Embedability between right-angled Artin groups

In this article we study the right-angled Artin subgroups of a given right-angled Artin group. Starting with a graph \gam, we produce a new graph through a purely combinatorial procedure, and call it the extension graph \gam^e of \gam. We produce a second graph \gam^e_k, the clique graph of \gam^e, by adding extra vertices for each complete subgraph of \gam^e. We prove that each finite induced subgraph $\Lambda$ of \gam^e gives rise to an inclusion A(\Lambda)\to A(\gam). Conversely, we show that if there is an inclusion A(\Lambda)\to A(\gam) then $\Lambda$ is an induced subgraph of \gam^e_k. These results have a number of corollaries. Let $P_4$ denote the path on four vertices and let $C_n$ denote the cycle of length $n$. We prove that $A(P_4)$ embeds in A(\gam) if and only if $P_4$ is an induced subgraph of \gam. We prove that if $F$ is any finite forest then $A(F)$ embeds in $A(P_4)$. We recover the first author's result on co--contraction of graphs and prove that if \gam has no triangles and A(\gam) contains a copy of $A(C_n)$ for some $n\geq 5$, then \gam contains a copy of $C_m$ for some $5\le m\le n$. We also recover Kambites' Theorem, which asserts that if $A(C_4)$ embeds in A(\gam) then \gam contains an induced square. Finally, we determine precisely when there is an inclusion $A(C_m)\to A(C_n)$ and show that there is no "universal" two--dimensional right-angled Artin group.Comment: 35 pages. Added an appendix and a proof that the extension graph is quasi-isometric to a tre

Slender-ribbon theory

Ribbons are long narrow strips possessing three distinct material length scales (thickness, width, and length) which allow them to produce unique shapes unobtainable by wires or filaments. For example when a ribbon has half a twist and is bent into a circle it produces a M\"obius strip. Significant effort has gone into determining the structural shapes of ribbons but less is know about their behavior in viscous fluids. In this paper we determine, asymptotically, the leading-order hydrodynamic behavior of a slender ribbon in Stokes flows. The derivation, reminiscent of slender-body theory for filaments, assumes that the length of the ribbon is much larger than its width, which itself is much larger than its thickness. The final result is an integral equation for the force density on a mathematical ruled surface, termed the ribbon plane, located inside the ribbon. A numerical implementation of our derivation shows good agreement with the known hydrodynamics of long flat ellipsoids, and successfully captures the swimming behavior of artificial microscopic swimmers recently explored experimentally. We also study the asymptotic behavior of a ribbon bent into a helix, that of a twisted ellipsoid, and we investigate how accurately the hydrodynamics of a ribbon can be effectively captured by that of a slender filament. Our asymptotic results provide the fundamental framework necessary to predict the behavior of slender ribbons at low Reynolds numbers in a variety of biological and engineering problems.This research was funded in part by the European Union through a Marie Curie CIG Grant and the Cambridge Trusts.This is the author accepted manuscript. The final version is available from American Institute of Physics via http://dx.doi.org/10.1063/1.493856

Tadpole Labelled Oriented Graph Groups and Cyclically Presented Groups

We study a class of Labelled Oriented Graph (LOG) group where the underlying graph is a tadpole graph. We show that such a group is the natural HNN extension of a cyclically presented group and investigate the relationship between the LOG group and the cyclically presented group. We relate the second homotopy groups of their presentations and show that hyperbolicity of the cyclically presented group implies solvability of the conjugacy problem for the LOG group. In the case where the label on the tail of the LOG spells a positive word in the vertices in the circuit we show that the LOGs and groups coincide with those considered by Szczepa�nski and Vesnin. We obtain new presentations for these cyclically presented groups and show that the groups of Fibonacci type introduced by Johnson and Mawdesley are of this form. These groups generalize the Fibonacci groups and the Sieradski groups and have been studied by various authors. We continue these investigations, using small cancellation and curvature methods to obtain results on hyperbolicity, automaticity, SQ-universality, and solvability of decision problems

Remnant inequalities and doubly-twisted conjugacy in free groups

We give two results for computing doubly-twisted conjugacy relations in free groups with respect to homomorphisms $\phi$ and $\psi$ such that certain remnant words from $\phi$ are longer than the images of generators under $\psi$. Our first result is a remnant inequality condition which implies that two words $u$ and $v$ are not doubly-twisted conjugate. Further we show that if $\psi$ is given and $\phi$, $u$, and $v$ are chosen at random, then the probability that $u$ and $v$ are not doubly-twisted conjugate is 1. In the particular case of singly-twisted conjugacy, this means that if $\phi$, $u$, and $v$ are chosen at random, then $u$ and $v$ are not in the same singly-twisted conjugacy class with probability 1. Our second result generalizes Kim's "bounded solution length". We give an algorithm for deciding doubly-twisted conjugacy relations in the case where $\phi$ and $\psi$ satisfy a similar remnant inequality. In the particular case of singly-twisted conjugacy, our algorithm suffices to decide any twisted conjugacy relation if $\phi$ has remnant words of length at least 2. As a consequence of our generic properties we give an elementary proof of a recent result of Martino, Turner, and Ventura, that computes the densities of injective and surjective homomorphisms from one free group to another. We further compute the expected value of the density of the image of a homomorphism.Comment: Totally reworked: bogus section removed, much new material adde

Salvage Fractionated Stereotactic Re-irradiation (FSRT) for Patients with Recurrent High Grade Gliomas Progressed after Bevacizumab Treatment

Purpose/Objectives: Bevacizumab failure is a major clinical problem in the manage- ment of high grade gliomas (HGG), with a median overall survival of less than 4 months (m). This study evaluated the efficacy of fractionated stereotactic re-irradiation (FSRT) for patients with HGG after progression on Bevacizumab. Materials/Methods: Retrospective review was conducted of patients treated with FSRT after progression on bevacizumab. A total of 36 patients were identified. FSRT was most commonly delivered in 3.5 Gy fractions to a total dose of 35 Gy. Survival from initial diagnosis, as well as from recurrence and re-irradiation, were utilized as study endpoints. Univariate and multivariate analysis was performed. Results: Among the 36 patients, 31 patients had recurrent glioblastoma, and 5 patients had recurrent anaplastic astrocytoma. The median time from initial bevacizumab treatment to FSRT was 8.5 m (range 2.3 – 32.0 m). The median plan target volume for FSRT was 27.5 cc (range 1.95 – 165 cc). With a median follow up of 20.4 m, the overall survival of the patients since initial diagnosis was also 24.9 m. The median overall survival after initiation of bevacizumab was 13.4 months. The median overall survival from FSRT was 4.8 m. FSRT treatment was well tolerated with no Grade \u3e3 toxicity. Conclusions: Favorable outcomes were observed in patients with recurrent HGG who received salvage FSRT after bevacizumab failure. The treatment was well tolerated. Prospective study is warranted to further evaluate the efficacy of salvage FSRT for selected patients with recurrent HGG amenable to FSRT, who had failed bevacizumab treatment

Co-expression of CD56 and CD30 in lymphomas with primary presentation in the skin: clinicopathologic, immunohistochemical and molecular analyses of seven cases

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74772/1/j.1600-0560.2000.027008392.x.pd

Phase I Study of Ipilimumab Combined with Whole Brain Radiation Therapy or Radiosurgery for Melanoma Patients with Brain Metastases

Purpose: We performed a phase I study to determine the maximum tolerable dose (MTD) and safety of ipilimumab with stereotactic radiosurgery (SRS) or whole brain radiotherapy (WBRT) in patients with brain metastases (BM) from melanoma. Methods: Based on intracranial (IC) disease burden, patients were treated with WBRT (Arm A) or SRS (Arm B). Ipilimumab starting dose was 3 mg/kg (every 3 weeks, starting on day 3 of WBRT or 2 days after SRS). Ipilimumab was escalated to 10 mg/kg using a two-stage, 3+3 design. The primary endpoint was to determine the MTD of ipilimumab combined with radiotherapy. Secondary endpoints were overall survival (OS), IC and extracranial (EC) control, progression free survival (PFS), and toxicity. This trial is regis- tered with ClinicalTrials.gov, number NCT01703507. Results: Characteristics of the 16 patients enrolled between 2011 and 2014 were: mean age, 60; median BM, 2 (1 to \u3e10); number with EC disease, 13 (81%). Treatment included WBRT (n=5), SRS (n=11), ipilimumab 3mg/kg (n=7), 10 mg/kg (n=9). Median follow-up was 8 months (Arm A) and 10.5 months (Arm B). There were 21 grade 1-2 neuro- toxic effects with no dose-limiting toxicities (DLTs). One patient experienced grade 3 neurotoxicity prior to ipilimumab administration. Ten additional grade 3 toxicities were reported with gastrointestinal (n=5, 31%) as the most common. There were no grade 4/5 toxicities. Median PFS and OS, respectively, in Arm A were 2.5 months and 8 months, and in Arm B were 2.1 months and not reached. Conclusion: Concurrent ipilimumab 10 mg/kg with SRS is safe. The WBRT arm was closed early due to slow accrual, but demonstrated safety with ipilimumab 3 mg/kg. No patient experienced DLT. Larger studies with ipilimumab 10 mg/kg and SRS are warranted

Short Communication: Lack of Support for Socially Connected HIV-1 Transmission among Young Adult Black Men Who Have Sex with Men

© Copyright 2017, Mary Ann Liebert, Inc. 2017. We explore the phylogenetic relationships among HIV sequences sampled from young adult black men who have sex with men (YAB-MSM), who are connected through peer referral/social ties and who attend common venues. Using 196 viral sequences sampled from the peripheral blood mononuclear cells of 10 individuals, our preliminary phylogenetic results indicate that these socially connected YAB-MSM are infected with distantly related viruses and provide no evidence for viral transmission between network members. Our results suggest that HIV-prevention strategies that target young adult MSM should extend beyond their network members and local community

Interstitial mycosis fungoides, a variant of mycosis fungoides resembling granuloma annulare and inflammatory morphea *

Interstitial mycosis fungoides (IMF) is a rare variant of mycosis fungoides that resembles the interstitial form of granuloma annulare and inflammatory morphea. IMF has received little attention in the literature. Methods:   Clinical, histological, immunophenotypical, and genotypical findings of five cases of IMF were reviewed. The histological and immunophenotypical findings were compared with those of eight cases of interstitial granuloma annulare and six cases of inflammatory morphea. Results:   Five patients with IMF presented with non-indurated, erythematous macules; ill-defined erythematous plaques with slight scale; and nodules on the trunk and proximal limbs. Two of five patients had a prior diagnosis of mycosis fungoides. Skin biopsies revealed a striking dermal interstitial infiltrate of lymphocytes with rare histiocytes that resembled the interstitial form of granuloma annulare or inflammatory morphea. Epidermotropic lymphocytes were present at least focally in all cases. A band-like lymphocytic infiltrate was observed in two of five cases. In contrast, many plasma cells and histiocytes were observed in cases of inflammatory morphea and interstitial granuloma annulare, respectively. With Movat-pentachrome stains, increased dermal mucin deposition was observed in two of five IMF cases, in all cases of interstitial granuloma annulare, and in one of six cases of inflammatory morphea. There was focal loss of elastic fibers in all cases of inflammatory morphea. Immunohistochemical studies of IMF highlighted a dominant population of T cells (CD3+) in the dermis and epidermis. In contrast, moderate numbers of B cells (CD20+) were admixed with T cells and plasma cells in inflammatory morphea. Almost equal numbers of histiocytes (CD68+) and T cells comprised the infiltrate of interstitial granuloma annulare. In two of five IMF cases, a clonal T-cell population was detected by PCR T-cell gamma gene rearrangement analysis. Conclusion:   Mycosis fungoides occasionally presents as an interstitial lymphocytic infiltrate that mimics granuloma annulare and inflammatory morphea. Hematoxylin & eosin (H&E) findings alone can sometimes distinguish the three disorders. Immunophenotyping and genotyping may be helpful in difficult cases. Su LD, Kim YH, LeBoit PE, Swetter SM, Kohler S. Interstitial mycosis fungoides, a variant of mycosis fungoides resembling granuloma annulare and inflammatory morphea. J Cutan Pathol 2002; 29: 135–141. © Blackwell Munksgaard 2002.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72026/1/j.1600-0560.2002.290302.x.pd