Simple groups separated by finiteness properties

We show that for every positive integer $n$ there exists a simple group that is of type $\mathrm{F}_{n-1}$ but not of type $\mathrm{F}_n$. For $n\ge 3$ these groups are the first known examples of this kind. They also provide infinitely many quasi-isometry classes of finitely presented simple groups. The only previously known infinite family of such classes, due to Caprace--R\'emy, consists of non-affine Kac--Moody groups over finite fields. Our examples arise from R\"over--Nekrashevych groups, and contain free abelian groups of infinite rank.Comment: 25 pages. v2: incorporated comments v3: final version, to appear, Invent. Mat

Otis Skipper to Jim, 18 May 1960

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Decision tree rating scales for workload estimation: Theme and variations

The Modified Cooper-Harper (MCH) scale which is a sensitive indicator of workload in several different types of aircrew tasks was examined. The study determined if variations of the scale might provide greater sensitivity and the reasons for the sensitivity of the scale. The MCH scale and five newly devised scales were examined in two different aircraft simulator experiments in which pilot loading was treated as an independent variable. It is indicated that while one of the new scales may be more sensitive in a given experiment, task dependency is a problem. The MCH scale exhibits consistent senstivity and remains the scale recommended for general use. The MCH scale results are consistent with earlier experiments. The rating scale experiments are reported and the questionnaire results which were directed to obtain a better understanding of the reasons for the relative sensitivity of the MCH scale and its variations are described

An Investigation of Tree Biomass in the Great Smoky Mountains National Park

We determined the biomass (carbon storage) of four forest types in the Great Smokey Mountains National Park: pine/oak, cove hardwood, northern hardwood, and spruce/fir. Based on the GLOBE Programs land cover protocols (www.globe.gov), and the University of New Hampshire\u27s GLOBE Carbon Cycle Program (http://globecarboncycle.unh.edu/), we knew that species and tree circumference would be the two most critical factors in determining biomass, but we also hypothesized that number of trees in a study site and the elevation of the site would impact biomass. We hypothesized that old growth forest would contain greater biomass than a young forest. We recorded tree species and circumference for every tree that had a circumference greater than 15 centimeters in each plot of 900 square. The circumference of a total of 219 trees represented by 22 different species, as well as forest type, elevation, and GPS coordinates for each plot, were recorded

Energy conservation for the Euler equations on T2 x R+ for weak solutions defined without reference to the pressure

We study weak solutions of the incompressible Euler equations on T2×R+; we use test functions that are divergence free and have zero normal component, thereby obtaining a definition that does not involve the pressure. We prove energy conservation under the assumptions that u∈L3(0,T;L3(T2×R+)), lim|y|→01|y|∫0T∫T2∫x3>|y|∞|u(x+y)−u(x)|3dxdt=0, and an additional continuity condition near the boundary: for some δ>0 we require u∈L3(0,T;C0(T2×[0,δ])). We note that all our conditions are satisfied whenever u(x,t)∈Cα, for some α>1/3, with Hölder constant C(x,t)∈L3(T2×R+×(0,T))

Finding core-periphery structures with node influences

Detecting core-periphery structures is one of the outstanding issues in complex network analysis. Various algorithms can identify core nodes and periphery nodes. Recent advances found that many networks from real-world data can be better modeled with multiple pairs of core-periphery nodes. In this study, we propose to use an influence propagation process to detect multiple pairs of core-periphery nodes. In this framework, we assume each node can emit a certain amount of influence and propagate it through the network. Then we identify nodes with large influences as core nodes, and we utilize a maximum influence chain to construct a node-pairing network to determine core-periphery pairs. This approach can take node interactions into consideration and can reduce noises in finding pairs. Experiments on randomly generated networks and real-world networks confirm the efficiency and accuracy of our algorithm

Energy conservation for the Euler equations on T2×R+\mathbb{T}^2\times \mathbb{R}_+ for weak solutions defined without reference to the pressure

We study weak solutions of the incompressible Euler equations on $\mathbb{T}^2\times \mathbb{R}_+$; we use test functions that are divergence free and have zero normal component, thereby obtaining a definition that does not involve the pressure. We prove energy conservation under the assumptions that $u\in L^3(0,T;L^3(\mathbb{T}^2\times \mathbb{R}_+))$, $$\lim_{|y|\to 0}\frac{1}{|y|}\int^T_0\int_{\mathbb{T}^2}\int^\infty_{x_3>|y|} |u(x+y)-u(x)|^3\mathrm{d} x\, \mathrm{d} t=0,$$ and an additional continuity condition near the boundary: for some $\delta>0$ we require $u\in L^3(0,T;C^0(\mathbb{T}^2\times [0,\delta])))$. We note that all our conditions are satisfied whenever $u(x,t)\in C^\alpha$, for some $\alpha>1/3$, with H\"older constant $C(x,t)\in L^3(\mathbb{T}^2\times\mathbb{R}^+\times(0,T))$.Comment: 21 page

Separating Stimulus-Induced and Background Components of Dynamic Functional Connectivity in Naturalistic fMRI

We consider the challenges in extracting stimulus-related neural dynamics from other intrinsic processes and noise in naturalistic functional magnetic resonance imaging (fMRI). Most studies rely on inter-subject correlations (ISC) of low-level regional activity and neglect varying responses in individuals. We propose a novel, data-driven approach based on low-rank plus sparse (L+S) decomposition to isolate stimulus-driven dynamic changes in brain functional connectivity (FC) from the background noise, by exploiting shared network structure among subjects receiving the same naturalistic stimuli. The time-resolved multi-subject FC matrices are modeled as a sum of a low-rank component of correlated FC patterns across subjects, and a sparse component of subject-specific, idiosyncratic background activities. To recover the shared low-rank subspace, we introduce a fused version of principal component pursuit (PCP) by adding a fusion-type penalty on the differences between the columns of the low-rank matrix. The method improves the detection of stimulus-induced group-level homogeneity in the FC profile while capturing inter-subject variability. We develop an efficient algorithm via a linearized alternating direction method of multipliers to solve the fused-PCP. Simulations show accurate recovery by the fused-PCP even when a large fraction of FC edges are severely corrupted. When applied to natural fMRI data, our method reveals FC changes that were time-locked to auditory processing during movie watching, with dynamic engagement of sensorimotor systems for speech-in-noise. It also provides a better mapping to auditory content in the movie than ISC

Superior multifunctional activity of nanoporous carbons with widely tuneable porosity: enhanced storage capacities for carbon-dioxide, hydrogen, water and electric charge

Nanoporous carbons (NPCs) with engineered specific pore sizes and sufficiently high porosities (both specific surface area and pore volume) are necessary for storing energy in the form of electric charges and molecules. Herein, NPCs, derived from biomass pine‐cones, coffee‐grounds, graphene‐oxide and metal‐organic frameworks, with systematically increased pore width (50 Wh kg−1 at high power density, 1000 W kg−1) are achieved to form the highest reported values among the range of carbons in the literature. The noteworthy energy storage performance of the NPCs for all five cases (CO2, H2, H2O, and capacitance in aqueous and organic electrolytes) is highlighted by direct comparison to numerous existing porous solids. A further analysis on the specific pore type governed physisorption capacities is presented