Michael S. Mahoney, 1939–2008

Perhaps the clearest testimony to the scholarly range and depth of Princeton's now‐lamented Michael S. Mahoney lies in the dismay of his colleagues in the last few years, as they contemplated his imminent retirement. How to maintain coverage of his fields? Fretting over this question, the program in history of science that he did so much to build recently found itself sketching a five-year plan that involved replacing him with no fewer than four new appointments: a historian of mathematics with the ability to handle the course on Greek antiquity, a historian of the core problems of the Scientific Revolution, a historian of technology who could cover the nineteenth‐century United States and Britain, and, finally, a historian of the computer-and-media revolution. In his passing we have lost a small department

The brainstem reticular formation is a small-world, not scale-free, network

Recently, it has been demonstrated that several complex systems may have simple graph-theoretic characterizations as so-called ‘small-world’ and ‘scale-free’ networks. These networks have also been applied to the gross neural connectivity between primate cortical areas and the nervous system of Caenorhabditis elegans. Here, we extend this work to a specific neural circuit of the vertebrate brain—the medial reticular formation (RF) of the brainstem—and, in doing so, we have made three key contributions. First, this work constitutes the first model (and quantitative review) of this important brain structure for over three decades. Second, we have developed the first graph-theoretic analysis of vertebrate brain connectivity at the neural network level. Third, we propose simple metrics to quantitatively assess the extent to which the networks studied are small-world or scale-free. We conclude that the medial RF is configured to create small-world (implying coherent rapid-processing capabilities), but not scale-free, type networks under assumptions which are amenable to quantitative measurement

A General, Practical Palladium-Catalyzed Cyanation of (Hetero)Aryl Chlorides and Bromides

Playing it safe: The nontoxic cyanide source K[subscript 4][Fe(CN)[subscript 6]⋅3 H[subscript 2]O can be used for the cyanation of (hetero)aryl halides. The application of palladacycle catalysts prevents poisoning during catalyst formation, thereby allowing for low catalyst loadings, fast reaction times, and wide heterocyclic substrate scope.National Institutes of Health (U.S.) (Award GM46059

A SPIRED\texttt{SPIRED} code for the reconstruction of spin distribution

In Nuclear Magnetic Resonance (NMR), it is of crucial importance to have an accurate knowledge of the sample probability distribution corresponding to inhomogeneities of the magnetic fields. An accurate identification of the sample distribution requires a set of experimental data that is sufficiently rich to extract all fundamental information. These data depend strongly on the control fields (and their number) used experimentally. In this work, we present and analyze a greedy reconstruction algorithm, and provide the corresponding $\texttt{SPIRED}$ code, for the computation of a set of control functions allowing the generation of data that are appropriate for the accurate reconstruction of a sample distribution. In particular, the focus is on NMR and the Bloch system with inhomogeneities in the magnetic fields in all spatial directions. Numerical examples illustrate this general study.Comment: 31 pages, 6 figure

A space-time hybrid hourly rainfall model for derived flood frequency analysis

For derived flood frequency analysis based on hydrological modelling long continuous precipitation time series with high temporal resolution are needed. Often, the observation network with recording rainfall gauges is poor, especially regarding the limited length of the available rainfall time series. Stochastic precipitation synthesis is a good alternative either to extend or to regionalise rainfall series to provide adequate input for long-term rainfall-runoff modelling with subsequent estimation of design floods. Here, a new two step procedure for stochastic synthesis of continuous hourly space-time rainfall is proposed and tested for the extension of short observed precipitation time series. First, a single-site alternating renewal model is presented to simulate independent hourly precipitation time series for several locations. The alternating renewal model describes wet spell durations, dry spell durations and wet spell intensities using univariate frequency distributions separately for two seasons. The dependence between wet spell intensity and duration is accounted for by 2-copulas. For disaggregation of the wet spells into hourly intensities a predefined profile is used. In the second step a multi-site resampling procedure is applied on the synthetic point rainfall event series to reproduce the spatial dependence structure of rainfall. Resampling is carried out successively on all synthetic event series using simulated annealing with an objective function considering three bivariate spatial rainfall characteristics. In a case study synthetic precipitation is generated for some locations with short observation records in two mesoscale catchments of the Bode river basin located in northern Germany. The synthetic rainfall data are then applied for derived flood frequency analysis using the hydrological model HEC-HMS. The results show good performance in reproducing average and extreme rainfall characteristics as well as in reproducing observed flood frequencies. The presented model has the potential to be used for ungauged locations through regionalisation of the model parameters.BMBF/FKZ:033068

Absence of a consistent classical equation of motion for a mass-renormalized point charge

The restrictions of analyticity, relativistic (Born) rigidity, and negligible O(a) terms involved in the evaluation of the self electromagnetic force on an extended charged sphere of radius "a" are explicitly revealed and taken into account in order to obtain a classical equation of motion of the extended charge that is both causal and conserves momentum-energy. Because the power-series expansion used in the evaluation of the self force becomes invalid during transition time intervals immediately following the application and termination of an otherwise analytic externally applied force, transition forces must be included during these transition time intervals to remove the noncausal pre-acceleration and pre-deceleration from the solutions to the equation of motion without the transition forces. For the extended charged sphere, the transition forces can be chosen to maintain conservation of momentum-energy in the causal solutions to the equation of motion within the restrictions of relativistic rigidity and negligible O(a) terms under which the equation of motion is derived. However, it is shown that renormalization of the electrostatic mass to a finite value as the radius of the charge approaches zero introduces a violation of momentum-energy conservation into the causal solutions to the equation of motion of the point charge if the magnitude of the external force becomes too large. That is, the causal classical equation of motion of a point charge with renormalized mass experiences a high acceleration catastrophe.Comment: 13 pages, No figure

Descartes, corpuscles and reductionism : mechanism and systems in Descartes' physiology

I argue that Descartes explains physiology in terms of whole systems, and not in terms of the size, shape and motion of tiny corpuscles (corpuscular mechanics). It is a standard, entrenched view that Descartes’s proper means of explanation in the natural world is through strict reduction to corpuscular mechanics. This view is bolstered by a handful of corpuscular-mechanical explanations in Descartes’s physics, which have been taken to be representative of his treatment of all natural phenomena. However, Descartes’s explanations of the ‘principal parts’ of physiology do not follow the corpuscular–mechanical pattern. Des Chene (2001) has identified systems in Descartes’s account of physiology, but takes them ultimately to reduce down to the corpuscle level. I argue that they do not. Rather, Descartes maintains entire systems, with components selected from multiple levels of organisation, in order to construct more complete explanations than corpuscular mechanics alone would allow

Atom chips on direct bonded copper substrates

We present the use of direct bonded copper (DBC) for the straightforward fabrication of high power atom chips. Atom chips using DBC have several benefits: excellent copper/substrate adhesion, high purity, thick (> 100 microns) copper layers, high substrate thermal conductivity, high aspect ratio wires, the potential for rapid (< 8 hr) fabrication, and three dimensional atom chip structures. Two mask options for DBC atom chip fabrication are presented, as well as two methods for etching wire patterns into the copper layer. The wire aspect ratio that optimizes the magnetic field gradient as a function of power dissipation is determined to be 0.84:1 (height:width). The optimal wire thickness as a function of magnetic trapping height is also determined. A test chip, able to support 100 A of current for 2 s without failing, is used to determine the thermal impedance of the DBC. An assembly using two DBC atom chips to provide magnetic confinement is also shown.Comment: 8 pages, 5 figure