arXiv subjects

Haibin Chen

Publications and source records attributed to Haibin Chen.

At least 37 records · Page 2Linked to original sources

arXiv2024

Density Distribution of Plasmas Resembling Dark Matter Halo Due to Ionization lag and Ambipolar Electric Field

In a spherically symmetric plasma constrained by its own gravity, the ionization degree lags behind changes in temperature and density. The ambipolar electric field accelerates ions radially and cools electrons. Ions lose energy and angular momentum in collisions with low-temperature electrons. The angular momentum of ions decreases much faster than their energy in cycles. The trajectories of ions are close to radial, and the density distribution resembles pseudo-isothermal. The velocity distributions of baryons moving outward and inward in galaxies tend to approach independent Maxwell distributions. This characteristic suppresses small-angle scattering of ions, reducing the ion collision cross-section by three orders of magnitude. In the massive galaxies, baryons can replace all dark matter.

astro-ph.GA↗

arXiv2024

Cross-domain Named Entity Recognition via Graph Matching

Cross-domain NER is a practical yet challenging problem since the data scarcity in the real-world scenario. A common practice is first to learn a NER model in a rich-resource general domain and then adapt the model to specific domains. Due to the mismatch problem between entity types across domains, the wide knowledge in the general domain can not effectively transfer to the target domain NER model. To this end, we model the label relationship as a probability distribution and construct label graphs in both source and target label spaces. To enhance the contextual representation with label structures, we fuse the label graph into the word embedding output by BERT. By representing label relationships as graphs, we formulate cross-domain NER as a graph matching problem. Furthermore, the proposed method has good applicability with pre-training methods and is potentially capable of other cross-domain prediction tasks. Empirical results on four datasets show that our method outperforms a series of transfer learning, multi-task learning, and few-shot learning methods.

cs.CL↗

arXiv2024

Temperature Separation in a Vortex Tube and convection driven by vorticity

Why the temperature gradient in the vortex tube deviates significantly from the adiabatic gradient is a very important but unresolved issue in vortex tube research. In compressible fluids, the vorticity of a fluid parcel that is different from its environment can affect its own pressure or density, just like temperature. Gases near the wall have very high vorticity, and when they detach from the wall, their higher vorticity compared to the environment makes their density lower than the environment. Driven by vorticity, some fluid parcels undergo multiple collisions near the axis, achieving temperature separation.

physics.flu-dyn↗

arXiv2024

ConceptMath: A Bilingual Concept-wise Benchmark for Measuring Mathematical Reasoning of Large Language Models

This paper introduces ConceptMath, a bilingual (English and Chinese), fine-grained benchmark that evaluates concept-wise mathematical reasoning of Large Language Models (LLMs). Unlike traditional benchmarks that evaluate general mathematical reasoning with an average accuracy, ConceptMath systematically organizes math problems under a hierarchy of math concepts, so that mathematical reasoning can be evaluated at different granularity with concept-wise accuracies. Based on our ConcepthMath, we evaluate a broad range of LLMs, and we observe existing LLMs, though achieving high average accuracies on traditional benchmarks, exhibit significant performance variations across different math concepts and may even fail catastrophically on the most basic ones. Besides, we also introduce an efficient fine-tuning strategy to enhance the weaknesses of existing LLMs. Finally, we hope ConceptMath could guide the developers to understand the fine-grained mathematical abilities of their models and facilitate the growth of foundation models.

cs.CL↗

arXiv2024

The Interaction between Solar Convection and Rotation

The rotational energy of a fluid parcel changes during isotropic expansion or compression. In solar convection, rotation absorbs energy from convection and inhibits it, causing the motion of fluid parcels larger than a critical size to become vibration. Turbulence and inertial oscillations can cause the deformation of fluid parcels to deviate from isotropic, altering the equilibrium position of the vibration and forming motion larger than the critical size, respectively, the large granules within the granules and probably the mesogranulation. The change in rotational energy of granules during convection causes their rotation speed to differ from the local speed, forming a statistically significant solar radial differential rotation. The meridional circulation driven by radial differential rotation transports angular momentum towards the equator, forming the latitudinal differential rotation. A model constructed by combining mixing length theory explains why granule size and temperature distribution are independent of latitude, and the structure produced by this mechanism is similar to the characteristics of supergranules.

astro-ph.SR↗

arXiv2024

Cosmological first-order phase transitions without bubbles

In the traditional view a cosmic first-order phase transition cannot occur without nucleating handful of bubbles in the entire Hubble volume. The presence of domain walls during the transition may, however, significantly alter the dynamics of the phase transitions. Using lattice simulation, we demonstrate that vacuum fluctuations induce the destabilization of the domain walls that will classically transform into the domain trenches of the true vacuum, resulting in successful phase transitions without bubbles. After providing an analytical method to estimate the temperature at which the domain trenches are produced, we take the Z2-odd singlet model as an example and conclude that the bubble-free mechanism developed in this Letter constitutes a competing means of completing the phase transition against with quantum tunneling, opening up the new viable parameter region.

hep-ph↗

arXiv2023

Preserving Commonsense Knowledge from Pre-trained Language Models via Causal Inference

Fine-tuning has been proven to be a simple and effective technique to transfer the learned knowledge of Pre-trained Language Models (PLMs) to downstream tasks. However, vanilla fine-tuning easily overfits the target data and degrades the generalization ability. Most existing studies attribute it to catastrophic forgetting, and they retain the pre-trained knowledge indiscriminately without identifying what knowledge is transferable. Motivated by this, we frame fine-tuning into a causal graph and discover that the crux of catastrophic forgetting lies in the missing causal effects from the pretrained data. Based on the causal view, we propose a unified objective for fine-tuning to retrieve the causality back. Intriguingly, the unified objective can be seen as the sum of the vanilla fine-tuning objective, which learns new knowledge from target data, and the causal objective, which preserves old knowledge from PLMs. Therefore, our method is flexible and can mitigate negative transfer while preserving knowledge. Since endowing models with commonsense is a long-standing challenge, we implement our method on commonsense QA with a proposed heuristic estimation to verify its effectiveness. In the experiments, our method outperforms state-of-the-art fine-tuning methods on all six commonsense QA datasets and can be implemented as a plug-in module to inflate the performance of existing QA models.

cs.CL↗

arXiv2023

How Dose Rotation Effect Convection Criterion and Solar Granule Size

The rotation of granules shows thermal properties similar to the thermal motion of molecules, which effects convection criterion and solar granule size.The granular rotation generates the rotational additional pressure and corresponding rotational equivalent temperature in the spherically symmetric expansion of the granule.The rotation equivalent temperature represented by the rotational speed and the granular size is combined with the Schwarzschild criterion to obtain a new convection criterion determined jointly by the granular size, temperature gradient, and rotational speed gradient.In most of the solar convection zone, the convection is driven by the temperature gradient and suppressed by the rotational speed gradient.In the solar quiet region, the larger the granular size, the weaker the convection.The small granules with the sizes smaller than the critical size are in natural convection, while the large granules with the sizes larger than the critical size are in forced convection.In the solar active region, the larger the rotational speed, the smaller the critical size and the temperature.So sunspots have smaller granules and lower temperatures.

astro-ph.SR↗

arXiv2023

Rotating Turbulent Thermal Convection and Solar Differential Rotation

The expansion of the rotating fluid will change the vorticity and rotational speed of the expanding region. In turbulent thermal convection, this microscopic effect is preserved. Tracking the fluid micelles shows that the average vorticity varies with density, producing vorticity transport and angular momentum transport from the low-density area to the high-density area, forming a macroscopic vorticity difference and rotational speed difference. Taking the axial thermal convection model of the solar polar region, it can generate axial differential rotation, and the centrifugal force difference generated by the axial differential rotation drives the meridional circulation, transporting angular momentum away from the axis of rotation, forming latitudinal differential rotation. The rotation of the fluid cell generates additional pressure and change the convection criterion. The temperature gradient in the solar troposphere is higher than in the non-rotating fluid model, It's the energy source of the differential rotating.

astro-ph.SR↗

arXiv2022

Variation of Vorticity Gradient and Formation of Sunspots

Based on the rotating turbulent thermal convection model and using the rotating equivalent temperature assumption and new convection criterion, this paper analyzed the repression of the vorticity gradient on the heat transport and explained that the formation of sunspots originated from the variation of the vorticity gradient in the solar troposphere.

astro-ph.SR↗

arXiv2022

Distilling Causal Effect from Miscellaneous Other-Class for Continual Named Entity Recognition

Continual Learning for Named Entity Recognition (CL-NER) aims to learn a growing number of entity types over time from a stream of data. However, simply learning Other-Class in the same way as new entity types amplifies the catastrophic forgetting and leads to a substantial performance drop. The main cause behind this is that Other-Class samples usually contain old entity types, and the old knowledge in these Other-Class samples is not preserved properly. Thanks to the causal inference, we identify that the forgetting is caused by the missing causal effect from the old data. To this end, we propose a unified causal framework to retrieve the causality from both new entity types and Other-Class. Furthermore, we apply curriculum learning to mitigate the impact of label noise and introduce a self-adaptive weight for balancing the causal effects between new entity types and Other-Class. Experimental results on three benchmark datasets show that our method outperforms the state-of-the-art method by a large margin. Moreover, our method can be combined with the existing state-of-the-art methods to improve the performance in CL-NER

cs.CL↗

arXiv2016

Copositive Tensor Detection and Its Applications in Physics and Hypergraphs

Copositivity of tensors plays an important role in vacuum stability of a general scalar potential, polynomial optimization, tensor complementarity problem and tensor generalized eigenvalue complementarity problem. In this paper, we propose a new algorithm for testing copositivity of high order tensors, and then present applications of the algorithm in physics and hypergraphs. For this purpose, we first give several new conditions for copositivity of tensors based on the representative matrix of a simplex. Then a new algorithm is proposed with the help of a proper convex subcone of the copositive tensor cone, which is defined via the copositivity of Z-tensors. Furthermore, by considering a sum-of-squares program problem, we define two new subsets of the copositive tensor cone and discuss their convexity. As an application of the proposed algorithm, we prove that the coclique number of a uniform hypergraph is equivalent with an optimization problem over the completely positive tensor cone, which implies that the proposed algorithm can be applied to compute an upper bound of the coclique number of a uniform hypergraph. Then we study another application of the proposed algorithm on particle physics in testing copositivity of some potential fields. At last, various numerical examples are given to show the performance of the algorithm.

math.CO↗

arXiv2016

Finding the maximum eigenvalue of a class of tensors with applications in copositivity test and hypergraphs

Finding the maximum eigenvalue of a symmetric tensor is an important topic in tensor computation and numerical multilinear algebra. This paper is devoted to a semi-definite program algorithm for computing the maximum $H$-eigenvalue of a class of tensors with sign structure called $W$-tensors. The class of $W$-tensors extends the well-studied nonnegative tensors and essentially nonnegative tensors, and covers some important tensors arising naturally from spectral hypergraph theory. Our algorithm is based on a new structured sums-of-squares (SOS) decomposition result for a nonnegative homogeneous polynomial induced by a $W$-tensor. This SOS decomposition enables us to show that computing the maximum $H$-eigenvalue of an even order symmetric $W$-tensor is equivalent to solving a semi-definite program, and hence can be accomplished in polynomial time. Numerical examples are given to illustrate that the proposed algorithm can be used to find maximum $H$-eigenvalue of an even order symmetric $W$-tensor with dimension up to $10,000$. We present two applications for our proposed algorithm: we first provide a polynomial time algorithm for computing the maximum $H$-eigenvalues of large size Laplacian tensors of hyper-stars and hyper-trees; second, we show that the proposed SOS algorithm can be used to test the copositivity of a multivariate form associated with symmetric extended $Z$-tensors, whose order may be even or odd. Numerical experiments illustrate that our structured semi-definite program algorithm is effective and promising.

math.SP↗

arXiv2016

Copositivity Detection of Tensors: Theory and Algorithm

A symmetric tensor is called copositive if it generates a multivariate form taking nonnegative values over the nonnegative orthant. Copositive tensors have found important applications in polynomial optimization and tensor complementarity problems. In this paper, we consider copositivity detection of tensors both from theoretical and computational points of view. After giving several necessary conditions for copositive tensors, we propose several new criteria for copositive tensors based on the representation of the multivariate form in barycentric coordinates with respect to the standard simplex and simplicial partitions. It is verified that, as the partition gets finer and finer, the concerned conditions eventually capture all strictly copositive tensors. Based on the obtained theoretical results with the help of simplicial partitions, we propose a numerical method to judge whether a tensor is copositive or not. The preliminary numerical results confirm our theoretical findings.

math.CO↗

arXiv2015

SOS Tensor Decomposition: Theory and Applications

In this paper, we examine structured tensors which have sum-of-squares (SOS) tensor decomposition, and study the SOS-rank of SOS tensor decomposition. We first show that several classes of even order symmetric structured tensors available in the literature have SOS tensor decomposition. These include positive Cauchy tensors, weakly diagonally dominated tensors, $B_0$-tensors, double $B$-tensors, quasi-double $B_0$-tensors, $MB_0$-tensors, $H$-tensors, absolute tensors of positive semi-definite $Z$-tensors and extended $Z$-tensors. We also examine the SOS-rank of SOS tensor decomposition and the SOS-width for SOS tensor cones. The SOS-rank provides the minimal number of squares in the SOS tensor decomposition, and, for a given SOS tensor cone, its SOS-width is the maximum possible SOS-rank for all the tensors in this cone. We first deduce an upper bound for general tensors that have SOS decomposition and the SOS-width for general SOS tensor cone using the known results in the literature of polynomial theory. Then, we provide an explicit sharper estimate for the SOS-rank of SOS tensor decomposition with bounded exponent and identify the SOS-width for the tensor cone consisting of all tensors with bounded exponent that have SOS decompositions. Finally, as applications, we show how the SOS tensor decomposition can be used to compute the minimum $H$-eigenvalue of an even order symmetric extended $Z$-tensor and test the positive definiteness of an associated multivariate form. Numerical experiments are also provided to show the efficiency of the proposed numerical methods ranging from small size to large size numerical examples.

math.SP↗

arXiv2015

Some Spectral Properties of Odd-Bipartite $Z$-Tensors and Their Absolute Tensors

Stimulated by odd-bipartite and even-bipartite hypergraphs, we define odd-bipartite (weakly odd-bipartie) and even-bipartite (weakly even-bipartite) tensors. It is verified that all even order odd-bipartite tensors are irreducible tensors, while all even-bipartite tensors are reducible no matter the parity of the order. Based on properties of odd-bipartite tensors, we study the relationship between the largest H-eigenvalue of a $Z$-tensor with nonnegative diagonal elements, and the largest H-eigenvalue of absolute tensor of that $Z$-tensor. When the order is even and the $Z$-tensor is weakly irreducible, we prove that the largest H-eigenvalue of the $Z$-tensor and the largest H-eigenvalue of the absolute tensor of that $Z$-tensor are equal, if and only if the $Z$-tensor is weakly odd-bipartite. Examples show the authenticity of the conclusions. Then, we prove that a symmetric $Z$-tensor with nonnegative diagonal entries and the absolute tensor of the $Z$-tensor are diagonal similar, if and only if the $Z$-tensor has even order and it is weakly odd-bipartite. After that, it is proved that, when an even order symmetric $Z$-tensor with nonnegative diagonal entries is weakly irreducible, the equality of the spectrum of the $Z$-tensor and the spectrum of absolute tensor of that $Z$-tensor, can be characterized by the equality of their spectral radii.

math.SP↗

arXiv2015

Further Results on Cauchy Tensors and Hankel Tensors

In this article, we present various new results on Cauchy tensors and Hankel tensors. { We first introduce the concept of generalized Cauchy tensors which extends Cauchy tensors in the current literature, and provide several conditions characterizing positive semi-definiteness of generalized Cauchy tensors with nonzero entries.} As a consequence, we show that Cauchy tensors are positive semi-definite if and only if they are SOS (Sum-of-squares) tensors.} Furthermore, we prove that all positive semi-definite Cauchy tensors are completely positive tensors, which means every positive semi-definite Cauchy tensor can be decomposed { as} the sum of nonnegative rank-1 tensors. We also establish that all the H-eigenvalues of nonnegative Cauchy tensors are nonnegative. Secondly, we present new mathematical properties of Hankel tensors. { We prove that an even order Hankel tensor is Vandermonde positive semi-definite if and only if its associated plane tensor is positive semi-definite. We also show that, if the Vandermonde rank of a Hankel tensor $\mathcal{A}$ is less than the dimension of the underlying space, then positive semi-definiteness of $\mathcal{A}$ is equivalent to the fact that $\mathcal{A}$ is a complete Hankel tensor, and so, is further equivalent to the SOS property of $\mathcal{A}$. Lastly, we introduce a new structured tensor called Cauchy-Hankel tensors, which is a special case of Cauchy tensors and Hankel tensors simultaneously.} Sufficient and necessary conditions are established for an even order Cauchy-Hankel tensor to be positive definite. Final remarks are listed at the end of the paper.

math.SP↗

arXiv2014

Centrosymmetric, Skew Centrosymmetric and Centrosymmetric Cauchy Tensors

Recently, Zhao and Yang introduced centrosymmetric tensors. In this paper, we further introduce skew centrosymmetric tensors and centrosymmetric Cauchy tensors, and discuss properties of these three classes of structured tensors. Some sufficient and necessary conditions for a tensor to be centrosymmetric or skew centrosymmetric are given. We show that, a general tensor can always be expressed as the sum of a centrosymmetric tensor and a skew centrosymmetric tensor. Some sufficient and necessary conditions for a Cauchy tensor to be centrosymmetric or skew centrosymmetric are also given. Spectral properties on H-eigenvalues and H-eigenvectors of centrosymmetric, skew centrosymmetric and centrosymmetric Cauchy tensors are discussed. Some further questions on these tensors are raised.

math.SP↗