某些三维流形不变量的计算

Ｔｈｅｃａｌｃｕａｌｔｉｏｎｏｆ〈ｚｋ１,ｚｋ２,…,ｚｋｎ〉ＬｏｆｔｈｉｓｐａｐｅｒｗｉｌｌｂｅｉｎｔｅｒｍｏｆｔｈｅＫａｕｆｆｍａｎｂｒａｃｋｅｔ－ｐｏｌｙｎｏｍｉａｌ［１,２,３］．ＴｈｅＫａｕｆｆｍａｎｂｒａｃｋｅｔｐｏｌｙｎｏｍｉａｌｏｆａｐｌａｎａｒｄｉａｇｒａｍｏｆａｎｕｎｏｒｉｅｎｔｅｄｌｉｎｋｉｓａｎｅｌｅｍｅｎｔ〈Ｄ〉∈Ｚ［Ａ,Ａ－１］ｄｅｆｉｎｅｄｂｙｔｈｅｆｏｌｌｏｗｉｎｇｐｒｏｃｅｓｓ．ＡｓｔａｔｅｏｆＤｉｓｄｅｆｉｎｅｄｔｏｂｅａｍａｐｓｆｒｏｍｔｈｅｃｒｏｓｓｉｎｇ…     

Mackey and Frobenius Structures on Odd Dimensional Surgery Obstruction Groups

C. T. C. Wall formulated surgery-obstruction groups L _n (Z[G]) in terms of quadratic modules and automorphisms. C. B. Thomas showed that the Wall-group functors L _n (Z[–],w|_–) are modules over the Hermitian-representation-ring functor G₁(Z, –) if the orientation homomorphism w is trivial. A. Bak generalized the notion of quadratic module by introducing quadratic-form parameters, and obtained various K-groups related to quadratic modules and automorphisms. One of the authors established that some Bak groups W _n (Z[G], w) are equivariant-surgery-obstruction groups and showed in the case of even dimension n that the Bak-group functor W _n (Z)[–], _–; w|_–) is a w-Mackey functor as well as a module over the Grothendieck–Witt-ring functor GW₀(Z, –), where w is possibly nontrivial. In this paper, we prove the same facts in the case of odd dimension n.     

Induction theorems of surgery obstruction groups

Let be a finite group. It is well known that a Mackey functor is a module over the Burnside ring functor , where ranges over the set of all subgroups of . For a fixed homomorphism , the Wall group functor is not a Mackey functor if is nontrivial. In this paper, we show that the Wall group functor is a module over the Burnside ring functor as well as over the Grothendieck-Witt ring functor . In fact, we prove a more general result, that the functor assigning the equivariant surgery obstruction group on manifolds with middle-dimensional singular sets to each subgroup of is a module over the Burnside ring functor as well as over the special Grothendieck-Witt ring functor. As an application, we obtain a computable property of the functor described with an element in the Burnside ring.

     

The putative use of alpha-1-acid glycoprotein as a non-invasive marker of fibrosis

The acute phase response to injury or infection results in alterations in the expression of the plasma proteins produced by the liver. Many of these biomolecules are glycosylated with oligosaccharide chains covalently attached to the polypeptide backbone and the extent and composition of this glycosylation can be altered in a disease-dependent manner. Of particular interest is the observation that the acute phase glycoprotein, alpha-1-acid glycoprotein (AGP) has altered glycosylation in several physiological and pathological conditions. It is posited that changes induced in liver diseases may reflect disease severity and may therefore act as a non-invasive marker of fibrosis. This study has investigated the glycosylation of AGP in the plasma of people with varying degrees of cirrhosis and fibrosis. Hyperfucosylation was observed in all disease samples in comparison to normal plasma and was significantly increased in cirrhosis. Both sialic acid and N-acetylgalactosamine (GalNAc) were negatively associated with fibrosis. Two samples were found to express GalNAc, which as a constituent of the glycosylation of serum proteins is rare. In conclusion, fucose, sialic acid and other aspects of the glycosylation of AGP are influenced by the degree of fibrosis and as such may prove a valuable prognostic indicator of the development of cirrhosis.     

Minimally separating sets, mediatrices, and Brillouin spaces

Brillouin zones and their boundaries were studied in [J.J.P. Veerman et al., Comm. Math. Phys. 212 (3) (2000) 725] because they play an important role in focal decomposition as first defined by Peixoto in [J. Differential Equations 44 (1982) 271] and in physics [N.W. Ashcroft, N.D. Mermin, Solid State Physics, Holt, Rhinehart, and Winston, 1976; L. Brillouin, Wave Propagation in Periodic Structures, Dover, 1953]. In so-called Brillouin spaces, the boundaries of the Brillouin zones have certain regularity properties which imply that they consist of pieces of mediatrices (or equidistant sets).The purpose of this note is two-fold. First, we give some simple conditions on a metric space which are sufficient for it to be a Brillouin space. These conditions show, for example, that all compact, connected Riemannian manifolds with their usual distance functions are Brillouin spaces. Second, we exhibit a restriction on the Z₂-homology of mediatrices in such manifolds in terms of the Z₂-homology of the manifolds themselves, based on the fact that they are Brillouin spaces. (This will used to obtain a classification up to homeomorphism of surface mediatrices in forthcoming paper [J. Bernhard, J.J.P. Veerman, The topology of surface mediatrices, Portland State University].)     

Preliminary observations on magnetic resonance imaging in refractory epilepsy

We are studying the use of magnetic resonance (MR) imaging in localization of epileptogenic foci in patients with medically refractory partial epilepsy. Imaging is performed using a prototype resistive unit operating at 0.15 T. All studies include 7 mm axial sections obtained with a partial saturation sequence (TR = 200 msec) in which signals are recovered with a spin echo (TE = 11 msec) and images reconstructed using a modified 2D Fourier transform technique. Since the temporal lobe and limbic system are the commonest site of seizure foci in this group of patients, examinations were performed with the plane of section parallel to the temporal horns of the lateral ventricles.

Consensus interpretations by a radiologist, neurologist and neurosurgeon have recognized findings considered possibly abnormal in six of 11 epilepsy patients and none of six normal volunteers.

These preliminary results indicate that further study is warranted in this group of patients. Critical evaluation of such findings must be carried out in a larger group including normals and patients with a variety of neurologic disorders.     

Identification of surgical practice patterns using evolutionary cluster analysis

Modern data analysis and machine learning are strongly dependent on efficient search techniques. However, in general, further exploration into high-dimensional and multi-modal spaces is needed, and moreover, many real-world problems exhibit inaccurate, noisy, discrete and complex data. Thus, robust methods of optimization are often required to generate results suitable for these data. Some algorithms that imitate certain natural principles, namely the so-called evolutionary algorithms, have been used in different fields with great success. In this paper, we apply a variant of Particle Swarm Optimization (PSO), recently introduced by the authors, to partitional clustering of a real-world data set to distinguish between perioperative practices and associate them with some unknown relevant facts. Our data were obtained from a survey conducted in Spain based on a pool of colorectal surgeons. The PSO derivative we consider here: (i) is adapted to consider mixed discrete-continuous optimization, with statistical clustering criteria arranged to take these types of mixed measures; (ii) is able to find optimum or near-optimum solutions much more efficiently and with considerably less computational effort because of the richer population diversity it introduces; and (iii) is able to select the right parameter values through self-adaptive dynamic parameter control, thus overcoming the cumbersome aspect common to all metaheuristics.     

Variation of the Alexander-Conway polynomial under Dehn surgery

Let ε₁ and ε₂ belong to {±1}. When the ε₁-surgery along a knot K₁ in S³ produces the same homology sphere as the ε₂-surgery along a knot K₂ in S³, then the Casson surgery formula implies that ε₁Δ_K1″(1)=ε₂Δ_K2″(1), where Δ(t) denotes the symmetric Alexander polynomial. For any pair (Λ₁(t),Λ₂(t)) of possible knot Alexander polynomials such that ε₁Λ₁″(1)=ε₂Λ₂″(1), we exhibit a pair (K₁,K₂) of knots in S³ such that Δ_K1(t)=Λ₁(t), Δ_K2(t)=Λ₂(t) and the ε₁-surgery along K₁ produces the same homology sphere as the ε₂-surgery along K₂.     

Minimally k-Edge-Connected Directed Graphs of Maximal Size

Let D=(V,E) be a minimally k-edge-connected simple directed graph. We prove that there is a function f(k) such that |V|f(k) implies |E|2k(|V|–k). We also determine the extremal graphs whose size attains this upper bound.Basic Research in Computer Science, funded by the Danish National Research Foundation.Supported by the MTA-ELTE Egerváry Research Group on Combinatorial Optimization, and the Hungarian Scientific Research Fund grant No. F034930, T037547, and FKFP grant No. 0143/2001. Part of this research was done when the second author visited BRICS, University of Aarhus, Denmark.     

Raman spectroscopic analysis of breast cancer tissues: identifying differences between normal,invasive ductal carcinoma and ductal carcinoma in situ of the breast tissue

A relatively non‐destructive method employing Raman spectroscopy for the analysis of histopathological specimens is described. Raman spectroscopy has allowed qualitative analysis of the same specimen used for histopathological evaluation. Breast cancer tissues have been analysed to demonstrate the feasibility of the chemical changes taking place in the biological tissue, which can be identified precisely, and the results are reproducible. Raman analysis of tissue sections provides distinct spectra that can be used to distinguish between the nuclear grades of ductal carcinoma in situ (DCIS) and invasive ductal carcinoma (IDC) of the breast. Sixty cases of breast carcinoma including DCIS and IDC and seven cases of normal breast tissues were studied employing the Raman spectroscopic technique. This study reports for the first time spectral differences between DCIS grades. It is concluded that Raman spectroscopy can objectively distinguish between DCIS and IDC grades and is non‐destructive and reproducible. It should become possible in future to use Raman spectroscopy as an informative and quantitative method suitable for classification of grades and diagnosis of breast carcinoma. Copyright © 2007 John Wiley & Sons, Ltd.