The largest singletons in weighted set partitions and its applications

Recently, Deutsch and Elizalde studied the largest and the smallest fixed points of permutations. Motivated by their work, we consider the analogous problems in weighted set partitions. Let $A_{n,k}(\mathbf{t})$ denote the total weight of partitions on $[n+1]$ with the largest singleton $\{k+1\}$. In this paper, explicit formulas for $A_{n,k}(\mathbf{t})$ and many combinatorial identities involving $A_{n,k}(\mathbf{t})$ are obtained by umbral operators and combinatorial methods. As applications, we investigate three special cases such as permutations, involutions and labeled forests. Particularly in the permutation case, we derive a surprising identity analogous to the Riordan identity related to tree enumerations, namely, \begin{eqnarray*} \sum_{k=0}^{n}\binom{n}{k}D_{k+1}(n+1)^{n-k} &=& n^{n+1}, \end{eqnarray*} where $D_{k}$ is the $k$-th derangement number or the number of permutations of $\{1,2,\dots, k\}$ with no fixed points.Comment: 15page

Efficient Commercial Bank Customer Credit Risk Assessment Based on LightGBM and Feature Engineering

Effective control of credit risk is a key link in the steady operation of commercial banks. This paper is mainly based on the customer information dataset of a foreign commercial bank in Kaggle, and we use LightGBM algorithm to build a classifier to classify customers, to help the bank judge the possibility of customer credit default. This paper mainly deals with characteristic engineering, such as missing value processing, coding, imbalanced samples, etc., which greatly improves the machine learning effect. The main innovation of this paper is to construct new feature attributes on the basis of the original dataset so that the accuracy of the classifier reaches 0.734, and the AUC reaches 0.772, which is more than many classifiers based on the same dataset. The model can provide some reference for commercial banks' credit granting, and also provide some feature processing ideas for other similar studies

Self-optimizing Feature Generation via Categorical Hashing Representation and Hierarchical Reinforcement Crossing

Feature generation aims to generate new and meaningful features to create a discriminative representation space.A generated feature is meaningful when the generated feature is from a feature pair with inherent feature interaction. In the real world, experienced data scientists can identify potentially useful feature-feature interactions, and generate meaningful dimensions from an exponentially large search space, in an optimal crossing form over an optimal generation path. But, machines have limited human-like abilities.We generalize such learning tasks as self-optimizing feature generation. Self-optimizing feature generation imposes several under-addressed challenges on existing systems: meaningful, robust, and efficient generation. To tackle these challenges, we propose a principled and generic representation-crossing framework to solve self-optimizing feature generation.To achieve hashing representation, we propose a three-step approach: feature discretization, feature hashing, and descriptive summarization. To achieve reinforcement crossing, we develop a hierarchical reinforcement feature crossing approach.We present extensive experimental results to demonstrate the effectiveness and efficiency of the proposed method. The code is available at https://github.com/yingwangyang/HRC_feature_cross.git

Self-optimizing Feature Generation via Categorical Hashing Representation and Hierarchical Reinforcement Crossing

Feature generation aims to generate new and meaningful features to create a discriminative representation space. A generated feature is meaningful when the generated feature is from a feature pair with inherent feature interaction. In the real world, experienced data scientists can identify potentially useful feature-feature interactions, and generate meaningful dimensions from an exponentially large search space in an optimal crossing form over an optimal generation path. But, machines have limited human-like abilities. We generalize such learning tasks as self-optimizing feature generation. Self-optimizing feature generation imposes several under-addressed challenges on existing systems: meaningful, robust, and efficient generation. To tackle these challenges, we propose a principled and generic representation-crossing framework to solve self-optimizing feature generation. To achieve hashing representation, we propose a three-step approach: feature discretization, feature hashing, and descriptive summarization. To achieve reinforcement crossing, we develop a hierarchical reinforcement feature crossing approach. We present extensive experimental results to demonstrate the effectiveness and efficiency of the proposed method. The code is available at https://github.com/yingwangyang/HRC_feature_cross.git

Analysis of the feasibility and necessity of special road construction for small passenger cars

The rapid development of social economy has caused many problems in highway transportation. The traffic on most roads is getting bigger and bigger. This trend not only increases traffic pressure but also poses a threat to the lives of travellers. In order to solve the current road traffic problem, this paper proposes a special route for the construction of small passenger vehicles. The basic idea of dedicated line construction is based on the secondary road and highway operation forms. Each line passes through 1 to 3 townships. The internal and external environment and advantages and disadvantages of the dedicated line construction were analyzed by SWOT method, and the SWOT matrix was constructed. The analysis results show that the small passenger dedicated line is feasible and necessary, and has a good development prospect. In this way, it provides a new idea for the development of China’s highways

Anti-PrPC monoclonal antibody infusion as a novel treatment for cognitive deficits in an alzheimer's disease model mouse

<p>Abstract</p> <p>Background</p> <p>Alzheimer's Disease (AD) is the most common of the conformational neurodegenerative disorders characterized by the conversion of a normal biological protein into a β-sheet-rich pathological isoform. In AD the normal soluble Aβ (sAβ) forms oligomers and fibrils which assemble into neuritic plaques. The most toxic form of Aβ is thought to be oligomeric. A recent study reveals the cellular prion protein, PrP^C, to be a receptor for Aβ oligomers. Aβ oligomers suppress LTP signal in murine hippocampal slices but activity remains when pretreated with the PrP monoclonal anti-PrP antibody, 6D11. We hypothesized that targeting of PrP^Cto prevent Aβ oligomer-related cognitive deficits is a potentially novel therapeutic approach. APP/PS1 transgenic mice aged 8 months were intraperitoneally (i.p.) injected with 1 mg 6D11 for 5 days/week for 2 weeks. Two wild-type control groups were given either the same 6D11 injections or vehicle solution. Additional groups of APP/PS1 transgenic mice were given either i.p. injections of vehicle solution or the same dose of mouse IgG over the same period. The mice were then subjected to cognitive behavioral testing using a radial arm maze, over a period of 10 days. At the conclusion of behavioral testing, animals were sacrificed and brain tissue was analyzed biochemically or immunohistochemically for the levels of amyloid plaques, PrP^C, synaptophysin, Aβ40/42 and Aβ oligomers.</p> <p>Results</p> <p>Behavioral testing showed a marked decrease in errors in 6D11 treated APP/PS1 Tg mice compared with the non-6D11 treated Tg groups (p < 0.0001). 6D11 treated APP/PS1 Tg mice behaved the same as wild-type controls indicating a recovery in cognitive learning, even after this short term 6D11 treatment. Brain tissue analysis from both treated and vehicle treated APP/PS1 groups indicate no significant differences in amyloid plaque burden, Aβ40/42, PrP^Cor Aβ oligomer levels. 6D11 treated APP/PS1 Tg mice had significantly greater synaptophysin immunoreactivity in the dentate gyrus molecular layer of the hippocampus compared to vehicle treated APP/PS1 Tg mice (p < 0.05).</p> <p>Conclusions</p> <p>Even short term treatment with monoclonal antibodies such as 6D11 or other compounds which block the binding of Aβ oligomers to PrP^Ccan be used to treat cognitive deficits in aged AD transgenic mice.</p