Related papers: Generalizing the Futurama Theorem
We generalize the problem of coin flipping to more than two outcomes and parties. We term this problem dice rolling, and study both its weak and strong variants. We prove by construction that in quantum settings (i) weak N-sided dice…
100 prisoners and a light bulb is a long standing mathematical puzzle. The problem was studied mostly in 2002 [5], 2003 [1], and 2004 [3]. Solutions in published articles had average number of visits above 3850, but best solutions on forums…
We explicitly show a protocol in which an arbitrary two qubit a|00> + b|01> + c|10> + d|11> is faithfully and deterministically teleported from Alice to Bob. We construct the 16 orthogonal generalized Bell states which can be used to…
Ensemble learning is a widespread technique to improve the prediction performance of neural networks. However, it comes at the price of increased memory and inference time. In this work we propose a novel model fusion technique called…
Coin-flipping is a fundamental task in two-party cryptography where two remote mistrustful parties wish to generate a shared uniformly random bit. While quantum protocols promising near-perfect security exist for weak coin-flipping -- when…
It has been suggested, on the one hand, that quantum states are just states of knowledge; and, on the other, that quantum theory is merely a theory of correlations. These suggestions are confronted with problems about the nature of…
Transformers achieve state-of-the-art performance for natural language processing tasks by pre-training on large-scale text corpora. They are extremely compute-intensive and have very high sample complexity. Memory replay is a mechanism…
Supertask theory is used here to prove a contradictory result which involves the consistency of w-order and the Axiom of Infinity.
A central limit theorem for arrays of symmetric row-wise exchangeable random variables is presented. The result is valid for finite and infinite extendable and non-extendable sequences. Unlike most reported versions of the central limit…
We derive a recursive formula for the moments of the number of flips using a possibly biased coin to produce a prescribed finite binary string $S$ when $S$ is either a run of heads or a run of heads followed by a tails. Our recursive…
The multiple puns in the title play on a curiosity, that the rescue of a person overboard at sea and the dominance of the second Born term in charge transfer in atomic collisions share common elements of physics. Essentials and commonality…
We analyze the main arguments that attempt to explain why there is no point in changing the envelope. Most people confuse estimation and calculation, conditional and unconditional probabilities, random and non-random variables, modelling…
We study a multi-armed bandit problem where the rewards exhibit regime switching. Specifically, the distributions of the random rewards generated from all arms are modulated by a common underlying state modeled as a finite-state Markov…
In this work, we study theoretical models of \emph{programmable matter} systems. The systems under consideration consist of spherical modules, kept together by magnetic forces and able to perform two minimal mechanical operations (or…
In the last few decades, numerous experiments have shown that humans do not always behave so as to maximize their material payoff. Cooperative behavior when non-cooperation is a dominant strategy (with respect to the material payoffs) is…
Synchronization of coupled oscillators is often described using the Kuramoto model. Here we study a generalization of the Kuramoto model where oscillators communicate with each other through an external medium. This generalized model…
It is a well known fact that a quantum state $|\psi(\theta,\phi)>$ are represented by a point on the Bloch sphere, characterized by two parameters $\theta$ and $\phi$. Here in this work, we find out another impossible operation in quantum…
In Newcomb's paradox you choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose though, an antagonist uses a prediction algorithm to deduce your choice,…
We introduce a framework uniting algorithmic randomness with exchangeable credences to address foundational questions in philosophy of probability and philosophy of science. To demonstrate its power, we show how one might use the framework…
The problem of how to achieve cooperation among rational peers in order to discourage free riding is one that has received a lot of attention in peer-to-peer computing and is still an important one. The field of game theory is applied to…