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In a previous work, we gave a construction of (not necessarily realizable) oriented matroids from a triangulation of a product of two simplices. In this follow-up paper, we use a variant of Viro's patchworking to derive a topological representation of the oriented matroid directly from the polyhedral structure of the triangulation, hence finding a combinatorial manifestation of patchworking besides tropical algebraic geometry. We achieve this by rephrasing the patchworking procedure as a controlled cell merging process, guided by the structure of tropical oriented matroids. A key insight is a new promising technique to show that the final cell complex is regular., Comment: This paper is an improved version of the second part of arXiv:2005.01787v1. 28 pages, 6 figures

It is well known that the topology of Su-Schrieffer-Heeger(SSH) model, which belongs to AIII symmetry class, is protected by chiral symmetry. In this article, instead of chiral symmetry, we constrain the bulk Hamiltonian by a magnetic point group symmetry, which can be generated by a unitary symmetry and an anti-unitary symmetry. Under these symmetries, a four-band model can be block diagonalized into two 2-band models and each 2-band model is analogous to an SSH model. As the two 2-band models are individual, we call the four-band model double independent SSH (DISSH) model. Interestingly, since the symmetry requirements of DISSH model can be fulfilled in ferromagnetic systems, the discovery in this manuscript extends SSH model into ferromagnetic systems. Furthermore, we presented an example of DISSH model with a set of reasonable parameters to show that it is possible to manipulate the topological phase of DISSH model by tuning the magnetic moment in experiment., Comment: 6 pages, 4 figures

We construct a new family of irreducible representations of $\mathcal{U}_q(\mathfrak{g}_\mathbb{R})$ and its modular double by quantizing the classical parabolic induction corresponding to arbitrary parabolic subgroups, such that the generators of $\mathcal{U}_q(\mathfrak{g}_\mathbb{R})$ act by positive self-adjoint operators on a Hilbert space. This generalizes the well-established positive representations which corresponds to induction by the minimal parabolic (i.e. Borel) subgroup. We also study in detail the special case of type $A_n$ acting on $L^2(\mathbb{R}^n)$ with minimal functional dimension, and establish the properties of its central characters and universal $\mathcal{R}$ operator. We construct a positive version of the evaluation module of the affine quantum group $\mathcal{U}_q(\widehat{\mathfrak{sl}}_{n+1})$ modeled over this minimal positive representation of type $A_n$., Comment: 62 pages, 12 figures

We introduce a construction of oriented matroids from a triangulation of a product of two simplices. For this, we use the structure of such a triangulation in terms of polyhedral matching fields. The oriented matroid is composed of compatible chirotopes on the cells in a matroid subdivision of the hypersimplex, which might be of independent interest. In particular, we generalize this using the language of matroids over hyperfields, which gives a new approach to construct matroids over hyperfields. A recurring theme in our work is that various tropical constructions can be extended beyond tropicalization with new formulations and proof methods., Comment: v2: The original submission was split in two parts. This is an improved version of the first part. 43 pages, 18 Figures; v1: 51 pages, 15 Figures

The Gravity Collaboration detected a near-infrared hotspot moving around Sgr A* during the 2018 July 22 flare. They fitted the partial loop the hotspot made on the sky with a circular Keplerian orbit of radius $\simeq7.5\,r_{\rm g}$ around the supermassive black hole (BH), where $r_{\rm g}$ is the gravitational radius. However, because the hotspot traversed the loop in a short time, models in which the hotspot tracks the motion of some fluid element tend to produce a best-fit trajectory smaller than the observed loop. This is true for a circular Keplerian orbit, even when BH spin is accounted for, and for motion along a RIAF streamline. A marginally bound geodesic suffers from the same problem; in addition, it is not clear what the origin of an object following the geodesic would be. The observed hotspot motion is more likely a pattern motion. Circular motion with $r\simeq12.5\,r_{\rm g}$ and a super-Keplerian speed $\simeq0.8\,c$ is a good fit. Such motion must be pattern motion because it cannot be explained by physical forces. The pattern speed is compatible with magnetohydrodynamic perturbations, provided that the magnetic field is sufficiently strong. Circular pattern motion of radius $\sim20\, r_{\rm g}$ on a plane above the BH is an equally good alternative; in this case, the hotspot may be caused by a precessing outflow interacting with a surrounding disk. As all our fits have relatively large radii, we cannot constrain the BH spin using these observations., Comment: 9 pages, 8 figures, 1 table, accepted for publication in MNRAS

The black hole of an active galactic nucleus is encircled by an accretion disk. The surface density of the disk is always too low to affect the tidal disruption of a star, but it can be high enough that a vigorous interaction results when the debris stream returns to pericenter and punches through the disk. Shocks excited in the disk dissipate the kinetic energy of the disk interior to the impact point and expedite inflow toward the black hole. Radiatively efficient disks with luminosity $\gtrsim10^{-3}$ Eddington have a high enough surface density that the initial stream-disk interaction leads to energy dissipation at a super-Eddington rate. Because of the rapid inflow, only part of this dissipated energy emerges as radiation, while the rest is advected into the black hole. Dissipation, inflow, and cooling balance to keep the bolometric luminosity at an Eddington-level plateau whose duration is tens of days, with an almost linear dependence on stellar mass. After the plateau, the luminosity decreases in proportion to the disk surface density, with a power-law index between $-3$ and $-2$ at earlier times, and possibly a steeper index at later times., Comment: 8 pages, 6 figures, 1 appendix, accepted by ApJ

Optimizing traffic flow is essential for easing congestion. However, even when globally-optimal, coordinated and individualized routes are provided, users may choose alternative routes which offer lower individual costs. By analyzing the impact of selfish route-choices on performance using the cavity method, we find that a small ratio of selfish route-choices improves the global performance of uncoordinated transportation networks, but degrades the efficiency of optimized systems. Remarkably, compliant users always gain in the former and selfish users may gain in the latter, under some parameter conditions. The theoretical results are in good agreement with large-scale simulations. Iterative route-switching by a small fraction of selfish users leads to Nash equilibria close to the globally optimal routing solution. Our theoretical framework also generalizes the use of the cavity method, originally developed for the study of equilibrium states, to analyze iterative game-theoretical problems. These results shed light on the feasibility of easing congestion by route coordination when not all vehicles follow the coordinated routes.

Thermalization in an isolated oscillating Bose-Einstein condensate in a disordered trap is investigated. We show Shannon entropy in $x$ or $p$ representation is the eligible one to describe the thermalization. Besides, we show that multiple scattering with the disorder generates more and more incoherent thermal particles and condensed and thermal particles act as mutual heat bath that results in the thermalization of the whole system. We also demonstrate that Loschmidt's paradox can be resolved in the present system.

The sandpile group of a connected graph $G$, defined to be the torsion part of the cokernel of the graph Laplacian, is a subtle graph invariant with combinatorial, algebraic, and geometric descriptions. Extending and improving previous works on the sandpile group of hypercubes, we study the sandpile groups of the Cayley graphs of $\mathbb{F}_2^r$, focusing on their poorly understood Sylow-$2$ component. We find the number of Sylow-$2$ cyclic factors for "generic" Cayley graphs and deduce a bound for the non-generic ones. Moreover, we provide a sharp upper bound for their largest Sylow-$2$ cyclic factors. In the case of hypercubes, we give exact formulae for the largest $n-1$ Sylow-$2$ cyclic factors. Some key ingredients of our work include the natural ring structure on these sandpile groups from representation theory, and calculation of the $2$-adic valuations of binomial sums via the combinatorics of carries., Comment: v2: 19 pages, 1 figure, 1 table; proved Conjecture 6.1 in older version (now Theorem 2.9), change of authorship. v3: 20 pages, 1 figure, 1 table; minor revision from v2

With the rapid development of modern technology, the Web has become an important platform for users to make friends and acquire information. However, since information on the Web is over-abundant, information filtering becomes a key task for online users to obtain relevant suggestions. As most Websites can be ranked according to users' rating and preferences, relevance to queries, and recency, how to extract the most relevant item from the over-abundant information is always a key topic for researchers in various fields. In this paper, we adopt tools used to analyze complex networks to evaluate user reputation and item quality. In our proposed accumulative time-based ranking (ATR) algorithm, we incorporate two behavioral weighting factors which are updated when users select or rate items, to reflect the evolution of user reputation and item quality over time. We showed that our algorithm outperforms state-of-the-art ranking algorithms in terms of precision and robustness on empirical datasets from various online retailers and the citation datasets among research publications.

Human mobility is an important characteristic of human behavior, but since tracking personalized position to high temporal and spatial resolution is difficult, most studies on human mobility patterns rely largely on mathematical models. Seminal models which assume frequently visited locations tend to be re-visited, reproduce a wide range of statistical features including collective mobility fluxes and numerous scaling laws. However, these models cannot be verified at a time-scale relevant to our daily travel patterns as most available data do not provide the necessary temporal resolution. In this work, we re-examined human mobility mechanisms via comprehensive cell-phone position data recorded at a high frequency up to every second. We found that the next location visited by users is not their most frequently visited ones in many cases. Instead, individuals exhibit origin-dependent, path-preferential patterns in their short time-scale mobility. These behaviors are prominent when the temporal resolution of the data is high, and are thus overlooked in most previous studies. Incorporating measured quantities from our high frequency data into conventional human mobility models shows contradictory statistical results. We finally revealed that the individual preferential transition mechanism characterized by the first-order Markov process can quantitatively reproduce the observed travel patterns at both individual and population levels at all relevant time-scales., Comment: 22 pages, 4 figures

Based on ab-initio calculated parameters, we apply a theoretical model on the iron-based BaFe2As2 superconductor that takes into account dramatic enhancements of the electron-phonon coupling of soft transverse phonons in the FeAs layers and antiferromagnetism. Our model is able to reproduce the Tc values of BaFe2As2 found under pressure in experiments. To calculate the Tc of the K-doped Ba1-xKxFe2As2 system as a function of the K content, we additionally consider the experimentally observed effective mass enhancements and Kondo temperatures in the strongly over-doped region (0.8 < x < 1), which decouple the antiferromagnetism and electron-phonon scattering. The highest theoretical Tc at the optimal doping concentration is reproduced after optimization of antiferromagnetic fluctuations and electron-phonon coupling. Our model is also able to reproduce the dip-like structure in Tc in the region where a re-entrant tetragonal phase of C4 symmetry is found (0.24 < x < 0.28) and indicates the weakening effect of local exchange correlation energy as responsible for Tc reduction. Our model thus demonstrates that the high transition temperatures and the exact doping and pressure dependence of this iron-based superconductor can be explained within an extended electron-phonon coupling model in which the structural, magnetic and electronic degrees of freedom are strongly intertwined.

Many major cities suffer from severe traffic congestion. Road expansion in the cites is usually infeasible, and an alternative way to alleviate traffic congestion is to coordinate the route of vehicles. Various path selection and planning algorithms are thus proposed, but most existing methods only plan paths separately and provide un-coordinated solutions. Recently, an analogy between the coordination of vehicular routes and the interaction of polymers is drawn; the spin glass theory in statistical physics is employed to optimally coordinate transportation routes. To further examine the advantages brought by path coordination, we incorporate the link congestion function developed by the Bureau of Public Roads (BPR) into the polymer routing algorithm. We then estimate in simulations the traveling time of all users saved by the polymer-BPR algorithm in randomly generated networks and real transportation networks in major cities including London, New York and Beijing. We found that a large amount of traveling time is saved in all studied networks, suggesting that the approach inspired by polymer physics is effective in minimizing the traveling time via path coordination, which is a promising tool for alleviating traffic congestions.

A fraction of tidal disruption events (TDEs) occur in active galactic nuclei (AGNs) whose black holes possess accretion disks; these TDEs can be confused with common AGN flares. The disruption itself is unaffected by the disk, but the evolution of the bound debris stream is modified by its collision with the disk when it returns to pericenter. The outcome of the collision is largely determined by the ratio of the stream mass current to the azimuthal mass current of the disk rotating underneath the stream footprint, which in turn depends on the mass and luminosity of the AGN. To characterize TDEs in AGNs, we simulated a suite of stream--disk collisions with various mass current ratios. The collision excites shocks in the disk, leading to inflow and energy dissipation orders of magnitude above Eddington; however, much of the radiation is trapped in the inflow and advected into the black hole, so the actual bolometric luminosity may be closer to Eddington. The emergent spectrum may not be thermal, TDE-like, or AGN-like. The rapid inflow causes the disk interior to the impact point to be depleted within a fraction of the mass return time. If the stream is heavy enough to penetrate the disk, part of the outgoing material eventually hits the disk again, dissipating its kinetic energy in the second collision; another part becomes unbound, emitting synchrotron radiation as it shocks with surrounding gas., Comment: 14 pages, 11 figures, accepted by ApJ, movie at https://youtu.be/hF4tcCAFvA8

Extending the notion of geometric bijections for regular matroids, introduced by the first and third author with Matthew Baker, we describe a family of bijections between bases of an oriented matroid and special orientations. These bijections are specified by a pair of circuit and cocircuit signatures coming respectively from a generic single-element lifting and extension. We then characterize generic single-element liftings and extensions using these bijections. We also explain the relation of our work with the works of Gioan--Las Vergnas and Ding. Some implications in oriented matroid programming and oriented matroid triangulations are also discussed., Comment: 24 pages, 1 figure, minor revision from v2

By introducing a simple model based on two-dimensional cellular automata, we reveal the relationship between the routing strategies of individual vehicles and the global behavior of transportation networks. Specifically, we characterize the routing strategies by a single parameter called path-greediness, which corresponds to the tendency for individuals to travel via a shortest path to the destination. Remarkably, when vehicles tend to travel via the shortest path, a congested-flow state emerges between the conventional free-flow and congested states, where traffic flow increases slowly with vehicle density in the presence of congestion. We also found that a high individual tendency to travel via the shortest path does not necessarily shorten the average journey time, as the system may benefit from less greedy routing strategies in congested situations. Finally, we show that adaptive routing strategies outperform controlled strategies in the free-flow state, but not in the congested state, implying that controlled strategies may increase coordination among vehicles and are beneficial for suppressing traffic congestion.

Recently it has been suggested that the role of electron-phonon coupling in the mechanism of iron-based superconductors may have been underestimated and that the antiferromagnetism and the induced xy potential may even have a dramatic amplification effect on electron-phonon coupling. To substantiate the recently announced xy potential in the literature, we create a two-channel model to separately superimpose the dynamics of the electron in the upper and lower tetrahedral plane. The results of our two-channel model support the literature data. While the scientists are still searching for a universal DFT functional that can describe the pairing mechanism of all iron-based superconductors, we are designing an empirical combination of DFT functional to calculate the electron-phonon coupling and antiferromagetism of LiFeAs, NaFeAs and FeSe. We use ARPES data to revise the electron-phonon scattering matrix in superconducting state to ensure that all electrons involved in iron-based superconductivity are included in the ab-inito calculation. We present an ab-initio theoretical approach that takes into account this amplifying effect of antiferromagnetism and the correction of the electron-phonon scattering matrix together with the abnormal soft out-of-plane lattice vibration of the layered structure, which allows us to calculate theoretical Tc values of LiFeAs, NaFeAs and FeSe as a function of pressure that correspond reasonably well to the experimental values.

Answering a question by Nisse and Sottile, we derive a formula for the dimension of the amoeba of an irreducible algebraic variety., Comment: 8 pages, several small improvements, final version

Coordination of dynamical routes can alleviate traffic congestion and is essential for the coming era of autonomous self-driving cars. However, dynamical route coordination is difficult and many existing routing protocols are either static or without inter-vehicle coordination. In this paper, we first apply the cavity approach in statistical physics to derive the theoretical behavior and an optimization algorithm for dynamical route coordination, but they become computational intractable as the number of time segments increases. We therefore map static spatial networks to space-time networks to derive a computational feasible message-passing algorithm compatible with arbitrary system parameters; it agrees well with the analytical and algorithmic results of conventional cavity approach and outperforms multi-start greedy search in saving total travel time by as much as 15% in simulations. The study sheds light on the design of dynamical route coordination protocols, and the solution to other dynamical problems via static analytical approaches on space-time networks., Comment: 12 pages, 11 figures