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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|统计物理代写Statistical Physics of Matter代考|DNA Condensation in Solution

Suppose that a DNA fragment of $N$ segments is immersed into a solution that is crowded with macromolecular solutes such as proteins (Fig. 10.14). What conformation will the fragment take? Following the argument of Sneppen and Zocchi (2005), we present a scenario that shows the DNA can collapse rather than be swollen or extended, due to excluded volume interaction between the DNA and solute.

For simplicity we consider $N_U$ mutually non-interacting solute molecules each with radius $r_U$ in a volume $V$. The partition function for the solute in the absence of the DNA is (4.85):
$$Z_U^0=\frac{1}{N_{U} !}\left(V / v_0\right)^{N_U}$$
Consider that a DNA fragment has $N$ segments each with length $l$. We assume that the solute and DNA do not interact except via the steric effect of the excluded volume $\delta=\pi\left(r_{D N A}+r_U\right)^2 l$, per DNA segment, where $r_{D N A}$ is cross-sectional radius. When the DNA chain does not coil but is extended, the volume available to the solutes is reduced by this interaction as $V \rightarrow V-N \delta$.

Now assume that the DNA collapses to a globule of radius $R$. With the solute depleted within the globule, the volume available to the solute in the solution increases. The fraction of such forbidden contacts between the solute and DNA in the globule is $\sim\left(N \delta / R^3\right)$, so the volume available to the solute particles becomes
$$V^{\prime}=V-N \delta+\frac{(N \delta)^2}{R^3}$$
Consequently, the free energy change of the solutes during transition to the collapsed state for the DNA is
\begin{aligned} \Delta F_U &=-N_U k_B T \ln \left(\left{V-N \delta+\frac{(N \delta)^2}{R^3}\right} /(V-N \delta)\right) \ & \cong-k_B T \frac{(N \delta)^2}{R^3} n_U \end{aligned}
where $n_U=N_U / V$ is the concentration of solutes and $N \delta / V \ll 1$ as well as $(N \delta)^2 / V R^3 \ll 1$ are to be noted.

## 物理代写|统计物理代写Statistical Physics of Matter代考|Worm-like Chain Model

We start with construction of the effective Hamiltonian for a free semi-flexible chain. As mentioned earlier, the effective Hamiltonian can be taken from the macroscopic, phenomenological energy, which, for a semi-flexible chain, is the energy required to bend an elastic string with a locally varying curvature:

$$\mathcal{F}-\frac{\kappa}{2} \int_0^L d s C(s)^2-\frac{\kappa}{2} \int_0^L d s\left(\frac{\partial \boldsymbol{u}(s)}{\partial s}\right)^2$$
Here $\kappa$ is an elastic constant called bending modulus (or bending rigidity) and the $L$ is the contour length, and $C(s)$ is the curvature at an arc length $s$ (Fig. 11.2). The curvature is given by $C(s)=1 / R(s)=|\partial u(s) / \partial s|$, where $R(s)$ is the local radius of curvature, $\boldsymbol{u}(s)$ is the unit tangent vector given by $\boldsymbol{u}(s)=\partial \boldsymbol{r}(s) / \partial s$, where $\boldsymbol{r}(s)$ is the position vector to the arc position. By considering the local curvature to thermally fluctuate, the energy (11.1) can gain the status of an effective Hamiltonian, or a free energy function. We may say that the Hamiltonian brings the macroscopic bending energy to life with the local curvatures therein thermally fluctuating. This model is called the worm-like chain (WLC). In the absence of an external potential on each segment, it stands in contrast with the flexible chain Hamiltonian $(10.52)$
$$\mathcal{F}=\frac{k_e}{2} \int_0^L d s\left(\frac{\partial \boldsymbol{r}(s)}{\partial s}\right)^2=\frac{k_e}{2} \int_0^L d s(\boldsymbol{u}(s))^2$$
which represents stretching energy with the entropic stretch modulus $k_e=3 k_B T / l^2$.

# 统计物理代考

## 物理代写|统计物理代写物质统计物理代考|浓缩在溶液中的DNA

$$Z_U^0=\frac{1}{N_{U} !}\left(V / v_0\right)^{N_U}$$

$$V^{\prime}=V-N \delta+\frac{(N \delta)^2}{R^3}$$

\begin{aligned} \Delta F_U &=-N_U k_B T \ln \left(\left{V-N \delta+\frac{(N \delta)^2}{R^3}\right} /(V-N \delta)\right) \ & \cong-k_B T \frac{(N \delta)^2}{R^3} n_U \end{aligned}
，其中$n_U=N_U / V$为溶质的浓度，$N \delta / V \ll 1$和$(N \delta)^2 / V R^3 \ll 1$值得注意

## 物理代写|统计物理代写物质统计物理代考|蠕虫-链模型

.

$$\mathcal{F}-\frac{\kappa}{2} \int_0^L d s C(s)^2-\frac{\kappa}{2} \int_0^L d s\left(\frac{\partial \boldsymbol{u}(s)}{\partial s}\right)^2$$

$$\mathcal{F}=\frac{k_e}{2} \int_0^L d s\left(\frac{\partial \boldsymbol{r}(s)}{\partial s}\right)^2=\frac{k_e}{2} \int_0^L d s(\boldsymbol{u}(s))^2$$

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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