Compact homogeneous lcK manifolds are Vaisman

We prove that any compact homogeneous locally conformally K\"ahler manifold has parallel Lee form.Comment: 6 pages; final version, to appear in Math. An

On the nonlinear statistics of range image patches

In [A. B. Lee, K. S. Pedersen, and D. Mumford, Int. J. Comput. Vis., 54 (2003), pp. 83–103], the authors study the distributions of 3 × 3 patches from optical images and from range images. In [G. Carlsson, T. Ishkanov, V. de Silva, and A. Zomorodian, Int. J. Comput. Vis., 76 (2008), pp. 1–12], the authors apply computational topological tools to the data set of optical patches studied by Lee, Pedersen, and Mumford and find geometric structures for high density subsets. One high density subset is called the primary circle and essentially consists of patches with a line separating a light and a dark region. In this paper, we apply the techniques of Carlsson et al. to range patches. By enlarging to 5×5 and 7×7 patches, we find core subsets that have the topology of the primary circle, suggesting a stronger connection between optical patches and range patches than was found by Lee, Pedersen, and Mumford

Lehan K. Tunks—A Tribute

Lee Tunks came to New Jersey as Dean of the two Rutgers Law Schools (Newark and Camden) in 1953 and served until 1962. Rutgers Law School had been only recently created; it had come into being in 1948 (from the merger of several municipal and private schools) as the law school of the contemporaneously created state university, Rutgers University. Lee\u27s charge and purpose was to build a major state law school. He had to position the school as a high priority claimant upon university resources: to effect large increases in library collection and staff, to break his faculty\u27s salaries free from the university pattern, to acquire research and administrative resources, all of which generated disputes within the university. He led the faculty to decisions that entangled the newly visible public institution in external fights with bar, alumni, or the legislature. There was one year in which Newark admissions standards were so boosted as to cut the entering class by almost 50%, and there was a several-year campaign to drop the school\u27s evening division as beyond its resources. All these disputes were intensified by the dedication and passion with which Lee pressed his positions, but it was the same dedication coupled with a superior tactical sense which saw them mostly won on Lee\u27s terms

Is it better to learn how to ‘hear’ the sounds of a new language, or practice saying them? (OASIS Summary)

Lee, B., Plonsky, L. & Saito, K. (2019). Is it better to learn how to ‘hear’ the sounds of a new language, or practice saying them?. OASIS Summary of Lee, B., Plonsky, L. & Saito, K. (2020) in System. https://oasis-database.org/concern/summaries/hx11xf416?locale=e

Lehan K. Tunks—A Personal Recollection

What follows are some observations about Lee Tunks, formed during my several years of assisting him with deaning duties at the Law School, and during the years since when we have been faculty colleagues and friends. I always think of Lee as a law school dean. Perhaps that is because he was a dean when I first met him. Perhaps it is because what I really know about deans and deaning I learned first from him. Whatever the cause, he seems to me to be one of those people destined to be a law school dean. I have known many fine deans since those days, but most feel the job is one they didn\u27t plan on having and one they will someday (hopefully soon) be well rid of. By contrast, Lee Tunks seemed to the manor born

Centrally symmetric polytopes with many faces

We present explicit constructions of centrally symmetric polytopes with many faces: first, we construct a d-dimensional centrally symmetric polytope P with about (1.316)^d vertices such that every pair of non-antipodal vertices of P spans an edge of P, second, for an integer k>1, we construct a d-dimensional centrally symmetric polytope P of an arbitrarily high dimension d and with an arbitrarily large number N of vertices such that for some 0 < delta_k < 1 at least (1-delta_k^d) {N choose k} k-subsets of the set of vertices span faces of P, and third, for an integer k>1 and a>0, we construct a centrally symmetric polytope Q with an arbitrary large number N of vertices and of dimension d=k^{1+o(1)} such that least (1 - k^{-a}){N choose k} k-subsets of the set of vertices span faces of Q.Comment: 14 pages, some minor improvement