We study the linear Arrow-Debreu’s model and derive a fix point method to find the market equilibrium. The convergence of this method is proved, while the speed is unknown. Besides that, properties about utility distribution and the partition of buyers are also studied. I. PROBLEM DEFINITION The problems of market equilibrium were initially studied in the domain of mathematical economics. We st...

Does not the theory of a general tendency of entropy to diminish [sic 1 ] take too much for granted? To a certain extent it is supported by experimental evidence. We must accept such evidence as far as it goes and no further. We have no right to supplement it by a large draft of the scientific imagination.

Two categorifications are given for the arrow polynomial, an extension of the Kauffman bracket polynomial for virtual knots. The arrow polynomial extends the bracket polynomial to infinitely many variables, each variable corresponding to an integer arrow number calculated from each loop in an oriented state summation for the bracket. The categorifications are based on new gradings associated wi...

CASE DESCRIPTION The serum protein electrophoresis pattern (SPEP) for an 82-year-old female patient with known monoclonal gammopathy of undetermined significance demonstrated 2 aberrant protein bands, one in the 21 interzone (Fig. 1A, fat arrow) and one in the 12 interzone (Fig. 1A, thin arrow). The immunofixation electrophoresis (IFE) (Fig. 1B) revealed a large IgA paraprotein in the 12 interz...

Quantum gravity, the initial low entropy state of the Universe, and the problem of time are interlocking puzzles. In this article, we address the origin of the arrow of time from a cosmological perspective motivated by a novel approach to quantum gravitation. Our proposal is based on a quantum counterpart of the equivalence principle, a general covariance of the dynamical phase space. We discus...

In light of research indicating that individual behavior may violate standard rationality assumptions, we introduce a model of preference aggregation in which neither individual nor collective preferences must satisfy transitivity or other coherence conditions. We introduce an ordinal rationality measure to compare preference relations in terms of their level of coherence. Using this measure, w...

This article formalizes two proofs of Arrow’s impossibility theorem due to Geanakoplos and derives the Gibbard-Satterthwaite theorem as a corollary. One formalization is based on utility functions, the other one on strict partial orders. For an article about these proofs see http://www.in.tum.de/∼nipkow/pubs/

An unresolved problem in physics is how the thermodynamic arrow of time arises from an underlying time reversible dynamics. We contribute to this issue by developing a measure of time-symmetry breaking, and by using the work fluctuation relations, we determine the time asymmetry of recent single molecule RNA unfolding experiments. We define time asymmetry as the Jensen-Shannon divergence betwee...

Arrow’s Impossibility Theorem states that any constitution which satisfies Independence of Irrelevant Alternatives (IIA) and Unanimity and is not a Dictator has to be non-transitive. In this paper we study quantitative versions of Arrow theorem. Consider n voters who vote independently at random, each following the uniform distribution over the 6 rankings of 3 alternatives. Arrow’s theorem impl...

The material was scraped off an arrow head removed from a wounded man. It was a moist earthy-looking material. An oleaginous resinous body was extracted which was soluble in alcohol (90 per cent.) and dilute acetic acid, also in ether and in chloroform, but insoluble in water. It gave the " croton oil reaction" on the tongue and in the pharynx. A little rubbed on the skin of forearm raised a cr...