arXiv subjects

Jianing Li

Publications and source records attributed to Jianing Li.

At least 91 records · Page 5Linked to original sources

arXiv2021

Differentiable Annealed Importance Sampling and the Perils of Gradient Noise

Annealed importance sampling (AIS) and related algorithms are highly effective tools for marginal likelihood estimation, but are not fully differentiable due to the use of Metropolis-Hastings correction steps. Differentiability is a desirable property as it would admit the possibility of optimizing marginal likelihood as an objective using gradient-based methods. To this end, we propose Differentiable AIS (DAIS), a variant of AIS which ensures differentiability by abandoning the Metropolis-Hastings corrections. As a further advantage, DAIS allows for mini-batch gradients. We provide a detailed convergence analysis for Bayesian linear regression which goes beyond previous analyses by explicitly accounting for the sampler not having reached equilibrium. Using this analysis, we prove that DAIS is consistent in the full-batch setting and provide a sublinear convergence rate. Furthermore, motivated by the problem of learning from large-scale datasets, we study a stochastic variant of DAIS that uses mini-batch gradients. Surprisingly, stochastic DAIS can be arbitrarily bad due to a fundamental incompatibility between the goals of last-iterate convergence to the posterior and elimination of the accumulated stochastic error. This is in stark contrast with other settings such as gradient-based optimization and Langevin dynamics, where the effect of gradient noise can be washed out by taking smaller steps. This indicates that annealing-based marginal likelihood estimation with stochastic gradients may require new ideas.

stat.ML↗

arXiv2021

Gauge independence of pion masses in a magnetic field within the Nambu--Jona-Lasinio model

We investigate the properties of neutral and charged pions in a constant background magnetic field mainly at zero temperature within the Nambu--Jona-Lasinio model. In the previous calculations, the Ritus method, involving Schwinger phases in a fixed gauge, was employed within the momentum-space random phase approximation (RPA)~[Phys. Lett. B $\textbf{782}$, 155-161 (2018)]. However, gauge invariance of the charged pion masses has not yet been examined. In this work, by adopting the linear response theory based on the imaginary-time path integral formalism, we derive the correlation functions for pions in the coordinate space, where the corresponding Schwinger phases show up automatically. At sufficiently large imaginary time $τ$, the meson correlation function approaches an exponential form $\sim\exp(-E_{\rm G}τ)$, where $E_{\rm G}$ is the ground-state energy of the one-meson state and hence determined as the meson mass. Furthermore, we show that the mass of the charged pions is gauge independent, i.e., independent of the choice of the vector potential for the magnetic field. Actually, we also find that the momentum-space RPA is equivalent to the imaginary-time method used here.

nucl-th↗

arXiv2021

On the $λ$-invariant of Selmer groups arising from certain quadratic twists of Gross curves

Let $q$ be a prime with $q \equiv 7 \mod 8$, and let $K=\mathbb{Q}(\sqrt{-q})$. Then $2$ splits in $K$, and we write $\mathfrak{p}$ for either of the primes $K$ above $2$. Let $K_\infty$ be the unique $\mathbb{Z}_2$-extension of $K$ unramified outside $\mathfrak{p}$ with $n$-th layer $K_n$. For certain quadratic extensions $F/K$, we prove a simple exact formula for the $λ$-invariant of the Galois group of the maximal abelian 2-extension unramified outside $\mathfrak{p}$ of the field $F_\infty = FK_\infty$. Equivalently, our result determines the exact $\mathbb{Z}_2$-corank of certain Selmer groups over $F_\infty$ of a large family of quadratic twists of the higher dimensional abelian variety with complex multiplication, which is the restriction of scalars to $K$ of the Gross curve with complex multiplication defined over the Hilbert class field of $K$. We also discuss computations of the associated Selmer groups over $K_n$ in the case when the $λ$-invariant is equal to $1$.

math.NT↗

arXiv2021

Mass spectra and decays of open-heavy tetraquark states

Open-heavy tetraquark states, especially those contain four different quarks have drawn much attention in both theoretical and experimental fields. In the framework of the improved chromomagnetic interaction (ICMI) model, we complete a systematic study on the mass spectra and possible strong decay channels of the $S$-wave open-heavy tetraquark states, $qq\bar{q}\bar{Q}$ ($q=u,d,s$ and $Q=c,b$), with different quantum number $J^P=0^+$, $1^+$, and $2^+$. The parameters in the ICMI model are extracted from the conventional hadron spectra and used directly to predict the mass of tetraquark states. Several compact bound states and narrow resonances are found in both charm-strange and bottom-strange tetraquark sectors, most of them as a product of the strong coupling between the different channels. Our results show the recently discovered four different flavors tetraquark candidates $X_0(2900)$ is probably compact $ud\bar{s}\bar{c}$ state with quantum number $J^P=0^+$. The predictions about $X_0(2900)$ and its partners are expected to be better checked with other theories and future experiments.

hep-ph↗

arXiv2021

Factorization of Hilbert class polynomials over prime fields

Let $D$ be a negative integer congruent to $0$ or $1\bmod{4}$ and $\mathcal{O}=\mathcal{O}_D$ be the corresponding order of $ K=\mathbb{Q}(\sqrt{D})$. The Hilbert class polynomial $H_D(x)$ is the minimal polynomial of the $j$-invariant $ j_D=j(\mathbb{C}/\mathcal{O})$ of $\mathcal{O}$ over $K$. Let $n_D=(\mathcal{O}_{\mathbb{Q}( j_D)}:\mathbb{Z}[ j_D])$ denote the index of $\mathbb{Z}[ j_D]$ in the ring of integers of $\mathbb{Q}(j_D)$. Suppose $p$ is any prime. We completely determine the factorization of $H_D(x)$ in $\mathbb{F}_p[x]$ if either $p\nmid n_D$ or $p\nmid D$ is inert in $K$ and the $p$-adic valuation $v_p(n_D)\leq 3$. As an application, we analyze the key space of Oriented Supersingular Isogeny Diffie-Hellman (OSIDH) protocol proposed by Colò and Kohel in 2019 which is the roots set of the Hilbert class polynomial in $\mathbb{F}_{p^2}$.

math.NT↗

arXiv2021

The $3$-class groups of $\mathbb{Q}(\sqrt[3]{p})$ and its normal closure

We determine the $3$-class groups of $\mathbb{Q}(\sqrt[3]{p})$ and $K=\mathbb{Q}(\sqrt[3]{p},\sqrt{-3})$ when $p\equiv 4,7\bmod 9$ is a prime and $3$ is a cubic modulo $p$. This confirms a conjecture made by Barrucand-Cohn, and proves the last remaining case of a conjecture of Lemmermeyer on the $3$-class group of $K$.

math.NT↗

arXiv2021

Confined dipole and exchange spin waves in a bulk chiral magnet with Dzyaloshinskii-Moriya interaction

The Dzyaloshinskii-Moriya interaction (DMI) has an impact on excited spin waves in the chiral magnet Cu$_2$OSeO$_3$ by means of introducing asymmetry on their dispersion relations. The confined eigenmodes of a chiral magnet are hence no longer the conventional standing spin waves. Here we report a combined experimental and micromagnetic modeling study by broadband microwave spectroscopy we observe confined spin waves up to eleventh order in bulk Cu$_2$OSeO$_3$ in the field-polarized state. In micromagnetic simulations we find similarly rich spectra. They indicate the simultaneous excitation of both dipole- and exchange-dominated spin waves with wavelengths down to (47.2 $\pm$ 0.05) nm attributed to the exchange interaction modulation. Our results suggest DMI to be effective to create exchange spin waves in a bulk sample without the challenging nanofabrication and thereby to explore their scattering with noncollinear spin textures.

cond-mat.mtrl-sci↗

arXiv2020

On the Aggregation State of Synergistic Antimicrobial Peptides

By integrating various simulation and experimental techniques, we discovered that antimicrobial peptides (AMPs) may achieve synergy at an optimal concentration and ratio, which can be caused by aggregation of the synergistic peptides. On multiple time and length scales, our studies obtain novel evidence of how peptide co-aggregation in solution can affect disruption of membranes by synergistic AMPs. Our findings provide crucial details about the complex molecular origins of AMP synergy, which will help guide the future development of synergistic AMPs as well as applications of anti-infective peptide cocktail therapies.

physics.bio-ph↗

arXiv2020

Classical Iwasawa theory and infinite descent on a family of abelian varieties

For primes $q \equiv 7 \mod 16$, the present manuscript shows that elementary methods enable one to prove surprisingly strong results about the Iwasawa theory of the Gross family of elliptic curves with complex multiplication by the ring of integers of the field $K = \mathbb{Q}(\sqrt{-q})$, which are in perfect accord with the predictions of the conjecture of Birch and Swinnerton-Dyer. We also prove some interesting phenomena related to a classical conjecture of Greenberg, and give a new proof of an old theorem of Hasse.

math.NT↗

arXiv2020

On the Relation between Quality-Diversity Evaluation and Distribution-Fitting Goal in Text Generation

The goal of text generation models is to fit the underlying real probability distribution of text. For performance evaluation, quality and diversity metrics are usually applied. However, it is still not clear to what extend can the quality-diversity evaluation reflect the distribution-fitting goal. In this paper, we try to reveal such relation in a theoretical approach. We prove that under certain conditions, a linear combination of quality and diversity constitutes a divergence metric between the generated distribution and the real distribution. We also show that the commonly used BLEU/Self-BLEU metric pair fails to match any divergence metric, thus propose CR/NRR as a substitute for quality/diversity metric pair.

cs.LG↗

arXiv2020

Joint Visual and Temporal Consistency for Unsupervised Domain Adaptive Person Re-Identification

Unsupervised domain adaptive person Re-IDentification (ReID) is challenging because of the large domain gap between source and target domains, as well as the lackage of labeled data on the target domain. This paper tackles this challenge through jointly enforcing visual and temporal consistency in the combination of a local one-hot classification and a global multi-class classification. The local one-hot classification assigns images in a training batch with different person IDs, then adopts a Self-Adaptive Classification (SAC) model to classify them. The global multi-class classification is achieved by predicting labels on the entire unlabeled training set with the Memory-based Temporal-guided Cluster (MTC). MTC predicts multi-class labels by considering both visual similarity and temporal consistency to ensure the quality of label prediction. The two classification models are combined in a unified framework, which effectively leverages the unlabeled data for discriminative feature learning. Experimental results on three large-scale ReID datasets demonstrate the superiority of proposed method in both unsupervised and unsupervised domain adaptive ReID tasks. For example, under unsupervised setting, our method outperforms recent unsupervised domain adaptive methods, which leverage more labels for training.

cs.CV↗

arXiv2020

The Chevalley-Gras formula over global fields

In this article we give an adelic proof of the Chevalley-Gras formula for global fields, which itself is a generalization of the ambiguous class number formula. The idea is to reduce the formula to the Hasse norm theorem, the local and global reciprocity laws. We also give an adelic proof of the Chevalley-Gras formula for $0$-th divisor class group in the function field case, which extends a result of Rosen.

math.NT↗

arXiv2020

On the $2$-adic logarithm of units of certain totally imaginary quartic fields

In this paper, we prove a result on the $2$-adic logarithm of the fundamental unit of the field $\mathbb{Q}(\sqrt[4]{-q}) $, where $q\equiv 3\bmod 4$ is a prime. When $q\equiv 15\bmod 16$, this result confirms a speculation of Coates-Li and has consequences for certain Iwasawa modules arising in their work.

math.NT↗

arXiv2020

$\ell$-Class groups of fields in Kummer towers

Let $\ell$ and $p$ be prime numbers and $K_{n,m}=\mathbb{Q}(p^{\frac{1}{\ell^n}},ζ_{2\ell^{m}})$. We study the $\ell$-class group of $K_{n,m}$ in this paper. When $\ell=2$, we determine the structure of the $2$-class group of $K_{n,m}$ for all $(n,m)\in \mathbb{Z}_{\geq 0}^2$ in the case $p=2$ or $p\equiv 3, 5\bmod{8}$, and for $(n,m)=(n,0)$, $(n,1)$ or $(1,m)$ in the case $p\equiv 7\bmod{16}$, eneralizing the results of Parry about the $2$-divisibility of the class number of $K_{2,0}$. We also obtain results about the $\ell$-class group of $K_{n,m}$ when $\ell$ is odd and in particular $\ell=3$. The main tools we use are class field theory, including Chevalley's ambiguous class number formula and its generalization by Gras, and a stationary result about the $\ell$-class groups in the $2$-dimensional Kummer tower $\{K_{n,m}\}$.

math.NT↗

arXiv2020

Improving Generalizability of Fake News Detection Methods using Propensity Score Matching

Recently, due to the booming influence of online social networks, detecting fake news is drawing significant attention from both academic communities and general public. In this paper, we consider the existence of confounding variables in the features of fake news and use Propensity Score Matching (PSM) to select generalizable features in order to reduce the effects of the confounding variables. Experimental results show that the generalizability of fake news method is significantly better by using PSM than using raw frequency to select features. We investigate multiple types of fake news methods (classifiers) such as logistic regression, random forests, and support vector machines. We have consistent observations of performance improvement.

cs.SI↗

arXiv2019

On Class Numbers of Pure Quartic fields

Let $p$ be a prime. The $2$-primary part of the class group of the pure quartic field $\mathbb{Q}(\sqrt[4]{p})$ has been determined by Parry and Lemmermeyer when $p \not\equiv \pm 1\bmod 16$. In this paper, we improve the known results in the case $p\equiv \pm 1\bmod 16$. In particular, we determine all primes $p$ such that $4$ does not divide the class number of $\mathbb{Q}(\sqrt[4]{p})$. We also conjecture a relation between the class numbers of $\mathbb{Q}(\sqrt[4]{p})$ and $\mathbb{Q}(\sqrt{-2p})$. We show that this conjecture implies a distribution result of the $2$-class numbers of $\mathbb{Q}(\sqrt[4]{p})$.

math.NT↗

arXiv2019

Global-Local Temporal Representations For Video Person Re-Identification

This paper proposes the Global-Local Temporal Representation (GLTR) to exploit the multi-scale temporal cues in video sequences for video person Re-Identification (ReID). GLTR is constructed by first modeling the short-term temporal cues among adjacent frames, then capturing the long-term relations among inconsecutive frames. Specifically, the short-term temporal cues are modeled by parallel dilated convolutions with different temporal dilation rates to represent the motion and appearance of pedestrian. The long-term relations are captured by a temporal self-attention model to alleviate the occlusions and noises in video sequences. The short and long-term temporal cues are aggregated as the final GLTR by a simple single-stream CNN. GLTR shows substantial superiority to existing features learned with body part cues or metric learning on four widely-used video ReID datasets. For instance, it achieves Rank-1 Accuracy of 87.02% on MARS dataset without re-ranking, better than current state-of-the art.

cs.CV↗

arXiv2019

GPU-based Efficient Join Algorithms on Hadoop

The growing data has brought tremendous pressure for query processing and storage, so there are many studies that focus on using GPU to accelerate join operation, which is one of the most important operations in modern database systems. However, existing GPU acceleration join operation researches are not very suitable for the join operation on big data. Based on this, this paper speeds up nested loop join, hash join and theta join, combining Hadoop with GPU, which is also the first to use GPU to accelerate theta join. At the same time, after the data pre-filtering and pre-processing, using Map-Reduce and HDFS in Hadoop proposed in this paper, the larger data table can be handled, compared to existing GPU acceleration methods. Also with Map-Reduce in Hadoop, the algorithm proposed in this paper can estimate the number of results more accurately and allocate the appropriate storage space without unnecessary costs, making it more efficient. The rigorous experiments show that the proposed method can obtain 1.5 to 2 times the speedup, compared to the traditional GPU acceleration equi join algorithm. And in the synthetic data set, the GPU version of the proposed method can get 1.3 to 2 times the speedup, compared to CPU version.

cs.DB↗