Alzheimer's disease (AD) is characterized by two molecular pathologies: cerebral β-amyloidosis in the form of β-amyloid (Aβ) plaques and tauopathy in the form of neurofibrillary tangles, neuritic plaques, and neuropil threads. Until recently, only Aβ could be studied in humans using positron emission tomography (PET) imaging owing to a lack of tau PET imaging agents. Clinical pathological studies have linked tau pathology closely to the onset and progression of cognitive symptoms in patients with AD. We report PET imaging of tau and Aβ in a cohort of cognitively normal older adults and those with mild AD. Multivariate analyses identified unique disease-related stereotypical spatial patterns (topographies) for deposition of tau and Aβ. These PET imaging tau and Aβ topographies were spatially distinct but correlated with disease progression. Cerebrospinal fluid measures of tau, often used to stage preclinical AD, correlated with tau deposition in the temporal lobe. Tau deposition in the temporal lobe more closely tracked dementia status and was a better predictor of cognitive performance than Ab deposition in any region of the brain. These data support models of AD where tau pathology closely tracks changes in brain function that are responsible for the onset of early symptoms in AD.

Graphical Abstract Highlights d Implementing FAIR data standards requires identification of experimental confounders d Five labs performed the same experiment on mammalian cells and compared results d Several factors affecting reproducibility were explored d Biological context had an unexpected impact on the robustness of cell-based assays

Most cancer cells harbor multiple drivers whose epistasis and interactions with expression context clouds drug and drug combination sensitivity prediction. We constructed a mechanistic computational model that is context-tailored by omics data to capture regulation of stochastic proliferation and death by pan-cancer driver pathways. Simulations and experiments explore how the coordinated dynamics of RAF/MEK/ERK and PI-3K/AKT kinase activities in response to synergistic mitogen or drug combinations control cell fate in a specific cellular context. In this MCF10A cell context, simulations suggest that synergistic ERK and AKT inhibitor-induced death is likely mediated by BIM rather than BAD, which is supported by prior experimental studies. AKT dynamics explain S-phase entry synergy between EGF and insulin, but simulations suggest that stochastic ERK, and not AKT, dynamics seem to drive cell-to-cell proliferation variability, which in simulations is predictable from pre-stimulus fluctuations in C-Raf/B-Raf levels. Simulations suggest MEK alteration negligibly influences transformation, consistent with clinical data. Tailoring the model to an alternate cell expression and mutation context, a glioma cell line, allows prediction of increased sensitivity of cell death to AKT inhibition. Our model mechanistically interprets context-specific landscapes between driver pathways and cell fates, providing a framework for designing more rational cancer combination therapy.

A recent paper of Arnold, Falk, and Winther (Bull. Am. Math. Soc. 47:281-354, 2010) showed that a large class of mixed finite element methods can be formulated naturally on Hilbert complexes, where using a Galerkin-like approach, one solves a variational problem on a finite-dimensional subcomplex. In a seemingly unrelated research direction, Dziuk (Lecture Notes in Math., vol. 1357, pp. 142-155, 1988) analyzed a class of nodal finite elements for the Laplace-Beltrami equation on smooth 2-surfaces approximated by a piecewise-linear triangulation; Demlow later extended this analysis (SIAM J. Numer. Anal. 47:805-827, 2009) to 3-surfaces, as well as to higher-order surface approximation. In this article, we bring these lines of research together, first developing a framework for the analysis of variational crimes in abstract Hilbert complexes, and then applying this abstract framework to the setting of finite element exterior calculus on hypersurfaces. Our framework extends the work of Arnold, Falk, and Winther to problems that violate their subcomplex assumption, allowing for the extension of finite element exterior calculus to approximate domains, most notably the Hodge-de Rham complex on approximate manifolds. As an application of the latter, we recover Dziuk's and Demlow's a priori estimates for 2-and 3-surfaces, demonstrating that surface finite element methods can be analyzed completely within this abstract framework. Moreover, our results gener- Communicated by 264 Found Comput Math (2012) 12:263-293 alize these earlier estimates dramatically, extending them from nodal finite elements for Laplace-Beltrami to mixed finite elements for the Hodge Laplacian, and from 2-and 3-dimensional hypersurfaces to those of arbitrary dimension. By developing this analytical framework using a combination of general tools from differential geometry and functional analysis, we are led to a more geometric analysis of surface finite element methods, whereby the main results become more transparent.

ABSTRACT. In this paper, we derive a variational integrator for certain highly oscillatory problems in mechanics. To do this, we take a new approach to the splitting of fast and slow potential forces: rather than splitting these forces at the level of the differential equations or the Hamiltonian, we split the two potentials with respect to the Lagrangian action integral. By using a different quadrature rule to approximate the contribution of each potential to the action, we arrive at a geometric integrator that is implicit in the fast force and explicit in the slow force. This can allow for significantly longer time steps to be taken (compared to standard explicit methods, such as Störmer/Verlet) at the cost of only a linear solve rather than a full nonlinear solve. We also analyze the stability of this method, in particular proving that it eliminates the linear resonance instabilities that can arise with explicit multiple-time-stepping methods. Next, we perform some numerical experiments, studying the behavior of this integrator for two test problems: a system of coupled linear oscillators, for which we compare against the resonance behavior of the r-RESPA method; and slow energy exchange in the Fermi-Pasta-Ulam problem, which couples fast linear oscillators with slow nonlinear oscillators. Finally, we prove that this integrator accurately preserves the slow energy exchange between the fast oscillatory components, which explains the numerical behavior observed for the Fermi-Pasta-Ulam problem.

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We study modified trigonometric integrators, which generalize the popular class of trigonometric integrators for highly oscillatory Hamiltonian systems by allowing the fast frequencies to be modified. Among all methods of this class, we show that the IMEX (implicit-explicit) method, which is equivalent to applying the midpoint rule to the fast, linear part of the system and the leapfrog (Störmer/Verlet) method to the slow, nonlinear part, is distinguished by the following properties: (i) it is symplectic; (ii) it is free of artificial resonances; (iii) it is the unique method that correctly captures slow energy exchange to leading order; (iv) it conserves the total energy and a modified oscillatory energy up to to second order; (v) it is uniformly second-order accurate in the slow components; and (vi) it has the correct magnitude of deviations of the fast oscillatory energy, which is an adiabatic invariant. These theoretical results are supported by numerical experiments on the Fermi-Pasta-Ulam problem and indicate that the IMEX method, for these six properties, dominates the class of modified trigonometric integrators.

Mass cytometry offers the advantage of allowing the simultaneous measurement of a greater number parameters than conventional flow cytometry. However, to date, mass cytometry has lacked a reliable alternative to the light scatter properties that are commonly used as a cell size metric in flow cytometry (forward scatter intensity—FSC). Here, we report the development of two plasma membrane staining assays to evaluate mammalian cell size in mass cytometry experiments. One is based on wheat germ agglutinin (WGA) staining and the other on Osmium tetroxide (OsO4) staining, both of which have preferential affinity for cell membranes. We first perform imaging and flow cytometry experiments to establish a relationship between WGA staining intensity and traditional measures of cell size. We then incorporate WGA staining in mass cytometry analysis of human whole blood and show that WGA staining intensity has reproducible patterns within and across immune cell subsets that have distinct cell sizes. Lastly, we stain PBMCs or dissociated lung tissue with both WGA and OsO4 ; mass cytometry analysis demonstrates that the two staining intensities correlate well with one another. We conclude that both WGA and OsO4 may be used to acquire cell size-related parameters in mass cytometry experiments, and expect these stains to be broadly useful in expanding the range of parameters that can be measured in mass cytometry experiments.