Searcharxiv⌕ Search

arXiv subjects

Yi Sun

Publications and source records attributed to Yi Sun.

At least 163 records · Page 9Linked to original sources
arXiv2016

The polynomial representation of the type $A_{n - 1}$ rational Cherednik algebra in characteristic $p \mid n$

We study the polynomial representation of the rational Cherednik algebra of type $A_{n-1}$ with generic parameter in characteristic $p$ for $p \mid n$. We give explicit formulas for generators for the maximal proper graded submodule, show that they cut out a complete intersection, and thus compute the Hilbert series of the irreducible quotient. Our methods are motivated by taking characteristic $p$ analogues of existing characteristic $0$ results.

math.RT↗
arXiv2016

Elementary symmetric polynomials in Stanley--Reisner face ring

Let $P$ be a simple polytope of dimension $n$ with $m$ facets. In this paper we pay our attention on those elementary symmetric polynomials in the Stanley--Reisner face ring of $P$ and study how the decomposability of the $n$-th elementary symmetric polynomial influences on the combinatorics of $P$ and the topology and geometry of toric spaces over $P$. We give algebraic criterions of detecting the decomposability of $P$ and determining when $P$ is $n$-colorable in terms of the $n$-th elementary symmetric polynomial. In addition, we define the Stanley--Reisner {\em exterior} face ring $\mathcal{E}(K_P)$ of $P$, which is non-commutative in the case of ${\Bbb Z}$ coefficients, where $K_P$ is the boundary complex of dual of $P$. Then we obtain a criterion for the (real) Buchstaber invariant of $P$ to be $m-n$ in terms of the $n$-th elementary symmetric polynomial in $\mathcal{E}(K_P)$. Our results as above can directly associate with the topology and geometry of toric spaces over $P$. In particular, we show that the decomposability of the $n$-th elementary symmetric polynomial in $\mathcal{E}(K_P)$ with ${\Bbb Z}$ coefficients can detect the existence of the almost complex structures of quasitoric manifolds over $P$, and if the (real) Buchstaber invariant of $P$ is $m-n$, then there exists an essential relation between the $n$-th equivariant characteristic class of the (real) moment-angle manifold over $P$ in $\mathcal{E}(K_P)$ and the characteristic functions of $P$.

math.AT↗
arXiv2015

Improved Algorithms for Exact and Approximate Boolean Matrix Decomposition

An arbitrary $m\times n$ Boolean matrix $M$ can be decomposed {\em exactly} as $M =U\circ V$, where $U$ (resp. $V$) is an $m\times k$ (resp. $k\times n$) Boolean matrix and $\circ$ denotes the Boolean matrix multiplication operator. We first prove an exact formula for the Boolean matrix $J$ such that $M =M\circ J^T$ holds, where $J$ is maximal in the sense that if any 0 element in $J$ is changed to a 1 then this equality no longer holds. Since minimizing $k$ is NP-hard, we propose two heuristic algorithms for finding suboptimal but good decomposition. We measure the performance (in minimizing $k$) of our algorithms on several real datasets in comparison with other representative heuristic algorithms for Boolean matrix decomposition (BMD). The results on some popular benchmark datasets demonstrate that one of our proposed algorithms performs as well or better on most of them. Our algorithms have a number of other advantages: They are based on exact mathematical formula, which can be interpreted intuitively. They can be used for approximation as well with competitive "coverage." Last but not least, they also run very fast. Due to interpretability issues in data mining, we impose the condition, called the "column use condition," that the columns of the factor matrix $U$ must form a subset of the columns of $M$.

cs.DM↗
arXiv2015

Sparsifying Neural Network Connections for Face Recognition

This paper proposes to learn high-performance deep ConvNets with sparse neural connections, referred to as sparse ConvNets, for face recognition. The sparse ConvNets are learned in an iterative way, each time one additional layer is sparsified and the entire model is re-trained given the initial weights learned in previous iterations. One important finding is that directly training the sparse ConvNet from scratch failed to find good solutions for face recognition, while using a previously learned denser model to properly initialize a sparser model is critical to continue learning effective features for face recognition. This paper also proposes a new neural correlation-based weight selection criterion and empirically verifies its effectiveness in selecting informative connections from previously learned models in each iteration. When taking a moderately sparse structure (26%-76% of weights in the dense model), the proposed sparse ConvNet model significantly improves the face recognition performance of the previous state-of-the-art DeepID2+ models given the same training data, while it keeps the performance of the baseline model with only 12% of the original parameters.

cs.CV↗
arXiv2015

A new integral formula for Heckman-Opdam hypergeometric functions

We provide Harish-Chandra type formulas for the multivariate Bessel functions and Heckman-Opdam hypergeometric functions as representation-valued integrals over dressing orbits. Our expression is the quasi-classical limit of the realization of Macdonald polynomials as traces of intertwiners of quantum groups given by Etingof-Kirillov Jr. Integration over the Liouville tori of the Gelfand-Tsetlin integrable system and adjunction for higher Calogero-Moser Hamiltonians recovers and gives a new proof of the integral realization over Gelfand-Tsetlin polytopes which appeared in the recent work of Borodin-Gorin on the beta-Jacobi corners ensemble.

math.RT↗
arXiv2015

Traces of intertwiners for quantum affine sl_2 and Felder-Varchenko functions

We show that the traces of $U_q(\widehat{\mathfrak{sl}}_2)$-intertwiners of Etingof-Schiffmann-Varchenko valued in the three-dimensional evaluation representation converge in a certain region of parameters and give a representation-theoretic construction of Felder-Varchenko's hypergeometric solutions to the $q$-KZB heat equation. This gives the first proof that such a trace function converges and resolves the first case of the Etingof-Varchenko conjecture. As applications, we prove a symmetry property for traces of intertwiners and prove Felder-Varchenko's conjecture that their elliptic Macdonald polynomials are related to the affine Macdonald polynomials defined as traces over irreducible integrable $U_q(\widehat{\mathfrak{sl}}_2)$-modules by Etingof-Kirillov Jr. In the trigonometric and classical limits, we recover results of Etingof-Kirillov Jr. and Etingof-Varchenko. Our method relies on an interplay between the method of coherent states applied to the free field realization of the $q$-Wakimoto module of Matsuo, convergence properties given by the theta hypergeometric integrals of Felder-Varchenko, and rationality properties originating from the representation-theoretic definition of the trace function.

math.QA↗
arXiv2015

From random walks to distances on unweighted graphs

Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the significance of this problem, statistical characterization of the proposed metrics has been limited. We introduce and develop a class of techniques for analyzing random walks on graphs using stochastic calculus. Using these techniques we generalize results on the degeneracy of hitting times and analyze a metric based on the Laplace transformed hitting time (LTHT). The metric serves as a natural, provably well-behaved alternative to the expected hitting time. We establish a general correspondence between hitting times of the Brownian motion and analogous hitting times on the graph. We show that the LTHT is consistent with respect to the underlying metric of a geometric graph, preserves clustering tendency, and remains robust against random addition of non-geometric edges. Tests on simulated and real-world data show that the LTHT matches theoretical predictions and outperforms alternatives.

stat.ML↗
arXiv2015

Design of a 325MHz Half Wave Resonator prototype at IHEP

A 325MHz beta=0.14 superconducting half wave resonator(HWR) prototype has been developed at the Institute of High Energy Physics(IHEP), which can be applied in continuous wave (CW) high beam proton accelerators. In this paper, the electromagnetic (EM) design, multipacting simulation, mechanical optimization, and fabrication are introduced in details. In vertical test at 4.2K, the cavity reached Eacc=7MV/m with Q0=1.4*10^9 and Eacc=15.9MV/m with Q0=4.3*10^8.

physics.acc-ph↗
arXiv2015

Thickness dependence of superconductivity and superconductor-insulator transition in ultrathin FeSe films on SrTiO3(001) substrate

Interface-enhanced high-temperature superconductivity in one unit-cell (UC) FeSe film on SrTiO3(001) (STO) substrate has recently attracted much attention in condensed matter physics and material science. Here, by ex situ transport measurements, we report on the superconductivity in FeSe ultra-thin films with different thickness on STO substrate. We find that the onset superconducting transition temperature (Tc) decreases with increasing film thickness of FeSe, which is opposite to the behavior usually observed in traditional superconductor films. By systematic post-annealing of 5 UC FeSe films, we observe an insulator to superconductor transition, which is accompanied with a sign change of the dominated charge carriers from holes to electrons at low temperatures according to the corresponding Hall measurement.

cond-mat.supr-con↗
arXiv2015

Teaching a machine to see: unsupervised image segmentation and categorisation using growing neural gas and hierarchical clustering

We present a novel unsupervised learning approach to automatically segment and label images in astronomical surveys. Automation of this procedure will be essential as next-generation surveys enter the petabyte scale: data volumes will exceed the capability of even large crowd-sourced analyses. We demonstrate how a growing neural gas (GNG) can be used to encode the feature space of imaging data. When coupled with a technique called hierarchical clustering, imaging data can be automatically segmented and labelled by organising nodes in the GNG. The key distinction of unsupervised learning is that these labels need not be known prior to training, rather they are determined by the algorithm itself. Importantly, after training a network can be be presented with images it has never 'seen' before and provide consistent categorisation of features. As a proof-of-concept we demonstrate application on data from the Hubble Space Telescope Frontier Fields: images of clusters of galaxies containing a mixture of galaxy types that would easily be recognised and classified by a human inspector. By training the algorithm using one field (Abell 2744) and applying the result to another (MACS0416.1-2403), we show how the algorithm can cleanly separate image features that a human would associate with early and late type galaxies. We suggest that the algorithm has potential as a tool in the automatic analysis and data mining of next-generation imaging and spectral surveys, and could also find application beyond astronomy.

astro-ph.IM↗
arXiv2015

Analyzing TCP Throughput Stability and Predictability with Implications for Adaptive Video Streaming

Recent work suggests that TCP throughput stability and predictability within a video viewing session can inform the design of better video bitrate adaptation algorithms. Despite a rich tradition of Internet measurement, however, our understanding of throughput stability and predictability is quite limited. To bridge this gap, we present a measurement study of throughput stability using a large-scale dataset from a video service provider. Drawing on this analysis, we propose a simple-but-effective prediction mechanism based on a hidden Markov model and demonstrate that it outperforms other approaches. We also show the practical implications in improving the user experience of adaptive video streaming.

cs.NI↗
arXiv2015

DDA: Cross-Session Throughput Prediction with Applications to Video Bitrate Selection

User experience of video streaming could be greatly improved by selecting a high-yet-sustainable initial video bitrate, and it is therefore critical to accurately predict throughput before a video session starts. Inspired by previous studies that show similarity among throughput of similar sessions (e.g., those sharing same bottleneck link), we argue for a cross-session prediction approach, where throughput measured on other sessions is used to predict the throughput of a new session. In this paper, we study the challenges of cross-session throughput prediction, develop an accurate throughput predictor called DDA, and evaluate the performance of the predictor with real-world datasets. We show that DDA can predict throughput more accurately than simple predictors and conventional machine learning algorithms; e.g., DDA's 80%ile prediction error of DDA is > 50% lower than other algorithms. We also show that this improved accuracy enables video players to select a higher sustainable initial bitrate; e.g., compared to initial bitrate without prediction, DDA leads to 4x higher average bitrate.

cs.NI↗
arXiv2015

LazyCtrl: Scalable Network Control for Cloud Data Centers

The advent of software defined networking enables flexible, reliable and feature-rich control planes for data center networks. However, the tight coupling of centralized control and complete visibility leads to a wide range of issues among which scalability has risen to prominence. To address this, we present LazyCtrl, a novel hybrid control plane design for data center networks where network control is carried out by distributed control mechanisms inside independent groups of switches while complemented with a global controller. Our design is motivated by the observation that data center traffic is usually highly skewed and thus edge switches can be grouped according to traffic locality. LazyCtrl aims at bringing laziness to the global controller by dynamically devolving most of the control tasks to independent switch groups to process frequent intra-group events near datapaths while handling rare inter-group or other specified events by the controller. We implement LazyCtrl and build a prototype based on Open vSwich and Floodlight. Trace-driven experiments on our prototype show that an effective switch grouping is easy to maintain in multi-tenant clouds and the central controller can be significantly shielded by staying lazy, with its workload reduced by up to 82%.

cs.NI↗
arXiv2015

DeepID3: Face Recognition with Very Deep Neural Networks

The state-of-the-art of face recognition has been significantly advanced by the emergence of deep learning. Very deep neural networks recently achieved great success on general object recognition because of their superb learning capacity. This motivates us to investigate their effectiveness on face recognition. This paper proposes two very deep neural network architectures, referred to as DeepID3, for face recognition. These two architectures are rebuilt from stacked convolution and inception layers proposed in VGG net and GoogLeNet to make them suitable to face recognition. Joint face identification-verification supervisory signals are added to both intermediate and final feature extraction layers during training. An ensemble of the proposed two architectures achieves 99.53% LFW face verification accuracy and 96.0% LFW rank-1 face identification accuracy, respectively. A further discussion of LFW face verification result is given in the end.

cs.CV↗
arXiv2015

Detection of a superconducting phase in a two-atom layer of hexagonal Ga film grown on semiconducting GaN(0001)

The recent observation of superconducting state at atomic scale has motivated the pursuit of exotic condensed phases in two-dimensional (2D) systems. Here we report on a superconducting phase in two-monolayer crystalline Ga films epitaxially grown on wide band-gap semiconductor GaN(0001). This phase exhibits a hexagonal structure and only 0.552 nm in thickness, nevertheless, brings about a superconducting transition temperature Tc as high as 5.4 K, confirmed by in situ scanning tunneling spectroscopy, and ex situ electrical magneto-transport and magnetization measurements. The anisotropy of critical magnetic field and Berezinski-Kosterlitz-Thouless-like transition are observed, typical for the 2D superconductivity. Our results demonstrate a novel platform for exploring atomic-scale 2D superconductor, with great potential for understanding of the interface superconductivity.

cond-mat.supr-con↗
arXiv2014

Deeply learned face representations are sparse, selective, and robust

This paper designs a high-performance deep convolutional network (DeepID2+) for face recognition. It is learned with the identification-verification supervisory signal. By increasing the dimension of hidden representations and adding supervision to early convolutional layers, DeepID2+ achieves new state-of-the-art on LFW and YouTube Faces benchmarks. Through empirical studies, we have discovered three properties of its deep neural activations critical for the high performance: sparsity, selectiveness and robustness. (1) It is observed that neural activations are moderately sparse. Moderate sparsity maximizes the discriminative power of the deep net as well as the distance between images. It is surprising that DeepID2+ still can achieve high recognition accuracy even after the neural responses are binarized. (2) Its neurons in higher layers are highly selective to identities and identity-related attributes. We can identify different subsets of neurons which are either constantly excited or inhibited when different identities or attributes are present. Although DeepID2+ is not taught to distinguish attributes during training, it has implicitly learned such high-level concepts. (3) It is much more robust to occlusions, although occlusion patterns are not included in the training set.

cs.CV↗
arXiv2014

A representation-theoretic proof of the branching rule for Macdonald polynomials

We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of U_q(gl_n). In the Gelfand-Tsetlin basis, we show that diagonal matrix elements of such intertwiners are given by application of Macdonald's operators to a simple kernel. An essential ingredient in the proof is a map between spherical parts of double affine Hecke algebras of different ranks based upon the Dunkl-Kasatani conjecture.

math.RT↗