Is Trump losing patience with Putin? Will sanctions against Russian oil giants hurt Putin? Russian forces have spread rapidly through Pokrovsk, the city in Ukraine's east where the warring sides have concentrated their manpower and tactical ingenuity during the past week, in what may be a final culmination of a 21-month battle. Geolocated footage placed Russian troops in central, northern and northeastern Pokrovsk, said the Institute for the Study of War (ISW), a Washington-based think tank. It set its sights on the city almost two years ago, after capturing Avdiivka, 39km (24 miles) to the east.

Is Trump losing patience with Putin? Will sanctions against Russian oil giants hurt Putin? Russian and Ukrainian troops have fought battles in the ruins of Pokrovsk, a transport and logistics hub in eastern Ukraine, with Ukraine's military reporting fierce fighting under way in a part of the city that was key for Kyiv's front-line logistics. Ukrainian President Volodymyr Zelenskyy said he visited troops fighting near the eastern city of Dobropillia, where Ukrainian forces are conducting a counteroffensive against Russian troops. Russia struck civilian energy and port infrastructure in a massive overnight drone attack on Ukraine's southern region of Odesa, the region's governor said in a post on the Telegram messaging app, adding that rescuers extinguished fires and there were no casualties.

Ukrainian President Volodymyr Zelensky says he has visited troops near the town of Pokrovsk, where the fiercest front line battle between Russia and Ukraine is currently taking place. Zelensky posted photos showing him meeting personnel at a command post in the Dobropillya sector, some 20km (12 miles) north of Pokrovsk in the Donetsk region. Kyiv's top military commander, Oleksandr Syrskiy, said on Monday that Ukraine was increasing pressure on the Dobropillya front to force the enemy to disperse its forces and make it impossible to concentrate their main efforts in the Pokrovsk area. Russia has been trying to seize Pokrovsk - a strategic frontline town and logistic hub - for over a year. Although it has taken them months to approach the town's borders, Russian soldiers have now infiltrated it and on Friday, Zelensky said Russia had amassed 170,000 troops on its outskirts.

We propose a novel and efficient method for link prediction in bipartite networks, using \textit{formal concept analysis} (FCA) and the Transformer encoder. Link prediction in bipartite networks finds practical applications in various domains such as product recommendation in online sales, and prediction of chemical-disease interaction in medical science. Since for link prediction, the topological structure of a network contains valuable information, many approaches focus on extracting structural features and then utilizing them for link prediction. Bi-cliques, as a type of structural feature of bipartite graphs, can be utilized for link prediction. Although several link prediction methods utilizing bi-cliques have been proposed and perform well in rather small datasets, all of them face challenges with scalability when dealing with large datasets since they demand substantial computational resources. This limits the practical utility of these approaches in real-world applications. To overcome the limitation, we introduce a novel approach employing iceberg concept lattices and the Transformer encoder. Our method requires fewer computational resources, making it suitable for large-scale datasets while maintaining high prediction performance. We conduct experiments on five large real-world datasets that exceed the capacity of previous bi-clique-based approaches to demonstrate the efficacy of our method. Additionally, we perform supplementary experiments on five small datasets to compare with the previous bi-clique-based methods for bipartite link prediction and demonstrate that our method is more efficient than the previous ones.

The article is devoted to the study of neural networks with one hidden layer and a modified activation function for solving physical problems. A rectified sigmoid activation function has been proposed to solve physical problems described by the ODE with neural networks. Algorithms for physics-informed data-driven initialization of a neural network and a neuron-by-neuron gradient-free fitting method have been presented for the neural network with this activation function. Numerical experiments demonstrate the superiority of neural networks with a rectified sigmoid function over neural networks with a sigmoid function in the accuracy of solving physical problems (harmonic oscillator, relativistic slingshot, and Lorentz system).

The article discusses the development of various methods and techniques for initializing and training neural networks with a single hidden layer, as well as training a separable physics-informed neural network consisting of neural networks with a single hidden layer to solve physical problems described by ordinary differential equations (ODEs) and partial differential equations (PDEs). A method for strictly deterministic initialization of a neural network with one hidden layer for solving physical problems described by an ODE is proposed. Modifications to existing methods for weighting the loss function are given, as well as new methods developed for training strictly deterministic-initialized neural networks to solve ODEs (detaching, additional weighting based on the second derivative, predicted solution-based weighting, relative residuals). An algorithm for physics-informed data-driven initialization of a neural network with one hidden layer is proposed. A neural network with pronounced generalizing properties is presented, whose generalizing abilities of which can be precisely controlled by adjusting network parameters. A metric for measuring the generalization of such neural network has been introduced. A gradient-free neuron-by-neuron fitting method has been developed for adjusting the parameters of a single-hidden-layer neural network, which does not require the use of an optimizer or solver for its implementation. The proposed methods have been extended to 2D problems using the separable physics-informed neural networks approach. Numerous experiments have been carried out to develop the above methods and approaches. Experiments on physical problems, such as solving various ODEs and PDEs, have demonstrated that these methods for initializing and training neural networks with one or two hidden layers (SPINN) achieve competitive accuracy and, in some cases, state-of-the-art results.

This paper examines the reconstruction of a family of dynamical systems with neuromorphic behavior using a single scalar time series. A model of a physiological neuron based on the Hodgkin-Huxley formalism is considered. Single time series of one of its variables is shown to be enough to train a neural network that can operate as a discrete time dynamical system with one control parameter. The neural network system is created in two steps. First, the delay-coordinate embedding vectors are constructed form the original time series and their dimension is reduced with by means of a variational autoencoder to obtain the recovered state-space vectors. It is shown that an appropriate reduced dimension can be determined by analyzing the autoencoder training process. Second, pairs of the recovered state-space vectors at consecutive time steps supplied with a constant value playing the role of a control parameter are used to train another neural network to make it operate as a recurrent map. The regimes of thus created neural network system observed when its control parameter is varied are in very good accordance with those of the original system, though they were not explicitly presented during training.

United States defence secretary Lloyd Austin has waded in on reports that North Korea was preparing to enter the Ukraine war with troops. "If they are co-belligerents, if their intention is to participate in this war on Russia's behalf, that is a very, very serious issue," Austin said. Austin was returning from his fourth visit to Kyiv, where he announced a 400m package of US weapons for Ukraine. John Kirby, White House national security spokesman, said Washington believes that at least 3,000 North Korean soldiers arrived this month by sea to Vladivostok, Russia's largest Pacific port. "These soldiers then travelled onward to multiple Russian military training sites in eastern Russia, where they are currently undergoing training," Kirby said on Wednesday.

Ukraine has struck a manufacturer of military explosives deep inside Russian territory overnight, as well as storage infrastructure at a military airfield in the Lipetsk region, Kyiv's General Staff has said in a statement. For their part, Russian air defence units downed 110 Ukrainian drones over the country, Russia's Ministry of Defence said Sunday, including one over the Moscow region, 43 over the border region of Kursk, and 27 over the southwestern Lipetsk region. The Russian SHOT Telegram channel reported that drones attempted to strike the Ya. The explosives plant, one of the largest manufacturers of its kind used by Russian forces in the war that Moscow launched against Ukraine in February 2022, is subject to sanctions by the United States and the European Union. Such large-scale aerial attacks are still relatively rare on Russia. Kyiv's General Staff said in a post on Telegram the Sverdlov factory had been making chemical components for artillery ammunition and aerial bombs, adding that it was still assessing the damage from its attack.

Ukraine launched a series of drones targeting Moscow and western Russia, according to regional officials. Russian air defence units downed 110 Ukrainian drones over Russia, the Ministry of Defence said, including one over the Moscow region, 43 over the border region of Kursk, and 27 over the southwestern Lipetsk region. Russia's air defence units destroyed at least one drone flying towards the capital, Moscow Mayor Sergei Sobyanin said on the Telegram messaging app, while drone debris sparked several short-lived fires in Lipetsk, the regional governor said on the app. No injuries or significant damage were reported from the attacks. Four firefighters suffered minor shrapnel wounds in a Ukrainian drone attack in an industrial zone in the city of Dzerzhinsk in Russia's Nizhny Novgorod region, the regional governor said.