Related papers: The Sleeping Beauty Problem -- A Real-World Soluti…
In the game of Matching Pennies, Alice and Bob each hold a penny, and at every tick of the clock they simultaneously display the head or the tail sides of their coins. If they both display the same side, then Alice wins Bob's penny; if they…
Proof-of-work allows Bitcoin to boast security amidst arbitrary fluctuations in participation of miners throughout time, so long as, at any point in time, a majority of hash power is honest. In recent years, however, the pendulum has…
The concept of beauty has been debated by philosophers and psychologists for centuries, but most definitions are subjective and metaphysical, and deficit in accuracy, generality, and scalability. In this paper, we present a novel study on…
Processes undergoing quantum mechanics, exhibit quantum interference effects. In this case quantum probabilities result to be different from classical probabilities because they contain an additional main point that in fact is called the…
I think we can agree that dealing with uncertainty is not easy. Probability is the main tool for dealing with uncertainty, and we know there are many probability-related puzzles and paradoxes. Here I describe a rather idiosyncratic…
Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are…
Statistical models of natural stimuli provide an important tool for researchers in the fields of machine learning and computational neuroscience. A canonical way to quantitatively assess and compare the performance of statistical models is…
Analysis of stochastic processes can be used to engender critical thinking. Quantum dots have a reversible, stochastic transition between luminescent and non-luminescent states. The luminescence intermittency is known as blinking, and is…
One of the most critical challenges in Large Language Models is their tendency to hallucinate, i.e., produce factually incorrect responses. Existing approaches show promising results in terms of hallucination correction, but still suffer…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
Topological quantum computations are built on a foundation of two basic tasks: preserving logical observables through time and moving logical observables through space. Memory experiments, which check how well logical observables are…
Identifying the boundary between classical and quantum computation is a central challenge in quantum information. In multi-qubit systems, entanglement and magic are the key resources underlying genuinely quantum behaviour. While…
A quantum version of the Monty Hall problem is proposed inspired by an experimentally-feasible, quantum-optical set-up that resembles the classical game. The expected payoff of the player is studied by analyzing the classical expectation…
A number of tricky problems in probability are discussed, having in common one or more infinite sequences of coin tosses, and a representation as a problem in dependent percolation. Three of these problems are of `Winkler' type, that is,…
Financial statement fraud detection is an important problem with a number of design aspects to consider. Issues such as (i) problem representation, (ii) feature selection, and (iii) choice of performance metrics all influence the perceived…
The origin and meaning of facial beauty represent a longstanding puzzle. Despite the profuse literature devoted to facial attractiveness, its very nature, its determinants and the nature of inter-person differences remain controversial…
Given a set of coins arranged in a line, we remove heads-up coins one at a time and flip any adjacent coins after each removal. The coin-removal problem is to determine for which arrangements of coins it is possible to remove all of the…
The quantum world is fascinating. It presents a description of nature that defies our most rooted concepts about what reality is. For example, quantum objects possess \lq\lq spooky\rq\rq\ properties that allow them to be in multiple places…
Consider $n$ independent, biased coins, each with a known probability of heads. Presented with an ordering of these coins, flip (i.e., toss) each coin once, in that order, until we have observed both a *head* and a *tail*, or flipped all…
The three-box problem is a gedankenexperiment designed to elucidate some interesting features of quantum measurement and locality. A particle is prepared in a particular superposition of three boxes, and later found in a different (but…