On plausible counterexamples to Lehnert's conjecture

A group whose co-word problem is a context free language is called co . Lehnert's conjecture states that a group is co if and only if embeds as a finitely generated subgroup of R. Thompson's group V . In this thesis we explore a class of groups, Faug, proposed by Berns-Zieze, Fry, Gillings, Hoganson, and Mathews to contain potential counterexamples to Lehnert's conjecture. We create infinite and finite presentations for such groups and go on to prove that a certain subclass of consists of groups that do embed into . By Anisimov a group has regular word problem if and only if it is finite. It is also known that a group is finite if and only if there exists an embedding of into such that its natural action on ₂:= {0, 1}[super] is free on the whole space. We show that the class of groups with a context free word problem, the class of groups, is precisely the class of finitely generated demonstrable groups for . A demonstrable group for V is a group which is isomorphic to a subgroup in whose natural action on ₂ acts freely on an open subset. Thus our result extends the correspondence between language theoretic properties of groups and dynamical properties of subgroups of V . Additionally, our result also shows that the final condition of the four known closure properties of the class of co groups also holds for the set of finitely generated subgroups of

Primary vs. Secondary Antibody Deficiency: Clinical Features and Infection Outcomes of Immunoglobulin Replacement

<div><p>Secondary antibody deficiency can occur as a result of haematological malignancies or certain medications, but not much is known about the clinical and immunological features of this group of patients as a whole. Here we describe a cohort of 167 patients with primary or secondary antibody deficiencies on immunoglobulin (Ig)-replacement treatment. The demographics, causes of immunodeficiency, diagnostic delay, clinical and laboratory features, and infection frequency were analysed retrospectively. Chemotherapy for B cell lymphoma and the use of Rituximab, corticosteroids or immunosuppressive medications were the most common causes of secondary antibody deficiency in this cohort. There was no difference in diagnostic delay or bronchiectasis between primary and secondary antibody deficiency patients, and both groups experienced disorders associated with immune dysregulation. Secondary antibody deficiency patients had similar baseline levels of serum IgG, but higher IgM and IgA, and a higher frequency of switched memory B cells than primary antibody deficiency patients. Serious and non-serious infections before and after Ig-replacement were also compared in both groups. Although secondary antibody deficiency patients had more serious infections before initiation of Ig-replacement, treatment resulted in a significant reduction of serious and non-serious infections in both primary and secondary antibody deficiency patients. Patients with secondary antibody deficiency experience similar delays in diagnosis as primary antibody deficiency patients and can also benefit from immunoglobulin-replacement treatment.</p></div

Groups with context-free co-word problem

The class of co-context-free groups is studied. A co-context-free group is defined as one whose coword problem (the complement of its word problem) is context-free. This class is larger than the subclass of context-free groups, being closed under the taking of finite direct products, restricted standard wreath products with context-free top groups, and passing to finitely generated subgroups and finite index overgroups. No other examples of co-context-free groups are known. It is proved that the only examples amongst polycyclic groups or the Baumslag–Solitar groups are virtually abelian. This is done by proving that languages with certain purely arithmetical properties cannot be context-free; this result may be of independent interest

Timed pushdown automata revisited

This paper contains two results on timed extensions of pushdown automata (PDA). As our first result we prove that the model of dense-timed PDA of Abdulla et al. collapses: it is expressively equivalent to dense-timed PDA with timeless stack. Motivated by this result, we advocate the framework of first-order definable PDA, a specialization of PDA in sets with atoms, as the right setting to define and investigate timed extensions of PDA. The general model obtained in this way is Turing complete. As our second result we prove NEXPTIME upper complexity bound for the non-emptiness problem for an expressive subclass. As a byproduct, we obtain a tight EXPTIME complexity bound for a more restrictive subclass of PDA with timeless stack, thus subsuming the complexity bound known for dense-timed PDA.Comment: full technical report of LICS'15 pape

RG flows with supersymmetry enhancement and geometric engineering

In this paper we study a class of $\mathcal{N}=2$ SCFTs with ADE global symmetry defined via Type IIB compactification on a class of hypersurfaces in $\mathbb{C}^3\times\mathbb{C}^*$. These can also be constructed by compactifying the 6d (2,0) theory of type ADE on a sphere with an irregular and a full punctures. When we couple to the ADE moment map a chiral multiplet in the adjoint representation and turn on a (principal) nilpotent vev for it, all the theories in this family display enhancement of supersymmetry in the infrared. We observe that all known examples of lagrangian theories which flow, upon the same type of deformation, to strongly coupled $\mathcal{N}=2$ theories fit naturally in our framework, thus providing a new perspective on this topic. We propose an infrared equivalence between this RG flow and a manifestly $\mathcal{N}=2$ preserving one and, as a byproduct, we extract a precise prescription to relate the SW curves describing the UV and IR fixed points for all theories with A or D global symmetry. We also find, for a certain subclass, a simple relation between UV and IR theories at the level of chiral algebras.Comment: clarifications added, version published in JHE