D}_{\infty}(\mathbf{T})$ induces $q$-stability conditions on $\mathcal{D}_{\mathbb{X}}(\mathbf{T})$. Geometrically, we identify the space of $q$-quadratic differentials on the logarithm surface $\log\mathbf{S}_\Delta$, with the space of induced $q$-stability conditions on $\mathcal{D}_{\mathbb{X}}(\mathbf{T})$, with a complex parameter $s$ satisfying $\operatorname{Re}(s)\gg1$. When $s=N$ is an integer, the result gives an $N$-analogue of Bridgeland-Smith's result for realizing stability conditions on the orbit Calabi-Yau-$N$ category $\mathcal{D}_{\mathbb{X}}(\mathbf{T})\mathbin{/\mkern-6mu/}[\mathbb{X}-N]$

Finite-Size Scaling Analysis of the Eigenstate Thermalization Hypothesis in a One-Dimensional Interacting Bose gas

By calculating correlation functions for the Lieb-Liniger model based on the algebraic Bethe ansatz method, we conduct a finite-size scaling analysis of the eigenstate thermalization hypothesis (ETH) which is considered to be a possible mechanism of thermalization in isolated quantum systems. We find that the ETH in the weak sense holds in the thermodynamic limit even for an integrable system although it does not hold in the strong sense. Based on the result of the finite-size scaling analysis, we compare the contribution of the weak ETH to thermalization with that of yet another thermalization mechanism, the typicality, and show that the former gives only a logarithmic correction to the latter.Comment: 5 pages, 3 figure

Community Structure and Its Stability on a Face-to-Face Interaction Network in Kyoto City

As social behavior plays an essential role in people’s lives, the features of face-to-face interaction networks must be examined to understand people’s social behavior. In this study, we focused on the stable community structure of a face-to-face interaction network because it explains the persistent communities caused by the stationary communication patterns of citizens and visitors in a city. We regarded citizens and visitors as two kinds of particles and the community as a phase and theorized the stability of the community structure using the equilibrium conditions among communities. We formulated the chemical potentials of the communities and examined whether they were in equilibrium under the assumption of a canonical ensemble. We estimated the chemical potentials of persistent communities and found that these values matched within approximately 10% error for each day. This result indicates that the cause of persistent communities is the stability of community structure

OPERA superluminal neutrinos and Kinematics in Finsler spacetime

The OPERA collaboration recently reported that muon neutrinos could be superluminal. More recently, Cohen and Glashow pointed that such superluminal neutrinos would be suppressed since they lose their energies rapidly via bremsstrahlung. In this Letter, we propose that Finslerian nature of spacetime could account for the superluminal phenomena of particles. The Finsler spacetime permits the existence of superluminal behavior of particles while the casuality still holds. A new dispersion relation is obtained in a class of Finsler spacetime. It is shown that the superluminal speed is linearly dependent on the energy per unit mass of the particle. We find that such a superluminal speed formula is consistent with data of OPERA, MINOS and Fermilab-1979 neutrino experiments as well as observations on neutrinos from SN1987a.Comment: 10 pages, 2 figures. Viewpoints of Finslerian special relativity on OPERA superluminal neutrino

Regional medical inter-institutional cooperation in medical provider network constructed using patient claims data from Japan

The aging world population requires a sustainable and high-quality healthcare system. To examine the efficiency of medical cooperation, medical provider and physician networks were constructed using patient claims data. Previous studies have shown that these networks contain information on medical cooperation. However, the usage patterns of multiple medical providers in a series of medical services have not been considered. In addition, these studies used only general network features to represent medical cooperation, but their expressive ability was low. To overcome these limitations, we analyzed the medical provider network to examine its overall contribution to the quality of healthcare provided by cooperation between medical providers in a series of medical services. This study focused on: i) the method of feature extraction from the network, ii) incorporation of the usage pattern of medical providers, and iii) expressive ability of the statistical model. Femoral neck fractures were selected as the target disease. To build the medical provider networks, we analyzed the patient claims data from a single prefecture in Japan between January 1, 2014 and December 31, 2019. We considered four types of models. Models 1 and 2 use node strength and linear regression, with Model 2 also incorporating patient age as an input. Models 3 and 4 use feature representation by node2vec with linear regression and regression tree ensemble, a machine learning method. The results showed that medical providers with higher levels of cooperation reduce the duration of hospital stay. The overall contribution of the medical cooperation to the duration of hospital stay extracted from the medical provider network using node2vec is approximately 20%, which is approximately 20 times higher than the model using strength

Oxygen molecule dissociation on carbon nanostructures with different types of nitrogen doping

Energy barrier of oxygen molecule dissociation on carbon nanotube or graphene with different types of nitrogen doping is investigated using density functional theory. The results show that the energy barriers can be reduced efficiently by all types of nitrogen doping in both carbon nanotubes and graphene. Graphite-like nitrogen and Stone-Wales defect nitrogen decrease the energy barrier more efficiently than pyridine-like nitrogen, and a dissociation barrier lower than 0.2 eV can be obtained. Higher nitrogen concentration reduces the energy barrier much more efficiently for graphite-like nitrogen. These observations are closely related to partial occupation of {\pi}* orbitals and change of work functions. Our results thus provide useful insights into the oxygen reduction reactions.Comment: Accepted by Nanoscal