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If ${\mathfrak {F}}$ is a type-definable family of commensurable subsets, subgroups or subvector spaces in a metric structure, then there is an invariant subset, subgroup or subvector space commensurable with ${\mathfrak {F}}$. This in particular applies to type-definable or hyper-definable objects in a classical first-order structure.

Flexible graphene oxide (GO) microsheets with attached positively charged polymers, termed GOX microsheets, are efficient at bacterial adsorption, as they bind electrostatically to bacterial membranes��� negative surface charge. The authors explore an antimicrobial water filter application for GOX's extremely high surface area and its previously described efficient bacterial adsorption.Cellulose-fiber carrier material is functionalized with GOX microsheets to create an adsorption-based bacteria filtration material. The morphology and charge density (7.8 �� 1019 g���1) of the prepared GOX fibers are determined by scanning electron microscopy and dye adsorption assay, and widefield fluorescence microscopy is used to visualize the adsorption of stained Escherichia coli bacterial cells on the fibers. GOX fibers are tested in filtration setups to investigate their bacteria removal performance. The experimental results, with 100 mg of GOX fibers filtering 2.4 �� 109 colony-forming units (CFU) from an E. coli bacterial culture with 99.5% bacterial reduction, demonstrate the fibers��� high bacteria loading capacity. The electrostatic adsorption-based filtration mechanism allows the filter to be operated at higher flow rates than micropore membrane filters, while maintaining 3-log bacterial reduction. GOX filter materials removing bacteria via adsorption are a high flow rate alternative to current water filtration processes that rely on size-exclusion.

Multi-drug resistant pathogens such as methicillin-resistant Staphylococcus aureus (MRSA) cause nosocomial infections that can have deleterious effects on human health. Thus, it is imperative to find solutions to treat these detrimental infections as well as to control their spread. We tested the effect of two different antimicrobial materials, functionalised graphene oxide (GOX), and AGXX® coated on cellulose fibres, on the growth and transcriptome of the clinical MRSA strain S. aureus 04-02981. In addition, we investigated the effect of a third material as a combination of GOX and AGXX® fibres on S. aureus 04-02981. Standard plate count assay revealed that the combination of fibres, GOX-AGXX® inhibited the growth of S. aureus 04-02981 by 99.98%. To assess the effect of these antimicrobials on the transcriptome of our strain, cultures of S. aureus 04-02981 were incubated with GOX, AGXX®, or GOX-AGXX® fibres for different time periods and then subjected to RNA-sequencing. Uncoated cellulose fibres were used as a negative control. The antimicrobial fibres had a huge impact on the transcriptome of S. aureus 04-02981 affecting the expression of 2650 genes. Primarily genes related to biofilm formation and virulence (such as agr, sarA, and those of the two-component system SaeRS), and genes crucial for survival in biofilms (like arginine metabolism arc genes) were repressed. In contrast, the expression of siderophore biosynthesis genes (sbn) was induced, a probable response to stress imposed by the antimicrobials and the conditions of iron-deficiency. Genes associated with potassium transport, intracellular survival and pathogenesis (kdp) were also differentially expressed. Our data suggest that the combination of GOX and AGXX® acts as an efficient antimicrobial against S. aureus 04-02981. Thus, these materials are potential candidates for applications in antimicrobial surface coatings.

Two novel antimicrobial surface coatings were assessed for their lasting antibacterial effect under simulated space conditions during the SIRIUS-19 study. Because long-term space travel can affect the human immune system, astronauts are particularly susceptible to infectious disease. Moreover, the space flight environment can alter the composition of microbial communities within the spacecraft and increase bacterial virulence and resistance to antibiotics. In addition to protecting the crew from infection by human pathogens, prevention and elimination of bacterial contamination is important to avoid corrosion and damage of the technical equipment. The antimicrobial coating AGXX(R)consists of micro-galvanic cells composed of silver and ruthenium which damage bacterial cells through the release of reactive oxygen species. Over the last years, several studies on the antimicrobial effect of AGXX(R)have demonstrated an effective inhibition of growth and even complete elimination of many pathogenic bacteria - including multiresistant microorganisms - as well as their biofilms. The second antimicrobial coating, GOX, consists of chemically modified graphene oxide. Through a positive surface charge and its flexible scaffold, GOX can multivalently bind and immobilize bacteria via electrostatic attraction. Here, AGXX(R)and GOX were applied to non-metallic carriers not previously tested. The antimicrobial coated materials, as well as uncoated control samples, were exposed in the SIRIUS artificial space module and analyzed at different time points during the 4-months isolation study. Survival and growth of airborne heterotrophic, aerobic bacteria on the surfaces were assessed by cultivation-based methods, employing growth conditions suitable for potential human pathogens. Human-associated, biofilm-forming Staphylococcus spp. (S. hominis, S. haemolyticus, and S. epidermidis) strongly dominated at all time points, most were resistant against erythromycin, kanamycin, and ampicillin. AGXX(R)coatings completely inhibited growth of these opportunistic pathogens on all tested surface materials. Particularly, AGXX(R)-cellulose fleece achieved a clear reduction in bacterial load able to recover post contact. GOX-cellulose fleece effectively immobilized bacteria. Sequence analysis of 16S rRNA gene amplicons revealed that the isolated Staphylococcus spp. did not dominate the overall bacterial community, accounting for only 0.1-0.4% of all sequences. Instead, molecular data revealed Lactobacillus, Comamonas, Pseudomonas, Sporosarcina, and Bacillusas the dominant genera across all samples and time points.

Aiming at the overall negative surface charge of bacteria, a new strategy of antibacterial agents based on large polymer-modified graphene oxide (GO) sheets is assessed. The presented flexible, polycationic Sheets match the size and charge density of the Escherichia coli surface charge density (2 × 1014 cm−2). These matching parameters create an unspecific but very strong bacteria adsorber by multivalent, electrostatic attraction. Their interaction with bacteria is visualized via atomic force and confocal microscopy and shows that they effectively bind and wrap around E. coli cells, and thereby immobilize them. The incubation of Gram-negative and -positive bacteria (E. coli and methicillin-resistant Staphylococcus aureus, MRSA) with these polycationic sheets leads to the inhibition of proliferation and a reduction of the colony forming bacteria over time. This new type of antibacterial agent acts in a different mode of Action than classical biocides and could potentially be employed in medicinal, technical, or agriculture applications. The presented microsheets and their unspecific binding of cell interfaces could further be employed as adsorber material for bacterial filtration or immobilization for imaging, analysis, or sensor technologies.

International audience

We define k-genericity and k-largeness for a subset of a group, and determine the value of k for which a k-large subset of G^n is already the whole of G^n , for various equationally defined subsets. We link this with the inner measure of the set of solutions of an equation in a group, leading to new results and/or proofs in equational probabilistic group theory., Comment: Annales math{\'e}matiques Blaise Pascal, cedram, In press

For a simply laced and hyperbolic Kac--Moody group $G=G(R)$ over a commutative ring $R$ with 1, we consider a map from a finite presentation of $G(R)$ obtained by Allcock and Carbone to a representation--theoretic construction $G^{\lambda}(R)$ corresponding to an integrable representation $V^{\lambda}$ with dominant integral weight $\lambda$. When $R=\Z$, we prove that this map extends to a group homomorphism $\rho_{\lambda,\Z}: G(\Z) \to G^{\lambda}(\Z).$ We prove that the kernel $K^{\lambda}$ of the map $\rho_{\lam,\Z}: G(\Z)\to G^{\lam}(\Z)$ lies in $H(\C)$ and if the group homomorphism $\varphi:G(\Z)\to G(\C)$ is injective, then $K^{\lambda}\leq H(\Z)\cong(\Z/2\Z)^{rank(G)}$.

International audience; We classify the groups definable in the coloured fields obtained by Hrushovski amalgamation. A group definable in the bad green field is isogenous to the quotient of a subgroup of an algebraic group by a Cartesian power of the group of green elements. A definable subgroup of an algebraic group in the green or red field is an extension of the coloured points of a multiplicative or additive algebraic group by an algebraic group. In particular, a simple group in a coloured field is algebraic.; Un groupe interprétable dans le mauvais corps vert est isogène à un quotient d'un sous-groupe définissable d'un groupe algébrique par une puissance du groupe vert. Un sous-groupe définissable d'un groupe algébrique dans un corps vert ou rouge est une extension des points colorés d'un groupe algébrique multiplicatif ou additif par un groupe algébrique. En particulier, tout groupe simple définissable dans un corps coloré est algébrique.

Bioremediation via floating treatment wetlands/islands (FTW/I) is a sustainable, upcoming strategy to clean over-fertilized waters. Heavy metal pollution could be addressed in the same system. For implementing this feature, heavy-metal-adsorbing filter papers were prepared in a scalable procedure. Polyamine-functionalized papers based on the grafting of polyethyleneimine (PEI) and chitosan were prepared in aqueous immersion baths and tested for their heavy metal adsorption capability. Compared to untreated cellulose, the prepared filter papers exhibited great heavy metal reduction in a filtration setup. Compellingly, the natural biopolymer functionalization with chitosan adsorbed similar or even higher amounts (80% Ni, 65% Co, 100% Cu, 85% Fe, 40% Cr, 90% Cd, and 66% Zn of the 5 ppm heavy metal sulfate solutions) compared to the PEI filters (48% Ni, 36% Co, 89% Cu, 96% Fe, 45% Cr, 84% Cd, and 62% Zn) at pH 6.5. Moreover, the filters can be re-used simply by acidic washing to desorb the heavy metals, which was demonstrated in five repeating cycles. The presented chitosan–cellulose papers were prepared from renewable resources in a 3-step production lane and are a sustainable choice for various heavy-metal-removing applications. The papers can be implemented into floating treatment wetland systems to protect plants and microorganisms during phytoremediation processes and to add the additional feature of heavy metal removal for FTWs.

We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimension. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that a pseudofinite $\widetilde {\mathfrak M}_c$ -group of finite positive dimension contains a finite-by-abelian subgroup of positive dimension, and a pseudofinite group of dimension 2 contains a soluble subgroup of dimension 2.

In this study, amphiphiles composed of linear polyglycerols (LPGs) with hydroxyl, methoxy, and ethoxy side groups and end capped with one or two perfluorooctyl chains (Rf8) have been designed to form supramolecular architectures. The amphiphiles and bolaamphiphiles are capable of self-assembling into spherical and flat micelles as well as nonionic unilamellar vesicles (niosomes) in aqueous solution. The fluorous compartments of the micelles preferentially encapsulate a trifluoromethylated Disperse Red 1 compared to the unaltered dye. Micellar solutions of methoxy LPG compounds show a transition in water at temperatures of 38 °C (2) and 33 °C (5) in which reversibly larger agglomerates are formed. Both amphiphiles also form very stable unilamellar vesicles with diameters ranging from 30 nm up to 10 μm, if prepared via a thin film hydration method, which remain intact above 38 °C.

Perfluoroalkyl-functionalized, hyperbranched polyglycerols that produce stable microbubbles are integrated into a microfluidic emulsion to create porous microspheres. In a previously-presented work a dendrimer with a perfluorinated shell was used. By replacing this dendrimer core with a hyperbranched core and evaluating different core sizes and degrees of fluorinated shell functionalization, we optimized the process to a more convenient synthesis and higher porosities. The new hyperbranched polyglycerol porogens produced more pores and can be used to prepare microspheres with porosity up to 12% (v/v). The presented preparation forms pores with a perfluoroalkyl-functionalized surface that enables the resulting microspheres to act as supramolecular host systems. The microspheres can incorporate gases into the pores and actives in the polymer matrix, while the perfluoroalkylated pore surface can be used to immobilize perfluoro-tagged molecules onto the pores by fluorous-fluorous interaction.

Overall this was a high quality meeting, with carefully chosen talks fitting in with the announced themes of the workshop.

We generalize Frecon's construction of the inevitable radical to groups in stable and even simple theories. Nous generalisons la construction de Frecon du radical inevitable aux groupes dans les theories stables et meme simples.

If is a pseudo-variety, then a supersimple residually group is nilpotent-by-poly-.

In droplet-based microfluidics, non-ionic, high-molecular weight surfactants are required to stabilize droplet interfaces. One of the most common structures that imparts stability as well as biocompatibility to water-in-oil droplets is a triblock copolymer surfactant composed of perfluoropolyether (PFPE) and polyethylene glycol (PEG) blocks. However, the fast growing applications of microdroplets in biology would benefit from a larger choice of specialized surfactants. PEG as a hydrophilic moiety, however, is a very limited tool in surfactant modification as one can only vary the molecular weight and chain-end functionalization. In contrast, linear polyglycerol offers further side-chain functionalization to create custom-tailored, biocompatible droplet interfaces. Herein, we describe the synthesis and characterization of polyglycerol-based triblock surfactants with tailored side-chain composition, and exemplify their application in cell encapsulation and in vitro gene expression studies in droplet-based microfluidics.

A small profinite ring has an open nil ideal of finite nil exponent. We also discuss various conjectures about small profinite rings, and give examples illustrating them.

This paper completes the proof of the group configuration theorem for simple theories started in [1]. We introduce the notion of an almost hyperdefinable (poly-)structure, and show that it has a reasonable model theory. We then construct an almost hyperdefinable group from a polygroup chunk.

1. We show that if p is a real type which is internal in a set Σ of partial types in a simple theory, then there is a type p′ interbounded with p, which is finitely generated over Σ, and possesses a fundamental system of solutions relative to Σ.2. If p is a possibly hyperimaginary Lascar strong type, almost Σ-internal, but almost orthogonal to Σω, then there is a canonical non-trivial almost hyperdefinable polygroup which multi-acts on p while fixing Σ generically In case p is Σ-internal and T is stable, this is the binding group of p over Σ.

We reconstruct the group action in the group configuration theorem. We apply it to show that in an ω-categorical theory a finitely based pseudolinear regular type is locally modular, and the geometry associated to a finitely based locally modular regular type is projective geometry over a finite field.

There is a model-completion T n of the theory of a (reflexive) n-coloured graph such that R n is total, and R i o Rj ⊆ R i+j for all i,j. For n > 2, the theory T n is not simple, and does not have the strict order property. The theories T n combine to yield a non-simple theory Too without the strict order property, which does not eliminate hyperimaginaries.

If there are infinitely many p -Mersenne prime numbers, there is no bad field of positive characteristic p .

A totally ordered group G (possibly with extra structure) is called coset-minimal if every definable subset of G is a finite union of cosets of definable subgroups intersected with intervals with endpoints in G ∪{±∞}. Continuing work in Belegradek et al. (J. Symbolic Logic 65(3) (2000) 1115) and Point and Wagner (Ann. Pure Appl. Logic 105(1–3) (2000) 261), we study coset-minimality, as well as two weak versions of the notion: eventual and ultimate coset-minimality. These groups are abelian; an eventually coset-minimal group, as a pure ordered group, is an ordered abelian group of finite regular rank. Any pure ordered abelian group of finite regular rank is ultimately coset-minimal and has the exchange property; moreover, every definable function in such a group is piecewise linear. Pure coset-minimal and eventually coset-minimal groups are classified. In a discrete coset-minimal group every definable unary function is piece-wise linear (this improves a result in Point and Wagner (Ann. Pure Appl. Logic 105(1–3) (2000) 261), where coset-minimality of the theory of the group was required). A dense coset-minimal group has the exchange property (which is false in the discrete case (M.S.R.I., preprint series, 1998-051)); moreover, any definable unary function is piecewise linear, except possibly for finitely many cosets of the smallest definable convex nonzero subgroup. Finally, we give some examples and open questions.

We study local strengthenings of the simplicity condition. In particular, we define and study a local Lascar rank, as well as short, low. supershort and superlow theories. An example of a low non supershort theory is given.

If K is a field of finite Morley rank, then for any parameter set A ⊆ Keq the prime model over A is equal to the model-theoretic algebraic closure of A. A field of finite Morley rank eliminates imaginaries. Simlar results hold for minimal groups of finite Morley rank with infinite acl(∅).

We study hyperdefinable groups, the most general kind of groups interpretable in a simple theory. After developing their basic theory, we prove the appropriate versions of Hrushovski's group quotient theorem and the Weil–Hrushovski group chunk theorem. We also study locally modular hyperdefinable groups and prove that they are bounded-by-Abelian-by-bounded. Finally, we analyze hyperdefinable groups in supersimple theories.

A totally ordered group G is essentially periodic if for every denable non-trivial convex subgroup H of G every denable subset of G is equal to a nite union of cosets of subgroups of G on some interval containing an end segment of H ;i t iscoset-minimal if all denable subsets are equal to a nite union of cosets, intersected with intervals. We study denable sets and functions in such groups, and relate them to the quasi-o-minimal groups introduced in Belegradek et al. (J. Symbolic Logic, to appear). Main results: An essentially periodic group G is abelian; if G is discrete, then denable functions in one variable are ultimately piecewise linear. A group such that every model elementarily equivalent to it is coset-minimal is quasi-o-minimal (and vice versa), and its denable functions in one variable are piecewise linear. c 2000 Elsevier Science B.V. All rights reserved. MSC: 03G10; 05E20; 20E36

A structure (M, quasi-o-minimal if in any structure elementarily equivalent to it the definable subsets are exactly the Boolean combinations of 0-definable subsets and intervals. We give a series of natural examples of quasi-o-minimal structures which are not o-minimal; one of them is the ordered group of integers. We develop a technique to investigate quasi-o-minimality and use it to study quasi-o-minimal ordered groups (possibly with extra structure). Main results: any quasi-o-minimal ordered group is abelian; any quasi-o-minimal ordered ring is a real closed field, or has zero multiplication; every quasi-o-minimal divisible ordered group is o-minimal; every quasi-o-minimal archimedian densely ordered group is divisible. We show that a counterpart of quasi-o-minimality in stability theory is the notion of theory of U-rank 1.

An ω-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU-rank. Every definable subgroup is commensurable with an acl(ø)-definable subgroup. Every finitely based regular type in a CM-trivial ω-categorical simple theory is non-orthogonal to a type of SU-rank 1. In particular, a supersimple ω-categorical CM-trivial theory has finite SU-rank.

The notion of a large set in an arbitrary group is introduced in analogy to the generic sets in an algebraic or stable group. The question is studied which properties “satisfied largely” by a group hold on the entire group. ZUSAMMENFASSUNG. Wir definieren den Begriff einer groβen Teilmenge einer be-liebigen Gruppe in Analogie zu den generischen Mengen einer algebraischen oder stabilen Gruppe und untersuchen, welche “grofiteils erfullten” Gruppeneigenschaften fur die ganze Gruppe gelten mussen.

The Sylow-2-subgroups of a periodic group with minimal condition on centralizers are locally finite and conjugate. The same holds for the Sylow-p-subgroups for any prime p, provided the subgroups generated by any two p-elements of the group are finite. In the non-periodic context, the bounded left Engel elements of a group with minimal condition on centralizers form the Fitting subgroup.

We define a generalized version of CM-triviality, and show that in the presence of enough regular types, or solubility, a stable CM-trivial group is nilpotent-by-finite. A torsion-free small CM-trivial stable group is abelian and connected. The first result makes use of a generalized version of the analysis of bad groups.

International audience; We prove a version of Hrushovski's socle lemma for rigid groups in an arbitrary simple theory.

International audience; The Fitting subgroup of a type-definable group in a simple theory is relatively definable and nilpotent. Moreover, the Fitting subgroup of a supersimple hyperdefinable group has a normal hyperdefinable nilpotent subgroup of bounded index, and is itself of bounded index in a hyperdefinable subgroup.

In this paper, we shall survey results about the group-theoretic properties of stable groups. These can be classified into three main categories, according to the strength of the assumptions needed: chain conditions, generic types, and some form of rank. Each category has its typical application: Chain conditions often allow us to deduce global properties from local ones, generic properties are used to get definable groups from undefinable ones, and rank (in some form or other) is necessary to interpret fields in certain group actions. While originally the main input came from algebraic group theory, founded on the similarities between (finite) rank and dimension, increasingly methods borrowed from finite group theory have come to play a role, emphasizing the study of characteristic subgroups and characteristic families of subgroups.

International audience; An elliptic curve over a supersimple field with exactly one extension of degree 2 has an s-generic point.

Non-n-ampleness as denned by Pillay [20] and Evans [5] is preserved under analysability. Generalizing this to a more general notion of Σ-ampleness, this gives an immediate proof for all simple theories of a weakened version of the Canonical Base Property (CBP) proven by Chatzidakis [4] for types of finite SU-rank. This is then applied to the special case of groups.

International audience; We prove that if $(H,G)$ is a small, $nm$-stable compact $G$-group, then $H$ is nilpotent-by-finite, and if additionally $\NM(H) \leq \omega$, then $H$ is abelian-by-finite. Both results are significant steps towards the proof of the conjecture that each small, $nm$-stable compact $G$-group is abelian-by-finite. We give examples of small, $nm$-stable compact $G$-groups of infinite ordinal $\NM$-rank, providing counter-examples to the $\NM$-gap conjecture.

International audience; In a simple CM-trivial theory every hyperimaginary is interbounded with a sequence of finitary hyperimaginaries. Moreover, such a theory eliminates hyperimaginaries whenever it eliminates finitary hyperimaginaries. In a supersimple CM-trivial theory, the independence relation is stable.