Conformal Bayes combines Bayesian posterior predictives with conformal calibration to produce prediction sets that are both statistically valid and geometrically efficient. We study conformal Bayes under label shift from a unified perspective, identifying two complementary approaches that restore nominal target-domain coverage through importance-weighted conformal calibration but operate through independent mechanisms. \emph{Post-hoc calibration} tilts the posterior predictive toward the target domain and corrects the conformal threshold via an importance-weighted quantile, leaving the parameter posterior unchanged. \emph{In-training adaptation} tilts the parameter posterior itself to the target domain, producing a corrected predictive whose highest predictive density region serves as the highest predictive density (HPD)-based prediction set under the fitted target predictive; efficiency is model-dependent and does not imply finite-sample conditional optimality. Two controlled experiments isolate the regime-dependence of each strategy: in the low-dimensional, well-estimated regime Strategy~A produces the narrowest valid intervals, while in the high-dimensional, underdetermined regime Strategy~B achieves up to $43\%$ width reduction at unchanged coverage, under the stated source-sampling and label-shift assumptions.

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The Chinese supercomputer LineShine was ranked as the fastest in the world, despite not using any GPUs. China now has the world's fastest supercomputer, overtaking the United States. The system, known as LineShine and installed at the National Supercomputing Center in Shenzhen, displaced the US system El Capitan from the top spot in the TOP500 ranking in terms of computing power. The breakthrough comes amid an intense competition between Beijing and Washington for technological supremacy, marked by high tariffs and restrictions on a wide range of hardware components and software. Since 1993, the TOP500 ranking has identified the world's most powerful supercomputers every six months through a series of standardized benchmarks that evaluate each system's performance, taking into account both its theoretical speed and its real-world performance, as well as its energy efficiency.

Could Israel sabotage the deal? Iran has launched attacks on Bahrain and Kuwait after the United States struck five Iranian targets, escalating tensions and threatening the fragile ceasefire agreed by the two sides earlier this month. The Islamic Revolutionary Guard Corps (IRGC) confirmed the attacks on Sunday, saying it launched ballistic missiles and drones at the US Ali Al Salem airbase in Kuwait and the US Fifth Naval Fleet at Port Salman in Bahrain. US Central Command (CENTCOM) said its navy and air force "conducted strikes tonight on 10 Iranian military targets at multiple locations in and near the Strait of Hormuz", saying the attacks were a response to an Iranian drone attack on the Kiku oil tanker. It said the Panama-flagged vessel was carrying more than two million barrels of crude oil when it was attacked as it transited near the strait early on Saturday.

Rep. Alexandria Ocasio-Cortez says Congress should break up companies like Apple amid reports the tech giant may raise prices due to AI-driven chip supply strain.

Could Israel sabotage the deal? The United States has bombed Iran for a second straight day, striking Sirik, Bandar-e Lengeh and Qeshm Island after a drone attack on a commercial vessel near the Strait of Hormuz. Air raid sirens sounded in Bahrain, while Kuwait said its air defences were responding to "hostile missile and drone threats", raising heightened tensions across the region. Meanwhile, Israel carried out new attacks on southern Lebanon, killing at least one person, just a day after reaching a framework agreement with the Lebanese government aimed at ending the fighting. Tehran-based political analyst Abas Aslani said Iran views the waterway as a deterrent against future US attacks.

Could Israel sabotage the deal? The US has bombed Iran for a second day, hitting the city of Sirik, Bandar-e Lengeh and Qeshm Island, following a drone attack on a commercial vessel near the Strait of Hormuz . Air raid sirens blare in Bahrain as Kuwait's military says its air defences are responding to "hostile missile and drone threats".

For years, buyers of tech could rely on a familiar trend - that older devices would get cheaper over time. That now seems to have stopped, or in some cases, completely reversed. Apple and Microsoft's Xbox have joined the firms hiking prices for devices and games consoles which are years old. They and other tech companies have pointed to the rising cost of crucial components needed to build their machines, laying the blame on AI. Compute-hungry data centres, which power AI, need more and more chips to keep up with demand from AI companies - which means the demand for them is far outstripping supply.

The US has conducted new strikes on Iran, following a drone attack on a Panama-flagged vessel in the Strait of Hormuz on Saturday. US Central Command (Centcom) said it hit multiple targets across Iran in direct response to continued aggression against commercial shipping, including military equipment, communication systems, air defense sites and drone storage facilities. Iran was given a chance to honor the ceasefire agreement but elected not to when its forces launched a one-way attack drone that hit MT Kiku, a Panama-flagged tanker, it said in a statement. Commercial vessels are continuing to operate in the Strait of Hormuz, Centcom said. Iran is yet to comment on the latest strikes. The latest strikes come less than a day after the US launched retaliatory strikes on Iran that it said were in response to a drone attack on Singapore-flagged cargo ship, MV Ever Lovely, on 25 June.