On the Arrangement of Cliques in Chordal Graphs with respect to the Cuts

A cut (A, B) (where B = V - A) in a graph G = (V, E) is called internal if and only if there exists a vertex x in A that is not adjacent to any vertex in B and there exists a vertex y is an element of B such that it is not adjacent to any vertex in A. In this paper, we present a theorem regarding the arrangement of cliques in a chordal graph with respect to its internal cuts. Our main result is that given any internal cut (A, B) in a chordal graph G, there exists a clique with kappa(G) + vertices (where kappa(G) is the vertex connectivity of G) such that it is (approximately) bisected by the cut (A, B). In fact we give a stronger result: For any internal cut (A, B) of a chordal graph, and for each i, 0 <= i <= kappa(G) + 1 such that vertical bar K-i vertical bar = kappa(G) + 1, vertical bar A boolean AND K-i vertical bar = i and vertical bar B boolean AND K-i vertical bar = kappa(G) + 1 - i. An immediate corollary of the above result is that the number of edges in any internal cut (of a chordal graph) should be Omega(k(2)), where kappa(G) = k. Prompted by this observation, we investigate the size of internal cuts in terms of the vertex connectivity of the chordal graphs. As a corollary, we show that in chordal graphs, if the edge connectivity is strictly less than the minimum degree, then the size of the mincut is at least kappa(G)(kappa(G)+1)/2 where kappa(G) denotes the vertex connectivity. In contrast, in a general graph the size of the mincut can be equal to kappa(G). This result is tight.

Size dependence and dispersion behavior of the first hyperpolarizability of copper nanoparticles

We have probed the size dependency of the first hyperpolarizability (b) of copper nanoparticles by hyper-Rayleigh scattering (HRS). Our results indicate that second harmonic generation (SHG) originates predominantly at the surface of the nanoparticles as long as the size (d) remains small compared to the wavelength (k). However, volume contribution to the SH response due to the retardation effect becomes important when particle size grows beyond the `small particle limit'. There is a significant dispersion in the b values of copper nanoparticles owing tothe presence of the strong surface plasmon resonance (SPR) band.

Doping Dependence of Semiconductor-Metal Transition in InP at High Pressures

The resistivity of selenium-doped n-InP single crystal layers grown by liquid-phase epitaxy with electron concentrations varying from 6.7 x 10$^18$ to 1.8 x 10$^20$ cm$^{-3}$ has been measured as a function of hydrostatic pressure up to 10 GPa. Semiconductor-metal transitions were observed in each case with a change in resistivity by two to three orders of magnitude. The transition pressure p$_c$ decreased monotonically from 7.24 to 5.90 GPa with increasing doping concentration n according to the relation $p_c = p_o [1 - k(n/n_m)^a]$, where n$_m$ is the concentration (per cubic centimetre) of phosphorus donor sites in InP atoms, p$_o$ is the transition pressure at low doping concentrations, k is a constant and $\alpha$ is an exponent found experimentally to be 0.637. The decrease in p$_c$ is considered to be due to increasing internal stress developed at high concentrations of ionized donors. The high-pressure metallic phase had a resistivity (2.02-6.47) x 10$^{-7}$ $\Omega$ cm, with a positive temperature coefficient dependent on doping.

Fractional power dependence of rate on activation energy for reactions with very low internal barriers

The dynamics of reactions with low internal barriers are studied both analytically and numerically for two different models. Exact expressions for the average rate,kI, are obtained by solving the associated first passage time problems. Both the average rate constant, kI, and the numerically calculated long-time rate constant, kL, show a fractional power law dependence on the barrier height for very low barriers. The crossover of the reaction dynamics from low to high barrier is investigated.

Temperature dependence of the surface conductivity of YBa2Cu3O7−δ accompanying the change in the concentration of dimerized oxygen holes

The intensity of inelastically scattered electrons measured by electron energy loss spectroscopy has been employed to monitor the surface conductivity of YBa2Cu3O6.9 as a function of temperature. The study shows a drastic change in surface conductivity precedes the superconducting transition at 90K. The increase in surface conductivity is accompanied by the formation of dimerized holes in the oxygen derived p-band. This phenomenon is not observed in the non-superconducting YBa2Cu3O6.2.

A necessary and sufficient condition for acyclic graphs

This letter gives a new necessary and sufficient condition to determine whether a directed graph is acyclic.

Effects of Isothermal and Adiabatic Thermal Loadings on Size and Strain Rate Dependence of Copper Nanowire

In the present paper, the size and strain rate effects on ultra-thin < 100 >/{100} Cu nanowires at an initial temperature of 10 K have been discussed. Extensive molecular dynamics (MD) simulations have been performed using Embedded atom method (EAM) to investigate the structural behaviours and properties under high strain rate. Velocity-Verlet algorithm has been used to solve the equation of motions. Two different thermal loading cases have been considered: (i) Isothermal loading, in which Nose-Hoover thermostat is used to maintain the constant system temperature, and (ii) Adiabatic loading, i.e., without any thermostat. Five different wire cross-sections were considered ranging from 0.723 x 0.723 nm(2) to 2.169 x 2.169 nm(2) The strain rates used in the present study were 1 x 10(9) s(-1), 1 x 10(8) s(-1), and 1 x 10(7) s(-1). The effect of strain rate on the mechanical properties of copper nanowires was analysed, which shows that elastic properties are independent of thermal loading for a given strain rate and cross-sectional dimension of nanowire. It showed a decreasing yield stress and yield strain with decreasing strain rate for a given cross- section. Also, a decreasing yield stress and increasing yield strain were observed for a given strain rate with increasing cross-sectional area. Elastic modulus was found to be similar to 100 GPa, which was independent of processing temperature, strain rate, and size for a given initial temperature. Reorientation of < 100 >/{100} square cross-sectional copper nanowire into a series of stable ultra-thin Pentagon copper nanobridge structures with dia of similar to 1 nm at 10 K was observed under high strain rate tensile loading. The effect of isothermal and adiabatic loading on the formation of such pentagonal nanobridge structure has been discussed.

Improvement On Brooks Chromatic Bound For A Class Of Graphs

Brooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 and G has an odd cycle as a component, or (2) n>2 and Kn+1 is a component of G. In this paper we prove that if a graph G has none of some three graphs (K1,3;K5−e and H) as an induced subgraph and if Δ(G)greater-or-equal, slanted6 and d(G)<Δ(G), then χ(G)<Δ(G). Also we give examples to show that the hypothesis Δ(G)greater-or-equal, slanted6 can not be non-trivially relaxed and the graph K5−e can not be removed from the hypothesis. Moreover, for a graph G with none of K1,3;K5−e and H as an induced subgraph, we verify Borodin and Kostochka's conjecture that if for a graph G,Δ(G)greater-or-equal, slanted9 and d(G)<Δ(G), then χ(G)<Δ(G).

Nicotine Dependence and Smoking Behaviour : A genetic and epidemiological study

The worldwide health burden caused by the tobacco epidemic highlights the importance of study-ing determinants of smoking behaviour and key factors sustaining nicotine dependence. Despite vast-ranging preventive efforts, smoking remains one of the most deleterious health behaviours, and its genetic and environmental factors warrant continuous investigation. The heritability of smoking behaviour and nicotine dependence has been suggested to be relatively high. Earlier smoking behaviour, nicotine dependence, socio-economic position and demographic factors have all been shown to be associated with smoking cessation. This thesis aimed to examine various aspects of smoking behaviour and nicotine dependence from an epidemiological and genetic per-spective. Data for Studies I and IV were obtained from the Older Finnish Twin Cohort, a postal health sur-vey conducted in 1975, 1981 and 1990 on same-sexed pairs and in 1996-1997 on male-female adult pairs. The number of ever-smoking participants was 8941 in Study I and 3069 in Study IV. Data for Studies II and III came from the Family Study of Cigarette Smoking - Vulnerability to Nicotine Addiction. This study is linked to the Older Finnish Twin Cohort with new data collec-tion during 2001-2006 that focused on smoking twin pairs and their family members. The meas-ures included intensive telephone interviews, blood samples and additional postal questionnaires. The numbers of ever-smoking participants was 1370 in Study II and 529 in Study III. Study I examined whether a genetic component underlies smoking behaviour among Finnish adults. Genetic factors were important in the amount smoked and smoking cessation, with about half of the phenotypic differences explained by genetic variance. A novel finding was that genetic influences on amount smoked and smoking cessation were largely independent of genetic influ-ences on age at initiation. This result has implications for defining phenotypes in the search for genes underlying smoking behaviour. Furthermore, even if smoking initiation is postponed to a later age, potential vulnerability to subsequent nicotine dependence cannot be completely inhib-ited. Study II investigated the effect of genetic and environmental factors on nicotine dependence, as measured by the novel multidimensional Nicotine Dependence Syndrome Scale (NDSS). This scale was validated in the Finnish data. The NDSS correlated highly with other established nico-tine dependence scales (FTND and DSM-IV), suggesting that this new scale would be a feasible and valid measure for identifying nicotine-dependent smokers among the ever-smoking popula-tion. About one-third of the phenotypic variation in nicotine dependence in this sample was ex-plained by genetic influences. Study III aimed at identifying chromosomal regions harbouring genes that influence smoking be-haviour and nicotine dependence. Linkage analysis of family data revealed that for smoker and nicotine dependence phenotypes as well as for co-morbidity between nicotine dependence and alcohol use signals on specific chromosome regions (chromosomes 2q33, 5q12, 5q34 7q21, 7q31, 10q25, 11p15, 20p13) exist. Results further support the hypothesis that smoking behaviour phe-notypes have a genetic background. Study IV examined associations of smoking behaviour, socio-economic position and transition of marital status with smoking cessation. Indicators of socio-economic position were important pre-dictors of smoking cessation even when adjusted for previous smoking behaviour. Getting married was associated with an increased probability of cessation in men, a finding confirmed among dis-cordant twin pairs. Thus, having a partner appears to have a positive impact on smoking cessation. In conclusion, nicotine dependence and smoking behaviour demonstrate significant genetic liabil-ity, but also substantial environmental influences among Finnish adults. Smoking initiation should be prevented or at least postponed to a later age. Although genetic factors are important in nicotine dependence and smoking behaviour, societal actions still have a primary role in tobacco control and smoking prevalence. Future studies should examine the complex interactions between genetic and environmental factors in nicotine dependence.

Implications of co-twin dependence for twins' social interactions, mental health and alcohol use : A follow-up study of Finnish twins from adolescence to early adulthood

Objective: The aim of the present study was to examine co-twin dependence and its impact on twins' social contacts, leisure-time activities and psycho-emotional well-being. The role of co-twin dependence was also examined as a moderator of genetic and environmental influences on alcohol use in adolescence and in early adulthood. Methods: The present report is based on the Finnish Twin Cohort Study (FinnTwin16), a population-based study of five consecutive birth cohorts of Finnish twins born in the years 1975-1979. Baseline assessments were collected through mailed questionnaires, within two months of the twins' sixteenth birthday yielding replies from 5563 twin individuals. All respondent twins were sent follow-up questionnaires at ages of 17, 18½, and in early adulthood, when twins were 22-27 years old. Measures: The questionnaires included a survey of health habits and attitudes, a symptom checklist and questions about twins' relationships with parents, peers and co-twin. Measures used were twins' self-reports of their own dependence and their co-twin's dependence at age 16, reports of twins' leisure-time activities and social contacts, alcohol use, psychological distress and somatic symptoms both in adolescence and in early adulthood. Results: In the present study 25.6% of twins reported dependence on their co-twin. There were gender and zygosity differences in dependence, females and MZ twins were more likely to report dependence than males and DZ twins. Co-twin dependence can be viewed on one hand as an individual characteristic, but on the other hand as a pattern of dyadic interaction that is mutually regulated and reciprocal. Most of the twins (80.7%) were either concordantly co-twin dependent or concordantly co-twin independent. The associations of co-twin dependence with twins' social interactions and psycho-emotional characteristics were relatively consistent both in adolescence and in early adulthood. Dependence was related to higher contact frequency and a higher proportion of shared leisure-time activities between twin siblings at the baseline and the follow-up. Additionally co-twin dependence was associated with elevated levels of psycho-emotional distress and somatic complaints, especially in adolescence. In the framework of gene-environment interaction, these results suggest that the genetic contribution to individual differences in drinking patterns is dependent on the nature of the pair-wise relationship of twin siblings. Conclusions: The results of this study indicate that co-twin dependence is a genuine feature of the co-twin relationship and shows the importance of studying the impact of various features of co-twin relationships on individual twins' social and psycho-emotional life and well-being. Our study also offers evidence that differences in inter-personal relationships contribute to the effects of genetic propensities.

Sequence dependence and role of 5'-phosphate in the B to Z transition

Spectroscopic studies on pd(CG)3 and pd(GC)3 have been carried out to elucidate the sequence dependence and effect of free 5'-phosphate on the B to Z transition. Unlike d(CG)3, pd(CG)3 fails to undergo salt-induced B to Z transition at ambient temperature. Model building studies have been carried out to determine the inhibitory role of the 5'-phosphate group, but have been unsuccessful.

Approximation algorithm for maximum independent set in planar traingle-free graphs

The maximum independent set problem is NP-complete even when restricted to planar graphs, cubic planar graphs or triangle free graphs. The problem of finding an absolute approximation still remains NP-complete. Various polynomial time approximation algorithms, that guarantee a fixed worst case ratio between the independent set size obtained to the maximum independent set size, in planar graphs have been proposed. We present in this paper a simple and efficient, O(|V|) algorithm that guarantees a ratio 1/2, for planar triangle free graphs. The algorithm differs completely from other approaches, in that, it collects groups of independent vertices at a time. Certain bounds we obtain in this paper relate to some interesting questions in the theory of extremal graphs.

Study on the pH dependence of diffraction efficiency of phase holograms in dye sensitized dichromated gelatin

Dichromated gelatin is thought to be a good substitute for photographic emulsions in some uses. The results of a systematic study of the effect of the pH of the developer on the diffraction efficiency of volume holographic gratings recorded in dye sensitized dichromated gelatin are presented.

Pressure dependence of 35Cl nuclear quadrupole resonance in 2,5-, 2,6- and 3,5-dichlorophenols

Pressure dependence of the 35Cl Nuclear Quadrupole Resonances (N.Q.R.) in 2,5-, 2,6- and 3,5-dichlorophenols (DCP) has been studied up to a pressure of about 6·5 kbar at room temperature. While the pressure dependence of the two resonance lines in 2,6-DCP is essentially similar, the lower frequency line in 2,5-DCP is almost pressure independent and the higher frequency line shows a linear variation with pressure upto about 3·5 kbar but shows a negative pressure coefficient beyond this pressure. The two lines in 3,5-DCP have a non-linear pressure dependence with the curvature changing smoothly with pressure. The pressure coefficient for both lines becomes negative beyond a pressure of 5 kbar. The pressure dependence of the N.Q.R. frequencies is discussed in relation to intra- and inter-molecular contacts. Also, a thermodynamic analysis of the data is carried out to determine the constant volume temperature derivative of the N.Q.R. frequency.

Algorithms for Constructing Hierarchical Graphs

An algorithm is described for developing a hierarchy among a set of elements having certain precedence relations. This algorithm, which is based on tracing a path through the graph, is easily implemented by a computer.