Related papers: Remembering Leo
Imitation is an important learning heuristic in animal and human societies. Previous explorations report that the fate of individuals with cooperative strategies is sensitive to the protocol of imitation, leading to a conundrum about how…
In this small note I try to summarize some observations about Euclid's remarkable role in mathematics and about the ambient philosophy.
Many of life's most fascinating phenomena emerge from interactions among many elements--many amino acids determine the structure of a single protein, many genes determine the fate of a cell, many neurons are involved in shaping our thoughts…
Humans and AIs are often paired on decision tasks with the expectation of achieving complementary performance -- where the combination of human and AI outperforms either one alone. However, how to improve performance of a human-AI team is…
In social networks, individuals constantly drop ties and replace them by new ones in a highly unpredictable fashion. This highly dynamical nature of social ties has important implications for processes such as the spread of information or…
Collaborative problem solving and learning are shaped by who or what is on the team. As large language models (LLMs) increasingly function as collaborators rather than tools, a key question is whether AI teammates can be aligned to express…
Jacobi said "man muss immer umkehren". And indeed it takes a genius like Michael Somos to take a specific non-linear recurrence, like a(n)=(a(n-1)a(n-3)+a(n-2)^2)/a(n-4), subject to a(1)=1, a(2)=1, a(3)=1, a(4)=1, and observe that surprise,…
This is, with minor modifications, a text read at the 114th Statistical Mechanics meeting, in honor of D.Ruelle and Y.Sinai, at Rutgers, Dec.13-15, 2015. It does not attempt to analyze, or not even just quote, all works of David Ruelle; I…
Inbreeding homophily is a prevalent feature of human social networks with important individual and group-level social, economic, and health consequences. The literature has proposed an overwhelming number of dimensions along which human…
The Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept$\unicode{x2013}$representing highly nonlinear dynamical systems by infinite-dimensional linear…
This paper is a top down historical perspective on the several phases in the development of probability from its prehistoric origins to its modern day evolution, as one of the key methodologies in artificial intelligence, data science, and…
As large language models (LLMs) demonstrate increasingly advanced capabilities, aligning their behaviors with human values and preferences becomes crucial for their wide adoption. While previous research focuses on general alignment to…
Koopman operators, since introduced by the French-born American mathematician Bernard Koopman in 1931, have been employed as a powerful tool for research in various scientific domains, such as ergodic theory, probability theory, geometry,…
We find an interesting relationship between the golden ratio, the Moebius function, the Euler totient function and the natural logarithm - central players in the theory of numbers. A number of identities involving the golden ratio and its…
The 75th anniversary of Turing's seminal paper and his centennial year anniversary occur in 2011 and 2012, respectively. It is natural to review and assess Turing's contributions in diverse fields in the light of new developments that his…
Large language models (LLMs) excel in both closed tasks (including problem-solving, and code generation) and open tasks (including creative writing), yet existing explanations for their capabilities lack connections to real-world human…
The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and…
Given $n$ i.i.d. samples from an unknown discrete distribution over an unknown set, the unseen species problem is to predict how many new outcomes would be observed in $m$ additional samples. For small $m$ we show that the Good-Toulmin…
Luck is considered to be a crucial ingredient to achieve impact in all creative domains, despite their diversity. For instance, in science, the movie industry, music, and art, the occurrence of the highest impact work and of a hot streak…
LLM assistant personalities play a critical role in user experience and perceived response quality. We present a large-scale experiment of frontier LLM personalities using external ELO-based traits scoring across 144 traits. We find that…