Paula J. Dempsey is an engineer whose documented research concerns fault detection and monitoring of aerospace propulsion and drive systems. Her2010 author biography identifies her as an aerospace research engineer at NASA Glenn, with mechanical- and industrial-engineering training. Her published work connects physical damage observations with the reliability of measured fault indicators.^[ref]

With David G. Lewicki, Gregory F. Heath and Perumal Shanthakumaran, Dempsey coauthored an evaluation of gear surface pitting detection using24 gear sets. The study compared vibration-based indicators with debris measurements from the oil circuit and checked the signals against observed damage. It used receiver operating characteristic analysis to examine the tradeoff between detecting a fault and raising a false alarm.^[ref]

For an illustrative dataset, a threshold that detects19 of20 damaged cases and flags2 of80 healthy cases has detection fraction $19/20=0.95$ and false-alarm fraction $2/80=0.025$. Raising the threshold can change both fractions. These example numbers are not results from the paper: they explain why a large vibration signal alone does not establish the quality of a detector. Dempsey's coauthored study addressed that distinction through repeated physical tests, rather than treating an indicator value as a direct measurement of damage.

Gregory F. Heath is a mechanical engineer whose documented research includes rotorcraft transmissions and face gear technology. His2010 author biography describes him as an associate technical fellow at Boeing Rotorcraft-Mesa and a technical integrator for an advanced rotorcraft-drive program.^[ref]

Heath coauthored Development of Face Gear Technology for Industrial and Aerospace Power Transmission by Gregory F. Heath and others with Robert R. Filler and Jie Tan. Their2002 report documents a250-horsepower proof-of-concept split-torque transmission using concentric face gears. The tests examined whether floating input pinions could divide the load nearly evenly between parallel transmission paths.^[ref]

The mechanical question is more demanding than obtaining the desired gear ratio. If two parallel paths have unequal geometry or effective stiffness, one can carry more torque than intended. In an ideal equal-speed example, dividing a100N·m input into50N·m in each path also divides input power equally. A60/40N·m split preserves the total transmitted torque but raises the larger path's load20% above the intended50N·m share. A floating pinion supplies freedom intended to improve load balance; the report's apparatus and measurements tested how that mechanism behaved in a manufactured transmission.

Heath also coauthored the later gear-pitting detection study with Paula J. Dempsey, David G. Lewicki and Perumal Shanthakumaran, linking transmission development with experimental assessment of damage indicators.^[ref]

Perumal Shanthakumaran is an engineer whose documented work includes rotorcraft monitoring and condition-based maintenance. His2010 author biography identifies him as a technical fellow at Boeing Rotorcraft-Mesa, with training in aerospace engineering and mechanics/structures, and describes his leadership of helicopter condition-monitoring work at that time.^[ref]

Shanthakumaran coauthored the gear-pitting investigation with David G. Lewicki, Paula J. Dempsey and Gregory F. Heath. The work tested whether vibration and oil-debris indicators tracked observed gear surface pitting, rather than assuming that one indicator would work equally well for every damage pattern. The inspection history supplied a physical basis for judging detection performance.^[ref]

This is a practical problem in condition-based maintenance: a measured change must be related to component condition while accounting for changes in load, speed and the measurement path. For a simple linear measurement model, $X(\omega )=H(\omega )F(\omega )$, so a20% rise in vibration amplitude can result from a20% change in forcing at fixed frequency response, or from the response path changing at fixed forcing. It is not a unique measure of damage. Comparing a gear vibration spectrum with inspections and a different physical channel, such as metallic debris in the oil, makes the interpretation more testable. The coauthored study investigated those complementary channels in a controlled endurance-test dataset.

Robert R. Filler is a coauthor of experimental mechanical-engineering work on face gear transmissions. The2002 report with Gregory F. Heath and Jie Tan identifies all three with The Boeing Company in Mesa, Arizona. Their report documents design, manufacture and testing of a scaled250-horsepower proof-of-concept split-torque transmission.^[ref]

The experiment made load balance measurable. The input pinions were slow-rolled under torque supplied through weights, pulleys and cables, while tooth-root strain gauges recorded deformation associated with load. Measurement calibration was needed to convert those indications into an estimate of the torque division. The reported full two-pinion/two-idler configuration gave approximately48% and52% at the upper and lower input-pinion meshes.^[ref]

For an illustrative normalization to100N·m total input torque, those fractions correspond to48 and52N·m. The larger branch is4% above an ideal50N·m equal share, even though the two branches differ by4N·m. The distinction matters when comparing a measured torque split with the load intended for each path. Filler's documented contribution is as a coauthor of the experimental transmission study; the result depends on the complete tested arrangement.

Jie Tan coauthored Development of Face Gear Technology for Industrial and Aerospace Power Transmission by Gregory F. Heath and others with Gregory F. Heath and Robert R. Filler. Its2002 title page identifies Tan with The Boeing Company in Mesa, Arizona. The work investigated concentric face gears and floating pinions as a means of distributing transmitted torque between parallel paths.^[ref]

The report is useful because its apparatus revealed that different load divisions in one split-torque transmission need not agree. While input-pinion mesh division was close to48/52, the idlers were reported near57/43. The authors related the idler imbalance to how backlash had been set using strain indications, and discussed the limitations of inferring the split from those indications alone.^[ref]

In an illustrative100-unit load normalization, a57-unit path is14% above the intended50-unit equal share. A geometric gear ratio can remain correct despite that unequal internal loading. Tan's coauthored study therefore provides a concrete connection between transmission geometry, adjustment and experimentally inferred forces, rather than treating the desired speed ratio as a complete description of mechanical performance.

Sutton Monro coauthored the 1951 stochastic approximation paper with Herbert Robbins. The original title page verifies both full names and their joint contribution.^[ref]

The problem is to find where an unknown mean response $M(x)$ reaches a target $\alpha$ when only noisy observations are available. An update $x_{n+1}=x_n-a_n(Y_n-\alpha )$ moves according to the observed error. Positive step sizes with $\sum a_n=\infty$ and $\sum a_n^2<\infty$, together with suitable response and noise hypotheses, balance continued movement against accumulated noise. The method replaces exact root evaluation by a convergent statistical procedure.^[ref]

J. Gil-Pelaez authored the 1951 Note on the inversion theorem by J. Gil-Pelaez, giving a way to recover a distribution function from its characteristic function. The primary journal byline supplies the verified initials.^[ref]

The inversion integrates an oscillatory expression involving the characteristic function. At a discontinuity, the formula naturally returns the midpoint of the two one-sided distribution values. Keeping this convention explicit matters for discrete laws as well as continuous ones: an inversion formula is not automatically a pointwise identity at every jump.^[ref]

Itai Benjamini studies random geometric and combinatorial structures. His joint work with Russell Lyons, Yuval Peres and Oded Schramm investigates uniform spanning forests as limits of finite uniform spanning trees.^[ref]

On an infinite graph, a limiting forest need not be a single tree. Free and wired boundary conditions can lead to different laws. The paper relates this distinction and the number of connected components to random walks and harmonic functions, making infinite-volume geometry accessible through probabilistic tests.^[ref]

Russell Lyons studies probability theory on graphs. With Itai Benjamini, Yuval Peres and Oded Schramm, he developed the theory of uniform spanning forests on infinite graphs.^[ref]

Finite spanning-tree laws can approach different limits depending on whether the boundary is left free or wired together. Their work connects these limits with random walks, potential theory and harmonic functions. One result characterizes the number of wired-forest components through intersections of independent walks, showing that global connectivity is encoded in stochastic paths.^[ref]

Robert Burton coauthored the transfer-impedance analysis of uniform spanning trees with Robin Pemantle. Their original paper verifies this byline.^[ref]

The method computes probabilities for small collections of edges from determinants, even when the graph is large. The relevant matrix entries depend on global electrical information, so a small determinant does not mean the problem is entirely local. This distinction is essential in extending the calculations to infinite periodic graphs.^[ref]

Robin Pemantle studies probability theory and random combinatorial structures. With Robert Burton, he developed methods for computing local probabilities in uniform spanning trees using electrical transfer impedances.^[ref]

The probability that several specified edges occur is a determinant of a small transfer matrix. This avoids enumerating all trees and relates joint edge events to Green's functions and network currents. Their work also applies these methods to domino tilings and entropy.^[ref]

David Aldous studies probability theory and random combinatorial structures. His random-walk construction of a uniform spanning tree keeps the first-entrance edge for each newly visited vertex of a finite connected graph.^[ref]

Those edges necessarily form a tree, but their uniform distribution requires a separate argument. The construction permits properties of random trees—degrees, leaves and diameter—to be studied through random walks. Its running time is tied to the walk's cover time, giving a direct link between a stochastic exploration process and a combinatorial sampling algorithm.^[ref]

David Bruce Wilson developed an exact sampling algorithm for uniform spanning trees. Wilson's algorithm grows a tree by adding loop-erased random walks, each stopped on first reaching the tree already constructed.^[ref]

Erasing loops ensures that an added path creates no cycle. The more surprising assertion is distributional: the resulting tree is uniform among spanning trees, despite the sequential construction and the choice of starting vertices. The algorithm makes a global random combinatorial object accessible through local walk operations.^[ref]

Jason Miller (mathematician) studies random planar geometry, including Schramm–Loewner evolution, the Gaussian free field, Liouville quantum gravity and random planar maps. His Cambridge research profile verifies these interests.^[ref]

His Random Planar Geometry by Jason Miller (2020) develops discrete-to-continuum connections through trees, maps and random curves. The trivial bijection between planar maps and quadrangulations is a concrete example: vertices of one type encode original map vertices and the other type encodes faces. Recovering the map from this bipartition explains why the correspondence is reversible.^[ref]

Thomas S. Ferguson works on statistics, probability theory and game theory. His UCLA page documents research on statistical decisions, stopping problems and games.^[ref]

His 1973 paper introduced a Bayesian framework built on the Dirichlet process, a probability distribution over probability measures. If the prior parameter measure is $\alpha$, observing $x_1,\dots ,x_n$ changes it to $\alpha +{\sum }_i{\delta }_{x_i}$. This conjugate update extends the familiar idea of adding category counts to inference about an entire unknown distribution, providing a foundation for Bayesian nonparametric statistics.^[ref]

Radford M. Neal works on Bayesian inference, machine learning and computational methods for complex probability distributions. His research page lists neural networks, Gaussian processes and Markov chain Monte Carlo.^[ref]

His MCMC Using Hamiltonian Dynamics by Radford M. Neal develops Hamiltonian Monte Carlo: introduce auxiliary momenta, simulate approximately energy-preserving motion and correct discretization error with a Metropolis–Hastings algorithm. Longer, directed proposals can explore a target more effectively than a diffusive random walk. The combination of volume preservation, reversibility and an acceptance correction explains why an approximate numerical trajectory can still produce the intended invariant distribution.^[ref]

Giacomo Zanella develops methods in computational statistics, applied probability theory and machine learning, especially Bayesian computation. His research statement identifies Markov chain Monte Carlo, random measures and variable selection among these interests.^[ref]

With Gareth Roberts, he proposed the Tempered Gibbs sampler. A modified coordinate-selection rule can explore difficult high-dimensional targets more effectively; importance sampling weights then recover averages under the desired probability distribution. Their analysis includes applications to Bayesian variable selection.^[ref]

Gareth Roberts studies Markov chain Monte Carlo and the mathematical efficiency of Bayesian computation. With Giacomo Zanella, he developed importance tempering for high-dimensional sampling.^[ref]

Their Tempered Gibbs sampler changes how coordinates are selected. Its invariant law differs from the intended target, so importance sampling weights correct the averages. This trades easier movement through the state space against the variability of the correcting weights, with explicit theoretical comparisons to ordinary sampling methods.^[ref]

P. H. Peskun authored the 1973 paper underlying Peskun ordering, a comparison of the efficiency of Markov chain Monte Carlo algorithms with the same stationary target.^[ref]

For finite reversible Markov chains, increasing every off-diagonal transition probability while preserving the stationary law cannot increase the asymptotic variance of time averages. The comparison formalizes why spending less time repeating the current state can help statistical estimation, provided the ordering's hypotheses hold. It compares the variance of estimators, not merely their one-step acceptance rates.^[ref]

Steffen Rohde works where complex analysis meets probability theory. His University of Washington profile also identifies interests in numerical analysis.^[ref]

With Oded Schramm, he established basic geometric properties of Schramm–Loewner evolution, in which a Brownian motion drives a conformal growth equation. Their paper proves a change in path behavior with the parameter: simple curves for $0\le \kappa \le 4$, self-intersections for $4<\kappa <8$, and space-filling paths for $\kappa >8$. These regimes connect an analytic differential equation with the geometry of random interfaces.^[ref]