On subgroups of minimal topological groups

A topological group is minimal if it does not admit a strictly coarser Hausdorff group topology. The Roelcke uniformity (or lower uniformity) on a topological group is the greatest lower bound of the left and right uniformities. A group is Roelcke-precompact if it is precompact with respect to the Roelcke uniformity. Many naturally arising non-Abelian topological groups are Roelcke-precompact and hence have a natural compactification. We use such compactifications to prove that some groups of isometries are minimal. In particular, if U_1 is the Urysohn universal metric space of diameter 1, the group Iso(U_1) of all self-isometries of U_1 is Roelcke-precompact, topologically simple and minimal. We also show that every topological group is a subgroup of a minimal topologically simple Roelcke-precompact group of the form Iso(M), where M is an appropriate non-separable version of the Urysohn space.Comment: To appear in Topology and its Applications. 39 page

Fraisse Limits, Ramsey Theory, and Topological Dynamics of Automorphism Groups

We study in this paper some connections between the Fraisse theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures.Comment: 73 pages, LaTeX 2e, to appear in Geom. Funct. Ana

Infinite dimensional integrals beyond Monte Carlo methods: yet another approach to normalized infinite dimensional integrals

An approach to (normalized) infinite dimensional integrals, including normalized oscillatory integrals, through a sequence of evaluations in the spirit of the Monte Carlo method for probability measures is proposed. in this approach the normalization through the partition function is included in the definition. For suitable sequences of evaluations, the ("classical") expectation values of cylinder functions are recoveredComment: Submitted as a communication in the ICMSQUARE conference, september 201

The Gravity Dual of a Density Matrix

For a state in a quantum field theory on some spacetime, we can associate a density matrix to any subset of a given spacelike slice by tracing out the remaining degrees of freedom. In the context of the AdS/CFT correspondence, if the original state has a dual bulk spacetime with a good classical description, it is natural to ask how much information about the bulk spacetime is carried by the density matrix for such a subset of field theory degrees of freedom. In this note, we provide several constraints on the largest region that can be fully reconstructed, and discuss specific proposals for the geometric construction of this dual region.Comment: 19 pages, LaTeX, 8 figures, v2: footnote and reference adde

Assessment of quality and safety of pork treated with low-temperature atmospheric-pressure plasma

It is known that processing methods ensuring partial or full microbial inactivation are quite limited. Therefore, it is of great interest to develop technique and technologies allowing the effective action on microorganisms without a significant influence on product properties. The use of cold plasma can be one of the promising methods of meat product treatment by cold sterilization. The present work examines a possibility of chilled meat treatment with low-temperature atmospheric-pressure plasma to increase its stability to microbial spoilage and extend shelf life. To obtain low temperature plasma, the equipment developed by the designing department “Plasmamed” was used. Chilled meat was treated with low-temperature atmospheric-pressure argon plasma for 5, 10, 20 and 30 min. Samples were stored at a temperature of 2–4 °C for 10 days. Organoleptic indices, moisture weight fraction, changes in pH and water activity were analyzed before treatment and during storage. Sanitary microbiological analyses were carried out by the following indicators: quantity of mesophilic aerobic and facultative anaerobic microorganisms (QMAFAnM), the presence and quantity of coliforms, Salmonella, Escherichia coli, Listeria monocytogenes, Proteus. It was shown that meat cold treatment with argon plasma inhibited the development of mesophilic microorganisms. The colony forming units detected in the samples after ten days of storage were determined by the duration of exposure to plasma. It was proved that meat treatment for 15 and 30 min had the bactericidal effect and facilitated an improvement in meat color during storage. The organoleptic indices of the samples treated with plasma corresponded to the requirements of standards and approved consumer characteristics