On defining partition entropy by inequalities

Partition entropy is the numerical metric of uncertainty within a partition of a finite set, while conditional entropy measures the degree of difficulty in predicting a decision partition when a condition partition is provided. Since two direct methods exist for defining conditional entropy based on its partition entropy, the inequality postulates of monotonicity, which conditional entropy satisfies, are actually additional constraints on its entropy. Thus, in this paper partition entropy is defined as a function of probability distribution, satisfying all the inequalities of not only partition entropy itself but also its conditional counterpart. These inequality postulates formalize the intuitive understandings of uncertainty contained in partitions of finite sets.We study the relationships between these inequalities, and reduce the redundancies among them. According to two different definitions of conditional entropy from its partition entropy, the convenient and unified checking conditions for any partition entropy are presented, respectively. These properties generalize and illuminate the common nature of all partition entropies

Hamiltonicity of 3-arc graphs

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two arcs $uv, xy$ are adjacent if and only if $(v,u,x,y)$ is a 3-arc of $G$. In this paper we prove that any connected 3-arc graph is Hamiltonian, and all iterative 3-arc graphs of any connected graph of minimum degree at least three are Hamiltonian. As a consequence we obtain that if a vertex-transitive graph is isomorphic to the 3-arc graph of a connected arc-transitive graph of degree at least three, then it is Hamiltonian. This confirms the well known conjecture, that all vertex-transitive graphs with finitely many exceptions are Hamiltonian, for a large family of vertex-transitive graphs. We also prove that if a graph with at least four vertices is Hamilton-connected, then so are its iterative 3-arc graphs.Comment: in press Graphs and Combinatorics, 201

Probing Spin-Flip Scattering in Ballistic Nanosystems

Because spin-flip length is longer than the electron mean-free path in a metal, past studies of spin-flip scattering are limited to the diffusive regime. We propose to use a magnetic double barrier tunnel junction to study spin-flip scattering in the nanometer sized spacer layer near the ballistic limit. We extract the voltage and temperature dependence of the spin-flip conductance Gs in the spacer layer from magnetoresistance measurements. In addition to spin scattering information including the mean-free path (70 nm) and the spin-flip length (1:0–2:6 m) at 4.2 K, this technique also yields information on the density of states and quantum well resonance in the spacer laye

Obvious enhancement of the total reaction cross sections for 27,28^{27,28}P with 28^{28}Si target and the possible relavent mechanisms

The reaction cross sections of $^{27,28}$P and the corresponding isotones on Si target were measured at intermediate energies. The measured reaction cross sections of the N=12 and 13 isotones show an abrupt increase at $$. The experimental results for the isotones with $Z\leq 14$ as well as $$P can be well described by the modified Glauber theory of the optical limit approach. The enhancement of the reaction cross section for $^{28}$P could be explained in the modified Glauber theory with an enlarged core. Theoretical analysis with the modified Glauber theory of the optical limit and few-body approaches underpredicted the experimental data of $^{27}$P. Our theoretical analysis shows that an enlarged core together with proton halo are probably the mechanism responsible for the enhancement of the cross sections for the reaction of $^{27}$P+$^{28}$Si.Comment: 16 pages, 5 figures, to be published in Phys.Rev.

Synthesizing SystemC Code from Delay Hybrid CSP

Delay is omnipresent in modern control systems, which can prompt oscillations and may cause deterioration of control performance, invalidate both stability and safety properties. This implies that safety or stability certificates obtained on idealized, delay-free models of systems prone to delayed coupling may be erratic, and further the incorrectness of the executable code generated from these models. However, automated methods for system verification and code generation that ought to address models of system dynamics reflecting delays have not been paid enough attention yet in the computer science community. In our previous work, on one hand, we investigated the verification of delay dynamical and hybrid systems; on the other hand, we also addressed how to synthesize SystemC code from a verified hybrid system modelled by Hybrid CSP (HCSP) without delay. In this paper, we give a first attempt to synthesize SystemC code from a verified delay hybrid system modelled by Delay HCSP (dHCSP), which is an extension of HCSP by replacing ordinary differential equations (ODEs) with delay differential equations (DDEs). We implement a tool to support the automatic translation from dHCSP to SystemC

Self-driven electron enrichment of ultrafine PdAu nanoparticles for electrochemical CO₂ reduction:High applicability of work function as an activity descriptor

Highly coupled metal/dopant-incorporated carbon dyads provide a possibility to modulate the electron density of metallic materials by forming a rectifying interface, thus showing an enhanced activity in electrochemical CO2 reduction reaction (ECRR). However, understanding the promotion effects of dopants for ECRR is limited to the prediction by theoretical interpretation and case-by-case studies. Herein, we report the direct experimental evidence that the work function, regulated by single structural factor-dopant contents, is significantly correlated to the ECRR reaction activity and kinetics. We prepared a series of PdAu/NxC electrocatalysts composed of ultrafine (∼5.7 nm) PdAu bimetallic nanoparticles and tailorable N-doped carbon supports. The wide range of the amount of N dopants allowed the modification of the band gap of the carbon easily. Using ultraviolet photoelectron spectroscopy (UPS) measurements, we demonstrate that the reactivity and kinetics trends of the PdAu/NxC in the ECRR can be intrinsically correlated with the work function of the catalysts. PdAu/N7.50C electrocatalyst with the highest N contents displays a 100% CO2-to-CO conversion and high conversion efficiency over a wide potential window, superior over other reported PdAu catalysts. This work provides a novel way to boost ECRR performance by deliberately lowering the work function of the metal/carbon electrocatalysts through the enhancement by dopants.</p

The active fault belts in eastern Tibet margin inferred using magnetotellurics

A magnetotelluric (MT) sounding has been carried out in the eastern margin of the Tibetan plateau. The survey line is about 145 km long, trending in NEE direction and crossing the Daliangshan block in the eastern edge of the Tibetan plateau. The field measurements acquired effective data of 68 sites. Through data processing and a 2-D inversion with consideration of topography, a 2-D electrical structure model of crust and upper mantle was constructed. The structure reveals that there is a deep electrical boundary between the Daliangshan block in the west and Sichuan block in the east. West to the boundary, the crust has a relatively low resistivity with respect to the east and can be divided into three layers, the middle layer has low resistivity with a minimum of 3-10 W•m, presumably associated with partial melt and/or salty fluids. Beneath the intersection area of the Anninghe fault, the Xianshuihe fault and the Longmenshan fault, which the MT profile crosses, the faults are separated into upper and lower sections. The upper section exhibits a nearly vertical low-resistivity zone in the upper crust, and the lower section manifests an electrical boundary in the lower crust and upper mantle. Other faults in the Daliangshan block are either nearly vertical low-resistivity zones or electrical boundaries. It is suggested that the formation of the low-resistivity layer in the middle crust is associated with the southeastward motion of the eastern margin of the Tibetan plateau, clockwise rotation of the Chuandian (Sichuan-Yunnan) block, and the westward obstruction from the Sichuan block in Huanan terrain. Seismicity, including the M 8.0 Wenchuan earthquake in the study area, is discussed

Fitting a Functional-Structural growth model with plant architectural data

GreenLab is a recurrent discrete-time functional-structural model of plant growth and architecture. A method is presented estimating its parameters: the model is fitted to plant morphological and architectural data observed at one point of time. Since GreenLab output variables (number, size and fresh mass of organs) implicitly and nonlinearly depend on the model parameters, the fitting problem is solved by minimizing a generalized least-squares criterion and by implementing an iterative procedure. Fitting is satisfactorily performed on unbranched plants (cotton, maize, sunflower) using real data. The method is extended to more complex plants (i.e. with branches): a preliminary test on a virtual tree shows that the fitting algorithm also applies to such structured plants

A comprehensive study of the open cluster NGC 6866

We present CCD $UBVRI$ photometry of the field of the open cluster NGC 6866. Structural parameters of the cluster are determined utilizing the stellar density profile of the stars in the field. We calculate the probabilities of the stars being a physical member of the cluster using their astrometric data and perform further analyses using only the most probable members. The reddening and metallicity of the cluster were determined by independent methods. The LAMOST spectra and the ultraviolet excess of the F and G type main-sequence stars in the cluster indicate that the metallicity of the cluster is about the solar value. We estimated the reddening $E(B-V)=0.074 \pm 0.050$ mag using the $U-B$ vs $B-V$ two-colour diagram. The distance modula, the distance and the age of NGC 6866 were derived as $\mu = 10.60 \pm 0.10$ mag, $d=1189 \pm 75$ pc and $t = 813 \pm 50$ Myr, respectively, by fitting colour-magnitude diagrams of the cluster with the PARSEC isochrones. The Galactic orbit of NGC 6866 indicates that the cluster is orbiting in a slightly eccentric orbit with $e=0.12$. The mass function slope $x=1.35 \pm 0.08$ was derived by using the most probable members of the cluster.Comment: 14 pages, including 16 figures and 7 tables, accepted for publication in MNRAS. Table 4 in the manuscript will be published electronicall