Signed graphs

A signed graph is a graph with a sign attached to each arc. This article introduces the matroids of signed graphs, which generalize both the polygon matroids and the even-circle (or unoriented cycle) matroids of ordinary graphs. The concepts of balance, switching, restriction and contraction, double covering graphs, and linear representation of signed graphs are treated in terms of the matroid, and a matrix-tree theorem for signed graphs is proved. The examples treated include the all-positive and all-negative graphs (whose matroids are the polygon and even-circle matroids), sign-symmetric graphs (related to the classical root systems), and signed complete graphs (equivalent to two-graphs).Replacing the sign group by an arbitrary group leads to voltage graphs. Most of our results on signed graphs extend to all voltage graphs.     

Method of quasiclassical approximation for c-number projection in coherent states basis

A method of deriving the equations for physical average values is proposed in the form of ? orders expansion. The method is based on c-number projection of Heisenberg equations on a coherent states basis. The analysis of quantum corrections for quantum nonlinear resonance as an example is carried out. It is shown that the structure of quantum corrections results in appearance of the terms increasing in time in nonlinear systems.An example of an exactly solvable model is considered and the main times at which the expansion of ? orders is correct are obtained. The property of non-Hamiltonity of the equations of motion of the system in the phase space of projection is discussed.     

Interatomic Coulomb interaction influence on the superradiance phase transition

The phase transition to the superradiance state, when the Coulomb interactions between atoms exist, is considered. It is shown that transition temperature decreases and field value threshold increases. The display of this effects in the photon echo observation is discussed.     

Action of surface-active substances on biological membranes I. Effect of chemical modification of membranes on hemolysis of erythrocytes by sodium alkyl sulfates

Summary The hemolytic action of a homologous series of sodium alkyl sulfates (C ₈ toC ₁₅) on dog and human erythrocytes was measured. The influence of trypsin, pronase and neuraminidase treatments on the lytic resistance of human red cells was studied. A new approach evaluating the hemolytic activity of ionic detergents is expressed as a ratio of a concentration providing 50% lysis to its CMC-value. The results obtained are examined for their bearing on the use of surface-active agents as a means to study the structure organization of biological membranes.

---

Zusammenfassung Es wurde die hämolytische Wirkung homologer Reihen von Natriumalkylsulfaten an Erythrozyten von Mensch und Hund gemessen. Um die hämolytische Aktivität der ionogenen Detergenzien zu charakterisieren, wurde das Verhältnis der Konzentration, welche eine 50%-ige Lyse bewirkt, zum cmc-Wert gewählt.

     

A combinatorial analysis of topological dissections

From a topological space remove certain subspaces (cuts), leaving connected components (regions). We develop an enumerative theory for the regions in terms of the cuts, with the aid of a theorem on the Möbius algebra of a subset of a distributive lattice. Armed with this theory we study dissections into cellular faces and dissections in the d-sphere. For example, we generalize known enumerations for arrangements of hyperplanes to convex sets and topological arrangements, enumerations for simple arrangements and the Dehn-Sommerville equations for simple polytopes to dissections with general intersection, and enumerations for arrangements of lines and curves and for plane convex sets to dissections by curves of the 2-sphere and planar domains.     

Inductive problem‐sequences for independent study of linear algebra

Three chapters of the syllabus of a basic mathematics course for engineering students at the Technion? ? Technion is the oldest and largest school of engineering in Israel. were adapted for the student's independent development of mathematical knowledge by means of solving a chain of inductive problem‐sequences: (i) vectors and scalars in the plane; (ii) vectors in the three‐dimensional space; (iii) planes and lines in the 3‐dimensional space. The main principles which guided the adaptation of course materials for this purpose are presented. In particular an inductive problem‐sequenceis defined as a sequence consisting of problems which lead the learner to investigate particular cases, discover a common regularity, make a conjecture about a unifying rule, and finally prove or refute the conjecture. The major part of the paper is an annotated analysis of an excerpt of the materials.     

Case Influence Analysis in Bayesian Inference

Abstract

We demonstrate how case influence analysis, commonly used in regression, can be applied to Bayesian hierarchical models. Draws from the joint posterior distribution of parameters are importance weighted to reflect the effect of deleting each observation in turn; the ensuing changes in the posterior distribution of each parameter are displayed graphically. The procedure is particularly useful when drawing a sample from the posterior distribution requires extensive calculations (as with a Markov Chain Monte Carlo sampler). The structure of hierarchical models, and other models with local dependence, makes the importance weights inexpensive to calculate with little additional programming. Some new alternative weighting schemes are described that extend the range of problems in which reweighting can be used to assess influence. Applications to a growth curve model and a complex hierarchical model for opinion data are described. Our focus on case influence on parameters is complementary to other work that measures influence by distances between posterior or predictive distributions.     

Tractable Partially Ordered Sets Derived from Root Systems and Biased Graphs

We study new posets Q obtained by removing from a geometric lattice L ofa biased graph certain flats indexed by a simplicial complex . (One example of L is the lattice of flats of thevector matroid of a root system B _n .) We study the structureand compute the characteristic polynomial of Q. With certainchoices of L and , including ones for which Q is alattice interpolating between those of B _n and D _n , we observe curious relationships among the roots of thecharacteristic polynomials of Q, L, and .