Auctions with Severely Bounded Communication

We study auctions with severe bounds on the communication allowed: each bidder may only transmit t bits of information to the auctioneer. We consider both welfare- and profit-maximizing auctions under this communication restriction. For both measures, we determine the optimal auction and show that the loss incurred relative to unconstrained auctions is mild. We prove non-surprising properties of these kinds of auctions, e.g., that in optimal mechanisms bidders simply report the interval in which their valuation lies in, as well as some surprising properties, e.g., that asymmetric auctions are better than symmetric ones and that multi-round auctions reduce the communication complexity only by a linear factor

Inhomogeneity and transverse voltage in superconductors

Voltages parallel and transverse to electric current in slightly inhomogeneous superconductors can contain components proportional to the field and temperature derivatives of the longitudinal and Hall resistivities. We show that these anomalous contributions can be the origin of the zero field and even-in-field transverse voltage occasionally observed at the superconductor to normal state transition. The same mechanism can also cause an anomaly in the odd-in-field transverse voltage interfering the Hall effect signal.Comment: 6 pages, 7 figure

The Utility of Outpatient Commitment: I. A Need for Treatment and a Least Restrictive Alternative to Psychiatric Hospitalization.

ObjectivesThis study examined whether psychiatric patients assigned to community treatment orders (CTOs), outpatient commitment in Victoria, Australia, have a greater need for treatment to protect their health and safety than patients not assigned to CTOs. It also considered whether such treatment is provided in a least restrictive manner-that is, in a way that contributes to reduced use of psychiatric hospitalization.MethodsThe sample included 11,424 patients first placed on a CTO between 2000 and 2010, and 16,161 patients not placed on a CTO. Need for treatment was independently assessed with the Health of the Nation Outcome Scales (HoNOS) at hospital admission and at discharge. Ordinary least-squares and Poisson regressions were used to assess savings in hospital days attributable to CTO placement.ResultsHoNOS ratings indicated that at admission and discharge, the CTO cohort's need for treatment exceeded that of the non-CTO cohort, particularly in areas indicating potential dangerous behavior. When analyses adjusted for the propensity to be selected into the CTO cohort and other factors, the mean duration of an inpatient episode was 4.6 days shorter for the CTO cohort than for the non-CTO cohort, and a reduction of 10.4 days per inpatient episode was attributable to each CTO placement.ConclusionsCTO placement may have helped patients with a greater need for treatment to experience shorter hospital stays. Whether the CTO directly enabled the fulfillment of unsought but required treatment needs that protected patient health and safety is a question that needs to be addressed in future research

A Geometric Model of Arbitrary Spin Massive Particle

A new model of relativistic massive particle with arbitrary spin (($m,s$)-particle) is suggested. Configuration space of the model is a product of Minkowski space and two-dimensional sphere, ${\cal M}^6 = {\Bbb R}^{3,1} \times S^2$. The system describes Zitterbewegung at the classical level. Together with explicitly realized Poincar\'e symmetry, the action functional turns out to be invariant under two types of gauge transformations having their origin in the presence of two Abelian first-class constraints in the Hamilton formalism. These constraints correspond to strong conservation for the phase-space counterparts of the Casimir operators of the Poincar\'e group. Canonical quantization of the model leads to equations on the wave functions which prove to be equivalent to the relativistic wave equations for the massive spin-$s$ field.Comment: 25 pages; v2: eq. (45.b) correcte

Mathematics and German politics: The national socialist experience

AbstractDuring the Nazi period in Germany, an attempt was made to discern a kind of mathematics that was German as distinct from other ethnic or “racial” types of mathematics: a “Deutsche Mathematik.” While not denying the universal validity of all mathematical truths, such a “German” mathematics stressed ideology in terms of research and pedagogical styles. Because mathematics was nearly independent of anything material, it was—for the “Deutsche Mathematiker”—especially amenable to the Nazi argument that different racial psychological types exhibit different racial characters and modes of thought. This paper is a brief examination of the nature and intellectual content of “Deutsche Mathematik.