arXiv subjects

Ning Xu

Publications and source records attributed to Ning Xu.

At least 163 records · Page 9Linked to original sources

arXiv2018

Revealing the Link between Structural Relaxation and Dynamic Heterogeneity in Glass-Forming Liquids

Despite the use of glasses for thousands of years, the nature of the glass transition is still mysterious. On approaching the glass transition, the growth of dynamic heterogeneity has long been thought to play a key role in explaining the abrupt slowdown of structural relaxation. However, it still remains elusive whether there is an underlying link between structural relaxation and dynamic heterogeneity. Here we unravel the link by introducing a characteristic time scale hiding behind an identical dynamic heterogeneity for various model glass-forming liquids. We find that the time scale corresponds to the kinetic fragility of liquids. Moreover, it leads to scaling collapse of both the structural relaxation time and dynamic heterogeneity for all liquids studied, together with a characteristic temperature associated with the same dynamic heterogeneity. Our findings imply that studying the glass transition from the viewpoint of dynamic heterogeneity is more informative than expected.

cond-mat.soft↗

arXiv2018

Learning $3$D-FilterMap for Deep Convolutional Neural Networks

We present a novel and compact architecture for deep Convolutional Neural Networks (CNNs) in this paper, termed $3$D-FilterMap Convolutional Neural Networks ($3$D-FM-CNNs). The convolution layer of $3$D-FM-CNN learns a compact representation of the filters, named $3$D-FilterMap, instead of a set of independent filters in the conventional convolution layer. The filters are extracted from the $3$D-FilterMap as overlapping $3$D submatrics with weight sharing among nearby filters, and these filters are convolved with the input to generate the output of the convolution layer for $3$D-FM-CNN. Due to the weight sharing scheme, the parameter size of the $3$D-FilterMap is much smaller than that of the filters to be learned in the conventional convolution layer when $3$D-FilterMap generates the same number of filters. Our work is fundamentally different from the network compression literature that reduces the size of a learned large network in the sense that a small network is directly learned from scratch. Experimental results demonstrate that $3$D-FM-CNN enjoys a small parameter space by learning compact $3$D-FilterMaps, while achieving performance compared to that of the baseline CNNs which learn the same number of filters as that generated by the corresponding $3$D-FilterMap.

cs.LG↗

arXiv2017

Deep GrabCut for Object Selection

Most previous bounding-box-based segmentation methods assume the bounding box tightly covers the object of interest. However it is common that a rectangle input could be too large or too small. In this paper, we propose a novel segmentation approach that uses a rectangle as a soft constraint by transforming it into an Euclidean distance map. A convolutional encoder-decoder network is trained end-to-end by concatenating images with these distance maps as inputs and predicting the object masks as outputs. Our approach gets accurate segmentation results given sloppy rectangles while being general for both interactive segmentation and instance segmentation. We show our network extends to curve-based input without retraining. We further apply our network to instance-level semantic segmentation and resolve any overlap using a conditional random field. Experiments on benchmark datasets demonstrate the effectiveness of the proposed approaches.

cs.CV↗

arXiv2017

$\left( β, \varpi \right)$-stability for cross-validation and the choice of the number of folds

In this paper, we introduce a new concept of stability for cross-validation, called the $\left( β, \varpi \right)$-stability, and use it as a new perspective to build the general theory for cross-validation. The $\left( β, \varpi \right)$-stability mathematically connects the generalization ability and the stability of the cross-validated model via the Rademacher complexity. Our result reveals mathematically the effect of cross-validation from two sides: on one hand, cross-validation picks the model with the best empirical generalization ability by validating all the alternatives on test sets; on the other hand, cross-validation may compromise the stability of the model selection by causing subsampling error. Moreover, the difference between training and test errors in q\textsuperscript{th} round, sometimes referred to as the generalization error, might be autocorrelated on q. Guided by the ideas above, the $\left( β, \varpi \right)$-stability help us derivd a new class of Rademacher bounds, referred to as the one-round/convoluted Rademacher bounds, for the stability of cross-validation in both the i.i.d.\ and non-i.i.d.\ cases. For both light-tail and heavy-tail losses, the new bounds quantify the stability of the one-round/average test error of the cross-validated model in terms of its one-round/average training error, the sample sizes $n$, number of folds $K$, the tail property of the loss (encoded as Orlicz-$Ψ_ν$ norms) and the Rademacher complexity of the model class $Λ$. The new class of bounds not only quantitatively reveals the stability of the generalization ability of the cross-validated model, it also shows empirically the optimal choice for number of folds $K$, at which the upper bound of the one-round/average test error is lowest, or, to put it in another way, where the test error is most stable.

stat.ML↗

arXiv2017

Type-I and type-II topological nodal superconductors with $s$-wave interaction

Topological nodal superconductors are generally realized based on unconventional pairings. In this work, we propose a minimal model to realize these topological nodal phases with only $s$-wave interaction. In our model the linear and quadratic spin-orbit couplings along the two directions break the isotropy in momentum space and introduce effective unconventional pairings on the Fermi surface. This model may support different nodal superconducting phases characterized by either winding number in BDI class or Pfaffian in D class at the particle-hole invariant axes. In the vicinity of the nodal points the effective Hamiltonian can be described by either type-I or type-II Dirac equation; and the crossover between these two nodal points can be driven by external Zeeman fields. We show that these nodal phases are robust against weak disorders, thus are possible to be realized in experiments with real materials. The smoking-gun evidences to verify these phases based on scanning tunneling spectroscopy are also briefly discussed.

cond-mat.supr-con↗

arXiv2017

Deep Image Matting

Image matting is a fundamental computer vision problem and has many applications. Previous algorithms have poor performance when an image has similar foreground and background colors or complicated textures. The main reasons are prior methods 1) only use low-level features and 2) lack high-level context. In this paper, we propose a novel deep learning based algorithm that can tackle both these problems. Our deep model has two parts. The first part is a deep convolutional encoder-decoder network that takes an image and the corresponding trimap as inputs and predict the alpha matte of the image. The second part is a small convolutional network that refines the alpha matte predictions of the first network to have more accurate alpha values and sharper edges. In addition, we also create a large-scale image matting dataset including 49300 training images and 1000 testing images. We evaluate our algorithm on the image matting benchmark, our testing set, and a wide variety of real images. Experimental results clearly demonstrate the superiority of our algorithm over previous methods.

cs.CV↗

arXiv2017

Instabilities of jammed packings of frictionless spheres under compression

We consider the contribution to the density of vibrational states and the distribution of energy barrier heights of incipient instabilities in a glass modeled by a jammed packing of spheres. On approaching an instability, the frequency of a normal mode and the height of the energy barrier to cross into a new ground state both vanish. These instabilities produce a contribution to the density of vibrational states that scales as $ω^3$ at low frequencies $ω$, but which vanishes in the thermodynamic limit. In addition, they affect an anharmonic property, the distribution of energy barriers $ΔH$, giving a contribution that scales as $ΔH^{-1/3}$ at low barrier heights, which should be universal for jammed and glassy systems.

cond-mat.soft↗

arXiv2017

Self-assembling two-dimensional quasicrystals in simple systems of monodisperse soft-core disks

In previous approaches to form quasicrystals, multiple competing length scales involved in particle size, shape or interaction potential are believed to be necessary. It is unexpected that quasicrystals can be self-assembled by monodisperse, isotropic particles interacting via a simple potential without multiple length scales. Here we report the surprising finding of the self-assembly of such quasicrystals in two dimensional systems of soft-core disks interacting via repulsions. We find not only dodecagonal but also octagonal quasicrystals, which have not been found yet in soft quasicrystals. In the self-assembly of such unexpected quasicrystals, particles tend to form pentagons, which are essential elements to form the quasicrystalline order. Our findings pave an unexpected and simple way to form quasicrystals and pose a new challenge for theoretical understanding of quasicrystals.

cond-mat.soft↗

arXiv2017

Role of disorder in determining the vibrational properties of mass-spring networks

By introducing four fundamental types of disorders into a two-dimensional triangular lattice separately, we determine the role of each type of disorder in the vibration of the resulting mass-spring networks. We are concerned mainly with the origin of the boson peak and the connection between the boson peak and the transverse Ioffe-Regel limit. For all types of disorders, we observe the emergence of the boson peak and Ioffe-Regel limits. With increasing disorder, the boson peak frequency $ω_{BP}$, transverse Ioffe-Regel frequency $ω_{IR}^T$, and longitudinal Ioffe-Regel frequency $ω_{IR}^L$ all decrease. We find that there are two ways for the boson peak to form: developing from and coexisting with (but remaining independent of) the transverse van Hove singularity without and with local coordination number fluctuation. In the presence of a single type of disorder, $ω_{IR}^T\ge ω_{BP}$, and $ω_{IR}^T\approx ω_{BP}$ only when the disorder is sufficiently strong and causes spatial fluctuation of the local coordination number. Moreover, if there is no positional disorder, $ω_{IR}^T\approx ω_{IR}^L$. Therefore, the argument that the boson peak is equivalent to the transverse Ioffe-Regel limit is not general. Our results suggest that both local coordination number and positional disorder are necessary for the argument to hold, which is actually the case for most disordered solids such as marginally jammed solids and structural glasses. We further combine two types of disorders to cause disorder in both the local coordination number and lattice site position. The density of vibrational states of the resulting networks resembles that of marginally jammed solids well. However, the relation between the boson peak and the transverse Ioffe-Regel limit is still indefinite and condition-dependent.

cond-mat.soft↗

arXiv2016

Magnetic excitations in the normal and nematic phases of iron pnictides

In this paper, we study theoretically the behaviors of the magnetic excitations(MEs) in the normal and nematic phases of iron pnictides. The normal state MEs exhibit commensurability to diamond and to square-like structure transition with the increase of energy. This structure transition persists in the spin and orbital scenarios of nematic phases, although the MEs show anisotropic behaviors due to the C4 symmetry breaking induced by the nematic orders. The MEs exhibit distinct energy evolution behaviors between the spin and orbital scenarios of nematicity. For the spinnematic scenario, the anisotropy of the MEs persists up to the high energy region. In contrast, for the orbital-nematic scenario, it reduces dramatically in the low energy region and is negligible in the high energy region. These distinct behaviors of the MEs are attributed to the different origins between the spin and orbital scenarios of nematic orders.

cond-mat.str-el↗

arXiv2016

Generalization error minimization: a new approach to model evaluation and selection with an application to penalized regression

We study model evaluation and model selection from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. We believe that GA is one way formally to address concerns about the external validity of a model. The GA of a model estimated on a sample can be measured by its empirical out-of-sample errors, called the generalization errors (GE). We derive upper bounds for the GE, which depend on sample sizes, model complexity and the distribution of the loss function. The upper bounds can be used to evaluate the GA of a model, ex ante. We propose using generalization error minimization (GEM) as a framework for model selection. Using GEM, we are able to unify a big class of penalized regression estimators, including lasso, ridge and bridge, under the same set of assumptions. We establish finite-sample and asymptotic properties (including $\mathcal{L}_2$-consistency) of the GEM estimator for both the $n \geqslant p$ and the $n < p$ cases. We also derive the $\mathcal{L}_2$-distance between the penalized and corresponding unpenalized regression estimates. In practice, GEM can be implemented by validation or cross-validation. We show that the GE bounds can be used for selecting the optimal number of folds in $K$-fold cross-validation. We propose a variant of $R^2$, the $GR^2$, as a measure of GA, which considers both both in-sample and out-of-sample goodness of fit. Simulations are used to demonstrate our key results.

stat.ML↗

arXiv2016

Finite-sample and asymptotic analysis of generalization ability with an application to penalized regression

In this paper, we study the performance of extremum estimators from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. By adapting the classical concentration inequalities, we derive upper bounds on the empirical out-of-sample prediction errors as a function of the in-sample errors, in-sample data size, heaviness in the tails of the error distribution, and model complexity. We show that the error bounds may be used for tuning key estimation hyper-parameters, such as the number of folds $K$ in cross-validation. We also show how $K$ affects the bias-variance trade-off for cross-validation. We demonstrate that the $\mathcal{L}_2$-norm difference between penalized and the corresponding un-penalized regression estimates is directly explained by the GA of the estimates and the GA of empirical moment conditions. Lastly, we prove that all penalized regression estimates are $L_2$-consistent for both the $n \geqslant p$ and the $n < p$ cases. Simulations are used to demonstrate key results. Keywords: generalization ability, upper bound of generalization error, penalized regression, cross-validation, bias-variance trade-off, $\mathcal{L}_2$ difference between penalized and unpenalized regression, lasso, high-dimensional data.

stat.ML↗

arXiv2016

Density affects the nature of the hexatic-liquid transition in two-dimensional melting of core-softened systems

We find that both continuous and discontinuous hexatic-liquid transitions can happen in the melting of two-dimensional solids of soft-core disks. For three typical model systems, Hertzian, harmonic, and Gaussian-core models, we observe the same scenarios. These systems exhibit reentrant crystallization (melting) with a maximum melting temperature $T_m$ happening at a crossover density $ρ_m$. The hexatic-liquid transition at a density smaller than $ρ_m$ is discontinuous. Liquid and hexatic phases coexist in a density interval, which becomes narrower with increasing temperature and tends to vanish approximately at $T_m$. Above $ρ_m$, the transition is continuous, in agreement with the Kosterlitz-Thouless-Halperin-Nelson-Young theory. For these soft-core systems, the nature of the hexatic-liquid transition depends on density (pressure), with the melting at $ρ_m$ being a plausible transition point from discontinuous to continuous hexatic-liquid transition.

cond-mat.soft↗

arXiv2016

Model selection consistency from the perspective of generalization ability and VC theory with an application to Lasso

Model selection is difficult to analyse yet theoretically and empirically important, especially for high-dimensional data analysis. Recently the least absolute shrinkage and selection operator (Lasso) has been applied in the statistical and econometric literature. Consis- tency of Lasso has been established under various conditions, some of which are difficult to verify in practice. In this paper, we study model selection from the perspective of generalization ability, under the framework of structural risk minimization (SRM) and Vapnik-Chervonenkis (VC) theory. The approach emphasizes the balance between the in-sample and out-of-sample fit, which can be achieved by using cross-validation to select a penalty on model complexity. We show that an exact relationship exists between the generalization ability of a model and model selection consistency. By implementing SRM and the VC inequality, we show that Lasso is L2-consistent for model selection under assumptions similar to those imposed on OLS. Furthermore, we derive a probabilistic bound for the distance between the penalized extremum estimator and the extremum estimator without penalty, which is dominated by overfitting. We also propose a new measurement of overfitting, GR2, based on generalization ability, that converges to zero if model selection is consistent. Using simulations, we demonstrate that the proposed CV-Lasso algorithm performs well in terms of model selection and overfitting control.

stat.ML↗

arXiv2016

Deep Interactive Object Selection

Interactive object selection is a very important research problem and has many applications. Previous algorithms require substantial user interactions to estimate the foreground and background distributions. In this paper, we present a novel deep learning based algorithm which has a much better understanding of objectness and thus can reduce user interactions to just a few clicks. Our algorithm transforms user provided positive and negative clicks into two Euclidean distance maps which are then concatenated with the RGB channels of images to compose (image, user interactions) pairs. We generate many of such pairs by combining several random sampling strategies to model user click patterns and use them to fine tune deep Fully Convolutional Networks (FCNs). Finally the output probability maps of our FCN 8s model is integrated with graph cut optimization to refine the boundary segments. Our model is trained on the PASCAL segmentation dataset and evaluated on other datasets with different object classes. Experimental results on both seen and unseen objects clearly demonstrate that our algorithm has a good generalization ability and is superior to all existing interactive object selection approaches.

cs.CV↗

arXiv2016

Shear induced solidification of athermal systems with weak attraction

We find that unjammed packings of frictionless particles with rather weak attraction can always be driven into solid-like states by shear. The structure of shear-driven solids evolves continuously with packing fraction from gel-like to jamming-like, but is almost independent of the shear stress. In contrast, both the density of vibrational states (DOVS) and force network evolve progressively with the shear stress. There exists a packing fraction independent shear stress $σ_c$, at which the shear-driven solids are isostatic and have a flattened DOVS. Solid-like states induced by a shear stress greater than $σ_c$ possess properties of marginally jammed solids and are thus strictly-defined shear jammed states. Below $σ_c$, states at all packing fractions are under isostaticity and share common features in the DOVS and force network, although their structures can be rather different. Our study reveals the significance of the shear stress in determining properties of shear-driven solids and leads to an enriched jamming phase diagram for weakly attractive particles.

cond-mat.soft↗

arXiv2015

From Crystals to Disordered Crystals: A Hidden Order-Disorder Transition

We find an order-disorder transition from crystals to disordered crystals for static packings of frictionless spheres. While the geometric indicators are mostly blind to the transition, disordered crystals already exhibit properties apart from crystals. The transition approaches the close packing of hard spheres, giving rise to the singularity of the close packing point. We evidence that both the transition and properties of disordered crystals are jointly determined by the structural orders and density. Near the transition, the elastic moduli and coordination number of disordered crystals show particular pressure dependence distinct from both crystals and jammed solids.

cond-mat.soft↗

arXiv2015

Increment entropy as a measure of complexity for time series

Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce increment entropy to measure the complexity of time series in which each increment is mapped into a word of two letters, one letter corresponding to direction and the other corresponding to magnitude. The Shannon entropy of the words is termed as increment entropy (IncrEn). Simulations on synthetic data and tests on epileptic EEG signals have demonstrated its ability of detecting the abrupt change, regardless of energetic (e.g. spikes or bursts) or structural changes. The computation of IncrEn does not make any assumption on time series and it can be applicable to arbitrary real-world data.

physics.data-an↗