Search

This paper investigates the simultaneous reconstruction of the running cost function and the internal topological structure within the mean-field games (MFG) system utilizing partial boundary data. The inverse problem is notably challenging due to factors such as nonlinear coupling, the necessity for multi-parameter reconstruction, constraints on probability measures, and the limited availability of measurement information. To address these challenges, we propose an innovative approach grounded in a higher-order linearization method. This method is tailored for inverse problems in MFG systems that involve Dirichlet and Neumann boundary conditions. Initially, we present unique reconstruction results for the cost function and internal topological structure of the MFG system under various homogeneous boundary conditions. Subsequently, we extend these results to accommodate inhomogeneous boundary conditions. These findings greatly enhance our understanding of simultaneous reconstruction in complex MFG systems.

Stellar flares originate from the sudden reconnection of magnetic flux lines within the star's atmosphere, particularly in the chromosphere. Automated flare detection enables exploiting vast photometric datasets from missions like Kepler. Prior methods rely on outlier detection, facing challenges of complexity, detection accuracy, and scalability. This paper presents FCN4Flare, a deep learning approach using fully convolutional networks for precise point-to-point flare prediction regardless of light curve length. Key innovations include the NaN Mask to handle missing data, dilated convolutions to preserve local information, and the MaskDice loss to mitigate severe class imbalance. Experiments demonstrate significantly improved detection performance over previous models, with a 0.64 Dice coefficient on Kepler data. Applying FCN4Flare to Kepler and LAMOST, we compile a catalog of 30,285 high-confidence flares across 1426 stars. Flare energies are estimated and stellar/exoplanet properties analyzed, identifying pronounced activity for an M-dwarf hosting a habitable zone planet. This work overcomes limitations of prior flare detection methods via deep learning, enabling new scientific discoveries through analysis of photometric time-series data., Comment: 13 pages, 6 figures

In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled systems, we enforce non-negativity of the solutions, aligning with realistic scenarios in biology and ecology. There are several salient features of our inverse problem study: the drastic reduction in measurement/observation data due to averaging effects, the nonlinear coupling between multiple equations, and the nonlocality arising from fractional-type derivatives. These factors present significant challenges to our inverse problem, and such inverse problems have never been explored in previous literature. To address these challenges, we develop new and effective schemes. Our approach involves properly controlling the injection of different source terms to obtain multiple sets of mean flux data. This allows us to achieve unique identifiability results and accurately determine the unknown parameters. Finally, we establish a connection between our study and practical applications in biology, further highlighting the relevance of our work in real-world contexts., Comment: Keywords: inverse problems, partial data measurements, nonlocal coupled parabolic systems, fractional coupled diffusion systems, mathematical biology

Magnetic skyrmions emerge as promising quasi-particles for encoding information in nextgeneration spintronic devices. Their innate flexibility in shape is essential for the applications although they were often ideally treated as rigid particles. In this work, we investigated the voltagecontrolled uniform strain mediated dynamics of deformed skyrmions in heterostructures with a flower-shaped magnetic nanostructure, using micromagnetic simulations. The simulated results revealed the possible states of isolated skyrmion nucleated in the nanostructure, which can be mutually switched by applying suitable in-plane strain pulses. In addition, it was found that the skyrmion motions are driven by the emerging internal forces and strain force, which originate from the asymmetric deformation of skyrmion structures. Furthermore, an analytical model of deformed skyrmions was proposed to interpret the dependences of internal forces and strain force on the asymmetric deformation of skyrmion, with some formulae derived for these forces in a semi-analytical approach. Further calculations based on these formulae verified the forces appearing in the skyrmion motion, with the resulting forces showing consistence with the simulated data. This suggested that our semi-analytical model successfully captures the main physics responsible for the motion of deformed skyrmion in the nanostructure. Our work extends the understanding of the mechanics emerging in deformed skyrmion, and provides an effective approach for deterministic manipulation of deformed skyrmion motion via strain forces and internal forces, which may be instructive to design of skyrmion-based spintronic devices.

Despite extensive exploration of acoustic vortices carrying orbital angular momentum (OAM), the generation of acoustic vortices with OAM orientations beyond the conventional longitudinal direction remains largely unexplored. Spatiotemporal (ST) vortices, featuring spiral phase twisting in the ST domain and carrying transverse OAM, have recently attracted considerable interest in optics and acoustics. Here, we report the generation of three-dimensional (3D) ST acoustic vortices with arbitrarily oriented OAM, thereby opening up a new dimension in acoustic OAM control. By utilizing a two-dimensional (2D) acoustic phased array, we introduce two approaches to manipulate the orientation of OAM: through the direct rotation of vortices in 3D space and the intersection of vortices carrying distinct types of OAM. These methods enable unprecedented control over the orientation of acoustic OAM, providing a new degree of freedom in the manipulation of acoustic waves. The arbitrarily oriented OAM holds promise for enhancing acoustic communication by broadening capacity and enabling more complex particle manipulation techniques. Our work establishes a foundation for future explorations into the complex dynamics of novel structured acoustic fields in the ST domain.

This study investigates the excesses observed in the diphoton and $b\bar b$ data around $95\;{\rm GeV}$ within the framework of the $B-L$ supersymmetric model (B-LSSM). Comparing with the minimal supersymmetric standard model, the B-LSSM incorporates two singlet chiral Higgs bosons which mix with the SM-like Higgs boson due to the gauge kinetic mixing effect. The richer Higgs sector indicates that designating the B-LSSM specific CP-even Higgs state as the lightest Higgs boson has great potential to explain the excesses at around $95\;{\rm GeV}$. Considering the two-loop effective potential corrections to the squared Higgs mass matrix, it is found that the signal strengthes $\mu(h_{95})_{\gamma\gamma}$, $\mu(h_{95})_{b b}$ can be described simultaneously in the experimental $1\sigma$ interval. And the B-LSSM specific parameters $\tan\beta'$, $B_\eta$, $g_{YB}$, $M_{Z'}$ affect the theoretical predictions on the light Higgs boson masses and signal strengthes $\mu(h_{95})_{\gamma\gamma}$, $\mu(h_{95})_{bb}$ significantly., Comment: 28 pages, 5 figures. arXiv admin note: text overlap with arXiv:2405.07243

Generative AI (GenAI) has spurred the expectation of being creative, due to its ability to generate content, yet so far, its creativity has somewhat disappointed, because it is trained using existing data following human intentions to generate outputs. The purpose of this paper is to explore what is required to evolve AI from generative to creative. Based on a reinforcement learning approach and building upon various research streams of computational creativity, we develop a triple prompt-response-reward engineering framework to develop the creative capability of GenAI. This framework consists of three components: 1) a prompt model for expected creativity by developing discriminative prompts that are objectively, individually, or socially novel, 2) a response model for observed creativity by generating surprising outputs that are incrementally, disruptively, or radically innovative, and 3) a reward model for improving creativity over time by incorporating feedback from the AI, the creator/manager, and/or the customers. This framework enables the application of GenAI for various levels of creativity strategically., Comment: 46 pages, 2 tables, 4 figures

This study focuses on the examination of the island rule within the context of four-dimensional Reissner-Nordstr\"om-AdS (4D RN-AdS) black holes, illuminating the intricate relationship between the entanglement entropy and phase transitions of black holes. The entanglement entropy of 4D RN-AdS black holes follows the anticipated linear growth pattern before ultimately declining to a constant value, in accordance with the well-established Page curve. The novelty of this study lies in the examination of the influence, previously unexplored, of the first-order phase transition on the shape and evolution of the Page curve in situations involving both eternal and evaporating black holes. Despite the morphological alterations of the curve induced by the transition, the inherent unitarity of the system persists. As the evaporation progresses, the Page curve displays diverse configurations, unveiling phenomena that are novel and defies traditional expectations, thereby enriching our comprehension of the thermodynamics of black holes interlinked with quantum information., Comment: 31 pages, 10 figures

Exploring the inverse problem tied to the Page curve phenomenon and island paradigm, we investigate the geometric conditions underpinning black hole evaporation where information is preserved and islands manifest, giving rise to the characteristic Page curve. Focusing on a broad class of static black hole metrics in asymptotically Minkowski or (anti-)de Sitter spacetimes, we derive a pivotal constraint on the blacken factor $f(r)$ for which the island exists and reproduce the Page curve. Specifically, we reveal that a sufficient yet not universally necessary criterion -- manifested in the negativity of the second derivative of $f(r)$, i.e. $f^{\prime \prime} (r)<0$, in proximity to the event horizon where $r \sim r_h+ {\cal O} (G_N)$, ensures the emergence of Page curves in a manner transcending specific theoretical models. This pivotal finding, supported by the tenets of the quantum focusing conjecture., Comment: 21 pages, 2 figures, references added

Spin and orbital angular momenta are fundamental physical characteristics described by polarization and spatial degrees of freedom, respectively. Polarization is a feature of vector fields while spatial phase gradient determines the orbital angular momentum ubiquitous to any scalar field. Common wisdom treats these two degrees of freedom as distinct and independent principles to manipulate wave propagations. Here, we demonstrate their synergy. This is achieved by introducing two orthogonal $p$-orbitals as eigenbases, whose spatial modal features are exploited to generate orbital angular momenta and the associated orbital orientations provide means to simultaneously manipulate polarizations. Through periodic modulation and directional coupling, we realize a full cyclic evolution of the synchronized and synergized spin-orbital angular momenta. Remarkably, this evolution acquires a nontrivial geometric phase, leading to its representation on a M\"obius strip. Experimentally, an acoustic cavity array is designed, whose dipole resonances precisely mimic the $p$-orbitals. The acoustic waves, uniquely, see the pressure (scalar) field as a spatial feature and carry an intrinsic polarization defined by the velocity (vector) field, serving as an ideal platform to observe the synergy of spin and orbital angular momenta. Based on such a property, we further showcase a spin-orbital-Hall effect, highlighting the intricate locking of handedness, directionality, spin density and spatial mode profile. Our study unveils a fundamental connection between spin and orbital angular momenta, promising avenues for novel applications in information coding and high-capacity communications.

In this paper, we revisit the bioluminescence tomography (BLT) problem, where one seeks to reconstruct bioluminescence signals (an internal light source) from external measurements of the Cauchy data. As one kind of optical imaging, the BLT has many merits such as high signal-to-noise ratio, non-destructivity and cost-effectiveness etc., and has potential applications such as cancer diagnosis, drug discovery and development as well as gene therapies and so on. In the literature, BLT is extensively studied based on diffusion approximation (DA) equation, where the distribution of peak sources is to be reconstructed and no solution uniqueness is guaranteed without adequate a priori information. Motivated by the solution uniqueness issue, several theoretical results are explored. The major contributions in this work that are new to the literature are two-fold: first, we show the theoretical uniqueness of the BLT problem where the light sources are in the shape of $C^2$ domains or polyhedral- or corona-shaped; second, we support our results with plenty of problem-orientated numerical experiments.

In this paper, by extending the classic stochastic integrals, we investigate three kinds of more general stochastic integrals: Lebesgue-Stieltjes integrals on predictable sets of interval type (in short: PSITs), stochastic integrals on PSITs of predictable processes with respect to local martingales, and stochastic integrals on PSITs of predictable processes with respect to semimartingales. Such stochastic integrals on PSITs are defined only on restricted stochastic subsets, and their values outside the subsets do not matter. Our study reveals that a stochastic integral on a PSIT can be characterized by a coupled sequence of classic stochastic integrals. Furthermore, the It\^{o}'s formula for semimartingales on PSITs is developed for stochastic calculus, and stochastic integrals on PSITs can be applied to more general problems in mathematical finance.

In this paper, we propose and study the utilization of the Dirichlet-to-Neumann (DN) map to uniquely identify the discount functions $r, k$ and cost function $F$ in a stationary mean field game (MFG) system. This study features several technical novelties that make it highly intriguing and challenging. Firstly, it involves a coupling of two nonlinear elliptic partial differential equations. Secondly, the simultaneous recovery of multiple parameters poses a significant implementation challenge. Thirdly, there is the probability measure constraint of the coupled equations to consider. Finally, the limited information available from partial boundary measurements adds another layer of complexity to the problem. Considering these challenges and problems, we present an enhanced higher-order linearization method to tackle the inverse problem related to the MFG system. Our proposed approach involves linearizing around a pair of zero solutions and fulfilling the probability measurement constraint by adjusting the positive input at the boundary. It is worth emphasizing that this technique is not only applicable for uniquely identifying multiple parameters using full-boundary measurements but also highly effective for utilizing partial-boundary measurements.

The island paradigm for the fine-grained entropy of Hawking radiation is applied to eternal charged accelerating black holes. In the absence of the island, the entanglement entropy grows linearly and divergent at late times, while once the island outside the event horizon is taken into account, the unitary Page curve is reproduced naturally. The impact of the charge and the acceleration is investigated at late times. For the Page time and the scrambling time, they both increase as the acceleration increases, while decreasing as the charge increases. In particular, neutral black holes have the largest Page time and scrambling time. It is worth noting that the Page time and the scrambling time are divergent in the extremal limit, which implies that islands may be related to the causal structure of spacetime., Comment: 6 figures, 25 pages, references added

In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems, we mainly consider the non-negative solutions of the coupled equations, which are consistent with realistic settings in biology and ecology. There are several salient features of our inverse problem study: the drastic reduction of the measurement/observation data due to averaging effects, the nonlinear coupling of multiple equations, and the non-negative constraints on the solutions, which pose significant challenges to the inverse problems. We develop a new and effective scheme to tackle the inverse problems and achieve unique identifiability results by properly controlling the injection of different source terms to obtain multiple sets of mean flux data. The approach relies on certain monotonicity properties which are related to the intrinsic structures of the coupled PDE system. We also connect our study to biological applications of practical interest.

Topological corner states are exotic topological boundary states that are bounded to zero-dimensional geometry even the dimension of systems is large than one. As an elegant physical correspondence, their numbers are dictated by the bulk topological invariants. So far, all previous realizations of HOTIs are hallmarked by $\mathbb{Z}_2$ topological invariants and therefore have only one corner state at each corner. Here we report an experimental demonstration of $\mathbb{Z}$-class HOTI phases in electric circuits, hosting $N$ corner modes at each single corner structure. By measuring the impedance spectra and distributions, we clearly demonstrate the $\mathbb{Z}$-class HOTI phases, including the zero-energy corner modes and their density distributions. Moreover, we reveal that the local density of states (LDOS) at each corner for $N=4$ are equally distributed at four corner unit cells, prominently differing from $\mathbb{Z}_2$-class case where the LDOS only dominates over one corner unit cell. Our results extend the observation of HOTIs from $\mathbb{Z}_2$ class to $\mathbb{Z}$ class and the coexistence of spatially overlapped large number of corner modes which may enable exotic topological devices that require high degeneracy boundary states., Comment: 8 pages, 4 figures

Up to November 2022, 267 pulsars have been discovered in 36 globular clusters (GCs). In this paper, we present our studies on the distribution of GC pulsar parameters and the detection efficiency. The power law relation between the average of dispersion measure ($\overline{\rm DM}$) and dispersion measure difference ($\Delta {\rm DM}$) of known pulsars in GCs is $\lg\Delta {\rm DM} \propto 1.52 \lg \overline{\rm DM}$. The sensitivity could be the key to find more pulsars. As a result, several years after the construction of a radio telescope, the GC pulsar number will be increased accordingly. We suggest that currently GCs in the southern hemisphere could have higher possibilities to find new pulsars., Comment: 9 pages,5 figures, accepted by RAA, comments are always welcomed!

We have calculated the three-dimensional potential energy surface (PES) for the fission of compound nucleus $^{236}$U using the covariant density functional theory with constraints on the axial quadrupole and octupole deformations $(\beta_2, \beta_3)$ as well as the nucleon number in the neck $q_N$. By considering the additonal degree of freedom $q_N$, coexistence of the elongated and compact fission modes is predicted for $0.9\lesssim \beta_3 \lesssim 1.3$. Remarkably, the PES becomes very shallow across a large range of quadrupole and octupole deformations for small $q_N$, and consequently, the scission line in $(\beta_2, \beta_3)$ plane will extend to a shallow band, which leads to a fluctuation for the estimated total kinetic energies by several to ten MeV and for the fragment masses by several to about ten nucleons.

As an important contributor to GDP growth, the construction industry is suffering from labor shortage due to population ageing, COVID-19 pandemic, and harsh environments. Considering the complexity and dynamics of construction environment, it is still challenging to develop fully automated robots. For a long time in the future, workers and robots will coexist and collaborate with each other to build or maintain a facility efficiently. As an emerging field, human-robot collaboration (HRC) still faces various open problems. To this end, this pioneer research introduces an agent-based modeling approach to investigate the coupling effect and scale effect of HRC in the bricklaying process. With multiple experiments based on simulation, the dynamic and complex nature of HRC is illustrated in two folds: 1) agents in HRC are interdependent due to human factors of workers, features of robots, and their collaboration behaviors; 2) different parameters of HRC are correlated and have significant impacts on construction productivity (CP). Accidentally and interestingly, it is discovered that HRC has a scale effect on CP, which means increasing the number of collaborated human-robot teams will lead to higher CP even if the human-robot ratio keeps unchanged. Overall, it is argued that more investigations in HRC are needed for efficient construction, occupational safety, etc.; and this research can be taken as a stepstone for developing and evaluating new robots, optimizing HRC processes, and even training future industrial workers in the construction industry.

We consider the entanglement island in a deformed Jackiw-Teitelboim black hole in the presence of the phase transition. This black hole has the van der Waals-Maxwell-like phase structure as it is coupled with a Maxwell field. We study the behavior of the Page curve of this black hole by using the island paradigm. In the fixed charge ensemble, we discuss different situations with different charges that influence the system's phase structure. There is only a Hawking-Page phase transition in the absence of charges, which leads to an unstable small black hole. Hence, the related Page curve does not exist. However, a van der Waals-Maxwell-like phase transition occurs in the presence of charges. This yields three black hole solutions. The Page curve of the middle size black hole does not exist. For the extremal black hole, the Page time approaches zero in the phase transition situation but becomes divergent without the phase transition. In a word, we study the Page curve and the island paradigm for different black hole phases and in different phase transition situations., Comment: 28 pages, 13 figures, references added, published version

Local density-of-states (LDOS) is a fundamental spectral property that plays a central role in various physical phenomena such as wave-matter interactions. Here, we report on the direct measurement of the LDOS of acoustic systems and derive from which the fractional topological number in an acoustic Su-Schrieffer-Heeger system. The acoustic LDOS is quantified here with a state-of-the-art technique through the measurement of the volume flow rate and the acoustic pressure with a local excitation-probe configuration. Based on this method, we study the acoustic Purcell effect and establish experimentally the important relation between the near-field LDOS and the far-field acoustic emission power. Moreover, we detect the LDOS in the one-dimensional acoustic Su-Schrieffer-Heeger model and observe the fractional topological number of the system. Our work unveils the important role of the LDOS in acoustic phenomena and paves the way toward characterizing and tailoring the LDOS in topological systems.

The Fabbri-Russo model is a generalized model of a two-dimensional dilaton gravity theory with various parameters "$n$" describing various specific gravities. Particularly, the Russo-Susskind-Thorlacius gravity model fits the case $n=1$. In the Fabbri-Russo model, we investigate Page curves and the entanglement island. Islands are considered in eternal and evaporating black holes. Surprisingly, in any black hole, the emergence of islands causes the rise of the entanglement entropy of the radiation to decelerate after the Page time, satisfying the principle of unitarity. For eternal black holes, the fine-grained entropy reaches a saturation value that is twice the Bekenstein-Hawking entropy. For evaporating black holes, the fine-grained entropy finally reaches zero. The parameter "$n$" significantly impacts the Page curve at extremely early times. However, at late times and large distance limit, the impact of the parameter "$n$" is a subleading term and is exponentially suppressed. As a result, the shape of Page curves is "$n$"-independent in the leading order. Furthermore, we discuss the relationship between islands and firewalls. We show that the island is a better candidate than firewalls for encountering the quantum entanglement-monogamy problem. Finally, we briefly review the gravity/ensemble duality as a potential resolution to the state conundrum resulting from the island formula., Comment: 43 pages,5 figures, references added

The past decades have witnessed the flourishing of non-Hermitian physics in non-conservative systems, leading to unprecedented phenomena of unidirectional invisibility, enhanced sensitivity and more recently the novel topological features such as bulk Fermi arcs. Among them, growing efforts have been invested to an intriguing phenomenon, known as the non-Hermitian skin effect (NHSE). Here, we review the recent progress in this emerging field. By starting from the one-dimensional (1D) case, the fundamental concepts of NHSE, its minimal model, the physical meanings and consequences are elaborated in details. In particular, we discuss the NHSE enriched by lattice symmetries, which gives rise to unique non-Hermitian topological properties with revised bulk-boundary correspondence (BBC) and new definitions of topological invariants. Then we extend the discussions to two and higher dimensions, where dimensional surprises enable even more versatile NHSE phenomena. Extensions of NHSE assisted with extra degrees of freedom such as long-range coupling, pseudospins, magnetism, non-linearity and crystal defects are also reviewed. This is followed by the contemporary experimental progress for NHSE. Finally, we provide the outlooks to possible future directions and developments.

Defects play a crucial role in the physical properties of crystals, whether for classical or quantum systems. For example, in photonic/phononic crystals, defects can serve as precise guidance and localization of classical electromagnetic or mechanical waves. Rainbow concentrating, a recently proposed exotic wave localization [Phys. Rev. Lett. 126, 113902 (2021)] exploits defects to enable the collection and frequency routing of weak signals in real space. In this paper, using a solid-state phononic crystal (PnC) plate, we experimentally verify this phenomenon by deliberately infusing a homogeneous graded dislocation, i.e., a line defect, into the PnC. Two PnCs separated by the defect will breed deterministic interface states along with the defect, offering rainbow trapping and concentrating for elastic waves. Our PnC-based rainbow trappers and concentrators are scalable and configurable, promising for advancing applications like energy harvesting, information processing, and acoustofluidic manipulating., Comment: 10 Page, 7 figures

Unpaired data has shown to be beneficial for low-resource automatic speech recognition~(ASR), which can be involved in the design of hybrid models with multi-task training or language model dependent pre-training. In this work, we leverage unpaired data to train a general sequence-to-sequence model. Unpaired speech and text are used in the form of data pairs by generating the corresponding missing parts in prior to model training. Inspired by the complementarity of speech-PseudoLabel pair and SynthesizedAudio-text pair in both acoustic features and linguistic features, we propose a complementary joint training~(CJT) method that trains a model alternatively with two data pairs. Furthermore, label masking for pseudo-labels and gradient restriction for synthesized audio are proposed to further cope with the deviations from real data, termed as CJT++. Experimental results show that compared to speech-only training, the proposed basic CJT achieves great performance improvements on clean/other test sets, and the CJT++ re-training yields further performance enhancements. It is also apparent that the proposed method outperforms the wav2vec2.0 model with the same model size and beam size, particularly in extreme low-resource cases., Comment: 5 pages, 3 figures

We propose a gedanken experiment on realizing thermofield double state (TFD) by using analog black holes and provide an approach to test the scrambling time. Through this approach, we demonstrate clearly how shock wave changes the TFD state as time evolves. As the whole system evolves forward in time, the perturbation of space-time geometry will increase exponentially. Finally, it will destroy the entanglement between the two states of the thermal field, and the mutual information between them is reduced to zero in the time scale of scrambling. The results show that for perturbations of analogue black holes embedded in AdS space, the scale of the scrambling time is closely related to the logarithm of entropy of the black hole. The results provide further theoretical argument for the scrambling time, which can be further falsified in experiments., Comment: 1+18 pages, 3 figures, published version

With the advance in self-supervised learning for audio and visual modalities, it has become possible to learn a robust audio-visual speech representation. This would be beneficial for improving the audio-visual speech recognition (AVSR) performance, as the multi-modal inputs contain more fruitful information in principle. In this paper, based on existing self-supervised representation learning methods for audio modality, we therefore propose an audio-visual representation learning approach. The proposed approach explores both the complementarity of audio-visual modalities and long-term context dependency using a transformer-based fusion module and a flexible masking strategy. After pre-training, the model is able to extract fused representations required by AVSR. Without loss of generality, it can be applied to single-modal tasks, e.g. audio/visual speech recognition by simply masking out one modality in the fusion module. The proposed pre-trained model is evaluated on speech recognition and lipreading tasks using one or two modalities, where the superiority is revealed., Comment: 5 pages

Wav2vec2.0 is a popular self-supervised pre-training framework for learning speech representations in the context of automatic speech recognition (ASR). It was shown that wav2vec2.0 has a good robustness against the domain shift, while the noise robustness is still unclear. In this work, we therefore first analyze the noise robustness of wav2vec2.0 via experiments. We observe that wav2vec2.0 pre-trained on noisy data can obtain good representations and thus improve the ASR performance on the noisy test set, which however brings a performance degradation on the clean test set. To avoid this issue, in this work we propose an enhanced wav2vec2.0 model. Specifically, the noisy speech and the corresponding clean version are fed into the same feature encoder, where the clean speech provides training targets for the model. Experimental results reveal that the proposed method can not only improve the ASR performance on the noisy test set which surpasses the original wav2vec2.0, but also ensure a tiny performance decrease on the clean test set. In addition, the effectiveness of the proposed method is demonstrated under different types of noise conditions., Comment: Accepted by ICASSP 2022

We study the Page curve and the information paradox for the BTZ black hole coupled to two thermal baths by applying the island paradigm. We prove that as the island locates outside the event horizon, the entanglement entropy of Hawking radiation for finite temperature black holes obeys the Page curve. However, for extremal rotating black holes, the Page time and the scrambling time become divergent. To avoid the ill-defined of the Page time, we consider the contribution of superradiance, which is a process that can extract rotational energy from black holes. The superradiance continues in a period much shorter than the Page time when the central charge $c$ is not too large. In this process, the Page time, the scrambling time and the black hole thermal entropy all decrease. Whenever the superradiance finishes, the black hole turn out to be a neutral black hole and the Hawking radiation dominates. The Page curve can then be well reproduced., Comment: 22 pages, 4 figures, typos corrected, Refs added

In this paper, we investigate the imaging inverse problem by employing an infinite-dimensional Bayesian inference method with a general fractional total variation-Gaussian (GFTG) prior. This novel hybrid prior is a development for the total variation-Gaussian (TG) prior and the non-local total variation-Gaussian (NLTG) prior, which is a combination of the Gaussian prior and a general fractional total variation regularization term, which contains a wide class of fractional derivative. Compared to the TG prior, the GFTG prior can effectively reduce the staircase effect, enhance the texture details of the images and also provide a complete theoretical analysis in the infinite-dimensional limit similarly to TG prior. The separability of the state space in Bayesian inference is essential for developments of probability and integration theory in infinite-dimensional setting, thus we first introduce the corresponding general fractional Sobolev space and prove that the space is a separable Banach space. Thereafter, we give the well-posedness and finite-dimensional approximation of the posterior measure of the Bayesian inverse problem based on the GFTG prior, and then the samples are extracted from the posterior distribution by using the preconditioned Crank-Nicolson (pCN) algorithm. Finally, we give several numerical examples of image reconstruction under liner and nonlinear models to illustrate the advantages of the proposed improved prior., Comment: arXiv admin note: substantial text overlap with arXiv:2110.15656

This paper studies the infinite-dimensional Bayesian inference method with Hadamard fractional total variation-Gaussian (HFTG) prior for solving inverse problems. First, Hadamard fractional Sobolev space is established and proved to be a separable Banach space under some mild conditions. Afterwards, the HFTG prior is constructed in this separable fractional space, and the proposed novel hybrid prior not only captures the texture details of the region and avoids step effects, but also provides a complete theoretical analysis in the infinite dimensional Bayesian inversion. Based on the HFTG prior, the well-posedness and finite-dimensional approximation of the posterior measure of the Bayesian inverse problem are given, and samples are extracted from the posterior distribution using the standard pCN algorithm. Finally, numerical results under different models indicate that the Bayesian inference method with HFTG prior is effective and accurate.

In this paper, we consider a dynamic asset pricing model in a cross-sectional economy with two firms where a controlling shareholder cannot divert output in one firm with perfect investor protection for minority shareholders and where he can divert a fraction of output in the other firm with imperfect protection. After obtaining the parameters of asset prices by solving the shareholders' consumption-portfolio problems in equilibrium, our model features the effect of investor protection and cross-section in the economy. Furthermore, some survival analysis of the shareholders is presented and sufficient conditions on extinction of the shareholders are given in either firm. Our numerical results are in line with some empirical evidence: (i) poorer investor protection in the cross-sectional economy enables the controlling shareholder to hold less shares of the firm with perfect protection and more shares of the firm with imperfect protection, decreases stock gross returns of both firms, increases stock volatilities of both firms, and decreases interest rates of the economy; (ii) compared with the economy with the single relative firm, for the firm with perfect protection, cross-section enables the controlling shareholder to hold less shares, decreases stock returns, increases stock volatilities slightly and decreases interest rates, while for the firm with imperfect protection, cross-section enables the controlling shareholder to hold more shares, increases stock returns and volatilities and increases interest rates.

We study the Page curve in the four dimensional asymptotically flat eternal Garfinkle-Horowitz-Strominger dilaton black holes by applying the "quantum extremal surface" prescription. The results demonstrate that without island, the entanglement entropy of Hawking radiation is proportional to time and divergent at late times. While taking account of the emergence of the island extending slightly outside the event horizon, the entanglement entropy of Hawking radiation stops growing and eventually reaches a saturation value, which is twice of the Bekenstein-Hawking entropy and consistent with the finiteness of the von Neumann entropy of eternal black holes. Moreover, we discuss the impact of the parameter $n$ and charge $Q$ on the Page time. The influence of $n$ on it can neglected when the ratio of the charge $Q$ to the black hole mass $M$ is sufficiently small, but the charge $Q$ has a significant impact on Page time. Importantly, at the extremal case, the Page time becomes divergent or vanishing, in which the semiclassical theory needs further investigation., Comment: minor corrections, references added

In this paper, we investigate a new model of a linear-quadratic mean-field stochastic Stackelberg differential game with one leader and two followers, in which the leader is allowed to stop her strategy at a random time. Our overarching goal is to find the Stackelberg solution of the leader and followers for such a model. By employing the backward induction method, the state equation is divided into two-stage equations. Moreover, by using the maximum principle and the verification theorem, the Stackelberg solution is obtained for such a model.

We study the shape reconstruction of an inclusion from the {faraway} measurement of the associated electric field. This is an inverse problem of practical importance in biomedical imaging and is known to be notoriously ill-posed. By incorporating Drude's model of the permittivity parameter, we propose a novel reconstruction scheme by using the plasmon resonance with a significantly enhanced resonant field. We conduct a delicate sensitivity analysis to establish a sharp relationship between the sensitivity of the reconstruction and the plasmon resonance. It is shown that when plasmon resonance occurs, the sensitivity functional blows up and hence ensures a more robust and effective construction. Then we combine the Tikhonov regularization with the Laplace approximation to solve the inverse problem, which is an organic hybridization of the deterministic and stochastic methods and can quickly calculate the minimizer while capture the uncertainty of the solution. We conduct extensive numerical experiments to illustrate the promising features of the proposed reconstruction scheme.

In this paper, we propose a weakly supervised multilingual representation learning framework, called cross-lingual self-training (XLST). XLST is able to utilize a small amount of annotated data from high-resource languages to improve the representation learning on multilingual un-annotated data. Specifically, XLST uses a supervised trained model to produce initial representations and another model to learn from them, by maximizing the similarity between output embeddings of these two models. Furthermore, the moving average mechanism and multi-view data augmentation are employed, which are experimentally shown to be crucial to XLST. Comprehensive experiments have been conducted on the CommonVoice corpus to evaluate the effectiveness of XLST. Results on 5 downstream low-resource ASR tasks shows that our multilingual pretrained model achieves relatively 18.6% PER reduction over the state-of-the-art self-supervised method, with leveraging additional 100 hours of annotated English data., Comment: 5 pages, 1 figure

Hermitian theories play a major role in understanding the physics of most phenomena. It has been found only in the past decade that non-Hermiticity enables unprecedented effects such as exceptional points, spectral singularities and bulk Fermi arcs. Recent studies further show that non-Hermiticity can fundamentally change the topological band theory, leading to the non-Hermitian band topology and non-Hermitian skin effect, as confirmed in one-dimensional (1D) systems. However, in higher dimensions, these non-Hermitian effects remain unexplored in experiments. Here, we demonstrate the spin-polarized, higher-order non-Hermitian skin effect in two-dimensional (2D) acoustic metamaterials. Using a lattice of coupled whisper-gallery acoustic resonators, we realize a spinful 2D higher-order topological insulator (HOTI) where the spin-up and spin-down states are emulated by the anti-clockwise and clockwise modes, respectively. We find that the non-Hermiticity drives wave localizations toward opposite edge boundaries depending on the spin polarizations. More interestingly, for finite systems with both edge and corner boundaries, the higher-order non-Hermitian skin effect leads to wave localizations toward two corner boundaries for the bulk, edge and corner states in a spin-dependent manner. We further show that such a non-Hermitian skin effect enables rich wave manipulation through the loss configuration in each unit-cell. The reported spin-dependent, higher-order non-Hermitian skin effect reveals the interplay between higher-order topology and non-Hermiticity, which is further enriched by the spin degrees of freedom. This unveils a new horizon in the study of non-Hermitian physics and the design of non-Hermitian metamaterials.

Energy usage monitoring on higher education campuses is an important step for providing satisfactory service, lowering costs and supporting the move to green energy. We present a collaboration between the Department of Statistics and Facilities Operations at an R1 research university to develop statistically based approaches for monitoring monthly energy usage and proportional yearly usage for several hundred utility accounts on campus. We compare the interpretability and power of model-free and model-based methods for detection of anomalous energy usage patterns in statistically similar groups of accounts. Ongoing conversation between the academic and operations teams enhances the practical utility of the project and enables implementation for the university. Our work highlights an application of thoughtful and continuing collaborative analysis using easy-to-understand statistical principles for real-world deployment.

In this paper, we solve an optimal control problem governed by a system of mean-field stochastic differential equations with multiple defaults (MMFSDEs). We transform the global optimal control problem into several optimal control subproblems governed by a system of mean-field stochastic differential equations with single default (SMFSDEs) and derive both the sufficient and necessary maximum principles for these subproblems. We also give the existence and uniqueness of solutions to the MMFSDEs and the mean-field backward stochastic differential equations with multiple defaults (MMFBSDEs), respectively. Finally, as an example, our results are applied to obtain the explicit solution for an optimal control problem whose cost function is considered as a recursive utility process with multiple defaults.

Developers usually select different open source licenses to restrain the conditions of using open source software, in order to protect intellectual property rights effectively and maintain the long-term development of the software. However, the open source community has a wide variety of licenses available, developers generally find it difficult to understand the differences between different open source license. And existing open source license selection tools require developers to understand the terms of the open source license and identify their business needs, which makes it hard for developers to make the right choice. Although academia has extensive research to the open source license, but there is no systematic analysis on the actual difficulties of the developers to choose the open source license, thus lacking a clear understanding, for this reason, the purpose of this paper is to understand the difficulties faced by open source developers in choosing open source licenses, analyze the components of open source license and the affecting factors of open source license selection, and to provide references for developers to choose open source licenses., Comment: 30 pages, in Chinese

Waveguides and resonators are core components in the large-scale integration of electronics, photonics, and phononics, both in existing and future scenarios. In certain situations, there is critical coupling of the two components; i.e., no energy passes through the waveguide after the incoming wave couples into the resonator. The transmission spectral characteristics resulting from this phenomenon are highly advantageous for signal filtering, switching, multiplexing, and sensing. In the present study, adopting an elastic-wave platform, we introduce topological insulator (TI), a remarkable achievement in condensed matter physics over the past decade, into a classical waveguide-ring-resonator configuration. Along with basic similarities with classical systems, a TI system has important differences and advantages, mostly owing to the spin-momentum locked transmission states at the TI boundaries. As an example, a two-port TI waveguide resonator can fundamentally eliminate upstream reflections while completely retaining useful transmission spectral characteristics, and maximize the energy in the resonator, with possible applications being novel signal processing, gyro/sensing, lasering, energy harvesting, and intense wave-matter interactions, using phonons, photons, or even electrons. The present work further enhances the confidence of using topological protection for practical device performance and functionalities, especially considering the crucial advantage of introducing (pseudo)spins to existing conventional configurations. More in-depth research on advancing phononics/photonics, especially on-chip, is foreseen.

In many applications, survey data are collected from different survey centers in different regions. It happens that in some circumstances, response variables are completely observed while the covariates have missing values. In this paper, we propose a joint spatial regression model for the response variable and missing covariates via a sequence of one-dimensional conditional spatial regression models. We further construct a joint spatial model for missing covariate data mechanisms. The properties of the proposed models are examined and a Markov chain Monte Carlo sampling algorithm is used to sample from the posterior distribution. In addition, the Bayesian model comparison criteria, the modified Deviance Information Criterion (mDIC) and the modified Logarithm of the Pseudo-Marginal Likelihood (mLPML), are developed to assess the fit of spatial regression models for spatial data. Extensive simulation studies are carried out to examine empirical performance of the proposed methods. We further apply the proposed methodology to analyze a real data set from a Chinese Health and Nutrition Survey (CHNS) conducted in 2011.

Higher-order topological insulator, as a newly found non-trivial material and structure, possesses a topological phase beyond the bulk-boundary correspondence. Here, we present an experimental observation of photonic higher-order topological crystalline insulator and its topological protection to quantum superposition and entanglement in a two-dimensional lattice. By freely writing the insulator structure with femtosecond laser and directly measuring evolution dynamics with single-photon imaging techniques, we are able to observe the distinct features of the topological corner states in C_4 and C_2 photonic lattice symmetry. Especially, we propose and experimentally identify the topological corner states by exciting the photonic lattice with single-photon superposition state, and we examine the protection impact of topology on quantum entanglement for entangled photon states. The single-photon dynamics and the protected entanglement reveal an intrinsic topological protection mechanism isolating multi-partite quantum states from diffusion-induced decoherence. The higher-order topological crystalline insulator, built-in superposition state generation, heralded single-photon imaging and quantum entanglement demonstrated here link topology, material, and quantum physics, opening the door to wide investigations of higher-order topology and applications of topological enhancement in genuine quantum regime., Comment: 46 pages, 6 figures in main text, 16 figures in Supplementary Materials

In this paper, a new measurement system based on integration method is presented,which can provide all-weather dependability and higher precision for the measurement of FAST's feed support system. The measurement system consists of three types of measuring equipments, and a processing software with the core data fusion algorithm. The Strapdown Inertial Navigation System(SINS) can autonomously measure the position, speed and attitude of the carrier. Its own shortcoming is the measurement data diverges rapidly over time. SINS must combine the Global Positioning System(GPS) and the Total Station(TS) to obtain high-precision measurement data. Kalman filtering algorithm is adopted for the integration measurement system, which is an optimal algorithm to estimate the measurement errors. To evaluate the performance, series of tests are carried out. For the feed cabin, the maximum RMS of the position is 14.56mm, the maximum RMS of the attitude is 0.095{\deg}, these value are less than 15mm and 0.1{\deg} as the precision for measuring the feed cabin. For the Stewart manipulator, the maximum RMS of the position is 2.99mm, the maximum RMS of the at titude is 0.093{\deg}, these value are less than 3mm and 0.1{\deg} as the precision for measuring the Stewart manipulator. As a result, the new measurement meets the requirement of measurement precision for FAST's feed support system., Comment: 14 pages, 12 figures

Macroscopic two-dimensional sonic crystals with inversion symmetry are studied to reveal higher-order topological physics in classical wave systems. By tuning a single geometry parameter, the band topology of the bulk and the edges can be controlled simultaneously. The bulk band gap forms an acoustic analog of topological crystalline insulators with edge states which are gapped due to symmetry reduction on the edges. In the presence of mirror symmetry, the band topology of the edge states can be characterized by the Zak phase, illustrating the band topology in a hierarchy of dimensions, which is at the heart of higher-order topology. Moreover, the edge band gap can be closed without closing the bulk band gap, revealing an independent topological transition on the edges. The rich topological transitions in both bulk and edges can be well-described by the symmetry eigenvalues at the high-symmetry points in the bulk and surface Brillouin zones. We further analyze the higher-order topology in the shrunken sonic crystals where slightly different physics but richer corner and edge phenomena are revealed. In these systems, the rich, multidimensional topological transitions can be exploited for topological transfer among zero-, one- and two- dimensional acoustic modes by controlling the geometry.

In this paper, we first introduce a new spatial-temporal interaction operator to describe the space-time dependent phenomena. Then we consider the stochastic optimal control of a new system governed by a stochastic partial differential equation with the spatial-temporal interaction operator. To solve such a stochastic optimal control problem, we derive an adjoint backward stochastic partial differential equation with spatial-temporal dependence by defining a Hamiltonian functional, and give both the sufficient and necessary (Pontryagin-Bismut-Bensoussan type) maximum principles. Moreover, the existence and uniqueness of solutions are proved for the corresponding adjoint backward stochastic partial differential equations. Finally, our results are applied to study the population growth problems with the space-time dependent phenomena.

Band topology and related spin (or pseudo-spin) physics of photons provide us with a new dimension for manipulating light, which is potentially useful for information communication and data storage. Especially, the quantum spin Hall effect of light, where electromagnetic waves propagate along surfaces of samples with strong spin-momentum locking, paves the way for achieving topologically protected photonic spin transport. Recently, the conventional bulk-edge correspondence of the band topology has been extended to higher-order cases that enables the explorations of topological states with codimensions larger than 1 such as hinge and corner states. Here, for the first time, we demonstrate a higherorder quantum spin Hall effect of light by utilizing an all-dielectric C6v-symmetric photonic crystal. We observe corner states with opposite pseudospin polarizations at different corners owing to nontrivial higher-order topology and finite spin-spin coupling. By applying the spin-polarized excitation sources, we can selectively excite the corner states at different spatial positions through spin-momentum-locked decaying edge states, resembling the quantum spin Hall effect in a higher-order manner. Our work which breaks the barriers between the spin photonics and higher-order topology opens the frontiers for studying lower-dimensional spinful classical surface waves and supports explorations in robust communications., Comment: 24 pages, 4 figures

In this paper, we consider a dynamic asset pricing model in an approximate fractional economy to address empirical regularities related to both investor protection and past information. Our newly developed model features not only in terms with a controlling shareholder who diverts a fraction of the output, but also good (or bad) memory in his budget dynamics which can be well-calibrated by a pathwise way from the historical data. We find that poorer investor protection leads to higher stock holdings of controlling holders, lower gross stock returns, lower interest rates, and lower modified stock volatilities if the ownership concentration is sufficiently high. More importantly, by establishing an approximation scheme for good (bad) memory of investors on the historical market information, we conclude that good (bad) memory would increase (decrease) aforementioned dynamics and reveal that good (bad) memory strengthens (weakens) investor protection for minority shareholder when the ownership concentration is sufficiently high, while good (bad) memory inversely weakens (strengthens) investor protection for minority shareholder when the ownership concentration is sufficiently low. Our model's implications are consistent with a number of interesting facts documented in the recent literature.

Selecting important spatial-dependent variables under the nonhomogeneous spatial Poisson process model is an important topic of great current interest. In this paper, we use the Deviance Information Criterion (DIC) and Logarithm of the Pseudo Marginal Likelihood (LPML) for Bayesian variable selection under the nonhomogeneous spatial Poisson process model. We further derive the new Monte Carlo estimation formula for LPML in the spatial Poisson process setting. Extensive simulation studies are carried out to evaluate the empirical performance of the proposed criteria. The proposed methodology is further applied to the analysis of two large data sets, the Earthquake Hazards Program of United States Geological Survey (USGS) earthquake data and the Forest of Barro Colorado Island (BCI) data.

In this paper, the existence and pathwise uniqueness of strong solutions for jump-type stochastic differential equations are investigated under non-Lipschitz conditions. A sufficient condition is obtained for ensuring the non-confluent property of strong solutions of jump-type stochastic differential equations. Moreover, some examples are given to illustrate our results., Comment: 16 pages