Heterochromatic paths in edge colored graphs without small cycles and heterochromatic-triangle-free graphs

Conditions for the existence of heterochromatic Hamiltonian paths and cycles in edge colored graphs are well investigated in literature. A related problem in this domain is to obtain good lower bounds for the length of a maximum heterochromatic path in an edge colored graph G. This problem is also well explored by now and the lower bounds are often specified as functions of the minimum color degree of G - the minimum number of distinct colors occurring at edges incident to any vertex of G - denoted by v(G). Initially, it was conjectured that the lower bound for the length of a maximum heterochromatic path for an edge colored graph G would be 2v(G)/3]. Chen and Li (2005) showed that the length of a maximum heterochromatic path in an edge colored graph G is at least v(G) - 1, if 1 <= v(G) <= 7, and at least 3v(G)/5] + 1 if v(G) >= 8. They conjectured that the tight lower bound would be v(G) - 1 and demonstrated some examples which achieve this bound. An unpublished manuscript from the same authors (Chen, Li) reported to show that if v(G) >= 8, then G contains a heterochromatic path of length at least 120 + 1. In this paper, we give lower bounds for the length of a maximum heterochromatic path in edge colored graphs without small cycles. We show that if G has no four cycles, then it contains a heterochromatic path of length at least v(G) - o(v(G)) and if the girth of G is at least 4 log(2)(v(G)) + 2, then it contains a heterochromatic path of length at least v(G) - 2, which is only one less than the bound conjectured by Chen and Li (2005). Other special cases considered include lower bounds for the length of a maximum heterochromatic path in edge colored bipartite graphs and triangle-free graphs: for triangle-free graphs we obtain a lower bound of 5v(G)/6] and for bipartite graphs we obtain a lower bound of 6v(G)-3/7]. In this paper, it is also shown that if the coloring is such that G has no heterochromatic triangles, then G contains a heterochromatic path of length at least 13v(G)/17)]. This improves the previously known 3v(G)/4] bound obtained by Chen and Li (2011). We also give a relatively shorter and simpler proof showing that any edge colored graph G contains a heterochromatic path of length at least (C) 2015 Elsevier Ltd. All rights reserved.

A common stochastic accumulator with effector-dependent noise can explain eye-hand coordination

The computational architecture that enables the flexible coupling between otherwise independent eye and hand effector systems is not understood. By using a drift diffusion framework, in which variability of the reaction time (RT) distribution scales with mean RT, we tested the ability of a common stochastic accumulator to explain eye-hand coordination. Using a combination of behavior, computational modeling and electromyography, we show how a single stochastic accumulator to threshold, followed by noisy effector-dependent delays, explains eye-hand RT distributions and their correlation, while an alternate independent, interactive eye and hand accumulator model does not. Interestingly, the common accumulator model did not explain the RT distributions of the same subjects when they made eye and hand movements in isolation. Taken together, these data suggest that a dedicated circuit underlies coordinated eye-hand planning.

Correlation Between Decay Rate and Amplitude of Solar Cycles as Revealed from Observations and Dynamo Theory

Using different proxies of solar activity, we have studied the following features of the solar cycle: i) The linear correlation between the amplitude of cycle and its decay rate, ii) the linear correlation between the amplitude of cycle and the decay rate of cycle , and iii) the anti-correlation between the amplitude of cycle and the period of cycle . Features ii) and iii) are very useful because they provide precursors for future cycles. We have reproduced these features using a flux-transport dynamo model with stochastic fluctuations in the Babcock-Leighton effect and in the meridional circulation. Only when we introduce fluctuations in meridional circulation, are we able to reproduce different observed features of the solar cycle. We discuss the possible reasons for these correlations.

Eye-hand coordination during a double-step task: evidence for a common stochastic accumulator

Many studies of reaching and pointing have shown significant spatial and temporal correlations between eye and hand movements. Nevertheless, it remains unclear whether these correlations are incidental, arising from common inputs (independent model); whether these correlations represent an interaction between otherwise independent eye and hand systems (interactive model); or whether these correlations arise from a single dedicated eye-hand system (common command model). Subjects were instructed to redirect gaze and pointing movements in a double-step task in an attempt to decouple eye-hand movements and causally distinguish between the three architectures. We used a drift-diffusion framework in the context of a race model, which has been previously used to explain redirect behavior for eye and hand movements separately, to predict the pattern of eye-hand decoupling. We found that the common command architecture could best explain the observed frequency of different eye and hand response patterns to the target step. A common stochastic accumulator for eye-hand coordination also predicts comparable variances, despite significant difference in the means of the eye and hand reaction time (RT) distributions, which we tested. Consistent with this prediction, we observed that the variances of the eye and hand RTs were similar, despite much larger hand RTs (similar to 90 ms). Moreover, changes in mean eye RTs, which also increased eye RT variance, produced a similar increase in mean and variance of the associated hand RT. Taken together, these data suggest that a dedicated circuit underlies coordinated eye-hand planning.

ELEVATION OF HEAT REJECTION TEMPERATURE IN TRANSCRITICAL CONDENSING CYCLES USING CO2+PROPANE MIXTURES

In this paper, a detailed thermodynamic performance analysis of a transcritical condensing (TC) cycle is performed with pure CO2 and a blend of 48.5 % propane with 51.5 % CO2 as working fluids. A realistic thermodynamic model is used incorporating irreversibilities in turbo-machineries and heat exchangers. The Key finding is that the addition of propane elevates the heat rejection temperature, but does not impair any of the performance indicators. Such a fluid may be useful for power generation in concentrated solar power applications by using which a hike of up to 2 % can be realized in the thermal efficiency of a power plant.

Common effect of chemical and external pressures on the magnetic properties of RCoPO (R = La, Pr, Nd, Sm). II.

We investigate the direct correspondence between Co band ferromagnetism and structural parameters in the pnictide oxides RCoPO for different rare-earth ions (R = La, Pr, Nd, Sm) by means of muon-spin spectroscopy and ab initio calculations, complementing our results published previously G. Prando et al., Common effect of chemical and external pressures on the magnetic properties of RCoPO (R = La, Pr), Phys. Rev. B 87, 064401 (2013)]. We find that both the transition temperature to the ferromagnetic phase T-C and the volume of the crystallographic unit cell V are conveniently tuned by the R ionic radius and/or external pressure. We report a linear correlation between T-C and V and our ab initio calculations unambiguously demonstrate a full equivalence of chemical and external pressures. As such, we show that R ions influence the ferromagnetic phase only via the induced structural shrinkage without involving any active role from the electronic f degrees of freedom, which are only giving a sizable magnetic contribution at much lower temperatures.

COOL CORE CYCLES: COLD GAS AND AGN JET FEEDBACK IN CLUSTER CORES

Using high-resolution 3D and 2D (axisymmetric) hydrodynamic simulations in spherical geometry, we study the evolution of cool cluster cores heated by feedback-driven bipolar active galactic nuclei (AGNs) jets. Condensation of cold gas, and the consequent enhanced accretion, is required for AGN feedback to balance radiative cooling with reasonable efficiencies, and to match the observed cool core properties. A feedback efficiency (mechanical luminosity approximate to epsilon(M) over dot(acc)c(2); where (M) over dot(acc). is the mass accretion rate at 1 kpc) as small as 6 x 10(-5) is sufficient to reduce the cooling/accretion rate by similar to 10 compared to a pure cooling flow in clusters (with M-200 less than or similar to 7 x 10(14) M-circle dot). This value is much smaller compared to the ones considered earlier, and is consistent with the jet efficiency and the fact that only a small fraction of gas at 1 kpc is accreted onto the supermassive black hole (SMBH). The feedback efficiency in earlier works was so high that the cluster core reached equilibrium in a hot state without much precipitation, unlike what is observed in cool-core clusters. We find hysteresis cycles in all our simulations with cold mode feedback: condensation of cold gas when the ratio of the cooling-time to the free-fall time (t(cool)/t(ff)) is less than or similar to 10 leads to a sudden enhancement in the accretion rate; a large accretion rate causes strong jets and overheating of the hot intracluster medium such that t(cool)/t(ff) > 10; further condensation of cold gas is suppressed and the accretion rate falls, leading to slow cooling of the core and condensation of cold gas, restarting the cycle. Therefore, there is a spread in core properties, such as the jet power, accretion rate, for the same value of core entropy t(cool)/t(ff). A smaller number of cycles is observed for higher efficiencies and for lower mass halos because the core is overheated to a longer cooling time. The 3D simulations show the formation of a few-kpc scale, rotationally supported, massive (similar to 10(11) M-circle dot) cold gas torus. Since the torus gas is not accreted onto the SMBH, it is largely decoupled from the feedback cycle. The radially dominant cold gas (T < 5 x 10(4) K; vertical bar v(r)vertical bar >vertical bar v(phi vertical bar)) consists of fast cold gas uplifted by AGN jets and freely infalling cold gas condensing out of the core. The radially dominant cold gas extends out to 25 kpc for the fiducial run (halo mass 7 x 10(14) M-circle dot and feedback efficiency 6 x 10(-5)), with the average mass inflow rate dominating the outflow rate by a factor of approximate to 2. We compare our simulation results with recent observations.

Reduced common-mode voltage operation of a new seven-level hybrid multilevel inverter topology with a single DC voltage source

In this study, analysis of extending the linear modulation range of a zero common-mode voltage (CMV) operated n-level inverter by allowing reduced CMV switching is presented. A new hybrid seven-level inverter topology with a single DC supply is also presented in this study and inverter operation for zero and reduced CMV is analysed. Each phase of the inverter is realised by cascading two three-level flying capacitor inverters with a half-bridge module in between. Proposed inverter topology is operated with zero CMV for modulation index <86% and is operated with a CMV magnitude of V-dc/18 to extend the modulation range up to 96%. Experimental results are presented for zero CMV operation and for reduced common voltage operation to extend the linear modulation range. A capacitor voltage balancing algorithm is designed utilising the pole voltage redundancies of the inverter, which works for every sampling instant to correct the capacitor voltage irrespective of load power factor and modulation index. The capacitor voltage balancing algorithm is tested for different modulation indices and for various transient conditions, to validate the proposed topology.