Say that a graph $G$ is emph{representable in $R ^n$} if there is a map $f$ from its vertex set into the Euclidean space $R ^n$ such that $| f(x) - f(x)| = | f(y) - f(y)|$ iff ${x,x}$ and ${y, y}$ are both edges or both non-edges in $G$. The purpose
of this note is to present the proof of the following result, due to Einhorn and Schoenberg: if $G$ finite is neither complete nor independent, then it is representable in $R ^{|G|-2}$. A similar result also holds in the case of finite complete edge-colored graphs.
When developing mobile apps, programmers rely heavily on standard API frameworks and libraries. However, learning and using those APIs is often challenging due to the fast-changing nature of API frameworks for mobile systems, the complexity of API us
ages, the insufficiency of documentation, and the unavailability of source code examples. In this paper, we propose a novel approach to learn API usages from bytecode of Android mobile apps. Our core contributions include: i) ARUS, a graph-based representation of API usage scenarios; ii) HAPI, a statistical, generative model of API usages; and iii) three algorithms to extract ARUS from apps bytecode, to train HAPI based on method call sequences extracted from ARUS, and to recommend method calls in code completion engines using the trained HAPI. Our empirical evaluation suggests that our approach can learn useful API usage models which can provide recommendations with higher levels of accuracy than the baseline n-gram model.
The Wiener-Hopf and Cagniard-de Hoop techniques are employed in order to solve a range of transient thermal mixed boundary value problems on the half-space. The thermal field is determined via a rapidly convergent integral, which can be evaluated straightforwardly and quickly on a desktop PC.
Graphene has attracted significant interest both for exploring fundamental science and for a wide range of technological applications. Chemical vapor deposition (CVD) is currently the only working approach to grow graphene at wafer scale, which is re
quired for industrial applications. Unfortunately, CVD graphene is intrinsically polycrystalline, with pristine graphene grains stitched together by disordered grain boundaries, which can be either a blessing or a curse. On the one hand, grain boundaries are expected to degrade the electrical and mechanical properties of polycrystalline graphene, rendering the material undesirable for many applications. On the other hand, they exhibit an increased chemical reactivity, suggesting their potential application to sensing or as templates for synthesis of one-dimensional materials. Therefore, it is important to gain a deeper understanding of the structure and properties of graphene grain boundaries. Here, we review experimental progress on identification and electrical and chemical characterization of graphene grain boundaries. We use numerical simulations and transport measurements to demonstrate that electrical properties and chemical modification of graphene grain boundaries are strongly correlated. This not only provides guidelines for the improvement of graphene devices, but also opens a new research area of engineering graphene grain boundaries for highly sensitive electrobiochemical devices.
In this article, we consider the limited data problem for spherical mean transform. We characterize the generation and strength of the artifacts in a reconstruction formula. In contrast to the thirds author work [Ngu15b], the observation surface cons
idered in this article is not flat. Our results are comparable to those obtained in [Ngu15b] for flat observation surface. For the two dimensional problem, we show that the artifacts are $k$ orders smoother than the original singularities, where $k$ is vanishing order of the smoothing function. Moreover, if the original singularity is conormal, then the artifacts are $k+frac{1}{2}$ order smoother than the original singularity. We provide some numerical examples and discuss how the smoothing effects the artifacts visually. For three dimensional case, although the result is similar to that [Ngu15b], the proof is significantly different. We introduce a new idea of lifting the space.
We present a novel spectroscopic method for probing the insitu~density of quantum gases. We exploit the density-dependent energy shift of highly excited {Rydberg} states, which is of the order $10$MHz,/,1E14,cm$^{text{-3}}$ for rubidium~for triplet s
-wave scattering. The energy shift combined with a density gradient can be used to localize Rydberg atoms in density shells with a spatial resolution less than optical wavelengths, as demonstrated by scanning the excitation laser spatially across the density distribution. We use this Rydberg spectroscopy to measure the mean density addressed by the Rydberg excitation lasers, and to monitor the phase transition from a thermal gas to a Bose-Einstein condensate (BEC).
The study of turbulent flows calls for measurements with high resolution both in space and in time. We propose a new approach to reconstruct High-Temporal-High-Spatial resolution velocity fields by combining two sources of information that are well-r
esolved either in space or in time, the Low-Temporal-High-Spatial (LTHS) and the High-Temporal-Low-Spatial (HTLS) resolution measurements. In the framework of co-conception between sensing and data post-processing, this work extensively investigates a Bayesian reconstruction approach using a simulated database. A Bayesian fusion model is developed to solve the inverse problem of data reconstruction. The model uses a Maximum A Posteriori estimate, which yields the most probable field knowing the measurements. The DNS of a wall-bounded turbulent flow at moderate Reynolds number is used to validate and assess the performances of the present approach. Low resolution measurements are subsampled in time and space from the fully resolved data. Reconstructed velocities are compared to the reference DNS to estimate the reconstruction errors. The model is compared to other conventional methods such as Linear Stochastic Estimation and cubic spline interpolation. Results show the superior accuracy of the proposed method in all configurations. Further investigations of model performances on various range of scales demonstrate its robustness. Numerical experiments also permit to estimate the expected maximum information level corresponding to limitations of experimental instruments.
User reviews of mobile apps often contain complaints or suggestions which are valuable for app developers to improve user experience and satisfaction. However, due to the large volume and noisy-nature of those reviews, manually analyzing them for use
ful opinions is inherently challenging. To address this problem, we propose MARK, a keyword-based framework for semi-automated review analysis. MARK allows an analyst describing his interests in one or some mobile apps by a set of keywords. It then finds and lists the reviews most relevant to those keywords for further analysis. It can also draw the trends over time of those keywords and detect their sudden changes, which might indicate the occurrences of serious issues. To help analysts describe their interests more effectively, MARK can automatically extract keywords from raw reviews and rank them by their associations with negative reviews. In addition, based on a vector-based semantic representation of keywords, MARK can divide a large set of keywords into more cohesive subsets, or suggest keywords similar to the selected ones.
For finite-dimensional Hopf algebras, their classification in characteristic $0$ (e.g. over $mathbb{C}$) has been investigated for decades with many fruitful results, but their structures in positive characteristic have remained elusive. In this pape
r, working over an algebraically closed field $mathbf{k}$ of prime characteristic $p$, we introduce the concept, called Primitive Deformation, to provide a structured technique to classify certain finite-dimensional connected Hopf algebras which are almost primitively generated; that is, these connected Hopf algebras are $p^{n+1}$-dimensional, whose primitive spaces are abelian restricted Lie algebras of dimension $n$. We illustrate this technique for the case $n=2$. Together with our preceding results in arXiv:1309.0286, we provide a complete classification of $p^3$-dimensional connected Hopf algebras over $mathbf{k}$ of characteristic $p>2$.
We show that the squared maximal height of the top path among $N$ non-intersecting Brownian bridges starting and ending at the origin is distributed as the top eigenvalue of a random matrix drawn from the Laguerre Orthogonal Ensemble. This result can
be thought of as a discrete version of K. Johanssons result that the supremum of the Airy$_2$ process minus a parabola has the Tracy-Widom GOE distribution, and as such it provides an explanation for how this distribution arises in models belonging to the KPZ universality class with flat initial data. The result can be recast in terms of the probability that the top curve of the stationary Dyson Brownian motion hits an hyperbolic cosine barrier.
