Related papers: It's Common Knowledge
Cosmology presents us with several puzzles that are related to the fundamental structure of quantum theory. We discuss three such puzzles, linking them to effects that arise in black hole physics. We speculate that puzzles in cosmology may…
Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.
A review of various definitions of "compatibility" expressed in terms of ordinary probability, and a discussion of the occurrence of incompatibility (and the related phenomenon of interference) in non-quantal probabilistic systems.
Gossip protocols aim at arriving, by means of point-to-point or group communications, at a situation in which all the agents know each other secrets. Recently a number of authors studied distributed epistemic gossip protocols. These…
Physics is introduced as a semantics of a formal set theory.
The recent proliferation of "fake news" has triggered a number of responses, most notably the emergence of several manual fact-checking initiatives. As a result and over time, a large number of fact-checked claims have been accumulated,…
We give a short proof of the well-known Knuth's old sum and provide some generalizations. Our approach utilizes the binomial theorem and integration formulas derived using the Beta function. Several new polynomial identities and…
Large probabilistic models are often shaped by a pool of known individuals (a universe) and relations between them. Lifted inference algorithms handle sets of known individuals for tractable inference. Universes may not always be known,…
Existing physical theories do not predict every feature of our experience but only certain regularities of that experience. That difference between what could be observed and what can be predicted is one kind of limit on scientific…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
Crossword puzzles are popular word games that require not only a large vocabulary, but also a broad knowledge of topics. Answering each clue is a natural language task on its own as many clues contain nuances, puns, or counter-intuitive…
This survey presents an overview of integrating prior knowledge into machine learning systems in order to improve explainability. The complexity of machine learning models has elicited research to make them more explainable. However, most…
We prove a new q-analogue of Nicomachus's Theorem about the sum of cubes and some related results.
A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.
We discuss variations of the zero-sum game where Bob selects two distinct numbers, and Alice learns one of them to make a guess which of the numbers is the larger.
Recent results about sums of cubes of Fibonacci numbers [Frontczak, 2018] are extended to arbitrary powers.
The concept of uncertainty quanta for a general system is introduced and applied to some important problems in physics and mathematics. EPR paradox gives new clue to the further understanding of particle correlation which turns out to be…
We use the middle convolution to obtain some old and new algebraic solutions of the Painlev\'e VI equations.
Over the course of the last 50 years, many questions in the field of computability were left surprisingly unanswered. One example is the question of $P$ vs $NP\cap co-NP$. It could be phrased in loose terms as "If a person has the ability…
While canonical quantization solves many problems there are some problems where it fails. A close examination of the classical/quantum connection leads to a new connection that permits quantum and classical realms to coexist, as is the case…