17,180 Works

Selective Detectors for High Energy Photons and Electrons

Clemens A. Heusch & Charles Y. Prescott
For fast identification of high-energy electrons and photons in heavy backgrounds, a counter was developed consisting of successive layers of lucite and lead. Čerenkov radiation emitted in the lucite slabs is collected onto the photocathode of one 5 inch phototube. The geometry as well as the thickness of inserted lead converters can be adapted to kinematical requirements. At 1 BeV/c incoming momentum, the rejection ratio of e, γ showers vs. π or μ is better...

Optimal Uncertainty Quantification

H. Owhadi, C. Scovel, T. J. Sullivan, M. McKerns & M. Ortiz
We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call Optimal Uncertainty Quantification (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as extreme values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to...

User-Friendly Tail Bounds for Sums of Random Matrices

Joel A. Tropp
This work presents probability inequalities for sums of independent, random, self-adjoint matrices. The results frame simple, easily verifiable hypotheses on the summands, and they yield strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of rectangular matrices follow as an immediate corollary, and similar techniques yield information about matrix-valued martingales. In other words, this paper provides noncommutative generalizations of the classical bounds associated...

Finding Structure with Randomness: Stochastic Algorithms for Constructing Approximate matrix Decompositions

N. Halko, P. G. Martinsson & J. A. Tropp
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys recent research which demonstrates that randomization offers a powerful tool for performing low-rank matrix approximation. These techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets. In particular, these techniques o®er a route toward principal component...

Non-intrusive and structure preserving multiscale integration of stiff ODEs, SDEs and Hamiltonian systems with hidden slow dynamics via flow averaging

Molei Tao, Houman Owhadi & Jerrold E. Marsden
We introduce a new class of integrators for stiff ODEs as well as SDEs. An example of subclass of systems that we treat are ODEs and SDEs that are sums of two terms one of which has large coefficients. These integrators are (i) Multiscale: they are based on ow averaging and so do not resolve the fast variables but rather employ step-sizes determined by slow variables (ii) Basis: the method is based on averaging the...

Discrete Geometric Structures in Homogenization and Inverse Homogenization with Application to EIT

Mathieu Desbrun, Roger D. Donaldson & Houman Owhadi
We introduce a new geometric approach for the homogenization and inverse homogenization of the divergence form elliptic operator with rough conductivity coefficients σ(x) in dimension two. We show that conductivity coefficients are in one-to-one correspondence with divergence-free matrices and convex functions s(x) over the domain Ω. Although homogenization is a non-linear and non-injective operator when applied directly to conductivity coefficients, homogenization becomes a linear interpolation operator over triangulations of Ω when re-expressed using convex functions,...

Computational Methods for Sparse Solution of Linear Inverse Problems

Joel A. Tropp & Stephen J. Wright
In sparse approximation problems, the goal is to find an approximate representation of a target signal using a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major algorithms that are used for solving sparse approximation problems in practice. Specific attention is paid to computational issues, to the circumstances in which individual methods tend to perform well, and to the theoretical guarantees available. Many fundamental questions in electrical...

Column Subset Selection, Matrix Factorization, and Eigenvalue Optimization

Joel A. Tropp
Given a fixed matrix, the problem of column subset selection requests a column submatrix that has favorable spectral properties. Most research from the algorithms and numerical linear algebra communities focuses on a variant called rank-revealing QR, which seeks a well-conditioned collection of columns that spans the (numerical) range of the matrix. The functional analysis literature contains another strand of work on column selection whose algorithmic implications have not been explored. In particular, a celebrated result...

CoSaMP: Iterative Signal Recovery from Incomplete and Inaccurate Samples

D. Needell & J. A. Tropp
Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery algorithm called CoSaMP that delivers the same guarantees as the best optimization-based approaches. Moreover, this algorithm offers rigorous bounds on computational cost and storage. It is likely to be extremely efficient for practical problems...

Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case

Joel A. Tropp & Anna C. Gilbert
This report demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(mln d) random linear measurements of that signal. This is a massive improvement over previous results, which require O(m2) measurements. The new results for OMP are comparable with recent results for another approach called Basis Pursuit (BP). In some settings, the OMP algorithm is faster and easier...

The Achievable Performance of Convex Demixing

Michael B. McCoy & Joel A. Tropp
Demixing is the problem of identifying multiple structured signals from a superimposed, undersampled, and noisy observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. When the constituent signals follow a generic incoherence model, this analysis leads to precise recovery guarantees. These results admit an attractive interpretation: each signal possesses an intrinsic degrees-of-freedom parameter, and demixing can succeed if and only if the dimension of the observation exceeds the total...

Empiricism and Mathematical Knowledge

Gideon J. Leeper
Empiricism asserts that sensory perceptions and experiences are the basis of all knowledge, i.e. essentially everything we know has either been directly perceived or deduced from perceived knowledge. This would seem to conflict with the wealth of mathematical knowledge that we have accrued as a civilization. Mathematics consists primarily of facts concerning ideal objects, such as topological spaces, groups, and categories, which we have never encountered in physical reality, and cannot reasonably expect to. Then...

Seismogeodetic Imaging of Active Crustal Faulting

Asaf Inbal
Monitoring microseismicity is important for illuminating active faults and for improving our understanding earthquake physics. These tasks are difficult in urban areas where the SNR is poor, and the level of background seismicity is low. One example is the Newport-Inglewood fault (NIFZ), an active fault that transverses the city of Long-Beach (LB). The catalog magnitude of completeness within this area is M=2, about one order of magnitude larger than along other, less instrumented faults in...

Why Was The Feminine Mystique Such a Phenomenon?: A Clarification

Crystal Liang
[Introduction] Since The Feminine Mystique was published in 1963, it has become so influential that it has gathered a mystique of its own. The controversial book has drawn both high praise for "[pulling] the trigger on history" and strong criticism from conservative groups for threatening family values, as well as from scholars for being riddled with methodological errors and for focusing only on white, middle-class women. Confusion abounds in the general public, too. In Stephanie...

Engineered Underdominance as a Method of Insect Population Replacement and Reproductive Isolation

Anna Basalova Buchman
Insect vector-borne diseases, such as malaria and dengue fever (both spread by mosquito vectors), continue to significantly impact health worldwide, despite the efforts put forth to eradicate them. Suppression strategies utilizing genetically modified disease-refractory insects have surfaced as an attractive means of disease control, and progress has been made on engineering disease-resistant insect vectors. However, laboratory-engineered disease refractory genes would probably not spread in the wild, and would most likely need to be linked to...

Situation Awareness Application

Judy Mou
This thesis describes the design and implementation of a situation awareness application. The application gathers data from sensors including accelerometers for monitoring earthquakes, carbon monoxide sensors for monitoring fires, radiation detectors, and dust sensors. The application also gathers Internet data sources including data about traffic congestion on daily commute routes, information about hazards, news relevant to the user of the application, and weather. The application sends the data to a Cloud computing service which aggregates...

Three-Dimensional Self-Assembly of Brush Block Copolymers to Photonic Crystals

Melody Ann Morris
The development of Ring Opening Metathesis Polymerization has allowed the world of block copolymers to expand into brush block copolymers. Brush block copolymers consist of a polymer backbone with polymeric side chains, forcing the backbone to hold a stretched conformation and giving it a worm-like shape. These brush block copolymers have a number of advantages over tradition block copolymers, including faster self-assembly behavior, larger domain sizes, and much less entanglement. This makes them an ideal...

Identification of Thermally-Tagged Coherent Structures in the Zero Pressure Gradient Turbulent Boundary Layer

Rebecca Lynn Rought
A zero pressure gradient boundary layer over a flat plate is subjected to step changes in thermal condition at the wall, causing the formation of internal, heated layers. The resulting temperature fluctuations and their corresponding density variations are associated with turbulent coherent structures. Aero-optical distortion occurs when light passes through the boundary layer, encountering the changing index of refraction resulting from the density variations. Instantaneous measurements of streamwise velocity, temperature and the optical deflection angle...

Geometric Quantization and Foliation Reduction

Paul Michael Skerritt
A standard question in the study of geometric quantization is whether symplectic reduction interacts nicely with the quantized theory, and in particular whether “quantization commutes with reduction.” Guillemin and Sternberg first proposed this question, and answered it in the affirmative for the case of a free action of a compact Lie group on a compact Kähler manifold. Subsequent work has focused mainly on extending their proof to non-free actions and non-Kähler manifolds. For realistic physical...

Engineering Multi Step Electron Tunneling Systems in Proteins

Heather R. Williamson
Multi-step electron tunneling, or “hopping,” has become a fast-developing research field with studies ranging from theoretical modeling systems, inorganic complexes, to biological systems. In particular, the field is exploring hopping mechanisms in new proteins and protein complexes, as well as further understanding the classical biological hopping systems such as ribonuclease reductase, DNA photolyases, and photosystem II. Despite the plethora of natural systems, only a few biologically engineered systems exist. Engineered hopping systems can provide valuable...

Planar Reflection of Gaseous Detonation

Jason Scott Damazo
Pipes containing flammable gaseous mixtures may be subjected to internal detonation. When the detonation normally impinges on a closed end, a reflected shock wave is created to bring the flow back to rest. This study built on the work of Karnesky (2010) and examined deformation of thin-walled stainless steel tubes subjected to internal reflected gaseous detonations. A ripple pattern was observed in the tube wall for certain fill pressures, and a criterion was developed that...

Aseismic Deformation in Subduction Megathrusts: Central Andes and North-East Japan

Francisco Hernan Ortega Culaciati
We aim to characterize fault slip behavior during all stages of the seismic cycle in subduction megathrust environments with the eventual goal of understanding temporal and spatial variations of fault zone rheology, and to infer possible causal relationships between inter-, co- and post-seismic slip, as well as implications for earthquake and tsunami hazard. In particular we focus on analyzing aseismic deformation occurring during inter-seismic and post-seismic periods of the seismic cycle. We approach the problem...

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