Non-commutative deformations and quasi-coherent modules

We identify a class of "quasi-compact semi-separated" (qcss) twisted presheaves of algebras A for which well-behaved Grothendieck abelian categories of quasi-coherent modules Qch(A) are defined. This class is stable under algebraic deformation, giving rise to a 1-1 correspondence between algebraic deformations of A and abelian deformations of Qch(A). For a qcss presheaf A, we use the Gerstenhaber-Schack (GS) complex to explicitely parameterize the first order deformations. For a twisted presheaf A with central twists, we descibe an alternative category QPr(A) of quasi-coherent presheaves which is equivalent to Qch(A), leading to an alternative, equivalent association of abelian deformations to GS cocycles of qcss presheaves of commutative algebras. Our construction applies to the restriction O of the structure sheaf of a scheme X to a finite semi-separating open affine cover (for which we have an equivalence between Qch(O) and Qch(X)). Under a natural identification of Gerstenhaber-Schack cohomology of O and Hochschild cohomology of X, our construction is shown to be equivalent to Toda's construction in the smooth case

Random walks on mutual microRNA-target gene interaction network improve the prediction of disease-associated microRNAs

Background: MicroRNAs (miRNAs) have been shown to play an important role in pathological initiation, progression and maintenance. Because identification in the laboratory of disease-related miRNAs is not straightforward, numerous network-based methods have been developed to predict novel miRNAs in silico. Homogeneous networks (in which every node is a miRNA) based on the targets shared between miRNAs have been widely used to predict their role in disease phenotypes. Although such homogeneous networks can predict potential disease-associated miRNAs, they do not consider the roles of the target genes of the miRNAs. Here, we introduce a novel method based on a heterogeneous network that not only considers miRNAs but also the corresponding target genes in the network model. Results: Instead of constructing homogeneous miRNA networks, we built heterogeneous miRNA networks consisting of both miRNAs and their target genes, using databases of known miRNA-target gene interactions. In addition, as recent studies demonstrated reciprocal regulatory relations between miRNAs and their target genes, we considered these heterogeneous miRNA networks to be undirected, assuming mutual miRNA-target interactions. Next, we introduced a novel method (RWRMTN) operating on these mutual heterogeneous miRNA networks to rank candidate disease-related miRNAs using a random walk with restart (RWR) based algorithm. Using both known disease-associated miRNAs and their target genes as seed nodes, the method can identify additional miRNAs involved in the disease phenotype. Experiments indicated that RWRMTN outperformed two existing state-of-the-art methods: RWRMDA, a network-based method that also uses a RWR on homogeneous (rather than heterogeneous) miRNA networks, and RLSMDA, a machine learning-based method. Interestingly, we could relate this performance gain to the emergence of "disease modules" in the heterogeneous miRNA networks used as input for the algorithm. Moreover, we could demonstrate that RWRMTN is stable, performing well when using both experimentally validated and predicted miRNA-target gene interaction data for network construction. Finally, using RWRMTN, we identified 76 novel miRNAs associated with 23 disease phenotypes which were present in a recent database of known disease-miRNA associations. Conclusions: Summarizing, using random walks on mutual miRNA-target networks improves the prediction of novel disease-associated miRNAs because of the existence of "disease modules" in these networks

Influence of Principle Parameters on the Average Stiffness of Optical Tweezer Using Pulsed Gaussian Beams

In this article expresions used to simulate the trap stiffness k of the optical trap are derived. The influence of principle parameters as total energy, beam waist and duration of pulsed laser beam, radius of dielectric particle, and viscosity of surrounding medium on the stiffness  is simulated and discussed

Automatic Crack Detection in Built Infrastructure Using Unmanned Aerial Vehicles

This paper addresses the problem of crack detection which is essential for health monitoring of built infrastructure. Our approach includes two stages, data collection using unmanned aerial vehicles (UAVs) and crack detection using histogram analysis. For the data collection, a 3D model of the structure is first created by using laser scanners. Based on the model, geometric properties are extracted to generate way points necessary for navigating the UAV to take images of the structure. Then, our next step is to stick together those obtained images from the overlapped field of view. The resulting image is then clustered by histogram analysis and peak detection. Potential cracks are finally identified by using locally adaptive thresholds. The whole process is automatically carried out so that the inspection time is significantly improved while safety hazards can be minimised. A prototypical system has been developed for evaluation and experimental results are included.Comment: In proceeding of The 34th International Symposium on Automation and Robotics in Construction (ISARC), pp. 823-829, Taipei, Taiwan, 201

Unsupervised deep learning-based reconfigurable intelligent surface aided broadcasting communications in industrial IoTs

This paper presents a general system framework which lays the foundation for Reconfigurable Intelligent Surface (RIS)-enhanced broadcast communications in Industrial Internet of Things (IIoTs). In our system model, we consider multiple sensor clusters co-existing in a smart factory where the direct links between these clusters and a central base station (BS) is blocked completely. In this context, an RIS is utilized to reflect signals broadcast from BS toward cluster heads (CHs) which act as a representative of clusters, where BS only has access to the statistical distribution of the channel state information (CSI). An analytical upper bound of the total ergodic spectral efficiency and an approximation of outage probability are derived. Based on these analytical results, two algorithms are introduced to control the phase shifts at RIS, which are the Riemannian conjugate gradient (RCG) method and the deep neural network (DNN) method. While the RCG algorithm operates based on the conventional iterative method, the DNN technique relies on unsupervised deep learning. Our numerical results show that the both algorithms achieve satisfactory performance based on only statistical CSI. In addition, compared to the RCG scheme, using deep learning reduces the computational latency by more than 10 times with an almost identical total ergodic spectral efficiency achieved. These numerical results reveal that while using conventional RCG method may provide unsatisfactory latency, DNN technique shows much promise for enabling RIS in ultra reliable and low latency communications (URLLC) in the context of IIoTs

Box operads and higher Gerstenhaber brackets

We introduce a symmetric operad $\square p$ ("box-op") which describes a certain calculus of rectangular labeled ``boxes''. Algebras over $\square p$, which we call box operads, have appeared under the name of fc multicategories in work by Leinster \cite{LeinsterFcmulticategories1999}. In our main result, we endow a suitable (graded, zero differential) totalisation $\square p_{\mathrm{td}}$ with a morphism $L_{\infty} \rightarrow \square p_{\mathrm{td}}$. We show that $\square p$ acts on an $\mathbb{N}^3$-graded enlargement of the $\mathbb{N}^2$-graded Gerstenhaber-Schack object $\mathbf{C}_{GS}(\mathbb{A})$ of a quiver $\mathbb{A}$ on a small category from \cite{DinhVanLowen2018}. This action restricts to an $L_{\infty}$-structure on $\mathbf{C}_{GS}(\mathbb{A})$ (with zero differential). For an element $\alpha = (m,f,c) \in \mathbf{C}_{GS}^2(\mathbb{A})$, the Maurer-Cartan equation holds precisely when $(\mathbb{A}, m, f, c)$ is a lax prestack with multiplications $m$, restrictions $f$, and twists $c$. As a consequence, the $\alpha$-twisted $L_{\infty}$-structure on $\mathbf{C}_{GS}(\mathbb{A})$ controls the deformation theory of $(\mathbb{A}, \alpha)$ as a lax prestack.Comment: 22 pages + 8 appendix. Minor changes, references update