Dynkin diagrams of rank 20 on supersingular K3 surfaces

We classify normal supersingular K 3 surfaces Y with total Milnor number 20 in characteristic p,where p is an odd prime that does not divide the discriminant of the Dynkin type of the rational double points on Y.This paper appeared in preprint form in the home page of the first author in the year 2005.     

Synthesis,Redox Behavior,Sensitizer Activity,and Oxygen Transfer of Covalently Bound Polymeric Porphyrins

Metal complexes of covalently bound porphyrins are used as sensitive probes for several investigations. Substituted derivatives of tetraphenyl-porphin, phthalocyanine, and naphthalocyanine are synthesized at positively and negatively charged as well as uncharged polymers. The photo-redox activities were studied under irradiation with visible light in the presence of a donor and an acceptor. The triplet life times of covalently bound porphyrin moieties are strongly enhanced compared with the analogous monomeric porphyrins. In addition, the polymer binding results in higher photocatalytic activity. The electron-transfer reactions of Mn(III)-containing porphyrins using the reducing agent dithionite are strongly influenced by the polymer environment. In contrast to monomeric Mn(III)-porphyrins, the porphyrins containing polymers exhibit a two-step reduction which may be due to the change of the conformation of the polymer coil. The catalytic epoxidation of 2,5-dihydrofuran with hypochlorite with formation of 3,4-epoxytetrahydrofuran occurs with water-soluble porphyrins in water. No influence of the polymer environment exists. The different reactions require reaction times from milliseconds up to hours.     

Fast Epitope Mapping for the Anti‐MUC1 Monoclonal Antibody by Combining a One‐Bead‐One‐Glycopeptide Library and a Microarray Platform

Anti‐MUC1 monoclonal antibodies (mAbs) are powerful tools that can be used to recognize cancer‐related MUC1 molecules, the O‐glycosylation status of which is believed to affect binding affinity. We demonstrate the feasibility of using a rapid screening methodology to elucidate those effects. The approach involves i) “one‐bead‐one‐compound”‐based preparation of bilayer resins carrying glycopeptides on the shell and mass‐tag tripeptides coding O‐glycan patterns in the core, ii) on‐resin screening with an anti‐MUC1 mAb, iii) separating positive resins by utilizing secondary antibody conjugation with magnetic beads, and (iv) decoding the mass‐tag that is detached from the positive resins pool by using mass spectrometric analysis. We tested a small library consisting of 27 MUC1 glycopeptides with different O‐glycosylations against anti‐MUC1 mAb clone VU‐3C6. Qualitative mass‐tag analysis showed that increasing the number of glycans leads to an increase in the binding affinity. Six glycopeptides selected from the library were validated by using a microarray‐based assay. Our screening provides valuable information on O‐glycosylations of epitopes leading to high affinity with mAb.     

ESR study of Mn2+ in GeTe and GeTeSi glasses

The electron spin resonance spectra of Mn²⁺ ions have been studied in Ge_xTe_100?x with x = 15, 17.5 and 20, and Ge_20?xTe₈₀Si_x with 0 ?x? 20. All samples are found to exhibit six hyperfine lines centered at g = 4.3 with hyperfine interaction constant A = 56 × 10^?4cm^?1. The g = 4.3 line is interpreted as being caused by Mn²⁺ ions incorporated in the amorphous network and surrounded by four Te atoms in an arrangement of orthorhombic symmetry. Some of the samples of GeTe show a g = 2.0 line. This line also appears after heat treatment in air at temperatures above the glass transition temperature. It is concluded that the g = 2.0 line is caused by Mn²⁺ ions in phase separated microcrystalline or concentrated regions of MnO in the glass.     

Raman and infrared spectra of the all-trans, 7-cis, 9-cis, 13-cis and 15-cis isomers of β-carotene: Key bands distinguishing stretched or terminal-bent configurations form central-bent configurations

Raman and infrared spectra in the region of 1800-150 cm⁻¹ were recorded for a set of cis-trans isomers of d̃-carotene, i.e. the all-trans, 7-cis, 9-cis, 13-cis and 15-cis isomers. Spectral comparison revealed Raman and infrared key bands which (1) distinguish stretched or terminal-bent configurations (all-trans, 7-cis and 9-cis) from central-bent configurations (13-cis and 15-cis), and (2) distinguish unmethylated 7-cis and 15-cis configuratios. Keybands (1) include Raman bands at 1160 and 1140 cm⁻¹ and infrared bands at 825 and 775 cm⁻¹ (the intensity varies with the position of the cis-bend) Key bands (2) include Raman bands at 1274 and 962 cm⁻¹ and an infrared band at 741 cm⁻¹ (characteristic of the 7-cis configuration), and also a Raman band at 1247 cm⁻¹ and an infrared band at 775 cm⁻¹ (characteristic of the 15-cis configuration). The normal modes for the key bands were determined by a set of normal coordinate calculations for the isomeric configurations of a simplified model of d̃-carotene. The key bands were mainly related to the C H in-plane bendings, coupled with the CC or C C stretching, or to the C H out-of-plane wagging vibrations, some of which coupled with the CC torsion.     

On the Nature of Functional Differentiation: The Role of Self-Organization with Constraints

The focus of this article is the self-organization of neural systems under constraints. In 2016, we proposed a theory for self-organization with constraints to clarify the neural mechanism of functional differentiation. As a typical application of the theory, we developed evolutionary reservoir computers that exhibit functional differentiation of neurons. Regarding the self-organized structure of neural systems, Warren McCulloch described the neural networks of the brain as being “heterarchical”, rather than hierarchical, in structure. Unlike the fixed boundary conditions in conventional self-organization theory, where stationary phenomena are the target for study, the neural networks of the brain change their functional structure via synaptic learning and neural differentiation to exhibit specific functions, thereby adapting to nonstationary environmental changes. Thus, the neural network structure is altered dynamically among possible network structures. We refer to such changes as a dynamic heterarchy. Through the dynamic changes of the network structure under constraints, such as physical, chemical, and informational factors, which act on the whole system, neural systems realize functional differentiation or functional parcellation. Based on the computation results of our model for functional differentiation, we propose hypotheses on the neuronal mechanism of functional differentiation. Finally, using the Kolmogorov–Arnold–Sprecher superposition theorem, which can be realized by a layered deep neural network, we propose a possible scenario of functional (including cell) differentiation.