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Category: mathematics – Page 37

When learning, patients with schizophrenia or depression have difficulty making optimal use of information that is new to them. In the learning process, both groups of patients give greater weight to less important information and, as a result, make less than ideal decisions.

This was the finding of a several-months-long study conducted by a team led by neuroscientist Professor Dr. med. Markus Ullsperger from the Institute of Psychology at Otto von Guericke University Magdeburg in collaboration with colleagues from the University Clinic for Psychiatry & Psychotherapy and the German Center for Mental Health.

By using electroencephalography (EEG) and complex mathematical computer modeling, the team of researchers discovered that learning deficits in depressive and schizophrenic are caused by diminished/reduced flexibility in the use of new information.

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3 million custom ChatGPTs

The new store is dubbed the GPT Store, where customers who have subscribed to their ChatGPT Plus service for $20 per month can browse through custom chatbots that offer a range of services such as book recommendations, math tutorials, and scientific paper searches. According to a blog post by the company, the store aims to assist users in discovering popular and practical custom versions of ChatGPT. In an official tweet, the company says users can now choose over 3 million different types of GPTs as per their choice and needs.

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A new study shows how quantum computing can be harnessed to discover new properties of polymer systems central to biology and material science.

The advent of quantum computing is opening previously unimaginable perspectives for solving problems deemed beyond the reach of conventional computers, from cryptography and pharmacology to the physical and chemical properties of molecules and materials. However, the computational capabilities of present-day quantum computers are still relatively limited. A newly published study in Science Advances fosters an unexpected alliance between the methods used in quantum and traditional computing.

The research team, formed by Cristian Micheletti and Francesco Slongo of SISSA in Trieste, Philipp Hauke of the University of Trento, and Pietro Faccioli of the University of Milano-Bicocca, used a mathematical approach called QUBO (from “Quadratic Unconstraint Binary Optimization”) that is ideally suited for specific quantum computers, called “quantum annealers.”

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Mathpresso, the creator of QANDA — Asia’s most extensive AI-driven learning platform — has announced that their large language model called MathGPT has achieved a new world record in math, beating OpenAI and Microsoft models.

MathGPT reportedly is now ranked no. 1 in benchmarks that evaluate mathematical ability such as ‘MATH’ (12,500 difficult math problems) and ‘GSM8K’ (8,500 elementary school math problems), beating Microsoft’s ‘ToRA 13B’, the model that held the previous record.

In the MATH benchmark, MathGPT surpassed the performance of OpenAI’s GPT-4.

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Scientists have grown a tiny brain-like organoid out of human stem cells, hooked it up to a computer, and demonstrated its potential as a kind of organic machine learning chip, showing it can quickly pick up speech recognition and math predictions.

Clusters of brain cells grown in the lab have shown potential as a new type of hybrid bio-computer.

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A #mathematics “A Bernoulli trial is a #random experiment with exactly two possible outcomes “success” and “failure” in which #probability of success is the same every time the experiment is conducted.”

In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, “success” and “failure”, in which the probability of success is the same every time the experiment is conducted.[1] It is named after Jacob Bernoulli, a 17th-century Swiss mathematician, who analyzed them in his Ars Conjectandi (1713).[2]

The mathematical formalisation of the Bernoulli trial is known as the Bernoulli process. This article offers an elementary introduction to the concept, whereas the article on the Bernoulli process offers a more advanced treatment.

Since a Bernoulli trial has only two possible outcomes, it can be framed as some “yes or no” question. For example:

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One of the greatest challenges of modern physics is to find a coherent method for describing phenomena, on the cosmic and microscale. For over a hundred years, to describe reality on a cosmic scale we have been using general relativity theory, which has successfully undergone repeated attempts at falsification.

Albert Einstein curved space-time to describe gravity, and despite still-open questions about or , it seems, today, to be the best method of analyzing the past and future of the universe.

To describe phenomena on the scale of atoms, we use the second great theory: , which differs from general relativity in basically everything. It uses flat space-time and a completely different mathematical apparatus, and most importantly, perceives reality radically differently.

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Scientists have fused brain-like tissue with electronics to make an ‘organoid neural network’ that can recognise voices and solve a complex mathematical problem. Their invention extends neuromorphic computing – the practice of modelling computers after the human brain – to a new level by directly including brain tissue in a computer.

The system was developed by a team of researchers from Indiana University, Bloomington; the University of Cincinnati and Cincinnati Children’s Hospital Medical Centre, Cincinnati; and the University of Florida, Gainesville. Their findings were published on December 11.

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Researchers taking part in the Human Brain Project have identified a mathematical rule that governs the distribution of neurons in our brains.

The rule predicts how neurons are distributed in different parts of the brain, and could help scientists create precise models to understand how the brain works and develop new treatments for neurological diseases.

In the wonderful world of statistics, if you consider any continuous random variable, the logarithm of that variable will often follow what’s known as a lognormal distribution. Defined by the mean and standard deviation, it can be visualized as a bell-shaped curve, only with the curve being wider than what you’d find in a normal distribution.

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