arXiv subjects

Hao Huang

Publications and source records attributed to Hao Huang.

At least 199 records · Page 11Linked to original sources

arXiv2019

Dynamic Graph Modules for Modeling Object-Object Interactions in Activity Recognition

Video action recognition, a critical problem in video understanding, has been gaining increasing attention. To identify actions induced by complex object-object interactions, we need to consider not only spatial relations among objects in a single frame, but also temporal relations among different or the same objects across multiple frames. However, existing approaches that model video representations and non-local features are either incapable of explicitly modeling relations at the object-object level or unable to handle streaming videos. In this paper, we propose a novel dynamic hidden graph module to model complex object-object interactions in videos, of which two instantiations are considered: a visual graph that captures appearance/motion changes among objects and a location graph that captures relative spatiotemporal position changes among objects. Additionally, the proposed graph module allows us to process streaming videos, setting it apart from existing methods. Experimental results on benchmark datasets, Something-Something and ActivityNet, show the competitive performance of our method.

cs.CV↗

arXiv2018

On subsets of the hypercube with prescribed Hamming distances

A celebrated theorem of Kleitman in extremal combinatorics states that a collection of binary vectors in $\{0, 1\}^n$ with diameter $d$ has cardinality at most that of a Hamming ball of radius $d/2$. In this paper, we give an algebraic proof of Kleitman's Theorem, by carefully choosing a pseudo-adjacency matrix for certain Hamming graphs, and applying the Cvetković bound on independence numbers. This method also allows us to prove several extensions and generalizations of Kleitman's Theorem to other allowed distance sets, in particular blocks of consecutive integers that do not necessarily grow linearly with $n$. We also improve on a theorem of Alon about subsets of $\mathbb{F}_{p}^{n}$ whose difference set does not intersect $\left\{0,1\right\}^{n}$ nontrivially.

math.CO↗

arXiv2018

Constructing Trivariate B-splines with Positive Jacobian by Pillow Operation and Geometric Iterative Fitting

The advent of isogeometric analysis has prompted a need for methods to generate Trivariate B-spline Solids (TBS) with positive Jacobian. However, it is difficult to guarantee a positive Jacobian of a TBS since the geometric pre-condition for ensuring the positive Jacobian is very complicated. In this paper, we propose a method for generating TBSs with guaranteed positive Jacobian. For the study, we used a tetrahedral (tet) mesh model and segmented it into sub-volumes using the pillow operation. Then, to reduce the difficulty in ensuring a positive Jacobian, we separately fitted the boundary curves and surfaces and the sub-volumes using a geometric iterative fitting algorithm. Finally, the smoothness between adjacent TBSs is improved. The experimental examples presented in this paper demonstrate the effectiveness and efficiency of the developed algorithm.

cs.GR↗

arXiv2018

Rainbow matchings in properly-colored hypergraphs

A hypergraph $H$ is properly colored if for every vertex $v\in V(H)$, all the edges incident to $v$ have distinct colors. In this paper, we show that if $H_{1}$, \cdots, $H_{s}$ are properly-colored $k$-uniform hypergraphs on $n$ vertices, where $n\geq3k^{2}s$, and $e(H_{i})>{{n}\choose {k}}-{{n-s+1}\choose {k}}$, then there exists a rainbow matching of size $s$, containing one edge from each $H_i$. This generalizes some previous results on the Erdős Matching Conjecture.

math.CO↗

arXiv2018

Two extremal problems on intersecting families

In this short note, we address two problems in extremal set theory regarding intersecting families. The first problem is a question posed by Kupavskii: is it true that given two disjoint cross-intersecting families $\mathcal{A}, \mathcal{B} \subset \binom{[n]}{k}$, they must satisfy $\min\{|\mathcal{A}|, |\mathcal{B}|\} \le \frac{1}{2} \binom{n-1}{k-1}$? We give an affirmative answer for $n \ge 2k^2$, and construct families showing that this range is essentially the best one could hope for, up to a constant factor. The second problem is a conjecture of Frankl. It states that for $n \ge 3k$, the maximum diversity of an intersecting family $\mathcal{F} \subset \binom{[n]}{k}$ is equal to $\binom{n-3}{k-2}$. We are able to find a construction beating the conjectured bound for $n$ slightly larger than $3k$, which also disproves a conjecture of Kupavskii.

math.CO↗

arXiv2017

On tight cycles in hypergraphs

A tight $k$-uniform $\ell$-cycle, denoted by $TC_\ell^k$, is a $k$-uniform hypergraph whose vertex set is $v_0, \cdots, v_{\ell-1}$, and the edges are all the $k$-tuples $\{v_i, v_{i+1}, \cdots, v_{i+k-1}\}$, with subscripts modulo $\ell$. Motivated by a classic result in graph theory that every $n$-vertex cycle-free graph has at most $n-1$ edges, Sós and, independently, Verstraëte asked whether for every integer $k$, a $k$-uniform $n$-vertex hypergraph without any tight $k$-uniform cycles has at most $\binom{n-1}{k-1}$ edges. In this paper, we answer this question in negative.

math.CO↗

arXiv2017

Spatiotemporal solitary modes in a twisted cylinder waveguide pipe with the self-focusing Kerr nonlinearity

We study the spatiotemporal solitary modes that propagate in a hollow twisted cylinder waveguide pipe with a self-focusing Kerr nonlinearity. Three generic solitary modes, one belonging to the zero-harmonic (0H) and the other two belonging to the first-harmonic (1H), are found in the first rotational Brillouin zone. The 0H solitary modes can be termed as a quasi-1D (one-dimensional) temporal soliton. Their characteristics depend only on the energy flow. The 1H solitary mode can be termed a quasi-2D (two-dimensional) bullet, whose width is much narrower than the angular domain of the waveguide. In contrast to the 0H mode, the characteristics of the 1H solitary mode depend on both their energy flow and the rotating speed of the waveguide. We demonstrate numerically that the 1H solitary modes are stable when their energy flow is smaller than the threshold norm of the \emph{Townes soliton}. The boundaries of the bistable area for these two types of solitary modes are predicted by the analyses via two-mode approximation. This prediction is in accordance with the numerical findings. We also demonstrate analytically that the 1H solitary mode of this system can be applied to emulate the nonlinear dynamics of solitary modes with 1D Rashba spin-orbit (SO) coupling by optics. Two degenerated states of the 1H solitary mode, semi-dipole and mixed mode, are found from this setting via the mechanism of SO coupling. Collisions between the pair of these two types of solitary modes are also discussed in the paper. The pair of the 0H solitary mode features only the elastic collision, whereas the pair of 1H solitary modes can feature both elastic and inelastic collision when the total energy flow of the two modes are smaller or close to the threshold norm of the \emph{Townes soliton}.

physics.optics↗

arXiv2017

Mandarin tone modeling using recurrent neural networks

We propose an Encoder-Classifier framework to model the Mandarin tones using recurrent neural networks (RNN). In this framework, extracted frames of features for tone classification are fed in to the RNN and casted into a fixed dimensional vector (tone embedding) and then classified into tone types using a softmax layer along with other auxiliary inputs. We investigate various configurations that help to improve the model, including pooling, feature splicing and utilization of syllable-level tone embeddings. Besides, tone embeddings and durations of the contextual syllables are exploited to facilitate tone classification. Experimental results on Mandarin tone classification show the proposed network setups improve tone classification accuracy. The results indicate that the RNN encoder-classifier based tone model flexibly accommodates heterogeneous inputs (sequential and segmental) and hence has the advantages from both the sequential classification tone models and segmental classification tone models.

cs.SD↗

arXiv2017

Dipolar bright solitons and solitary vortices in a radial lattice

Stabilizing vortex solitons with high values of the topological charge, S, is a challenging issue in optics, studies of Bose-Einstein condensates (BECs) and other fields. To develop a new approach to the solution of this problem, we consider a two-dimensional dipolar BEC under the action of an axisymmetric radially periodic lattice potential, $V(r)\sim \cos (2r+δ)$, with dipole moments polarized perpendicular to the system's plane, which gives rise to isotropic repulsive dipole-dipole interactions (DDIs). Two radial lattices are considered, with $δ=0$ and $π$, i.e., a potential maximum or minimum at $r=0$, respectively. Families of vortex gapsoliton (GSs) with $S=1$ and $S\geq 2$, the latter ones often being unstable in other settings, are completely stable in the present system (at least, up to $S=11$), being trapped in different annular troughs of the radial potential. The vortex solitons with different $S$ may stably coexist in sufficiently far separated troughs. Fundamental GSs, with $S=0$, are found too. In the case of $δ=0$, the fundamental solitons are ring-shaped modes, with a local minimum at $r=0.$At $δ=π$, they place a density peak at the center.

cond-mat.quant-gas↗

arXiv2017

Automatically Redundant Features Removal for Unsupervised Feature Selection via Sparse Feature Graph

The redundant features existing in high dimensional datasets always affect the performance of learning and mining algorithms. How to detect and remove them is an important research topic in machine learning and data mining research. In this paper, we propose a graph based approach to find and remove those redundant features automatically for high dimensional data. Based on the sparse learning based unsupervised feature selection framework, Sparse Feature Graph (SFG) is introduced not only to model the redundancy between two features, but also to disclose the group redundancy between two groups of features. With SFG, we can divide the whole features into different groups, and improve the intrinsic structure of data by removing detected redundant features. With accurate data structure, quality indicator vectors can be obtained to improve the learning performance of existing unsupervised feature selection algorithms such as multi-cluster feature selection (MCFS). Our experimental results on benchmark datasets show that the proposed SFG and feature redundancy remove algorithm can improve the performance of unsupervised feature selection algorithms consistently.

cs.LG↗

arXiv2017

A degree version of the Hilton--Milner theorem

An intersecting family of sets is trivial if all of its members share a common element. Hilton and Milner proved a strong stability result for the celebrated Erdős--Ko--Rado theorem: when $n> 2k$, every non-trivial intersecting family of $k$-subsets of $[n]$ has at most $\binom{n-1}{k-1}-\binom{n-k-1}{k-1}+1$ members. One extremal family $\mathcal{HM}_{n, k}$ consists of a $k$-set $S$ and all $k$-subsets of $[n]$ containing a fixed element $x\not\in S$ and at least one element of $S$. We prove a degree version of the Hilton--Milner theorem: if $n=Ω(k^2)$ and $\mathcal{F}$ is a non-trivial intersecting family of $k$-subsets of $[n]$, then $δ(\mathcal{F})\le δ(\mathcal{HM}_{n.k})$, where $δ(\mathcal{F})$ denotes the minimum (vertex) degree of $\mathcal{F}$. Our proof uses several fundamental results in extremal set theory, the concept of kernels, and a new variant of the Erdős--Ko--Rado theorem.

math.CO↗

arXiv2016

Degree versions of the Erdos-Ko-Rado Theorem and Erdos hypergraph matching conjecture

We use an algebraic method to prove a degree version of the celebrated Erd\H os-Ko-Rado theorem: given $n>2k$, every intersecting $k$-uniform hypergraph $H$ on $n$ vertices contains a vertex that lies on at most $\binom{n-2}{k-2}$ edges. This result can be viewed as a special case of the degree version of a well-known conjecture of Erdős on hypergraph matchings. Improving the work of Bollobás, Daykin, and Erd\H os from 1976, we show that given integers $n, k, s$ with $n\ge 3k^2 s$, every $k$-uniform hypergraph $H$ on $n$ vertices with minimum vertex degree greater than $\binom{n-1}{k-1}-\binom{n-s}{k-1}$ contains $s$ disjoint edges.

math.CO↗

arXiv2016

A note on the double-critical graph conjecture

A connected $n$-chromatic graph $G$ is double-critical if for all the edges $xy$ of $G$, the graph $G-x-y$ is $(n-2)$-chromatic. In 1966, Erd\H os and Lovász conjectured that the only double-critical $n$-chromatic graph is $K_n$. This conjecture remains unresolved for $n \ge 6.$ In this short note, we verify this conjecture for claw-free graphs $G$ of chromatic number $6$.

math.CO↗

arXiv2015

On graphs decomposable into induced matchings of linear sizes

We call a graph $G$ an $(r,t)$-Ruzsa-Szemerédi graph if its edge set can be partitioned into $t$ edge-disjoint induced matchings, each of size $r$. These graphs were introduced in 1978 and has been extensively studied since then. In this paper, we consider the case when $r=cn$. For $c>1/4$, we determine the maximum possible $t$ which is a constant depending only on $c$. On the other hand, when $c=1/4$, there could be as many as $Ω(\log n)$ induced matchings. We prove that this bound is tight up to a constant factor. Finally, when $c$ is fixed strictly between $1/5$ and $1/4$, we give a short proof that the number $t$ of induced matchings is $O(n/\log n)$. We are also able to further improve the upper bound to $o(n/\log n)$ for fixed $c> 1/4-b$ for some positive constant $b$.

math.CO↗

arXiv2015

Large Supports are required for Well-Supported Nash Equilibria

We prove that for any constant $k$ and any $ε<1$, there exist bimatrix win-lose games for which every $ε$-WSNE requires supports of cardinality greater than $k$. To do this, we provide a graph-theoretic characterization of win-lose games that possess $ε$-WSNE with constant cardinality supports. We then apply a result in additive number theory of Haight to construct win-lose games that do not satisfy the requirements of the characterization. These constructions disprove graph theoretic conjectures of Daskalakis, Mehta and Papadimitriou, and Myers.

cs.GT↗

arXiv2014

4 X 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer

Vector modes are spatial modes that have spatially inhomogeneous states of polarization, such as, radial and azimuthal polarization. They can produce smaller spot sizes and stronger longitudinal polarization components upon focusing. As a result, they are used for many applications, including optical trapping and nanoscale imaging. In this work, vector modes are used to increase the information capacity of free space optical communication via the method of optical communication referred to as mode division multiplexing. A mode (de)multiplexer for vector modes based on a liquid crystal technology referred to as a q-plate is introduced. As a proof of principle, using the mode (de)multiplexer four vector modes each carrying a 20 Gbit/s quadrature phase shift keying signal on a single wavelength channel (~1550nm), comprising an aggregate 80 Gbit/s, were transmitted ~1m over the lab table with <-16.4 dB (<2%) mode crosstalk. Bit error rates for all vector modes were measured at the forward error correction threshold with power penalties < 3.41dB.

physics.optics↗

arXiv2014

More on the bipartite decomposition of random graphs

For a graph $G=(V,E)$, let $bc(G)$ denote the minimum number of pairwise edge disjoint complete bipartite subgraphs of $G$ so that each edge of $G$ belongs to exactly one of them. It is easy to see that for every graph $G$, $bc(G) \leq n -α(G)$, where $α(G)$ is the maximum size of an independent set of $G$. Erdős conjectured in the 80s that for almost every graph $G$ equality holds, i.e., that for the random graph $G(n,0.5)$, $bc(G)=n-α(G)$ with high probability, that is, with probability that tends to 1 as $n$ tends to infinity. The first author showed that this is slightly false, proving that for most values of $n$ tending to infinity and for $G=G(n,0.5)$, $bc(G) \leq n-α(G)-1$ with high probability. We prove a stronger bound: there exists an absolute constant $c>0$ so that $bc(G) \leq n-(1+c)α(G)$ with high probability.

math.CO↗

arXiv2014

Performance Metrics and Design Parameters for a Free-space Communication Link Based on Multiplexing of Multiple Orbital-Angular-Momentum Beams

We study the design parameters for an orbital angular momentum (OAM) multiplexed free-space data link. Power loss, channel crosstalk and power penalty of the link are analyzed in the case of misalignment between the transmitter and receiver (lateral displacement, receiver angular error, or transmitter pointing error). The relationship among the system power loss and link distance, transmitted beam size and receiver aperture size are discussed based on the beam divergence due to free space propagation. We also describe the trade-offs for different receiver aperture sizes and mode spacing of the transmitted OAM beams under given lateral displacements or receiver angular errors. Through simulations and some experiments, we show that (1) a system with a larger transmitted beam size and a larger receiver aperture is more tolerant to the lateral displacement but less tolerant to the receiver angular error; (2) a system with a larger mode spacing, which uses larger OAM charges, suffers more system power loss but less channel crosstalk; thus, a system with a small mode spacing shows lower system power penalty when system power loss dominates (e.g., small lateral displacement or receiver angular error) while that with a larger mode spacing shows lower power penalty when channel crosstalk dominates (e.g., larger lateral displacement or receiver angular error); (3) the effects of lateral displacement and receiver angular error are not necessarily independent; as an example of them combined, the effects of the transmitter pointing error on the system are also investigated.

physics.optics↗