This paper introduces the use of per-class regularization hyperparameters in Gabriel graph-based binary classifiers. We demonstrate how the quality index used for regularization behaves both in the margin region and in the presence of outliers, and how incorporating this regularization flexibility can lead to solutions that effectively eliminate outliers while training the classifier. We also show how it can address class imbalance by generating higher and lower thresholds for the majority and minority classes, respectively. Thus, rather than having a single solution based on fixed thresholds, flexible thresholds expand the solution space and can be optimized through hyperparameter tuning algorithms. Friedman test shows that flexible thresholds are capable of improving Gabriel graph-based classifiers.

Middle-mile logistics describes the problem of routing parcels through a network of hubs, which are linked by a fixed set of trucks. The main challenge comes from the finite capacity of the trucks. The decision to allocate a parcel to a specific truck might block another parcel from using the same truck. It is thus necessary to solve for all parcel routes simultaneously. Exact solution methods scale poorly with the problem size and real-world instances are intractable.

We study the problem of black-box optimization of a function f of any dimension, given function evaluations perturbed by noise. The function is assumed to be locally smooth around one of its global optima, but this smoothness is unknown. Our contribution is an adaptive optimization algorithm, POO or parallel optimistic optimization, that is able to deal with this setting. POO performs almost as well as the best known algorithms requiring the knowledge of the smoothness. Furthermore, POO works for a larger class of functions than what was previously considered, especially for functions that are difficult to optimize, in a very precise sense. We provide a finite-time analysis of POO's performance, which shows that its error after n evaluations is at most a factor of sqrt(ln n) away from the error of the best known optimization algorithms using the knowledge of the smoothness.

Despite being confined within the interior darkness of the skull, the human brain possesses a remarkable ability to interpret, understand and analyse the world out there, plan for unseen futures, and make decisions that can alter the course of events. This extraordinary capability is conjectured to come from the brain's function as a predictive machine, constantly inferring the hidden causes of its sensory inputs to maintain a coherent model of its environment. This view, which dates back to Helmholtz's idea of "perception as unconscious inference" (von Helmholtz, 1866)--evolving into the "Bayesian brain" hypothesis (Doya et al., 2007)--suggests that the brain operates as a constructive statistical organ. It updates its beliefs about the external world based on incoming sensory data under a generative model (GM). The GM furnishes the brain with a structured representation that supports probabilistic beliefs over both the latent dynamical states of the external world, corresponding to the generative process (GP), as well as the observation mappings through which these states give rise to sensory signals. Essentially, the brain continually refines its probabilistic beliefs about both the latent states and the causal mechanisms of the world through a process of online triple estimation, jointly optimising beliefs over: hidden states, model parameters, and their associated uncertainties in accordance with the principles of Bayesian inference (Eells, 2004; Parr et al., 2022). More technically, given a sensory observation yt at time t, perception can be formulated as an online triple estimation scheme, whose three components are: 1) online hidden state inference, 2) online parameter learning, and 3) online uncertainty estimation, all three of which are the core components of our proposed online generalised PC scheme and are elaborated in Section.

The dust at this busy recycling plant is pervasive and the steady noise of hoppers and conveyor belts makes this a challenging environment to work in. The facility in Rainham, east London is owned by Sharp Group, a family-run skip and waste management firm. Along the conveyor belts runs everything you could imagine, from shoes, to old VHS cassettes and blocks of concrete. The team here processes up to 280,000 tonnes of mixed recycling every year with 24 agency workers on its rapid conveyor belts. This is a hazardous industry.

Early writing is a tale of two scripts. Egyptian hieroglyphs and Mesopotamian cuneiform both emerged independently about 5300 years ago. The political powers of ancient Egypt and Mesopotamia flourished in the centuries to come, partly because writing helped states control the flow of goods and consolidate power. The pen (or ancient stylus) was mightier than the sword. Or so the conventional story goes. But there is a glaring omission here because, at the dawn of writing, there weren't two scripts. That third, mysterious script, called proto-Elamite, appeared in ancient Iran while cuneiform and hieroglyphs were both in their infancy - and has been shockingly overlooked by all but a handful of scholars since its discovery 125 years ago.

What are Russia's gains from the Iran war? 'We are not losers; we are winners' Russian missile attacks have killed at least eight people in Ukraine following a rare overnight drone strike on Moscow. A Russian strike midmorning on Monday on the town of Merefa in Ukraine's northeastern Kharkiv region killed six people and wounded more than 30 others officials said. "Today during the day, the occupiers attacked civilian infrastructure of a town quite far from the front with a missile," he said on Telegram, adding that it will take another day or two to clear the debris. Officials said Russian forces appeared to have used an Iskander-type ballistic missile. To the south, two men were killed during various attacks on the Kherson region, according to the regional prosecutor's office.

A Ukrainian drone hit an upmarket residential high-rise in Moscow in the early hours of Monday, resulting in no casualties but causing visible damage to the façade of the building. It was the third night in a row that the Russian capital came under attack from drones, days before Russia holds a scaled-back 9 May parade to mark the Soviet Union's victory over Nazi Germany. An unverified video circulating on social media showed firemen entering a heavily damaged flat covered in dust and rubble and with blown-out windows, while another showed drone debris strewn across the street below. Two other drones were intercepted, Mayor Sergei Sobyanin said. Vnukovo and Domodedovo international airports suspended operations overnight.

Video game retail chain GamesStop confirmed to the BBC on Sunday that it is making a $56bn (£41bn) unsolicited takeover offer for e-commerce firm eBay. GameStop's chief executive Ryan Cohen told the Wall Street Journal that he sees potential to make eBay a much bigger rival to Amazon, worth hundreds of billions of dollars. Cohen said his company has built a stake of around 5% in eBay and that the cash and stock takeover offer would value eBay at $125 a share, around 20% higher than its closing price on Friday. The BBC has contacted eBay for comment. Cohen also said that GameStop has a commitment letter from TD Bank to provide around $20bn in debt to help finance the deal. There is nobody who is more qualified, based on my experience, to run the eBay business, added Cohen, who is also the co-founder of online pet-products retailer Chewy.

Despite rapid recent advances in quantum machine learning, the field is in many ways stuck. Existing approaches can exhibit serious limitations, and we still lack learning frameworks that are simple, interpretable, scalable, and naturally suited to quantum data. To address this, here we introduce quantum Gaussian processes, a Bayesian framework for learning from quantum systems through priors over unknown quantum transformations. We show that, under suitable conditions, unitary quantum stochastic processes define Gaussian processes, thereby enabling regression, classification, and Bayesian optimization directly on quantum data. The key ingredient in this framework is sufficient knowledge of a quantum process's structure and symmetries to define an informative prior through its corresponding quantum kernel, effectively injecting a strong, physics-informed inductive bias into the learning model. We then prove that matchgate, or free-fermionic, evolutions give rise to provable and scalable quantum Gaussian processes, providing the first family in our framework where the unknown unitary acts non-trivially on all qubits. Finally, we demonstrate accurate long-range extrapolation, phase-diagram learning in many-body systems, and sample-efficient Bayesian optimization in a quantum sensing task. Our results identify quantum Gaussian processes as a promising route toward simpler and more structured forms of quantum learning.