After a year in which industry was knocked off its axis by the coming of age of artificial intelligence and the transition to an online world continued apace, new businesses are emerging and old industries reinventing themselves to adapt. Here, we look at five companies making the most of these turbulent times. It's been a difficult year for the operators of electric scooters, bikes and mopeds: most notably in Paris, where its e-scooter rental scheme was shut down by city authorities after a popular vote. One big player, Tier, nominated here a year ago as a company to watch, also lost its business in London when trial licences were renewed. Increasingly, in the crowded streets of the UK, rental ebikes are looking a better bet than the e-scooter: a more familiar mode of transport for occasional users, feeling safer and with the bonus of sitting rather than standing.

Gradient-based first-order convex optimization algorithms find widespread applicability in a variety of domains, including machine learning tasks. Motivated by the recent advances in fixed-time stability theory of continuous-time dynamical systems, we introduce a generalized framework for designing accelerated optimization algorithms with strongest convergence guarantees that further extend to a subclass of non-convex functions. In particular, we introduce the GenFlow algorithm and its momentum variant that provably converge to the optimal solution of objective functions satisfying the Polyak-{\L}ojasiewicz (PL) inequality in a fixed time. Moreover, for functions that admit non-degenerate saddle-points, we show that for the proposed GenFlow algorithm, the time required to evade these saddle-points is uniformly bounded for all initial conditions. Finally, for strongly convex-strongly concave minimax problems whose optimal solution is a saddle point, a similar scheme is shown to arrive at the optimal solution again in a fixed time. The superior convergence properties of our algorithm are validated experimentally on a variety of benchmark datasets.