I read this book the same weekend that the Packers took on the Rams, and the experience of the latter event, obviously, colored my judgment. Although I abhor anything that smacks of being a handbook (like, \"How to Earn a Merit Badge in Neurosurgery\") because too many volumes in biomedical science already evince a boyscout-like approach, I must confess that parts of this volume are fast, scholarly, and significant, with certain reservations. I like parts of this well-illustrated book because Dr. Sj6strand, without so stating, develops certain subjects on technique in relation to the acquisition of judgment and sophistication. And this is important! So, given that the author (like all of us) is somewhat deficient in some areas, and biased in others, the book is still valuable if the uninitiated reader swallows it in a general fashion, realizing full well that what will be required from the reader is a modulation to fit his vision, propreception, adaptation and response, and the kind of problem he is undertaking. A major deficiency of this book is revealed by comparison of its use of physics and of chemistry to provide understanding and background for the application of high resolution electron microscopy to problems in biology. Since the volume is keyed to high resolution electron microscopy, which is a sophisticated form of structural analysis, but really morphology in a modern guise, the physical and mechanical background of The instrument and its ancillary tools are simply and well presented. The potential use of chemical or cytochemical information as it relates to biological fine structure , however, is quite deficient. I wonder when even sophisticated morphol-ogists will consider fixation a reaction and not a technique; only then will the fundamentals become self-evident and predictable and this sine qua flon will become less mystical. Staining reactions (the most inadequate chapter) ought to be something more than a technique to selectively enhance contrast of morphological elements; it ought to give the structural addresses of some of the chemical residents of cell components. Is it pertinent that auto-radiography gets singled out for more complete coverage than other significant aspects of cytochemistry by a high resolution microscopist, when it has a built-in minimal error of 1,000 A in standard practice? I don't mean to blind-side (in strict football terminology) Dr. Sj6strand's efforts for what is \"routinely used in our laboratory\"; what is done is usually well done. It's just that …

Methods in Enzymology.

Let's read! We will often find out this sentence everywhere. When still being a kid, mom used to order us to always read, so did the teacher. Some books are fully read in a week and we need the obligation to support reading. What about now? Do you still love reading? Is reading only for you who have obligation? Absolutely not! We here offer you a new book enPDFd the perception of the visual world to read.

The Perception of the Visual World. By James J. Gibson. U.S.A.: Houghton Mifflin Company, 1950 (George Allen & Unwin, Ltd., London). Price 35s.

An important feature of modern science and engineering is that data of various kinds is being produced at an unprecedented rate This is so in part because of new experimental methods, and in part because of the increase in the availability of high powered computing technology It is also clear that the nature of the data we are obtaining is significantly different For example, it is now often the case that we are given data in the form of very long vectors, where all but a few of the coordinates turn out to be irrelevant to the questions of interest, and further that we don’t necessarily know which coordinates are the interesting ones A related fact is that the data is often very high-dimensional, which severely restricts our ability to visualize it The data obtained is also often much noisier than in the past and has more missing information (missing data) This is particularly so in the case of biological data, particularly high throughput data from microarray or other sources Our ability to analyze this data, both in terms of quantity and the nature of the data, is clearly not keeping pace with the data being produced In this paper, we will discuss how geometry and topology can be applied to make useful contributions to the analysis of various kinds of data Geometry and topology are very natural tools to apply in this direction, since geometry can be regarded as the study of distance functions, and what one often works with are distance functions on large finite sets of data The mathematical formalism which has been developed for incorporating geometric and topological techniques deals with point clouds, ie finite sets of points equipped with a distance function It then adapts tools from the various branches of geometry to the study of point clouds The point clouds are intended to be thought of as finite samples taken from a geometric object, perhaps with noise Here are some of the key points which come up when applying these geometric methods to data analysis • Qualitative information is needed: One important goal of data analysis is to allow the user to obtain knowledge about the data, ie to understand how it is organized on a large scale For example, if we imagine that we are looking at a data set constructed somehow from diabetes patients, it would be important to develop the understanding that there are two types of the disease, namely the juvenile and adult onset forms Once that is established, one of course wants to develop quantitative methods for distinguishing them, but the first insight about the distinct forms of the disease is key

Topology and data

MUCKE aims to mine a large volume of images, to structure them conceptually and to use this conceptual structuring in order to improve large-scale image retrieval. The last decade witnessed important progress concerning low-level image representations. However, there are a number problems which need to be solved in order to unleash the full potential of image mining in applications. The central problem with low-level representations is the mismatch between them and the human interpretation of image content. This problem can be instantiated, for instance, by the incapability of existing descriptors to capture spatial relationships between the concepts represented or by their incapability to convey an explanation of why two images are similar in a content-based image retrieval framework. We start by assessing existing local descriptors for image classification and by proposing to use co-occurrence matrices to better capture spatial relationships in images. The main focus in MUCKE is on cleaning large scale Web image corpora and on proposing image representations which are closer to the human interpretation of images. Consequently, we introduce methods which tackle these two problems and compare results to state of the art methods. Note: some aspects of this deliverable are withheld at this time as they are pending review. Please contact the authors for a preview.

http://ieeexplore.ieee.org/iel2/4524/12820/00592460.pdf

Image Processing

We show that two natural approaches to quantum gravity coincide. This identity is nontrivial and relies on the equivalence of each approach to KdV equations. We also investigate related mathematical problems.

/pdf/intersection-theory-on-the-moduli-space-of-curves-and-the-2zk9zv56ec.pdf

Intersection theory on the moduli space of curves and the matrix Airy function

Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.

Computational Topology: An Introduction

The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the persistence diagram is stable: small changes in the function imply only small changes in the diagram. We apply this result to estimating the homology of sets in a metric space and to comparing and classifying geometric shapes.

https://link.springer.com/content/pdf/10.1007%2Fs00454-006-1276-5.pdf

Stability of Persistence Diagrams

Stability of persistence diagrams

Let Fg 1, g> 1, be the mapping class group consisting of all isotopy classes of base-point and orientation preserving homeomorphisms of a closed, oriented surface F of genus g. Let )~(~1) be its Euler characteristic in the sense of Wall, that is Z(F~I)= [Fgl: F] l z(E/F), where F is any torsion free subgroup of finite index in F~ 1 and E is a contractible space on which F acts freely and properly discontinuously. An example of such a space is the Teichmiiller space ~-~1, and g(F~ ~) can be interpreted as the orbifold Euler characteristic of ~-~'/F~I =JOin, the moduli space of curves of genus g with base point. The purpose of this paper is to prove the following formula for )~(F~I):

http://people.mpim-bonn.mpg.de/zagier/files/doi/10.1007/BF01390325/fulltext.pdf

The Euler characteristic of the moduli space of curves

Let F = F ~ r be the mapping class group of a surface F of genus g with s punctures and r boundary components. The purpose of this paper is to establish cohomology properties of F parallel to those of the arithmetic groups. If G is a linear algebraic group defined over Q, X is the symmetric space associated to G and A is an arithmetic subgroup of G, then A is virtually torsion free and acts properly discontinuously on X. The rational homology of A is the same as that of X/A. Furthermore there is a "bordification" of X ([BS]) to a manifold with corners 3~ and an extension of the action of A to a properly discontinuous action on Jf so that the quotient X / A is compact. The boundary of Jf is homotopy equivalent to a wedge of spheres, say of dimension d, and the virtual cohomological dimension of A is n d + 1, where n is the dimension of X. In the case of the mapping class group there is no analog for G, Ivanov (unpublished) has proven that F is not arithmetic. Nevertheless, F acts properly discontinuously on Teichmiiller space r which is homeomorphic to Euclidean space (of dimension 6 g 6 + 2 s ) ; 3"will play the role of the symmetric space. The quotient of .9by F is the moduli space of curves whose rational homology is then identified with that of E Harvey [Har] has constructed a Borel-Serre bordification J of 3-by analytic methods. In the case where F has punctures, we will build g by a different, combinatorial method. In addition, we will explicitly describe inside Y a cell complex Y of dimension 4 g 4 + s onto which J may be F-equivariantly retracted, thus establishing an analog of the constructions for SL n by Serre, Soul6 ([Sol) and Ash ([A]). This complex will be of the lowest possible dimension because we will use J= to prove our main result:

John Harer

Papers

Computational Topology: An Introduction

Stability of Persistence Diagrams

Stability of persistence diagrams

The Euler characteristic of the moduli space of curves

The virtual cohomological dimension of the mapping class group of an orientable surface