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

http://science.sciencemag.org/content/sci/201/4359/899.2.full.pdf

Phenomenology of perception.

Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

Lévy processes and infinitely divisible distributions

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Difference and Repetition

Doing philosophy means reasoning about questions that are of basic importance to the human experience—questions like, What is a good life? What is reality? How are knowledge and understanding possible? What should we believe? What norms should govern our societies, our relationships, and our activities? Philosophers critically analyze ideas and practices that often are assumed without reflection. Wesleyan’s philosophy faculty draws on multiple traditions of inquiry, offering a wide variety of perspectives and methods for addressing these questions.

What is philosophy

We present a mathematical model of perceptual completion and formation of subjective surfaces, which is at the same time inspired by the architecture of the visual cortex, and is the lifting in the 3-dimensional rototranslation group of the phenomenological variational models based on elastica functional. The initial image is lifted by the simple cells to a surface in the rototranslation group and the completion process is modeled via a diffusion driven motion by curvature. The convergence of the motion to a minimal surface is proved. Results are presented both for modal and amodal completion in classic Kanizsa images.

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A Cortical Based Model of Perceptual Completion in the Roto-Translation Space

We propose to model the functional architecture of the primary visual cortex V1 as a principal fiber bundle where the two-dimensional retinal plane is the base manifold and the secondary variables of orientation and scale constitute the vertical fibers over each point as a rotation–dilation group. The total space is endowed with a natural symplectic structure neurally implemented by long range horizontal connections. The model shows what could be the deep structure for both boundary and figure completion and for morphological structures, such as the medial axis of a shape.

The symplectic structure of the primary visual cortex

Harnack's inequality for sum of squares of vector fields plus a potential

In (1), (2), ~=(x , y, t) denotes the point of R 3, ut is the first derivative of u with respect to t, and analogous notations are used for the other firstand second-order derivatives of u. The notion of Levi curvature for a real manifold was introduced by E.E. Levi in 1909 in order to characterize the holomorphy domains of C 2. Since then, it has played a crucial role in the geometric theory of several complex variables. In looking for the polynomial hull of a graph, Slodkowski and Tomassini implicitly introduced in 1991 the following definition of Levi curvature for Lipschitz-continuous graphs [16].

/pdf/smoothness-of-lipschitz-continuous-graphs-with-nonvanishing-11uyggv8e0.pdf

Smoothness of Lipschitz-continuous graphs with nonvanishing Levi curvature

Minimal surfaces in the sub-Riemannian Heisenberg group can be constructed by means of a Riemannian approximation scheme, as limit of Riemannian minimal surfaces. We study the regularity of Lipschitz, non-characteristic minimal surfaces which arise as such limits. Our main results are a-priori estimates on the solutions of the approximating Riemannian PDE and the ensuing C ∞ regularity of the sub-Riemannian minimal surface along its Legendrian foliation.

Giovanna Citti

Papers

A Cortical Based Model of Perceptual Completion in the Roto-Translation Space

The symplectic structure of the primary visual cortex

Harnack's inequality for sum of squares of vector fields plus a potential

Smoothness of Lipschitz-continuous graphs with nonvanishing Levi curvature

Regularity of non-characteristic minimal graphs in the Heisenberg group mathbb{H}^{1}