New mathematical models of our Milky Way Galaxy are helping a team of Argentine, Chilean and Spanish astrophysicists trace the origins of our galaxy back through time.
Logical reasoning is still a major challenge for language models. DeepMind has found a way to support reasoning tasks.
A study by Google’s AI division DeepMind shows that the order of the premises in a task has a significant impact on the logical reasoning performance of language models.
They work best when the premises are presented in the same order as they appear in the logical conclusions. According to the researchers, this is also true for mathematical problems. The researchers make the systematically generated tests available in the R-GSM benchmark for further investigation.
This past October, dozens of mathematicians gathered in Pasadena to create the third version of “Kirby’s list” — a compendium of the most important unsolved problems in the field.
What is universal in natural languages? To answer that, deep connections need to be made between universal grammar, written codes, statistical patterns and Universal Turing machines.
Human language is a prime example of a complex system characterized by multiple scales of description. Understanding its origins and distinctiveness has sparked investigations with very different approaches, ranging from the Universal Grammar to statistical analyses of word usage, all of which highlight, from different angles, the potential existence of universal patterns shared by all languages. Yet, a cohesive perspective remains elusive. In this paper we address this challenge. First, we provide a basic structure of universality, and define recursion as a special case thereof. We cast generative grammars of formal languages, the Universal Grammar and the Greenberg Universals in our basic structure of universality, and compare their mathematical properties. We then define universality for writing systems and show that only those using the rebus principle are universal.
The surprisingly subtle geometry of a familiar game shows how quickly math gets complicated.
The technology can reconstruct a hidden scene in just minutes using advanced mathematical algorithms.
Potential use case scenarios
Law enforcement agencies could use the technology to gather critical information about a crime scene without disturbing the evidence. This could be especially useful in cases where the scene is dangerous or difficult to access. For example, the technology could be used to reconstruct the scene of a shooting or a hostage situation from a safe distance.
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The universe, with its myriad mysteries, has long captivated our curiosity, and among its enigmatic phenomena, black holes have held a prominent place. These collapsed cores of dead stars, known for devouring everything in their vicinity, have a cosmic counterpart that challenges our understanding – the elusive ‘white holes.’
Imagine delving into the intricacies of space-time around a black hole, subtracting the collapsed star’s mass, and unveiling the mathematical description of a white hole – a massless singularity. Unlike their gravitational counterparts, black holes, where matter disappears into an event horizon, white holes defy entry. They expel matter at an astonishing rate, akin to hitting a cosmic ‘rewind’ button.
The critical role of the mammalian hippocampus in the formation, translation and retrieval of memory has been documented over many decades. There are many theories of how the hippocampus operates to encode events and a precise mechanism was recently identified in rats performing a short-term memory task which demonstrated that successful information encoding was promoted via specific patterns of activity generated within ensembles of hippocampal neurons. In the study presented here, these “representations” were extracted via a customized non-linear multi-input multi-output (MIMO) mathematical model which allowed prediction of successful performance on specific trials within the testing session. A unique feature of this characterization was demonstrated when successful information encoding patterns were derived online from well-trained “donor” animals during difficult long-delay trials and delivered via online electrical stimulation to synchronously tested naïve “recipient” animals never before exposed to the delay feature of the task. By transferring such model-derived trained (donor) animal hippocampal firing patterns via stimulation to coupled naïve recipient animals, their task performance was facilitated in a direct “donor–recipient” manner. This provides the basis for utilizing extracted appropriate neural information from one brain to induce, recover, or enhance memory related processing in the brain of another subject.
To understand the neural basis of memory, several features of the context in which the memories occur and are utilized, and the functional aspects of the brain areas involved, need to be identified and controlled (Hampson et al., 2008; Eichenbaum and Fortin, 2009). In prior studies we achieved both of these important contingencies as well as overcoming possible alternative interpretations of the relationship between recorded hippocampal ensemble activity and the behavioral task in which short-term memory formation is necessary (Deadwyler and Hampson, 2006; Deadwyler et al., 2007), and developing an effective mathematical/operational model for online prediction of CA1 hippocampal cell activity from simultaneously recorded input firing patterns from synaptically connected CA3 neurons (Song et al., 2009; Berger et al., 2011; Hampson et al., 2011).
Physicists found that the music of Johann Sebastian Bach contains mathematical patterns that help convey information.
By Elise Cutts
An innovative new chip uses light for fast, efficient AI computations, promising a leap in processing speeds and privacy.
Penn Engineers have developed a new chip that uses light waves, rather than electricity, to perform the complex math essential to training AI. The chip has the potential to radically accelerate the processing speed of computers while also reducing their energy consumption.
The silicon-photonic (SiPh) chip’s design is the first to bring together Benjamin Franklin Medal Laureate and H. Nedwill Ramsey Professor Nader Engheta’s pioneering research in manipulating materials at the nanoscale to perform mathematical computations using light — the fastest possible means of communication — with the SiPh platform, which uses silicon, the cheap, abundant element used to mass-produce computer chips.
