In this paper, we introduce a comprehensive benchmark for Persian (Farsi) text embeddings, built upon the Massive Text Embedding Benchmark (MTEB). Our benchmark includes 63 datasets spanning seven different tasks: classification, clustering, pair classification, reranking, retrieval, summary retrieval, and semantic textual similarity. The datasets are formed as a combination of existing, translated, and newly generated data, offering a diverse evaluation framework for Persian language models. Given the increasing use of text embedding models in chatbots, evaluation datasets are becoming inseparable ingredients in chatbot challenges and Retrieval-Augmented Generation systems. As a contribution, we include chatbot evaluation datasets in the MTEB benchmark for the first time. In addition, in this paper, we introduce the new task of summary retrieval which is not part of the tasks included in standard MTEB. Another contribution of this paper is the introduction of a substantial number of new Persian language NLP datasets suitable for training and evaluation, some of which have no previous counterparts in Persian. We evaluate the performance of several Persian and multilingual embedding models in a range of tasks. This work introduces an open-source benchmark with datasets, code and a public leaderboard.

In this paper, a new fast algorithm for path planning and a collision prediction framework for two dimensional dynamically changing environments are introduced. The method is called Time Distance (TD) and benefits from the space-time space idea. First, the TD concept is defined as the time interval that must be spent in order for an object to reach another object or a location. Next, TD functions are derived as a function of location, velocity and geometry of objects. To construct the configuration-time space, TD functions in conjunction with another function named "Z-Infinity" are exploited. Finally, an explicit formula for creating the length optimal collision free path is presented. Length optimization in this formula is achieved using a function named "Route Function" which minimizes a cost function. Performance of the path planning algorithm is evaluated in simulations. Comparisons indicate that the algorithm is fast enough and capable to generate length optimal paths as the most effective methods do. Finally, as another usage of the TD functions, a collision prediction framework is presented. This framework consists of an explicit function which is a function of TD functions and calculates the TD of the vehicle with respect to all objects of the environment.