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Predicting cellular responses to various perturbations is a critical focus in drug discovery and personalized therapeutics, with deep learning models playing a significant role in this endeavor. Single-cell datasets contain technical artifacts that may hinder the predictability of such models, which poses quality control issues highly regarded in this area. To address this, we propose CRADLE-VAE, a causal generative framework tailored for single-cell gene perturbation modeling, enhanced with counterfactual reasoning-based artifact disentanglement. Throughout training, CRADLE-VAE models the underlying latent distribution of technical artifacts and perturbation effects present in single-cell datasets. It employs counterfactual reasoning to effectively disentangle such artifacts by modulating the latent basal spaces and learns robust features for generating cellular response data with improved quality. Experimental results demonstrate that this approach improves not only treatment effect estimation performance but also generative quality as well. The CRADLE-VAE codebase is publicly available at https://github.com/dmis-lab/CRADLE-VAE.

Chalcogenide perovskites such as BaZrS3 are promising candidates for next generation optoelectronics such as photodetectors and solar cells. Compared to widely studied polycrystalline thin films, single crystals of BaZrS3 with minimal extended and point defects, are ideal platform to study the material's intrinsic transport properties and to make first-generation optoelectronic devices. However, the surface dielectrics formed on BaZrS3 single crystals due to sulfating or oxidation have led to significant challenges to achieving high quality electrical contacts, and hence, realizing the high-performance optoelectronic devices. Here, we report the development of electrical contact fabrication processes on BaZrS3 single crystals, where various processes were employed to address the surface dielectric issue. Moreover, with optimized electrical contacts fabricated through dry etching, high-performance BaZrS3 photoconductive devices with a low dark current of 0.1 nA at 10 V bias and a fast transient photoresponse with rise and decay time of <0.2 s were demonstrated.

For some positive integer $m$, a real polynomial $P(x)=\sum\limits_{k=0}^ma_kx^k$ with $a_k\geqslant 0$ is called log-concave (resp. ultra log-concave) if $a_k^2\geqslant a_{k-1}a_{k+1}$ (resp. $a_k^2\geqslant \left(1+\frac{1}{k}\right)\left(1+\frac{1}{m-k}\right)\cdot$ $a_{k-1}a_{k+1}$) for all $1\leqslant k\leqslant m-1$. If $P(x)$ has only real roots, then it is called real-rooted. It is well-known that the conditions of log-concavity, ultra log-concavity and real-rootedness are ever-stronger. For a graph $G$, a dependent set is a set of vertices which is not independent, i.e., the set of vertices whose induced subgraph contains at least one edge. The dependence polynomial of $G$ is defined as $D(G, x):=\sum\limits_{k\geqslant 0}d_k(G)x^k$, where $d_k(G)$ is the number of dependent sets of size $k$ in $G$. Horrocks proved that $D(G, x)$ is log-concave for every graph $G$ [J. Combin. Theory, Ser. B, 84 (2002) 180--185]. In the present paper, we prove that, for a graph $G$, $D(G, x)$ is ultra log-concave if $G$ is $(K_2\cup 2K_1)$-free or contains an independent set of size $|V(G)|-2$, and give the characterization of graphs whose dependence polynomials are real-rooted. Finally, we focus more attention to the problems of log-concavity about independence systems and pose several conjectures closely related the famous Mason's Conjecture., Comment: 17 pages, 5 figures

Miniaturized spectrometers hold great promise for in situ, in vitro, and even in vivo sensing applications. However, their size reduction imposes vital performance constraints in meeting the rigorous demands of spectroscopy, including fine resolution, high accuracy, and ultra-wide observation window. The prevailing view in the community holds that miniaturized spectrometers are most suitable for the coarse identification of signature peaks. In this paper, we present an integrated reconstructive spectrometer that enables near-infrared (NIR) spectroscopic metrology, and demonstrate a fully packaged sensor with auxiliary electronics. Such a sensor operates over a 520 nm bandwidth together with a resolution of less than 8 pm, which translates into a record-breaking bandwidth-to-resolution ratio of over 65,000. The classification of different types of solid substances and the concentration measurement of aqueous and organic solutions are performed, all achieving approximately 100% accuracy. Notably, the detection limit of our sensor matches that of the commercial benchtop counterparts, which is as low as 0.1% (i.e. 100 mg/dL) for identifying the concentration of glucose solution.

We propose a semiparametric model for dyadic link formations in directed networks. The model contains a set of degree parameters that measure different effects of popularity or outgoingness across nodes, a regression parameter vector that reflects the homophily effect resulting from the nodal attributes or pairwise covariates associated with edges, and a set of latent random noises with unknown distributions. Our interest lies in inferring the unknown degree parameters and homophily parameters. The dimension of the degree parameters increases with the number of nodes. Under the high-dimensional regime, we develop a kernel-based least squares approach to estimate the unknown parameters. The major advantage of our estimator is that it does not encounter the incidental parameter problem for the homophily parameters. We prove consistency of all the resulting estimators of the degree parameters and homophily parameters. We establish high-dimensional central limit theorems for the proposed estimators and provide several applications of our general theory, including testing the existence of degree heterogeneity, testing sparse signals and recovering the support. Simulation studies and a real data application are conducted to illustrate the finite sample performance of the proposed methods., Comment: 28 pages, 3 figures

Scalable isomorphic physical neural networks (PNNs) are emerging NN acceleration paradigms for their high-bandwidth, in-propagation computation. Despite backpropagation (BP)-based training is often the industry standard for its robustness and fast gradient convergences, existing BP-PNN training methods need to truncate the propagation of analogue signal at each layer and acquire accurate hidden neuron readouts for deep networks. This compromises the incentive of PNN for fast in-propagation processing. In addition, the required readouts introduce massive bottlenecks due to the conversions between the analogue-digital interfaces to shuttle information across. These factors limit both the time and energy efficiency during training. Here we introduce the asymmetrical training (AT) method, a BP-based method that can perform training on an encapsulated deep network, where the information propagation is maintained within the analogue domain until the output layer. AT's minimum information access bypass analogue-digital interface bottleneck wherever possible. For any deep network structure, AT offers significantly improved time and energy efficiency compared to existing BP-PNN methods, and scales well for large network sizes. We demonstrated AT's error-tolerant and calibration-free training for encapsulated integrated photonic deep networks to achieve near ideal BP performances. AT's well-behaved training is demonstrated repeatably across different datasets and network structures, Comment: 21 pages, 6 figures

BaTiS3, a quasi-1D complex chalcogenide, has gathered considerable scientific and technological interest due to its giant optical anisotropy and electronic phase transitions. However, the synthesis of high-quality BaTiS3 crystals, particularly those featuring crystal sizes of millimeters or larger, remains a challenge. Here, we investigate the growth of BaTiS3 crystals utilizing a molten salt flux of either potassium iodide, or a mixture of barium chloride and barium iodide. The crystals obtained through this method exhibit a substantial increase in volume compared to those synthesized via the chemical vapor transport method, while preserving their intrinsic optical and electronic properties. Our flux growth method provides a promising route towards the production of high-quality, large-scale single crystals of BaTiS3, which will greatly facilitate advanced characterizations of BaTiS3 and its practical applications that require large crystal dimensions. Additionally, our approach offers an alternative synthetic route for other emerging complex chalcogenides.

Recent theoretical and experimental studies of the interlayer Dzyaloshinskii-Moriya interaction (DMI) has sparked great interest in its implementation into practical magnetic random-access memory (MRAM) devices, due to its capability to mediate long-range chiral spin textures. So far, experimental reports focused on the observation of interlayer DMI, leaving the development of strategies to control interlayer DMI's magnitude unaddressed. Here, we introduce an azimuthal symmetry engineering protocol capable of additive/subtractive tuning of interlayer DMI through the control of wedge deposition of separate layers, and demonstrate its capability to mediate field-free spin-orbit torque (SOT) magnetization switching in both orthogonally magnetized and synthetic antiferromagnetically coupled systems. Furthermore, we showcase the spatial inhomogeneity brought about by wedge depositon can be suppressed by specific azimuthal engineering design, ideal for practical implementation. Our findings provide guidelines for effective manipulations of interlayer DMI strength, beneficial for future design of SOT-MRAM or other spintronic devices utilizing interlayer DMI., Comment: 32 pages, 10 figures

How to achieve the tradeoff between privacy and utility is one of fundamental problems in private data analysis.In this paper, we give a rigourous differential privacy analysis of networks in the appearance of covariates via a generalized $\beta$-model, which has an $n$-dimensional degree parameter $\beta$ and a $p$-dimensional homophily parameter $\gamma$.Under $(k_n, \epsilon_n)$-edge differential privacy, we use the popular Laplace mechanism to release the network statistics.The method of moments is used to estimate the unknown model parameters. We establish the conditions guaranteeing consistency of the differentially private estimators $\widehat{\beta}$ and $\widehat{\gamma}$ as the number of nodes $n$ goes to infinity, which reveal an interesting tradeoff between a privacy parameter and model parameters. The consistency is shown by applying a two-stage Newton's method to obtain the upper bound of the error between $(\widehat{\beta},\widehat{\gamma})$ and its true value $(\beta, \gamma)$ in terms of the $\ell_\infty$ distance, which has a convergence rate of rough order $1/n^{1/2}$ for $\widehat{\beta}$ and $1/n$ for $\widehat{\gamma}$, respectively. Further, we derive the asymptotic normalities of $\widehat{\beta}$ and $\widehat{\gamma}$, whose asymptotic variances are the same as those of the non-private estimators under some conditions. Our paper sheds light on how to explore asymptotic theory under differential privacy in a principled manner; these principled methods should be applicable to a class of network models with covariates beyond the generalized $\beta$-model. Numerical studies and a real data analysis demonstrate our theoretical findings., Comment: 34 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2107.10735 by other authors

We explore the Wilks phenomena in two random graph models: the $\beta$-model and the Bradley-Terry model. For two increasing dimensional null hypotheses, including a specified null $H_0: \beta_i=\beta_i^0$ for $i=1,\ldots, r$ and a homogenous null $H_0: \beta_1=\cdots=\beta_r$, we reveal high dimensional Wilks' phenomena that the normalized log-likelihood ratio statistic, $[2\{\ell(\widehat{\mathbf{\beta}}) - \ell(\widehat{\mathbf{\beta}}^0)\} -r]/(2r)^{1/2}$, converges in distribution to the standard normal distribution as $r$ goes to infinity. Here, $\ell( \mathbf{\beta})$ is the log-likelihood function on the model parameter $\mathbf{\beta}=(\beta_1, \ldots, \beta_n)^\top$, $\widehat{\mathbf{\beta}}$ is its maximum likelihood estimator (MLE) under the full parameter space, and $\widehat{\mathbf{\beta}}^0$ is the restricted MLE under the null parameter space. For the homogenous null with a fixed $r$, we establish Wilks-type theorems that $2\{\ell(\widehat{\mathbf{\beta}}) - \ell(\widehat{\mathbf{\beta}}^0)\}$ converges in distribution to a chi-square distribution with $r-1$ degrees of freedom, as the total number of parameters, $n$, goes to infinity. When testing the fixed dimensional specified null, we find that its asymptotic null distribution is a chi-square distribution in the $\beta$-model. However, unexpectedly, this is not true in the Bradley-Terry model. By developing several novel technical methods for asymptotic expansion, we explore Wilks type results in a principled manner; these principled methods should be applicable to a class of random graph models beyond the $\beta$-model and the Bradley-Terry model. Simulation studies and real network data applications further demonstrate the theoretical results., Comment: This paper supersedes arxiv article arXiv:2211.10055 titled "Wilks' theorems in the $\beta$-model" by T. Yan, Y. Zhang, J. Xu, Y. Yang and J. Zhu

The early afterglow of a Gamma-ray burst (GRB) can provide critical information on the jet and progenitor of the GRB. The extreme brightness of GRB 221009A allows us to probe its early afterglow in unprecedented detail. In this letter, we report comprehensive observation results of the early afterglow of GRB 221009A (from $T_0$+660 s to $T_0$+1860 s, where $T_0$ is the \textit{Insight}-HXMT/HE trigger time) in X/$\gamma$-ray energy band (from 20 keV to 20 MeV) by \textit{Insight}-HXMT/HE, GECAM-C and \textit{Fermi}/GBM. We find that the spectrum of the early afterglow in 20 keV-20 MeV could be well described by a cutoff power-law with an extra power-law which dominates the low and high energy bands respectively. The cutoff power-law $E_{\rm peak}$ is $\sim$ 30 keV and the power-law photon index is $\sim$ 1.8 throughout the early afterglow phase. By fitting the light curves in different energy bands, we find that a significant achromatic break (from keV to TeV) is required at $T_0$ + 1246$^{+27}_{-26}$ s (i.e. 1021 s since the afterglow starting time $T_{\rm AG}$=$T_0$+225 s), providing compelling evidence of a jet break. Interestingly, both the pre-break and post-break decay slopes vary with energy, and these two slopes become closer in the lower energy band, making the break less identifiable. Intriguingly, the spectrum of the early afterglow experienced a slight hardening before the break and a softening after the break. These results provide new insights into the understanding of this remarkable GRB., Comment: Accepted for publication in ApJ Letters on 19-Jan-2024, 11 pages, 7 figures and 2 tables

It is crucial to realize field-free, deterministic, current-induced switching in spin-orbit torque magnetic random-access memory (SOT-MRAM) with perpendicular magnetic anisotropy (PMA). A tentative solution has emerged recently, which employs the interlayer chiral exchange coupling or the interlayer Dzyaloshinskii-Moriya interaction (i-DMI) to achieve symmetry breaking. We hereby investigate the interlayer DMI in a Pt/Co multilayer system with orthogonally magnetized layers, using repeatedly stacked [Pt/Co]n structure with PMA, and a thick Co layer with in-plane magnetic anisotropy (IMA). We clarify the origin and the direction of such symmetry breaking with relation to the i-DMI effective field, and show a decreasing trend of the said effective field magnitude to the stacking number (n). By comparing the current-induced field-free switching behavior for both PMA and IMA layers, we confirm the dominating role of i-DMI in such field-free switching, excluding other possible mechanisms such as tilted-anisotropy and unconventional spin currents that may have arisen from the symmetry breaking.

Magnetar is a neutron star with an ultrahigh magnetic field ($\sim 10^{14}-10^{15}$ G) which usually manifests as soft gamma-ray repeater (SGR) or anomalous X-ray pulsar (AXP). SGR J1935+2154 is not only one of the most active magnetar detected so far, but also the unique confirmed source of fast radio burst (FRB). Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor (GECAM) are dedicated to monitor gamma-ray transients all over the sky, including SGR bursts. Here we report the GECAM observation of the burst activity of SGR J1935+2154 from January 2021 to December 2022, which results in a unique and valuable data set for this important magnetar. With a targeted search of GECAM data, 164 bursts from SGR J1935+2154 are detected by GECAM-B while 97 bursts by GECAM-C, including the X-ray burst associated with a fast radio burst (FRB 20221014). We find that both the burst duration and the waiting time between two successive bursts follow lognormal distributions. The period of burst activity is $134\pm20$ days, thus the burst activity could be generally divided into 4 active episodes over these two years. Interestingly, the hardness ratio of X-ray bursts tends to be softer and more concentrated over these two years, especially during the active episode with FRBs detected.

The discovery of efficient magnetization switching activated by the spin Hall effect (SHE)-induced spin-orbit torque (SOT) changed the course of magnetic random-access memory (MRAM) research and development. However, for systems with perpendicular magnetic anisotropy (PMA), the use of SOT is still hampered by the necessity of a longitudinal magnetic field to break the magnetic symmetry to achieve deterministic switching. In this work, we first demonstrate that a robust and tunable field-free current-driven SOT switching of perpendicular magnetization can be controlled by the growth protocol in Pt-based magnetic heterostructures. It is further elucidated that such growth-dependent symmetry breaking is originated from the laterally tilted magnetic anisotropy of the ferromagnetic layer with PMA, which has been largely neglected in previous studies and its critical role should be re-focused. We show by both experiments and simulations that in a PMA system with tilted anisotropy, the deterministic field-free switching possesses a conventional SHE-induced damping-like torque feature and the resulting current-induced effective field has a non-linear dependence on the applied current density, which could be potentially misattributed to an unconventional SOT origin.

Dynamic network data analysis requires joint modelling individual snapshots and time dynamics. This paper proposes a new two-way heterogeneity model towards this goal. The new model equips each node of the network with two heterogeneity parameters, one to characterize the propensity of forming ties with other nodes and the other to differentiate the tendency of retaining existing ties over time. Though the negative log-likelihood function is non-convex, it is locally convex in a neighbourhood of the true value of the parameter vector. By using a novel method of moments estimator as the initial value, the consistent local maximum likelihood estimator (MLE) can be obtained by a gradient descent algorithm. To establish the upper bound for the estimation error of the MLE, we derive a new uniform deviation bound, which is of independent interest. The usefulness of the model and the associated theory are further supported by extensive simulation and the analysis of some real network data sets.

We extend the well-known $\beta$-model for directed graphs to dynamic network setting, where we observe snapshots of adjacency matrices at different time points. We propose a kernel-smoothed likelihood approach for estimating $2n$ time-varying parameters in a network with $n$ nodes, from $N$ snapshots. We establish consistency and asymptotic normality properties of our kernel-smoothed estimators as either $n$ or $N$ diverges. Our results contrast their counterparts in single-network analyses, where $n\to\infty$ is invariantly required in asymptotic studies. We conduct comprehensive simulation studies that confirm our theory's prediction and illustrate the performance of our method from various angles. We apply our method to an email data set and obtain meaningful results.

Inspired by the observation of the $X(6900)$ by LHCb and the $X(6600)$ (with mass $6552\pm 10$ $\pm 12$ MeV) recently by CMS and ATLAS experiments of the LHC in the di-$J/\Psi $ invariant mass spectrum, we systemically study masses of all ground-state configurations of the hidden heavy-flavor tetraquarks $q_{1}Q_{2}\bar{q}_{3}\bar{Q}_{4}$ and $Q_{1}Q_{2}\bar{Q}_{3}\bar{Q}_{4}$ ($Q=c,b$;$q=u,d,s$) contaning two and four heavy quarks in the MIT bag model with chromomagnetic interaction and enhanced binding energy. Considering color-spin mixing due to chromomagnetic interaction, our mass computation indicates that the observed $X(6600)$ is likely to be the $0^{++}$ ground states of hidden-charm tetraquark $cc\bar{c}\bar{c}$ with computed masses $6572$ MeV, which has a $0^{++}$ color partner around $6469$ MeV. The fully bottom system of tetraquark $bb\bar{b}\bar{b}$ has masses of 19685 MeV and 19717 MeV for the the $0^{++}$ ground states. Further computation is given to the tetraquark systems $sc\bar{s}\bar{c}$, $sb\bar{s}\bar{b}$, $cb\bar{c}\bar{b}$, $nc\bar{n}\bar{c}$ and $nb\bar{n}\bar{b}$, suggesting that the $Z_{c}(4200)$ is the tetraquark $nc\bar{n}\bar{c}$ with $J^{PC}=1^{+-}$. All of these tetraquarks are above their lowest thresholds of two mesons and unstable against the strong decays.

Partial cubes are the graphs which can be embedded into hypercubes. The {\em cube polynomial} of a graph $G$ is a counting polynomial of induced hypercubes of $G$, which is defined as $C(G,x):=\sum_{i\geqslant 0}\alpha_i(G)x^i$, where $\alpha_i(G)$ is the number of induced $i$-cubes (hypercubes of dimension $i$) of $G$. The {\em clique polynomial} of $G$ is defined as $Cl(G,x):=\sum_{i\geqslant 0}a_i(G)x^i$, where $a_i(G)$ ($i\geqslant 1$) is the number of $i$-cliques in $G$ and $a_0(G)=1$. Equivalently, $Cl(G, x)$ is exactly the independence polynomial of the complement $\overline{G}$ of $G$. The {\em crossing graph} $G^{\#}$ of a partial cube $G$ is the graph whose vertices are corresponding to the $\Theta$-classes of $G$, and two $\Theta$-classes are adjacent in $G^{\#}$ if and only if they cross in $G$. In the present paper, we prove that for a partial cube $G$, $C(G,x)\leqslant Cl(G^{\#}, x+1)$ and the equality holds if and only if $G$ is a median graph. Since every graph can be represented as the crossing graph of a median graph [SIAM J. Discrete Math., 15 (2002) 235--251], the above necessary-and-sufficient result shows that the study on the cube polynomials of median graphs can be transformed to the one on the clique polynomials of general graphs (equivalently, on the independence polynomials of their complements). In addition, we disprove the conjecture that the cube polynomials of median graphs are unimodal., Comment: 13 pages,2 figures

GRB 221009A is the brightest gamma-ray burst ever detected since the discovery of this kind of energetic explosions. However, an accurate measurement of the prompt emission properties of this burst is very challenging due to its exceptional brightness. With joint observations of \textit{Insight}-HXMT and GECAM-C, we made an unprecedentedly accurate measurement of the emission during the first $\sim$1800 s of GRB 221009A, including its precursor, main emission (ME, which dominates the burst in flux), flaring emission and early afterglow, in the hard X-ray to soft gamma-ray band from $\sim$ 10 keV to $\sim$ 6 MeV. Based on the GECAM-C unsaturated data of the ME, we measure a record-breaking isotropic equivalent energy ($E_{\rm iso}$) of $\bf \sim 1.5 \times 10^{55}$ erg, which is about eight times the total rest-mass energy of the Sun. The early afterglow data require a significant jet break between 650 s and 1100 s, most likely at $\sim950$ s from the afterglow starting time $T_{AG}$, which corresponds to a jet opening angle of $\sim {0.7^\circ} \ (\eta_\gamma n)^{1/8}$, where $n$ is the ambient medium density in units of $\rm cm^{-3}$ and $\eta_\gamma$ is the ratio between $\gamma$-ray energy and afterglow kinetic energy. The beaming-corrected total $\gamma$-ray energy $E_{\gamma}$ is $\sim 1.15 \times10^{51} \ (\eta_\gamma n)^{1/4}$ erg, which is typical for long GRBs. These results suggest that this GRB may have a special central engine, which could launch and collimate a very narrowly beamed jet with an ordinary energy budget, leading to exceptionally luminous gamma-ray radiation per unit solid angle. Alternatively, more GRBs might have such a narrow and bright beam, which are missed by an unfavorable viewing angle or have been detected without distance measurement., Comment: Submitted to National Science Review. This paper is under press embargo, contact the corresponding author for details

We experimentally test the compliance with 5G/NR 3GPP technical specifications of an analog radio-over-FSO link at 9 {\mu}m. The ACLR and EVM transmitter requirements are fulfilled validating the suitability of LWIR FSO for 6G fronthaul., Comment: Accepted in Optical Fiber Communication Conference (OFC) 2023, 3 pages, 2 figures

Partial cubes are graphs that can be isometrically embedded into hypercubes. Convex cycles play an important role in the study of partial cubes. In this paper, we prove that a regular partial cube is a hypercube (resp., a Doubled Odd graph, an even cycle of length $2n$ where $n\geqslant 4$) if and only if all its convex cycles are 4-cycles (resp., 6-cycles, $2n$-cycles). In particular, the partial cubes whose all convex cycles are 4-cycles are equivalent to almost-median graphs. Therefore, we conclude that regular almost-median graphs are exactly hypercubes, which generalizes the result by Mulder [J. Graph Theory, 4 (1980) 107--110] -- regular median graphs are hypercubes., Comment: 8 pages, 0 figures

Continuous time network data have been successfully modeled by multivariate counting processes, in which the intensity function is characterized by covariate information. However, degree heterogeneity has not been incorporated into the model which may lead to large biases for the estimation of homophily effects. In this paper, we propose a degree-corrected Cox network model to simultaneously analyze the dynamic degree heterogeneity and homophily effects for continuous time directed network data. Since each node has individual-specific in- and out-degree effects in the model, the dimension of the time-varying parameter vector grows with the number of nodes, which makes the estimation problem non-standard. We develop a local estimating equations approach to estimate unknown time-varying parameters, and establish consistency and asymptotic normality of the proposed estimators by using the powerful martingale process theories. We further propose test statistics to test for trend and degree heterogeneity in dynamic networks. Simulation studies are provided to assess the finite sample performance of the proposed method and a real data analysis is used to illustrate its practical utility., Comment: 60 pages, 10 figures

Likelihood ratio tests and the Wilks theorems have been pivotal in statistics but have rarely been explored in network models with an increasing dimension. We are concerned here with likelihood ratio tests in the $\beta$-model for undirected graphs. For two growing dimensional null hypotheses including a specified null $H_0: \beta_i=\beta_i^0$ for $i=1,\ldots, r$ and a homogenous null $H_0: \beta_1=\cdots=\beta_r$, we reveal high dimensional Wilks' phenomena that the normalized log-likelihood ratio statistic, $[2\{\ell(\widehat{\boldsymbol{\beta}}) - \ell(\widehat{\boldsymbol{\beta}}^0)\} - r]/(2r)^{1/2}$, converges in distribution to the standard normal distribution as $r$ goes to infinity. Here, $\ell( \boldsymbol{\beta})$ is the log-likelihood function on the vector parameter $\boldsymbol{\beta}=(\beta_1, \ldots, \beta_n)^\top$, $\widehat{\boldsymbol{\beta}}$ is its maximum likelihood estimator (MLE) under the full parameter space, and $\widehat{\boldsymbol{\beta}}^0$ is the restricted MLE under the null parameter space. For the corresponding fixed dimensional null $H_0: \beta_i=\beta_i^0$ for $i=1,\ldots, r$ and the homogenous null $H_0: \beta_1=\cdots=\beta_r$ with a fixed $r$, we establish Wilks type of results that $2\{\ell(\widehat{\boldsymbol{\beta}}) - \ell(\widehat{\boldsymbol{\beta}}^0)\}$ converges in distribution to a Chi-square distribution with respective $r$ and $r-1$ degrees of freedom, as the total number of parameters, $n$, goes to infinity. The Wilks type of results are further extended into a closely related Bradley--Terry model for paired comparisons, where we discover a different phenomenon that the log-likelihood ratio statistic under the fixed dimensional specified null asymptotically follows neither a Chi-square nor a rescaled Chi-square distribution. Simulation studies and an application to NBA data illustrate the theoretical results., Comment: This article supersedes arxiv article arXiv:1201.0058 by Yan et al

We propose a general model that jointly characterizes degree heterogeneity and homophily in weighted, undirected networks. We present a moment estimation method using node degrees and homophily statistics. We establish consistency and asymptotic normality of our estimator using novel analysis. We apply our general framework to three applications, including both exponential family and non-exponential family models. Comprehensive numerical studies and a data example also demonstrate the usefulness of our method., Comment: 48pages, 1 figure. This article supersedes arxiv article 1806.02550 by Ting Yan

We establish a theoretical model to analyze the photoassociative (PA) spectroscopy of $(3)^3\Sigma^+$ state of $^{85}$Rb$^{133}$Cs molecule. The term energy, spin-spin coupling constants and hyperfine interaction constant of nine vibrational levels in the $(3)^3\Sigma^+$ state are determined. Based on the fitted term energy and rotation constant, the potential energy curve of $(3)^3\Sigma^+$ state is obtained by using the RKR method which is compared with the ab initial potential curve., Comment: 9 pages, 2 figures

We compile experimental data for the averaged transverse momentum ($\left\langle p_{T}\right\rangle $) of proton, $\Lambda$, $\Xi^{-}$, $\Omega^{-}$ and $\phi$ at mid-rapidity in Au+Au collisions at $\sqrt{s_{NN}}=$ 200, 39, 27, 19.6, 11.5, 7.7 GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}=$ 2.76 TeV, and find that experimental data of these hadrons exhibit systematic correlations. We apply a quark combination model with equal-velocity combination approximation to derive analytic formulas of hadronic $\left\langle p_{T}\right\rangle $ in the case of exponential form of quark $p_{T}$ spectra at hadronization. We use them to successfully explain the systematic correlations exhibited in $\left\langle p_{T}\right\rangle $ data of $p\Lambda$, $\Lambda\Xi^{-}$, $\Xi^{-}\Omega^{-}$ and $\Xi^{-}\phi$ pairs. We also use them to successfully explain the regularity observed in $\left\langle p_{T}\right\rangle $ of these hadrons as the function of $(dN_{ch}/dy)/(N_{part}/2)$ at mid-rapidity in central heavy-ion collisions at both RHIC and LHC energies. Our results suggest that the constituent quark degrees of freedom and the equal-velocity combination of these constituent quarks at hadronization play important role in understanding the production of baryons and $\phi$ meson at these RHIC and LHC energies., Comment: 10 pages, 7 figures

The main aim to build models capable of simulating the spreading of infectious diseases is to control them. And along this way, the key to find the optimal strategy for disease control is to obtain a large number of simulations of disease transitions under different scenarios. Therefore, the models that can simulate the spreading of diseases under scenarios closer to the reality and are with high efficiency are preferred. In the realistic social networks, the random contact, including contacts between people in the public places and the public transits, becomes the important access for the spreading of infectious diseases. In this paper, a model can efficiently simulate the spreading of infectious diseases under random contacts is proposed. In this approach, the random contact between people is characterized by the random matrix with elements randomly generated and the spread of the diseases is simulated by the Markov process. We report an interesting property of the proposed model: the main indicators of the spreading of the diseases such as the death rate are invariant of the size of the population. Therefore, representative simulations can be conducted on models consist of small number of populations. The main advantage of this model is that it can easily simulate the spreading of diseases under more realistic scenarios and thus is able to give a large number of simulations needed for the searching of the optimal control strategy. Based on this work, the reinforcement learning will be introduced to give the optimal control strategy in the following work.

With the kinetic freeze-out nucleons and antinucleons obtained from the quark combination model, we study the production of light nuclei and antinuclei in the (anti-)nucleon coalescence mechanism in relativistic heavy ion collisions. We derive analytic formulas of the momentum distributions of different light nuclei and apply them to compute transverse momentum ($p_T$) spectra of (anti-)deuterons ($d$, $\bar d$) and (anti-)tritons ($t$, $\bar t$) in Au-Au collisions at $\sqrt{s_{NN}}=$7.7, 11.5, 19.6, 27, 39, 54.4 GeV. We find that the experimental data available for these $p_T$ spectra can be well reproduced. We further study the yields and yield ratios of different light (anti-)nuclei and naturally explain their interesting behaviors as a function of the collision energy. We especially point out that the multi-particle yield ratio $tp/d^2$ should be carefully corrected from hyperon weak decays for protons to probe the production characteristics of light nuclei. All of our results show that the coalescence mechanism for (anti-)nucleons plays a dominant role for the production of light nuclei and antinuclei at the RHIC beam energy scan energies., Comment: 14 pages,10 figures

We explore the viable $f(R)$ gravity models in FLRW backgrounds with a free spatial curvature parameter $\Omega_{K}$. In our numerical calculation, we concentrate on the exponential $f(R)$ model of $f(R) = R - \lambda R_{ch}(1-\exp{(-R/R_{ch}}))$, where $R_{ch}$ is the characteristic curvature scale, which is independent of $\Omega_K$, and $\lambda$ corresponds to the model parameter, while $R_{ch}\lambda=2\Lambda$ with $\Lambda$ the cosmological constant. In particular, we study the evolutions of the dark energy density and equation of state for exponential $f(R)$ gravity in open, flat and closed universe, and compare with those for $\Lambda$CDM. From the current observational data, we find that $\lambda^{-1}=0.42927^{+0.39921}_{-0.32927}$ at 68$\%$ C.L and $\Omega_K=-0.00050^{+0.00420}_{-0.00414}$ at 95$\%$ C.L. in the exponential $f(R)$ model. By using Akaike information criterion (AIC), Bayesian information criterion (BIC) and Deviance Information Criterion (DIC), we conclude that there is no strong preference between the exponential $f(R)$ gravity and $\Lambda$CDM models in the non-flat universe., Comment: 16 pages, 3 figures, accepted for publication in the Astrophysical Journal

The $\beta$-model is a powerful tool for modeling large and sparse networks driven by degree heterogeneity, where many network models become infeasible due to computational challenge and network sparsity. However, existing estimation algorithms for $\beta$-model do not scale up. Also, theoretical understandings remain limited to dense networks. This paper brings several significant improvements over existing results to address the urgent needs of practice. We propose a new $\ell_2$-penalized MLE algorithm that can comfortably handle sparse networks of millions of nodes with much-improved memory parsimony. We establish the first rate-optimal error bounds and high-dimensional asymptotic normality results for $\beta$-models, under much weaker network sparsity assumptions than best existing results. Application of our method to large COVID-19 network data sets and discover meaningful results.

Nonreciprocal transmission of optical or microwave signals is indispensable in various applications involving sensitive measurements. In this paper, we study optomechanically induced directional amplification and isolation in a generic setup including two cavities and two mechanical oscillators by exclusively using blue-sideband drive tones. The input and output ports defined by the two cavity modes are coupled through coherent and dissipative paths mediated by the two mechanical resonators, respectively. By choosing appropriate transfer phases and strengths of the driving fields, either a directional amplifier or an isolator can be implemented at low thermal temperature, and both of them show bi-directional nonreciprocity working at two mirrored frequencies. The nonreciprocal device can potentially be demonstrated by opto- and electro-mechanical setups in both optical and microwave domains., Comment: 5 pages, 3 figures

Using type-x spin-orbit torque (SOT) switching scheme, in which the easy axis (EA) of the ferromagnetic (FM) layer and the charge current flow direction are collinear, is possible to realize a lower-power-consumption, higher-density, and better-performance SOT magnetoresistive random access memory (SOT-MRAM) as compared to the conventional type-y design. Here, we systematically investigate type-x SOT switching properties by both macrospin and micromagnetic simulations. The out-of-plane external field and anisotropy field dependence of the switching current density ($J_{sw}$) is first examined in the ideal type-x configuration. Next, we study the FM layer canting angle ($\phi_{EA}$) dependence of $J_{sw}$ through macrospin simulations and experiments, which show a transformation of switching dynamics from type-x to type-y with increasing $\phi_{EA}$. By further integrating field-like torque (FLT) into the simulated system, we find that a positive FLT can assist type-x SOT switching while a negative one brings about complex dynamics. More crucially, with the existence of a sizable FLT, type-x switching mode results in a lower critical switching current than type-y at current pulse width less than ~ 10 ns, indicating the advantage of employing type-x design for ultrafast switching using materials systems with FLT. Our work provides a thorough examination of type-x SOT scheme with various device/materials parameters, which can be informative for designing next-generation SOT-MRAM.

A large unidirectional magnetoresistance (UMR) ratio of UMR/$R_{xx}\sim$ $0.36\%$ is found in W/CoFeB metallic bilayer heterostructures at room temperature. Three different regimes in terms of the current dependence of UMR ratio are identified: A spin-dependent-scattering mechanism regime at small current densities $J \sim$ $10$$^{9}$A/m$^{2}$ (UMR ratio $\propto$ $J$), a spin-magnon-interaction mechanism regime at intermediate $J \sim$ $10$$^{10}$A/m$^{2}$ (UMR ratio $\propto$ $J$$^{3}$), and a spin-transfer torque (STT) regime at $J \sim$ $10$$^{11}$A/m$^{2}$ (UMR ratio independent of $J$). We verify the direct correlation between this large UMR and the transfer of spin angular momentum from the W layer to the CoFeB layer by both field-dependent and current-dependent UMR characterizations. Numerical simulations further confirm that the large STT-UMR stems from the tilting of the magnetization affected by the spin Hall effect-induced spin-transfer torques. An alternative approach to estimate damping-like spin-torque efficiencies from magnetic heterostructures is also proposed.

We consider a specific dark energy model, which only includes the Lagrangian up to the cubic order in terms of the vector field self-interactions in the generalized Proca theory. We examine the cosmological parameters in the model by using the data sets of CMB and CMB+HST, respectively. In particular, the Hubble constant is found to be $H_0=71.80^{+1.07}_{-0.72}$ ($72.48^{+0.72}_{-0.60}$) $\rm kms^{-1}Mpc^{-1}$ at $68\%$~C.L. with CMB (CMB+HST), which would alleviate the Hubble constant tension. We also obtain that the reduced $\chi^2$ values in our model are close to unity when fitting with CMB and CMB+HST, illustrating that our model is a good candidate to describe the cosmological evolutions of the universe., Comment: 18 pages, 5 figures, accepted by Physics of the Dark Universe

Modelling edge weights play a crucial role in the analysis of network data, which reveals the extent of relationships among individuals. Due to the diversity of weight information, sharing these data has become a complicated challenge in a privacy-preserving way. In this paper, we consider the case of the non-denoising process to achieve the trade-off between privacy and weight information in the generalized $\beta$-model. Under the edge differential privacy with a discrete Laplace mechanism, the Z-estimators from estimating equations for the model parameters are shown to be consistent and asymptotically normally distributed. The simulations and a real data example are given to further support the theoretical results., Comment: 32 pages, 11 figures, to appear in Statistics and Its Interface

It has been shown that the spin Hall effect from heavy transition metals can generate sufficient spin-orbit torque and further produce current-induced magnetization switching in the adjacent ferromagnetic layer. However, if the ferromagnetic layer has in-plane magnetic anisotropy, probing such switching phenomenon typically relies on tunneling magnetoresistance measurement of nano-sized magnetic tunnel junctions, differential planar Hall voltage measurement, or Kerr imaging approaches. We show that in magnetic heterostructures with spin Hall metals, there exist current-induced in-plane spin Hall effective fields and unidirectional magnetoresistance that will modify their anisotropic magnetoresistance behavior. We also demonstrate that by analyzing the response of anisotropic magnetoresistance under such influences, one can directly and electrically probe magnetization switching driven by the spin-orbit torque, even in micron-sized devices. This pump-probe method allows for efficient and direct determination of key parameters from spin-orbit torque switching events without lengthy device fabrication processes.

We investigate observational constraints on the running vacuum model (RVM) of $\Lambda=3\nu (H^{2}+K/a^2)+c_0$ in the spatially curved universe, where $\nu$ is the model parameter, $K$ corresponds to the spatial curvature constant, and $c_{0}$ is a constant defined by the boundary conditions. As $\dot{\Lambda} \ne 0$, there are energy exchanges between vacuum, matter and radiation in RVM. We study the "geometrical degeneracy" of RVM on the CMB power spectra. By fitting the cosmological data, we find that the values of $\chi^2$ in RVM and $\Lambda$CDM are similar to each other for the non-flat universe. Explicitly, we obtain the constraints of $\nu\leq O(10^{-4})$ (68 $\%$ C.L.) and $|\Omega_K|\leq O(10^{-2})$ (95 $\%$ C.L.) in our study. In addition, we show that the cosmological constraints of $\Sigma m_{\nu}=0.416^{+0.311}_{-0.407}$ (RVM) and $\Sigma m_{\nu}=0.497^{+0.335}_{-0.387}$ ($\Lambda$CDM) at 95$\%$ C.L. for the neutrino mass sum are relaxed in both models in the spatially curved universe., Comment: 13 pages, 8 figures, revised version accepted by Chinese Physics C

We apply the first law of thermodynamics to the apparent horizon of the universe with the power-law corrected and non-extensive Tsallis entropies rather than the Bekenstein-Hawking one. We examine the cosmological properties in the two entropy models by using the CosmoMC package. In particular, the first numerical study for the cosmological observables with the power-law corrected entropy is performed. We also show that the neutrino mass sum has a non-zero central value with a relaxed upper bound in the Tsallis entropy model comparing with that in the $\Lambda$CDM one., Comment: 17 pages, 12 figures, published version in EPJC

For an $n\times n$ diagonally dominant matrix $T=(t_{i,j})_{n\times n}$ with positive elements satisfying certain bounding conditions, we propose to use a diagonal matrix $S=(s_{i,j})_{n\times n}$ to approximate the inverse of $T$, where $s_{i,j}=\delta_{i,j}/t_{i,i}$ and $\delta_{i,j}$ is the Kronecker delta function. We derive an explicitly upper bound on the approximation error, which is in the magnitude of $O(n^{-2})$. It shows that $S$ is a very good approximation to $T^{-1}$., Comment: 8 pages

The degree heterogeneity and homophily are two typical features in network data. In this paper, we formulate a general model for undirected networks with these two features and present the moment estimation for inferring the degree and homophily parameters. The binary or nonbinary network edges are simultaneously considered. We establish a unified theoretical framework under which the consistency of the moment estimator holds as the size of networks goes to infinity. We also derive the asymptotic representation of the moment estimator that can be used to characterize its limiting distribution. The asymptotic representation of the moment estimator of the homophily parameter contains a bias term. Two applications are provided to illustrate the theoretical result. Numerical studies and a real data analysis demonstrate our theoretical findings., Comment: 33 pages. Major revision. Add simulations. Changed the original title to "A Unified Framework for Inference in Network Models with Degree Heterogeneity and Homophily"

In this paper, we adopt a latent variable method to formulate a network model with arbitrarily dependent structure. We assume that the latent variables follow a multivariate normal distribution and a link between two nodes forms if the sum of the corresponding node parameters exceeds the latent variable. The dependent structure among edges is induced by the covariance matrix of the latent variables. The marginal distribution of an edge is a probit function. We refer this model to as the \emph{Probit Network Model}. We show that the moment estimator of the node parameter is consistent. To the best of our knowledge, this is the first time to derive consistency result in a single observed network with globally dependent structures. We extend the model to allow node covariate information., Comment: 16 pages

We propose a method for semi-supervised semantic segmentation using an adversarial network. While most existing discriminators are trained to classify input images as real or fake on the image level, we design a discriminator in a fully convolutional manner to differentiate the predicted probability maps from the ground truth segmentation distribution with the consideration of the spatial resolution. We show that the proposed discriminator can be used to improve semantic segmentation accuracy by coupling the adversarial loss with the standard cross entropy loss of the proposed model. In addition, the fully convolutional discriminator enables semi-supervised learning through discovering the trustworthy regions in predicted results of unlabeled images, thereby providing additional supervisory signals. In contrast to existing methods that utilize weakly-labeled images, our method leverages unlabeled images to enhance the segmentation model. Experimental results on the PASCAL VOC 2012 and Cityscapes datasets demonstrate the effectiveness of the proposed algorithm., Comment: Accepted in BMVC 2018. Code and models available at https://github.com/hfslyc/AdvSemiSeg

We report a systematic study on Edelstein magnetoresistance (Edelstein MR) in Co25Fe75/Cu/Bi2O3 heterostructures with a strong spin-orbit interaction at the Cu/Bi2O3 interface. We succeed in observing a significant dependence of the Edelstein MR on both Cu layer thickness and temperature, and also develop a general analytical model considering distinct bulk and interface contributions on spin relaxation. Our analysis, based on the above model, quantitatively illustrates a unique property of the spin transport near the Rashba interface, revealing a prominent role of the spin relaxation process by determining the ratios of the spin relaxation inside and outside the interface. We further find the characteristic spin transport is unaffected by temperature. Our results provide an essential tool for exploring the transport in a system with spin-momentum-locked two-dimensional states., Comment: 18 pages, 5 figures, Accepted in Phys. Rev. B Rapid Communications

Although a lot of approaches are developed to release network data with a differentially privacy guarantee, inference using noisy data in many network models is still unknown or not properly explored. In this paper, we release the bi-degree sequences of directed networks using the Laplace mechanism and use the $p_0$ model for inferring the degree parameters. The $p_0$ model is an exponential random graph model with the bi-degree sequence as its exclusively sufficient statistic. We show that the estimator of the parameter without the denoised process is asymptotically consistent and normally distributed. This is contrast sharply with some known results that valid inference such as the existence and consistency of the estimator needs the denoised process. Along the way, a new phenomenon is revealed in which an additional variance factor appears in the asymptotic variance of the estimator when the noise becomes large. Further, we propose an efficient algorithm for finding the closet point lying in the set of all graphical bi-degree sequences under the global $L_1$ optimization problem. Numerical studies demonstrate our theoretical findings., Comment: 21 pages, 3 figures, minor revision

The stochastic block model is widely used for detecting community structures in network data. How to test the goodness-of-fit of the model is one of the fundamental problems and has gained growing interests in recent years. In this article, we propose a novel goodness-of-fit test based on the maximum entry of the centered and re-scaled adjacency matrix for the stochastic block model. One noticeable advantage of the proposed test is that the number of communities can be allowed to grow linearly with the number of nodes ignoring a logarithmic factor. We prove that the null distribution of the test statistic converges in distribution to a Gumbel distribution, and we show that both the number of communities and the membership vector can be tested via the proposed method. Further, we show that the proposed test has asymptotic power guarantee against a class of alternatives. We also demonstrate that the proposed method can be extended to the degree-corrected stochastic block model. Both simulation studies and real-world data examples indicate that the proposed method works well., Comment: 31 pages

Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. Although a number of statistical models are proposed to analyze affiliation networks, the asymptotic behaviors of the estimator are still unknown or have not been properly explored. In this paper, we study an affiliation model with the degree sequence as the exclusively natural sufficient statistic in the exponential family distributions. We establish the uniform consistency and asymptotic normality of the maximum likelihood estimator when the numbers of actors and events both go to infinity. Simulation studies and a real data example demonstrate our theoretical results., Comment: 24 pages,2 figures,4 tables

In many biological, agricultural, military activity problems and in some quality control problems, it is almost impossible to have a fixed sample size, because some observations are always lost for various reasons. Therefore, the sample size itself is considered frequently to be a random variable (rv). The class of limit distribution functions (df's) of the random bivariate extreme generalized order statistics (GOS) from independent and identically distributed RV's are fully characterized. When the random sample size is assumed to be independent of the basic variables and its df is assumed to converge weakly to a non-degenerate limit, the necessary and sufficient conditions for the weak convergence of the random bivariate extreme GOS are obtained. Furthermore, when the interrelation of the random size and the basic rv's is not restricted, sufficient conditions for the convergence and the forms of the limit df's are deduced. Illustrative examples are given which lend further support to our theoretical results., Comment: 15 pages

Estimating the number of communities is one of the fundamental problems in community detection. We re-examine the Bayesian paradigm for stochastic block models and propose a "corrected Bayesian information criterion",to determine the number of communities and show that the proposed estimator is consistent under mild conditions. The proposed criterion improves those used in Wang and Bickel (2016) and Saldana et al. (2017) which tend to underestimate and overestimate the number of communities, respectively. Along the way, we establish the Wilks theorem for stochastic block models. Moreover, we show that, to obtain the consistency of model selection for stochastic block models, we need a so-called "consistency condition". We also provide sufficient conditions for both homogenous networks and non-homogenous networks. The results are further extended to degree corrected stochastic block models. Numerical studies demonstrate our theoretical results., Comment: 42 pages, major revision. Change the title to "Corrected Bayesian information criterion for stochastic block models"

Networks are often characterized by node heterogeneity for which nodes exhibit different degrees of interaction and link homophily for which nodes sharing common features tend to associate with each other. In this paper, we propose a new directed network model to capture the former via node-specific parametrization and the latter by incorporating covariates. In particular, this model quantifies the extent of heterogeneity in terms of outgoingness and incomingness of each node by different parameters, thus allowing the number of heterogeneity parameters to be twice the number of nodes. We study the maximum likelihood estimation of the model and establish the uniform consistency and asymptotic normality of the resulting estimators. Numerical studies demonstrate our theoretical findings and a data analysis confirms the usefulness of our model., Comment: 29 pages. minor revision

The observation of the spin Hall effect triggered intense research on pure spin current transport. With the spin Hall effect, the spin Seebeck effect, and the spin Peltier effect already observed, our picture of pure spin current transport is almost complete. The only missing piece is the spin Nernst (-Ettingshausen) effect, that so far has only been discussed on theoretical grounds. Here, we report the observation of the spin Nernst effect. By applying a longitudinal temperature gradient, we generate a pure transverse spin current in a Pt thin film. For readout, we exploit the magnetization-orientation-dependent spin transfer to an adjacent Yttrium Iron Garnet layer, converting the spin Nernst current in Pt into a controlled change of the longitudinal thermopower voltage. Our experiments show that the spin Nernst and the spin Hall effect in Pt are of comparable magnitude, but differ in sign, as corroborated by first-principles calculations.