On Turing dynamical systems and the Atiyah problem

Main theorems of the article concern the problem of M. Atiyah on possible values of l^2-Betti numbers. It is shown that all non-negative real numbers are l^2-Betti numbers, and that "many" (for example all non-negative algebraic) real numbers are l^2-Betti numbers of simply connected manifolds with respect to a free cocompact action. Also an explicit example is constructed which leads to a simply connected manifold with a transcendental l^2-Betti number with respect to an action of the threefold direct product of the lamplighter group Z/2 wr Z. The main new idea is embedding Turing machines into integral group rings. The main tool developed generalizes known techniques of spectral computations for certain random walk operators to arbitrary operators in groupoid rings of discrete measured groupoids.Comment: 35 pages; essentially identical to the published versio

An algorithm to identify automorphisms which arise from self-induced interval exchange transformations

We give an algorithm to determine if the dynamical system generated by a positive automorphism of the free group can also be generated by a self-induced interval exchange transformation. The algorithm effectively yields the interval exchange transformation in case of success.Comment: 26 pages, 8 figures. v2: the article has been reorganized to make for a more linear read. A few paragraphs have been added for clarit

Converging and diverging burn rates in North American boreal forests from the Little Ice Age to the present

Warning. This article contains terms, descriptions, and opinions used for historical context that may be culturally sensitive for some readers. Background. Understanding drivers of boreal forest dynamics supports adaptation strategies in the context of climate change. Aims. We aimed to understand how burn rates varied since the early 1700s in North American boreal forests. Methods. We used 16 fire-history study sites distributed across such forests and investigated variation in burn rates for the historical period spanning 1700-1990. These were benchmarked against recent burn rates estimated for the modern period spanning 1980-2020 using various data sources. Key results. Burn rates during the historical period for most sites showed a declining trend, particularly during the early to mid 1900s. Compared to the historical period, the modern period showed less variable and lower burn rates across sites. Mean burn rates during the modern period presented divergent trends among eastern versus northwestern sites, with increasing trends in mean burn rates in most northwestern North American sites. Conclusions. The synchronicity of trends suggests that large spatial patterns of atmospheric conditions drove burn rates in addition to regional changes in land use like fire exclusion and suppression. Implications. Low burn rates in eastern Canadian boreal forests may continue unless climate change overrides the capacity to suppress fire.Peer reviewe

Plate tectonics drive tropical reef biodiversity dynamics

The Cretaceous breakup of Gondwana strongly modified the global distribution of shallow tropical seas reshaping the geographic configuration of marine basins. However, the links between tropical reef availability, plate tectonic processes and marine biodiversity distribution patterns are still unknown. Here, we show that a spatial diversification model constrained by absolute plate motions for the past 140 million years predicts the emergence and movement of diversity hotspots on tropical reefs. The spatial dynamics of tropical reefs explains marine fauna diversification in the Tethyan Ocean during the Cretaceous and early Cenozoic, and identifies an eastward movement of ancestral marine lineages towards the Indo-Australian Archipelago in the Miocene. A mechanistic model based only on habitat-driven diversification and dispersal yields realistic predictions of current biodiversity patterns for both corals and fishes. As in terrestrial systems, we demonstrate that plate tectonics played a major role in driving tropical marine shallow reef biodiversity dynamics

Phase Transitions on Nonamenable Graphs

We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive graphs and trees

Microbiota Sensing by Mincle-Syk Axis in Dendritic Cells Regulates Interleukin-17 and -22 Production and Promotes Intestinal Barrier Integrity

We are grateful to members of the D.S. laboratory and Dr. E. Fernández-Malavé for discussions and critical reading of the manuscript. We appreciate the support of A. Tomás-Loba, G. Sabio, P. Martín, A. Tsilingiri, A.R. Ramiro, C.L. Abram, C.A. Lowell, J.M. García-Lobo, M. Molina, and M.C. Rodríguez for providing reagents and support. We thank the staff at the Fundación Centro Nacional de Investigaciones Cardiovasculares Carlos III (CNIC) facilities for technical support. M.M.-L. received a Formación de Personal Universitario (FPU) fellowship (AP2010-5935) from the Spanish Ministerio de Educación. S.I. is funded by grant SAF2015-74561-JIN from the Spanish Ministerio de Ciencia, Innovación, y Universidades (MCIU) and Fondos Europeos de Desarrollo Regional (FEDER). G.D.B and D.M.R. are supported by the Wellcome Trust and the MRC Centre for Medical Mycology at the University of Aberdeen. S.L.L. is supported by the Swiss National Science Foundation (PP00P3_150758). Work in the D.S. laboratory is funded by the CNIC and grant SAF2016-79040-R from MCIU, the Agencia Estatal de Investigación, and FEDER; B2017/BMD-3733 Immunothercan-CM from Comunidad de Madrid; RD16/0015/0018-REEM from FIS-Instituto de Salud Carlos III, MCIU, and FEDER; the Acteria Foundation; the Constantes y Vitales prize (Atresmedia); La Marató de TV3 Foundation (201723); the European Commission (635122-PROCROP H2020), and the European Research Council (ERC-2016-Consolidator Grant 725091). The CNIC is supported by the MCIU and the Pro-CNIC Foundation and is a Severo Ochoa Center of Excellence (SEV-2015-0505).Peer reviewedPublisher PD

To respond or not to respond - a personal perspective of intestinal tolerance

For many years, the intestine was one of the poor relations of the immunology world, being a realm inhabited mostly by specialists and those interested in unusual phenomena. However, this has changed dramatically in recent years with the realization of how important the microbiota is in shaping immune function throughout the body, and almost every major immunology institution now includes the intestine as an area of interest. One of the most important aspects of the intestinal immune system is how it discriminates carefully between harmless and harmful antigens, in particular, its ability to generate active tolerance to materials such as commensal bacteria and food proteins. This phenomenon has been recognized for more than 100 years, and it is essential for preventing inflammatory disease in the intestine, but its basis remains enigmatic. Here, I discuss the progress that has been made in understanding oral tolerance during my 40 years in the field and highlight the topics that will be the focus of future research

Intersection form, laminations and currents on free groups

Let $F_N$ be a free group of rank $N\ge 2$, let $\mu$ be a geodesic current on $F_N$ and let $T$ be an $\mathbb R$-tree with a very small isometric action of $F_N$. We prove that the geometric intersection number $$ is equal to zero if and only if the support of $\mu$ is contained in the dual algebraic lamination $L^2(T)$ of $T$. Applying this result, we obtain a generalization of a theorem of Francaviglia regarding length spectrum compactness for currents with full support. As another application, we define the notion of a \emph{filling} element in $F_N$ and prove that filling elements are "nearly generic" in $F_N$. We also apply our results to the notion of \emph{bounded translation equivalence} in free groups.Comment: revised version, to appear in GAF

The Intestinal Microbiota Plays a Role in Salmonella-Induced Colitis Independent of Pathogen Colonization

The intestinal microbiota is composed of hundreds of species of bacteria, fungi and protozoa and is critical for numerous biological processes, such as nutrient acquisition, vitamin production, and colonization resistance against bacterial pathogens. We studied the role of the intestinal microbiota on host resistance to Salmonella enterica serovar Typhimurium-induced colitis. Using multiple antibiotic treatments in 129S1/SvImJ mice, we showed that disruption of the intestinal microbiota alters host susceptibility to infection. Although all antibiotic treatments caused similar increases in pathogen colonization, the development of enterocolitis was seen only when streptomycin or vancomycin was used; no significant pathology was observed with the use of metronidazole. Interestingly, metronidazole-treated and infected C57BL/6 mice developed severe pathology. We hypothesized that the intestinal microbiota confers resistance to infectious colitis without affecting the ability of S. Typhimurium to colonize the intestine. Indeed, different antibiotic treatments caused distinct shifts in the intestinal microbiota prior to infection. Through fluorescence in situ hybridization, terminal restriction fragment length polymorphism, and real-time PCR, we showed that there is a strong correlation between the intestinal microbiota composition before infection and susceptibility to Salmonella-induced colitis. Members of the Bacteroidetes phylum were present at significantly higher levels in mice resistant to colitis. Further analysis revealed that Porphyromonadaceae levels were also increased in these mice. Conversely, there was a positive correlation between the abundance of Lactobacillus sp. and predisposition to colitis. Our data suggests that different members of the microbiota might be associated with S. Typhimurium colonization and colitis. Dissecting the mechanisms involved in resistance to infection and inflammation will be critical for the development of therapeutic and preventative measures against enteric pathogens