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Let $G$ be a free-by-cyclic group or a 2-dimensional right-angled Artin group. We provide an algebraic and a geometric characterization for when each aspherical simplicial complex with fundamental group isomorphic to $G$ has minimal volume entropy equal to 0. In the nonvanishing case, we provide a positive lower bound to the minimal volume entropy of an aspherical simplicial complex of minimal dimension for these two classes of groups. Our results rely upon a criterion for the vanishing of the minimal volume entropy for 2-dimensional groups with uniform uniform exponential growth. This criterion is shown by analyzing the fiber $\pi_1$-growth collapse and non-collapsing assumptions of Babenko-Sabourau., Comment: 25 pages, 2 figures; v2: corrected error in statement and proof of Theorem 3.3, main results unchanged

For any right-angled Artin group $A_{\Gamma}$ we construct a finite-dimensional space $\mathcal{O}_{\Gamma}$ on which the group $\text{Out}(A_{\Gamma})$ of outer automorphisms of $A_{\Gamma}$ acts with finite point stabilizers. We prove that $\mathcal{O}_{\Gamma}$ is contractible, so that the quotient is a rational classifying space for $\text{Out}(A_{\Gamma})$. The space $\mathcal{O}_{\Gamma}$ blends features of the symmetric space of lattices in $\mathbb{R}^n$ with those of Outer space for the free group $F_n$. Points in $\mathcal{O}_{\Gamma}$ are locally CAT(0) metric spaces that are homeomorphic (but not isometric) to certain locally CAT(0) cube complexes, marked by an isomorphism of their fundamental group with $A_{\Gamma}$., Comment: 61 pages, 17 figures. Modified statement of the main theorem, changed exposition, added a figure

Background Pediatric low-grade gliomas (pLGGs) are the most common childhood brain tumor. Progression-free survival (PFS) is much lower than overall survival, emphasizing the need for alternative treatments. Sporadic (without neurofibromatosis type 1) optic pathway and hypothalamic gliomas (OPHGs) are often multiply recurrent and cause significant visual deficits. Recently, there has been a prioritization of functional outcomes. Methods We present results from children with recurrent/progressive OPHGs treated on a PBTC (Pediatric Brain Tumor Consortium) phase II trial evaluating efficacy of selumetinib (AZD6244, ARRY-142886) a MEK-1/2 inhibitor. Stratum 4 of PBTC-029 included patients with sporadic recurrent/progressive OPHGs treated with selumetinib at the recommended phase II dose (25mg/m2/dose BID) for a maximum of 26 courses. Results Twenty-five eligible and evaluable patients were enrolled with a median of 4 (1-11) previous therapies. Six of 25 (24%) had partial response, 14/25 (56%) had stable disease, and 5 (20%) had progressive disease while on treatment. The median treatment courses were 26 (2-26); 14/25 patients completed all 26 courses. Two-year PFS was 78 ± 8.5%. Nineteen of 25 patients were evaluable for visual acuity which improved in 4/19 patients (21%), was stable in 13/19 (68%), and worsened in 2/19 (11%). Five of 19 patients (26%) had improved visual fields and 14/19 (74%) were stable. The most common toxicities were grade 1/2 CPK elevation, anemia, diarrhea, headache, nausea/emesis, fatigue, AST and ALT increase, hypoalbuminemia, and rash. Conclusions Selumetinib was tolerable and led to responses and prolonged disease stability in children with recurrent/progressive OPHGs based upon radiographic response, PFS, and visual outcomes.

Cognitive dysfunction is a major concern for children with brain tumors. A valid, user-friendly screening tool could facilitate prompt referral for comprehensive neuropsychological assessments and therefore early intervention. Applications of the pediatric perceived cognitive function item bank (pedsPCF) such as computerized adaptive testing can potentially serve as such a tool given its brevity and user-friendly nature. This study aimed to evaluate whether pedsPCF was a valid indicator of cerebral compromise using the criterion of structural brain changes indicated by leukoencephalopathy grades.Data from 99 children (mean age = 12.6 years) with brain tumors and their parents were analyzed. Average time since diagnosis was 5.8 years; time since last treatment was 4.3 years. Leukoencephalopathy grade (range 0-4) was based on white matter damage and degree of deep white matter volume loss shown on MRI. Parents of patients completed the pedsPCF. Scores were based on the US general population-based T-score metric (mean = 50; SD = 10). Higher scores reflect better function.Leukoencephalopathy grade distributions were as follows: 36 grade 0, 27 grade 1, 22 grade 2, 13 grade 3, and 1 grade 4. The mean pedsPCF T-score was 48.3 (SD = 8.3; range 30.5-63.7). The pedsPCF scores significantly discriminated patients with different leukoencephalopathy grades, F = 4.14, p = 0.0084. Effect sizes ranged from 0.09 (grade 0 vs. 1) to 1.22 (grade 0 vs. 3/4).This study demonstrates that the pedsPCF is a valid indicator of leukoencephalopathy and provides support for its use as a screening tool for more comprehensive neurocognitive testing.

A Kodaira fibration is a compact, complex surface admitting a holomorphic submersion onto a complex curve, such that the fibers have nonconstant moduli. We consider Kodaira fibrations X with nontrivial invariant rational cohomology in degree 1, proving that if the dimension of the holomorphic invariants is 1 or 2, then X admits a branch covering over a product of curves inducing an isomorphism on rational cohomology in degree 1. We also study the class of Kodaira fibrations possessing a holomorphic section, and demonstrate that having a section imposes no restriction on possible monodromies., Comment: 17 pages, no figures. Comments welcome

The period mapping assigns to each rank n, marked metric graph Gamma a positive definite quadratic form on H_1(Gamma). This defines maps Phi* and Phi on Culler--Vogtmann's outer space CV_n, and its Torelli space quotient T_n, respectively. The map Phi is a free group analog of the classical period mapping that sends a marked Riemann surface to its Jacobian. In this paper, we analyze the fibers of Phi in T_n, showing that they are aspherical, pi_1-injective subspaces. Metric graphs admitting a 'hyperelliptic involution' play an important role in the structure of Phi, leading us to define the hyperelliptic Torelli group, ST(n) < Out(F_n). We obtain generators for ST(n), and apply them to show that the connected components of the locus of 'hyperelliptic' graphs in T_n become simply-connected when certain degenerate graphs at infinity are added., 40 pages, 9 figures, statement and proof of Theorem A corrected

OBJECTIVE: Cognitive dysfunction is a major concern for children with brain tumors. A valid, user-friendly screening tool can facilitate prompt referral for comprehensive neuropsychological assessments facilitating early intervention. The pediatric perceived cognitive function item bank (pedsPCF) was developed to fill this need. The pedsPCF discriminated known groups of patients with brain tumor versus other cancer, and significantly correlated with neuropsychological testing scores. This study aims to evaluate the relationship between the pedsPCF and imaging data by evaluating whether pedsPCF could differentiate patients with different leukoencephalopathy grades. METHODS: Data from 59 children (mean age =12.3 yrs; 51.7% males) with brain tumors from Lurie Children's Hospital of Chicago were analyzed. Of them, 26.7% had a ganglioglioma and 23.3% had a medulloblastoma; 90% received chemotherapy, 60% radiation and 61.7% surgery. Average years since diagnosis were 5.4, and since last treatment were 3.5 years. Leukoencephalopathy grade was assessed using the Common Terminology Criteria for Adverse Events (CTCAE 4.0): 0 = no symptoms, 4 = life-threatening consequences. Parents of patients completed the pedsPCF and their scores were reported using the US general population based T-score matrix (mean = 50 and standard deviation = 10), in which higher scores mean better function. RESULTS: 17 patients had a leukoencephalopathy grade of 0; 19 with a grade = 1; 13 with a grade = 2 and 11 with a grade = 3 or 4. Averaged pedsPCF T-scores = 47.9 (SD = 7.9, range: 34.6-63.7). PedsPCF scores were significantly correlated with leukoencephalopathy grade, rho = -0.37 (p < 0.01), and significantly differentiated patients with different grades, F = 4.49, p = 0.016, and effect sizes ranged from 0.38 to 1.01. CONCLUSIONS: This pilot study indicated that the pedsPCF could differentiate patients with different leukoencephalopathy grades and has potential to serve as a screening tool for referral. The pedsPCF is a brief and user-friendly tool, which can be completed by using computerized adaptive testing or static short-forms.

We construct the first known examples of infinite subgroups of the outer automorphism group of Out(A_Gamma), for certain right-angled Artin groups A_Gamma. This is achieved by introducing a new class of graphs, called focused graphs, whose properties allow us to exhibit (infinite) projective linear groups as subgroups of Out(Out(A_Gamma)). This demonstrates a marked departure from the known behavior of Out(Out(A_Gamma)) when A_Gamma is free or free abelian, as in these cases Out(Out(A_Gamma)) has order at most 4. We also disprove a previous conjecture of the second author, producing new examples of finite order members of certain Out(Aut(A_Gamma)).

Given a matrix $A\in SL(N,\Z)$, form the semidirect product $G=\Z^N\rtimes_A \Z$ where the $\Z$ factor acts on $\Z^N$ by $A$. Such a $G$ arises naturally as the fundamental group of an $N$-dimensional torus bundle which fibers over the circle. In this paper we prove that if $A$ has distinct eigenvalues not lying on the unit circle, then there exists a finite index subgroup $H\leq G$ possessing rational growth series for some generating set. In contrast, we show that if $A$ has at least one eigenvalue not lying on the unit circle, then $G$ is not almost convex for any generating set., Comment: 31 pages. Added a reference and a remark concerning previous work on the result in Theorem 1.2

To assess frequency of neural stem cell compartment (NSC) involvement in adult and pediatric gliomas [World Health Organization (WHO) grades 1–4], and to assess whether NSC involvement at presentation impacts on survival, recurrence rates, and/or transformation from low grade (WHO grade 1–2) to high grade disease (WHO grades 3–4). Cranial MRIs for 154 pediatric and 223 adult glioma patients treated from 2000 to 2012 were reviewed. NSC involvement was documented. Tumors were stratified by age (adult vs. pediatric), histology, tumor grade, tumor location, and involvement of midline structures. Odds ratios (OR) for death were calculated based on NSC status at presentation. Rates of transformation and recurrence rates (ORR) were compared using Fisher’s Exact Test. Time to recurrence (TTR) was calculated using student t test. Among recurrent and transformed tumors, we also assessed the rate of NSC involvement at time of recurrence or transformation. 74.8 % of tumors had NSC involvement. Higher rates of NSC involvement were seen among adult (p = .0001); high grade (p = .0001)); grade 2 versus grade 1 (p = .0001) and other grade 1 histologies (p = .0001) versus JPA (juvenile pilocytic astrocytoma) patients); grade 2–4 tumors (p = .0001); and supratentorial tumors (p