arXiv subjects

Hao Yu

Publications and source records attributed to Hao Yu.

At least 253 records · Page 14Linked to original sources

arXiv2020

Constraint on the radius of five-dimensional dS spacetime with GW170817 and GRB 170817A

The recent detections of the gravitational wave (GW) event GW170817 and its electromagnetic counterpart GRB 170817A produced by a binary neutron star (NS) merger is a new milestone of multimessenger astronomy. The time interval between these two signals has attracted widespread attention from physicists. In the braneworld scenario, GWs could propagate through the bulk while electromagnetic waves (EMWs) are bounded on the brane, i.e., our Universe. Therefore, the trajectories of GWs and EMWs may follow different pathes. If GWs and EMWs are originated simultaneously from the same source on the brane, they are expected to arrive at the observer successively. Consequently, the time delay between GW170817 and GRB 170817A may carry the information of the extra dimension. In this paper, we try to investigate the phenomenon in the context of a five-dimensional dS ($\text{dS}_5$) spacetime. We first study two special Universe models, i.e., de Sitter and Einstein-de Sitter models, and calculate the gravitation horizon radius in each case. For the real Universe, we then consider the $Λ$CDM model. Our results show that for the de Sitter model of the Universe, the $\text{dS}_5$ radius could not contribute to the time delay. With the data of the observation, we constrain the $\text{dS}_5$ radius to $\ell\gtrsim7.5\times10^{2}\,\text{Tpc}$ for the Einstein-de Sitter model and $\ell\gtrsim2.4\times10^{3}\,\text{Tpc}$ for the $Λ$CDM model. After considering the uncertainty in the source redshift and the time-lags given by different astrophysical processes of the binary NS merger, we find that our constraints are not sensitive to the redshift in the range of (0.005, 0.01) and the time-lag in the range of (-100s, 1.734s).

gr-qc↗

arXiv2020

A Low Complexity Algorithm with $O(\sqrt{T})$ Regret and $O(1)$ Constraint Violations for Online Convex Optimization with Long Term Constraints

This paper considers online convex optimization over a complicated constraint set, which typically consists of multiple functional constraints and a set constraint. The conventional online projection algorithm (Zinkevich, 2003) can be difficult to implement due to the potentially high computation complexity of the projection operation. In this paper, we relax the functional constraints by allowing them to be violated at each round but still requiring them to be satisfied in the long term. This type of relaxed online convex optimization (with long term constraints) was first considered in Mahdavi et al. (2012). That prior work proposes an algorithm to achieve $O(\sqrt{T})$ regret and $O(T^{3/4})$ constraint violations for general problems and another algorithm to achieve an $O(T^{2/3})$ bound for both regret and constraint violations when the constraint set can be described by a finite number of linear constraints. A recent extension in \citet{Jenatton16ICML} can achieve $O(T^{\max\{θ,1-θ\}})$ regret and $O(T^{1-θ/2})$ constraint violations where $θ\in (0,1)$. The current paper proposes a new simple algorithm that yields improved performance in comparison to prior works. The new algorithm achieves an $O(\sqrt{T})$ regret bound with $O(1)$ constraint violations.

math.OC↗

arXiv2020

A Very Simple Estimate Of Rational Homological Dimension Of Moduli Spaces Of Riemann Surfaces With Boundary And Marked Points

The moduli spaces of compact and connected Riemann surfaces has been a central topic in modern mathematics in recent years. Thus their homological dimensions become important invariants. Motivated by the emergence mathematical counterparts of open-closed string theory, we give an estimate of rational homological dimension of Riemann suraces with possible boundary and marked points(can lie on both interior and boundary). We hope it will have applications in open-closed theory, for example, open-closed Gromov-Witten theory in the future.

math.QA↗

arXiv2020

Topology control of human cells monolayer by liquid crystal elastomer

Biological cells in living tissues form dynamic patterns with local orientational order and topological defects. Here we demonstrate an approach to produce cell monolayer with the predesigned orientational patterns using human dermal fibroblast cells (HDF) placed onto a photoaligned liquid crystal elastomer (LCE). The alignment of cells is caused by anisotropic swelling of the substrates in contact with the aqueous cell growth medium. The patterns predesigned in the LCE cause a strong spatial variation of cell phenotype (evidenced by shape variations), their surface density and number density fluctuations. The concentration of cells is significantly higher near the cores of positive-strength defects as compared to negative-strength defects. Unbinding of defect pairs intrinsic to active matter is suppressed by anisotropic surface anchoring. The geometry of arrays allows one to estimate the elastic and surface anchoring characteristics of the tissues. The demonstrated patterned LCE approach could be used to control the collective behavior of cells in living tissues, cell differentiation, and tissue morphogenesis.

physics.bio-ph↗

arXiv2020

HOTCAKE: Higher Order Tucker Articulated Kernels for Deeper CNN Compression

The emerging edge computing has promoted immense interests in compacting a neural network without sacrificing much accuracy. In this regard, low-rank tensor decomposition constitutes a powerful tool to compress convolutional neural networks (CNNs) by decomposing the 4-way kernel tensor into multi-stage smaller ones. Building on top of Tucker-2 decomposition, we propose a generalized Higher Order Tucker Articulated Kernels (HOTCAKE) scheme comprising four steps: input channel decomposition, guided Tucker rank selection, higher order Tucker decomposition and fine-tuning. By subjecting each CONV layer to HOTCAKE, a highly compressed CNN model with graceful accuracy trade-off is obtained. Experiments show HOTCAKE can compress even pre-compressed models and produce state-of-the-art lightweight networks.

cs.LG↗

arXiv2020

Particle and entropy production in the Running Vacuum Universe

We study particle production and the corresponding entropy increase in the context of cosmology with dynamical vacuum. We focus on the particular form that has been called "running vacuum model" (RVM), which is known to furnish a successful description of the overall current observations at a competitive level with the concordance $Λ$CDM model. It also provides an elegant global explanation of the cosmic history from a non-singular initial state in the very early universe up to our days and further into the final de Sitter era. The model has no horizon problem and provides an alternative explanation for the early inflation and its graceful exit, as well as a powerful mechanism for generating the large entropy of the current universe. The energy-momentum tensor of matter is generally non-conserved in such context owing to particle creation or annihilation. We analyze general thermodynamical aspects of particle and entropy production in the RVM. We first study the entropy of particles in the comoving volume during the early universe and late universe. Then, in order to obtain a more physical interpretation, we pay attention to the entropy contribution from the cosmological apparent horizon, its interior and its surface. On combining the inner volume entropy with the entropy on the horizon, we elucidate with detailed calculations whether the evolution of the entropy of the RVM universe satisfies the Generalized Second Law of Thermodynamics. We find it is so and we prove that the essential reason for it is the existence of a positive cosmological constant.

gr-qc↗

arXiv2020

Polar jets of swimming bacteria condensed by a patterned liquid crystal

Active matter exhibits remarkable collective behavior in which flows, continuously generated by active particles, are intertwined with the orientational order of these particles. The relationship remains poorly understood as the activity and order are difficult to control independently. Here we demonstrate important facets of this interplay by exploring dynamics of swimming bacteria in a liquid crystalline environment with pre-designed periodic splay and bend in molecular orientation. The bacteria are expelled from the bend regions and condense into polar jets that propagate and transport cargo unidirectionally along the splay regions. The bacterial jets remain stable even when the local concentration exceeds the threshold of bending instability in a non-patterned system. Collective polar propulsion and different role of bend and splay are explained by an advection-diffusion model and by numerical simulations that treat the system as a two-phase active nematic. The ability of prepatterned liquid crystalline medium to streamline the chaotic movements of swimming bacteria into polar jets that can carry cargo along a predesigned trajectory opens the door for potential applications in cell sorting, microscale delivery and soft microrobotics.

cond-mat.soft↗

arXiv2019

Learning Aided Optimization for Energy Harvesting Devices with Outdated State Information

This paper considers utility optimal power control for energy harvesting wireless devices with a finite capacity battery. The distribution information of the underlying wireless environment and harvestable energy is unknown and only outdated system state information is known at the device controller. This scenario shares similarity with Lyapunov opportunistic optimization and online learning but is different from both. By a novel combination of Zinkevich's online gradient learning technique and the drift-plus-penalty technique from Lyapunov opportunistic optimization, this paper proposes a learning-aided algorithm that achieves utility within $O(ε)$ of the optimal, for any desired $ε>0$, by using a battery with an $O(1/ε)$ capacity. The proposed algorithm has low complexity and makes power investment decisions based on system history, without requiring knowledge of the system state or its probability distribution.

math.OC↗

arXiv2019

Online Primal-Dual Mirror Descent under Stochastic Constraints

We consider online convex optimization with stochastic constraints where the objective functions are arbitrarily time-varying and the constraint functions are independent and identically distributed (i.i.d.) over time. Both the objective and constraint functions are revealed after the decision is made at each time slot. The best known expected regret for solving such a problem is $\mathcal{O}(\sqrt{T})$, with a coefficient that is polynomial in the dimension of the decision variable and relies on the Slater condition (i.e. the existence of interior point assumption), which is restrictive and in particular precludes treating equality constraints. In this paper, we show that such Slater condition is in fact not needed. We propose a new primal-dual mirror descent algorithm and show that one can attain $\mathcal{O}(\sqrt{T})$ regret and constraint violation under a much weaker Lagrange multiplier assumption, allowing general equality constraints and significantly relaxing the previous Slater conditions. Along the way, for the case where decisions are contained in a probability simplex, we reduce the coefficient to have only a logarithmic dependence on the decision variable dimension. Such a dependence has long been known in the literature on mirror descent but seems new in this new constrained online learning scenario.

math.OC↗

arXiv2019

Thick brane in reduced Horndeski theory

Horndeski theory is the most general scalar-tensor theory retaining second-order field equations, although the action includes higher-order terms. This is achieved by a special choice of coupling constants. In this paper, we investigate thick brane system in reduced Horndeski theory, especially the effect of the non-minimal derivative coupling on thick brane. First, the equations of motion are presented and a set of analytic background solutions are obtained. Then, to investigate the stability of the background scalar profile, we present a novel canonically normalized method, and show that although the original background scalar field is unstable, the canonical one is stable. The stability of the thick brane under tensor perturbation is also considered. It is shown that the tachyon is absent and the graviton zero mode can be localized on the brane. The localized graviton zero mode recovers the four-dimensional Newtonian potential and the presence of the non-minimal derivative coupling results in a splitting of its wave function. The correction of the massive graviton KK modes to the Newtonian potential is also analyzed briefly.

gr-qc↗

arXiv2019

Gravitational waves and extra dimensions: a short review

We give a brief review on the recent development of gravitational waves in extra-dimensional theories of gravity. Studying extra-dimensional theories with gravitational waves provides a new way to constrain extra dimensions. After a flash look at the history of gravitational waves and a brief introduction to several major extra-dimensional theories, we focus on the sources and spectra of gravitational waves in extra-dimensional theories. It is shown that one can impose limits on the size of extra dimensions and the curvature of the universe by researching the propagations of gravitational waves and the corresponding electromagnetic waves. Since gravitational waves can propagate throughout the bulk, how the amplitude of gravitational waves decreases determines the number of extra dimensions for some models. In addition, we also briefly present some other characteristics of gravitational waves in extra-dimensional theories.

gr-qc↗

arXiv2019

On the Computation and Communication Complexity of Parallel SGD with Dynamic Batch Sizes for Stochastic Non-Convex Optimization

For SGD based distributed stochastic optimization, computation complexity, measured by the convergence rate in terms of the number of stochastic gradient calls, and communication complexity, measured by the number of inter-node communication rounds, are two most important performance metrics. The classical data-parallel implementation of SGD over $N$ workers can achieve linear speedup of its convergence rate but incurs an inter-node communication round at each batch. We study the benefit of using dynamically increasing batch sizes in parallel SGD for stochastic non-convex optimization by charactering the attained convergence rate and the required number of communication rounds. We show that for stochastic non-convex optimization under the P-L condition, the classical data-parallel SGD with exponentially increasing batch sizes can achieve the fastest known $O(1/(NT))$ convergence with linear speedup using only $\log(T)$ communication rounds. For general stochastic non-convex optimization, we propose a Catalyst-like algorithm to achieve the fastest known $O(1/\sqrt{NT})$ convergence with only $O(\sqrt{NT}\log(\frac{T}{N}))$ communication rounds.

math.OC↗

arXiv2019

On the Linear Speedup Analysis of Communication Efficient Momentum SGD for Distributed Non-Convex Optimization

Recent developments on large-scale distributed machine learning applications, e.g., deep neural networks, benefit enormously from the advances in distributed non-convex optimization techniques, e.g., distributed Stochastic Gradient Descent (SGD). A series of recent works study the linear speedup property of distributed SGD variants with reduced communication. The linear speedup property enable us to scale out the computing capability by adding more computing nodes into our system. The reduced communication complexity is desirable since communication overhead is often the performance bottleneck in distributed systems. Recently, momentum methods are more and more widely adopted in training machine learning models and can often converge faster and generalize better. For example, many practitioners use distributed SGD with momentum to train deep neural networks with big data. However, it remains unclear whether any distributed momentum SGD possesses the same linear speedup property as distributed SGD and has reduced communication complexity. This paper fills the gap by considering a distributed communication efficient momentum SGD method and proving its linear speedup property.

math.OC↗

arXiv2018

Localization of Gravitino Field on $f(R)$ Thick Branes

In this paper, we consider the localization of a five-dimensional gravitino field on $f(R)$-thick branes. We obtain the coupled chiral equations of the Kaluza-Klein (KK) modes of gravitinos with the gauge condition $Ψ_z=0$. The chiral equations of a gravitino's KK modes are found to be almost identical to those of the Dirac fermion. However, their chiralities are exactly opposite. The chiral KK modes of gravitinos could be localized in some types of $f(R)$-thick branes on introducing a coupling term. We investigate the localization of a gravitino on three types of $f(R)$-thick branes through a Yukawa-like coupling term with background scalar fields. It has been shown that all the KK modes of gravitinos cannot be localized in the pure geometric $f(R)$-thick branes by adding a five-dimensional gravitino mass term. However, for the $f(R)$-thick branes generated by one or two background scalar fields, only the left- or right-handed zero mode could be localized in the branes, and the massive KK resonant modes are the same for both left- and right-handed gravitinos despite their opposing chiralities. All these results are consistent with those of the five-dimensional Dirac fermion except their chiralities, which may be an important sign to distinguish the gravitino field and the Dirac fermion field.

hep-th↗

arXiv2018

Parallel Restarted SGD with Faster Convergence and Less Communication: Demystifying Why Model Averaging Works for Deep Learning

In distributed training of deep neural networks, parallel mini-batch SGD is widely used to speed up the training process by using multiple workers. It uses multiple workers to sample local stochastic gradient in parallel, aggregates all gradients in a single server to obtain the average, and update each worker's local model using a SGD update with the averaged gradient. Ideally, parallel mini-batch SGD can achieve a linear speed-up of the training time (with respect to the number of workers) compared with SGD over a single worker. However, such linear scalability in practice is significantly limited by the growing demand for gradient communication as more workers are involved. Model averaging, which periodically averages individual models trained over parallel workers, is another common practice used for distributed training of deep neural networks since (Zinkevich et al. 2010) (McDonald, Hall, and Mann 2010). Compared with parallel mini-batch SGD, the communication overhead of model averaging is significantly reduced. Impressively, tremendous experimental works have verified that model averaging can still achieve a good speed-up of the training time as long as the averaging interval is carefully controlled. However, it remains a mystery in theory why such a simple heuristic works so well. This paper provides a thorough and rigorous theoretical study on why model averaging can work as well as parallel mini-batch SGD with significantly less communication overhead.

math.OC↗

arXiv2018

Hide-and-Seek: A Data Augmentation Technique for Weakly-Supervised Localization and Beyond

We propose 'Hide-and-Seek' a general purpose data augmentation technique, which is complementary to existing data augmentation techniques and is beneficial for various visual recognition tasks. The key idea is to hide patches in a training image randomly, in order to force the network to seek other relevant content when the most discriminative content is hidden. Our approach only needs to modify the input image and can work with any network to improve its performance. During testing, it does not need to hide any patches. The main advantage of Hide-and-Seek over existing data augmentation techniques is its ability to improve object localization accuracy in the weakly-supervised setting, and we therefore use this task to motivate the approach. However, Hide-and-Seek is not tied only to the image localization task, and can generalize to other forms of visual input like videos, as well as other recognition tasks like image classification, temporal action localization, semantic segmentation, emotion recognition, age/gender estimation, and person re-identification. We perform extensive experiments to showcase the advantage of Hide-and-Seek on these various visual recognition problems.

cs.CV↗

arXiv2018

MOHONE: Modeling Higher Order Network Effects in KnowledgeGraphs via Network Infused Embeddings

Many knowledge graph embedding methods operate on triples and are therefore implicitly limited by a very local view of the entire knowledge graph. We present a new framework MOHONE to effectively model higher order network effects in knowledge-graphs, thus enabling one to capture varying degrees of network connectivity (from the local to the global). Our framework is generic, explicitly models the network scale, and captures two different aspects of similarity in networks: (a) shared local neighborhood and (b) structural role-based similarity. First, we introduce methods that learn network representations of entities in the knowledge graph capturing these varied aspects of similarity. We then propose a fast, efficient method to incorporate the information captured by these network representations into existing knowledge graph embeddings. We show that our method consistently and significantly improves the performance on link prediction of several different knowledge-graph embedding methods including TRANSE, TRANSD, DISTMULT, and COMPLEX(by at least 4 points or 17% in some cases).

cs.CL↗

arXiv2018

Solving Non-smooth Constrained Programs with Lower Complexity than $\mathcal{O}(1/\varepsilon)$: A Primal-Dual Homotopy Smoothing Approach

We propose a new primal-dual homotopy smoothing algorithm for a linearly constrained convex program, where neither the primal nor the dual function has to be smooth or strongly convex. The best known iteration complexity solving such a non-smooth problem is $\mathcal{O}(\varepsilon^{-1})$. In this paper, we show that by leveraging a local error bound condition on the dual function, the proposed algorithm can achieve a better primal convergence time of $\mathcal{O}\left(\varepsilon^{-2/(2+β)}\log_2(\varepsilon^{-1})\right)$, where $β\in(0,1]$ is a local error bound parameter. As an example application of the general algorithm, we show that the distributed geometric median problem, which can be formulated as a constrained convex program, has its dual function non-smooth but satisfying the aforementioned local error bound condition with $β=1/2$, therefore enjoying a convergence time of $\mathcal{O}\left(\varepsilon^{-4/5}\log_2(\varepsilon^{-1})\right)$. This result improves upon the $\mathcal{O}(\varepsilon^{-1})$ convergence time bound achieved by existing distributed optimization algorithms. Simulation experiments also demonstrate the performance of our proposed algorithm.

math.OC↗