Marshall's lemma for convex density estimation

Marshall's [Nonparametric Techniques in Statistical Inference (1970) 174--176] lemma is an analytical result which implies $\sqrt{n}$--consistency of the distribution function corresponding to the Grenander [Skand. Aktuarietidskr. 39 (1956) 125--153] estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on $[0,\infty)$.Comment: Published at http://dx.doi.org/10.1214/074921707000000292 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Limit distribution theory for maximum likelihood estimation of a log-concave density

We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, that is, a density of the form $f_0=\exp\varphi_0$ where $\varphi_0$ is a concave function on $\mathbb{R}$. The pointwise limiting distributions depend on the second and third derivatives at 0 of $H_k$, the "lower invelope" of an integrated Brownian motion process minus a drift term depending on the number of vanishing derivatives of $\varphi_0=\log f_0$ at the point of interest. We also establish the limiting distribution of the resulting estimator of the mode $M(f_0)$ and establish a new local asymptotic minimax lower bound which shows the optimality of our mode estimator in terms of both rate of convergence and dependence of constants on population values.Comment: Published in at http://dx.doi.org/10.1214/08-AOS609 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Preliminary Survey of the Terrestrial Isopods (Isopoda), Millipedes (Diplopoda), Harvestmen (Opiliones), and Spiders (Araneae) of Toft Point Natural Area, Door County, Wisconsin

Toft Point Natural Area is a National Natural Landmark owned and managed by the University of Wisconsin – Green Bay and located on the Lake Michigan shore of Wisconsin’s Door Peninsula. With twelve biotic communities on 700 acres, Toft Point contains considerable biological diversity. We conducted a preliminary survey of the arachnids (spiders and harvestmen, excluding mites and pseudoscorpions), millipedes (diplopods), and terrestrial isopods (Isopoda: Oniscoidea). Sampling occurred on three dates in 2001 using leaf litter collection with Berlese extraction and a timed collection by hand that incorporated a variety of techniques. Specimens from a 1992 survey and assorted collecting events were also used to compile a species list. The list includes five isopods, four millipedes, six harvestmen, and 113 spiders, including 16 new state records (two millipedes and 14 spiders) and 90 new Door County records. Litter collection and sampling in wetland habitats were both especially productive

Optimal time-dependent lattice models for nonequilibrium dynamics

Lattice models are abundant in theoretical and condensed-matter physics. Generally, lattice models contain time-independent hopping and interaction parameters that are derived from the Wannier functions of the noninteracting problem. Here, we present a new concept based on time-dependent Wannier functions and the variational principle that leads to optimal time-dependent lattice models. As an application, we use the Bose-Hubbard model with time-dependent Wannier functions to study a quench scenario involving higher bands. We find a separation of times scales in the dynamics and show that under some circumstances the multi-band nonequilibrium dynamics of a quantum system can be obtained essentially at the cost of a single-band model.Comment: 14 pages, 3 figure

Precision Stellar Characterization of FGKM Stars using an Empirical Spectral Library

Classification of stars, by comparing their optical spectra to a few dozen spectral standards, has been a workhorse of observational astronomy for more than a century. Here, we extend this technique by compiling a library of optical spectra of 404 touchstone stars observed with Keck/HIRES by the California Planet Search. The spectra have high resolution (R ≈ 60,000), high signal-to-noise ratio (S/N ≈ 150/pixel), and are registered onto a common wavelength scale. The library stars have properties derived from interferometry, asteroseismology, LTE spectral synthesis, and spectrophotometry. To address a lack of well-characterized late-K dwarfs in the literature, we measure stellar radii and temperatures for 23 nearby K dwarfs, using modeling of the spectral energy distribution and Gaia parallaxes. This library represents a uniform data set spanning the spectral types ~M5–F1 (T_(eff) ≈ 3000–7000 K, R_★ ≈ 0.1–16 R ⊙). We also present "Empirical SpecMatch" (SpecMatch-Emp), a tool for parameterizing unknown spectra by comparing them against our spectral library. For FGKM stars, SpecMatch-Emp achieves accuracies of 100 K in effective temperature (T_(eff)), 15% in stellar radius (R_★), and 0.09 dex in metallicity ([Fe/H]). Because the code relies on empirical spectra it performs particularly well for stars ~K4 and later, which are challenging to model with existing spectral synthesizers, reaching accuracies of 70 K in T_(eff), 10% in R_★, and 0.12 dex in [Fe/H]. We also validate the performance of SpecMatch-Emp, finding it to be robust at lower spectral resolution and S/N, enabling the characterization of faint late-type stars. Both the library and stellar characterization code are publicly available

Dispersion strengthening in vanadium microalloyed steels processed by simulated thin slab casting and direct charging. Part 2 - chemical characterisation of dispersion strengthening precipitates

The composition of the sub-15 nm particles in six related vanadium high strength low alloy steels, made by simulated thin slab direct charged casting, has been determined using electron energy loss spectroscopy (EELS). Such particles are considered to be responsible for dispersion hardening. For the first time, particles down to 4 nm in size have had their composition fully determined. In all the steels, the particles were nitrogen and vanadium rich and possibly slightly sub-stoichiometric carbonitrides. Equilibrium thermodynamics predicted much higher carbon to metal atomic ratios than observed in all cases so that kinetics and mechanical deformation clearly control the precipitation process. Thus it is important to formulate the steel with this in mind

Coagglutination and Enzyme Capture Tests for Detection of \u3ci\u3eEscherichia coli\u3c/i\u3e β-Galactosidase, β-Glucuronidase, and Glutamate Decarboxylase

Polyclonal antibodies to Escherichia coli β-galactosidase, β-glucuronidase, and glutamate decarboxylase were used in coagglutination tests for identification of these three enzymes in cell lysates. Enzyme capture assays were also developed for the detection of E. coli β-galactosidase and β-glucuronidase. The enzymes were released by using a gentle lysis procedure that did not interfere with antibody-enzyme interactions. All three enzymes were detected in 93% (51 of 55) of the E. coli strains tested by coagglutination; two of the three enzymes were identified in the remaining 7%. Of 42 non-E. coli tested by coagglutination, only four nonspecifically agglutinated either two or three of the anti-enzyme conjugates. Thirty-two (76%) non-E. coli isolates were negative by coagglutination for all three enzymes. The enzyme capture assay detected the presence of β-galactosidase in seven of eight and β-glucuronidase in all eight strains of E. coli tested. Some strains of β-galactosidase-positive Citrobacterfreundii and Enterobacter cloacae were also positive by the enzyme capture assay, indicating that the antibodies were not entirely specific for E. coli β-galactosidase; however, five other gas-positive non-E. coli isolates were negative by the enzyme capture assay. The coagglutination tests and enzyme capture assays were rapid and sensitive methods for the detection of E. coli ,β-galactosidase, β-glucuronidase, and glutamate decarboxylase