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Consider the linear differential equation $$ f^{(n)}+A_{n-1}f^{(n-1)}+\cdots+A_{0}f=0 $$ where the coefficients $A_j,j=0,\ldots,n-1,$ are exponential polynomials. It is known that every solution is entire. This paper will show that all transcendental solutions of finite growth order are of completely regular growth. This problem was raised in Heittokangas et al.[8, p.33], which involves an extensive question about Gol'dberg-Ostrovski\v{i}'s Problem [5, p.300]. Moreover, we define functions in a generalized class concluding exponential polynomial functions, which are also of completely regular growth.

GRB 230812B, detected by the Gamma-Ray Integrated Detectors (GRID) constellation mission, is an exceptionally bright gamma-ray burst (GRB) with a duration of only 3 seconds. Sitting near the traditional boundary ($\sim$ 2 s) between long and short GRBs, GRB 230812B is notably associated with a supernova (SN), indicating a massive star progenitor. This makes it a rare example of a short-duration GRB resulting from stellar collapse. Our analysis, using a time-evolving synchrotron model, suggests that the burst has an emission radius of approximately $10^{14.5}$~cm. We propose that the short duration of GRB 230812B is due to the combined effects of the central engine's activity time and the time required for the jet to break through the stellar envelope. Our findings provide another case that challenges the conventional view that short-duration GRBs originate exclusively from compact object mergers, demonstrating that a broader range of durations exists for GRBs arising from the collapse of massive stars., Comment: 10 pages, 3 tables, 11 figures

This paper studies community detection for a nonlinear opinion dynamics model from its equilibria. It is assumed that the underlying network is generated from a stochastic block model with two communities, where agents are assigned with community labels and edges are added independently based on these labels. Agents update their opinions following a nonlinear rule that incorporates saturation effects on interactions. It is shown that clustering based on a single equilibrium can detect most community labels (i.e., achieving almost exact recovery), if the two communities differ in size and link probabilities. When the two communities are identical in size and link probabilities, and the inter-community connections are denser than intra-community ones, the algorithm can achieve almost exact recovery under negative influence weights but fails under positive influence weights. Utilizing fixed point equations and spectral methods, we also propose a detection algorithm based on multiple equilibria, which can detect communities with positive influence weights. Numerical experiments demonstrate the performance of the proposed algorithms.

This paper studies the formation of final opinions for the Friedkin-Johnsen (FJ) model with a community of partially stubborn agents. The underlying network of the FJ model is symmetric and generated from a random graph model, in which each link is added independently from a Bernoulli distribution. It is shown that the final opinions of the FJ model will concentrate around those of an FJ model over the expected graph as the network size grows, on the condition that the stubborn agents are well connected to other agents. Probability bounds are proposed for the distance between these two final opinion vectors, respectively for the cases where there exist non-stubborn agents or not. Numerical experiments are provided to illustrate the theoretical findings. The simulation shows that, in presence of non-stubborn agents, the link probability between the stubborn and the non-stubborn communities affect the distance between the two final opinion vectors significantly. Additionally, if all agents are stubborn, the opinion distance decreases with the agent stubbornness.

The discovery of the superconductivity in the infinite-layer nickelates, as topotactically reduced from their respective perovskite percussors via co-annealing with CaH2, extends the understanding in superconductivity. Nevertheless, whether the incorporated 1H composition is critical to the infinite-layer superconductivity recently arouses considerable debates, while the central challenge lies in the quantification of 1H that is easily interfered by the conventional electron or orbital associated processes. Herein, we demonstrate the irrelevance between the superconductivity in the infinite-layer nickelates and their incorporated 1H composition, assisted by nuclear reaction analysis (NRA) and heavy ion energy recoil detection analysis (HIERDA) based on the nuclear interactions at MeV energy scale. These approaches completely overwhelm the conventional interferes, such as ionization, activation and chemical bonds, and achieves the 1H quantification within superconducting La0.8Sr0.2NiO2 (or Nd0.8Sr0.2NiO2). A large diversity of 1H composition far beyond the previously expected critical dome was observed, while their TC were not changed significantly. Furthermore, the superconductivity was demonstrated to be achievable for La0.8Sr0.2NiO2 reduced by Al without any hydrogen associated process, while the superconducting properties for the CaH2 reduced La0.8Sr0.2NiO2 is rather stable after long term exposure in air, despite the high volatility of 1H within oxides. All these results indicate that the 1H incorporation composition is not critical to the superconductivity of the infinite-layer nickelates.

We have studied the leptonic EDM and the LFV decays relating with the recent data of anomalous magnetic moment of muon, $(g-2)_{\mu}$, in the framework of the SMEFT with the Stringy Ansatz. We have adopted the successful $\Gamma_2$ modular invariant model by Meloni-Parriciatu as the flavor symmetry of leptons. Suppose the anomaly of $(g-2)_{\mu}$, $\Delta a_{\mu}$ to be evidence of New Physics (NP), we have related it with the anomalous magnetic moment of the electron $\Delta a_e$, the electron EDM $d_e$ and the $\mu\to e \gamma$ decay. We found that the NP contributions to $\Delta a_{e(\mu)}$ are proportional to the lepton masses squared likewise the naive scaling $\Delta a_\ell \propto m^2_\ell$. The experimental constraint of $|d_e|$ is much tight compared with the one from the branching ratio $\mathcal{B}(\mu \to e \gamma)$ in our framework. Supposing the phase of our model parameter $\delta_{\alpha}$ for the electron to be of order one, we have estimated the upper-bound of $\mathcal{B}(\mu \to e \gamma)$, which is at most $10^{-21}-10^{-20}$. If the model parameters $\delta_{\alpha}$, $\delta_{\beta}$ (for muon) and $\delta_{\gamma}$ (for tauon) are real, leptonic EDMs vanish since the CP phase of the modular form due to modulus $\tau$ does not contribute to the EDM. However, we can obtain $\mathcal{B}(\mu \to e \gamma)\simeq 10^{-13}$ with non-vanishing $d_e$, that is the case, only $\delta_{\alpha}$ is real while the others are complex. Then, the imaginary part of $\delta_{\beta}$ can lead to $d_e$ in the next-to-leading contribution. The predicted electron EDM is below $10^{-32}$e\,cm, while $\mathcal{B}(\mu \to e \gamma)$ is close to the experimental upper-bound. The predicted upper-bound of $|d_\mu|$ is rather large, around $10^{-23}$e\,cm and of $|d_\tau|$ is $ 10^{-22}$e\,cm. The branching ratios of $\tau\to e\gamma$ and $\tau\to \mu\gamma$ are also discussed., Comment: 37 pages, 12 figures. arXiv admin note: text overlap with arXiv:2310.16325

The doping evolution behaviors of the normal state magnetic excitations (MEs) of the nickelate La3Ni2O7 are theoretically studied in this paper. For a filling of n = 3.0 which corresponds roughly to the material which realizes the superconductivity of about 80 K under moderately high pressures above 14 GPa, the MEs exhibit a square-like pattern centered at (0,0) which originates from the intrapocket particle-hole scatterings. Furthermore, it was found that the MEs show very strong modulations on the interlayer momentum qz. With the increasing of qz, the patterns of the MEs change dramatically. In the large qz regime, they turn to be ruled by the interpocket excitation modes with significantly larger intensity which may play a vital role in the superconducting pairing. This hidden feature of the MEs was not revealed by previous studies. The established features of the MEs are found to be very robust against doping. They persist in the wide hole- or electron-doping regime around n = 3.0. However, in the heavily electron-doped regime, a Lifshitz transition will occur. Consequently, the behaviors of the MEs change qualitatively across this transition. With the absence of the hole pocket, we predict that a strong tendency toward the spin-density-wave (SDW) order will develop due to the perfect nesting between the electron and the hole pockets at n = 4.0. Thus, we have investigated the normal state behaviors of the MEs and their doping evolutions which may shed light on the mechanism of superconductivity in pressurized La3Ni2O7., Comment: 9 pages, 9 figures

We leverage gravitational wave observations to explore physics beyond the Standard Model, focusing on axion-like particles (ALPs). This study investigates the resonant effects of ALPs with binary black hole systems, where their oscillatory nature induces time-dependent forces on the black holes. By employing a detailed Fisher matrix analysis, we not only probe a new parameter space for ALPs, characterized by their mass and decay constants, but also assess how these parameters affect gravitational waveforms during black hole mergers. Our approach is distinct as it does not assume interactions of ALPs with photons or nucleons. We demonstrate that as binary black holes spiral inward and lose energy, their orbital frequencies may resonate with those of ALPs, producing distinct oscillatory patterns in gravitational waves detectable by upcoming experiments such as the Laser Interferometer Space Antenna (LISA). This work broadens the potential of gravitational wave astronomy as a tool for dark matter searches, offering a promising avenue for studying elusive components of the universe., Comment: 11 pages, 9 figures

This paper investigates the neutrino transition magnetic moment in the $U(1)_X$SSM. $U(1)_X$SSM is the $U(1)$ extension of Minimal Supersymmetric Standard Model (MSSM) and its local gauge group is extended to $SU(3)_C\times SU(2)_L \times U(1)_Y\times U(1)_X$. To obtain this model, three singlet new Higgs superfields and right-handed neutrinos are added to the MSSM, which can explain the results of neutrino oscillation experiments. The neutrino transition magnetic moment is induced by electroweak radiative corrections. By applying effective Lagrangian method and on-shell scheme, we study the associated Feynman diagrams and the transition magnetic moment of neutrinos in the model. We fit experimental data for neutrino mass variances and mixing angle. Based on the range of data selection, the influences of different sensitive parameters on the results are analysed. The numerical analysis shows that many parameters have an effect on the neutrino transition moment, such as $g_X$, $M_2$, $\lambda_H$ and $g_{YX}$. For our numerical results, the order of magnitude of $\mu_{ij}^M/\mu_B$ is around $10^{-20}$ $\sim$ $10^{-19}$.

We investigate the evolution of cosmological scalar perturbations in the case that the background radiation is weakly coupled to a light scalar field $\phi$. The light scalar $\phi$ is a homogeneous background field with a large initial value. In the radiation-dominated Universe, the coupling term introduces an effective mass to $\phi$ and the background ultra-relativistic particles. The oscillations of $\phi$ result in the periodic change of the equation of state parameter and the sound speed, which provides a novel mechanism to amplify subhorizon scalar perturbations through parametric resonance. The amplification of scalar perturbations leads to a stochastic gravitational-waves background~(SGWB) expected to be observed by multiband gravitational wave observers. The observation of the SGWB helps to determine the initial value of $\phi$ and the coupling strength of the interaction. This mechanism is generally applicable to the interactions that introduce an effective mass, and we take the interaction between $\phi$ and electrons as a concrete example to illustrate the result. We find that under the condition that the coupling coefficient $\lambda=10^{-16}$ and the initial value $\phi_i=10^{18}$ GeV, the resulting SGWB spectrum is expected to be observed by the future observers including LISA, $Taiji$, DECIGO and BBO., Comment: 13 pages, 4 figures

In the $U(1)_X$SSM, we delve into the flavor violation of $h \rightarrow bs$, where $h$ is identified with the SM-like Higgs boson discovered at the LHC. As the U(1) extension of the minimal supersymmetric standard model (MSSM), the U(1)XSSM has new super fields such as right-handed neutrinos and three Higgs singlets. We conduct a thorough analysis of the underlying mechanisms and parameter dependencies of $h \rightarrow bs$ in the $U(1)_X$SSM. In the $U(1)_X$SSM, we discover that the Br$(h \rightarrow bs)$ for the Higgs decay to $bs$ could significantly differ from the expectation in the standard model (SM), depending on the values of the new parameters introduced in the model. Our research not only contributes to a deeper understanding of Higgs physics within the $U(1)_X$SSM, but also provides valuable guidance for new physics (NP)., Comment: 24 pages,8 figures

It is well known that the muon magnetic dipole moment (MDM) has close relation with the new physics (NP) in the development of the Standard Model (SM). Combined with the Fermilab National Accelerator Laboratory (FNAL) and the Brookhaven National Laboratory (BNL) E821 result, the departure from the SM prediction is about 5.0 $\sigma$. We study the electroweak corrections from several type two-loop SUSY diagrams and the virtual SUSY particles include chargino, neutralino, scalar lepton and scalar neutrino. Based on the latest experimental constraints, we study the muon MDM under the next to the minimal supersymmetric extension of the SM with local B-L gauge symmetry (N-B-LSSM). The abundant numerical results verify that $\tan{\beta},~T_e,~M^2_L,~M^2_e,~M_{BB'}$ and $M^2_{eij}$ play an important role in muon MDM. $M^2_e,~\tan{\beta}$ and $T_e$ are sensitive parameters to muon MDM. From the data obtained in all the figures of the numerical results, most of the values of $a_{\mu}^{NBL}$ are in 2$\sigma$ interval, which can compensate the departure between the experiment data and the SM prediction.

We address the online combinatorial choice of weight multipliers for multi-objective optimization of many loss terms parameterized by neural works via a probabilistic graphical model (PGM) for the joint model parameter and multiplier evolution process, with a hypervolume based likelihood promoting multi-objective descent. The corresponding parameter and multiplier estimation as a sequential decision process is then cast into an optimal control problem, where the multi-objective descent goal is dispatched hierarchically into a series of constraint optimization sub-problems. The subproblem constraint automatically adapts itself according to Pareto dominance and serves as the setpoint for the low level multiplier controller to schedule loss landscapes via output feedback of each loss term. Our method is multiplier-free and operates at the timescale of epochs, thus saves tremendous computational resources compared to full training cycle multiplier tuning. It also circumvents the excessive memory requirements and heavy computational burden of existing multi-objective deep learning methods. We applied it to domain invariant variational auto-encoding with 6 loss terms on the PACS domain generalization task, and observed robust performance across a range of controller hyperparameters, as well as different multiplier initial conditions, outperforming other multiplier scheduling methods. We offered modular implementation of our method, admitting extension to custom definition of many loss terms.

Numerous applications at the photon-starved regime require a free-space coupling singlephoton detector with a large active area, low dark count rate (DCR), and superior time resolutions. Here,we developed a superconducting microstrip single-photon detector (SMSPD), with a large active area of 260 um in diameter, a DCR of ~5 kcps, and a low time jitter of ~171 ps, operated at near-infrared of 1550 nm. As a demonstration, we applied the detector to a single-pixel galvanometer scanning system and successfully reconstructed object information in depth and intensity using a time-correlated photon counting technology., Comment: 12 pages, 6 figures

The astrophysical origin of binary black hole (BBH) mergers remains uncertain though many events have been observed by the LIGO-Virgo-KAGRA network. Such mergers are predicted to originate in the vicinity of massive black holes (MBHs). Especially, GW190814, due to its secondary mass and mass ratio being beyond the expectations of isolated stellar evolution theories, is a promising event that has happened in an active galactic nucleus(AGN) disk. In this model, a compact object resides in the vicinity of a merging BBH. Here we report multiple pieces of evidence pointing to the fact that GW190814 is a BBH merging near a compact object. The orbital motion of BBHs around the third body produces a line-of-sight acceleration (LSA) and induces a varying Doppler shift. Using a waveform template that considers LSA, we perform Bayesian inference on a few BBH events with a high signal-to-noise ratio in the gravitational-wave transient catalog (GWTC). Compared to the model for isolated BBH mergers, we obtain significantly higher network signal-to-noise ratios for GW190814 by that with the LSA and constrain the LSA to $a = 0.0014^{+0.0014}_{-0.0022} ~c~\mathrm{s}^{-1}$. In addition, the logarithmic Bayes factor for the LSA case over the isolated case is $16.6$, which means the LSA model is significantly preferred by the GW data. We conclude that this is the first indication showing merging BBHs are located near a compact object., Comment: 19 pages, 4 figures

The discovery of superconductivity at 80 K under high pressure in La$_3$Ni$_2$O$_7$ presents the groundbreaking confirmation that high-$T_c$ superconductivity is a property of strongly correlated materials beyond cuprates. We use density functional theory (DFT) calculations of the band structure of La$_3$Ni$_2$O$_7$ under pressure to verify that the low-energy bands are composed almost exclusively of Ni 3$d_{x^2-y^2}$ and O 2$p$ orbitals. We deduce that the Ni 3$d_{z^2}$ orbitals are essentially decoupled by the geometry of the high-pressure structure and by the effect of the Ni Hund coupling being strongly suppressed, which results from the enhanced interlayer antiferromagnetic interaction between $d_{z^2}$ orbitals and the strong intralayer hybridization of the $d_{x^2-y^2}$ orbitals with O 2$p$. By introducing a tight-binding model for the Fermi surfaces and low-energy dispersions, we arrive at a bilayer $t$-$t_\perp$-$J$ model with strong interlayer hopping, which we show is a framework unifying La$_3$Ni$_2$O$_7$ with cuprate materials possessing similar band structures, particularly the compounds La$_2$CaCu$_2$O$_6$, Pb$_2$Sr$_2$YCu$_3$O$_8$, and EuSr$_2$Cu$_2$NbO$_8$. We use a renormalized mean-field theory to show that these systems should have ($d$+$is$)-wave superconductivity, with a dominant $d$-wave component and the high $T_c$ driven by the near-optimally doped $\beta$ band, while the $\alpha$ band adds an $s$-wave component that should lead to clear experimental signatures., Comment: 11 pages, 4 figures

We study community detection based on state observations from gossip opinion dynamics over stochastic block models (SBM). It is assumed that a network is generated from a two-community SBM where each agent has a community label and each edge exists with probability depending on its endpoints' labels. A gossip process then evolves over the sampled network. We propose two algorithms to detect the communities out of a single trajectory of the process. It is shown that, when the influence of stubborn agents is small and the link probability within communities is large, an algorithm based on clustering transient agent states can achieve almost exact recovery of the communities. That is, the algorithm can recover all but a vanishing part of community labels with high probability. In contrast, when the influence of stubborn agents is large, another algorithm based on clustering time average of agent states can achieve almost exact recovery. Numerical experiments are given for illustration of the two algorithms and the theoretical results of the paper.

We reveal the gate-tunable Berry curvature dipole polarizability in Dirac semimetal Cd3As2 nanoplates through measurements of the third-order nonlinear Hall effect. Under an applied electric field, the Berry curvature exhibits an asymmetric distribution, forming a field-induced Berry curvature dipole, resulting in a measurable third-order Hall voltage with a cubic relationship to the longitudinal electric field. Notably, the magnitude and polarity of this third-order nonlinear Hall effect can be effectively modulated by gate voltages. Furthermore, our scaling relation analysis demonstrates that the sign of the Berry curvature dipole polarizability changes when tuning the Fermi level across the Dirac point, in agreement with theoretical calculations. The results highlight the gate control of nonlinear quantum transport in Dirac semimetals, paving the way for promising advancements in topological electronics.

In the past decade, there has been a systematic investigation of symmetry-protected topological (SPT) phases in interacting fermion systems. Specifically, by utilizing the concept of equivalence classes of finite-depth fermionic symmetric local unitary (FSLU) transformations and the fluctuating decorated symmetry domain wall picture, a large class of fixed-point wave functions have been constructed for fermionic SPT (FSPT) phases. Remarkably, this construction coincides with the Atiyah-Hirzebruch spectral sequence, enabling a complete classification of FSPT phases. However, unlike bosonic SPT phases, the stacking group structure in fermion systems proves to be much more intricate. The construction of fixed-point wave functions does not explicitly provide this information. In this paper, we employ FSLU transformations to investigate the stacking group structure of FSPT phases. Specifically, we demonstrate how to compute stacking FSPT data from the input FSPT data in each layer, considering both unitary and anti-unitary symmetry, up to 2+1 dimensions. As concrete examples, we explicitly compute the stacking group structure for crystalline FSPT phases in all 17 wallpaper groups and the mixture of wallpaper groups with onsite time-reversal symmetry using the fermionic crystalline equivalence principle. Importantly, our approach can be readily extended to higher dimensions, offering a versatile method for exploring the stacking group structure of FSPT phases., Comment: Correct some errors in 1+1D case. Add more examples for 2+1D crystalline FSPT protected by symmetries being the mixture of wallpaper groups with onsite time-reversal symmetry

Understanding the excitation spectrum in two-dimensional quantum many-body systems has long been a challenging task. We present an approach by introducing an excitation ansatz based on an infinite matrix product state (MPS) on a helix structure. With the canonical form of MPS states, we can accurately extract key properties such as energy, degeneracy, spectrum weight, and scaling behavior of low-energy excited states simultaneously. To validate the effectiveness of this method, we begin by applying it to the critical point of the transverse-field Ising model. The extracted scaling exponent of the energy gap closely aligns with the conformal bootstrap results. Subsequently, we apply this approach to the $J_1$-$J_2$ Heisenberg model on a square lattice. We discover that the degeneracy of lowest-energy excitations serves as a reliable metric for distinguishing different phases. The phase boundary identified by our method is consistent with some of the previous findings. The present method provides a promising avenue for studying the excitation spectrum of two-dimensional quantum many-body systems.

In the present study, we investigate the decays of the top quark $t\rightarrow c\gamma$, $t\rightarrow cg$, $t\rightarrow cZ$ and $t\rightarrow ch$. They are extremely rare processes in the Standard Model (SM). As the $U(1)$ extension of the minimal supersymmetric standard model (MSSM), the $U(1)_X$SSM features new superfields such as the right-handed neutrinos and three Higgs singlets. We analyze the effects of different sensitive parameters on the results and make reasonable theorecial predictions, which provides a useful reference for future experimental development. Considering the constraint of the updated experimental data, the numerical results show that the branching ratios of all four processes $t\rightarrow c\gamma,~cg,~cZ,~ch$ can reach the same order of magnitude as their experimental upper limits. Among them, $\tan\beta$ has the most obvious effect on each process and is the main parameter. $g_X$, $g_{YX}$, $\mu$, $M_2$, $\lambda_H$, $M_{U23}^2$ and $M_{Q23}^2$ are important parameters for the processes, and have effects on the numerical results., Comment: pages 25, figures 27

The pulsar timing array (PTA) collaborations have recently suggested the presence of a gravitational wave background at nano-Hertz frequencies. In this paper, we explore potential inflationary interpretation of this signal within the context of a simple and health parity-violating gravity model termed the Nieh-Yan modified Teleparallel Gravity. Through this model, two inflationary scenarios are evaluated, both yielding significant polarized primordial gravitational waves (PGWs) that align well with the results from PTA observations. Furthermore, the resulting PGWs can display strong circular polarization and significant anisotropies in the PTA frequency band, which are distinct features to be verified by observations of both PTA and the cosmic microwave background.The detection of such a distinctive background of PGWs is expected to provide strong evidence supporting our scenarios and insights into inflationary dynamics and gravity theory., Comment: 9 pages, 8 figures

As the feature size of integrated circuits continues to decrease, optical proximity correction (OPC) has emerged as a crucial resolution enhancement technology for ensuring high printability in the lithography process. Recently, level set-based inverse lithography technology (ILT) has drawn considerable attention as a promising OPC solution, showcasing its powerful pattern fidelity, especially in advanced process. However, massive computational time consumption of ILT limits its applicability to mainly correcting partial layers and hotspot regions. Deep learning (DL) methods have shown great potential in accelerating ILT. However, lack of domain knowledge of inverse lithography limits the ability of DL-based algorithms in process window (PW) enhancement and etc. In this paper, we propose an inverse lithography physics-informed deep neural level set (ILDLS) approach for mask optimization. This approach utilizes level set based-ILT as a layer within the DL framework and iteratively conducts mask prediction and correction to significantly enhance printability and PW in comparison with results from pure DL and ILT. With this approach, computation time is reduced by a few orders of magnitude versus ILT. By gearing up DL with knowledge of inverse lithography physics, ILDLS provides a new and efficient mask optimization solution.

Very recently, several pulsar timing array collaborations, including CPTA, EPTA, and NANOGrav, reported their results from searches for an isotropic stochastic gravitational wave background (SGWB), with each finding positive evidence for SGWB. In this work, we assessed the credibility of interpreting the Hellings-Downs correlated free-spectrum process of EPTA, PPTA, and NANOGrav as either the result of supermassive black hole binary mergers or various stochastic SGWB sources that originated in the early Universe, including first-order phase transitions, cosmic strings, domain walls, and large-amplitude curvature perturbations. Our observations show that the current new datasets do not display a strong preference for any specific SGWB source based on Bayesian analysis., Comment: 10 pages, 8 figures, 2 tables

We study joint learning of network topology and a mixed opinion dynamics, in which agents may have different update rules. Such a model captures the diversity of real individual interactions. We propose a learning algorithm based on multi-armed bandit algorithms to address the problem. The goal of the algorithm is to find each agent's update rule from several candidate rules and to learn the underlying network. At each iteration, the algorithm assumes that each agent has one of the updated rules and then modifies network estimates to reduce validation error. Numerical experiments show that the proposed algorithm improves initial estimates of the network and update rules, decreases prediction error, and performs better than other methods such as sparse linear regression and Gaussian process regression.