There is a road and there are many atoms and trees beside it and there is a building in the right corner.

Numerous real-world systems, ranging from healthcare to energy grids, involve users competing for finite and potentially scarce resources. Designing policies for repeated resource allocation in such real-world systems is challenging for many reasons, including the changing nature of user types and their (possibly urgent) need for resources. Researchers have developed numerous machine learning solutions for determining repeated resource allocation policies in these challenging settings. However, a key limitation has been the absence of good methods and test-beds for benchmarking these policies; almost all resource allocation policies are benchmarked in environments which are either completely synthetic or do not allow any deviation from historical data. In this paper we introduce AllSim, which is a benchmarking environment for realistically simulating the impact and utility of policies for resource allocation in systems in which users compete for such scarce resources. Building such a benchmarking environment is challenging because it needs to successfully take into account the entire collective of potential users and the impact a resource allocation policy has on all the other users in the system. AllSim's benchmarking environment is modular (each component being parameterized individually), learnable (informed by historical data), and customizable (adaptable to changing conditions). These, when interacting with an allocation policy, produce a dataset of simulated outcomes for evaluation and comparison of such policies. We believe AllSim is an essential step towards a more systematic evaluation of policies for scarce resource allocation compared to current approaches for benchmarking such methods.

We developed a new method PROTES for black-box optimization, which is based on the probabilistic sampling from a probability density function given in the low-parametric tensor train format. We tested it on complex multidimensional arrays and discretized multivariable functions taken, among others, from real-world applications, including unconstrained binary optimization and optimal control problems, for which the possible number of elements is up to 21000. In numerical experiments, both on analytic model functions and on complex problems, PROTES outperforms popular discrete optimization methods (Particle Swarm Optimization, Covariance Matrix Adaptation, Differential Evolution, and others).

What does the data tell us about immigration in Wales? Like many countries, Wales sees a steady flow of people arriving and leaving for other countries each year. The difference between those arriving and those leaving is known as net migration. Focusing on people moving from abroad, latest estimates say Wales' population - which was 3.2 million in June 2024 - had increased by about 23,000 over the previous year as a result of net international migration. A recent YouGov poll found a quarter of people surveyed in Wales believed that immigration, alongside the economy, should be among the issues prioritised by the Welsh government, even though immigration is controlled by the UK government.

Image caption, Will Pep Guardiola or Mikel Arteta be lifting the Premier League trophy next month? With five games to go, Manchester City and Arsenal are only separated on goals scored at the top of the Premier League table. It's a new league now, says Gunners boss Mikel Arteta, whose side had been top of the table for 209 days until Wednesday. Manchester City's 2-1 win over Arsenal on Sunday boosted their hopes - and a 1-0 victory at Burnley on Wednesday sent them top. Who is going to win the title now?

Andon Market in San Francisco represents a vision, however flawed, of a future when more sophisticated AI agents take over work traditionally done by humans. In San Francisco's upscale Cow Hollow district, the introduction of a boutique selling coffee table games, tote bags and other household items would be pretty unremarkable. However, Andon Market has one key differentiator: It's run by AI. At this store, an artificial intelligence agent named Luna effectively acts as the chief executive officer of the operation. It decides what products to offer and how much to charge for them.