Non-equilibrium dynamics of stochastic point processes with refractoriness

Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse, and the counting of particles by detector devices. Here we present an extension of renewal theory to describe ensembles of point processes with time varying input. This is made possible by a representation in terms of occupation numbers of two states: Active and refractory. The dynamics of these occupation numbers follows a distributed delay differential equation. In particular, our theory enables us to uncover the effect of refractoriness on the time-dependent rate of an ensemble of encoding point processes in response to modulation of the input. We present exact solutions that demonstrate generic features, such as stochastic transients and oscillations in the step response as well as resonances, phase jumps and frequency doubling in the transfer of periodic signals. We show that a large class of renewal processes can indeed be regarded as special cases of the model we analyze. Hence our approach represents a widely applicable framework to define and analyze non-stationary renewal processes.Comment: 8 pages, 4 figure

Structure, Stability, and Origin of (2×n) Phases on Si(100)

Phases with (2×n) structure (6<n<10) can be formed on Si(100) by rapid quenching from high temperatures. The nominal (2×7) phase has been investigated by high-resolution low-energy electron diffraction. The structure involves two atomic levels, is metastable, and decays with first-order kinetics. The structure can be explained by ordering of excess missing-dimer defects, which apparently are present on the surface with any of the standard surface preparation techniques for Si(100)

Quantitative Determination of Temperature in the Approach to Magnetic Order of Ultracold Fermions in an Optical Lattice

We perform a quantitative simulation of the repulsive Fermi-Hubbard model using an ultracold gas trapped in an optical lattice. The entropy of the system is determined by comparing accurate measurements of the equilibrium double occupancy with theoretical calculations over a wide range of parameters. We demonstrate the applicability of both high-temperature series and dynamical mean-field theory to obtain quantitative agreement with the experimental data. The reliability of the entropy determination is confirmed by a comprehensive analysis of all systematic errors. In the center of the Mott insulating cloud we obtain an entropy per atom as low as 0.77k(B) which is about twice as large as the entropy at the Neel transition. The corresponding temperature depends on the atom number and for small fillings reaches values on the order of the tunneling energy

Surface Geometry of C60 on Ag(111)

The geometry of adsorbed C60 influences its collective properties. We report the first dynamical low-energy electron diffraction study to determine the geometry of a C60 monolayer, Ag(111)-(23×23)30°-C60, and related density functional theory calculations. The stable monolayer has C60 molecules in vacancies that result from the displacement of surface atoms. C60 bonds with hexagons down, with their mirror planes parallel to that of the substrate. The results indicate that vacancy structures are the rule rather than the exception for C60 monolayers on close-packed metal surfaces. © 2009 The American Physical Society

Maximal length of trapped one-dimensional Bose-Einstein condensates

I discuss a Bogoliubov inequality for obtaining a rigorous bound on the maximal axial extension of inhomogeneous one-dimensional Bose-Einstein condensates. An explicit upper limit for the aspect ratio of a strongly elongated, harmonically trapped Thomas-Fermi condensate is derived.Comment: 6 pages; contributed paper for Quantum Fluids and Solids, Trento 2004, to appear in JLT

Evolutionary biology for the 21st century

New theoretical and conceptual frameworks are required for evolutionary biology to capitalize on the wealth of data now becoming available from the study of genomes, phenotypes, and organisms - including humans - in their natural environments.Molecular and Cellular BiologyOrganismic and Evolutionary Biolog

Alemtuzumab pre-conditioning with tacrolimus monotherapy in pediatric renal transplantation

We employed antibody pre-conditioning with alemtuzumab and posttransplant immunosuppression with low-dose tacrolimus monotherapy in 26 consecutive pediatric kidney transplant recipients between January 2004 and December 2005. Mean recipient age was 10.7 ± 5.8 years, 7.7% were undergoing retransplantation, and 3.8% were sensitized, with a PRA >20%. Mean donor age was 32.8 ± 9.2 years. Living donors were utilized in 65% of the transplants. Mean cold ischemia time was 27.6 ± 6.4 h. The mean number of HLA mismatches was 3.3 ± 1.3. Mean follow-up was 25 ± 8 months. One and 2 year patient survival was 100% and 96%. One and 2 year graft survival was 96% and 88%. Mean serum creatinine was 1.1 ± 0.6 mg/dL, and calculated creatinine clearance was 82.3 ± 29.4 mL/min/1.73 m 2. The incidence of pre-weaning acute rejection was 11.5%; the incidence of delayed graft function was 7.7%. Eighteen (69%) of the children were tapered to spaced tacrolimus monotherapy, 10.5 ± 2.2 months after transplantation. The incidence of CMV, PTLD and BK virus was 0%; the incidence of posttransplant diabetes was 7.7%. Although more follow-up is clearly needed, antibody pre-conditioning with alemtuzumab and tacrolimus monotherapy may be a safe and effective regimen in pediatric renal transplantation. © 2007 The Authors

Inelastic chaotic scattering on a Bose-Einstein condensate

We devise a microscopic scattering approach to probe the excitation spectrum of a Bose-Einstein condensate. We show that the experimentally accessible scattering cross section exhibits universal Ericson fluctuations, with characteristic properties rooted in the underlying classical field equations.Comment: 11 pages, 5 figure

50 Years of Test (Un)fairness: Lessons for Machine Learning

Quantitative definitions of what is unfair and what is fair have been introduced in multiple disciplines for well over 50 years, including in education, hiring, and machine learning. We trace how the notion of fairness has been defined within the testing communities of education and hiring over the past half century, exploring the cultural and social context in which different fairness definitions have emerged. In some cases, earlier definitions of fairness are similar or identical to definitions of fairness in current machine learning research, and foreshadow current formal work. In other cases, insights into what fairness means and how to measure it have largely gone overlooked. We compare past and current notions of fairness along several dimensions, including the fairness criteria, the focus of the criteria (e.g., a test, a model, or its use), the relationship of fairness to individuals, groups, and subgroups, and the mathematical method for measuring fairness (e.g., classification, regression). This work points the way towards future research and measurement of (un)fairness that builds from our modern understanding of fairness while incorporating insights from the past.Comment: FAT* '19: Conference on Fairness, Accountability, and Transparency (FAT* '19), January 29--31, 2019, Atlanta, GA, US