103,833 research outputs found
On the optimal design of wall-to-wall heat transport
We consider the problem of optimizing heat transport through an
incompressible fluid layer. Modeling passive scalar transport by
advection-diffusion, we maximize the mean rate of total transport by a
divergence-free velocity field. Subject to various boundary conditions and
intensity constraints, we prove that the maximal rate of transport scales
linearly in the r.m.s. kinetic energy and, up to possible logarithmic
corrections, as the rd power of the mean enstrophy in the advective
regime. This makes rigorous a previous prediction on the near optimality of
convection rolls for energy-constrained transport. Optimal designs for
enstrophy-constrained transport are significantly more difficult to describe:
we introduce a "branching" flow design with an unbounded number of degrees of
freedom and prove it achieves nearly optimal transport. The main technical tool
behind these results is a variational principle for evaluating the transport of
candidate designs. The principle admits dual formulations for bounding
transport from above and below. While the upper bound is closely related to the
"background method", the lower bound reveals a connection between the optimal
design problems considered herein and other apparently related model problems
from mathematical materials science. These connections serve to motivate
designs.Comment: Minor revisions from review. To appear in Comm. Pure Appl. Mat
Targeted Undersmoothing
This paper proposes a post-model selection inference procedure, called
targeted undersmoothing, designed to construct uniformly valid confidence sets
for a broad class of functionals of sparse high-dimensional statistical models.
These include dense functionals, which may potentially depend on all elements
of an unknown high-dimensional parameter. The proposed confidence sets are
based on an initially selected model and two additionally selected models, an
upper model and a lower model, which enlarge the initially selected model. We
illustrate application of the procedure in two empirical examples. The first
example considers estimation of heterogeneous treatment effects using data from
the Job Training Partnership Act of 1982, and the second example looks at
estimating profitability from a mailing strategy based on estimated
heterogeneous treatment effects in a direct mail marketing campaign. We also
provide evidence on the finite sample performance of the proposed targeted
undersmoothing procedure through a series of simulation experiments
Low rank matrix recovery from rank one measurements
We study the recovery of Hermitian low rank matrices from undersampled measurements via nuclear norm minimization. We
consider the particular scenario where the measurements are Frobenius inner
products with random rank-one matrices of the form for some
measurement vectors , i.e., the measurements are given by . The case where the matrix to be recovered
is of rank one reduces to the problem of phaseless estimation (from
measurements, via the PhaseLift approach,
which has been introduced recently. We derive bounds for the number of
measurements that guarantee successful uniform recovery of Hermitian rank
matrices, either for the vectors , , being chosen independently
at random according to a standard Gaussian distribution, or being sampled
independently from an (approximate) complex projective -design with .
In the Gaussian case, we require measurements, while in the case
of -designs we need . Our results are uniform in the
sense that one random choice of the measurement vectors guarantees
recovery of all rank -matrices simultaneously with high probability.
Moreover, we prove robustness of recovery under perturbation of the
measurements by noise. The result for approximate -designs generalizes and
improves a recent bound on phase retrieval due to Gross, Kueng and Krahmer. In
addition, it has applications in quantum state tomography. Our proofs employ
the so-called bowling scheme which is based on recent ideas by Mendelson and
Koltchinskii.Comment: 24 page
An Assessment to Benchmark the Seismic Performance of a Code-Conforming Reinforced-Concrete Moment-Frame Building
This report describes a state-of-the-art performance-based earthquake engineering methodology
that is used to assess the seismic performance of a four-story reinforced concrete (RC) office
building that is generally representative of low-rise office buildings constructed in highly seismic
regions of California. This “benchmark” building is considered to be located at a site in the Los
Angeles basin, and it was designed with a ductile RC special moment-resisting frame as its
seismic lateral system that was designed according to modern building codes and standards. The
building’s performance is quantified in terms of structural behavior up to collapse, structural and
nonstructural damage and associated repair costs, and the risk of fatalities and their associated
economic costs. To account for different building configurations that may be designed in
practice to meet requirements of building size and use, eight structural design alternatives are
used in the performance assessments.
Our performance assessments account for important sources of uncertainty in the ground
motion hazard, the structural response, structural and nonstructural damage, repair costs, and
life-safety risk. The ground motion hazard characterization employs a site-specific probabilistic
seismic hazard analysis and the evaluation of controlling seismic sources (through
disaggregation) at seven ground motion levels (encompassing return periods ranging from 7 to
2475 years). Innovative procedures for ground motion selection and scaling are used to develop
acceleration time history suites corresponding to each of the seven ground motion levels.
Structural modeling utilizes both “fiber” models and “plastic hinge” models. Structural
modeling uncertainties are investigated through comparison of these two modeling approaches,
and through variations in structural component modeling parameters (stiffness, deformation
capacity, degradation, etc.). Structural and nonstructural damage (fragility) models are based on
a combination of test data, observations from post-earthquake reconnaissance, and expert
opinion. Structural damage and repair costs are modeled for the RC beams, columns, and slabcolumn connections. Damage and associated repair costs are considered for some nonstructural
building components, including wallboard partitions, interior paint, exterior glazing, ceilings,
sprinkler systems, and elevators. The risk of casualties and the associated economic costs are
evaluated based on the risk of structural collapse, combined with recent models on earthquake
fatalities in collapsed buildings and accepted economic modeling guidelines for the value of
human life in loss and cost-benefit studies.
The principal results of this work pertain to the building collapse risk, damage and repair
cost, and life-safety risk. These are discussed successively as follows.
When accounting for uncertainties in structural modeling and record-to-record variability
(i.e., conditional on a specified ground shaking intensity), the structural collapse probabilities of
the various designs range from 2% to 7% for earthquake ground motions that have a 2%
probability of exceedance in 50 years (2475 years return period). When integrated with the
ground motion hazard for the southern California site, the collapse probabilities result in mean
annual frequencies of collapse in the range of [0.4 to 1.4]x10
-4
for the various benchmark
building designs. In the development of these results, we made the following observations that
are expected to be broadly applicable:
(1) The ground motions selected for performance simulations must consider spectral
shape (e.g., through use of the epsilon parameter) and should appropriately account for
correlations between motions in both horizontal directions;
(2) Lower-bound component models, which are commonly used in performance-based
assessment procedures such as FEMA 356, can significantly bias collapse analysis results; it is
more appropriate to use median component behavior, including all aspects of the component
model (strength, stiffness, deformation capacity, cyclic deterioration, etc.);
(3) Structural modeling uncertainties related to component deformation capacity and
post-peak degrading stiffness can impact the variability of calculated collapse probabilities and
mean annual rates to a similar degree as record-to-record variability of ground motions.
Therefore, including the effects of such structural modeling uncertainties significantly increases
the mean annual collapse rates. We found this increase to be roughly four to eight times relative
to rates evaluated for the median structural model;
(4) Nonlinear response analyses revealed at least six distinct collapse mechanisms, the
most common of which was a story mechanism in the third story (differing from the multi-story
mechanism predicted by nonlinear static pushover analysis);
(5) Soil-foundation-structure interaction effects did not significantly affect the structural
response, which was expected given the relatively flexible superstructure and stiff soils.
The potential for financial loss is considerable. Overall, the calculated expected annual
losses (EAL) are in the range of 97,000 for the various code-conforming benchmark
building designs, or roughly 1% of the replacement cost of the building (3.5M, the fatality rate translates to an EAL due to
fatalities of 5,600 for the code-conforming designs, and 66,000, the monetary value associated with life loss is small,
suggesting that the governing factor in this respect will be the maximum permissible life-safety
risk deemed by the public (or its representative government) to be appropriate for buildings.
Although the focus of this report is on one specific building, it can be used as a reference
for other types of structures. This report is organized in such a way that the individual core
chapters (4, 5, and 6) can be read independently. Chapter 1 provides background on the
performance-based earthquake engineering (PBEE) approach. Chapter 2 presents the
implementation of the PBEE methodology of the PEER framework, as applied to the benchmark
building. Chapter 3 sets the stage for the choices of location and basic structural design. The subsequent core chapters focus on the hazard analysis (Chapter 4), the structural analysis
(Chapter 5), and the damage and loss analyses (Chapter 6). Although the report is self-contained,
readers interested in additional details can find them in the appendices
Block design performance in the Williams syndrome phenotype: A problem with mental imagery?
Williams syndrome (WS) is a rare genetic disorder which, among other characteristics, has a distinctive cognitive profile. Non-verbal abilities are generally poor in relation to verbal abilities, but also show varying levels of ability in relation to each other. Performance on block construction tasks represents arguably the weakest non-verbal ability in WS. In this study we examined two requirements of block construction tasks in 21 individuals with WS and 21 typically developing (TD) control individuals. The Squares task, a novel two-dimensional block construction task, manipulated patterns by segmentation and perceptual cohesiveness to investigate the first factor, processing preference (local or global), and by obliqueness to examine the second factor, the ability to use mental imagery. These two factors were investigated directly by the Children?s Embedded Figures Test (CEFT; Witkin, Oltman, Raskin & Karp, 1971) and a mental rotation task respectively. Results showed that individuals with WS did not differ from the TD group in their processing style. However, the ability to use mental imagery was significantly poorer in the WS group than the TD group. This suggests that weak performance on the block construction tasks in WS may relate to an inability to use mental imagery
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