We propose a deep convolutional neural network architecture codenamed Inception that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14). The main hallmark of this architecture is the improved utilization of the computing resources inside the network. By a carefully crafted design, we increased the depth and width of the network while keeping the computational budget constant. To optimize quality, the architectural decisions were based on the Hebbian principle and the intuition of multi-scale processing. One particular incarnation used in our submission for ILSVRC14 is called GoogLeNet, a 22 layers deep network, the quality of which is assessed in the context of classification and detection.

/pdf/going-deeper-with-convolutions-1yobw2o2ds.pdf

Going deeper with convolutions

There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.

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Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

We simulate the axisymmetric pipeline transportation of oil and water numerically under the assumption that the densities of the two fluids are different and that the viscosity of the oil core is very large. We develop the appropriate equations for core-annular flows using the level set methodology. Our method consists of a finite difference scheme for solving the model equations, and a level set approach for capturing the interface between two liquids (oil and water). A variable density projection method combined with a TVD Runge---Kutta scheme is used to advance the computed solution in time. The simulations succeed in predicting the spatially periodic waves called bamboo waves, which have been observed in the experiments of [Bai et al. (1992) J. Fluid Mech. 240, 97---142.] on up-flow in vertical core flow. In contrast to the stable case, our simulations succeed in cases where the oil breaks up in the water, and then merging occurs. Comparisons are made with other numerical methods and with both theoretical and experimental results.

Level Set Based Simulations of Two-Phase Oil-Water Flows in Pipes

In this paper we derive a generalizing concept of G-norms, which we call G-sets, which is used to characterize minimizers of non-difierentiable regularization functionals. Moreover, the concept is closely related to the deflnition of slopes as published in a recent book by Ambrosio, Gigli, Savare. A paradigm of regularization models fltting in this framework is robust bounded variation regularization. Two essential properties of this regularization technique are documented in the literature and it is shown that these properties can also be achieved with metric regularization techniques.

/pdf/slope-and-g-set-characterization-of-set-valued-functions-and-4dznbrp9c2.pdf

Slope and $G$-set characterization of set-valued functions and applications to non-differentiable optimization problems

Given a graph where vertices represent alternatives and arcs represent pairwise comparison data, the statistical ranking problem is to find a potential function, defined on the vertices, such that the gradient of the potential function agrees with the pairwise comparisons. Our goal in this paper is to develop a method for collecting data for which the least squares estimator for the ranking problem has maximal information. Our approach, based on experimental design, is to view data collection as a bi-level optimization problem where the inner problem is the ranking problem and the outer problem is to identify data which maximizes the informativeness of the ranking. Under certain assumptions, the data collection problem decouples, reducing to a problem of finding graphs with large algebraic connectivity. This reduction of the data collection problem to graph-theoretic questions is one of the primary contributions of this work. As an application, we study the 2011-12 NCAA football schedule and propose schedules with the same number of games which are significantly more informative. Using spectral clustering methods to identify highly-connected communities within the division, we argue that the NCAA could improve its notoriously poor rankings by simply scheduling more out-of-conference games.

Optimal Data Collection for Improved Rankings Expose Well-Connected Graphs

Alternating projection based methods, such as ePIE and rPIE, have been used widely in ptychography. However, they only work well if there are adequate measurements (diffraction patterns); in the case of sparse data (i.e. fewer measurements) alternating projection underperforms and might not even converge. In this paper, we propose semi-implicit relaxed Douglas-Rachford (sDR), an accelerated iterative method, to solve the classical ptychography problem. Using both simulated and experimental data, we show that sDR improves the convergence speed and the reconstruction quality relative to extended ptychographic iterative engine (ePIE) and regularized ptychographic iterative engine (rPIE). Furthermore, in certain cases when sparsity is high, sDR converges while ePIE and rPIE fail or encounter slow convergence. To facilitate others to use the algorithm, we post the Matlab source code of sDR on a public website (www.physics.ucla.edu/research/imaging/sDR/index.html). We anticipate that this algorithm can be generally applied to the ptychographic reconstruction of a wide range of samples in the physical and biological sciences.

Semi-implicit relaxed Douglas-Rachford algorithm (sDR) for ptychography.

The coronavirus disease 2019 (COVID-19) pandemic is changing and impacting lives on a global scale. In this paper, we introduce a mean-field game model in controlling the propagation of epidemics on a spatial domain. The control variable, the spatial velocity, is first introduced for the classical disease models, such as the SIR model. For this proposed model, we provide fast numerical algorithms based on proximal primal-dual methods. Numerical experiments demonstrate that the proposed model illustrates how to separate infected patients in a spatial domain effectively.

Stanley Osher

Papers

Level Set Based Simulations of Two-Phase Oil-Water Flows in Pipes

Slope and $G$-set characterization of set-valued functions and applications to non-differentiable optimization problems

Optimal Data Collection for Improved Rankings Expose Well-Connected Graphs

Semi-implicit relaxed Douglas-Rachford algorithm (sDR) for ptychography.

Controlling Propagation of epidemics via mean-field games