As for the liquid water content distributions, the liquid saturations in gas diffusion layers are shown in Fig. 6. For both case1 and case 2, the liquid water appears in the vapor saturation areas which locate between the mid area and cathode outlet area. For both cases, the cathode side exhibits apparent higher liquid water content than anode side does. Moreover, the liquid water accumulates in the porous media under the ribs rather than the gas channels, due to the elimination effects of liquid water in gas channels by convective flows. The maximum value of liquid saturation locates at the edge areas of cathode flow field without coverage by the wavy air channels where the oxygen supply is hindered by both blockage of liquid water in porous media and farther distance for gas permeation. The liquid water content of case 2 shows slightly higher than that of case 1, which is a result of tradeoff between operating temperature and pressure. Increasing temperature alleviates the condensation of water vapor, while the increased back pressure lowers volumetric gas flow rate and enhances liquid water accumulation inside the porous media.

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Make sure that we grade your HW based solely on your R code script. If we don’t see the correct results when we run your code, you will get 0 point for those questions. 1. Create a R function to show the central limit theorem. This function should have the following properties: - In the argument of the function, you have an option to consider poisson, exponential, uniform, normal distributions as the population distribution. - Depending on the choice of the population distribution in part (1), the function will receive extra argument(s) for the parameters of the distribution. For example, if a normal distri- bution is chosen, the mean and SD are needed in the function argument. Note that each distribution has a different parameter setting. - If the distribution is not selected from (“Normal”, “Poisson”, “Uniform”, “Exponential”), the function needs to print the following error message: check the distributional setting: consider ("Normal", "Poisson", "Uniform", "Exponential") and stop. - The function should give the summary statistics (minimum, 1st quartile, median, mean, 3rd quartile, maximum) of 1, 000 sample mean values for given n values (n = 10, 50, 100, 500). - The result should have the following statement at the beginning, for example, if a normal distribution with mean 1 and SD 0.5 was chosen: ‘‘For the Normal distribution, the central limit theorem is tested’’ where the term “Normal” is automatically inserted in the statement based on the argument. And the output should have the following form: For the Normal distribution, the central limit theorem is tested When n=10: Min. 1st Qu. Median Mean 3rd Qu. Max. 0.5187 0.8930 1.0016 0.9993 1.1019 1.4532 When n=50: Min. 1st Qu. Median Mean 3rd Qu. Max. 0.7964 0.9508 1.0010 0.9997 1.0493 1.2309 1 When n=100: Min. 1st Qu. Median Mean 3rd Qu. Max. 0.8534 0.9679 0.9972 0.9992 1.0325 1.1711 When n=500: Min. 1st Qu. Median Mean 3rd Qu. Max. 0.9258 0.9836 1.0006 0.9997 1.0154 1.0678 I Using your own function, test the N(−1,0.52) and the Unif(−3,6) case.

Here's the R code for the function that meets the requirements: {r} central_limit_theorem (distribution, ...) { # check if the selected distribution is valid if (!(distribution %in% c("Normal...

用中文总结以下内容： A number of experimental and numerical investigations have been conducted to study the MBPP stack and wavy flow field characteristics with various designs [10,11]. T. Chu et al. conducted the durability test of a 10-kW MBPP fuel cell stack containing 30 cells under dynamic driving cycles and analyzed the performance degradation mechanism [12]. X. Li et al. studied the deformation behavior of the wavy flow channels with thin metallic sheet of 316 stainless steel from both experimental and simulation aspects [13]. J. Owejan et al. designed a PEMFC stack with anode straight flow channels and cathode wavy flow channels and studied the in situ water distributions with neutron radiograph [14]. T. Tsukamoto et al. simulated a full-scale MBPP fuel cell stack of 300 cm2 active area at high current densities and used the 3D model to analyze the in-plane and through-plane parameter distributions [15]. G. Zhang et al. developed a two-fluid 3D model of PEMFC to study the multi-phase and convection effects of wave-like flow channels which are symmetric between anode and cathode sides [16]. S. Saco et al. studied the scaled up PEMFC numerically and compared straight parallel, serpentine zig-zag and straight zig-zag flow channels cell with zig-zag flow field with a transient 3D numerical model to analyze the subfreezing temperature cold start operations [18]. P. Dong et al. introduced discontinuous S-shaped and crescent ribs into flow channels based on the concept of wavy flow field for optimized design and improved energy performance [19]. I. Anyanwu et al. investigated the two-phase flow in sinusoidal channel of different geometric configurations for PEMFC and analyzed the effects of key dimensions on the droplet removal in the flow channel [20]. Y. Peng et al. simulated 5-cell stacks with commercialized flow field designs, including Ballard-like straight flow field, Honda-like wavy flow field and Toyota-like 3D mesh flow field, to investigate their thermal management performance [21]. To note, the terms such as sinusoidal, zig-zag, wave-like and Sshaped flow channels in the aforementioned literatures are similar to the so called wavy flow channels in this paper with identical channel height for the entire flow field. The through-plane constructed wavy flow channels with periodically varied channel heights are beyond the scope of this paper [22,23].

Owejan等人设计了具有阳极直流道和阴极波浪流道的PEMFC堆，并用中子射线图研究了原位水分布（14），Tsukamoto等人模拟了300 cm2有效面积的全尺寸MBPP燃料电池堆，利用3D模型分析了平面及穿越面参数分布（15），Zhang...

To the best of our knowledge, no research has studied the inversely phased wavy flow fields of anode and cathode in a MBPP structure to investigate the 3D distributions of internal parameters inside the stack. There are two distinguished features of the mentioned design: (1) the wavy flow fields are asymmetric between the anode and cathode sides with a phase deviation of 180◦; (2) the inversely phased wavy coolant channels at the back sides of anode and cathode metallic plates construct the intercrossed two-layered coolant flow fields. In such a complicated 3D geometry of the MBPP stack, the detailed parameter distributions inside the stack should be studied under different operating conditions for the design optimization.

該設計有兩個突出的特徵：（1）陽極和陰極之間的波浪流場是不對稱的，其相位差為180°；（2）陽極和陰極金屬板背面的反相波浪冷卻通道組成了交叉的兩層冷卻流場。在如此複雜的MBPP結構中，在不同工作條件下應對結構...

# How to Build libplctag The build system uses CMake to bootstrap a local build. On Linux. On Windows, this makes a Visual Studio project. CMake is also used to create a build on macOS. Note that as of version 2.0.22, pre-built binaries are included in the GitHub releases. # Instructions for Linux ## Install the compilers ### Debian/Ubuntu #### Install Build Essentials, CMake and Git text $> sudo apt-get install build-essential cmake git Use your distro-specific instructions to install Clang if you want to use that compiler. ### RHEL/CentOS These instructions probably work with few modifications for Red Hat and Oracle Linux. Please file a GitHub ticket if they need changes for SUSE and other RPM-based distributions. #### Install Compilers, CMake and Git You need to become root or, if your Linux distribution supports it, run these commands with sudo. text $> yum install gcc gcc-c++ cmake git 翻译

# 如何构建libplctag 构建系统使用CMake来启动本地构建。在Linux上，它使用CMake创建一个Visual Studio项目。在macOS上也使用CMake来创建构建。请注意，从版本2.0.22开始，预编译的二进制文件已包含在GitHub发布...

以下是一篇即将投稿Minerals期刊（MDPI出版社）的论文初稿的部分内容，请按照该期刊对论文格式的要求，将以下内容进行压缩凝练（注意：可对内容进行删减，对错误进行修正，对语句顺序进行调整，符合美式英语标准，符合英语母语者语言习惯，句子简明易懂，术语使用准确，保留文章结构、不偏离论文主要内容）： Rocks and ore components directly enter the soil and water system sediments through physical weathering and chemical weathering, and the geochemical anomalies originally present in the rocks further spread with the entry into the soil or directly into the water system, forming soil anomalies and water system sediment anoma-lies.Geochemical anomaly detection is essentially the detection of signal anomalies in geochemical data, which refers to finding out the anomalous distribution of chemical elements themselves and the anomalous distribution of multiple elements in combination through feature extraction and analysis processing of geochemical data in the study area, and reflecting the mineral distribution through the distribution of geochemical ele-ments.Through the method of geochemical anomaly finding, the detected anomalies may contain information indicating specific minerals, which facilitates the rapid tracing of prospective areas and favorable areas for mineralization, identifies possible mineralizing elements and distribution characteristics in the work area, provides basic information for the strategic deployment of mineralization search, and provides good indications for later mineralization search.

Rocks and ore components enter soil and water system sediments through physical and chemical weathering, causing the spread of geochemical anomalies. Detecting geochemical anomalies involves ...

function dist=KLDiv(P,Q) % dist = KLDiv(P,Q) Kullback-Leibler divergence of two discrete probability % distributions % P and Q are automatically normalised to have the sum of one on rows % have the length of one at each % P = n x nbins % Q = 1 x nbins or n x nbins(one to one) % dist = n x 1 if size(P,2)~=size(Q,2) error('the number of columns in P and Q should be the same'); end if sum(~isfinite(P(:))) + sum(~isfinite(Q(:))) error('the inputs contain non-finite values!') end % normalizing the P and Q if size(Q,1)==1 Q = Q ./sum(Q); P = P ./repmat(sum(P,2),[1 size(P,2)]); temp = P.log(P./repmat(Q,[size(P,1) 1])); temp(isnan(temp))=0;% resolving the case when P(i)==0 dist = sum(temp,2); elseif size(Q,1)==size(P,1) Q = Q ./repmat(sum(Q,2),[1 size(Q,2)]); P = P ./repmat(sum(P,2),[1 size(P,2)]); temp = P.log(P./Q); temp(isnan(temp))=0; % resolving the case when P(i)==0 dist = sum(temp,2); end

如果输入的 Q 是一个 $1 \times nbins$ 的向量，则会将其转换为一个与 P 相同大小的矩阵。最后的输出 dist 是一个 $n \times 1$ 的向量，表示每个概率分布与 Q 之间的 Kullback-Leibler 散度。具体来说，这个函数...

def estimate_variance(xs: np.ndarray, ys: np.ndarray, affine: np.ndarray, translation: np.ndarray, responsibility: np.ndarray) -> float: """ Estimate the variance of GMM. For simplification, we assume all the Gaussian distributions share the same variance, and each feature dimension is independent, so the variance can be represented as a scalar. :param xs: a set of points with size (N, D), N is the number of samples, D is the dimension of points :param ys: a set of points with size (M, D), M is the number of samples, D is the dimension of points :param affine: an affine matrix with size (D, D) :param translation: a translation vector with size (1, D) :param responsibility: the responsibility matrix with size (N, M) :return: the variance of each Gaussian distribution, a float """ # TODO: change the code below and compute the variance of each Gaussian return 1

1. Transform the xs using the affine matrix and translation vector: xs_transformed = xs.dot(affine) + translation 2. Compute the pairwise distance matrix between xs_transformed and ys: ...

Consider the monthly returns for Abbott Laboratories (ABT), CRSP value-weighted index(VW), CRSP equal-weighted index (EW), and the S&P composite index (SP) from January 1972 to December 2012. The returns include dividend distributions.Data file is m-abt3dx.txt (date, RET, vw, ew, sp). (a) Compute the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of each simple return series. (Hint: use the R command basicStats of fBasics) (b) Transform the simple returns to log returns. Compute the sample mean, standard deviation,skewness, excess kurtosis, minimum, and maximum of each log return series. (c) Test the null hypothesis that the mean of the log returns of Abbott Laboratories is zero. (Hint: usethe R command t.test) (d) Obtain the histogram (with nclass=40) and sample density plot of the monthly log returns of Abbott Laboratories.

(a) To compute the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of each simple return series, we can use the R package fBasics and the basicStats function....

from ldm.util import log_txt_as_img, exists, default, ismap, isimage, mean_flat, count_params, instantiate_from_config from ldm.modules.ema import LitEma from ldm.modules.distributions.distributions import normal_kl, DiagonalGaussianDistribution from ldm.models.autoencoder import VQModelInterface, IdentityFirstStage, AutoencoderKL from ldm.modules.diffusionmodules.util import make_beta_schedule, extract_into_tensor, noise_like from ldm.models.diffusion.ddim import DDIMSampler解析

1. log_txt_as_img：一个用于将文本日志记录为图像的函数。 2. exists：一个用于判断文件或目录是否存在的函数。 3. default：一个用于设置缺省值的函数。 4. ismap：一个用于判断是否为映射（Python中...

class PPO(object): def init(self): self.sess = tf.Session() self.tfs = tf.placeholder(tf.float32, [None, S_DIM], 'state') # critic with tf.variable_scope('critic'): l1 = tf.layers.dense(self.tfs, 100, tf.nn.relu) self.v = tf.layers.dense(l1, 1) self.tfdc_r = tf.placeholder(tf.float32, [None, 1], 'discounted_r') self.advantage = self.tfdc_r - self.v self.closs = tf.reduce_mean(tf.square(self.advantage)) self.ctrain_op = tf.train.AdamOptimizer(C_LR).minimize(self.closs) # actor pi, pi_params = self._build_anet('pi', trainable=True) oldpi, oldpi_params = self._build_anet('oldpi', trainable=False) with tf.variable_scope('sample_action'): self.sample_op = tf.squeeze(pi.sample(1), axis=0) # choosing action with tf.variable_scope('update_oldpi'): self.update_oldpi_op = [oldp.assign(p) for p, oldp in zip(pi_params, oldpi_params)] self.tfa = tf.placeholder(tf.float32, [None, A_DIM], 'action') self.tfadv = tf.placeholder(tf.float32, [None, 1], 'advantage') with tf.variable_scope('loss'): with tf.variable_scope('surrogate'): # ratio = tf.exp(pi.log_prob(self.tfa) - oldpi.log_prob(self.tfa)) ratio = pi.prob(self.tfa) / (oldpi.prob(self.tfa) + 1e-5) surr = ratio * self.tfadv if METHOD['name'] == 'kl_pen': self.tflam = tf.placeholder(tf.float32, None, 'lambda') kl = tf.distributions.kl_divergence(oldpi, pi) self.kl_mean = tf.reduce_mean(kl) self.aloss = -(tf.reduce_mean(surr - self.tflam * kl)) else: # clipping method, find this is better self.aloss = -tf.reduce_mean(tf.minimum( surr, tf.clip_by_value(ratio, 1.-METHOD['epsilon'], 1.+METHOD['epsilon'])*self.tfadv))

这段代码是使用 PPO（Proximal Policy Optimization）算法实现的一个 actor-critic 模型。其中，critic 用来评价当前状态的价值，actor 用来生成在当前状态下采取的动作。在训练过程中，会使用 advantage（优势值）...

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