The fully compressed subgroup membership problem

Suppose that F is a free group and k is a natural number. We show that the fully compressed membership problem for k-generated subgroups of F is solvable in polynomial time. In order to do this, we adapt the theory of Stallings' foldings to handle edges with compressed labels. This partially answers a question of Markus Lohrey

Hyperbolic one-relator groups

We introduce two families of two-generator one-relator groups called primitive extension groups and show that a one-relator group is hyperbolic if its primitive extension subgroups are hyperbolic. This reduces the problem of characterising hyperbolic one-relator groups to characterising hyperbolic primitive extension groups. These new groups moreover admit explicit decompositions as graphs of free groups with adjoined roots. In order to obtain this result, we characterise 2-free one-relator groups with exceptional intersection in terms of Christoffel words, show that hyperbolic one-relator groups have quasi-convex Magnus subgroups and build upon the one-relator tower machinery developed in previous work of the author

Hyperbolic one-relator groups

We introduce two families of two-generator one-relator groups called primitive extension groups and show that a one-relator group is hyperbolic if its primitive extension subgroups are hyperbolic. This reduces the problem of characterising hyperbolic one-relator groups to characterising hyperbolic primitive extension groups. These new groups moreover admit explicit decompositions as graphs of free groups with adjoined roots. In order to obtain this result, we characterise $2$-free one-relator groups with exceptional intersection in terms of Christoffel words, show that hyperbolic one-relator groups have quasi-convex Magnus subgroups and build upon the one-relator tower machinery developed in the authors previous article.Comment: 21 pages, 5 figure

The Atiyah conjecture for three-manifold groups

We show that finitely generated fundamental groups of three-manifolds satisfy the Strong Atiyah Conjecture over the complex numbers. This implies that when the group is additionally torsion-free, then its complex group ring satisfies the Kaplansky Zero-divisor Conjecture. As an application, we give a very short proof of a significant generalisation of a recent result of Shalen dealing with the minimal index of freedom of three-manifold groups.Comment: 8 page

Virtually free-by-cyclic groups

We obtain a homological characterisation of virtually free-by-cyclic groups among groups that are hyperbolic and virtually compact special. As a consequence, we show that many groups known to be coherent actually possess the stronger property of being virtually free-by-cyclic. In particular, we show that all one-relator groups with torsion are virtually free-by-cyclic, solving a conjecture of Baumslag.Comment: 30 pages. Incorporated the referee's comments and corrections. Final version to appear in Geometric and Functional Analysi

One-relator hierarchies

The Magnus hierarchy has been used for almost a century to study one-relator groups. Taking a topological viewpoint, we refine the Magnus hierarchy. With this new tool, we characterise quasi-convex one-relator hierarchies in the sense of Wise. This new characterisation has several applications: we confirm a conjecture of Louder and Wilton on one-relator groups with negative immersions, we characterise hyperbolic one-relator groups with exceptional intersection, and answer a question of Baumslag’s on parafree one-relator groups. Finally, we introduce two new families of two-generator one-relator groups and prove that Gersten’s hyperbolicity conjecture is true for all one-relator groups if and only if it is true for these families

Immunosenescence and lymphomagenesis

One of the most important determinants of aging-related changes is a complex biological process emerged recently and called \u201cimmunosenescence\u201d. Immunosenescence refers to the inability of an aging immune system to produce an appropriate and effective response to challenge. This immune dysregulation may manifest as increased susceptibility to infection, cancer, autoimmune disease, and vaccine failure. At present, the relationship between immunosenescence and lymphoma in elderly patients is not defined in a satisfactory way. This review presents a brief overview of the interplay between aging, cancer and lymphoma, and the key topic of immunosenescence is addressed in the context of two main lymphoma groups, namely Non Hodgkin Lymphoma (NHL) and Hodgkin Lymphoma (HL). Epstein Barr Virus (EBV) plays a central role in the onset of neoplastic lymphoproliferation associated with immunological changes in aging, although the pathophysiology varies vastly among different disease entities. The interaction between immune dysfunction, immunosenescence and Epstein Barr Virus (EBV) infection appears to differ between NHL and HL, as well as between NHL subtypes

Induction therapy with the MATRix regimen in patients with newly diagnosed primary diffuse large B-cell lymphoma of the central nervous system - an international study of feasibility and efficacy in routine clinical practice

The MATRix chemoimmunotherapy regimen is highly effective in patients with newly diagnosed primary diffuse large B-cell lymphoma of the central nervous system (PCNSL). However, nothing is known about its feasibility and efficacy in everyday practice, where patients are more often older/frailer than those enrolled in clinical trials. We conducted a retrospective study addressing tolerability/efficacy of MATRix in 156 consecutive patients with newly diagnosed PCNSL treated outside a clinical trial. Median age and ECOG Performance Status of considered patients were 62 years (range 28–78) and 2 (range 0–4). The overall response rate after MATRix was 79%. Nine (6%) treatment-related deaths were recorded. After a median follow-up of 27.4 months (95% confidence interval [CI] 24.4–31.9%), the two-year progression-free and overall survival were 56% (95% CI 48.4–64.9%) and 64.1% (95% CI 56.7–72.5%) respectively. Patients not eligible for the IELSG32 trial were treated with lower dose intensity and had substantially worse outcomes than those fulfilling inclusion criteria. This is the largest series of PCNSL patients treated with MATRix outside a trial and recapitulates the IELSG32 trial outcomes in the non-trial setting for patients who fit the trial criteria. These data underscore the feasibility and efficacy of MATRix as induction treatment for fit patients in routine practice

Fast Computing Betweenness Centrality with Virtual Nodes on Large Sparse Networks

Betweenness centrality is an essential index for analysis of complex networks. However, the calculation of betweenness centrality is quite time-consuming and the fastest known algorithm uses time and space for weighted networks, where and are the number of nodes and edges in the network, respectively. By inserting virtual nodes into the weighted edges and transforming the shortest path problem into a breadth-first search (BFS) problem, we propose an algorithm that can compute the betweenness centrality in time for integer-weighted networks, where is the average weight of edges and is the average degree in the network. Considerable time can be saved with the proposed algorithm when , indicating that it is suitable for lightly weighted large sparse networks. A similar concept of virtual node transformation can be used to calculate other shortest path based indices such as closeness centrality, graph centrality, stress centrality, and so on. Numerical simulations on various randomly generated networks reveal that it is feasible to use the proposed algorithm in large network analysis

The Feasibility and Impact of Delivering a Mind-Body Intervention in a Virtual World

Introduction: Mind-body medical approaches may ameliorate chronic disease. Stress reduction is particularly helpful, but face-to-face delivery systems cannot reach all those who might benefit. An online, 3-dimensional virtual world may be able to support the rich interpersonal interactions required of this approach. In this pilot study, we explore the feasibility of translating a face-to-face stress reduction program into an online virtual setting and estimate the effect size of the intervention. Methods and Findings: Domain experts in virtual world technology joined with mind body practitioners to translate an existing 8 week relaxation response-based resiliency program into an 8-week virtual world-based program in Second Life™ (SL). Twenty-four healthy volunteers with at least one month's experience in SL completed the program. Each subject filled out the Perceived Stress Scale (PSS) and the Symptom Checklist 90- Revised (SCL-90-R) before and after taking part. Participants took part in one of 3 groups of about 10 subjects. The participants found the program to be helpful and enjoyable. Many reported that the virtual environment was an excellent substitute for the preferred face-to-face approach. On quantitative measures, there was a general trend toward decreased perceived stress, (15.7 to 15.0), symptoms of depression, (57.6 to 57.0) and anxiety (56.8 to 54.8). There was a significant decrease of 2.8 points on the SCL-90-R Global Severity Index (p<0.05). Conclusions: This pilot project showed that it is feasible to deliver a typical mind-body medical intervention through a virtual environment and that it is well received. Moreover, the small reduction in psychological distress suggests further research is warranted. Based on the data collected for this project, a randomized trial with less than 50 subjects would be appropriately powered if perceived stress is the primary outcome