A shop owner has described how she locks her door during opening hours and customers have to ring the bell to get in after her store was targeted by thieves last year. Paige Mengers, who runs a designer boutique in Surrey, has been speaking about the impact of shoplifting, with recorded offences remaining above pre-pandemic levels. Home Office figures show there were 42,674 shoplifting offences across Kent, Surrey and Sussex in 2025/26 compared with 28,048 cases in 2019/20. The government said overall offences in England and Wales fell 4% last year, with more suspects being charged. Mengers, who has stores in Cobham and south-west London, said she boosted security after a raid in January 2025 involving men with wire cutters.

Railway services were plunged into chaos after a train derailed in Essex. The Greater Anglia service from Southend Victoria to London Liverpool Street came off the tracks in Wickford at 14:12 BST on Friday, leading to all trips being cancelled . About 45 passengers were on board the commuter-line train but nobody was injured and it remained upright, according to investigators. It happened less than 24 hours after two passengers were seriously injured in a separate derailment in East Sussex . 'The train swung wildly,' says passenger on board derailed service Network Rail has warned passengers that major disruption will continue until at least Saturday, including for those going to Southminster and Braintree.

A large-scale wildfire in north Wales as been declared a major incident by emergency services, as firefighters tackle fires across England and Wales during the record-breaking heatwave. Residents near Conwy Mountain and the Sychnant Pass have been evacuated, while members of the public were warned to avoid the area. In Greater Manchester, fire crews are working to contain a moorland fire near a reservoir, while in Camberley, Hampshire, crews are extinguishing a large heathland fire. Wildfires burned in County Durham, Derbyshire, East Sussex, West Sussex, Devon and Somerset over the weekend, during a warning that parts of the country were facing an exceptional risk for fires. North Wales Fire and Rescue Service said in an update on Sunday afternoon that it was working in challenging conditions in order to contain the Conwy Mountain fire, with operations expected to continue for some time.

We propose ODER as a new strategy for improving the efficiency of DEQ through stochastic approximations of the measurement models. We theoretically analyze ODER giving insights intoits ability to approximate the traditional DEQ approach for solving inverse problems.

While it possesses many desirable structural properties, the estimation of high-dimensional MI from samples suffers from the curse of dimensionality.

While this could be done using thesynthesis formulation, we demonstrate that this leads to slower performances. The main difficulty inapplying suchmethods intheanalysisformulation liesinproposing a way to compute the derivatives through the proximal operator.