On the involution fixity of exceptional groups of Lie type

The involution fixity ${\rm ifix}(G)$ of a permutation group $G$ of degree $n$ is the maximum number of fixed points of an involution. In this paper we study the involution fixity of primitive almost simple exceptional groups of Lie type. We show that if $T$ is the socle of such a group, then either ${\rm ifix}(T) > n^{1/3}$, or ${\rm ifix}(T) = 1$ and $T = {}^2B_2(q)$ is a Suzuki group in its natural $2$-transitive action of degree $n=q^2+1$. This bound is best possible and we present more detailed results for each family of exceptional groups, which allows us to determine the groups with ${\rm ifix}(T) \leqslant n^{4/9}$. This extends recent work of Liebeck and Shalev, who established the bound ${\rm ifix}(T) > n^{1/6}$ for every almost simple primitive group of degree $n$ with socle $T$ (with a prescribed list of exceptions). Finally, by combining our results with the Lang-Weil estimates from algebraic geometry, we determine bounds on a natural analogue of involution fixity for primitive actions of exceptional algebraic groups over algebraically closed fields.Comment: 45 pages; to appear in Int. J. Algebra Compu

Preparing Digital Natives to Teach: Time to Redesign Teacher Education Programs

Since the emergence of Marc Prensky\u27s concept of Digital Natives being taught by Digital Immigrants, education\u27s challenge has been to find a way to effectively teach those who have grown up in a net generation. Now that the first of these millenniel students are preparing to become teachers themselves, we have the opportunity, perhaps for the first time, to witness true digital natives teaching their own. This article will examine the paradigm shift required of teacher education programs if they are to prepare this digital teaching generation effectively for the educational challenge that lies ahead of them

Synthesis, X-ray Structures, Electronic Properties, and O\u3csub\u3e2\u3c/sub\u3e/NO Reactivities of Thiol Dioxygenase Active-Site Models

Mononuclear non-heme iron complexes that serve as structural and functional mimics of the thiol dioxygenases (TDOs), cysteine dioxygenase (CDO) and cysteamine dioxygenase (ADO), have been prepared and characterized with crystallographic, spectroscopic, kinetic, and computational methods. The high-spin Fe(II) complexes feature the facially coordinating tris(4,5-diphenyl-1-methylimidazol-2-yl)phosphine (Ph2TIP) ligand that replicates the three histidine (3His) triad of the TDO active sites. Further coordination with bidentate l-cysteine ethyl ester (CysOEt) or cysteamine (CysAm) anions yielded five-coordinate (5C) complexes that resemble the substrate-bound forms of CDO and ADO, respectively. Detailed electronic-structure descriptions of the [Fe(Ph2TIP)(LS,N)]BPh4 complexes, where LS,N = CysOEt (1) or CysAm (2), were generated through a combination of spectroscopic techniques [electronic absorption, magnetic circular dichroism (MCD)] and density functional theory (DFT). Complexes 1 and 2 decompose in the presence of O2 to yield the corresponding sulfinic acid (RSO2H) products, thereby emulating the reactivity of the TDO enzymes and related complexes. Rate constants and activation parameters for the dioxygenation reactions were measured and interpreted with the aid of DFT calculations for O2-bound intermediates. Treatment of the TDO models with nitric oxide (NO)—a well-established surrogate of O2—led to a mixture of high-spin and low-spin {FeNO}7 species at low temperature (−70 °C), as indicated by electron paramagnetic resonance (EPR) spectroscopy. At room temperature, these Fe/NO adducts convert to a common species with EPR and infrared (IR) features typical of cationic dinitrosyl iron complexes (DNICs). To complement these results, parallel spectroscopic, computational, and O2/NO reactivity studies were carried out using previously reported TDO models that feature an anionic hydrotris(3-phenyl-5-methyl-pyrazolyl)borate (Ph,MeTp–) ligand. Though the O2 reactivities of the Ph2TIP- and Ph,MeTp-based complexes are quite similar, the supporting ligand perturbs the energies of Fe 3d-based molecular orbitals and modulates Fe–S bond covalency, suggesting possible rationales for the presence of neutral 3His coordination in CDO and ADO

Target search on a dynamic DNA molecule

We study a protein-DNA target search model with explicit DNA dynamics applicable to in vitro experiments. We show that the DNA dynamics plays a crucial role for the effectiveness of protein "jumps" between sites distant along the DNA contour but close in 3D space. A strongly binding protein that searches by 1D sliding and jumping alone, explores the search space less redundantly when the DNA dynamics is fast on the timescale of protein jumps than in the opposite "frozen DNA" limit. We characterize the crossover between these limits using simulations and scaling theory. We also rationalize the slow exploration in the frozen limit as a subtle interplay between long jumps and long trapping times of the protein in "islands" within random DNA configurations in solution.Comment: manuscript and supplementary material combined into a single documen

A Power Variance Test for Nonstationarity in Complex-Valued Signals

We propose a novel algorithm for testing the hypothesis of nonstationarity in complex-valued signals. The implementation uses both the bootstrap and the Fast Fourier Transform such that the algorithm can be efficiently implemented in O(NlogN) time, where N is the length of the observed signal. The test procedure examines the second-order structure and contrasts the observed power variance - i.e. the variability of the instantaneous variance over time - with the expected characteristics of stationary signals generated via the bootstrap method. Our algorithmic procedure is capable of learning different types of nonstationarity, such as jumps or strong sinusoidal components. We illustrate the utility of our test and algorithm through application to turbulent flow data from fluid dynamics

A note on extremely primitive affine groups

Let G be a nite primitive permutation group on a set with nontrivial point stabilizer G . We say that G is extremely primitive if G acts primitively on each of its orbits in n f g. In earlier work, Mann, Praeger and Seress have proved that every extremely primitive group is either almost simple or of a ne type and they have classi ed the a ne groups up to the possibility of at most nitely many exceptions. More recently, the almost simple extremely primitive groups have been completely determined. If one assumes Wall's conjecture on the number of maximal subgroups of almost simple groups, then the results of Mann et al. show that it just remains to eliminate an explicit list of a ne groups in order to complete the classi cation of the extremely primitive groups. Mann et al. have conjectured that none of these a ne candidates are extremely primitive and our main result con rms this conjecture