In multi-objective (MO) heuristic search, solution costs, as well as heuristic values, are sets of multi-dimensional cost vectors, representing possible non-dominated trade-offs between objectives. The maximum of two or more such vector sets, which is an important operation in creating informative admissible MO heuristics, can be defined in several ways: Geißer et al. recently proposed two MO maximum operators, the component-wise maximum (comax) and the anti-dominance maximum (admax), which represent different trade-offs between informativeness and computational cost. We show that the anti-dominance maximum is not admissibility-preserving, and propose an alternative, the "select one" maximum (somax). We also show that the comax operator is the greatest admissibility-preserving MO maximum, and briefly investigate its efficient implementation. The conclusion of our experimental results is that somax achieves a trade-off similar to that intended with admax - cheaper to compute but less informed - also when compared to an improved comax implementation.

Model-based diagnosis has always been conceived as set-oriented, meaning that a candidate is a set of faults, or faulty components, that explains a collection of observations. This perspective applies equally to both static and dynamical systems. Diagnosis of discrete-event systems (DESs) is no exception: a candidate is traditionally a set of faults, or faulty events, occurring in a trajectory of the DES that conforms with a given sequence of observations. As such, a candidate does not embed any temporal relationship among faults, nor does it account for multiple occurrences of the same fault. To improve diagnostic explanation and support decision making, a sequence-oriented perspective to diagnosis of DESs is presented, where a candidate is a sequence of faults occurring in a trajectory of the DES, called a fault sequence. Since a fault sequence is possibly unbounded, as the same fault may occur an unlimited number of times in the trajectory, the set of (output) candidates may be unbounded also, which contrasts with set-oriented diagnosis, where the set of candidates is bounded by the powerset of the domain of faults. Still, a possibly unbounded set of fault sequences is shown to be a regular language, which can be defined by a regular expression over the domain of faults, a property that makes sequence-oriented diagnosis feasible in practice. The task of monitoring-based diagnosis is considered, where a new candidate set is generated at the occurrence of each observation. The approach is based on three different techniques: .1/ blind diagnosis, with no compiled knowledge, .2/ greedy diagnosis, with total knowledge compilation, and .3/ lazy diagnosis, with partial knowledge compilation. By knowledge we mean a data structure slightly similar to a classical DES diagnoser, which can be generated (compiled) either entirely offline (greedy diagnosis) or incrementally online (lazy diagnosis). Experimental evidence suggests that, among these techniques, only lazy diagnosis may be viable in non-trivial application domains.

In this paper we propose a new model to represent human debates and methods to obtain collective conclusions from them. This model overcomes two drawbacks of existing approaches. First, our model does not assume that participants agree on the structure of the debate. It does this by allowing participants to express their opinion about all aspects of the debate. Second, our model does not assume that participants' opinions are rational, an assumption that significantly limits current approaches. Instead, we define a weaker notion of rationality that characterises coherent opinions, and we consider different scenarios based on the coherence of individual opinions and the level of consensus. We provide a formal analysis of different opinion aggregation functions that compute a collective decision based on the individual opinions and the debate structure. In particular, we demonstrate that aggregated opinions can be coherent even if there is a lack of consensus and individual opinions are not coherent. We conclude with an empirical evaluation demonstrating that collective opinions can be computed efficiently for real-sized debates.

Schwan Park, father of speed cuber Max Park, 21, tells Fox News Digital the story of his son's record-breaking achievement with Rubik's Cube: "We always knew he was good," he said. A young man from Cerritos, California, has beaten the world record for the fastest time to solve a Rubik's Cube. Park has been competing in Rubik's competitions since he was 10 years old -- and has defied the odds as a fierce competitor who also has severe autism. Park's father, Schwan Park, commended his son's record-breaking accomplishment and shared the young man's story with Fox News Digital. "We didn't realize how good he was," Park's father said, referencing the earlier years.

When the U.S. first embraced "de-risking" to get Europe on board with measures to deny key technology to China, officials in Beijing dismissed the term as no different than decoupling. Now they are trying a new strategy: redefining the concept. Chinese Premier Li Qiang last week acknowledged the legitimacy of de-risking while speaking to CEOs on a trip to Germany, but said it should be decided by business leaders instead of governments. He also warned that risks shouldn't be "exaggerated" -- opening a discussion on what exactly poses a serious threat to national security. Li touched on the theme again Tuesday at a high-profile economic forum in China known as "Summer Davos," where he told delegates "if there is risk in a certain industry, it's not the call or decision of a particular organization or a single government.

The mother of the 19-year-old killed aboard the Titan submersible said the plan had been for her to accompany her husband on a trip to see the wreck of the Titanic at the bottom of the sea. She "stepped back" from going on the trip because of her son's enthusiasm, Christine Dawood told the BBC, and he boarded the ill-fated craft carrying a Rubik's Cube and dreaming of setting a world record. He and his father, Shahzada Dawood, died when the vessel imploded. Christine Dawood told the news outlet the original plan was for her to accompany her husband on the underwater trek roughly 12,500 feet below the surface to view the Titanic. The original trip, however, was canceled because of the COVID-19 pandemic.

Suleman Dawood, the 19-year-old who died aboard OceanGate's Titan submersible last week, hoped to set the world record for solving a Rubik's Cube in the deep ocean, his mother said Monday. Dawood and his father, Shahzada, had finished the process of applying to the Guinness World Records and entered the submersible equipped with a camera to record the achievement. Christine Dawood and her daughter remained aboard the Polar Prince mother ship while the submersible descended toward the wreck of the Titanic earlier this month, she told the BBC in an interview. Christine spoke of the moment the crew of the Prince informed her they had lost communications with the submersible. "I didn't comprehend at that moment what it meant – and then it just went downhill from there," she said.

As well as Suleman and his father Shahzada Dawood, three other people died on board: Stockton Rush, the 61-year-old CEO of OceanGate which owned the Titan, British businessman Hamish Harding, 58, and Paul-Henry Nargeolet, 77, a former French navy diver and renowned explorer.

Max Park spent about 10 seconds studying the jumbled Rubik's Cube in front of him at the Pride in Long Beach World Cube Assn. Cracking it took less than a third of that time. With a deep breath, steady hands and just 3.13 seconds, the 21-year-old solved the colorful mind game with 43 quintillion possible combinations, aligning each side perfectly by color. In a video capturing the moment, Park slams his hands down to stop the clock, claps and yells "Yes!" -- knowing he had just broke the world record for fastest solve of a single 3x3x3 Rubik's Cube. A watching crowd went wild, celebrating the achievement with him.

Fox News Flash top headlines are here. Check out what's clicking on Foxnews.com. American Max Park has set a new world record by solving a 3x3x3 Rubik's Cube in just 3.13 seconds. The 21-year-old achieved the feat at an event in Long Beach, California over the weekend, according to Guinness World Records. The previous record was 3.47 seconds, set by China's Yusheng Du in 2018, it said.