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Exact Sampling of Permutations with a Fixed Longest Increasing Subsequence
arXiv:2606.02263v1 Announce Type: new Abstract: We study exact uniform sampling of permutations of length $n$ whose longest increasing subsequence (LIS) has prescribed length $k$. For $k \in \Theta(n)$, we give a direct rejection sampler whose expected running time is $O(n\log\log n)$ in the word-RAM model. The sampler uses an expanded proposal space consisting of permutations together with a specified increasing subsequence, and accepts exactly those proposals whose specified subsequence is...
macOS Container Machines
Container machine provides a highly integrated Linux environment that works seamlessly on your Mac. Container machines are fast, lightweight and persistent. They are based on standard OCI images that can be built and shared.
Faster algorithms for k-Orthogonal Vectors in low dimension
Announce Type: replace Abstract: In the Orthogonal Vectors problem (OV), we are given two families $A, B$ of subsets of $\{1,\ldots,d\}$, each of size $n$, and the task is to decide whether there exists a pair $a \in A$ and $b \in B$ such that $a \cap b = \emptyset$. Straightforward algorithms for this problem run in $\mathcal{O}(n^2 \cdot d)$ or $\mathcal{O}(2^d \cdot n)$ time, and assuming SETH, there is no $2^{o(d)}\cdot n^{2-\varepsilon}$ time algorithm that solves this problem for any...
Implicit Geographic Inference in LLM Medical Triage: Language-Driven Disparities in Emergency Recommendations
arXiv:2606.01204v1 Announce Type: new Abstract: We investigate whether large language models produce different medical triage recommendations for identical symptoms based solely on the language of the patient prompt. Using Gemini 3.5 Flash, we evaluate a neurological symptom profile (persistent headache, blurred vision, nausea) across six languages (English, Spanish, Chinese, Hindi, Japanese, Arabic) with 30 runs per condition (n=450 total API calls). We find that the model recommends...
Coke can hair rollers and Puerto Rican pride: the street photography of Janette Beckman – in pictures
Four decades of Janette Beckman’s images will be on view until 18 April 2027 at Seattle’s Museum of Pop Culture (MoPOP). The exhibit Rebels + Icons: The Photography of Janette Beckman will feature 700-plus archival and newly taken images. Among many iconic photographs, Beckman is known for photographing musical legends like Salt-N-Pepa and Run-DMC, and her striking approach to street photography Continue reading...
An extremal problem for completely unclustered Burrows-Wheeler images
arXiv:2606.01267v1 Announce Type: cross Abstract: The Burrows--Wheeler transform is usually viewed as a clustering transform: it tends to group equal letters into long runs. We study the opposite extremal regime, where the BWT output is completely unclustered, that is, has as many equal-letter runs as positions. Known results imply, on the one hand, that the number of runs in the BWT of a Lyndon word can increase by at most a factor of two, and, on the other hand, that over every alphabet of...
‘I was dazzled. I thought the walls would fall down’: the oral history of DMZ, the label and club night that gave dubstep its soul
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‘I was dazzled. I thought the walls would fall down’: the oral history of DMZ, the label and club night that gave dubstep its soul
In an extract from Aftershock, a definitive new history of dubstep, DMZ’s Mala, Coki and Loefah recall the bass drops and pacifist mentality that went into their creationBy the turn of the millennium, British electronic music had some growing pains. The jungle and drum’n’bass scenes that energised the 1990s were running out of creative gas, and garage had shifted from the moody underground into champagne flash and chart hits. Across pockets of London, Croydon and Essex, a tiny group of...
WATCH: AOC leaves door open to 2028 White House bid: 'Maybe, maybe not'
Rep. Alexandria Ocasio-Cortez, D-N.Y., refused to rule out a 2028 presidential run, but said expanding healthcare remains more important than pursuing higher office. "Could I be president?" "Could I not be president?
WATCH: AOC leaves door open to 2028 White House bid: 'Maybe, maybe not'
Rep. Alexandria Ocasio-Cortez, D-N.Y., refused to rule out a 2028 presidential run, but said expanding healthcare remains more important than pursuing higher office. "Could I be president?" "Could I not be president?