On the Stability of Stochastic Parametrically Forced Equations with Rank One Forcing

We derive simplified formulas for analyzing the stability of stochastic parametrically forced linear systems. This extends the results in [T. Blass and L.A. Romero, SIAM J. Control Optim. 51(2):1099--1127, 2013] where, assuming the stochastic excitation is small, the stability of such systems was computed using a weighted sum of the extended power spectral density over the eigenvalues of the unperturbed operator. In this paper, we show how to convert this to a sum over the residues of the extended power spectral density. For systems where the parametric forcing term is a rank one matrix, this leads to an enormous simplification.Comment: 16 page

On the length of chains of proper subgroups covering a topological group

We prove that if an ultrafilter L is not coherent to a Q-point, then each analytic non-sigma-bounded topological group G admits an increasing chain <G_a : a of its proper subgroups such that: (i) U_{a in b(L)} G_a=G; and $(ii)$ For every sigma-bounded subgroup H of G there exists a such that H is a subset of G_a. In case of the group Sym(w) of all permutations of w with the topology inherited from w^w this improves upon earlier results of S. Thomas

Sub-unit cell layer-by-layer growth of Fe3O4, MgO, and Sr2RuO4 thin films

The use of oxide materials in oxide electronics requires their controlled epitaxial growth. Recently, it was shown that Reflection High Energy Electron Diffraction (RHEED) allows to monitor the growth of oxide thin films even at high oxygen pressure. Here, we report the sub-unit cell molecular or block layer growth of the oxide materials Sr2RuO4, MgO, and magnetite using Pulsed Laser Deposition (PLD) from stoichiometric targets. Whereas for perovskites such as SrTiO3 or doped LaMnO3 a single RHEED intensity oscillation is found to correspond to the growth of a single unit cell, in materials where the unit cell is composed of several molecular layers or blocks with identical stoichiometry, a sub-unit cell molecular or block layer growth is established resulting in several RHEED intensity oscillations during the growth of a single unit-cell

Concurrent abstract state machines

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The Generic Model of Computation

Over the past two decades, Yuri Gurevich and his colleagues have formulated axiomatic foundations for the notion of algorithm, be it classical, interactive, or parallel, and formalized them in the new generic framework of abstract state machines. This approach has recently been extended to suggest a formalization of the notion of effective computation over arbitrary countable domains. The central notions are summarized herein.Comment: In Proceedings DCM 2011, arXiv:1207.682

Manipulating Entitativity Affects Implicit Behavioral and Neural Attentional Biases Toward Gay Couples

This study investigated whether attentional bias toward homosexual couples differs as a function of the manipulation of perceived entitativity, the degree to which group members are perceived to share common values and pursue common goals. Across two experiments, heterosexual college students were randomly assigned to read statements that suggested that homosexual and heterosexual couples were either high or low in entitativity. Following this task, 199 participants completed a dot probe task in Experiment 1 and electroencephalogram (EEG) activity was recorded for 74 participants in Experiment 2 to measure the implicit attentional processing that resulted from viewing pictures of gay, lesbian, and straight couples. Results indicated that participants exposed to low entitativity statements directed less behavioral and neural attention toward gay relative to straight couples compared to those exposed to high entitativity statements. Given the apparent malleability of attentional biases, future research should strive to better understand the factors involved in reducing attentional bias, and by extension, discriminatory behaviors toward minority groups

Concurrent Computing with Shared Replicated Memory

The behavioural theory of concurrent systems states that any concurrent system can be captured by a behaviourally equivalent concurrent Abstract State Machine (cASM). While the theory in general assumes shared locations, it remains valid, if different agents can only interact via messages, i.e. sharing is restricted to mailboxes. There may even be a strict separation between memory managing agents and other agents that can only access the shared memory by sending query and update requests to the memory agents. This article is dedicated to an investigation of replicated data that is maintained by a memory management subsystem, whereas the replication neither appears in the requests nor in the corresponding answers. We show how the behaviour of a concurrent system with such a memory management can be specified using concurrent communicating ASMs. We provide several refinements of a high-level ground model addressing different replication policies and internal messaging between data centres. For all these refinements we analyse their effects on the runs such that decisions concerning the degree of consistency can be consciously made.Comment: 23 page

Semantics and Proof Theory of the Epsilon Calculus

The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. The application of this undervalued formalism has been hampered by the absence of well-behaved proof systems on the one hand, and accessible presentations of its theory on the other. One significant early result for the original axiomatic proof system for the epsilon-calculus is the first epsilon theorem, for which a proof is sketched. The system itself is discussed, also relative to possible semantic interpretations. The problems facing the development of proof-theoretically well-behaved systems are outlined.Comment: arXiv admin note: substantial text overlap with arXiv:1411.362

The Epsilon Calculus and Herbrand Complexity

Hilbert's epsilon-calculus is based on an extension of the language of predicate logic by a term-forming operator $\epsilon_{x}$. Two fundamental results about the epsilon-calculus, the first and second epsilon theorem, play a role similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential theorems obtained by this elimination procedure.Comment: 23 p

Hypernatural Numbers as Ultrafilters

In this paper we present a use of nonstandard methods in the theory of ultrafilters and in related applications to combinatorics of numbers