This article is devoted to the mass-less energy critical Maxwell-Klein-Gordon
system in 4+1 dimensions. In earlier work of the second author, joint with
Krieger and Sterbenz, we have proved that this problem has global
well-posedness and scattering in the Coulomb gauge for small initial data. This
article is the second of a sequence of three papers of the authors, whose goal
is to show that the same result holds for data with arbitrarily large energy.
Our aim here is to show that large data solutions persist for as long as one
has small energy dispersion; hence failure of global well-posedness must be
accompanied with a non-trivial energy dispersion.

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## Type of Work

Article (43) Book (0) Theses (0) Multimedia (0)

## Peer Review

Peer-reviewed only (40)

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## Publication Year

## Campus

UC Berkeley (5) UC Davis (4) UC Irvine (3) UCLA (9) UC Merced (0) UC Riverside (1) UC San Diego (2) UCSF (1) UC Santa Barbara (4) UC Santa Cruz (0) UC Office of the President (7) Lawrence Berkeley National Laboratory (25) UC Agriculture & Natural Resources (0)

## Department

Research Grants Program Office (RGPO) (7) University of California Research Initiatives (UCRI) (2) Multicampus Research Programs and Initiatives (MRPI); a funding opportunity through UC Research Initiatives (UCRI) (2)

Microbiology and Plant Pathology (1)

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Physical Sciences and Mathematics (2)

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## Scholarly Works (43 results)

This paper is the first part of a trilogy dedicated to a proof of global
well-posedness and scattering of the (4+1)-dimensional mass-less
Maxwell-Klein-Gordon equation (MKG) for any finite energy initial data. The
main result of the present paper is a large energy local well-posedness theorem
for MKG in the global Coulomb gauge, where the lifespan is bounded from below
by the energy concentration scale of the data. Hence the proof of global
well-posedness is reduced to establishing non-concentration of energy. To deal
with non-local features of MKG we develop initial data excision and gluing
techniques at critical regularity, which might be of independent interest.

This article constitutes the final and main part of a three-paper sequence,
whose goal is to prove global well-posedness and scattering of the energy
critical Maxwell-Klein-Gordon equation (MKG) on $\mathbb{R}^{1+4}$ for
arbitrary finite energy initial data. Using the successively stronger
continuation/scattering criteria established in the previous two papers, we
carry out a blow-up analysis and deduce that the failure of global
well-posedness and scattering implies the existence of a nontrivial stationary
or self-similar solution to MKG. Then, by establishing that such solutions do
not exist, we complete the proof.

© 2014 Royal Statistical Society. Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l1-penalties to either parametric likelihoods, or regularized regression/pseudolikelihoods, with the latter having the distinct advantage that they do not explicitly assume Gaussianity. As none of the popular methods proposed for solving pseudolikelihood-based objective functions have provable convergence guarantees, it is not clear whether corresponding estimators exist or are even computable, or if they actually yield correct partial correlation graphs. We propose a new pseudolikelihood-based graphical model selection method that aims to overcome some of the shortcomings of current methods, but at the same time retain all their respective strengths. In particular, we introduce a novel framework that leads to a convex formulation of the partial covariance regression graph problem, resulting in an objective function comprised of quadratic forms. The objective is then optimized via a co-ordinatewise approach. The specific functional form of the objective function facilitates rigorous convergence analysis leading to convergence guarantees; an important property that cannot be established by using standard results, when the dimension is larger than the sample size, as is often the case in high dimensional applications. These convergence guarantees ensure that estimators are well defined under very general conditions and are always computable. In addition, the approach yields estimators that have good large sample properties and also respect symmetry. Furthermore, application to simulated and real data, timing comparisons and numerical convergence is demonstrated. We also present a novel unifying framework that places all graphical pseudolikelihood methods as special cases of a more general formulation, leading to important insights.

Recent Work (2018)

Across a variety of scientific disciplines, sparse inverse covariance
estimation is a popular tool for capturing the underlying dependency
relationships in multivariate data. Unfortunately, most estimators are not
scalable enough to handle the sizes of modern high-dimensional data sets (often
on the order of terabytes), and assume Gaussian samples. To address these
deficiencies, we introduce HP-CONCORD, a highly scalable optimization method
for estimating a sparse inverse covariance matrix based on a regularized
pseudolikelihood framework, without assuming Gaussianity. Our parallel proximal
gradient method uses a novel communication-avoiding linear algebra algorithm
and runs across a multi-node cluster with up to 1k nodes (24k cores), achieving
parallel scalability on problems with up to ~819 billion parameters (1.28
million dimensions); even on a single node, HP-CONCORD demonstrates
scalability, outperforming a state-of-the-art method. We also use HP-CONCORD to
estimate the underlying dependency structure of the brain from fMRI data, and
use the result to identify functional regions automatically. The results show
good agreement with a clustering from the neuroscience literature.

Using high sensitivity visible-pump/THz-probe spectroscopy we investigate the dynamics of the complex optical conductivity in optimally-doped Bi2Sr2CaCu2O8+d films directly after photoexcitation. The photoinduced change in the imaginary part, indicative of a reduction in the superconducting condensate density, saturates at higher laser-fluences and shows a complete destruction of the condensate.

Malignant Pleural Effusions (MPE) may be useful as a model to study hierarchical progression of cancer and/or intratumoral heterogeneity. To strengthen the rationale for developing the MPE-model for these purposes, we set out to find evidence for the presence of cancer stem cells (CSC) in MPE and demonstrate an ability to sustain intratumoral heterogeneity in MPE-primary cultures. Our studies show that candidate lung CSC-expression signatures (PTEN, OCT4, hTERT, Bmi1, EZH2 and SUZ12) are evident in cell pellets isolated from MPE, and MPE-cytopathology also labels candidate-CSC (CD44, cMET, MDR-1, ALDH) subpopulations. Moreover, in primary cultures that use MPE as the source of both tumor cells and the tumor microenvironment (TME), candidate CSC are maintained over time. This allows us to live-sort candidate CSC-fractions from the MPE-tumor mix on the basis of surface markers (CD44, c-MET, uPAR, MDR-1) or differences in xenobiotic metabolism (ALDH). Thus, MPE-primary cultures provide an avenue to extract candidate CSC populations from individual (isogenic) MPE-tumors. This will allow us to test whether these cells can be discriminated in functional bioassays. Tumor heterogeneity in MPE-primary cultures is evidenced by variable immunolabeling, differences in colony-morphology, and differences in proliferation rates of cell subpopulations. Collectively, these data justify the ongoing development of the MPE-model for the investigation of intratumoral heterogeneity, tumor-TME interactions, and phenotypic validation of candidate lung CSC, in addition to providing direction for the pre-clinical development of rational therapeutics.

A versatile new class of organic photochromic molecules that offers an unprecedented combination of physical properties including tunable photoswitching using visible light, excellent fatigue resistance, and large polarity changes is described. These unique features offer significant opportunities in diverse fields ranging from biosensors to targeted delivery systems while also allowing non-experts ready synthetic access to these materials. © 2014 American Chemical Society.