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Learning operators for parametric partial differential equations (PDEs) using neural networks has gained significant attention in recent years. However, standard approaches like Deep Operator Networks (DeepONets) require extensive labeled data, and physics-informed DeepONets encounter training challenges. In this paper, we introduce a novel physics-informed tailored finite point operator network (PI-TFPONet) method to solve parametric interface problems without the need for labeled data. Our method fully leverages the prior physical information of the problem, eliminating the need to include the PDE residual in the loss function, thereby avoiding training challenges. The PI-TFPONet is specifically designed to address certain properties of the problem, allowing us to naturally obtain an approximate solution that closely matches the exact solution. Our method is theoretically proven to converge if the local mesh size is sufficiently small and the training loss is minimized. Notably, our approach is uniformly convergent for singularly perturbed interface problems. Extensive numerical studies show that our unsupervised PI-TFPONet is comparable to or outperforms existing state-of-the-art supervised deep operator networks in terms of accuracy and versatility.

We introduce Seed-Music, a suite of music generation systems capable of producing high-quality music with fine-grained style control. Our unified framework leverages both auto-regressive language modeling and diffusion approaches to support two key music creation workflows: controlled music generation and post-production editing. For controlled music generation, our system enables vocal music generation with performance controls from multi-modal inputs, including style descriptions, audio references, musical scores, and voice prompts. For post-production editing, it offers interactive tools for editing lyrics and vocal melodies directly in the generated audio. We encourage readers to listen to demo audio examples at https://team.doubao.com/seed-music "https://team.doubao.com/seed-music"., Comment: Seed-Music technical report, 20 pages, 5 figures

Interface problems pose significant challenges due to the discontinuity of their solutions, particularly when they involve singular perturbations or high-contrast coefficients, resulting in intricate singularities that complicate resolution. The increasing adoption of deep learning techniques for solving partial differential equations has spurred our exploration of these methods for addressing interface problems. In this study, we introduce Tailored Finite Point Operator Networks (TFPONets) as a novel approach for tackling parameterized interface problems. Leveraging DeepONets and integrating the Tailored Finite Point method (TFPM), TFPONets offer enhanced accuracy in reconstructing solutions without the need for intricate equation manipulation. Experimental analyses conducted in both one- and two-dimensional scenarios reveal that, in comparison to existing methods such as DeepONet and IONet, TFPONets demonstrate superior learning and generalization capabilities even with limited locations.

Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing differential equations motivates us to employ these methods for solving SPDEs. In this manuscript, we introduce Component Fourier Neural Operator (ComFNO), an innovative operator learning method that builds upon Fourier Neural Operator (FNO), while simultaneously incorporating valuable prior knowledge obtained from asymptotic analysis. Our approach is not limited to FNO and can be applied to other neural network frameworks, such as Deep Operator Network (DeepONet), leading to potential similar SPDEs solvers. Experimental results across diverse classes of SPDEs demonstrate that ComFNO significantly improves accuracy compared to vanilla FNO. Furthermore, ComFNO exhibits natural adaptability to diverse data distributions and performs well in few-shot scenarios, showcasing its excellent generalization ability in practical situations.

First-order methods, such as gradient descent (GD) and stochastic gradient descent (SGD), have been proven effective in training neural networks. In the context of over-parameterization, there is a line of work demonstrating that randomly initialized (stochastic) gradient descent converges to a globally optimal solution at a linear convergence rate for the quadratic loss function. However, the learning rate of GD for training two-layer neural networks exhibits poor dependence on the sample size and the Gram matrix, leading to a slow training process. In this paper, we show that for the $L^2$ regression problems, the learning rate can be improved from $\mathcal{O}(\lambda_0/n^2)$ to $\mathcal{O}(1/\|\bm{H}^{\infty}\|_2)$, which implies that GD actually enjoys a faster convergence rate. Furthermore, we generalize the method to GD in training two-layer Physics-Informed Neural Networks (PINNs), showing a similar improvement for the learning rate. Although the improved learning rate has a mild dependence on the Gram matrix, we still need to set it small enough in practice due to the unknown eigenvalues of the Gram matrix. More importantly, the convergence rate is tied to the least eigenvalue of the Gram matrix, which can lead to slow convergence. In this work, we provide the convergence analysis of natural gradient descent (NGD) in training two-layer PINNs, demonstrating that the learning rate can be $\mathcal{O}(1)$, and at this rate, the convergence rate is independent of the Gram matrix.

Reed-Solomon (RS) codes are widely used to correct errors in storage systems. Finding the error locator polynomial is one of the key steps in the error correction procedure of RS codes. Modular Approach (MA) is an effective algorithm for solving the Welch-Berlekamp (WB) key-equation problem to find the error locator polynomial that needs $2t$ steps, where $t$ is the error correction capability. In this paper, we first present a new MA algorithm that only requires $2e$ steps and then propose two fast decoding algorithms for RS codes based on our MA algorithm, where $e$ is the number of errors and $e\leq t$. We propose Improved-Frequency Domain Modular Approach (I-FDMA) algorithm that needs $2e$ steps to solve the error locator polynomial and present our first decoding algorithm based on the I-FDMA algorithm. We show that, compared with the existing methods based on MA algorithms, our I-FDMA algorithm can effectively reduce the decoding complexity of RS codes when $e

Optimization algorithms are crucial in training physics-informed neural networks (PINNs), as unsuitable methods may lead to poor solutions. Compared to the common gradient descent (GD) algorithm, implicit gradient descent (IGD) outperforms it in handling certain multi-scale problems. In this paper, we provide convergence analysis for the IGD in training over-parameterized two-layer PINNs. We first demonstrate the positive definiteness of Gram matrices for some general smooth activation functions, such as sigmoidal function, softplus function, tanh function, and others. Then, over-parameterization allows us to prove that the randomly initialized IGD converges a globally optimal solution at a linear convergence rate. Moreover, due to the distinct training dynamics of IGD compared to GD, the learning rate can be selected independently of the sample size and the least eigenvalue of the Gram matrix. Additionally, the novel approach used in our convergence analysis imposes a milder requirement on the network width. Finally, empirical results validate our theoretical findings.

In recent years, neural networks have achieved remarkable progress in various fields and have also drawn much attention in applying them on scientific problems. A line of methods involving neural networks for solving partial differential equations (PDEs), such as Physics-Informed Neural Networks (PINNs) and the Deep Ritz Method (DRM), has emerged. Although these methods outperform classical numerical methods in certain cases, the optimization problems involving neural networks are typically non-convex and non-smooth, which can result in unsatisfactory solutions for PDEs. In contrast to deterministic neural networks, the hidden weights of random neural networks are sampled from some prior distribution and only the output weights participate in training. This makes training much simpler, but it remains unclear how to select the prior distribution. In this paper, we focus on Barron type functions and approximate them under Sobolev norms by random neural networks with clear prior distribution. In addition to the approximation error, we also derive bounds for the optimization and generalization errors of random neural networks for solving PDEs when the solutions are Barron type functions.

Maximum distance separable (MDS) codes facilitate the achievement of elevated levels of fault tolerance in storage systems while incurring minimal redundancy overhead. Reed-Solomon (RS) codes are typical MDS codes with the sub-packetization level being one, however, they require large repair bandwidth defined as the total amount of symbols downloaded from other surviving nodes during single-node failure/repair. In this paper, we present the {\em set transformation}, which can transform any MDS code into set transformed code such that (i) the sub-packetization level is flexible and ranges from 2 to $(n-k)^{\lfloor\frac{n}{n-k}\rfloor}$ in which $n$ is the number of nodes and $k$ is the number of data nodes, (ii) the new code is MDS code, (iii) the new code has lower repair bandwidth for any single-node failure. We show that our set transformed codes have both lower repair bandwidth and lower field size than the existing related MDS array codes, such as elastic transformed codes \cite{10228984}. Specifically, our set transformed codes have $2\%-6.6\%$ repair bandwidth reduction compared with elastic transformed codes \cite{10228984} for the evaluated typical parameters.

Reed-Solomon (RS) codes are constructed over a finite field that have been widely employed in storage and communication systems. Many fast encoding/decoding algorithms such as fast Fourier transform (FFT) and modular approach are designed for RS codes to reduce the encoding/decoding complexity defined as the number of XORs involved in the encoding/decoding procedure. In this paper, we present the construction of RS codes over the cyclic polynomial ring $ \mathbb{F}_2[x]/(1+x+\ldots+x^{p-1})$ and show that our codes are maximum distance separable (MDS) codes. Moreover, we propose the FFT and modular approach over the ring that can be employed in our codes for encoding/decoding complexity reduction. We show that our codes have 17.9\% encoding complexity reduction and 7.5\% decoding complexity reduction compared with RS codes over finite field, for $(n,k)=(2048,1984)$.

Nonreciprocal interaction crowd systems, such as human-human, human-vehicle, and human-robot systems, often have serious impacts on pedestrian safety and social order. A more comprehensive understanding of these systems is needed to optimize system stability and efficiency. Despite the importance of these interactions, empirical research in this area remains limited. Thus, in our study we explore this underresearched area, focusing on scenarios where nonreciprocity plays a critical role, such as mass stabbings, which pose a substantial risk to public safety. We conducted the first experiments on this system and analysed high-accuracy data obtained from these experiments. The extent of the direct threat zone is determined by the speed of the moving threat and the radius of danger occurrence. We further categorize potential threats into direct, adjacent, and rear-view zones, quantifying the level of threat for pedestrians. Our study revealed that a pedestrian's desired velocity correlated positively with potential threat intensity, increasing until near the direct threat zone. An emerging steady state is observed when escape routes are blocked by moving threats. This deviation affects the density-velocity relationship, making it distinct from the general relationship. This deviation signifies unique pedestrian behaviour in the presence of moving threats. Additionally, the rate of change in the angle for pedestrian motion in various desired directions is synchronized. This indicates the emergence of collective intelligence in nonreciprocal interaction crowd systems. As a result, our study may constitute a pioneering step towards understanding nonreciprocal interactions in crowd systems through laboratory experiments. These findings may enhance pedestrian safety and inform not only government crowd management strategies but also individual self-protection measures.

Finding cohesive subgraphs in a large graph has many important applications, such as community detection and biological network analysis. Clique is often a too strict cohesive structure since communities or biological modules rarely form as cliques for various reasons such as data noise. Therefore, $k$-plex is introduced as a popular clique relaxation, which is a graph where every vertex is adjacent to all but at most $k$ vertices. In this paper, we propose a fast branch-and-bound algorithm as well as its task-based parallel version to enumerate all maximal $k$-plexes with at least $q$ vertices. Our algorithm adopts an effective search space partitioning approach that provides a lower time complexity, a new pivot vertex selection method that reduces candidate vertex size, an effective upper-bounding technique to prune useless branches, and three novel pruning techniques by vertex pairs. Our parallel algorithm uses a timeout mechanism to eliminate straggler tasks, and maximizes cache locality while ensuring load balancing. Extensive experiments show that compared with the state-of-the-art algorithms, our sequential and parallel algorithms enumerate large maximal $k$-plexes with up to $5 \times$ and $18.9 \times$ speedup, respectively. Ablation results also demonstrate that our pruning techniques bring up to $7 \times$ speedup compared with our basic algorithm., Comment: Accepted by EDBT2025. Camera-ready version

In this paper, we present refined generalization bounds for the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs). For the DRM, we focus on two prototype elliptic PDEs: Poisson equation and static Schr\"odinger equation on the $d$-dimensional unit hypercube with the Neumann boundary condition. And sharper generalization bounds are derived based on the localization techniques under the assumptions that the exact solutions of the PDEs lie in the Barron spaces or the general Sobolev spaces. For the PINNs, we investigate the general linear second elliptic PDEs with Dirichlet boundary condition via the local Rademacher complexity in the multi-task learning.

In millimeter-wave (mmWave) cellular systems, reconfigurable intelligent surfaces (RISs) are foreseeably deployed with a large number of reflecting elements to achieve high beamforming gains. The large-sized RIS will make radio links fall in the near-field localization regime with spatial non-stationarity issues. Moreover, the discrete phase restriction on the RIS reflection coefficient incurs exponential complexity for discrete beamforming. It remains an open problem to find the optimal RIS reflection coefficient design in polynomial time. To address these issues, we propose a scalable partitioned-far-field protocol that considers both the near-filed non-stationarity and discrete beamforming. The protocol approximates near-field signal propagation using a partitioned-far-field representation to inherit the sparsity from the sophisticated far-field and facilitate the near-field localization scheme. To improve the theoretical localization performance, we propose a fast passive beamforming (FPB) algorithm that optimally solves the discrete RIS beamforming problem, reducing the search complexity from exponential order to linear order. Furthermore, by exploiting the partitioned structure of RIS, we introduce a two-stage coarse-to-fine localization algorithm that leverages both the time delay and angle information. Numerical results demonstrate that centimeter-level localization precision is achieved under medium and high signal-to-noise ratios (SNR), revealing that RISs can provide support for low-cost and high-precision localization in future cellular systems., Comment: 13 pages

Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed bits. We establish an achievable rate region by designing an efficient layered coding scheme, where the coding rate is reduced by introducing auxiliary random variables and local decoding is achieved by exploiting the expander graph code. Then we show the rate region is optimal under mild regularity conditions on source distributions. The proof relies on the reverse hypercontractivity and a rounding technique to construct auxiliary random variables. The rate region is strictly smaller than that for the classical problem without the constant locality constraint in most cases, which indicates that more rate is required in order to achieve lower coding complexity. Moreover, a coding for computing problem with side information is analogously studied. We also develop graph characterizations, which simplifies the computation of the achievable rate region.

This paper considers the problem of calculating the matrix multiplication of two massive matrices $\mathbf{A}$ and $\mathbf{B}$ distributedly. We provide a modulo technique that can be applied to coded distributed matrix multiplication problems to reduce the recovery threshold. This technique exploits the special structure of interpolation points and can be applied to many existing coded matrix designs. Recently studied discrete Fourier transform based code achieves a smaller recovery threshold than the optimal MatDot code with the expense that it cannot resist stragglers. We also propose a distributed matrix multiplication scheme based on the idea of locally repairable code to reduce the recovery threshold of MatDot code and provide resilience to stragglers. We also apply our constructions to a type of matrix computing problems, where generalized linear models act as a special case.

In this letter, we delve into a scenario where a user aims to compute polynomial functions using their own data as well as data obtained from distributed sources. To accomplish this, the user enlists the assistance of $N$ distributed workers, thereby defining a problem we refer to as privacy-preserving polynomial computing over distributed data. To address this challenge, we propose an approach founded upon Lagrange encoding. Our method not only possesses the ability to withstand the presence of stragglers and byzantine workers but also ensures the preservation of security. Specifically, even if a coalition of $X$ workers collude, they are unable to acquire any knowledge pertaining to the data originating from the distributed sources or the user.

In a real-time transmission scenario, messages are transmitted through a channel that is subject to packet loss. The destination must recover the messages within the required deadline. In this paper, we consider a setup where two different types of messages with distinct decoding deadlines are transmitted through a channel that can introduce burst erasures of a length at most $B$, or $N$ random erasures. The message with a short decoding deadline $T_u$ is referred to as an urgent message, while the other one with a decoding deadline $T_v$ ($T_v > T_u$) is referred to as a less urgent message. We propose a merging method to encode two message streams of different urgency levels into a single flow. We consider the scenario where $T_v > T_u + B$. We establish that any coding strategy based on this merging approach has a closed-form upper limit on its achievable sum rate. Moreover, we present explicit constructions within a finite field that scales quadratically with the imposed delay, ensuring adherence to the upper bound. In a given parameter configuration, we rigorously demonstrate that the sum rate of our proposed streaming codes consistently surpasses that of separate encoding, which serves as a baseline for comparison.

Maximum distance separable (MDS) codes have the optimal trade-off between storage efficiency and fault tolerance, which are widely used in distributed storage systems. As typical non-MDS codes, simple regenerating codes (SRCs) can achieve both smaller repair bandwidth and smaller repair locality than traditional MDS codes in repairing single-node erasure. In this paper, we propose {\em generalized simple regenerating codes} (GSRCs) that can support much more parameters than that of SRCs. We show that there is a trade-off between sub-packetization and fault tolerance in our GSRCs, and SRCs achieve a special point of the trade-off of GSRCs. We show that the fault tolerance of our GSRCs increases when the sub-packetization increases linearly. We also show that our GSRCs can locally repair any singe-symbol erasure and any single-node erasure, and the repair bandwidth of our GSRCs is smaller than that of the existing related codes.

Singularly perturbed problems present inherent difficulty due to the presence of a thin boundary layer in its solution. To overcome this difficulty, we propose using deep operator networks (DeepONets), a method previously shown to be effective in approximating nonlinear operators between infinite-dimensional Banach spaces. In this paper, we demonstrate for the first time the application of DeepONets to one-dimensional singularly perturbed problems, achieving promising results that suggest their potential as a robust tool for solving this class of problems. We consider the convergence rate of the approximation error incurred by the operator networks in approximating the solution operator, and examine the generalization gap and empirical risk, all of which are shown to converge uniformly with respect to the perturbation parameter. By utilizing Shishkin mesh points as locations of the loss function, we conduct several numerical experiments that provide further support for the effectiveness of operator networks in capturing the singular boundary layer behavior.

We define a graph-based rate optimization problem and consider its computation, which provides a unified approach to the computation of various theoretical limits, such as the (conditional) graph entropy, rate-distortion functions and capacity-cost functions with two-sided information. Our contributions are twofold. On the theoretical side, we simplify the graph-based problem by constructing explicit graph contractions in some special cases. These efforts reduce the number of decision variables in the optimization problem. Graph characterizations for rate-distortion and capacity-cost functions with two-sided information are simplified by specializing the results. On the computational side, we design an alternating minimization algorithm for the graph-based problem, which deals with the inequality constraint by a flexible multiplier update strategy. Moreover, deflation techniques are introduced, so that the computing time can be largely reduced. Theoretical analysis shows that the algorithm converges to an optimal solution. The accuracy and efficiency of the algorithm are illustrated by numerical experiments.

Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and sink. Based on this setting, constrained optimal transport has numerous applications, e.g., finance, network flow. However, due to the large number of constraints in this problem, existing algorithms are both time-consuming and space-consuming. In this paper, inspired by entropic regularization for the classical optimal transport problem, we introduce a novel regularization term for capacity constrained optimal transport. The regularized problem naturally satisfies the capacity constraints and consequently makes it possible to analyze the duality. Unlike the matrix-vector multiplication in the alternate iteration scheme for solving classical optimal transport, in our algorithm, each alternate iteration step is to solve several single-variable equations. Fortunately, we find that each of these equations corresponds to a single-variable monotonic function, and we convert solving these equations into finding the unique zero point of each single-variable monotonic function with Newton's method. Extensive numerical experiments demonstrate that our proposed method has a significant advantage in terms of accuracy, efficiency, and memory consumption compared with existing methods., Comment: 17 pages, 3 figures

Few-Shot Learning (FSL) alleviates the data shortage challenge via embedding discriminative target-aware features among plenty seen (base) and few unseen (novel) labeled samples. Most feature embedding modules in recent FSL methods are specially designed for corresponding learning tasks (e.g., classification, segmentation, and object detection), which limits the utility of embedding features. To this end, we propose a light and universal module named transformer-based Semantic Filter (tSF), which can be applied for different FSL tasks. The proposed tSF redesigns the inputs of a transformer-based structure by a semantic filter, which not only embeds the knowledge from whole base set to novel set but also filters semantic features for target category. Furthermore, the parameters of tSF is equal to half of a standard transformer block (less than 1M). In the experiments, our tSF is able to boost the performances in different classic few-shot learning tasks (about 2% improvement), especially outperforms the state-of-the-arts on multiple benchmark datasets in few-shot classification task.

As a special class of array codes, $(n,k,m)$ piggybacking codes are MDS codes (i.e., any $k$ out of $n$ nodes can retrieve all data symbols) that can achieve low repair bandwidth for single-node failure with low sub-packetization $m$. In this paper, we propose two new piggybacking codes that have lower repair bandwidth than the existing piggybacking codes given the same parameters. Our first piggybacking codes can support flexible sub-packetization $m$ with $2\leq m\leq n-k$, where $n - k > 3$. We show that our first piggybacking codes have lower repair bandwidth for any single-node failure than the existing piggybacking codes when $n - k = 8,9$, $m = 6$ and $30\leq k \leq 100$. Moreover, we propose second piggybacking codes such that the sub-packetization is a multiple of the number of parity nodes (i.e., $(n-k)|m$), by jointly designing the piggyback function for data node repair and transformation function for parity node repair. We show that the proposed second piggybacking codes have lowest repair bandwidth for any single-node failure among all the existing piggybacking codes for the evaluated parameters $k/n = 0.75, 0.8, 0.9$ and $n-k\geq 4$.

In this paper, we propose a numerical method for turning point problems in one dimension based on Petrov-Galerkin finite element method (PGFEM). We first give a priori estimate for the turning point problem with a single boundary turning point. Then we use PGFEM to solve it, where test functions are the solutions to piecewise approximate dual problems. We prove that our method has a first-order convergence rate in both $L^\infty$ norm and an energy norm when we select the exact solutions to dual problems as test functions. Numerical results show that our scheme is efficient for turning point problems with different types of singularities, and the convergency coincides with our theoretical results.

The Wasserstein distance has been an attractive tool in many fields. But due to its high computational complexity and the phenomenon of the curse of dimensionality in empirical estimation, various extensions of the Wasserstein distance have been proposed to overcome the shortcomings such as the Sliced Wasserstein distance. It enjoys a low computational cost and dimension-free sample complexity, but there are few distributional limit results of it. In this paper, we focus on Sliced 1-Wasserstein distance and its variant max-Sliced 1-Wasserstein distance. We utilize the central limit theorem in Banach space to derive the limit distribution for the Sliced 1-Wasserstein distance. Through viewing the empirical max-Sliced 1-Wasserstein distance as a supremum of an empirical process indexed by some function class, we prove that the function class is P-Donsker under mild moment assumption. Moreover, for computing Sliced p-Wasserstein distance based on Monte Carlo method, we explore that how many random projections that can make sure the error small in high probability. We also provide upper bound of the expected max-Sliced 1-Wasserstein between the true and the empirical probability measures under different conditions and the concentration inequalities for max-Sliced 1-Wasserstein distance are also presented. As applications of the theory, we utilize them for two-sample testing problem., Comment: 36pages

Piggybacking codes are a special class of MDS array codes that can achieve small repair bandwidth with small sub-packetization by first creating some instances of an $(n,k)$ MDS code, such as a Reed-Solomon (RS) code, and then designing the piggyback function. In this paper, we propose a new piggybacking coding design which designs the piggyback function over some instances of both $(n,k)$ MDS code and $(n,k')$ MDS code, when $k\geq k'$. We show that our new piggybacking design can significantly reduce the repair bandwidth for single-node failures. When $k=k'$, we design piggybacking code that is MDS code and we show that the designed code has lower repair bandwidth for single-node failures than all existing piggybacking codes when the number of parity node $r=n-k\geq8$ and the sub-packetization $\alpha

Seismic tomography solves high-dimensional optimization problems to image subsurface structures of Earth. In this paper, we propose to use random batch methods to construct the gradient used for iterations in seismic tomography. Specifically, we use the frozen Gaussian approximation to compute seismic wave propagation, and then construct stochastic gradients by random batch methods. The method inherits the spirit of stochastic gradient descent methods for solving high-dimensional optimization problems. The proposed idea is general in the sense that it does not rely on the usage of the frozen Gaussian approximation, and one can replace it with any other efficient wave propagation solvers, e.g., Gaussian beam methods and spectral element methods. We prove the convergence of the random batch method in the mean-square sense, and show the numerical performance of the proposed method by two-dimensional and three-dimensional examples of wave-equation-based travel-time inversion and full-waveform inversion, respectively. As a byproduct, we also prove the convergence of the accelerated full-waveform inversion using dynamic mini-batches and spectral element methods., Comment: 20 pages

Currently, there is an increasing number of super high-rise buildings in urban cities, the issue of evacuation in emergencies from such buildings comes to the fore. An evacuation experiment was carried out by our group in Shanghai Tower, it was found that the evacuation speed of pedestrians evacuated from the 126th floor was always slower than that of those from the 117th floor. Therefore, we propose a hypothesis that the expected evacuation distance will affect pedestrians' movement speed. In order to verify our conjecture, we conduct an experiment in a 12-story office building, that is, to study whether there would be an influence and what kind of influence would be caused on speed by setting the evacuation distance for participants in advance. According to the results, we find that with the increase of expected evacuation distance, the movement speed of pedestrians will decrease, which confirms our hypothesis. At the same time, we give the relation between the increase rate of evacuation distance and the decrease rate of speed. It also can be found that with the increase of expected evacuation distance, the speed decrease rate of the male is greater than that for female. In addition, we study the effects of actual evacuation distance, gender, BMI on evacuation speed. Finally, we obtain the correlation between heart rate and speed during evacuation. The results in this paper are beneficial to the study of pedestrian evacuation in super high-rise buildings., Comment: 20 pages

In this paper, we propose an iterative splitting method to solve the partial differential equations in option pricing problems. We focus on the Heston stochastic volatility model and the derived two-dimensional partial differential equation (PDE). We take the European option as an example and conduct numerical experiments using different boundary conditions. The iterative splitting method transforms the two-dimensional equation into two quasi one-dimensional equations with the variable on the other dimension fixed, which helps to lower the computational cost. Numerical results show that the iterative splitting method together with an artificial boundary condition (ABC) based on the method by Li and Huang (2019) gives the most accurate option price and Greeks compared to the classic finite difference method with the commonly-used boundary conditions in Heston (1993).

Objectives: Simulate the transmission process of COVID-19 in a cruise ship, and then to judge how many infections there will be in the 3711 people in the "Diamond Princess" and analyze measures that could have prevented mass transmission. Methods: Based on the crowd flow model, the virus transmission rule between pedestrians is established, to simulate the spread of the virus caused by the close contact during pedestrians' daily activities on the cruise ship. Measurements and main results: Three types of simulation scenarios are designed, the Basic scenario focus on the process of virus transmission caused by a virus carrier and the effect of the personal protective measure against the virus. The condition that the original virus carriers had disembarked halfway and more and more people strengthen self-protection are considered in the Self-protection scenario, which would comparatively accord with the actual situation of "Diamond princess" cruise. Control scenario are set to simulate the effect of taking recommended or mandatory measures on virus transmission Conclusions: There are 850~1009 persons (with large probability) who have been infected with COVID-19 during the voyage of "Diamond Princess". The crowd infection percentage would be controlled effectively if the recommended or mandatory measures can be taken immediately during the alert phase of COVID-19 outbreaks.

This paper considers the valuation of a European call option under the Heston stochastic volatility model. We present the asymptotic solution to the option pricing problem in powers of the volatility of variance. Then we introduce the artificial boundary method for solving the problem on a truncated domain, and derive several artificial boundary conditions (ABCs) on the artificial boundary of the bounded computational domain. A typical finite difference scheme and quadrature rule are used for the numerical solution of the reduced problem. Numerical experiments show that the proposed ABCs are able to improve the accuracy of the results and have a significant advantage over the widely-used boundary conditions by Heston in the original paper (Heston, 1993).