Existential questions in (relatively) hyperbolic groups {\it and} Finding relative hyperbolic structures

This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". The first part is entitled "Existential questions in (relatively) hyperbolic groups". We study there the existential theory of torsion free hyperbolic and relatively hyperbolic groups, in particular those with virtually abelian parabolic subgroups. We show that the satisfiability of systems of equations and inequations is decidable in these groups. In the second part, called "Finding relative hyperbolic structures", we provide a general algorithm that recognizes the class of groups that are hyperbolic relative to abelian subgroups.Comment: Two independant parts 23p + 9p, revised. To appear separately in Israel J. Math, and Bull. London Math. Soc. respectivel

Parabolic groups acting on one-dimensional compact spaces

Given a class of compact spaces, we ask which groups can be maximal parabolic subgroups of a relatively hyperbolic group whose boundary is in the class. We investigate the class of 1-dimensional connected boundaries. We get that any non-torsion infinite f.g. group is a maximal parabolic subgroup of some relatively hyperbolic group with connected one-dimensional boundary without global cut point. For boundaries homeomorphic to a Sierpinski carpet or a 2-sphere, the only maximal parabolic subgroups allowed are virtual surface groups (hyperbolic, or virtually $\mathbb{Z} + \mathbb{Z}$).Comment: 10 pages. Added a precision on local connectedness for Lemma 2.3, thanks to B. Bowditc

Assessment of dysarthric speech through rhythm metrics

AbstractThis paper reports the results of acoustic investigation based on rhythmic classifications of speech from duration measurements carried out to distinguish dysarthric speech from healthy speech. The Nemours database of American dysarthric speakers is used throughout experiments conducted for this study. The speakers are eleven young adult males with dysarthria caused by cerebral palsy (CP) or head trauma (HT) and one non-dysarthric adult male. Eight different sentences for each speaker were segmented manually to vocalic and intervocalic segmentation (176 sentences). Seventy-four different sentences for each speaker were automatically segmented to voiced and non-voiced intervals (1628 sentences). A two-parameters classification related to rhythm metrics was used to determine the most relevant measures investigated through bi-dimensional representations. Results show the relevance of rhythm metrics to distinguish healthy speech from dysarthrias and to discriminate the levels of dysarthria severity. The majority of parameters was more than 54% successful in classifying speech into its appropriate group (90% for the dysarthric patient classification in the feature space (%V, ΔV)). The results were not significant for voiced and unvoiced intervals relatively to the vocalic and intervocalic intervals (the highest recognition rates were: 62.98 and 90.30% for dysarthric patient and healthy control classification respectively in the feature space (ΔDNV, %DV))

No-splitting property and boundaries of random groups

We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on trees. This implies that their Gromov boundaries, defined at density less than 1/2, are Menger curves.Comment: 20 page

Magnetic properties of LaFe1-xCrxO3 and Fe2-2xCr2xO3 mixed oxides

Mixed oxides with formula LaFe1-xCrxO3 and Fe2-2xCr2xO3, where 0≤x≤1, are studied. The samples have been prepared using solid state reaction technique in air. The X-ray diffraction spectra indicated that the samples crystallize in a corundum phase with space group ( R3c ) for Fe2-2xCr2xO3 and in the perovskite structure for LaFe1-xCrxO3. Many techniques have been used to explore the magnetic properties of the systems. High field, ZFC and FC magnetization vs. temperature, d.c. susceptibility and Mössbauer spectroscopy were carried out. High temperature magnetic susceptibility measurements and high field magnetic magnetization (H ≤ 20 T) show that the behavior of the susceptibility and the magnetization are complex. Mössbauer spectra of the solid solutions have been measured at 4.2 K and in the temperature range 77 K to 300 K. The shapes of spectra are unusual, showing strong relaxation phenomena in a wide temperature range as recently observed for many frustrated systems. The results are discussed by establishing the existence of various magnetic structures, inducing intermediate magnetic phases between the antiferromagnetic and the paramagnetic states. Preliminary magnetic phase diagrams of the systems have been established.Mixed oxides with formula LaFe1-xCrxO3 and Fe2-2xCr2xO3, where 0≤x≤1, are studied. The samples have been prepared using solid state reaction technique in air. The X-ray diffraction spectra indicated that the samples crystallize in a corundum phase with space group ( R3c ) for Fe2-2xCr2xO3 and in the perovskite structure for LaFe1-xCrxO3. Many techniques have been used to explore the magnetic properties of the systems. High field, ZFC and FC magnetization vs. temperature, d.c. susceptibility and Mössbauer spectroscopy were carried out. High temperature magnetic susceptibility measurements and high field magnetic magnetization (H ≤ 20 T) show that the behavior of the susceptibility and the magnetization are complex. Mössbauer spectra of the solid solutions have been measured at 4.2 K and in the temperature range 77 K to 300 K. The shapes of spectra are unusual, showing strong relaxation phenomena in a wide temperature range as recently observed for many frustrated systems. The results are discussed by establishing the existence of various magnetic structures, inducing intermediate magnetic phases between the antiferromagnetic and the paramagnetic states. Preliminary magnetic phase diagrams of the systems have been established

Finding All Solutions of Equations in Free Groups and Monoids with Involution

The aim of this paper is to present a PSPACE algorithm which yields a finite graph of exponential size and which describes the set of all solutions of equations in free groups as well as the set of all solutions of equations in free monoids with involution in the presence of rational constraints. This became possible due to the recently invented emph{recompression} technique of the second author. He successfully applied the recompression technique for pure word equations without involution or rational constraints. In particular, his method could not be used as a black box for free groups (even without rational constraints). Actually, the presence of an involution (inverse elements) and rational constraints complicates the situation and some additional analysis is necessary. Still, the recompression technique is general enough to accommodate both extensions. In the end, it simplifies proofs that solving word equations is in PSPACE (Plandowski 1999) and the corresponding result for equations in free groups with rational constraints (Diekert, Hagenah and Gutierrez 2001). As a byproduct we obtain a direct proof that it is decidable in PSPACE whether or not the solution set is finite.Comment: A preliminary version of this paper was presented as an invited talk at CSR 2014 in Moscow, June 7 - 11, 201

Observation of Collective-Emission-Induced Cooling inside an Optical Cavity

We report the observation of collective-emission-induced, velocity-dependent light forces. One third of a falling sample containing 3 x 10^6 cesium atoms illuminated by a horizontal standing wave is stopped by cooperatively emitting light into a vertically oriented confocal resonator. We observe decelerations up to 1500 m/s^2 and cooling to temperatures as low as 7 uK, well below the free space Doppler limit. The measured forces substantially exceed those predicted for a single two-level atom.Comment: 10 pages, 5 figure

Emergence of Anaplasma Species Related to A. phagocytophilum and A. platys in Senegal

The genus Anaplasma (Anaplasmataceae, Rickettsiales) includes tick-transmitted bacterial species of importance to both veterinary and human medicine. Apart from the traditionally recognized six Anaplasma species (A. phagocytophilum, A. platys, A. bovis, A. ovis, A. centrale, A. marginale), novel strains and candidate species, also of relevance to veterinary and human medicine, are emerging worldwide. Although species related to the zoonotic A. platys and A. phagocytophilum have been reported in several African and European Mediterranean countries, data on the presence of these species in sub-Saharan countries are still lacking. This manuscript reports the investigation of Anaplasma strains related to zoonotic species in ruminants in Senegal by combining different molecular tests and phylogenetic approaches. The results demonstrated a recent introduction of Candidatus (Ca) Anaplasma turritanum, a species related to the pathogenic A. platys, possibly originating by founder effect. Further, novel undetected strains related to Candidatus (Ca) Anaplasma cinensis were detected in cattle. Based on groEL and gltA molecular comparisons, we propose including these latter strains into the Candidatus (Ca) Anaplasma africanum species. Finally, we also report the emergence of Candidatus (Ca) A. boleense in Senegal. Collectively, results confirm that Anaplasma species diversity is greater than expected and should be further investigated, and that Anaplasma routine diagnostic procedures and epidemiological surveillance should take into account specificity issues raised by the presence of these novel strains, suggesting the use of a One Health approach for the management of Anaplasmataceae in sub-Saharan Africa