Showing papers by "Hungarian Academy of Sciences published in 1982"

Crossing-Free Subgraphs

Abstract: If m⩾4 then every planar drawing of a graph with n vertices and m edges contains more than m3/100n2 edge-crossings and fewer than 1013n crossing-free subgraphs. The first result settles a conjecture of Erdos and Guy and the second result settles a conjecture of Newborn and Moser.

Linear codes for sources and source networks: Error exponents, universal coding

Abstract: For Slepian-Wolf source networks, the error exponents obtained by Korner,Marton, and the author are shown to be universally attainable by linear codes also. Improved exponents are derived for linear codes with "large rates." Specializing the results to simple discrete memoryless sources reveals their relationship to the random coding and expurgated bounds for channels with additive noise. One corollary is that there are universal linear codes for this class of channels which attain the random coding error exponent for each channel in the class. The combinatorial approach of Csiszar-Korner-Marton is used. In particular, all results are derived from a lemma specifying good encoders in terms of purely combinatorial properties.

Electronic Structure of Polymers

Abstract: Publisher Summary This chapter discusses the development of microscopic models of the electronic structure of polymers in general and of conjugated organic polymers in particular The underlying physical model—namely, the one-particle picture, is being widely used in this field and is considered basically correct On a practical level, this means that periodic models are usually constructed, which justify using the terminology of energy–band theory With refinements of calculation tools, self-consistent calculations at even the ab initio level have become widespread The chapter focuses on methodological problems related to the treatment of the electronic structure of polymers, such as the boundary conditions and problems related to the large size of these systems, ab initio techniques, and a symmetry dilemma connected with the quasidegeneracy of partially filled bands The results of the application of these and semi-empirical techniques to the carbon atomic chain to (CH) x and a series of related polymers, polydiacetylene (PDA), and some further conjugated polymers, are compared with experimental results Most of the discussion is based on one-dimensional (1D) model

Compactness results in extremal graph theory

Abstract: Let L be a given family of so called prohibited graphs. Let ex (n, L) denote the maximum number of edges a simple graph of ordern can have without containing subgraphs from L. A typical extremal graph problem is to determine ex (n, L), or at least, find good bounds on it. Results asserting that for a given L there exists a much smaller L*⫅L for which ex (n, L) ≈ ex (n, L*) will be calledcompactness results. The main purpose of this paper is to prove some compactness results for the case when L consists of cycles. One of our main tools will be finding lower bounds on the number of pathsP k+1 in a graph ofn vertices andE edges., witch is, in fact, a “super-saturated” version of a wellknown theorem of Erdős and Gallai.

Largest random component of a k -cube

Abstract: LetC k denote the graph with vertices (ɛ 1, ...,ɛ k ),ɛ i =0,1 and vertices adjacent if they differ in exactly one coordinate. We callC k thek-cube. LetG=G k, p denote the random subgraph ofC k defined by letting $$Prob(\{ i,j\} \in G) = p$$ for alli, j ∈ C k and letting these probabilities be mutually independent. We show that forp=λ/k, λ>1,G k, p almost surely contains a connected component of sizec2 k ,c=c(λ). It is also true that the second largest component is of sizeo(2 k ).

Fourier transform infrared difference spectroscopy of bacteriorhodopsin and its photoproducts.

Abstract: Fourier transform infrared difference spectroscopy has been used to obtain the vibrational modes in the chromophore and apoprotein that change in intensity or position between light-adapted bacteriorhodopsin and the K and M intermediates in its photocycle and between dark-adapted and light-adapted bacteriorhodopsin. Our infrared measurements provide independent verification of resonance Raman results that in light-adapted bacteriorhodopsin the protein-chromophore linkage is a protonated Schiff base and in the M state the Schiff base is unprotonated. Although we cannot unambiguously identify the Schiff base stretching frequency in the K state, the most likely interpretation of deuterium shifts of the chromophore hydrogen out-of-plane vibrations is that the Schiff base in K is protonated. The intensity of the hydrogen out-of-plane vibrations in the K state compared with the intensities of those in light-adapted and dark-adapted bacteriorhodopsin shows that the conformation of the chromophore in K is considerably distorted. In addition, we find evidence that the conformation of the protein changes during the photocycle.

A Lower Bound for Heilbronn'S Problem

Abstract: We disprove Heilbronn's conjecture—that N points lying in the unit disc necessarily contain a triangle of area less than c/N. Introduction We think that the best account of the problem can be achieved by simply copying the corresponding paragraphs from Roth's paper [6]. \"Let Pv, P2,..., Pn (where n ^ 3) be a distribution of n points in a (closed) disc of unit area, such that the minimum of the areas of the triangles PiPjPk (taken over 1 < i < j < k ^ n) assumes its maximum possible value A = A(n). \"Heilbronn conjectured that A(n) c2(n/t)(\\ogt) . Remark 1. For any 3-graph one has the Turan-type estimate a > n/(3t), since a random (spanned) subgraph of size n/(2t) expectedly contains n/(24t) edges; delete all vertices in edges (see Spencer [8]). This is sharp up to constant multiple, for the Turan 3-graph (n/t disjoint cliques of size t) has t ~ t/2 and a = 2n/t. Thus the condition that G is uncrowded improves the bound on a by a factor (log t). This is again sharp, as is shown by random 3-graphs (choose nt triples at random and delete the few short cycles). Remark 2. Lemma 1 is an analogue of Lemma 1 in [1] or Theorem 2 in [2], which state that for a 2-graph with average valency t = 2e/n the Turan bound a ^ n(t+\\) can be improved to a > (i/\\00)(n/t)\\ogt if only the graph is trianglefree. The proof will also be analogous to the (complicated) one in [1], which uses random methods, rather than to the simple inductive one in [2], which was thoroughly rewritten and simplified by Joel Spencer. The reader is challenged to give a simple, non-probabilistic proof for Lemma 1. 2. The proof of the theorem If we drop N points to the unit disc at random, then (as will be seen shortly) we can select half of them with smallest triangle c/N (an alternative proof for Erdos' lower bound). We shall improve on this method by dropping N points and then selecting an appropriate subset of N points. Define the numbers t and n by the implicit equations t = n / 1 0 0 , N = c2(n/t)(\\ogt) 112 . Set A = (1/200) t/n; then n = -Nt(\\ogty' 2 and A = c3(log0/iV 2 = Cl(\\ogN)/N 2 . Let us drop n points to the unit disc at random, independently of each other, each with a uniform distribution. We define a 3-graph G on these n points (as vertices) by {a, b, c} € G if the points a, b, c form a triangle of area less than A. Now the probability that three random points form a triangle of area less than A is less than 2 2 — d{rn) = — Inrdr = 32TIA < t/n r J r o 16 JANOS KOML6S, JANOS PINTZ AND ENDRE SZEMERED1 (fix two points at a distance r, and then average over r). Hence the expected number of triangles of area less than A is less than nt/6. Thus the expected value of f is less than t/2. Hence, by Markov's inequality (see §4), with probability greater than 1/2, weget a 3-graph with t < t. Now we show that, with large probability, only o(n) short cycles occur in this 3-graph. All calculations will be based on the simple remark (already used above) that once two vertices have been chosen at a distance r, in order to get a triangle of area less than A, the third point has to belong to a strip of area less than 8A/r. The number of pairs of points at a distance less than d = n~° 6 is, with large probability, less than We discard these points. The number of 2-cycles is, with large probability, less than 2 f A c 4 n 4 —Inrdr < c5t \\ogn < n . The number of simple 3-cycles is, with large probability, less than

Remarks on positional games. I

Abstract: 1. Introduction and results We start with some terminology. A hypergraph is a collection of sets. The sets in the hypergraph are called edges, and the elements of these edges are called vertices. We deal with finite hypergraphs only. IA [ denotes the number of elements of the set A. Let p and q be positive integers and ~ be a hypergraph. A (p, q, ,r is a game in which two players select previously unselected vertices of ~. The first player selects p vertices per move and the second player selects q vertices per move. The first player wins whenever he selects all the vertices of some eddge of aye, other wise the second player wins. In the case p=q=l, ERD6S and SELFRIDGE [3] have found a sufficient condition for the second player's win: If 2-lal < 1/2, AE~

Effects of histamine on brain capillaries. Fine structural and immunohistochemical studies after intracarotid infusion.

Abstract: The effect of histamine administered via the common carotid artery on the transport processes of brain capillaries was investigated in rats. The fine structure of endothelial cells and the glial end-feet system was studied by electron microscopy and the serum albumin was visualized for light microscopy by the peroxidase-antiperoxidase (PAP) immunohisto-chemical reaction. Sixty microgram per milliliter histamine enhanced the penetration of serum albumin into the capillaries while the number of pinocytotic and coated vesicles significantly increased in the capillary endothelium. Oedematous swelling of the glial end-feet system was also observed. The stimulatory effect of histamine on the transcapillary transport could not be inhibited by a histamine H1-receptor antagonist, mepyramine. By contrast, metiamide, a histamine H2-receptor antagonist prevented both ultrastructural changes and albumin penetration in the brain capillaries to occur.

Mobilization of a Rhizobium meliloti megaplasmid carrying nodulation and nitrogen fixation genes into other rhizobia and Agrobacterium

Abstract: The indigenous megaplasmid pRme41b of Rhizobium meliloti 41 was made susceptible to mobilization with the P-1 type plasmid pJB3JI by inserting the mobilization (mob) region of RP4 into it. First the mob region together with a kanamycin resistance marker was inserted in vitro into a fragment of pRme41b cloned into pBR322. The recombinant plasmids so formed (pAK11 and pAK12) were then mobilized into R. meliloti. Since these recombinant plasmids were unable to replicate in R. meliloti, selection for kanamycin resistant derivatives allowed the isolation of pRme41b::pAK11 or pRme41b::pAK12 cointegrates. It was shown that in the majority of these recombinants, pAK11 or pAK12 was integrated into the homologous fragment of pRme41b. The pRme41b cointegrates were transferred into nod-nif deletion mutants of R. meliloti 41 where it was shown that both Nod+ and Fix+ phenotypes could be restored. The pRme41b cointegrates were also transferred into two other Rhizobium strains and into Agrobacterium tumefaciens. The Rhizobium strains and A. tumefaciens carrying pRme41b formed nodules of variable size on Medicago sativa roots, indicating that at least the early steps of nodulation of M. sativa are coded by pRme41b and are expressed in these bacteria.

Effect of radiation dosage on efficiency of chloroplast transfer by protoplast fusion in nicotiana

Abstract: Chloroplasts of Nicotiana tabacum SR1 were transferred into Nicotiana plumbaginifolia by protoplast fusion. The protoplasts of the organelle donor were irradiated with different lethal doses using a (60)Co source, to facilitate the elimination of their nuclei from the fusion products. After fusion induction, clones derived from fusion products and containing streptomycin-resistant N. tabacum SR1 chloroplasts were selected by their ability to green on a selective medium. When N. tabacum protoplasts were inactivated by iodoacetate instead of irradiation, the proportion of N. plumbaginifolia nuclear segregant clones was low (1-2%). Irradiation markedly increased this value: Using 50, 120, 210 and 300 J kg(-1) doses, the frequency of segregant clones was 44, 57, 84 and 70 percent, respectively. Regeneration of resistant N. plumbaginifolia plants with SR1 chloroplasts indicated that plastids can be rescued from the irradiated cells by fusion with untreated protoplasts. Resistant N. plumbaginifolia plants that were regenerated (43 clones studied) had diploid (2n = 2X = 20) or tetraploid chromosome numbers and were identical morphologically to parental plants. The absence of aneuploids suggests that in these clones irradiation resulted in complete elimination of the irradiated N. tabacum nuclei. Resistance is inherited maternally (five clones tested). The demonstration of chloroplast transfer and the presence of N. tabacum plastids in the N. plumbaginifolia plants was confirmed by chloroplast DNA fragmentation patterns after EcoRI digestion.

Nitrate reductase deficient cell lines from haploid protoplast cultures ofNicotiana plumbaginifolia

Abstract: Nitrate reductase deficient (NR-) cell lines were selected indirectly by their resistance to 40 mM chlorate in protoplast cultures of haploidNicotiana plumbaginifolia. Frequency of the chlorate resistant clones was 5.8×10-5 in non-mutagenized cultures, which could be increased up to 25 times by treatment with N-ethyl-N-nitrosourea (NEU) or gamma irradiation.

An experimental system for creating and presenting interactive graphical documents

Abstract: An experimental system is described for the design, development, and presentation of computer-based documents that combine pictures and text on a high-resolution color raster display. Such documents can be used, for example, for maintenance and repair tasks, videotex databases, or computer-aided instruction. Documents are directed graphs whose nodes we refer to as pages, in analogy to the pages of a paper book. A page includes a set of simultaneously displayed pictures, actions (procedures and processes), and indexing information. Pages may be nested arbitrarily deeply in chapters that serve much the same organizing function as those of conventional books. The system is comprised of separate programs for laying out and drawing pictures, for graphically specifying the contents of pages, chapters, and their interconnections, and for displaying the document for user interaction. Examples are given from a prototype maintenance and repair manual in which emphasis was placed on designing actions that allow simple real-time animation and assist in finding one's way around the document.

New telechelic polymers and sequential copolymers by polyfunctional initiator-transfer agents (inifers)

Abstract: The possibility of undesirable intramolecular cycloalkylation exists in the polymerization of iso-butylene induced by the p-dicumyl chloride/BCl3 inifer system. A scheme has been proposed which shows the sequence of reactions leading to indane skeletons. The structure of the indane derivatives has been characterized by 1H NMR spectroscopy. Systematic experiments have been carried out using low isobutylene and high p-dicumyl chloride concentrations leading to polyisobutylene oligomers needed for accurate endgroup analysis. The effect of temperature, solvent composition (polar/nonpolar) , isobutylene and BCl3 concentration on the extent of indane skeleton formation has been investigated. Indane skeleton formation can be completely suppressed by the use of relatively non-polar media, e.g., 1∶1 mixture of CH2Cl2 :n-C6H14, at or below −40°C, and conditions under which symmetrical telechelic polyisobutylenes can be obtained have been defined.

Storing a sparse table with O(1) worst case access time

Abstract: We describe a data structure for representing a set of n items from a universe of m items, which uses space n+o(n) and accommodates membership queries in constant time. Both the data structure and the query algorithm are easy to implement.

Complementation in somatic hybrids indicates four types of nitrate reductase deficient lines in Nicotiana plumbaginifolia

Abstract: Allelism of nine nitrate reductase deficient (NR−) Nicotiana plumbaginifolia cell lines was tested by complementation after protoplast fusion. Complementation was recognized by the appearance of somatic hybrid colonies growing on a selective NH4+/NO3− medium which cannot support the growth of NR− lines. All five apoenzyme defective (NA) lines were non-complementing and therefore allelic. The apoenzyme and the cofactor defective (NX) lines were complementing, as expected, and gave somatic hybrids with restored nitrate reductase activity. The four cofactor defective lines were found to belong to three complementation groups (NX1 and NX9; NX21; NX24). Two of these (NX21 and NX24) are of new types which have not been previously described in flowering plants. In the somatic hybrids restoration of NR activity was accompanied by the restoration of plant regeneration ability.

On Ramsey—Turán type theorems for hypergraphs

Abstract: LetH r be anr-uniform hypergraph. Letg=g(n;H r ) be the minimal integer so that anyr-uniform hypergraph onn vertices and more thang edges contains a subgraph isomorphic toH r . Lete =f(n;H r ,en) denote the minimal integer such that everyr-uniform hypergraph onn vertices with more thane edges and with no independent set ofen vertices contains a subgraph isomorphic toH r .

On graphs which contain all sparse graphs

Abstract: Publisher Summary This chapter presents a study on graphs which contain all sparse graphs. Let ℋ n denote the class of all graphs with n edges and denote by s ( n ) the minimum number of edges a graph G can have, which contains all H ∊ ℋ n as subgraphs. The chapter discusses the problem of determining the minimum number of edges, denoted by s' ( n ) a graph can have, which contains every planar graph on n edges as a subgraph. The chapter discusses a lower bound for s ( n ) and while discussing an upper bound for s ( n ), it is proved (by the probability method) that there exists a graph with cn 2 log log n /log n edges that contains all graphs with at most n edges. The chapter presents a theorem to give an upper bound of n 3/2 for the universal graphs that contain all planar graphs on n edges.