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Hao Yin

Publications and source records attributed to Hao Yin.

At least 91 records · Page 5Linked to original sources
arXiv2020

Measuring Directed Triadic Closure with Closure Coefficients

Recent work studying triadic closure in undirected graphs has drawn attention to the distinction between measures that focus on the "center" node of a wedge (i.e., length-2 path) vs. measures that focus on the "initiator," a distinction with considerable consequences. Existing measures in directed graphs, meanwhile, have all been center-focused. In this work, we propose a family of eight directed closure coefficients that measure the frequency of triadic closure in directed graphs from the perspective of the node initiating closure. The eight coefficients correspond to different labelled wedges, where the initiator and center nodes are labelled, and we observe dramatic empirical variation in these coefficients on real-world networks, even in cases when the induced directed triangles are isomorphic. To understand this phenomenon, we examine the theoretical behavior of our closure coefficients under a directed configuration model. Our analysis illustrates an underlying connection between the closure coefficients and moments of the joint in- and out-degree distributions of the network, offering an explanation of the observed asymmetries. We also use our directed closure coefficients as predictors in two machine learning tasks. We find interpretable models with AUC scores above 0.92 in class-balanced binary prediction, substantially outperforming models that use traditional center-focused measures.

cs.SI↗
arXiv2019

Optical Superoscillatory Poisson-Arago Spots

Optical diffraction limit has been a long-term scientific issue since Ernst Abbe first introduced the concept in 1873. It is a constraint on the smallest light spot that can be achieved. Substantial effort has been invested in the past decade to beat this limit by exploiting evanescent waves. But this method encounters serious near-field limitations. A more promising route to breaking the constraint is to explore optical superoscillation in the far field with engineered metamaterials. However, these particular structures involve with very complicated optimization-based design that requires precisely tailoring the interference of propagating waves with low spatial frequency. To overcome these limitations, here we explore a new approach based on the two-hundred-year-old discovery: Possion-Arago spots. We show for the first time that by using a single disc, constructive interference of propagating waves with high-spatial-frequency wavevectors can be realized, generating a diffraction-unlimited localized Possion-Arago spot with achievable size down to $λ/$20. Actually, such an element permits creation of an ultra-long nearly nondiffracting superoscillatory needle with appreciable field of view. This easy-to-fabrication element provides a promising route to overcome the diffraction limit, thus might open new avenues to exploit various applications in different fields.

physics.optics↗
arXiv2019

Closed-Loop Sparse Channel Estimation for Wideband Millimeter-Wave Full-Dimensional MIMO Systems

This paper proposes a closed-loop sparse channel estimation (CE) scheme for wideband millimeter-wave hybrid full-dimensional multiple-input multiple-output and time division duplexing based systems, which exploits the channel sparsity in both angle and delay domains. At the downlink CE stage, random transmit precoder is designed at base station (BS) for channel sounding, and receive combiners at user devices (UDs) are designed to visualize hybrid array as a low-dimensional digital array for facilitating the multi-dimensional unitary ESPRIT (MDU-ESPRIT) algorithm to estimate respective angle-of-arrivals (AoAs). At the uplink CE stage, the estimated downlink AoAs, namely, uplink angle-of-departures (AoDs), are exploited to design multi-beam transmit precoder at UDs to enable BS to estimate the uplink AoAs, i.e., the downlink AoDs, and delays of different UDs using the MDU-ESPRIT algorithm based on the designed receive combiners at BS. Furthermore, a maximum likelihood approach is proposed to pair the channel parameters acquired at the two stages, and the path gains are then obtained using least squares estimator. According to spectrum estimation theory, our solution can acquire the super-resolution estimations of the AoAs/AoDs and delays of sparse multipath components with low training overhead. Simulation results verify the better CE performance and lower computational complexity of our solution over existing state-of-the-art approaches.

cs.IT↗
arXiv2019

Higher order neck analysis of harmonic maps and its applications

In this paper, we prove some refined estimate in the neck region when a sequence of harmonic maps from surfaces blow up. The new estimate allows us to see the shape of the center of the neck region. As an application, we prove an inequality about the nullity and index when blow-up occurs.

math.DG↗
arXiv2018

Uniqueness of tangent cone for biharmonic map with isolated singularity

In this paper, we study the problem of uniqueness of tangent cone for minimizing extrinsic biharmonic maps. Following the celebrated result of Simon, we prove that if the target manifold is a compact analytic submanifold in R p and if there is one tangent map whose singularity set consists of the origin only, then this tangent map is unique.

math.AP↗
arXiv2018

Schauder estimates on smooth and singular spaces

In this paper, we present a proof of Schauder estimate on Euclidean space and use it to generalize Donaldson's Schauder estimate on space with conical singularities in the following two directions. The first is that we allow the total cone angle to be larger than 2$π$ and the second is that we discuss higher order estimates.

math.AP↗
arXiv2018

Higher-order clustering in networks

A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a triangle in the network. However, higher-order cliques beyond triangles are crucial to understanding complex networks, and the clustering behavior with respect to such higher-order network structures is not well understood. Here we introduce higher-order clustering coefficients that measure the closure probability of higher-order network cliques and provide a more comprehensive view of how the edges of complex networks cluster. Our higher-order clustering coefficients are a natural generalization of the traditional clustering coefficient. We derive several properties about higher-order clustering coefficients and analyze them under common random graph models. Finally, we use higher-order clustering coefficients to gain new insights into the structure of real-world networks from several domains.

cs.SI↗
arXiv2017

Strong NP-Hardness for Sparse Optimization with Concave Penalty Functions

Consider the regularized sparse minimization problem, which involves empirical sums of loss functions for $n$ data points (each of dimension $d$) and a nonconvex sparsity penalty. We prove that finding an $\mathcal{O}(n^{c_1}d^{c_2})$-optimal solution to the regularized sparse optimization problem is strongly NP-hard for any $c_1, c_2\in [0,1)$ such that $c_1+c_2<1$. The result applies to a broad class of loss functions and sparse penalty functions. It suggests that one cannot even approximately solve the sparse optimization problem in polynomial time, unless P $=$ NP.

math.OC↗
arXiv2016

Analysis aspects of Ricci flow on conical surfaces

In this paper, we establish a framework for the analysis of linear parabolic equations on conical surfaces and use them to study the conical Ricci flow. In particular, we prove the long time existence of the conical Ricci flow for general cone angle and show that this solution has the optimal regularity, namely, the time derivatives of the conformal factor are bounded and for each fixed time, the conformal factor has an explicit asymptotic expansion near the cone points.

math.AP↗
arXiv2015

Sharp decay estimates for the logarithmic fast diffusion equation and the Ricci flow on surfaces

We prove the sharp local L^1 - L^\infty smoothing estimate for the logarithmic fast diffusion equation, or equivalently, for the Ricci flow on surfaces. Our estimate almost instantly implies an improvement of the known L^p - L^\infty estimate for p larger than 1. It also has several applications in geometry, providing the missing step in order to pose the Ricci flow with rough initial data in the noncompact case, for example starting with a general noncompact Alexandrov surface, and giving the sharp asymptotics for the contracting cusp Ricci flow, as we show elsewhere.

math.AP↗
arXiv2015

Ricci flow on surfaces with conical singularities

This paper studies the normalized Ricci flow on surfaces with conical singularities. It's proved that the normalized Ricci flow has a solution for a short time for initial metrics with conical singularities. Moreover, the solution makes good geometric sense. For some simple surfaces of this kind, for example, the tear drop and the football, it's shown that they admit Ricci soliton metric.

math.DG↗
arXiv2015

Ricci flow on surfaces with conical singularities, II

In this paper, we study the (normalized) Ricci flow on surfaces with conical singularities. Long time existence is proved for cone angle smaller than $2π$. In this case, convergence results are obtained if the Euler number is nonpositive.

math.DG↗
arXiv2013

Neck analysis for biharmonic maps

In this paper, we study the blow up of a sequence of (both extrinsic and intrinsic) biharmonic maps in dimension four with bounded energy and show that there is no neck in this process. Moreover, we apply the method to provide new proofs to the removable singularity theorem and energy identity theorem of biharmonic maps.

math.AP↗
arXiv2013

The Yang-Mills α-flow in vector bundles over four manifolds and its applications

In this paper, we introduce an α-flow for the Yang-Mills functional in vector bundles over four dimensional Riemannian manifolds, and establish global existence of a unique smooth solution to the α-flow with smooth initial value. We prove that the limit of solutions of the α-flow as α\to 1 is a weak solution to the Yang-Mills flow. By an application of the α-flow, we then follow the idea of Sacks and Uhlenbeck to prove some existence results for Yang-Mills connections and improve the minimizing result of the Yang-Mills functional of Sedlacek.

math.DG↗