On the intersection of free subgroups in free products of groups

Let (G_i | i in I) be a family of groups, let F be a free group, and let G = F *(*I G_i), the free product of F and all the G_i. Let FF denote the set of all finitely generated subgroups H of G which have the property that, for each g in G and each i in I, H \cap G_i^{g} = {1}. By the Kurosh Subgroup Theorem, every element of FF is a free group. For each free group H, the reduced rank of H is defined as r(H) = max{rank(H) -1, 0} in \naturals \cup {\infty} \subseteq [0,\infty]. To avoid the vacuous case, we make the additional assumption that FF contains a non-cyclic group, and we define sigma := sup{r(H\cap K)/(r(H)r(K)) : H, K in FF and r(H)r(K) \ne 0}, sigma in [1,\infty]. We are interested in precise bounds for sigma. In the special case where I is empty, Hanna Neumann proved that sigma in [1,2], and conjectured that sigma = 1; almost fifty years later, this interval has not been reduced. With the understanding that \infty/(\infty -2) = 1, we define theta := max{|L|/(|L|-2) : L is a subgroup of G and |L| > 2}, theta in [1,3]. Generalizing Hanna Neumann's theorem, we prove that sigma in [theta, 2 theta], and, moreover, sigma = 2 theta if G has 2-torsion. Since sigma is finite, FF is closed under finite intersections. Generalizing Hanna Neumann's conjecture, we conjecture that sigma = theta whenever G does not have 2-torsion.Comment: 28 pages, no figure

EBF1-deficient bone marrow stroma elicits persistent changes in HSC potential

Crosstalk between mesenchymal stromal cells (MSCs) and hematopoietic stem cells (HSCs) is essential for hematopoietic homeostasis and lineage output. Here, we investigate how transcriptional changes in bone marrow (BM) MSCs result in long-lasting effects on HSCs. Single-cell analysis of Cxcl12-abundant reticular (CAR) cells and PDGFRα+Sca1+ (PαS) cells revealed an extensive cellular heterogeneity but uniform expression of the transcription factor gene Ebf1. Conditional deletion of Ebf1 in these MSCs altered their cellular composition, chromatin structure and gene expression profiles, including the reduced expression of adhesion-related genes. Functionally, the stromal-specific Ebf1 inactivation results in impaired adhesion of HSCs, leading to reduced quiescence and diminished myeloid output. Most notably, HSCs residing in the Ebf1-deficient niche underwent changes in their cellular composition and chromatin structure that persist in serial transplantations. Thus, genetic alterations in the BM niche lead to long-term functional changes of HSCs

Global long terminal repeat activation participates in establishing the unique gene expression programme of classical Hodgkin lymphoma

Long terminal repeat (LTR) elements are wide-spread in the human genome and have the potential to act as promoters and enhancers. Their expression is therefore under tight epigenetic control. We previously reported in classical Hodgkin Lymphoma (cHL) that a member of the THE1B class of LTR elements acted as a promoter for the proto-oncogene and growth factor receptor gene CSF1R and that expression of this gene is required for cHL tumour survival. However, to which extent and how such elements participate in globally shaping the unique cHL gene expression programme is unknown. To address this question we mapped the genome-wide activation of THE1-LTRs in cHL cells using a targeted next generation sequencing approach (RACE-Seq). Integration of these data with global gene expression data from cHL and control B cell lines showed a unique pattern of LTR activation impacting on gene expression, including genes associated with the cHL phenotype. We also show that global LTR activation is induced by strong inflammatory stimuli. Together these results demonstrate that LTR activation provides an additional layer of gene deregulation in classical Hodgkin lymphoma and highlight the potential impact of genome-wide LTR activation in other inflammatory diseases

Extended Fe-4 butterfly complexes: theoretical analysis of magnetic properties and magnetostructural maps

The inclusion of additional metal atoms in Fe-4 butterfly complexes drastically modifies their magnetic properties. Exchange interactions of a Fe4Y2 complex have been calculated using theoretical methods based on density functional theory. The calculated values are in good agreement with experimental data showing that the change in the nature of bridging ligands induces a dramatic decrease of the antiferromagnetic wing-body interaction while the body-body interaction between the two central iron atoms is ferromagnetic. Finally, we propose a new tool to facilitate the understanding of the magnetic properties in polynuclear iron complexes. Magnetostructural maps allow us to correlate the calculated exchange coupling constants with metal-metal distances for the dinuclear or polynuclear iron complexes that we have studied

Stochastic Line-Motion and Stochastic Conservation Laws for Non-Ideal Hydromagnetic Models. I. Incompressible Fluids and Isotropic Transport Coefficients

We prove that smooth solutions of non-ideal (viscous and resistive) incompressible magnetohydrodynamic equations satisfy a stochastic law of flux conservation. This property involves an ensemble of surfaces obtained from a given, fixed surface by advecting it backward in time under the plasma velocity perturbed with a random white-noise. It is shown that the magnetic flux through the fixed surface is equal to the average of the magnetic fluxes through the ensemble of surfaces at earlier times. This result is an analogue of the well-known Alfven theorem of ideal MHD and is valid for any value of the magnetic Prandtl number. A second stochastic conservation law is shown to hold at unit Prandtl number, a random version of the generalized Kelvin theorem derived by Bekenstein-Oron for ideal MHD. These stochastic conservation laws are not only shown to be consequences of the non-ideal MHD equations, but are proved in fact to be equivalent to those equations. We derive similar results for two more refined hydromagnetic models, Hall magnetohydrodynamics and the two-fluid plasma model, still assuming incompressible velocities and isotropic transport coefficients. Finally, we use these results to discuss briefly the infinite-Reynolds-number limit of hydromagnetic turbulence and to support the conjecture that flux-conservation remains stochastic in that limit.Comment: 20 pages, no figures, submitted to J. Math. Phys

Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

A Cauchy-Dirac delta function

The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.Comment: 24 pages, 2 figures; Foundations of Science, 201

Computer-assisted liver graft steatosis assessment via learning-based texture analysis

Purpose: Fast and accurate graft hepatic steatosis (HS) assessment is of primary importance for lowering liver dysfunction risks after transplantation. Histopathological analysis of biopsied liver is the gold standard for assessing HS, despite being invasive and time consuming. Due to the short time availability between liver procurement and transplantation, surgeons perform HS assessment through clinical evaluation (medical history, blood tests) and liver texture visual analysis. Despite visual analysis being recognized as challenging in the clinical literature, few efforts have been invested to develop computer-assisted solutions for HS assessment. The objective of this paper is to investigate the automatic analysis of liver texture with machine learning algorithms to automate the HS assessment process and offer support for the surgeon decision process. Methods: Forty RGB images of forty different donors were analyzed. The images were captured with an RGB smartphone camera in the operating room (OR). Twenty images refer to livers that were accepted and 20 to discarded livers. Fifteen randomly selected liver patches were extracted from each image. Patch size was 100 × 100. This way, a balanced dataset of 600 patches was obtained. Intensity-based features (INT), histogram of local binary pattern (HLBPriu2), and gray-level co-occurrence matrix (FGLCM) were investigated. Blood-sample features (Blo) were included in the analysis, too. Supervised and semisupervised learning approaches were investigated for feature classification. The leave-one-patient-out cross-validation was performed to estimate the classification performance. Results: With the best-performing feature set (HLBPriu2+INT+Blo) and semisupervised learning, the achieved classification sensitivity, specificity, and accuracy were 95, 81, and 88%, respectively. Conclusions: This research represents the first attempt to use machine learning and automatic texture analysis of RGB images from ubiquitous smartphone cameras for the task of graft HS assessment. The results suggest that is a promising strategy to develop a fully automatic solution to assist surgeons in HS assessment inside the OR