arXiv subjects

Biao Wang

Publications and source records attributed to Biao Wang.

At least 91 records · Page 5Linked to original sources

arXiv2021

Analogues of Alladi's formula over global function fields

In this paper, we show an analogue of Kural, McDonald and Sah's result on Alladi's formula for global function fields. Explicitly, we show that for a global function field $K$, if a set $S$ of prime divisors has a natural density $δ(S)$ within prime divisors, then $$-\lim_{n\to\infty} \sum_{\substack{1\le °D\le n\\ D\in \mathfrak{D}(K,S)}}\frac{μ(D)}{|D|}=δ(S),$$ where $μ(D)$ is the Möbius function on divisors and $\mathfrak{D}(K,S)$ is the set of all effective distinguishable divisors whose smallest prime factors are in $S$. As applications, we get the analogue of Dawsey's and Sweeting and Woo's results to the Chebotarev Density Theorem for function fields, and the analogue of Alladi's result to the Prime Polynomial Theorem for arithmetic progressions. We also display a connection between the Möbius function and the Fourier coefficients of modular form associated to elliptic curves. The proof of our main theorem is similar to the approach in Kural et al.'s article.

math.NT↗

arXiv2021

On Identification of Boolean Control Networks

A new analytical framework consisting of two phenomena: single sample and multiple samples, is proposed to deal with the identification problem of Boolean control networks (BCNs) systematically and comprehensively. Under this framework, the existing works on identification can be categorized as special cases of these two phenomena. Several effective criteria for determining the identifiability and the corresponding identification algorithms are proposed. Three important results are derived: (1) If a BN is observable, it is uniquely identifiable; (2) If a BCN is O1-observable, it is uniquely identifiable, where O1-observability is the most general form of the existing observability terms; (3) A BN or BCN may be identifiable, but not observable. In addition, remarks present some challenging future research and contain a preliminary attempt about how to identify unobservable systems.

eess.SY↗

arXiv2021

AIBench Training: Balanced Industry-Standard AI Training Benchmarking

Earlier-stage evaluations of a new AI architecture/system need affordable benchmarks. Only using a few AI component benchmarks like MLPerfalone in the other stages may lead to misleading conclusions. Moreover, the learning dynamics are not well understood, and the benchmarks' shelf-life is short. This paper proposes a balanced benchmarking methodology. We use real-world benchmarks to cover the factors space that impacts the learning dynamics to the most considerable extent. After performing an exhaustive survey on Internet service AI domains, we identify and implement nineteen representative AI tasks with state-of-the-art models. For repeatable performance ranking (RPR subset) and workload characterization (WC subset), we keep two subsets to a minimum for affordability. We contribute by far the most comprehensive AI training benchmark suite. The evaluations show: (1) AIBench Training (v1.1) outperforms MLPerfTraining (v0.7) in terms of diversity and representativeness of model complexity, computational cost, convergent rate, computation, and memory access patterns, and hotspot functions; (2) Against the AIBench full benchmarks, its RPR subset shortens the benchmarking cost by 64%, while maintaining the primary workload characteristics; (3) The performance ranking shows the single-purpose AI accelerator like TPU with the optimized TensorFlowframework performs better than that of GPUs while losing the latter's general support for various AI models. The specification, source code, and performance numbers are available from the AIBench homepage https://www.benchcouncil.org/aibench-training/index.html.

cs.AI↗

arXiv2020

Failure of Griffith Theory on Prediction of Theoretical Strength of Ideal Materials

Ever since its publication, the Griffith theory is the most widely used criterion for estimating the ideal strength and fracture strength of materials depending on whether the materials contain cracks or not. A Griffith strength limit of ~E/9 is the upper bound for ideal strengths of materials. With the improved quality of fabricated samples and the power of computational modeling, people have recently reported the possibility of exceeding the ideal strength predicted by the Griffith theory. In this study, a new strength criterion was established based on the stable analysis of thermodynamical systems; then first-principles density functional theory (DFT) is used to study the ideal strength of four materials (diamond, c-BN, Cu, and CeO2) under uniaxial tensile loading along the [100], [110], and [111] low-index crystallographic directions. By comparing the ideal strengths between DFT results and the Griffith theory, it is found that the Griffith theory fails in all the four materials. Further analysis of the fracture mechanism demonstrates that the failure of the Griffith theory is because the ideal strength point does not correspond to creating of new surfaces, which is against the Griffith assumption that the crack intrinsically exists all the time; the failure point corresponds to the crack at the start of propagation.

cond-mat.mtrl-sci↗

arXiv2020

All-fiber mode-locked ytterbium-doped fiber laser with a saturable absorber based on nonlinear Kerr beam cleanup effect

We theoretically and experimentally demonstrate a novel mode-locked ytterbium-doped fiber laser with a saturable absorber based on nonlinear Kerr beam cleanup effect. The saturable absorber was formed by a 2-m graded-index multimode fiber and a single-mode fiber segment served as a diaphragm. With an all-normal-dispersion-fiber configuration, the laser generated dissipative soliton pulses with pulse duration of 26.38 ps and pulse energy more than 0.25 nJ; output pulses could be compressed externally to 615.7 fs. Moreover, the self-starting mode-locking operation of this laser exhibited a high stability with a measured signal-to-noise ratio of 73.4 dB in the RF spectrum.

physics.optics↗

arXiv2020

On an identity for the projection operators of automorphic forms

In this note, we revisit an identity that Miller and Schmid showed in their article on a general Voronoi summation formula for $GL(n,\mathbb{Z})$ in 2009. For the proof, we mainly follow Cogdell and Piatetski-Shapiro's ideas in their work on converse theorems for $GL(n)$.

math.NT↗

arXiv2020

Effects of applied mechanical strain on vacancy clustering in FCC Ni

Irradiation-induced vacancy evolution in face-centered cubic (FCC) Ni under mechanical strains was studied using molecular dynamics simulations. Applied hydrostatic strain led to different stable forms of vacancy clusters, i.e., voids under strain >= +2% and stacking fault tetrahedras (SFTs) under strain <= 0. Direct transitions between SFT and void revealed that increasing strain magnitude facilitated the thermodynamic stability and dynamical evolution. The estimated free energy difference could well validate the dynamical simulations results by accounting for entropic contribution, which was revealed to play an important role in the thermodynamic stability of vacancy clusters in FCC Ni.

cond-mat.mtrl-sci↗

arXiv2020

The Ramanujan sum and Chebotarev densities

In this short note, we show an analogue of one of Alladi's and Dawsey's formulas with respect to the Ramanujan sum $c_n(m)$ for $m\geq1$. Their formulas may be viewed as the case $m=1$ in our result.

math.NT↗

arXiv2020

Analogues of Alladi's formula

In this note, we mainly show the analogue of one of Alladi's formulas over $\mathbb{Q}$ with respect to the Dirichlet convolutions involving the Möbius function $μ(n)$, which is related to the natural densities of sets of primes by recent work of Dawsey, Sweeting and Woo, and Kural et al. This would give us several new analogues. In particular, we get that if $(k, \ell)=1$, then $$-\sum_{\begin{smallmatrix}n\geq 2\\ p(n)\equiv \ell (\operatorname{mod} k) \end{smallmatrix}} \frac{μ(n)}{φ(n)} = \frac1{φ(k)},$$ where $p(n)$ is the smallest prime divisor of $n$, and $φ(n)$ is Euler's totient function. This refines one of Hardy's formulas in 1921. At the end, we give some examples for the $φ(n)$ replaced by functions "near $n$", which include the sum-of-divisors function.

math.NT↗

arXiv2020

On the effectiveness of local vortex identification criteria in the compressed representation of wall-bounded turbulence

Compressing complex flows into a tangle of vortex filaments is the basic implication of the classical notion of the vortex representation. Various vortex identification criteria have been proposed to extract the vortex filaments from available velocity fields, which is an essential procedure in the practice of the vortex representation. This work focuses on the effectiveness of those identification criteria in the compressed representation of wall-bounded turbulence. Five local identification criteria regarding the vortex strength and three criteria for the vortex axis are considered. To facilitate the comparisons, this work first non-dimensionalize the criteria of the vortex strength based on their dimensions and root mean squares, with corresponding equivalent thresholds prescribed. The optimal definition for the vortex vector is discussed by trialling all the possible combinations of the identification criteria for the vortex strength and the vortex axis. The effectiveness of those criteria in the compressed representation is evaluated based on two principles: (1) efficient compression, which implies the less information required, the better for the representation; (2) accurate decompression, which stresses that the original velocity fields could be reconstructed based on the vortex representation in high accuracy. In practice, the alignment of the identified vortex axis and vortex isosurface, and the accuracy for decompressed velocity fields based on those criteria are quantitatively compared. The alignment degree is described by using the differential geometry method, and the decompressing process is implemented via the two-dimensional field-based linear stochastic estimation. The results of this work provide some reference for the applications of vortex identification criteria in wall-bounded turbulence.

physics.flu-dyn↗

arXiv2020

Vortex-to-velocity reconstruction for wall-bounded turbulence via a data-driven model

Modelling the vortex structures and then translating them into the corresponding velocity fields are two essential aspects for the vortex-based modelling works in wall-bounded turbulence. This work develops a datadriven method, which allows an effective reconstruction for the velocity field based on a given vortex field. The vortex field is defined as a vector field by combining the swirl strength and the real eigenvector of the velocity gradient tensor. The distinctive properties for the vortex field are investigated, with the relationship between the vortex magnitude and orientation revealed by the differential geometry. The vortex-to-velocity reconstruction method incorporates the vortex-vortex and vortex-velocity correlation information and derives the inducing model functions under the framework of the linear stochastic estimation. Fast Fourier transformation is employed to improve the computation efficiency in implementation. The reconstruction accuracy is accessed and compared with the widely-used Biot-Savart law. Results show that the method can effectively recover the turbulent motions in a large scale range, which is very promising for the turbulence modelling. The method is also employed to investigate the inducing effects of vortices at different heights, and some revealing results are discussed and linked to the hot research topics in wall-bounded turbulence.

physics.flu-dyn↗

arXiv2020

Continual Local Replacement for Few-shot Learning

The goal of few-shot learning is to learn a model that can recognize novel classes based on one or few training data. It is challenging mainly due to two aspects: (1) it lacks good feature representation of novel classes; (2) a few of labeled data could not accurately represent the true data distribution and thus it's hard to learn a good decision function for classification. In this work, we use a sophisticated network architecture to learn better feature representation and focus on the second issue. A novel continual local replacement strategy is proposed to address the data deficiency problem. It takes advantage of the content in unlabeled images to continually enhance labeled ones. Specifically, a pseudo labeling method is adopted to constantly select semantically similar images on the fly. Original labeled images will be locally replaced by the selected images for the next epoch training. In this way, the model can directly learn new semantic information from unlabeled images and the capacity of supervised signals in the embedding space can be significantly enlarged. This allows the model to improve generalization and learn a better decision boundary for classification. Our method is conceptually simple and easy to implement. Extensive experiments demonstrate that it can achieve state-of-the-art results on various few-shot image recognition benchmarks.

cs.CV↗

arXiv2020

AIBench: An Agile Domain-specific Benchmarking Methodology and an AI Benchmark Suite

Domain-specific software and hardware co-design is encouraging as it is much easier to achieve efficiency for fewer tasks. Agile domain-specific benchmarking speeds up the process as it provides not only relevant design inputs but also relevant metrics, and tools. Unfortunately, modern workloads like Big data, AI, and Internet services dwarf the traditional one in terms of code size, deployment scale, and execution path, and hence raise serious benchmarking challenges. This paper proposes an agile domain-specific benchmarking methodology. Together with seventeen industry partners, we identify ten important end-to-end application scenarios, among which sixteen representative AI tasks are distilled as the AI component benchmarks. We propose the permutations of essential AI and non-AI component benchmarks as end-to-end benchmarks. An end-to-end benchmark is a distillation of the essential attributes of an industry-scale application. We design and implement a highly extensible, configurable, and flexible benchmark framework, on the basis of which, we propose the guideline for building end-to-end benchmarks, and present the first end-to-end Internet service AI benchmark. The preliminary evaluation shows the value of our benchmark suite---AIBench against MLPerf and TailBench for hardware and software designers, micro-architectural researchers, and code developers. The specifications, source code, testbed, and results are publicly available from the web site \url{http://www.benchcouncil.org/AIBench/index.html}.

cs.PF↗

arXiv2020

An analogue of a formula for Chebotarev Densities

In this short note, we show an analogue of Dawsey's formula on Chebotarev densities for finite Galois extensions of $\mathbb{Q}$ with respect to the Riemann zeta function $ζ(ms)$ for any integer $m\geqslant2$. Her formula may be viewed as the limit version of ours as $m\to\infty$.

math.NT↗

arXiv2020

Asymptotic Plateau Problem for Two Contours

For two disjoint rectifiable star-shaped Jordan curves (including round circles) in the asymptotic boundary of hyperbolic 3-space, if the distance (see Definition 1.8) between these two Jordan curves are bounded from above by some constant, then there exists an annulus-type area minimizing (or equivalently least area) minimal surface asymptotic to these two Jordan curves. The main results of this paper are Theorem 1.7 and Theorem 1.11.

math.DG↗

arXiv2019

SolarNet: A Deep Learning Framework to Map Solar Power Plants In China From Satellite Imagery

Renewable energy such as solar power is critical to fight the ever more serious climate change. China is the world leading installer of solar panel and numerous solar power plants were built. In this paper, we proposed a deep learning framework named SolarNet which is designed to perform semantic segmentation on large scale satellite imagery data to detect solar farms. SolarNet has successfully mapped 439 solar farms in China, covering near 2000 square kilometers, equivalent to the size of whole Shenzhen city or two and a half of New York city. To the best of our knowledge, it is the first time that we used deep learning to reveal the locations and sizes of solar farms in China, which could provide insights for solar power companies, market analysts and the government.

cs.CV↗

arXiv2019

AIBench: An Industry Standard Internet Service AI Benchmark Suite

Today's Internet Services are undergoing fundamental changes and shifting to an intelligent computing era where AI is widely employed to augment services. In this context, many innovative AI algorithms, systems, and architectures are proposed, and thus the importance of benchmarking and evaluating them rises. However, modern Internet services adopt a microservice-based architecture and consist of various modules. The diversity of these modules and complexity of execution paths, the massive scale and complex hierarchy of datacenter infrastructure, the confidential issues of data sets and workloads pose great challenges to benchmarking. In this paper, we present the first industry-standard Internet service AI benchmark suite---AIBench with seventeen industry partners, including several top Internet service providers. AIBench provides a highly extensible, configurable, and flexible benchmark framework that contains loosely coupled modules. We identify sixteen prominent AI problem domains like learning to rank, each of which forms an AI component benchmark, from three most important Internet service domains: search engine, social network, and e-commerce, which is by far the most comprehensive AI benchmarking effort. On the basis of the AIBench framework, abstracting the real-world data sets and workloads from one of the top e-commerce providers, we design and implement the first end-to-end Internet service AI benchmark, which contains the primary modules in the critical paths of an industry scale application and is scalable to deploy on different cluster scales. The specifications, source code, and performance numbers are publicly available from the benchmark council web site http://www.benchcouncil.org/AIBench/index.html.

cs.CV↗

arXiv2019

Learning Continually from Low-shot Data Stream

While deep learning has achieved remarkable results on various applications, it is usually data hungry and struggles to learn over non-stationary data stream. To solve these two limits, the deep learning model should not only be able to learn from a few of data, but also incrementally learn new concepts from data stream over time without forgetting the previous knowledge. Limited literature simultaneously address both problems. In this work, we propose a novel approach, MetaCL, which enables neural networks to effectively learn meta knowledge from low-shot data stream without catastrophic forgetting. MetaCL trains a model to exploit the intrinsic feature of data (i.e. meta knowledge) and dynamically penalize the important model parameters change to preserve learned knowledge. In this way, the deep learning model can efficiently obtain new knowledge from small volume of data and still keep high performance on previous tasks. MetaCL is conceptually simple, easy to implement and model-agnostic. We implement our method on three recent regularization-based methods. Extensive experiments show that our approach leads to state-of-the-art performance on image classification benchmarks.

cs.LG↗