About …fty years ago, Efron noted some counterintuitive properties of the long-term behavior of contests involving dice. For instance, consider the 6-sided dice whose sides are labeled (4,4,4,4,0,0), (3,3,3,3,3,3), (6,6,2,2,2,2), and (5,5,5,1,1,1). Each die has a 2/3 probability of rolling a higher number than the next one in the list, and the last has the same 2/3 probability of rolling a high...

Einstein initially objected to the probabilistic aspect of quantum mechanics— the idea that God is playing at dice. Later he changed his ground, and focussed instead on the point that the Copenhagen Interpretation leads to what Einstein saw as the abandonment of physical realism. We argue here that Einstein's initial intuition was perfectly sound, and that it is precisely the fact that quantum ...

LetK, L be congruent regular polyhedra in R. Let g denote a rigid motion of R, that is, g(x) = Φx+τ where Φ is a 3×3 rotation matrix and τ is a translation 3-vector. The polyhedraK, g(L) are said to touch ifK∩g(L) 6= ∅ but int(K)∩int(g(L)) = ∅. Alternatively, we may think of ΦL moving toward K in the direction τ , stopping precisely when the two polyhedra collide. Let us sample the space SO3 of...

We introduce a protocol through which a pair of quantum mechanical devices may be used to generate n random bits that are ε-close in statistical distance from n uniformly distributed bits, starting from a seed of uniform bits. The bits generated are certifiably random, based only on a simple statistical test that can be performed by the user, and on the assumption that the devices obey the no...

Albert Einstein once said that he does not believe in a God who plays dice. He was referring to the fundamental principle that quantum theory permits only statistical assertions concerning the values of physical quantities. This issue, namely, whether the description of Nature in statistical terms is complete or even consistent, was the subject of a very lively debate-dialogue between Einstein ...

The object of the jeopardy dice game Pig is to be the first player to reach 100 points. Each player's turn consists of repeatedly rolling a die. After each roll, the player is faced with two choices: roll again, or hold (decline to roll again). • If the player rolls a 1, the player scores nothing and it becomes the opponent's turn. • If the player rolls a number other than 1, the number is adde...

DICE (the DSPCAD Integrative Command Line Environment) is a package of utilities that facilitates efficient management of software projects. Key areas of emphasis in DICE are cross-platform operation, support for projects that integrate heterogeneous programming languages, and support for applying and integrating different kinds of design and testing methodologies. The package is being develope...

OBJECTIVES To assess decision-making under explicit risk conditions in relapsing-remitting multiple sclerosis patients and its relationship to decisions made under conditions of ambiguity. To assess cognitive functions related to decision-making performance in patients with multiple sclerosis (MS). SETTING MS center in Buenos Aires, Argentina. PARTICIPANTS 27 patients with relapsing-remitti...

DICE is a shared-bus multiprocessor based on a distributed shared-memory architecture, known as Cache-Only Memory Architecture (COMA). Unlike previous COMA proposals for large-scale multiprocessing, DICE utilizes the COMA to effectively decrease the gap between modern high-performance microprocessors and the bus. As microprocessors become faster and demand more bandwidth, the already limited sc...