Science Space Deep Space Scientists predict the universe will end in'big crunch' Starts with a bang, ends with a crunch. Breakthroughs, discoveries, and DIY tips sent every weekday. Our vast universe might not be infinitely expanding after all. Some newly reviewed dark energy data may contradict the theory first posed in 1922 by the astronomer Alexander Friedmann. According to a study recently published in the, the cosmos will actually conclude with a "big crunch."

Long before the world had ever heard of covid-19, Kay Tye set out to answer a question that has taken on new resonance in the age of social distancing: When people feel lonely, do they crave social interactions in the same way a hungry person craves food? And could she and her colleagues detect and measure this "hunger" in the neural circuits of the brain? "Loneliness is a universal thing. If I were to ask people on the street, 'Do you know what it means to be lonely?' probably 99 or 100% of people would say yes," explains Tye, a neuroscientist at the Salk Institute of Biological Sciences. "It seems reasonable to argue that it should be a concept in neuroscience. It's just that nobody ever found a way to test it and localize it to specific cells. That's what we are trying to do."

As a child, Kay Tye was immersed in a life of science. "I grew up in my mom's lab," she says. At the age of five or six, she earned 25 cents a box for "restocking" bulk-ordered pipette tips into boxes for sterilization as her mother, an acclaimed biochemist at Cornell University, probed the genetics of yeast. Today, Tye runs her own neuroscience lab at MIT. Under large black lights reminiscent of a fashion shoot, she and her team at the Picower Institute for Learning and Memory can observe how mice behave when particular brain circuits are turned on or off.

Characteristic models are an alternative, model based, representation for Horn expressions. It has been shown that these two representations are incomparable and each has its advantages over the other. It is therefore natural to ask what is the cost of translating, back and forth, between these representations. Interestingly, the same translation questions arise in database theory, where it has applications to the design of relational databases. This paper studies the computational complexity of these problems. Our main result is that the two translation problems are equivalent under polynomial reductions, and that they are equivalent to the corresponding decision problem. Namely, translating is equivalent to deciding whether a given set of models is the set of characteristic models for a given Horn expression. We also relate these problems to the hypergraph transversal problem, a well known problem which is related to other applications in AI and for which no polynomial time algorithm is known. It is shown that in general our translation problems are at least as hard as the hypergraph transversal problem, and in a special case they are equivalent to it.