arXiv subjects

Yu Qiu

Publications and source records attributed to Yu Qiu.

At least 73 records · Page 4Linked to original sources

arXiv2019

Many Turan exponents via subdivisions

Given a graph $H$ and a positive integer $n$, the {\it Turán number} $\ex(n,H)$ is the maximum number of edges in an $n$-vertex graph that does not contain $H$ as a subgraph. A real number $r\in(1,2)$ is called a {\it Turán exponent} if there exists a bipartite graph $H$ such that $\ex(n,H)=Θ(n^r)$. A long-standing conjecture of Erdős and Simonovits states that $1+\frac{p}{q}$ is a Turán exponent for all positive integers $p$ and $q$ with $q> p$. In this paper, we build on recent developments on the conjecture to establish a large family of new Turán exponents. In particular, it follows from our main result that $1+\frac{p}{q}$ is a Turán exponent for all positive integers $p$ and $q$ with $q> p^2$.

math.CO↗

arXiv2019

Turan numbers of bipartite subdivisions

Given a graph $H$, the Turán number $ex(n,H)$ is the largest number of edges in an $H$-free graph on $n$ vertices. We make progress on a recent conjecture of Conlon, Janzer, and Lee on the Turán numbers of bipartite graphs, which in turn yields further progress on a conjecture of Erdős and Simonovits. Let $s,t,k\geq 2$ be integers. Let $K_{s,t}^k$ denote the graph obtained from the complete bipartite graph $K_{s,t}$ by replacing each edge $uv$ in it with a path of length $k$ between $u$ and $v$ such that the $st$ replacing paths are internally disjoint. It follows from a general theorem of Bukh and Conlon that $ex(n,K_{s,t}^k)=Ω(n^{1+\frac{1}{k}-\frac{1}{sk}})$. Conlon, Janzer, and Lee recently conjectured that for any integers $s,t,k\geq 2$, $ex(n,K_{s,t}^k)=O(n^{1+\frac{1}{k}-\frac{1}{sk}})$. Among many other things, they settled the $k=2$ case of their conjecture. As the main result of this paper, we prove their conjecture for $k=3,4$. Our main results also yield infinitely many new so-called Turán exponents: rationals $r\in (1,2)$ for which there exists a bipartite graph $H$ with $ex(n, H)=Θ(n^r)$, adding to the lists recently obtained by Jiang, Ma, Yepremyan, by Kang, Kim, Liu, and by Conlon, Janzer, Lee. Our method builds on an extension of the Conlon-Janzer-Lee method. We also note that the extended method also gives a weaker version of the Conlon-Janzer-Lee conjecture for all $k\geq 2$.

math.CO↗

arXiv2019

Salient Object Detection via High-to-Low Hierarchical Context Aggregation

Recent progress on salient object detection mainly aims at exploiting how to effectively integrate convolutional side-output features in convolutional neural networks (CNN). Based on this, most of the existing state-of-the-art saliency detectors design complex network structures to fuse the side-output features of the backbone feature extraction networks. However, should the fusion strategies be more and more complex for accurate salient object detection? In this paper, we observe that the contexts of a natural image can be well expressed by a high-to-low self-learning of side-output convolutional features. As we know, the contexts of an image usually refer to the global structures, and the top layers of CNN usually learn to convey global information. On the other hand, it is difficult for the intermediate side-output features to express contextual information. Here, we design an hourglass network with intermediate supervision to learn contextual features in a high-to-low manner. The learned hierarchical contexts are aggregated to generate the hybrid contextual expression for an input image. At last, the hybrid contextual features can be used for accurate saliency estimation. We extensively evaluate our method on six challenging saliency datasets, and our simple method achieves state-of-the-art performance under various evaluation metrics. Code will be released upon paper acceptance.

cs.CV↗

arXiv2019

Using H$α$ Filaments to Probe AGN Feedback in Galaxy Clusters

Recent observations of giant ellipticals and brightest cluster galaxies (BCGs) provide tentative evidence for a correlation between the luminosity of the H$α$ emitting gas filaments and the strength of feedback associated with the active galactic nucleus (AGN). Motivated by this, we use 3D radiation-hydrodynamic simulations with the code Enzo to examine and quantify the relationship between the observable properties of the H$α$ filaments and the kinetic and radiative feedback from supermassive black holes in BCGs. We find that the spatial extent and total mass of the filaments show positive correlations with AGN feedback power and can therefore be used as probes of the AGN activity. We also examine the relationship between the AGN feedback power and velocity dispersion of the H$α$ filaments and find that the kinetic luminosity shows statistically significant correlation with the component of the velocity dispersion along the jet axis but not the components perpendicular to it.

astro-ph.GA↗

arXiv2018

Decorated Marked Surfaces: Calabi-Yau categories and related topics

This is a survey on the project `Decorated Marked Surfaces', where we introduce the decoration $Δ$ on a marked surfaces $\mathbf{S}$, to study Calabi-Yau-2 (cluster) categories, Calabi-Yau-3 (Fukaya) categories, braid groups for quivers with potential, quadratic differentials and stability conditions.

math.RT↗

arXiv2018

Topological structure of spaces of stability conditions and topological Fukaya type categories

This is a survey on two closely related subjects. First, we review the study of topological structure of `finite type' components of spaces of Bridgeland's stability conditions on triangulated categories. The key is to understand Happel-Reiten-Smalo tilting as tiling of cells. Second, we review topological realizations of various Fukaya type categories, namely cluster/Calabi-Yau and derived categories from surfaces. The corresponding spaces of stability conditions are of `tame' nature and can be realized as moduli spaces of quadratic differentials due to Bridgeland-Smith and Haiden-Katzarkov-Kontsevich.

math.RT↗

arXiv2018

Smoothed SVD-based Beamforming for FBMC/OQAM Systems Based on Frequency Spreading

The combination of singular value decomposition (SVD)-based beamforming and filter bank multicarrier with offset quadrature amplitude modulation (FBMC/OQAM) has not been successful to date. The difficulty of this combination is that, the beamformers may experience significant changes between adjacent subchannels, therefore destroy the orthogonality among FBMC/OQAM real-valued symbols, even under channels with moderate frequency selectivity. In this paper, we address this problem from two aspects: i) an SVD-FS-FBMC architecture is adopted to support beamforming with finer granularity in frequency domain, based on the frequency spreading FBMC (FS-FBMC) structure, i.e., beamforming on FS-FBMC tones rather than on subchannels; ii) criterion and methods are proposed to smooth the beamformers from tone to tone. The proposed finer beamforming and smoothing greatly improve the smoothness of beamformers, therefore effectively suppress the leaked ICI/ISI. Simulations are conducted under the scenario of IEEE 802.11n wireless LAN. Results show that the proposed SVD-FS-FBMC system shares close BER performance with its orthogonal frequency division multiplexing (OFDM) counterpart under the frequency selective channels.

eess.SP↗

arXiv2018

Contractible stability spaces and faithful braid group actions

We prove that any `finite-type' component of a stability space of a triangulated category is contractible. The motivating example of such a component is the stability space of the Calabi--Yau-$N$ category $\mathcal{D}(Γ_N Q)$ associated to an ADE Dynkin quiver. In addition to showing that this is contractible we prove that the braid group $\operatorname{Br}(Q)$ acts freely upon it by spherical twists, in particular that the spherical twist group $\operatorname{Br}(Γ_N Q)$ is isomorphic to $\operatorname{Br}(Q)$. This generalises Brav-Thomas' result for the $N=2$ case. Other classes of triangulated categories with finite-type components in their stability spaces include locally-finite triangulated categories with finite rank Grothendieck group and discrete derived categories of finite global dimension.

math.AG↗

arXiv2018

Decorated marked surfaces III: The derived category of a decorated marked surface

We study the Ginzburg dg algebra $Γ_\mathbf{T}$ associated to the quiver with potential arising from a triangulation $\mathbf{T}$ of a decorated marked surface $\mathbf{S}_\bigtriangleup$, in the sense of Qiu. We show that there is a canonical way to identify all finite dimensional derived categories $\mathcal{D}_{fd}(Γ_\mathbf{T})$, denoted by $\mathcal{D}_{fd}(\mathbf{S}_\bigtriangleup)$. As an application, we show that the spherical twist group $\operatorname{ST}(\mathbf{S}_\bigtriangleup)$ associated to $\mathcal{D}_{fd}(\mathbf{S}_\bigtriangleup)$ acts faithfully on its space of stability conditions.

math.RT↗

arXiv2018

The braid group for a quiver with superpotential

We survey and compare various generalizations of braid groups for quivers with superpotential and focus on the cluster braid groups, which are introduced in a joint work with A.~King. Our motivations come from the study of cluster algebras, Calabi-Yau categories and Bridgeland stability conditions.

math.RT↗

arXiv2018

Decorated marked surfaces: spherical twists versus braid twists

We are interested in the 3-Calabi-Yau categories $\mathcal{D}$ arising from quivers with potential associated to a triangulated marked surface $\mathbf{S}$ (without punctures). We prove that the spherical twist group ST of $\mathcal{D}$ is isomorphic to a subgroup (generated by braid twists) of the mapping class group of the decorated marked surface $\mathbf{S}_{\bigtriangleup}$. Here $\mathbf{S}_{\bigtriangleup}$ is the surface obtained from $\mathbf{S}$ by decorating with a set of decorated points, where the number of points equals the number of triangles in any triangulations of $\mathbf{S}$. For instance, when $\mathbf{S}$ is an annulus, the result implies the corresponding spaces of stability conditions on $\mathcal{D}$ is contractible.

math.RT↗

arXiv2018

Some sharp results on the generalized Turán numbers

For graphs $T, H$, let $ex(n,T,H)$ denote the maximum number of copies of $T$ in an $n$-vertex $H$-free graph. In this paper we prove some sharp results on this generalization of Turán numbers, where our focus is for the graphs $T,H$ satisfying $χ(T)<χ(H)$. This can be dated back to Erdős, where he generalized the celebrated Turán's theorem by showing that for any $r\geq m$, the Turán graph $T_r(n)$ uniquely attains $ex(n,K_m,K_{r+1})$. For general graphs $H$ with $χ(H)=r+1>m$, Alon and Shikhelman showed that $ex(n,K_m,H)=\binom{r}{m}(\frac{n}{r})^m+o(n^m)$. Here we determine this error term $o(n^m)$ up to a constant factor. We prove that $ex(n,K_m,H)=\binom{r}{m}(\frac{n}{r})^m+biex(n,H)\cdotΘ(n^{m-2})$, where $biex(n,H)$ is the Turán number of the decomposition family of $H$. As a special case, we extend Erdős' result, by showing that $T_r(n)$ uniquely attains $ex(n,K_m,H)$ for any edge-critical graph $H$. We also consider $T$ being non-clique, where even the simplest case seems to be intricate. Following from a more general result, we show that for all $s\leq t$, $T_2(n)$ maximizes the number of $K_{s,t}$ in $n$-vertex triangle-free graphs if and only if $t<s+\frac12+\sqrt{2s+\frac14}$.

math.CO↗

arXiv2017

Fog Radio Access Networks: Mobility Management, Interference Mitigation and Resource Optimization

In order to make Internet connections ubiquitous and autonomous in our daily lives, maximizing the utilization of radio resources and social information is one of the major research topics in future mobile communication technologies. Fog radio access network (FRAN) is regarded as a promising paradigm for the fifth generation (5G) of mobile networks. FRAN integrates fog computing with RAN and makes full use of the edge of networks. FRAN would be different in networking, computing, storage and control as compared with conventional radio access networks (RAN) and the emerging cloud RAN. In this article, we provide a description of the FRAN architecture, and discuss how the distinctive characteristics of FRAN make it possible to efficiently alleviate the burden on the fronthaul, backhaul and backbone networks, as well as reduce content delivery latencies. We will focus on the mobility management, interference mitigation, and resource optimization in FRAN. Our simulation results show that the proposed FRAN architecture and the associated mobility and resource management mechanisms can reduce the signaling cost and increase the net utility for the RAN.

cs.IT↗

arXiv2017

Decorated marked surfaces II: Intersection numbers and dimensions of Homs

We study the 3-Calabi-Yau categories $\mathcal{D}$ arising from quivers with potential associated to a decorated marked surface $\mathbf{S}_\bigtriangleup$ introduced by the first author. We prove two conjectures in the prequel, that under a bijection between certain objects in $\mathcal{D}$ and certain arcs in $\mathbf{S}_\bigtriangleup$, the dimensions of morphisms between these objects equal the intersection numbers between the corresponding arcs.

math.RT↗

arXiv2017

Optical performance analysis of a porous open volumetric air receiver in a solar power tower

An optical model for a solar power tower with an open volumetric air receiver (OVAR) was developed in this paper, and the optical performance and characteristics of the OVAR were studied based on the model. Firstly, the detailed distributions of the non-uniform solar flux (qsr) on the aperture and the solar source (Ssr) in the OVAR were studied. The solar flux was found to be relatively uniform across the aperture for a single OVAR. However the incident angle of the rays varies between 0o and 42o, which indicates that the parallel assumption of the rays is not appropriate at this condition. Furthermore, the Ssr in the absorber decreases from the inlet to the outlet, and the maximum source (Ssr,max) of 2.414X108 Wm-3 appears at the inlet. Moreover, the Ssr,max was found to appear at the region near the wall rather than the center of the receiver as usual for the combined effect of the non-parallel incident rays and the diffuse reflection on the wall. In addition, study on effects of the porous parameters indicates that the solid emissivity influences both the Ssr distribution and the receiver efficiency significantly. However, the pore diameter and the porosity influence Ssr distribution importantly, but have negligible effect on the efficiency. Finally, the optical efficiency of 86.70%, reflection loss of 13.20% and transmission loss of 0.10% were found to be achieved by the OVAR.

physics.gen-ph↗

arXiv2017

Cluster categories for marked surfaces: punctured case

We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we show that there is a bijection between tagged curves and string objects. Applications include interpreting dimensions of $\operatorname{Ext}^1$ as intersection numbers of tagged curves and Auslander-Reiten translation as tagged rotation. An important consequence is that the cluster(-tilting) exchange graphs of such cluster categories are connected.

math.RT↗

arXiv2016

Turán number and decomposition number of intersecting odd cycles

An extremal graph for a given graph $H$ is a graph on $n$ vertices with maximum number of edges that does not contain $H$ as a subgraph. Let $s,t$ be integers and let $H_{s,t}$ be a graph consisting of $s$ triangles and $t$ cycles of odd lengths at least 5 which intersect in exactly one common vertex. Erdős et al. (1995) determined the extremal graphs for $H_{s,0}$. Recently, Hou et al. (2016) determined the extremal graphs for $H_{0,t}$, where the $t$ cycles have the same odd length $q$ with $q\ge 5$. In this paper, we further determine the extremal graphs for $H_{s,t}$ with $s\ge 0$ and $t\ge 1$. Let $ϕ(n,H)$ be the largest integer such that, for all graphs $G$ on $n$ vertices, the edge set $E(G)$ can be partitioned into at most $ϕ(n, H)$ parts, of which every part either is a single edge or forms a graph isomorphic to $H$. Pikhurko and Sousa conjectured that $ϕ(n,H)=\ex(n,H)$ for $χ(H)\geqs3$ and all sufficiently large $n$. Liu and Sousa (2015) verified the conjecture for $H_{s,0}$. In this paper, we further verify Pikhurko and Sousa's conjecture for $H_{s,t}$ with $s\ge 0$ and $t\ge 1$.

math.CO↗

arXiv2015

Extremal graph for intersecting odd cycles

An extremal graph for a graph $H$ on $n$ vertices is a graph on $n$ vertices with maximum number of edges that does not contain $H$ as a subgraph. Let $T_{n,r}$ be the Turán graph, which is the complete $r$-partite graph on $n$ vertices with part sizes that differ by at most one. The well-known Turán Theorem states that $T_{n,r}$ is the only extremal graph for complete graph $K_{r+1}$. Erdös et al. (1995) determined the extremal graphs for intersecting triangles and Chen et al. (2003) determined the maximum number of edges of the extremal graphs for intersecting cliques. In this paper, we determine the extremal graphs for intersecting odd cycles.

math.CO↗