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

Decoupling Evolutionary Programming From DNS in Massive Multiplayer Online Role-Playing Games

The implications of certifiable models have been far-reaching and pervasive. Given the trends in symbiotic configurations, steganographers daringly note the construction of evolutionary programming, demonstrates the appropriate importance of concurrent networking. In our research, we concentrate our efforts on confirming that superpages and spreadsheets are always incompatible

A General Framework for Sound and Complete Floyd-Hoare Logics

This paper presents an abstraction of Hoare logic to traced symmetric monoidal categories, a very general framework for the theory of systems. Our abstraction is based on a traced monoidal functor from an arbitrary traced monoidal category into the category of pre-orders and monotone relations. We give several examples of how our theory generalises usual Hoare logics (partial correctness of while programs, partial correctness of pointer programs), and provide some case studies on how it can be used to develop new Hoare logics (run-time analysis of while programs and stream circuits).Comment: 27 page

A Vernacular for Coherent Logic

We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called coherent logic. Coherent logic has been recognized by a number of researchers as a suitable logic for many ev- eryday mathematical developments. The proposed proof representation is accompanied by a corresponding XML format and by a suite of XSL transformations for generating formal proofs for Isabelle/Isar and Coq, as well as proofs expressed in a natural language form (formatted in LATEX or in HTML). Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014

On entanglement evolution across defects in critical chains

We consider a local quench where two free-fermion half-chains are coupled via a defect. We show that the logarithmic increase of the entanglement entropy is governed by the same effective central charge which appears in the ground-state properties and which is known exactly. For unequal initial filling of the half-chains, we determine the linear increase of the entanglement entropy.Comment: 11 pages, 5 figures, minor changes, reference adde

On the word problem for SP-categories, and the properties of two-way communication

International audienceThe word problem for categories with free products and coproducts (sums), SP-categories, is directly related to the problem of determining the equivalence of certain processes. Indeed, the maps in these categories may be directly interpreted as processes which communicate by two-way channels. The maps of an SP-category may also be viewed as a proof theory for a simple logic with a game theoretic intepretation. The cut-elimination procedure for this logic determines equality only up to certain permuting conversions. As the equality classes under these permuting conversions are finite, it is easy to see that equality between cut-free terms (even in the presence of the additive units) is decidable. Unfortunately, this does not yield a tractable decision algorithm as these equivalence classes can contain exponentially many terms. However, the rather special properties of these free categories -- and, thus, of two-way communication -- allow one to devise a tractable algorithm for equality. We show that, restricted to cut-free terms s,t : X --> A, the decision procedure runs in time polynomial on |X||A|, the product of the sizes of the domain and codomain type

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

Growing Environmental Activists: Developing Environmental Agency and Engagement Through Children’s Fiction.

We explore how story has the potential to encourage environmental engagement and a sense of agency provided that critical discussion takes place. We illuminate this with reference to the philosophies of John Macmurray on personal agency and social relations; of John Dewey on the primacy of experience for philosophy; and of Paul Ricoeur on hermeneutics, dialogue, dialectics and narrative. We view the use of fiction for environmental understanding as hermeneutic, a form of conceptualising place which interprets experience and perception. The four writers for young people discussed are Ernest Thompson Seton, Kenneth Grahame, Michelle Paver and Philip Pullman. We develop the concept of critical dialogue, and link this to Crick's demand for active democratic citizenship. We illustrate the educational potential for environmental discussions based on literature leading to deeper understanding of place and environment, encouraging the belief in young people that they can be and become agents for change. We develop from Zimbardo the key concept of heroic resister to encourage young people to overcome peer pressure. We conclude with a call to develop a greater awareness of the potential of fiction for learning, and for writers to produce more focused stories engaging with environmental responsibility and activism

Randomized Clinical Stroke Trials in 2007

This article reviews the randomized control trials (RCT’s) that were published in 2007 of emerging pharmacotherapies in patients with acute (≤ 2 weeks), sub-acute (2 to 12 weeks) and chronic (≥ 12 weeks) stroke. A Medline search generated 22 RCT’s in stroke in the year 2007 in the English language. These trials were primarily efficacy studies. These included the role of statins (an anti-lipid agent) in reducing post-stroke morbidity and mortality, and decreasing the carotid atherosclerotic plaque in middle aged patients at increased risk of cardiovascular disease; glucose-potassium-insulin infusion in hyperglyceamic acute stroke patients; pioglitazone (an anti-diabetic medication) to reduce recurrence of stroke in Type 2 diabetic patients; administration of intra-arterial urokinase (a thrombolytic agent) and the role of laser therapy in clot dissolution given that at present there is only one FDA approved thrombolytic agent (r TPA); benefit of warfarin (an anticoagulant) in elderly patients with atrial fibrillation in the community; NXY (a free radical trapping agent) and minocycline both tested as neuroprotectants; and zoledronate (an intravenous bisphosphonate) to prevent loss of bone mineral density of the affected extremity, and finally the role of nicardipine (a Calcium channel blocker) in the prevention of vasospasm, and hydrocortisone to prevent hyponatraemia after sub-arachnoid hemorrhage. Finally the role of non-pharmacotherapy like stents for patient’s with internal carotid artery dissection with tandem internal carotid and middle cerebral artery occlusion and in vertebral artery stenosis