The Strahler number was originally proposed to characterize the complexity of river bifurcation and has found various applications. This article proposes computation of the Strahler number's upper and lower limits for natural language sentence tree structures. Through empirical measurements across grammatically annotated data, the Strahler number of natural language sentences is shown to be almost 3 or 4, similarly to the case of river bifurcation as reported by Strahler (1957). From the theory behind the number, we show that it is one kind of lower limit on the amount of memory required to process sentences. We consider the Strahler number to provide reasoning that explains reports showing that the number of required memory areas to process sentences is 3 to 4 for parsing (Schuler et al., 2010), and reports indicating a psychological "magical number" of 3 to 5 (Cowan, 2001). An analytical and empirical analysis shows that the Strahler number is not constant but grows logarithmically; therefore, the Strahler number of sentences derives from the range of sentence lengths. Furthermore, the Strahler number is not different for random trees, which could suggest that its origin is not specific to natural language.

A pair-trading strategy is an approach that utilizes the fluctuations between prices of a pair of stocks in a short-term time frame, while in the long-term the pair may exhibit a strong association and co-movement pattern. When the prices of the stocks exhibit significant divergence, the shares of the stock that gains in price are sold (a short strategy) while the shares of the other stock whose price falls are bought (a long strategy). This paper presents a cointegration-based approach that identifies stocks listed in the five sectors of the National Stock Exchange (NSE) of India for designing efficient pair-trading portfolios. Based on the stock prices from Jan 1, 2018, to Dec 31, 2020, the cointegrated stocks are identified and the pairs are formed. The pair-trading portfolios are evaluated on their annual returns for the year 2021. The results show that the pairs of stocks from the auto and the realty sectors, in general, yielded the highest returns among the five sectors studied in the work. However, two among the five pairs from the information technology (IT) sector are found to have yielded negative returns.

The majority of artificial intelligence (AI) is a game of numbers. Deep neural networks, a type of AI that learns to recognize patterns in data, began outperforming standard algorithms 10 years ago because we ultimately had enough data and processing capabilities to fully utilize them. Today's neural nets are even more data and power-hungry. Training them necessitates fine-tuning the values of millions, if not billions, of parameters that define these networks and represent the strength of interconnections between artificial neurons. The goal is to obtain near-ideal settings for them, a process called optimization, but teaching the networks to get there is difficult.

This paper aims to improve the reliability of optimal control using models constructed by machine learning methods. Optimal control problems based on such models are generally non-convex and difficult to solve online. In this paper, we propose a model that combines the Hammerstein-Wiener model with input convex neural networks, which have recently been proposed in the field of machine learning. An important feature of the proposed model is that resulting optimal control problems are effectively solvable exploiting their convexity and partial linearity while retaining flexible modeling ability. The practical usefulness of the method is examined through its application to the modeling and control of an engine airpath system.

The massive integration of information technologies, under different aspects of the modern world, has led to the treatment of vehicles as conceptual resources in information systems. Since an autonomous information system has no meaning without any data, there is a need to reform vehicle information between reality and the information system.This can be achieved by human agents or by special intelligent equipment that will allow identification of vehicles by their registration plates in real environments. Among intelligent equipment, mention is made of the system of detection and recognition of the number plates of vehicles.The system of vehicle number plate detection and recognition is used to detect the plates then make the recognition of the plate that is to extract the text from an image and all that thanks to the calculation modules that use location algorithms, segmentation plate and character recognition.The detection and reading of license plates is a kind of intelligent system and it is considerable because of the potential applications in several sectors which are quoted: The detected plates are compared to those of the reported vehicles. In order to detect licence we will use Yolo ( You Only Look One) deep learning object detection architecture based on convolution neural networks. This architecture was introduced by Joseph Redmon, Ali Farhadi, Ross Girshick and Santosh Divvala first version in 2015 and later version 2 and 3. Yolo is a single network trained end to end to perform a regression task predicting both object bounding box and object class.

The fuzzy ROC extends Receiver Operating Curve (ROC) visualization to the situation where some data points, falling in an indeterminacy region, are not classified. It addresses two challenges: definition of sensitivity and specificity bounds under indeterminacy; and visual summarization of the large number of possibilities arising from different choices of indeterminacy zones.

Suppose the data consist of a set $S$ of points $x_j, 1 \leq j \leq J$, distributed in a bounded domain $D \subset R^N$, where $N$ and $J$ are large numbers. In this paper an algorithm is proposed for checking whether there exists a manifold $\mathbb{M}$ of low dimension near which many of the points of $S$ lie and finding such $\mathbb{M}$ if it exists. There are many dimension reduction algorithms, both linear and non-linear. Our algorithm is simple to implement and has some advantages compared with the known algorithms. If there is a manifold of low dimension near which most of the data points lie, the proposed algorithm will find it. Some numerical results are presented illustrating the algorithm and analyzing its performance compared to the classical PCA (principal component analysis) and Isomap.

Mode {also called MAP} estimation, mean estimation and median estimation are examined here to determine when they can be safely used to derive {posterior) cost minimizing estimates. (These are all Bayes procedures, using the mode. mean. or median of the posterior distribution). It is found that modal estimation only returns cost minimizing estimates when the cost function is 0-t. If the cost function is a function of distance then mean estimation only returns cost minimizing estimates when the cost function is squared distance from the true value and median estimation only returns cost minimizing estimates when the cost function ts the distance from the true value. Results are presented on the goodness or modal estimation with non 0-t cost functions