Generating large synthetic attributed graphs with node labels is an important task to support various experimental studies for graph analysis methods. Existing graph generators fail to simultaneously simulate the relationships between labels, attribu
tes, and topology which real-world graphs exhibit. Motivated by this limitation, we propose GenCAT, an attributed graph generator for controlling those relationships, which has the following advantages. (i) GenCAT generates graphs with user-specified node degrees and flexibly controls the relationship between nodes and labels by incorporating the connection proportion for each node to classes. (ii) Generated attribute values follow user-specified distributions, and users can flexibly control the correlation between the attributes and labels. (iii) Graph generation scales linearly to the number of edges. GenCAT is the first generator to support all three of these practical features. Through extensive experiments, we demonstrate that GenCAT can efficiently generate high-quality complex attributed graphs with user-controlled relationships between labels, attributes, and topology.
The main objects of the present paper are (i) Hibi rings (toric rings arising from order polytopes of posets), (ii) stable set rings (toric rings arising from stable set polytopes of perfect graphs), and (iii) edge rings (toric rings arising from edg
e polytopes of graphs satisfying the odd cycle condition). The goal of the present paper is to analyze those three toric rings and to discuss their structures in the case where their class groups have small rank. We prove that the class groups of (i), (ii) and (iii) are torsionfree. More precisely, we give descriptions of their class groups. Moreover, we characterize the posets or graphs whose associated toric rings have rank $1$ or $2$. By using those characterizations, we discuss the differences of isomorphic classes of those toric rings with small class groups.
We present a novel mechanism for the outward transport of crystalline dust particles: the outward radial drift of pebbles. The dust ring structure is frequently observed in protoplanetary disks. One of the plausible mechanisms of the formation of dus
t rings is the accumulation of pebbles around the pressure maximum, which is formed by the mass loss due to magnetically driven disk winds. In evolving protoplanetary disks due to magnetically driven disk winds, dust particles can migrate outwardly from the crystallization front to the pressure maximum by radial drift. We found that the outward radial drift process can transport crystalline dust particles efficiently when the radial drift timescale is shorter than the advection timescale. Our model predicts that the crystallinity of silicate dust particles could be as high as 100% inside the dust ring position.
Graph representation learning is a fundamental problem for modeling relational data and benefits a number of downstream applications. Traditional Bayesian-based graph models and recent deep learning based GNN either suffer from impracticability or la
ck interpretability, thus combined models for undirected graphs have been proposed to overcome the weaknesses. As a large portion of real-world graphs are directed graphs (of which undirected graphs are special cases), in this paper, we propose a Deep Latent Space Model (DLSM) for directed graphs to incorporate the traditional latent variable based generative model into deep learning frameworks. Our proposed model consists of a graph convolutional network (GCN) encoder and a stochastic decoder, which are layer-wise connected by a hierarchical variational auto-encoder architecture. By specifically modeling the degree heterogeneity using node random factors, our model possesses better interpretability in both community structure and degree heterogeneity. For fast inference, the stochastic gradient variational Bayes (SGVB) is adopted using a non-iterative recognition model, which is much more scalable than traditional MCMC-based methods. The experiments on real-world datasets show that the proposed model achieves the state-of-the-art performances on both link prediction and community detection tasks while learning interpretable node embeddings. The source code is available at https://github.com/upperr/DLSM.
Chondrules are often surrounded by fine-grained rims or igneous rims. The properties of these rims reflect their formation histories. While the formation of fine-grained rims is modeled by the accretion of dust grains onto chondrules, the accretion s
hould be followed by the growth of dust grains due to the shorter growth timescale than the accretion. In this paper, we investigate the formation of rims, taking into account the growth of porous dust aggregates. We estimate the rim thickness as a function of the chondrule fraction at a time when dust aggregate accretion onto chondrules is switched to collisions between these chondrules. Our estimations are consistent with the measured thicknesses of fine-grained rims in ordinary chondrites. However, those of igneous rims are thicker than our estimations. The thickness of igneous rims would be enlarged in remelting events.
We use first-principles methods to study doped strong ferroelectrics (taking BaTiO$_3$ as a prototype). Here we find a strong coupling between itinerant electrons and soft polar phonons in doped BaTiO$_3$, contrary to Anderson/Blounts weakly coupled
electron mechanism for ferroelectric-like metals. As a consequence, across a polar-to-centrosymmetric phase transition in doped BaTiO$_3$, the total electron-phonon coupling is increased to about 0.6 around the critical concentration, which is sufficient to induce phonon-mediated superconductivity of about 2 K. Lowering the crystal symmetry of doped BaTiO$_3$ by imposing epitaxial strain can further increase the superconducting temperature via a sizable coupling between itinerant electrons and acoustic phonons. Our work demonstrates a viable approach to modulating electron-phonon coupling and inducing phonon-mediated superconductivity in doped strong ferroelectrics and potentially in polar metals. Our results also show that the weakly coupled electron mechanism for ferroelectric-like metals is not necessarily present in doped strong ferroelectrics.
We propose novel chemical reaction networks to translate levels of concentration into unique DNA strand species, which we call concentration translators. Our design of the concentration translators is based on combination of two chemical reaction net
works, consensus network and conversion network with any number of chemical species. We give geometric analysis of the proposed CRNs from the viewpoint of nonlinear dynamical systems and show that the CRNs can actually operate as translator. Our concentration translators exploit DNA strand displacement (DSD) reaction, which is known for a universal reaction that can implement arbitrary chemical reaction networks. We demonstrate two specific types of concentration translators (translator A and B) with different switching behavior and biochemical cost and compared their characteristics computationally. The proposed concentration translators have an advantage of being able to readout the concentration of targeted nucleic acid strand without any fluorescence-based techniques. These characteristics can be tailored according to requirements from applications, including dynamic range, sensitivity and implementation cost.
Levelness and almost Gorensteinness are well-studied properties on graded rings as a generalized notion of Gorensteinness. In the present paper, we study those properties for the edge rings of the complete multipartite graphs, denoted by $Bbbk[K_{r_1
,ldots,r_n}]$ with $1 leq r_1 leq cdots leq r_n$. We give the complete characterization of which $Bbbk[K_{r_1,ldots,r_n}]$ is level in terms of $n$ and $r_1,ldots,r_n$. Similarly, we also give the complete characterization of which $Bbbk[K_{r_1,ldots,r_n}]$ is almost Gorenstein in terms of $n$ and $r_1,ldots,r_n$.
Recent observations have revealed the existence of multiple-planet systems composed of Earth-mass planets around late M dwarfs. Most of their orbits are close to commensurabilities, which suggests that planets were commonly trapped in resonant chains
in their formation around low-mass stars. We investigate the formation of multiple-planet systems in resonant chains around low-mass stars. A time-evolution model of the multiple-planet formation via pebble accretion in the early phase of the disk evolution is constructed based on the formation model for the TRAPPIST-1 system by Ormel et al. (2017). Our simulations show that knowing the protoplanet appearance timescale is important for determining the number of planets and their trapped resonances: as the protoplanet appearance timescale increases, fewer planets are formed, which are trapped in more widely separated resonances. We find that there is a range of the protoplanet appearance timescale for forming the stable multiple-planet systems in resonant chains. This range depends on the stellar mass and disk size. We suggest that the protoplanet appearance timescale is a key parameter for studying the formation of multiple-planet systems with planets in resonant chains around low-mass stars. The composition of the planets in our model is also discussed.
The first goal of the present paper is to study the class groups of the edge rings of complete multipartite graphs, denoted by $Bbbk[K_{r_1,ldots,r_n}]$, where $1 leq r_1 leq cdots leq r_n$. More concretely, we prove that the class group of $Bbbk[K_{
r_1,ldots,r_n}]$ is isomorphic to $mathbb{Z}^n$ if $n =3$ with $r_1 geq 2$ or $n geq 4$, while it turns out that the excluded cases can be deduced into Hibi rings. The second goal is to investigate the special class of divisorial ideals of $Bbbk[K_{r_1,ldots,r_n}]$, called conic divisorial ideals. We describe conic divisorial ideals for certain $K_{r_1,ldots,r_n}$ including all cases where $Bbbk[K_{r_1,ldots,r_n}]$ is Gorenstein. Finally, we give a non-commutative crepant resolution (NCCR) of $Bbbk[K_{r_1,ldots,r_n}]$ in the case where it is Gorenstein.
