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Circular-shift linear network coding (LNC) is a class of vector LNC with low encoding and decoding complexities, and with local encoding kernels chosen from cyclic permutation matrices. When $L$ is a prime with primitive root $2$, it was recently shown that a scalar linear solution over GF($2^{L-1}$) induces an $L$-dimensional circular-shift linear solution at rate $(L-1)/L$. In this work, we prove that for arbitrary odd $L$, every scalar linear solution over GF($2^{m_L}$), where $m_L$ refers to the multiplicative order of $2$ modulo $L$, can induce an $L$-dimensional circular-shift linear solution at a certain rate. Based on the generalized connection, we further prove that for such $L$ with $m_L$ beyond a threshold, every multicast network has an $L$-dimensional circular-shift linear solution at rate $\phi(L)/L$, where $\phi(L)$ is the Euler's totient function of $L$. An efficient algorithm for constructing such a solution is designed. Finally, we prove that every multicast network is asymptotically circular-shift linearly solvable.

We present a robust and precise localization system that achieves centimeter-level localization accuracy in disparate city scenes. Our system adaptively uses information from complementary sensors such as GNSS, LiDAR, and IMU to achieve high localization accuracy and resilience in challenging scenes, such as urban downtown, highways, and tunnels. Rather than relying only on LiDAR intensity or 3D geometry, we make innovative use of LiDAR intensity and altitude cues to significantly improve localization system accuracy and robustness. Our GNSS RTK module utilizes the help of the multi-sensor fusion framework and achieves a better ambiguity resolution success rate. An error-state Kalman filter is applied to fuse the localization measurements from different sources with novel uncertainty estimation. We validate, in detail, the effectiveness of our approaches, achieving 5-10cm RMS accuracy and outperforming previous state-of-the-art systems. Importantly, our system, while deployed in a large autonomous driving fleet, made our vehicles fully autonomous in crowded city streets despite road construction that occurred from time to time. A dataset including more than 60 km real traffic driving in various urban roads is used to comprehensively test our system., Comment: 8 pages, 6 figures, 2 tables, Accepted by ICRA 2018

It has been an active research issue for many years to construct new bent functions. For $k$ odd with $\gcd(n, k)=1$, and $a\in\mathbb{F}_{3^n}^{*}$, the function $f(x)=Tr(ax^{\frac{3^k+1}{2}})$ is weakly regular bent over $\mathbb{F}_{3^n}$, where $Tr(\cdot):\mathbb{F}_{3^n}\rightarrow\mathbb{F}_3$ is the trace function. This is the well-known Coulter-Matthews bent function. In this paper, we determine the dual function of $f(x)$ completely. As a consequence, we find many classes of ternary bent functions not reported in the literature previously. Such bent functions are not quadratic if $k>1$, and have $\left(\left(\frac{1+\sqrt{5}}{2}\right)^{w+1}-\right.$ $\left.\left(\frac{1-\sqrt{5}}{2}\right)^{w+1}\right)/\sqrt{5}$ or $\left(\left(\frac{1+\sqrt{5}}{2}\right)^{n-w+1}-\right.$ $\left.\left(\frac{1-\sqrt{5}}{2}\right)^{n-w+1}\right)/\sqrt{5}$ trace terms, where $0

PKS 1155+251 is a radio-loud quasar source at z=0.203. Observations using very long baseline interferometry (VLBI) at ~2, 5, 8 and 15 GHz show that the structure of the radio source is quite complicated on parsec scales and that the outer hot spots are apparently undergoing a significant contraction. Because these results cannot be fully explained based on the compact symmetric object (CSO) scenario with a radio core located between the northern and southern complexes, we made observations with the Very Long Baseline Array (VLBA) at 24 and 43 GHz to search for compact substructures and alternative interpretations. The results show that the radio core revealed in the previous VLBI observations remains compact with a flat spectrum in our sub-milli-arcsecond--resolution images; the northern lobe emission becomes faint at 24 GHz and is mostly resolving out at 43 GHz; the southern complex is more bright but has been resolved into the brightest southern-end (S1) and jet or tail alike components westwards. Explaining the southern components aligned westward with a standard CSO scenario alone remains a challenge. As for the flatter spectral index of the southern-end component S1 between 24 and 43 GHz in our observations and the significant 15 GHz VLBA flux variability of S1, an alternative scenario is that the southern complex may be powered by a secondary black hole residing at S1. But more sensitive and high-resolution VLBI monitoring is required to discriminate the CSO and the binary black hole scenarios., Comment: 7 pages, 3 figures, accepted by MNRAS

We study a class of linear network coding (LNC) schemes, called circular-shift LNC, whose encoding operations consist of only circular-shifts and bit-wise additions (XOR). Formulated as a special vector linear code over GF($2$), an $L$-dimensional circular-shift linear code of degree $\delta$ restricts its local encoding kernels to be the summation of at most $\delta$ cyclic permutation matrices of size $L$. We show that on a general network, for a certain block length $L$, every scalar linear solution over GF($2^{L-1}$) can induce an $L$-dimensional circular-shift linear solution with 1-bit redundancy per-edge transmission. Consequently, specific to a multicast network, such a circular-shift linear solution of an arbitrary degree $\delta$ can be efficiently constructed, which has an interesting complexity tradeoff between encoding and decoding with different choices of $\delta$. By further proving that circular-shift LNC is insufficient to achieve the exact capacity of certain multicast networks, we show the optimality of the efficiently constructed circular-shift linear solution in the sense that its 1-bit redundancy is inevitable. Finally, both theoretical and numerical analysis imply that with increasing $L$, a randomly constructed circular-shift linear code has linear solvability behavior comparable to a randomly constructed permutation-based linear code, but has shorter overheads.

This paper investigates the size effect on the coalescence process of contacting nanoparticles. It is revealed by molecular dynamics that the nanometer-sized surface curvature coupled with the effective melting temperature exhibits a strong influence on the atom diffusion at the interface, and is therefore critical to the coalescence time. This effect is particularly pronouncing for surface curvatures below 20 nm. A phenomenological model is derived from the melting-point reduction approach to describe the kinetic process of nanowire coalescence and is validated against a variety of simulation datasets. The quantitative correlation between the sample size, the sintering temperature and the contact morphology evolution is demonstrated., Comment: 4 figures

We study the effect of asperity size on the adhesion properties of metal contact using atomistic simulations. The simulated size effect of individual nanoscale asperityies is applied to macroscopic rough surfaces by introducing a curvature radius distribution to a continuum-mechanics-based contact model. Our results indicate that the contact adhesion can be optimized by changing the curvature radius distribution of the asperity summits., Comment: 8 figures

We study the effect of nanoscale precipitates on lattice thermal conduction in thermoelectric PbTe using a combination of ab-initio phonon calculations and molecular dynamics. We take into account the effects of mass difference and change in force constants, and find an enhanced influence of the latter with increased precipitate concentration. As a consequence, our inclusion of the change in force constants in the calculation affords a smaller predicted optimal nano-precipitate size that minimizes the thermal conductivity. These results suggest that the phonon scattering by nanoprecipitates in thermoelectric composites could be stronger than previously thought.

Understanding phonon scattering by topological defects in graphene is of particular interest for thermal management in graphene-based devices. We present a study that quantifies the roles of the different mechanisms governing defect phonon scattering by comparing the effects of ten different defect structures using molecular dynamics. Our results show that phonon scattering is mainly influenced by mass density difference, with general trends governed by the defect formation energy and typical softening behaviors in the phonon density of state. The phonon scattering cross-section is found to be far larger than that geometrically occupied by the defects. We also show that the lattice thermal conductivity can be reduced by a factor of up to ~30 in the presence of the grain boundaries formed by these defects.

We calculate the thermal conductivity of PbTe and PbS with seven different types of nanoprecipitates using an ab-initio-based Boltzmann transport approach. We find that precipitates with realistic size distributions can reduce the thermal conductivity well below the predictions of theoretical models assuming a single precipitate size.We explore the question of how to tune this distribution to reduce the thermal conductivity even further. The predicted minimum value is strongly correlated with the phonon spectrum of the host material and with the mass density difference between the host and the inclusions.

The structural stability of thermoelectric materials is a subject of growing importance for their energy harvesting applications. Here, we study the microscopic mechanisms governing the structural stability change of zinc antimony at its working temperature, using molecular dynamics combined with experimental measurements of the electrical and thermal conductivity. Our results show that the temperature-dependence of the thermal and electrical transport coefficients is strongly correlated with a structural transition. This is found to be associated with a relaxation process, in which a group of Zn atoms migrates between interstitial sites. This atom migration gradually leads to a stabilizing structural transition of the entire crystal framework, and then results in a more stable crystal structure of $\beta-$ Zn4Sb3 at high temperature.