887 research outputs found
Convergence of trust-region methods based on probabilistic models
In this paper we consider the use of probabilistic or random models within a
classical trust-region framework for optimization of deterministic smooth
general nonlinear functions. Our method and setting differs from many
stochastic optimization approaches in two principal ways. Firstly, we assume
that the value of the function itself can be computed without noise, in other
words, that the function is deterministic. Secondly, we use random models of
higher quality than those produced by usual stochastic gradient methods. In
particular, a first order model based on random approximation of the gradient
is required to provide sufficient quality of approximation with probability
greater than or equal to 1/2. This is in contrast with stochastic gradient
approaches, where the model is assumed to be "correct" only in expectation. As
a result of this particular setting, we are able to prove convergence, with
probability one, of a trust-region method which is almost identical to the
classical method. Hence we show that a standard optimization framework can be
used in cases when models are random and may or may not provide good
approximations, as long as "good" models are more likely than "bad" models. Our
results are based on the use of properties of martingales. Our motivation comes
from using random sample sets and interpolation models in derivative-free
optimization. However, our framework is general and can be applied with any
source of uncertainty in the model. We discuss various applications for our
methods in the paper
Network Inference via the Time-Varying Graphical Lasso
Many important problems can be modeled as a system of interconnected
entities, where each entity is recording time-dependent observations or
measurements. In order to spot trends, detect anomalies, and interpret the
temporal dynamics of such data, it is essential to understand the relationships
between the different entities and how these relationships evolve over time. In
this paper, we introduce the time-varying graphical lasso (TVGL), a method of
inferring time-varying networks from raw time series data. We cast the problem
in terms of estimating a sparse time-varying inverse covariance matrix, which
reveals a dynamic network of interdependencies between the entities. Since
dynamic network inference is a computationally expensive task, we derive a
scalable message-passing algorithm based on the Alternating Direction Method of
Multipliers (ADMM) to solve this problem in an efficient way. We also discuss
several extensions, including a streaming algorithm to update the model and
incorporate new observations in real time. Finally, we evaluate our TVGL
algorithm on both real and synthetic datasets, obtaining interpretable results
and outperforming state-of-the-art baselines in terms of both accuracy and
scalability
Some Problems in Probabilistic Tomography
Given probability distributions F1 , F2 , . . ., Fk on R and distinct directions θ1, . . ., θk, one may ask whether there is a probability measure μ on R2 such that the marginal of μ in direction θj is Fj, j = 1, . . ., k. For example for k = 3 we ask what the marginal of μ at 45° can be if the x and y marginals are each say standard normal? In probabilistic language, if X and Y are each standard normal with an arbitrary joint distribution, what can the distribution of X + Y or X - Y be? This type of question is familiar to probabilists and is also familiar (except perhaps in that μ is positive) to tomographers, but is difficult to answer in special cases. The set of distributions for Z = X - Y is a convex and compact set, C, which contains the single point mass Z ≡ 0 since X ≡ Y, standard normal, is possible. We show that Z can be 3-valued, Z=0, ±a for any a, each with positive probability, but Z cannot have any (genuine) two-point distribution. Using numerical linear programming we present convincing evidence that Z can be uniform on the interval [-ε, ε] for ε small and give estimates for the largest such ε. The set of all extreme points of C seems impossible to determine explicitly.
We also consider the more basic question of finding the extreme measures on the unit square with uniform marginals on both coordinates, and show that not every such measure has a support which has only one point on each horizontal or vertical line, which seems surprising
ORB5: a global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry
This paper presents the current state of the global gyrokinetic code ORB5 as
an update of the previous reference [Jolliet et al., Comp. Phys. Commun. 177
409 (2007)]. The ORB5 code solves the electromagnetic Vlasov-Maxwell system of
equations using a PIC scheme and also includes collisions and strong flows. The
code assumes multiple gyrokinetic ion species at all wavelengths for the
polarization density and drift-kinetic electrons. Variants of the physical
model can be selected for electrons such as assuming an adiabatic response or a
``hybrid'' model in which passing electrons are assumed adiabatic and trapped
electrons are drift-kinetic. A Fourier filter as well as various control
variates and noise reduction techniques enable simulations with good
signal-to-noise ratios at a limited numerical cost. They are completed with
different momentum and zonal flow-conserving heat sources allowing for
temperature-gradient and flux-driven simulations. The code, which runs on both
CPUs and GPUs, is well benchmarked against other similar codes and analytical
predictions, and shows good scalability up to thousands of nodes
Bone marrow-derived endothelial progenitor cells are a major determinant of nascent tumor neovascularization
Tumors build vessels by cooption of pre-existing vasculature and de novo recruitment of bone marrow (BM)-derived endothelial progenitor cells (EPCs). However, the contribution and the functional role of EPCs in tumor neoangiogenesis are controversial. Therefore, by using genetically marked BM progenitor cells, we demonstrate the precise spatial and temporal contribution of EPCs to the neovascularization of three transplanted and one spontaneous breast tumor in vivo using high-resolution microscopy and flow cytometry. We show that early tumors recruit BM-derived EPCs that differentiate into mature BM-derived endothelial cells (ECs) and luminally incorporate into a subset of sprouting tumor neovessels. Notably, in later tumors, these BM-derived vessels are diluted with non-BM-derived vessels from the periphery, which accounts for purported differences in previously published reports. Furthermore, we show that specific ablation of BM-derived EPCs with alpha-particle-emitting anti-VE-cadherin antibody markedly impaired tumor growth associated with reduced vascularization. Our results demonstrate that BM-derived EPCs are critical components of the earliest phases of tumor neoangiogenesis
Amenability of algebras of approximable operators
We give a necessary and sufficient condition for amenability of the Banach
algebra of approximable operators on a Banach space. We further investigate the
relationship between amenability of this algebra and factorization of
operators, strengthening known results and developing new techniques to
determine whether or not a given Banach space carries an amenable algebra of
approximable operators. Using these techniques, we are able to show, among
other things, the non-amenability of the algebra of approximable operators on
Tsirelson's space.Comment: 20 pages, to appear in Israel Journal of Mathematic
Progress and challenges to the global waste management system
Rapid economic growth, urbanization and increasing population have caused (materially intensive) resource consumption to increase, and consequently the release of large amounts of waste to the environment. From a global perspective, current waste and resource management lacks a holistic approach covering the whole chain of product design, raw material extraction, production, consumption, recycling and waste management. In this article, progress and different sustainability challenges facing the global waste management system are presented and discussed. The study leads to the conclusion that the current, rather isolated efforts, in different systems for waste management, waste reduction and resource management are indeed not sufficient in a long term sustainability perspective. In the future, to manage resources and wastes sustainably, waste management requires a more systems-oriented approach that addresses the root causes for the problems. A specific issue to address is the development of improved feedback information (statistics) on how waste generation is linked to consumption
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