Related papers: Chameleon Coins
Chameleons are light scalar fields with remarkable properties. Through the interplay of self-interactions and coupling to matter, chameleon particles have a mass that depends on the ambient matter density. The manifestation of the fifth…
We investigate a coin-weighing puzzle that appeared in the Moscow Math Olympiad in 1991. We generalize the puzzle by varying the number of participating coins, and deduce an upper bound on the number of weighings needed to solve the puzzle…
Expanding on recent results of another an algorithm is presented that provides solution to the Frobenius Coin Problem in worst case O(n^2) in the magnitude of the largest denomination.
We discuss the objectives of automation equipped with non-trivial decision making, or creating artificial intelligence, in the financial markets and provide a possible alternative. Intelligence might be an unintended consequence of…
How many fair coin tosses to choose 1 of $n$ options with uniform probability? Although a probability problem, the solution is essentially number-theoretic, with special roles for Mersenne numbers, Fermat numbers, and the haupt exponent. We…
We consider different methods to probe chameleons with slow neutrons. Chameleon modify the potential of bouncing neutrons over a flat mirror in the terrestrial gravitational field. This induces a shift in the energy levels of the neutrons…
Coin flipping is a cryptographic primitive in which two distrustful parties wish to generate a random bit in order to choose between two alternatives. This task is impossible to realize when it relies solely on the asynchronous exchange of…
We devised a protocol that allows two parties, who may malfunction or intentionally convey incorrect information in communication through a quantum channel, to verify each other's measurements and agree on each other's results. This has…
We harness both human ingenuity and the power of symbolic computation to study the number of coin tosses until reaching $n$ Heads or $m$ Tails. We also talk about the closely related problem of reaching $n$ Heads and $m$ Tails. This paper…
While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more that a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set $X$ may be coded as a…
The problem of creating a three-sided dice with the probability of it landing on each of its sides being equal to 1/3 has been around for many years. Various approaches have been attempted, but as different authors achieved at different…
Automatic authentication of paper money has been targeted. Indian bank notes are taken as reference to show how a system can be developed for discriminating fake notes from genuine ones. Image processing and pattern recognition techniques…
We propose an alternative to the Turing test that removes the inherent asymmetry between humans and machines in Turing's original imitation game. In this new test, both humans and machines judge each other. We argue that this makes the test…
Two works related to the concept of probability in the framework of the many-worlds interpretation are presented. The first deals with recent controversy in classical probability theory. Elga and D. Lewis argues that Sleeping Beauty should…
In a quantum money scheme, a bank can issue money that users cannot counterfeit. Similar to bills of paper money, most quantum money schemes assign a unique serial number to each money state, thus potentially compromising the privacy of the…
The top quark is by far the heaviest known fermion [1]. In consequence, experiment is just beginning to explore its properties, and some of them may yet prove to be distinctly non-standard. The very size of the top quark's mass even hints…
Stablecoins have gained significant popularity recently, with their market cap rising to over $180 billion. However, recent events have raised concerns about their stability. In this paper, we classify stablecoins into four types based on…
We study the Colored Bin Packing Problem: we are given a set of items where each item has a weight and color. We must pack the items in bins of uniform capacity such that no two items of the same color may be adjacent within in a bin. The…
Verifying equivalence between two quantum circuits is a hard problem, that is nonetheless crucial in compiling and optimizing quantum algorithms for real-world devices. This paper gives a Turing reduction of the (universal) quantum circuits…
We construct a financial "Turing test" to determine whether human subjects can differentiate between actual vs. randomized financial returns. The experiment consists of an online video-game (http://arora.ccs.neu.edu) where players are…