Academy of Mathematics and Systems Science

This letter reports the finding of a new chaotic attractor in a simple three-dimensional autonomous system, which connects the Lorenz attractor and Chen's attractor and represents the transition from one to the other.

Y Artificial intelligence (AI) coupled with promising machine learning (ML) techniques well known from computer science is broadly affecting many aspects of various fields including science and technology, industry, and even our day-to-day life. The ML techniques have been developed to analyze high-throughput data with a view to obtaining useful insights, categorizing, predicting, and making evidence-based decisions in novel ways, which will promote the growth of novel applications and fuel the sustainable booming of AI. This paper undertakes a comprehensive survey on the development and application of AI in different aspects of fundamental sciences, including information science, mathematics, medical science, materials science, geoscience, life science, physics, and chemistry. The challenges that each discipline of science meets, and the potentials of AI techniques to handle these challenges, are discussed in detail. Moreover, we shed light on new research trends entailing the integration of AI into each scientific discipline. The aim of this paper is to provide a broad research guideline on fundamental sciences with potential infusion of AI, to help motivate researchers to deeply understand the state-of-the-art applications of AI-based fundamental sciences, and thereby to help promote the continuous development of these fundamental sciences.

Graphene-based $s{p}^{2}$-carbon nanostructures such as carbon nanotubes and nanofibers can fail near their ideal strengths due to their exceedingly small dimensions. We have calculated the phonon spectra of graphene as a function of uniaxial tension by density functional perturbation theory to assess the first occurrence of phonon instability on the strain path, which controls the strength of a defect-free crystal at $0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Uniaxial tensile strain is applied in the $x$ (nearest-neighbor) and $y$ (second nearest-neighbor) directions, related to tensile deformation of zigzag and armchair nanotubes, respectively. The Young's modulus $E=1050\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ and Poisson's ratio $\ensuremath{\nu}=0.186$ from our small-strain results are in good agreement with previous calculations. We find that in both $x$ and $y$ uniaxial tensions, phonon instabilities occur near the center of the Brillouin zone, at (${\ensuremath{\epsilon}}_{xx}=0.194$, ${\ensuremath{\sigma}}_{xx}=110\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, ${\ensuremath{\epsilon}}_{yy}=\ensuremath{-}0.016$) and (${\ensuremath{\epsilon}}_{yy}=0.266$, ${\ensuremath{\sigma}}_{yy}=121\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, ${\ensuremath{\epsilon}}_{xx}=\ensuremath{-}0.027$), respectively. Both soft phonons are longitudinal elastic waves in the pulling direction, suggesting that brittle cleavage fracture may be an inherent behavior of graphene and carbon nanotubes at low temperatures. We also predict that a phonon band gap will appear in highly stretched graphene, which could be a useful spectroscopic signature for highly stressed carbon nanotubes.

Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. 88, 017901 (2001)], is a measure of the discrepancy between two natural yet different quantum analogs of the classical mutual information. This notion characterizes and quantifies quantumness of correlations in bipartite states from a measurement perspective, and is fundamentally different from the various entanglement measures in the entanglement vs separability paradigm. The phenomenon of nonzero quantum discord is a manifestation of quantum correlations due to noncommutativity rather than due to entanglement, and has interesting and significant applications in revealing the advantage of certain quantum tasks. We will evaluate analytically the quantum discord for a large family of two-qubit states, and make a comparative study of the relationships between classical and quantum correlations in terms of the quantum discord. We furthermore compare the quantum discord with the entanglement of formation, and illustrate that the latter may be larger than the former, although for separable states, the entanglement of formation always vanishes and thus is less than the quantum discord.

In this article, we describe a long-non-coding RNA (lncRNA) and disease association database (LncRNADisease), which is publicly accessible at http://cmbi.bjmu.edu.cn/lncrnadisease. In recent years, a large number of lncRNAs have been identified and increasing evidence shows that lncRNAs play critical roles in various biological processes. Therefore, the dysfunctions of lncRNAs are associated with a wide range of diseases. It thus becomes important to understand lncRNAs' roles in diseases and to identify candidate lncRNAs for disease diagnosis, treatment and prognosis. For this purpose, a high-quality lncRNA-disease association database would be extremely beneficial. Here, we describe the LncRNADisease database that collected and curated approximately 480 entries of experimentally supported lncRNA-disease associations, including 166 diseases. LncRNADisease also curated 478 entries of lncRNA interacting partners at various molecular levels, including protein, RNA, miRNA and DNA. Moreover, we annotated lncRNA-disease associations with genomic information, sequences, references and species. We normalized the disease name and the type of lncRNA dysfunction and provided a detailed description for each entry. Finally, we developed a bioinformatic method to predict novel lncRNA-disease associations and integrated the method and the predicted associated diseases of 1564 human lncRNAs into the database.

Today, complex networks have attracted increasing attention from various fields of science and engineering. It has been demonstrated that many complex networks display various synchronization phenomena. In this note, we introduce a time-varying complex dynamical network model. We then further investigate its synchronization phenomenon and prove several network synchronization theorems. Especially, we show that synchronization of such a time-varying dynamical network is completely determined by the inner-coupling matrix, and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network.

A Boolean network is a logical dynamic system, which has been used to describe cellular networks. Using a new matrix product, called semi-tensor product of matrices, a logical function can be expressed as an algebraic function. This expression can covert the Boolean networks into discrete-time linear dynamic systems. Similarly, the Boolean control networks can also be converted into discrete time bilinear dynamic systems. Under these forms the standard matrix analysis can be used to consider the structure and the control problems of Boolean (control) networks. After the detailed description of this new approach, the controllability of Boolean control networks is considered in the paper as an application.

This paper introduces a unified chaotic system that contains the Lorenz and the Chen systems as two dual systems at the two extremes of its parameter spectrum. The new system represents the continued transition from the Lorenz to the Chen system and is chaotic over the entire spectrum of the key system parameter. Dynamical behaviors of the unified system are investigated in somewhat detail.

The primary circulating form of vitamin D, 25-hydroxy-vitamin D [25(OH)D], is associated with multiple medical outcomes, including rickets, osteoporosis, multiple sclerosis and cancer. In a genome-wide association study (GWAS) of 4501 persons of European ancestry drawn from five cohorts, we identified single-nucleotide polymorphisms (SNPs) in the gene encoding group-specific component (vitamin D binding) protein, GC, on chromosome 4q12-13 that were associated with 25(OH)D concentrations: rs2282679 (P=2.0x10(-30)), in linkage disequilibrium (LD) with rs7041, a non-synonymous SNP (D432E; P=4.1x10(-22)) and rs1155563 (P=3.8x10(-25)). Suggestive signals for association with 25(OH)D were also observed for SNPs in or near three other genes involved in vitamin D synthesis or activation: rs3829251 on chromosome 11q13.4 in NADSYN1 [encoding nicotinamide adenine dinucleotide (NAD) synthetase; P=8.8x10(-7)], which was in high LD with rs1790349, located in DHCR7, the gene encoding 7-dehydrocholesterol reductase that synthesizes cholesterol from 7-dehydrocholesterol; rs6599638 in the region harboring the open-reading frame 88 (C10orf88) on chromosome 10q26.13 in the vicinity of ACADSB (acyl-Coenzyme A dehydrogenase), involved in cholesterol and vitamin D synthesis (P=3.3x10(-7)); and rs2060793 on chromosome 11p15.2 in CYP2R1 (cytochrome P450, family 2, subfamily R, polypeptide 1, encoding a key C-25 hydroxylase that converts vitamin D3 to an active vitamin D receptor ligand; P=1.4x10(-5)). We genotyped SNPs in these four regions in 2221 additional samples and confirmed strong genome-wide significant associations with 25(OH)D through meta-analysis with the GWAS data for GC (P=1.8x10(-49)), NADSYN1/DHCR7 (P=3.4x10(-9)) and CYP2R1 (P=2.9x10(-17)), but not C10orf88 (P=2.4x10(-5)).

Consensusability of multi-agent systems (MASs) is a fundamental problem in the MAS research area, since when starting to design a consensus protocol, one should know whether or not there exists such a protocol that has the ability to make the MAS involved consensus. This technical note is aimed at studying the joint impact of the agent dynamic structure and the communication topology on consensusability. For the MASs with fixed topology and agents described by linear time-invariant systems, a necessary condition of consensusability with respect to a set of admissible consensus protocols is given, which is shown, under some mild conditions, to be necessary and sufficient.

Abstract The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on ‘Black holes, Gravitational waves and Fundamental Physics’.

A new matrix product, called semi-tensor product of matrices, is reviewed. Using it, a matrix expression of logic is proposed, where a logical variable is expressed as a vector, a logical function is expressed as a multiple linear mapping. Under this framework, a Boolean network equation is converted into an equivalent algebraic form as a conventional discrete-time linear system. Analyzing the transition matrix of the linear system, formulas are obtained to show a) the number of fixed points; b) the numbers of cycles of different lengths; c) transient period, for all points to enter the set of attractors; and d) basin of each attractor. The corresponding algorithms are developed and used to some examples.

Summary. Quantile regression offers a more complete statistical model than mean regression and now has widespread applications. Consequently, we provide a review of this technique. We begin with an introduction to and motivation for quantile regression. We then discuss some typical application areas. Next we outline various approaches to estimation. We finish by briefly summarizing some recent research areas.

The space-based Laser Interferometer Space Antenna (LISA) will be able to observe the gravitational-wave signals from systems comprised of a massive black hole and a stellar-mass compact object. These systems are known as extreme-mass-ratio inspirals (EMRIs) and are expected to complete $\ensuremath{\sim}1{0}^{4}--1{0}^{5}$ cycles in band, thus allowing exquisite measurements of their parameters. In this work, we attempt to quantify the astrophysical uncertainties affecting the predictions for the number of EMRIs detectable by LISA, and find that competing astrophysical assumptions produce a variance of about three orders of magnitude in the expected intrinsic EMRI rate. However, we find that irrespective of the astrophysical model, at least a few EMRIs per year should be detectable by the LISA mission, with up to a few thousands per year under the most optimistic astrophysical assumptions. We also investigate the precision with which LISA will be able to extract the parameters of these sources. We find that typical fractional statistical errors with which the intrinsic parameters (redshifted masses, massive black hole spin and orbital eccentricity) can be recovered are $\ensuremath{\sim}{10}^{\ensuremath{-}6}--{10}^{\ensuremath{-}4}$. Luminosity distance (which is required to infer true masses) is inferred to about 10% precision and sky position is localized to a few square degrees, while tests of the multipolar structure of the Kerr metric can be performed to percent-level precision or better.

This note further investigates the locally and globally adaptive synchronization of an uncertain complex dynamical network. Several network synchronization criteria are deduced. Especially, our hypotheses and designed adaptive controllers for network synchronization are rather simple in form. It is very useful for future practical engineering design. Moreover, numerical simulations are also given to show the effectiveness of our synchronization approaches.

Recent advances in spatially resolved transcriptomics have enabled comprehensive measurements of gene expression patterns while retaining the spatial context of the tissue microenvironment. Deciphering the spatial context of spots in a tissue needs to use their spatial information carefully. To this end, we develop a graph attention auto-encoder framework STAGATE to accurately identify spatial domains by learning low-dimensional latent embeddings via integrating spatial information and gene expression profiles. To better characterize the spatial similarity at the boundary of spatial domains, STAGATE adopts an attention mechanism to adaptively learn the similarity of neighboring spots, and an optional cell type-aware module through integrating the pre-clustering of gene expressions. We validate STAGATE on diverse spatial transcriptomics datasets generated by different platforms with different spatial resolutions. STAGATE could substantially improve the identification accuracy of spatial domains, and denoise the data while preserving spatial expression patterns. Importantly, STAGATE could be extended to multiple consecutive sections to reduce batch effects between sections and extracting three-dimensional (3D) expression domains from the reconstructed 3D tissue effectively.

MOTIVATION: More and more evidences have indicated that long-non-coding RNAs (lncRNAs) play critical roles in many important biological processes. Therefore, mutations and dysregulations of these lncRNAs would contribute to the development of various complex diseases. Developing powerful computational models for potential disease-related lncRNAs identification would benefit biomarker identification and drug discovery for human disease diagnosis, treatment, prognosis and prevention. RESULTS: In this article, we proposed the assumption that similar diseases tend to be associated with functionally similar lncRNAs. Then, we further developed the method of Laplacian Regularized Least Squares for LncRNA-Disease Association (LRLSLDA) in the semisupervised learning framework. Although known disease-lncRNA associations in the database are rare, LRLSLDA still obtained an AUC of 0.7760 in the leave-one-out cross validation, significantly improving the performance of previous methods. We also illustrated the performance of LRLSLDA is not sensitive (even robust) to the parameters selection and it can obtain a reliable performance in all the test classes. Plenty of potential disease-lncRNA associations were publicly released and some of them have been confirmed by recent results in biological experiments. It is anticipated that LRLSLDA could be an effective and important biological tool for biomedical research. AVAILABILITY: The code of LRLSLDA is freely available at http://asdcd.amss.ac.cn/Software/Details/2.

In this paper, we propose multi-input multi-output (MIMO) beamforming designs towards joint radar sensing and multi-user communications. We employ the Cramér-Rao bound (CRB) as a performance metric of target estimation, under both point and extended target scenarios. We then propose minimizing the CRB of radar sensing while guaranteeing a pre-defined level of signal-to-interference-plus-noise ratio (SINR) for each communication user. For the single-user scenario, we derive a closed form for the optimal solution for both cases of point and extended targets. For the multi-user scenario, we show that both problems can be relaxed into semidefinite programming by using the semidefinite relaxation approach, and prove that the global optimum can be generally obtained. Finally, we demonstrate numerically that the globally optimal solutions are reachable via the proposed methods, which provide significant gains in target estimation performance over state-of-the-art benchmarks.

This paper investigates the average-consensus problem of first-order discrete-time multi-agent networks in uncertain communication environments. Each agent can only use its own and neighbors' information to design its control input. To attenuate the communication noises, a distributed stochastic approximation type protocol is used. By using probability limit theory and algebraic graph theory, consensus conditions for this kind of protocols are obtained: (A) For the case of fixed topologies, a necessary and sufficient condition for mean square average-consensus is given, which is also sufficient for almost sure consensus. (B) For the case of time-varying topologies, sufficient conditions for mean square average-consensus and almost sure consensus are given, respectively. Especially, if the network switches between jointly-containing-spanning-tree, instantaneously balanced graphs, then the designed protocol can guarantee that each individual state converges, both almost surely and in mean square, to a common random variable, whose expectation is right the average of the initial states of the whole system, and whose variance describes the static maximum mean square error between each individual state and the average of the initial states of the whole system.

Communication data rate and energy constraints are important factors which have to be considered when investigating distributed coordination of multi-agent networks. Although many proposed average-consensus protocols are available, a fundamental theoretic problem remains open, namely, how many bits of information are necessary for each pair of adjacent agents to exchange at each time step to ensure average consensus? In this paper, we consider average-consensus control of undirected networks of discrete-time first-order agents under communication constraints. Each agent has a real-valued state but can only exchange symbolic data with its neighbors. A distributed protocol is proposed based on dynamic encoding and decoding. It is proved that under the protocol designed, for a connected network, average consensus can be achieved with an exponential convergence rate based on merely one bit information exchange between each pair of adjacent agents at each time step. An explicit form of the asymptotic convergence rate is given. It is shown that as the number of agents increases, the asymptotic convergence rate is related to the scale of the network, the number of quantization levels and the ratio of the second smallest eigenvalue to the largest eigenvalue of the Laplacian of the communication graph. We also give a performance index to characterize the total communication energy to achieve average consensus and show that the minimization of the communication energy leads to a tradeoff between the convergence rate and the number of quantization levels.