Semismooth and Semiconvex Functions in Constrained Optimization

We introduce semismooth and semiconvex functions and discuss their properties with respect to nonsmooth nonconvex constrained optimization problems. These functions are locally Lipschitz, and hence have generalized gradients. The author has given an optimization algorithm that uses generalized gradients of the problem functions and converges to stationary points if the functions are semismooth. If the functions are semiconvex and a constraint qualification is satisfied, then we show that a stationary point is an optimal point. We show that the pointwise maximum or minimum over a compact family of continuously differentiable functions is a semismooth function and that the pointwise maximum over a compact family of semiconvex functions is a semiconvex function. Furthermore, we show that a semismooth composition of semismooth functions is semismooth and gives a type of chain rule for generalized gradients

An Algorithm for Constrained Optimization with Semismooth Functions

We present an implementable algorithm for solving constrained optimization problems defined by functions that are not everywhere differentiable. The method is based on combining, modifying and extending the nonsmooth optimization work of Wolfe, Lemarechal, Feuer, Poljak, and Merrill. It can be thought of as a generalized reset conjugate gradient algorithm. We also introduce the class of weakly upper semismooth functions. These functions are locally Lipschitz and have a semicontinuous relationship between their generalized gradient sets and their directional derivatives. The algorithm is shown to converge to stationary points of the optimization problem if the objective and constraint functions are weakly upper semismooth. Such points are optimal points if the problem functions are also semiconvex and a constraint qualification is satisfied. Under stronger convexity assumptions, bounds on the deviation from optimality of the algorithm iterates are given

Putting Private Papers on Deposit: A Case Study

As the part-time Archivist and Curator of the Massachusetts General Hospital, I am occasionally free to moonlight as a consultant for other organizations in need of advice about what to do with their historical records. For several years I have served as Consulting Archivist for the Wakefield Charitable Trust, an educational foundation that administers the buildings, grounds, and fortune bequeathed by Mary M. B. Wakefield, the heiress of a venerable Brahmin family. Mrs. Wakefield lived on a twenty-one-acre estate (now known as the Wakefield Estate and Arboretum) in a semi-rural part of Milton, a Boston suburb. In younger years she was a talented landscape architect and an advocate for environmental causes. She died at an advanced age in 2004 after years of illness accompanied by mental confusion. Her will stipulated that her property (buildings and grounds, as well as investment income) should be used for some worthwhile educational purpose. The terms were not clearly defined, but it was known that she wanted the estate’s gardens and arboretum maintained for public enjoyment

Shipwrecks, Hospital Wards, and Landscape Architecture: On the Unexpected Utility of Maps in Archival Collections

An obsessive cartographer in Reif Larsen’s novel, The Selected Works of T.S. Spivet, describes a 25-year project of attempting to compile and catalogue maps of all kinds to arrive at “a totally comprehensive understanding of the history, geology, archaeology, botany, and zoology of the land.” Mr. Benefideo realizes that the task is too much for one person or even one generation and hopes that a new generation of cartographers will pick up where he left off. “A map does not just chart,” he suggests, “it unlocks and formulates meaning; it forms bridges between here and there, between disparate ideas that we did not know were previously connected.” Maps are among the best tools available for historical analysis, much as charts and graphs are essential to science. They come in many varieties. Good maps are a graphic, succinct summary of information, fertile with potential applications that may never have been predicted by their creators. This article summarizes how maps, and closely related documents, have been used in innovative ways by visitors and staff at three archival repositories where the author has provided reference services

Faded but Not Forgotten: Thinking about the Records and Relics of America\u27s Earliest Forays in Photography

The first documented photographs in America were taken in the spring of 1839 by enthusiastic experimenters after studying recently arrived publications from England, detailing William Henry Fox Talbot\u27s instructions for making photogenic drawings. The images have not survived, but meaning can nevertheless be found in the circumstances surrounding their production and disappearance

Modulation of Body Weight by Intestinal Flora in Orphan Nuclear Receptor SHP-/- Mice

The whole-body deletion of small heterodimer partner (SHP) in mice is associated with protection from diet-induced obesity and hepatic steatosis upon feeding of a western diet. This protection was reported to be mediated through decreases in hepatic gene expression for lipogenesis, as well as increases in gene expression for fatty acid oxidation. SHP has been known to regulate the expression of the CYP7A1 gene, encoding the rate-limiting enzyme for bile acid synthesis, thereby altering the bile acid pool. The effects of this altered bile acid profile on the gut microbiome are unknown, as some bacteria in the gut are responsible for bile acid metabolism while others are killed by the detergent effect of bile acids. This study shows that mice without SHP display a distinctly different microbiome from wild-type mice, characterized by a reduction of phylogenetic diversity and an increased abundance of the Bacteroidetes phylum with a proportional decrease in Firmicutes abundance. Cohousing mice led to increased microbiome similarity between genotypes, with a blunted reduction of phylogenetic diversity in SHP-/- mice. Furthermore, cohoused mice displayed reductions in the hepatic gene expression for synthesis of fatty acids, lipid droplets, and bile acids without altering fat and liver mass. These results may suggest a relationship between SHP and the microbiome in the development of diet-induced obesity but not hepatic steatosis

The Effect of Heat Treatment of Fresh Frozen Vells on Rennin Extractability

A procedure was developed for the extraction of rennet from fresh frozen vells. Frozen vells were minced in a Model VCM-25 Hobart Vertical Cutter/Mixer. Dry sodium chloride was added until the salt concentration in the moisture of the tissue was 10%. Salted tissue was placed in galvanized steel cells and heated in a water bath to 49, 54, 57 and 60 C for 0, 15, 30, 45 and 60 minutes. The heated tissue was dried to about 4% moisture at ambient temperature with the aid of an electric fan. The dried salted tissue was extracted with a sodium chloride solution adjusted to give a salt concentration of 10% in the extraction solution. Salted vell tissue heated to 49 C for 60 minutes and to 54 C for 30 minutes prior to drying produced 82 and 55%, respectively, more recoverable enzyme activity than unheated salted tissue. However, tissue which was salted, heated and not dried prior to extraction produced less recoverable activity than unheated samples. Unsalted vell tissue which was heated to 49, 54, 57 and 60 C for 15, 30, 45 and 60 minutes and extracted without being dried yielded lower recoverable activity than unheated samples. Heating unsalted vell tissue to 54, 57 and 60 C for 15, 30, 45 and 60 minutes prior to drying did not increase recoverable enzyme activity over unheated samples. Unsalted tissue heated to 49 C produced a slightly higher recovery than unheated samples

Letter from Houghton, Mifflin & Co. to John Muir, 1905 Nov 24.

HOUGHTON, MIFFLIN AND COMPANY[illegible]4 PARK STREET: BOSTONNov.24, 1905.Mr. John Muir,Martinez, Cal.Dear Mr. Muir:We are sending you under a separate cover a copy of our Holiday Bulletin of the hooks for the year. Over one-hundred thousand copies of this Bulletin have been printed and distributed, and we are in hopes that its attractive appearance may lead to the successful sale for your hooks during the coming season.Faithfully yours,Houghton, Mifflin & Co

Letter from Houghton Mifflin Co. to John Muir, 1911 Feb 8.

February 8.: 1911.Dear Mr. Muir:We take pleasure in sending you enclosed a circular of our Travel Books in which you will find your book included.We are distributing these circulare ourselves, and have also arranged with Raymond & whit[illegible] Company to mail 25O0 to intending tourists.Very truly yours,Houghton Mifflin Co,Mr. John Muir,Martinez, Cal