Loss of Ergodicity in the Transition from Annealed to Quenched Disorder in a Finite Kinetic Ising Model

We consider a kinetic Ising model which represents a generic agent-based model for various types of socio-economic systems. We study the case of a finite (and not necessarily large) number of agents N as well as the asymptotic case when the number of agents tends to infinity. The main ingredient are individual decision thresholds which are either fixed over time (corresponding to quenched disorder in the Ising model, leading to nonlinear deterministic dynamics which are generically non-ergodic) or which may change randomly over time (corresponding to annealed disorder, leading to ergodic dynamics). We address the question how increasing the strength of annealed disorder relative to quenched disorder drives the system from non-ergodic behavior to ergodicity. Mathematically rigorous analysis provides an explicit and detailed picture for arbitrary realizations of the quenched initial thresholds, revealing an intriguing “jumpy” transition from non-ergodicity with many absorbing sets to ergodicity. For large N we find a critical strength of annealed randomness, above which the system becomes asymptotically ergodic. Our theoretical results suggests how to drive a system from an undesired socio-economic equilibrium (e.g. high level of corruption) to a desirable one (low level of corruption).     

Localization for a Random Walk in Slowly Decreasing Random Potential

We consider a continuous time random walk X in a random environment on ?⁺ such that its potential can be approximated by the function V:?⁺→? given by $V(x)=\sigma W(x) -\frac {b}{1-\alpha}x^{1-\alpha}$ where σW a Brownian motion with diffusion coefficient σ>0 and parameters b, α are such that b>0 and 0<α<1/2. We show that P-a.s. (where P is the averaged law) $\lim_{t\to\infty} \frac{X_{t}}{(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}}=1$ with $C^{*}=\frac{2\alpha b}{\sigma^{2}(1-2\alpha)}$ . In fact, we prove that by showing that there is a trap located around $(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}$ (with corrections of smaller order) where the particle typically stays up to time t. This is in sharp contrast to what happens in the “pure” Sinai’s regime, where the location of this trap is random on the scale ln² t.     

Separating Characters by Blocks

We investigate the problem of finding a set of prime divisorsof the order of a finite group, such that no two irreduciblecharacters are in the same p-block for all primes p in the set.Our main focus is on the simple and quasi-simple groups. Forresults on the alternating and symmetric groups and their doublecovers, some combinatorial results on the cores of partitionsare proved, which may be of independent interest. We also studythe problem for groups of Lie type. The sporadic groups (andtheir relatives) are checked using GAP.     

Coexistence of Two Different Distorted Octahedral [MnF6]3− Sites in K3[MnF6]: Manifestation in Spectroscopy and Magnetism

As a consequence of the static Jahn-Teller effect of the ⁵E ground state of Mn^III in cubic structures with octahedral parent geometries, their octahedral coordination spheres become distorted. In the case of six fluorido ligands, [MnF₆]³⁻ anions with two longer and four shorter Mn−F bonds making elongated octahedra are usually observed. Herein, we report the synthesis of the compound K₃[MnF₆] through a high-temperature approach and its crystallization by a high-pressure/high-temperature route. The main structural motifs are two quasi-isolated, octahedron-like [MnF₆]³⁻ anions of quite different nature compared to that met in ideal octahedral Mn^III Jahn-Teller systems. Owing to the internal electric field of C_i symmetry dominated by the next-neighbour K⁺ ions acting on the Mn^III sites, both sites, the pseudo-rhombic (site 1) and the pseudo-tetragonally elongated (site 2) [MnF₆]³⁻ anions are present in K₃[MnF₆]. The compound was characterized by single-crystal and powder X-ray diffraction, and magnetometry as well as by FTIR, Raman, and ligand field spectroscopy. A theoretical interpretation of the electronic structure and molecular geometry of the two Mn sites in the lattice is given by using a vibronic coupling model with parameters adjusted from multireference ab-initio cluster calculations.     

Simultaneous extraction of organotin, organolead and organomercury species from soils and litter

Extracting organotin compounds (OTC) from soils is difficult due to the high cation exchange and complexation capacity of soils, and little information about OTC in soils is available. In this study, a new extraction method, combining 1 M CaCl₂, 0.1% tropolone, and glacial acetic acid was developed. Recoveries of mono-substituted OTC from spiked plant litter, and soil samples were improved substantially to 40% compared to classical glacial acetic acid extraction commonly used in sedimentology, yielding <10% recovery in C-rich soil samples. Simultaneously, the recovery of other OTC, trimethyllead and monomethylmercury was satisfactory. The recoveries of most species from the spiked litter, upland and wetland soils exceeded 70%. The new method extracted much more organometallics from unspiked organic soils and litter than microwave- and ultrasound-assisted extraction and accelerated solvent extraction, most likely due to exchange of organometallics from the solid phase by Ca²⁺. The method is simple, highly efficient and with low contamination. Together with GC-ICP-mass spectrometry, the method allows the detection of these organometallics in the pg g⁻¹ range and it is particularly suitable for soil and plant materials with low organometallics contents.     

Nucleotides. Part XLVIII. Synthesis of 2′-amino-2′-deoxyarabinonucleoside phosphoramidite building blocks

Chemical syntheses of 2′-amino-2′-deoxyarabinonucleosides of uracil, thymine, cytosine, adenine, and guanine and their conversion into suitably protected 3′-phosphoramidite building blocks 24–28 for oligonucleotide synthesis are described. The 2-(4-nitrophenyl)ethoxycarbonyl (npeoc) group was used for protection of the aglycon and the 2′-amino functions.     

Bayesian Object Identification: Variants

We present a Bayesian theory of object identification. Here, identifying an object means selecting a particular observation from a group of observations (variants), this observation (the regular variant) being characterized by a distributional model. In this sense, object identification means assigning a given model to one of several observations. Often, it is the statistical model of the regular variant, only, that is known. We study an estimator which relies essentially on this model and not on the characteristics of the “irregular” variants. In particular, we investigate under what conditions this variant selector is optimal. It turns out that there is a close relationship with exchangeability and Markovian reversibility. We finally apply our theory to the case of irregular variants generated from the regular variant by a Gaussian linear model.