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.

/pdf/distributed-optimization-and-statistical-learning-via-the-8s9gtddw0d.pdf

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

Boundary value problems for equations of mixed type I. the lavrent'ev - bitsadze model

https://ntrs.nasa.gov/api/citations/19860020305/downloads/19860020305.pdf

An entropy correction method for unsteady full potential flows with strong shocks

Kreiss and Lundquist [1], have recently obtained certain results about the decay of influence of wrong boundary conditions in overdetermined difference approximations to a hyperbolic partial differential equation. We have extended this result to include systems of hyperbolic partial differential equations in several space variables and their corresponding overdetermined difference approximations. The technique of proof involves examining sections of the resolvent of the difference operator for analyticity within the unit circle as in Kreiss [6] and Osher [2].

/pdf/on-systems-of-difference-equations-with-wrong-boundary-2d6n8yvvae.pdf

On systems of difference equations with wrong boundary conditions

In the past decade, information theory has been studied exte nsively in medical imaging. In particular, image matching by maximizing mutual information has been shown to yield good results in multi-modal image registration. However, there has been few rigorous studies to date that investigate the statistical aspect of the resulting deformation fields. Different regularization te chniques have been proposed, sometimes generating deformations very different from one another. In this paper , we apply information theory to quantifying the magnitude of deformations. We examine the statistical dist ributions of Jacobian maps in the logarithmic space, and develop a new framework for constructing log-unb iased image registration methods. The proposed framework yields both theoretically and intuitively corre ct deformation maps, and is compatible with largedeformation models. In the results section, we tested the pr oposed method using pairs of synthetic binary images, two-dimensional serial MRI images, and three-dime nsional serial MRI volumes. We compared our results to those computed using the viscous fluid registrati on method, and demonstrated that the proposed method is advantageous when recovering voxel-wise local ti ssue change.

Log-unbiased large-deformation image registration

Given a monotone function $z(x)$ which connects two constant states, $u_L u_R )$, we find the unique (up to a constant) convex (concave) flux function, $\hat f(u)$, such that $z({x / t})$ is the physically correct solution to the associated Riemann problem. For $z({x / t})$, an approximate Riemann solver to a given conservation law, we derive simple necessary and sufficient conditions for it to be consistent with any entropy inequality. Associated with any member of a general class of consistent numerical fluxes, $h_f (u_R ,u_L )$, we have an approximate Riemann solver defined through $z(\zeta ) = ({{ - d} / {d_\zeta }})h_{f_\zeta } (u_R ,u_L )$, where $f_\zeta (u) = f(u) - \zeta u$. We obtain the corresponding $\hat f(u)$ via a Legendre transform and show that it is consistent with all entropy inequalities iff $h_{f_\zeta } (u_R ,u_L )$ is an E flux for each relevant $\zeta $. Examples involving commonly used two point numerical fluxes are given, as are comparisons with related work.

Stanley Osher

Papers

Boundary value problems for equations of mixed type I. the lavrent'ev - bitsadze model

An entropy correction method for unsteady full potential flows with strong shocks

On systems of difference equations with wrong boundary conditions

Log-unbiased large-deformation image registration

Approximate Riemann solvers and numerical flux functions