Existence theorems for a crystal surface model involving the p-Laplace operator

The manufacturing of crystal films lies at the heart of modern nanotechnology. How to accurately predict the motion of a crystal surface is of fundamental importance. Many continuum models have been developed for this purpose, including a number of PDE models, which are often obtained as the continuum limit of a family of kinetic Monte Carlo models of crystal surface relaxation that includes both the solid-on-solid and discrete Gaussian models. In this paper we offer an analytical perspective into some of these models. To be specific, we study the existence of a weak solution to the boundary value problem for the equation - \Delta e^{-\mbox{div}\left(|\nabla u|^{p-2}\nabla u\right)}+au=f, where $p>1, a>0$ are given numbers and $f$ is a given function. This problem is derived from a crystal surface model proposed by J.L.~Marzuola and J.~Weare (2013 Physical Review, E 88, 032403). The mathematical challenge is due to the fact that the principal term in our equation is an exponential function of a p-Laplacian. Existence of a suitably-defined weak solution is established under the assumptions that $p\in(1,2], \ N\leq 4$, and $f\in W^{1,p}$. Our investigations reveal that the key to our existence assertion is how to control the set where -\mbox{div}\left(|\nabla u|^{p-2}\nabla u\right) is $\pm\infty$

FACTORS AFFECTING THE TRANSFER OF INTER-ORGANIZATIONAL SYSTEMS TO CHINA: A CASE STUDY OF HIGH-TECH ENTERPRISES

Due to the huge market potentiality, profuse production resource such as workforce and land, and low production costs in China, many international high-tech enterprises are moving their production line to China. Accompanying production offshoring is the transfer of Information Technology (IT) to ensure that the production processes remain efficient and effective at home and abroad. Many enterprises however encounter problems in transferring their IT to China, especially when the IT is an inter-organizational system (IOS), which is across organizational boundaries and involves the management of relationships among participants. In order to understand how to successfully transfer IOS to China, we aim to find out key relational factors of IOS performance in China through an observation of a binary relationship built upon an e-procurement system between a Taiwanese PC ODM (Original Design Manufacturer) and its Chinese suppliers. Based on the relational view of the firm, four relational factors are proposed and examined. The results show that IOS specific investments and effective IOS governance most strongly affects the result of IOS transfer to China, whereas complementary resource endowment has least influence

2,2′-[(1E)-3-Phenyl­prop-2-ene-1,1-di­yl]bis­(3-hy­droxy-5,5-dimethyl­cyclo­hex-2-en-1-one)

In the title mol­ecule, C25H30O4, the two cyclo­hexene rings adopt envelope conformations. The two hy­droxy groups are involved in the formation of intra­molecular O—H⋯O hydrogen bonds. In the crystal structure, weak inter­molecular C—H⋯O hydrogen bonds link mol­ecules related by translation along the axis a into chains

A novel method to identify cooperative functional modules: study of module coordination in the Saccharomyces cerevisiae cell cycle

<p>Abstract</p> <p>Background</p> <p>Identifying key components in biological processes and their associations is critical for deciphering cellular functions. Recently, numerous gene expression and molecular interaction experiments have been reported in <it>Saccharomyces cerevisiae</it>, and these have enabled systematic studies. Although a number of approaches have been used to predict gene functions and interactions, tools that analyze the essential coordination of functional components in cellular processes still need to be developed.</p> <p>Results</p> <p>In this work, we present a new approach to study the cooperation of functional modules (sets of functionally related genes) in a specific cellular process. A cooperative module pair is defined as two modules that significantly cooperate with certain functional genes in a cellular process. This method identifies cooperative module pairs that significantly influence a cellular process and the correlated genes and interactions that are essential to that process. Using the yeast cell cycle as an example, we identified 101 cooperative module associations among 82 modules, and importantly, we established a cell cycle-specific cooperative module network. Most of the identified module pairs cover cooperative pathways and components essential to the cell cycle. We found that 14, 36, 18, 15, and 20 cooperative module pairs significantly cooperate with genes regulated in early G1, late G1, S, G2, and M phase, respectively. Fifty-nine module pairs that correlate with Cdc28 and other essential regulators were also identified. These results are consistent with previous studies and demonstrate that our methodology is effective for studying cooperative mechanisms in the cell cycle.</p> <p>Conclusions</p> <p>In this work, we propose a new approach to identifying condition-related cooperative interactions, and importantly, we establish a cell cycle-specific cooperation module network. These results provide a global view of the cell cycle and the method can be used to discover the dynamic coordination properties of functional components in other cellular processes.</p

A Pair of Early- and Late-Forming Galaxy Cluster Samples: Implications for Detection of Halo Assembly Bias

The halo assembly bias, a phenomenon referring to dependencies of the large-scale bias of a dark matter halo other than its mass, is a fundamental property of our standard cosmological model. First discovered in 2005 via high-resolution numerical simulations, it has been proven very difficult to be detected observationally, with only a few convincing claims of detection thus far. The main obstacle lies in finding an accurate proxy of the halo formation time. In this study, by utilizing a constrained simulation that can faithfully reproduce the observed structures larger than $\sim 2\,$Mpc in the local universe, for a sample of about 630 massive clusters at $z\le 0.12$, we find their counterpart halos in the simulation and use the mass growth history of the matched halos to estimate the formation time of the observed clusters. This allows us to construct a pair of early- and late-forming clusters, with similar mass as measured via weak gravitational lensing, and large-scale bias differing at $\gtrsim 4\sigma$ level, clearly showing the signature of assembly bias.Comment: MNRAS letters, submitted; 5 pages and 3 figure

Seeing through the Brain: Image Reconstruction of Visual Perception from Human Brain Signals

Seeing is believing, however, the underlying mechanism of how human visual perceptions are intertwined with our cognitions is still a mystery. Thanks to the recent advances in both neuroscience and artificial intelligence, we have been able to record the visually evoked brain activities and mimic the visual perception ability through computational approaches. In this paper, we pay attention to visual stimuli reconstruction by reconstructing the observed images based on portably accessible brain signals, i.e., electroencephalography (EEG) data. Since EEG signals are dynamic in the time-series format and are notorious to be noisy, processing and extracting useful information requires more dedicated efforts; In this paper, we propose a comprehensive pipeline, named NeuroImagen, for reconstructing visual stimuli images from EEG signals. Specifically, we incorporate a novel multi-level perceptual information decoding to draw multi-grained outputs from the given EEG data. A latent diffusion model will then leverage the extracted information to reconstruct the high-resolution visual stimuli images. The experimental results have illustrated the effectiveness of image reconstruction and superior quantitative performance of our proposed method.Comment: A preprint version of an ongoing wor

Transmission of H7N9 influenza virus in mice by different infective routes.

BackgroundOn 19 February 2013, the first patient infected with a novel influenza A H7N9 virus from an avian source showed symptoms of sickness. More than 349 laboratory-confirmed cases and 109 deaths have been reported in mainland China since then. Laboratory-confirmed, human-to-human H7N9 virus transmission has not been documented between individuals having close contact; however, this transmission route could not be excluded for three families. To control the spread of the avian influenza H7N9 virus, we must better understand its pathogenesis, transmissibility, and transmission routes in mammals. Studies have shown that this particular virus is transmitted by aerosols among ferrets.MethodsTo study potential transmission routes in animals with direct or close contact to other animals, we investigated these factors in a murine model.ResultsViable H7N9 avian influenza virus was detected in the upper and lower respiratory tracts, intestine, and brain of model mice. The virus was transmissible between mice in close contact, with a higher concentration of virus found in pharyngeal and ocular secretions, and feces. All these biological materials were contagious for naïve mice.ConclusionsOur results suggest that the possible transmission routes for the H7N9 influenza virus were through mucosal secretions and feces