数学代写|理论计算机代写theoretical computer science代考|On the Complexity of the Upper $r$-Tolerant Edge Cover Problem

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数学代写|理论计算机代写theoretical computer science代考|On the Complexity of the Upper $r$-Tolerant Edge Cover Problem

数学代写|理论计算机代写theoretical computer science代考|On the Complexity of the Upper $r$-Tolerant Edge Cover Problem

In this paper we define and study tolerant edge cover problems. An edge cover of a graph $G=(V, E)$ without isolated vertices is a subset of edges $S \subseteq E$ which covers all vertices of $G$, that is, each vertex of $G$ is an endpoint of at least one edge in $S$. The edge cover number of a graph $G=(V, E)$, denoted by ec $(G)$, is the minimum size of an edge cover of $G$ and it can be computed in polynomial time (see Chapter 19 in [29]). An edge cover $S \subseteq E$ is called minimal (with respect to inclusion) if no proper subset of $S$ is an edge cover. Minimal edge cover is also known in the literature as an enclaveless set [30] or as a nonblocker set [14]. While a minimum edge cover can be computed efficiently, finding the largest minimal edge cover is NP-hard [27], where it is shown that the problem is equivalent to finding a dominating set of minimum size. The associated optimization problem is called upper edge cover (and denoted UPPER EC) [1] and the corresponding optimal value will be denoted uec $(G)$ in this paper for the graph $G=(V, E)$.
Here, we are interested in minimal edge cover solutions tolerant to the failures of at most $r-1$ edges. Formally, given an integer $r \geq 1$, an edge subset $S \subseteq E$ of $G=(V, E)$ is a tight $r$-tolenant edge-cover ( $r$-tec for short) if the deletion of

any set of at most $r-1$ edges from $S$ maintains an edge cover ${ }^{1}$ and the deletion of any edge from $S$ yields a set which is not a (tight) $r$-tolerant edge cover. Equivalently, we seek an edge subset $S$ of $G$ such that the subgraph $(V, S)$ has minimum degree $r$ and it is minimal with this property. For the sake of brevity we will omit the word ‘tight’ in the rest of the paper. Note that the case $r=1$ corresponds to the standard notion of minimal edge cover.

As an illustrating example consider the situation in which the mayor of a big city seeks to hire a number of guards, from a security company, who will be constantly patrolling streets between important buildings. An $r$-tolerant edge cover reflects the desire of the mayor to guarantee that the security is not compromised even if $r-1$ guards are attacked. Providing a maximum cover would be the goal of a selfish security company, who would like to propose a patrolling schedule with as many guards as possible, but in which all the proposed guards are necessary in the sense that removing any of them would leave some building not $r$-covered.

Related Work. UPPER EC has been investigated intensively during recent years, mainly using the terminologies of spanning star forests and dominating sets. A dominating set in a graph is a subset $S$ of vertices such that any vertex not in $S$ has at least one neighbor in $S$. The minimum dominating set problem (denoted MinDS) seeks the smallest dominating set of $G$ of value $\gamma(G)$. We have the equality $\operatorname{uec}(G)=n-\gamma(G)[27]$.

Thus, using the complexity results known for MinDS, we deduce that UPPER EDGE COVER is NP-hard in planar graphs of maximum degree 3 [20], chordal graphs [6] (even in undirected path graphs, the class of vertex intersection graphs of a collection of paths in a tree), bipartite graphs, split graphs [5] and $k$-trees with arbitrary $k[12]$, and it is polynomial in $k$-trees with fixed $k$, convex bipartite graphs [13], strongly chordal graphs [16]. Concerning the approximability, an APX-hardness proof with explicit inapproximability bound and a combinatorial 0.6-approximation algorithm is proposed in [28]. Better algorithms with approximation ratio $0.71$ and $0.803$ are given respectively in [9] and [2]. For any $\varepsilon>0$, UPPER EDGE COVER is hard to approximate within a factor of $\frac{259}{260}+\varepsilon$ unless $\mathbf{P}=\mathbf{N P}$ [28]. The weighted version of the problem, denoted as UPPER WEIGHTED EDGE CoVER, have been recently studied in [24], in which it is proved that the problem is not $O\left(\frac{1}{n^{1 / 2-\varepsilon}}\right)$ approximable nor $O\left(\frac{1}{\Delta^{1-\varepsilon}}\right)$ in edge weighted graphs of order $n$ and maximum degree $\Delta$.

数学代写|理论计算机代写theoretical computer science代考|Definitions

Graph Notation and Terminology. Let $G=(V, E)$ be a graph and $S \subseteq V$; $N_{G}(S)={v \in V: \exists u \in S, v u \in E}$ denotes the neighborhood of $S$ in $G$ and $N_{G}[S]=S \cup N_{G}(S)$ denotes the closed neighborhood of $S$. For singleton sets $S={s}$, we simply write $N_{G}(s)$ or $N_{G}[s]$, even omitting $G$ if clear from the context. The maximum degree and minimum degree of a graph are denoted $\Delta(G)$ and $\delta(G)$ respectively. For a subset of edges $S, V(S)$ denotes the vertices that are incident to edges in $S$. A vertex set $U \subseteq V$ induces the graph $G[U]$ with vertex set $U$ and $e \in E$ being an edge in $G[U]$ iff both endpoints of $e$ are in $U$. If $S \subseteq E$ is an edge set, then $\vec{S}=E \backslash S$, edge set $S$ induces the graph $G[V(S)]$, while $G_{S}=(V, S)$ denotes the partial graph induced by $S$. In particular, $G_{\bar{S}}=(V, E \backslash S)$. Let also $\alpha(G)$ and $\gamma(G)$ denote the size of the largest independent and smallest dominating set of $G$, respectively.

An edge set $S$ is called edge cover if the partial graph $G_{S}$ is spanning and it is a matching if $S$ is a set of pairwise non adjacent edges. An edge set $S$ is

minimal (resp., maximal) with respect to a graph property if $S$ satisfies the graph property and any proper subset $S^{\prime} \subset S$ of $S$ (resp., any proper superset $S^{\prime} \supset S$ of $S$ ) does not satisfy the graph property. For instance, an edge set $S \subseteq E$ is a maximal matching (resp., minimal edge cover) if $S$ is a matching and $S+e$ is not a matching for some $e \in \bar{S}$ (resp., $S$ is an edge cover and $S-e$ is not an edge cover for some $e \in \bar{S}$ ).

Problem Definitions. Let $G=(V, E)$ be a graph where the minimum degree is at least $r \geq 1$, i.e., $\delta(G) \geq r$. We assume $r$ is a constant fixed greater than one (but all results given here hold even if $r$ depends on the graph). A $r$-DEGREE EDGE-COVER $^{3}$ is defined as a subset of edges $G^{\prime}=G_{S}=(V, S)$, such that each vertex of $G$ is incident to at least $r \geq 1$ distinct edges $e \in S$. As $r$-tolerant edge-cover (or simply $r$-tec) we will call an edge set $S \subseteq E$ if it is a minimal $r$-degree edge-cover i.e. if for every $e \in S, G^{\prime}-e=(V, S \backslash{e})$ is not an $r$-degree edge-cover. Alternatively, $\delta\left(G^{\prime}\right)=r$, and $\delta\left(G^{\prime}-e\right)=r-1$. If you seek the minimization version, all the problems are polynomial-time solvable. Actually, the case of $r=1$ corresponds to the edge cover in graphs. The optimization version of a generalization of $r$-EC known as the MIN LOWER-UPPER-COVER PROBLEM (MIN LUCP), consists of, given a graph $G$ where $G=(V, E)$ and two non-negative functions $a, b$ from $V$ such that $\forall v \in V, 0 \leq a(v) \leq b(v) \leq d_{G}(v)$, of finding a subset $M \subseteq E$ such that the partial graph $G_{M}=(V, M)$ induced by $M$ satisfies $a(v) \leq d_{G_{M}}(v) \leq b(v)$ (such a solution will be called a lowerupper-cover) and minimizing its total size $|M|$ among all such solutions (if any). Hence, an $r$-EC solution corresponds to a lower-upper-cover with $a(v)=r$ and $b(v)=d_{G}(v)$ for every $v \in V$. Min LUCP is known to be solvable in polynomial time even for edge-weighted graphs (Theorem $35.2$ in Chap. 35 of Volume A in [29]). We are considering two associated problems, formally described as follows.

数学代写|理论计算机代写theoretical computer science代考|Basic Properties of r-Tolerant Solutions

The next property presents a simple characterization of feasible $r$-tec solution generalizing the well known result given for minimal edge covers, i.e., 1-tec, affirming that $S$ is a 1-tec solution of $G$ if and only if $S$ is spanning and the subgraph $(V, S)$ induced by $S$ is $\left(K_{3}, P_{4}\right)$-free.

Property 1. Let $r \geq 1$ and let $G=(V, E)$ be a graph with minimum degree $\delta \geq r$. $S$ is an $r$-tec solution of $G$ if and only if the following conditions meet on $G_{S}=(V, S)$ :
(1) $V=V_{1}(S) \cup V_{2}(S)$ where $V_{1}(S)=\left{v \in V: d_{G_{S}}(v)=r\right}$ and $V_{2}(S)=\left{v \in V: d_{G_{S}}(v)>r\right}$.
(2) $V_{2}(S)$ is an independent set of $G_{S}$.

Proof. Let $r \geq 1$ be a fixed integer and let $G=(V, E)$ be a graph instance of UPPER $r$-EC, i.e., a graph of minimum degree at least $r$. Let us prove the necessary conditions: if $S \subseteq E$ is an $r$-tec solution, then by construction, $V=$ $V_{1}(S) \cup V_{2}(S)$ is a partition of vertices with minimum degree $r$ in $S$. Now, if $u v \in S$ with $u, v \in V_{2}(S)$, then $S-u v$ is also $r$-tec which is a contradiction of minimality.

Now, let us prove the other direction. Consider a subgraph $G^{\prime}=(V, S)$ induced by edge set $S$ satisfying $(1)$ and $(2)$. By (1) it is clear $G S$ has minimum degree at least $r$. If $u v \in S$, then by (2) one vertex, say $u \in V_{1}(S)$ because $V_{2}(S)$ is an independent set. Hence, the deletion of $u v$ leaves $u$ of degree $r-1$ in the subgraph induced by $G_{S \backslash{u v}}$ and then $S$ is an $r$-tec solution.

Property 2. Let $r \geq 1$, for all graphs $G=(V, E)$ of minimum degree at least $r$, the following inequality holds:
$$
2 \mathrm{ec}{T}(G) \geq \operatorname{lec}{r}(G)
$$
Proof. For a given graph $G=(V, E)$ with $n$ vertices, let $S^{}$ be an optimal solution of UPPER $r$-EC, that is $\left|S^{}\right|=\operatorname{uec}{r}(G)$. Let $\left(V{1}^{}, V_{2}^{}\right)$ be the associated partition related to solution $S^{}$ as indicated in Property 1. Using this characterization, we deduce $\operatorname{uec}{r}(G) \leq r\left|V{1}^{}\right| \leq r n$. On the other side, if $G^{\prime}$ denotes the subgraph induced by a minimum $r$-tec solution of value ec $(G)$, we get $2 \operatorname{ec}{r}(G)=\sum{v \in V} d_{G^{\prime}}(v) \geq r n$. Combining these two inequalities, the results follows.

In particular, inequality (1) of Property 2 shows that any $r$-tec solution is a $\frac{1}{2}$-approximation of UPPER $r$-EC.

The next property is quite natural for induced subgraphs and indicates that the size of an optimal solution of a maximization problem does not decrease with the size of the graph. Nevertheless, this property is false in general when we deal with partial subgraphs; for instance, for the upper domination number, we get $\operatorname{uds}\left(K_{3}\right)=1<2=\operatorname{uds}\left(P_{3}\right)$. It turns out that this inequality is valid for the upper edge cover number.

Property 3. Let $G=(V, E)$ be a graph such that $0<r \leq \delta(G)$. For every partial subgraph $G^{\prime} \subseteq G$ with $\delta\left(G^{\prime}\right) \geq r$, the following inequality holds:
$$
\operatorname{uec}{r}(G) \geq \operatorname{uec}{\mathrm{r}}\left(G^{\prime}\right)
$$
Proof. Fix an integer $r \geq 1$ and a graph $G=(V, E)$ with $\delta(G) \geq r$. Let $G^{\prime}=$ ( $V^{\prime}, E^{\prime}$ ) with $\delta\left(G^{\prime}\right) \geq r$ be a partial subgraph of $G$, i.e., $V^{\prime} \subseteq V$ and $E^{\prime} \subseteq E$. Consider an upper $r$-tec solution $S^{\prime}$ of $G^{\prime}$ with size $\left|S^{\prime}\right|=$ uec $_{r}\left(G^{\prime}\right)$. We prove inequality (2) by starting from $S=S^{\prime}$ and by iteratively repeating the following procedure:

  1. Select a vertex $v \in V$ with $d_{G_{S}}(v)<r$ and $e=u v \in E \backslash S$.
  2. If $u$ is covered less or more than $r$ times by $S$, then $S:=S+e$.
  3. If vertex $u$ is covered exactly $r$ times by $S$, consider two cases.
数学代写|理论计算机代写theoretical computer science代考|On the Complexity of the Upper $r$-Tolerant Edge Cover Problem

理论计算机代写

数学代写|理论计算机代写theoretical computer science代考|On the Complexity of the Upperr-容忍边缘覆盖问题

在本文中,我们定义和研究了容错边缘覆盖问题。图的边缘覆盖G=(在,和)没有孤立顶点是边的子集小号⊆和覆盖所有顶点G,即每个顶点G是至少一条边的端点小号. 图的边覆盖数G=(在,和),记为 ec(G), 是边缘覆盖的最小尺寸G它可以在多项式时间内计算(参见 [29] 中的第 19 章)。边盖小号⊆和如果没有适当的子集,则称为最小(关于包含)小号是一个边缘覆盖。最小边缘覆盖在文献中也称为无飞地集 [30] 或非阻塞集 [14]。虽然可以有效地计算最小边缘覆盖,但找到最大的最小边缘覆盖是 NP-hard [27],其中表明该问题等同于找到最小尺寸的支配集。相关的优化问题称为上边缘覆盖(并表示为 UPPER EC)[1],相应的最优值将表示为 uec(G)在本文中为图表G=(在,和).
在这里,我们对最多可以容忍失败的最小边缘覆盖解决方案感兴趣r−1边缘。形式上,给定一个整数r≥1, 边子集小号⊆和的G=(在,和)是紧r- 容错边缘覆盖(r-tec 简称)如果删除

最多任何一组r−1边缘从小号保持边缘覆盖1并删除任何边缘小号产生一个不是(紧)的集合r- 容错边缘覆盖。等效地,我们寻找一个边子集小号的G这样子图(在,小号)有最低学位r并且这个属性是最小的。为简洁起见,我们将在本文的其余部分省略“紧”这个词。请注意,案例r=1对应于最小边缘覆盖的标准概念。

作为一个说明性的例子,考虑一个大城市的市长试图从一家保安公司雇佣一些警卫的情况,这些警卫将不断地在重要建筑物之间的街道上巡逻。一个r- 宽容的边缘覆盖反映了市长的愿望,即保证安全不受损害,即使r−1守卫受到攻击。提供最大的掩护是自私的保安公司的目标,他们想提出一个由尽可能多的警卫组成的巡逻时间表,但其中所有建议的警卫都是必要的,因为移除其中任何一个都会留下一些建筑物不是r-覆盖。

相关工作。近年来,对 UPPER EC 进行了深入研究,主要使用跨越星林和支配集的术语。图中的支配集是子集小号顶点,使得任何顶点不在小号至少有一个邻居在小号. 最小支配集问题(记为 MinDS)寻求最小支配集G有价值的C(G). 我们有平等统考⁡(G)=n−C(G)[27].

因此,使用 MinDS 已知的复杂性结果,我们推断 UPPER EDGE COVER 在最大度数为 3 的平面图 [20]、弦图 [6] 中是 NP-hard(即使在无向路径图中,顶点相交图的类树中路径的集合)、二分图、分裂图 [5] 和ķ- 任意树ķ[12],并且它是多项式的ķ- 固定的树ķ,凸二部图[13],强弦图[16]。关于近似性,在 [28] 中提出了具有显式不可近似界和组合 0.6 近似算法的 APX 硬度证明。具有近似比的更好算法0.71和0.803分别在[9]和[2]中给出。对于任何e>0, UPPER EDGE COVER 很难在一个因子内近似259260+e除非磷=ñ磷[28]。该问题的加权版本,表示为 UPPER WEIGHTED EDGE Cover,最近在 [24] 中进行了研究,其中证明该问题不是这(1n1/2−e)近似也不这(1Δ1−e)在边加权顺序图中n和最大程度Δ.

数学代写|理论计算机代写theoretical computer science代考|Definitions

图形符号和术语。让G=(在,和)是一个图形和小号⊆在; ñG(小号)=在∈在:∃在∈小号,在在∈和表示邻域小号在G和ñG[小号]=小号∪ñG(小号)表示的封闭邻域小号. 对于单例集小号=s,我们简单地写ñG(s)或者ñG[s], 甚至省略G如果从上下文中清楚。表示图的最大度数和最小度数Δ(G)和d(G)分别。对于边的子集小号,在(小号)表示与边缘相关的顶点小号. 一个顶点集在⊆在引出图G[在]有顶点集在和和∈和成为优势G[在]当当且两个端点和在在. 如果小号⊆和是一个边集,那么小号→=和∖小号, 边集小号引出图G[在(小号)], 尽管G小号=(在,小号)表示由小号. 尤其,G小号¯=(在,和∖小号). 也让一种(G)和C(G)表示最大独立集和最小支配集的大小G, 分别。

边集小号如果部分图被称为边缘覆盖G小号是跨越的,如果是匹配的小号是一组成对的非相邻边。边集小号是

关于图属性的最小(分别,最大)如果小号满足图属性和任何真子集小号′⊂小号的小号(分别,任何适当的超集小号′⊃小号的小号) 不满足图属性。例如,一个边集小号⊆和是最大匹配(分别是最小边缘覆盖)如果小号是一个匹配和小号+和不适合某些人和∈小号¯(分别,小号是一个边缘覆盖和小号−和对某些人来说不是边缘覆盖和∈小号¯ ).

问题定义。让G=(在,和)是最小度数至少为的图r≥1, IE,d(G)≥r. 我们猜测r是一个大于一的固定常数(但这里给出的所有结果都成立,即使r取决于图表)。一种r-DEGREE EDGE-COVER3被定义为边的子集G′=G小号=(在,小号),使得每个顶点G至少是偶然的r≥1明显的边缘和∈小号. 作为r- 宽容的边缘覆盖(或简单地说r-tec) 我们将调用一个边集小号⊆和如果是最小的r-度边缘覆盖,即如果对于每个和∈小号,G′−和=(在,小号∖和)不是一个r度边缘覆盖。或者,d(G′)=r, 和d(G′−和)=r−1. 如果您寻求最小化版本,所有问题都是多项式时间可解决的。其实,案例r=1对应于图中的边缘覆盖。泛化的优化版本r-EC 称为 MIN LOWER-UPPER-COVER PROBLEM (MIN LUCP),由给定图形组成G在哪里G=(在,和)和两个非负函数一种,b从在这样∀在∈在,0≤一种(在)≤b(在)≤dG(在),找到一个子集米⊆和使得部分图G米=(在,米)由…介绍米满足一种(在)≤dG米(在)≤b(在)(这样的解决方案将被称为下上盖)并最小化其总尺寸|米|在所有此类解决方案中(如果有)。因此,一个r-EC 解决方案对应于带有一种(在)=r和b(在)=dG(在)对于每个在∈在. 已知最小 LUCP 可以在多项式时间内求解,即使对于边加权图(定理35.2在第一章。[29] 中 A 卷第 35 页)。我们正在考虑两个相关的问题,正式描述如下。

数学代写|理论计算机代写theoretical computer science代考|Basic Properties of r-Tolerant Solutions

下一个性质提出了可行的简单表征r-tec 解决方案概括了为最小边缘覆盖给出的众所周知的结果,即 1-tec,确认小号是 1-tec 解决方案G当且仅当小号是跨越和子图(在,小号)由…介绍小号是(ķ3,磷4)-自由。

属性 1. 让r≥1然后让G=(在,和)是一个度数最小的图d≥r. 小号是一个r-tec 解决方案G当且仅当以下条件满足G小号=(在,小号) :
(1) 在=在1(小号)∪在2(小号)在哪里V_{1}(S)=\left{v \in V: d_{G_{S}}(v)=r\right}V_{1}(S)=\left{v \in V: d_{G_{S}}(v)=r\right}和V_{2}(S)=\left{v \in V: d_{G_{S}}(v)>r\right}V_{2}(S)=\left{v \in V: d_{G_{S}}(v)>r\right}.
(2) 在2(小号)是一个独立的集合G小号.

证明。让r≥1是一个固定的整数,让G=(在,和)是 UPPER 的图实例r-EC,即至少最小度数的图r. 让我们证明必要条件:如果小号⊆和是一个r-tec 解决方案,然后通过施工,在= 在1(小号)∪在2(小号)是具有最小度数的顶点的分区r在小号. 现在,如果在在∈小号和在,在∈在2(小号), 然后小号−在在也是r-tec 这是极简主义的矛盾。

现在,让我们证明另一个方向。考虑一个子图G′=(在,小号)由边集诱导小号令人满意的(1)和(2). 由 (1) 明确G小号至少有最低学位r. 如果在在∈小号,然后由(2)一个顶点,说在∈在1(小号)因为在2(小号)是一个独立的集合。因此,删除在在树叶在学位r−1在子图中由G小号∖在在进而小号是一个r-tec 解决方案。

属性 2. 让r≥1, 对于所有图G=(在,和)至少最低学历r,以下不等式成立:
2和C吨(G)≥莱克⁡r(G)
证明。对于给定的图G=(在,和)和n顶点,让小号是UPPER的最优解r-EC,即|小号|=统考⁡r(G). 让(在1,在2)是与解决方案相关的关联分区小号如属性 1 所示。使用此表征,我们推断统考⁡r(G)≤r|在1|≤rn. 另一方面,如果G′表示由最小值诱导的子图r-tec 价值 ec 解决方案(G),我们得到2欧共体⁡r(G)=∑在∈在dG′(在)≥rn. 结合这两个不等式,结果如下。

特别是,性质 2 的不等式 (1) 表明,任何r-tec 解决方案是12- UPPER 的近似值r-EC。

下一个性质对于诱导子图来说是很自然的,它表明最大化问题的最优解的大小不会随着图的大小而减小。然而,当我们处理部分子图时,这个属性通常是错误的。例如,对于上支配数,我们得到uds⁡(ķ3)=1<2=uds⁡(磷3). 事实证明,这个不等式对上边缘覆盖数有效。

属性 3. 让G=(在,和)是这样的图0<r≤d(G). 对于每个部分子图G′⊆G和d(G′)≥r,以下不等式成立:
统考⁡r(G)≥统考⁡r(G′)
证明。修复一个整数r≥1和一张图G=(在,和)和d(G)≥r. 让G′= ( 在′,和′) 和d(G′)≥r是的部分子图G, IE,在′⊆在和和′⊆和. 考虑一个鞋面r-tec 解决方案小号′的G′有大小|小号′|=统考r(G′). 我们证明不等式 (2) 从小号=小号′并通过迭代重复以下过程:

  1. 选择一个顶点在∈在和dG小号(在)<r和和=在在∈和∖小号.
  2. 如果在被覆盖少于或多于r次由小号, 然后小号:=小号+和.
  3. 如果顶点在被准确覆盖r次由小号,考虑两种情况。
数学代写|理论计算机代写theoretical computer science代考 请认准statistics-lab™

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金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题,以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法,其中不假设数据来自于由少数参数决定的规定模型;这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型(GLM)归属统计学领域,是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。

有限元方法代写

有限元方法(FEM)是一种流行的方法,用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

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随机分析代写


随机微积分是数学的一个分支,对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。

回归分析代写

多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。

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。

R语言代写问卷设计与分析代写
PYTHON代写回归分析与线性模型代写
MATLAB代写方差分析与试验设计代写
STATA代写机器学习/统计学习代写
SPSS代写计量经济学代写
EVIEWS代写时间序列分析代写
EXCEL代写深度学习代写
SQL代写各种数据建模与可视化代写

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