Asymptotic normality and efficiency of the maximum likelihood estimator for the parameter of a ballistic random walk in a random environment

We consider a one-dimensional ballistic random walk evolving in a parametric independent and identically distributed random environment. We study the asymptotic properties of the maximum likelihood estimator of the parameter based on a single observation of the path till the time it reaches a distant site. We prove asymptotic normality for this consistent estimator as the distant site tends to infinity and establish that it achieves the Cramér-Rao bound. We also explore in a simulation setting the numerical behavior of asymptotic confidence regions for the parameter value.     

Conformal dimension and canonical splittings of hyperbolic groups

We prove a general criterion for a metric space to have conformal dimension one. The conditions are stated in terms of the existence of enough local cut points in the space. We then apply this criterion to the boundaries of hyperbolic groups and show an interesting relationship between conformal dimension and some canonical splittings of the group.     

Recent Emission Channeling Studies in Wide Band Gap Semiconductors

We present results of recent emission channeling experiments on the lattice location of implanted Fe and rare earths in wurtzite GaN and ZnO. In both cases the majority of implanted atoms are found on substitutional cation sites. The root mean square displacements from the ideal substitutional Ga and Zn sites are given and the stability of the Fe and rare earth lattice location against thermal annealing is discussed.     

Truthful mechanism design via correlated tree rounding

A powerful algorithmic technique for truthful mechanism design is the maximal-in-distributional-range (MIDR) paradigm. Unfortunately, many such algorithms use heavy algorithmic machinery, e.g., the ellipsoid method and (approximate) solution of convex programs. In this paper, we present a correlated rounding technique for designing mechanisms that are truthful in expectation. It is elementary and can be implemented quickly. The main property we rely on is that the domain offers fractional optimum solutions with a tree structure. In auctions based on the generalized assignment problem, each bidder has a publicly known knapsack constraint that captures the subsets of items that are of value to him. He has a private valuation for each item and strives to maximize the value of assigned items minus payment. For this domain we design a truthful 2-approximate MIDR mechanism for social welfare maximization. It avoids using the ellipsoid method or convex programming. In contrast to some previous work, our mechanism achieves exact truthfulness. In restricted-related scheduling with selfish machines, each job comes with a public weight, and it must be assigned to a machine from a public job-specific subset. Each machine has a private speed and strives to maximize payments minus workload of jobs assigned to it. Here we design a mechanism for makespan minimization. This is a single-parameter domain, but the approximation status of the optimization problem is similar to unrelated machine scheduling: The best known algorithm obtains a (non-truthful) 2-approximation for unrelated machines, and there is 1.5-hardness. Our mechanism matches this bound with a truthful 2-approximation.     

Differentiation of Isomeric Hydroxypyridine <Emphasis Type="Italic">N</Emphasis>-Oxides Using Metal Complexation and Electrospray Ionization Mass Spectrometry

Differentiation between two isomers of hydroxypyridine N-oxide according to the metal cation adducts generated by electrospray ionization (ESI) was investigated for different metal cations, namely Mg (II), Al (III), Ca (II), Sc (III), Fe (III), Co (II), Ni (II), Cu (II), Zn (II), Ga (III), besides the diatomic cation VO(IV). Protonated molecules of the isomeric hydroxypyridine N-oxides as well as the singly/doubly charged adducts formed from neutral or deprotonated ligands and a doubly/triply charged cation were produced in the gas phase using ESI, recording mass spectra with different metal ions for each isomer. While complex formation was successful for 2-hydroxypyridine N-oxide with trivalent ions, in the case of 3-hydroxypyridine N-oxide, only peaks related to the protonated molecule were present. On the other hand, divalent cations formed specific species for each isomer, giving characteristic spectra in every case. Hence, differentiation was possible irrespective of the metal cation utilized. In addition, quantum chemical calculations at the B3LYP/6-31 + G(d,p) level of theory were performed in order to gain insight into the different complexation of calcium(II) with the isomers of hydroxypyridine N-oxide. The relative stability in the gas phase of the neutral complexes of calcium made up of two ligands, as well as the singly charged and doubly charged complexes, was investigated. The results of these calculations improved the understanding of the differences observed in the mass spectra obtained for each isomer.     

Crystallization and characterization of an inflammatory lectin purified from the seeds of Dioclea wilsonii

DwL, a lectin extracted from the seeds of Dioclea wilsonii, is a metalloprotein with strong agglutinating activity against rabbit and ABO erythrocytes, inhibited by glucose and mannose. DwL was purified by affinity chromatography on a Sephadex G-50 column and ion exchange chromatography on a HiTrap SP XL column. SDS-PAGE revealed three electrophoretic bands corresponding to the α (25,634 ± 2 Da), β (12,873 ± 2 Da) and γ (12,779 ± 2 Da) chains. Protein sequencing was done by Tandem Mass Spectrometry. The primary sequence featured 237 amino acids and was highly homologous to other reported Diocleinae lectins. A complete X-ray dataset was collected at 2.0 ? for X-Man-complexed DWL crystals produced by the vapor diffusion method. The crystals were orthorhombic and belonged to the space group I222, with the unit-cell parameters a = 59.6, b = 67.9 and c = 109.0 ?. DWL differed in potency from other ConA-like lectins and was found to induce neutrophil migration in rats, making it particularly useful in structural/functional studies of this class of proteins.     

Correlation between Luminescence and EPR Spectroscopy as Evidence of Ytterbium Pair Formation in Li6Ln(BO3)3:Yb3+ (Ln=Gd,Y) Borate Single Crystals

Synthesized powders and grown single crystals of nominal compositions Li₆Ln(BO₃)₃:Yb³⁺ (Ln=Y, Gd) were investigated by means of powder and single‐crystal X‐ray diffraction (XRD), as well as optical near‐IR spectroscopy in conjunction with electron paramagnetic resonance (EPR) spectroscopy. The appearance of two distinct zero‐phonon lines suggests the existence of two kinds of Yb³⁺ ions in the single crystals. The XRD results exclude the possibility of a phase transition occurring between room and low temperatures. EPR spectra of single crystals show the presence of both isolated ions and pairs of ytterbium ions substituted for Y³⁺. A strong temperature dependence of the intensity of Yb–Yb pairs resonance lines coincides with temperature dependence of emission peak at 978 nm, confirming a common origin of the defect giving rise to these spectra. Calculated from EPR spectra, the distance between pairs of Yb³⁺ is in good agreement with crystallographic ones: R=3.856 Å, R_cryst=3.849 Å.     

Attracting graphs of skew products with non-contracting fiber maps

We study attracting graphs of step skew products from the topological and ergodic points of view where the usual contracting-like assumptions of the fiber dynamics are replaced by weaker merely topological conditions. In this context, we prove the existence of an attracting invariant graph and study its topological properties. We prove the existence of globally attracting measures and we show that (in some specific cases) the rate of convergence to these measures is exponential.

     

The Tallest Column—A Dynamical System Approach Using a Symmetry Solution

A classic problem, the design of the tallest column, is solved again using a different method. By the use of a similarity solution the equations are transformed and the difficult singularity at the endpoint is peeled away. The resulting autonomous system has a critical point and the solution must be on its stable manifold. The solution is found by starting near the critical point in the direction of the stable manifold, and solving backward numerically. This removes the need for an iterative integration method that was previously used. The method is shown to work for clamped or hinged boundary condition and can also be used for other problems involving singularities at the endpoints.