Abstract: A method of evaluating an ability of a large language model (LLM) to generate an accurate hypothesis model (HM) of a linear programming word problem (LPWP) is provided. An attributed bipartite graph of the HM is transformed into an attributed bipartite graph of the ground truth model of the LPWP. The number of transformation steps required for the transformation effectively measures the ability of the LLM to generate an accurate HM. The use of attributed bipartite graphs provide invariance in the order to LPWP variables and constraints. Corresponding apparatus and systems are also provided.

Abstract: An online system hosts a retailer storefront user interface for a third-party retailer that includes content associated with items offered by the retailer for procurement and delivery through the online system. A retailer may provide preferences for where different candidate content is placed in the retailer storefront user interface. The online system applies a machine learning model to the retailer preferences and other contextual information relating to a particular presentation of the retailer storefront user interface to dynamically rank content for different possible placement positions. The ranking scores may relate to predicted performance metrics associated with operations of the online system. Content is then placed in the retailer storefront user interface based on the respective ranking scores.

Abstract: Methods and systems for selecting a target model for an unlabeled dataset of a dataset provider, the target model for generating labels for the unlabeled dataset. The method comprises acquiring the unlabeled dataset from the dataset provider; acquiring a first candidate model from a first model provider and a second candidate model from a second model provider, generating a first usefulness score for the first candidate model and a second usefulness score for the second candidate model using the unlabeled dataset, the first and second usefulness scores being indicative of likelihood that the first and second candidate models generate accurate labels for the unlabeled dataset respectively; selecting the first candidate model as the target model using the first usefulness score and the second usefulness score; and causing generation of the labels from the unlabeled dataset using the target model.

Abstract: A vaneless contra-rotating compressor with multiple contra-rotating interfaces and application of the vaneless contra-rotating compressor is provided, which includes at least two vaneless contra-rotating interfaces. For each of the at least two contra-rotating interfaces, the contra-rotating interface corresponds to two of vaneless contra-rotating rotors. A rotating direction of an upstream rotor of the two vaneless contra-rotating rotors and a rotating direction of a downstream rotor of the two vaneless contra-rotating rotors are opposite. Rectifier stator vanes are not provided among all the rotors to supply sufficient inlet negative pre-swirl for the downstream rotors through the upstream rotors. Only the outlet guide vanes of the last stage, of the vaneless contra-rotating rotors are provided. The number of stages and the number of vaneless contra-rotating interfaces may be set flexibly according to the actual pressurization requirements.

Abstract: A vaneless contra-rotating compressor with multiple contra-rotating interfaces and application of the vaneless contra-rotating compressor is provided, which includes at least two vaneless contra-rotating interfaces. For each of the at least two contra-rotating interfaces, the contra-rotating interface corresponds to two of vaneless contra-rotating rotors. A rotating direction of an upstream rotor of the two vaneless contra-rotating rotors and a rotating direction of a downstream rotor of the two vaneless contra-rotating rotors are opposite. Rectifier stator vanes are not provided among all the rotors to supply sufficient inlet negative pre-swirl for the downstream rotors through the upstream rotors. Only the outlet guide vanes of the last stage, of the vaneless contra-rotating rotors are provided. The number of stages and the number of vaneless contra-rotating interfaces may be set flexibly according to the actual pressurization requirements.

Abstract: A preparation method for polyoxymethylene dimethyl ether (DMMn, generally, n=3-8 or 2-8) and mixture thereof may include one or more of the following: mixture of aqueous formaldehyde solution and polyalcohol is heated and dehydrated under vacuum conditions to yield flowing polyoxymethylene containing low moisture, which is heated and gasified to obtain relatively pure gaseous formaldehyde, which is mixed with methylal, previous batch of low-boiling-point substances applied, macromolecules, etc. in presence of catalyst. Or, the method mainly includes: aqueous formaldehyde solution, polyalcohol, and previous batch of macromolecular mixture applied are heated under vacuum conditions to remove moisture so as to obtain anhydrous flowable polyoxymethylene etherate, which is mixed with methylal, previous batch of low-boiling-point substances applied, macromolecules, etc. in presence of catalyst.