Two Literal Crypto Bros Built a Real Estate Empire. In 2019, two Canadian brothers blew into Detroit with an irresistible pitch: For $50, almost anyone could become a property owner. When houses decayed and the city intervened, the blame games began. A fire broke out at 10410 Cadieux in March 2025, burning a hole in the roof. The smell hit me first: damp brick, stagnant water, mold, and bleach. I was partway down a flight of wooden stairs that led to the basement of a 1920s duplex in east Detroit, Michigan. Leading the way was Cornell Dorris, a tenant in the building for nearly a decade. Dorris is in his early forties, has two daughters who visit on weekends, and makes a living smoking meat and cooking for events. As my eyes adjusted, I made out rodent droppings and a black puddle that spread across the basement floor. "Anytime it rains, the water comes down," Dorris said. The air was unnaturally heavy, and I felt a nagging urge to leave. Dorris doesn't have a typical landlord. Almost four years ago, his building was acquired by a startup called RealToken, or RealT.

Should You Leave Your Phone Charging Overnight? It used to be common wisdom that leaving your phone charging overnight degrades the battery. But handset design has evolved to mitigate the harm caused by constant charging. You may have heard that leaving your smartphone charging overnight--either plugged in or atop a wireless charger --can damage your battery. But is it actually harmful or dangerous to do that?

Kernel-based quadrature rules are becoming important in machine learning and statistics, as they achieve super-$¥sqrt{n}$ convergence rates in numerical integration, and thus provide alternatives to Monte Carlo integration in challenging settings where integrands are expensive to evaluate or where integrands are high dimensional. These rules are based on the assumption that the integrand has a certain degree of smoothness, which is expressed as that the integrand belongs to a certain reproducing kernel Hilbert space (RKHS). However, this assumption can be violated in practice (e.g., when the integrand is a black box function), and no general theory has been established for the convergence of kernel quadratures in such misspecified settings. Our contribution is in proving that kernel quadratures can be consistent even when the integrand does not belong to the assumed RKHS, i.e., when the integrand is less smooth than assumed. Specifically, we derive convergence rates that depend on the (unknown) lesser smoothness of the integrand, where the degree of smoothness is expressed via powers of RKHSs or via Sobolev spaces.

America's drone industry lags behind China's dominance, but Congress and Trump's $2.5 billion investment aims to rebuild U.S. military and commercial drone production by 2027.

Missing records are a perennial problem in analysis of complex data of all types, when the target of inference is some function of the full data law. In simple cases, where data is missing at random or completely at random (Rubin, 1976), well-known adjustments exist that result in consistent estimators of target quantities. Assumptions underlying these estimators are generally not realistic in practical missing data problems. Unfortunately, consistent estimators in more complex cases where data is missing not at random, and where no ordering on variables induces monotonicity of missingness status are not known in general, with some notable exceptions (Robins, 1997), (Tchetgen Tchetgen et al, 2016), (Sadinle and Reiter, 2016). In this paper, we propose a general class of consistent estimators for cases where data is missing not at random, and missingness status is non-monotonic. Our estimators, which are generalized inverse probability weighting estimators, make no assumptions on the underlying full data law, but instead place independence restrictions, and certain other fairly mild assumptions, on the distribution of missingness status conditional on the data. The assumptions we place on the distribution of missingness status conditional on the data can be viewed as a version of a conditional Markov random field (MRF) corresponding to a chain graph. Assumptions embedded in our model permit identification from the observed data law, and admit a natural fitting procedure based on the pseudo likelihood approach of (Besag, 1975). We illustrate our approach with a simple simulation study, and an analysis of risk of premature birth in women in Botswana exposed to highly active anti-retroviral therapy.

Ukrainian President Volodymyr Zelensky is set to visit Prime Minister Sir Keir Starmer in the UK on Tuesday to agree a new defence partnership aimed at tackling cheap attack drones. Downing Street said the deal would bring together Ukrainian expertise and the UK's industrial base to manufacture and supply drones and other capabilities. The two leaders are also expected to discuss further support Ukraine against Russia's full-scale invasion, now in its fourth year. Their meeting comes as the US-Israeli war with Iran enters a third week, during which US President Donald Trump has criticised the UK and other countries over the extent of their response to the conflict. Under the partnership between the UK and Ukraine, closer co-operation in the defence industries will also be sought with third countries as part of efforts to bolster international security.

US President Donald Trump has renewed his criticism of the UK government over its response to the Iran conflict, after Prime Minister Sir Keir Starmer said the country would not be drawn into the wider war. Trump told reporters on Monday he was not happy with the UK, adding it should be involved enthusiastically in efforts to reopen the Strait of Hormuz - a vital oil shipping channel . He later told a press conference there were some countries that greatly disappointed me before he singled out the UK, which he said had been considered the Rolls-Royce of allies. Trump's remarks came after Sir Keir said the UK was working with allies on a viable, collective plan to reopen the strait. Sir Keir also said the UK already had minehunters in the region but there was no decision yet on what action would be taken.

We provide two fundamental results on the population (infinite-sample) likelihood function of Gaussian mixture models with $M \geq 3$ components. Our first main result shows that the population likelihood function has bad local maxima even in the special case of equally-weighted mixtures of well-separated and spherical Gaussians. We prove that the log-likelihood value of these bad local maxima can be arbitrarily worse than that of any global optimum, thereby resolving an open question of Srebro (2007). Our second main result shows that the EM algorithm (or a first-order variant of it) with random initialization will converge to bad critical points with probability at least $1-e^{-\Omega(M)}$. We further establish that a first-order variant of EM will not converge to strict saddle points almost surely, indicating that the poor performance of the first-order method can be attributed to the existence of bad local maxima rather than bad saddle points. Overall, our results highlight the necessity of careful initialization when using the EM algorithm in practice, even when applied in highly favorable settings.

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We present Cyclades, a general framework for parallelizing stochastic optimization algorithms in a shared memory setting. Cyclades is asynchronous during model updates, and requires no memory locking mechanisms, similar to Hogwild!-type algorithms. Unlike Hogwild!, Cyclades introduces no conflicts during parallel execution, and offers a black-box analysis for provable speedups across a large family of algorithms. Due to its inherent cache locality and conflict-free nature, our multi-core implementation of Cyclades consistently outperforms Hogwild!-type algorithms on sufficiently sparse datasets, leading to up to 40% speedup gains compared to Hogwild!, and up to 5\times gains over asynchronous implementations of variance reduction algorithms.