Sudan's army has denied it carried out a deadly attack on a major hospital on Friday night in a city in the west of the country held by its rivals, the paramilitary Rapid Support Forces (RSF). The head of the World Health Organization (WHO) said 64 people - including 13 children, two nurses and a doctor - had died in the strike on el-Daein Teaching Hospital and 89 others had been wounded. Enough blood has been spilled, Tedros Adhanom Ghebreyesus posted on X, urging the warring parties to end the conflict, which started nearly three years ago. The RSF said an army drone had hit the hospital in el-Daein, the capital of East Darfur state, on the day Muslims were marking the festival of Eid. Sudan was plunged into a civil war in April 2023 when a vicious struggle for power broke out between the military and the RSF, who had once been allies after coming to power in a coup in 2021.

Your Out-of-Distribution Detection Method is Not Robust!

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We study the fundamental problem of clustering $n$ points into $K$ groups drawn from a mixture of isotropic Gaussians in $\mathbb{R}^d$. Specifically, we investigate the requisite minimal distance $Δ$ between mean vectors to partially recover the underlying partition. While the minimax-optimal threshold for $Δ$ is well-established, a significant gap exists between this information-theoretic limit and the performance of known polynomial-time procedures. Although this gap was recently characterized in the high-dimensional regime ($n \leq dK$), it remains largely unexplored in the moderate-dimensional regime ($n \geq dK$). In this manuscript, we address this regime by establishing a new low-degree polynomial lower bound for the moderate-dimensional case when $d \geq K$. We show that while the difficulty of clustering for $n \leq dK$ is primarily driven by dimension reduction and spectral methods, the moderate-dimensional regime involves more delicate phenomena leading to a "non-parametric rate". We provide a novel non-spectral algorithm matching this rate, shedding new light on the computational limits of the clustering problem in moderate dimension.

Convergence to a simplex ETF: Class means tend towards equinorm and equiangular vectors when centred about the global average.

Throughout this paper, we assume that the entries of W are subgaussian.