Vertex-Edge Degree Based Indices of Honey Comb Derived Network

Chemical graph theory is a branch of mathematics which combines graph theory and chemistry. Chemical reaction network theory is a territory of applied mathematics that endeavors to display the conduct of genuine compound frameworks. It pulled the research community due to its applications in theoretical and organic chemistry since 1960. Additionally, it also increases the interest the mathematicians due to the interesting mathematical structures and problems are involved. The structure of an interconnection network can be represented by a graph. In the network, vertices represent the processor nodes and edges represent the links between the processor nodes. Graph invariants play a vital feature in graph theory and distinguish the structural properties of graphs and networks. In this paper, we determined the newly introduced topological indices namely, first -degree Zagreb index, first -degree Zagreb index, second -degree Zagreb index, -degree Randic index, -degree atom-bond connectivity index, -degree geometric-arithmetic index, -degree harmonic index and -degree sum-connectivity index for honey comb derived network. In the analysis of the quantitative structure property relationships (QSPRs) and the quantitative structureactivity relationships (QSARs), graph invariants are important tools to approximate and predicate the properties of the biological and chemical compounds. Also, we give the numerical and graphical representation of our outcomes.     

基于拓扑单向波导的电磁诱导透明效应研究

为了研究电磁诱导透明效应在拓扑单向波导中的表现，设计了一种基于磁性光子晶体的耦合谐振腔波导。通过对谐振腔位置的调控实现了具有单向性质的电磁诱导透明效应，并利用有限时域差分仿真证明了电磁诱导透明效应在单向拓扑波导中的相关特性。该研究可为拓扑波导中实现光延迟、光开关等提供参考。     

Large neighborhood search for the bike request scheduling problem

This paper introduces an efficient algorithm for the bike request scheduling problem (BRSP). The BRSP is built around the concept of request, defined as the pickup or dropoff of a number of identical items (bikes) at a specific station, within a certain time window, and with a certain priority. The aim of the BRSP is to sequence requests on (and hence determine the routes of) a set of vehicles, in such a way that the sum of the priorities of the executed requests is maximized, all time windows are respected, and the capacity of the vehicles is not exceeded. The generation of the set of requests is explicitly not a part of the problem definition of the BRSP. The primary application of the BRSP, from which it derives its name, is to determine the routes of a set of repositioning vehicles in a bike sharing system, although other applications exist. The algorithm introduced in this paper is based on a set of related greedy randomized adaptive search procedure followed by variable neighborhood descent (GRASP + VND) operators embedded in a large neighborhood search (LNS) framework. Since this paper presents the first heuristic for the BRSP, a computational comparison to existing approaches is not possible. We therefore compare the solutions found by our LNS heuristic to those found by an exact solver (Gurobi). These experiments confirm that the proposed algorithm scales to realistic dimensions and is able to find near‐optimal solutions in seconds.     

Evolution of linear edge dislocation in atmospheric turbulence and free space

In accordance with the extended Huygens–Fresnel principle, the evolution of linear edge dislocation propagating through atmospheric turbulence is studied, and the effects of waist width and the slope of linear edge dislocation are investigated. It is shown that when linear edge dislocation beams propagate through atmospheric turbulence, if the waist width is not equal and the slope is not zero, then the linear edge dislocation vanishes and transforms into an optical vortex with a topological charge of ?1 or +1. The optical vortex and an optical vortex that is created annihilate when the transmission distance is far enough. The linear edge dislocation vanishes when the slope is zero. If the waist width is equal, then the linear edge dislocation will vanish regardless of the slope value. For linear edge dislocation beams in free space, when selecting specific parameters, linear edge dislocation always exists.     

Automated delineation of non-small cell lung cancer: A step toward quantitative reasoning in medical decision science

Quantitative reasoning in medical decision science relies on the delineation of pathological objects. For example, evidence-based clinical decisions regarding lung diseases require the segmentation of nodules, tumors, or cancers. Non-small cell lung cancer (NSCLC) tends to be large sized, irregularly shaped, and grows against surrounding structures imposing challenges in the segmentation, even for expert clinicians. An automated delineation tool based on spatial analysis was developed and studied on 25 sets of computed tomography scans of NSCLC. Manual and automated delineations were compared, and the proposed method exhibited robustness in terms of the tumor size (5.32–18.24 mm), shape (spherical or irregular), contouring (lobulated, spiculated, or cavitated), localization (solitary, pleural, mediastinal, endobronchial, or tagging), and laterality (left or right lobe) with accuracy between 80% and 99%. Small discrepancies observed between the manual and automated delineations may arise from the variability in the practitioners' definitions of region of interest or imaging artifacts that reduced the tissue resolution.     

Criteria on existence of horseshoes near homoclinic tangencies of arbitrary orders

Consider (m + 1)-dimensional, m ≥ 1, diffeomorphisms that have a saddle fixed point O with m-dimensional stable manifold W^s(O), one-dimensional unstable manifold W^u(O), and with the saddle value σ different from 1. We assume that W^s(O) and W^u(O) are tangent at the points of some homoclinic orbit and we let the order of tangency be arbitrary. In the case when σ < 1, we prove necessary and sufficient conditions of existence of topological horseshoes near homoclinic tangencies. In the case when σ > 1, we also obtain the criterion of existence of horseshoes under the additional assumption that the homoclinic tangency is simple.     

Off‐grid DoA estimation method of wideband signals

In this paper, an off‐grid direction of arrival (DoA) estimation method is proposed for wideband signals. This method is based on the sparse representation (SR) of the array covariance matrix. Similar to the time domain DoA estimation methods, the correlation function of the sources was assumed to be the same and known. A new measurement vector is obtained using the lower‐left triangular elements of the covariance matrix. The DoAs are estimated by quantizing the entire range of continuous angle space into discrete grid points. However, the exact DoAs may be located between two grid points; therefore, this estimation has errors. The accuracy of DoA estimation is improved by the minimization of the difference between the new measurement vector and its estimated values. Simulation results revealed that the proposed method can enhance the DoA estimation accuracy of wideband signals.     

Fix-and-relax approaches for controlled tabular adjustment

Controlled tabular adjustment (CTA) is a relatively new protection technique for tabular data protection. CTA formulates a mixed integer linear programming problem, which is challenging for tables of moderate size. Even finding a feasible initial solution may be a challenging task for large instances. On the other hand, end users of tabular data protection techniques give priority to fast executions and are thus satisfied in practice with suboptimal solutions. This work has two goals. First, the fix-and-relax (FR) strategy is applied to obtain good feasible initial solutions to large CTA instances. FR is based on partitioning the set of binary variables into clusters to selectively explore a smaller branch-and-cut tree. Secondly, the FR solution is used as a warm start for a block coordinate descent (BCD) heuristic (approach named FR+BCD); BCD was confirmed to be a good option for large CTA instances in an earlier paper by the second and third co-authors (Comput Oper Res 2011;38:1826–35 [23]). We report extensive computational results on a set of real-world and synthetic CTA instances. FR is shown to be competitive compared to CPLEX branch-and-cut in terms of quickly finding either a feasible solution or a good upper bound. FR+BCD improved the quality of FR solutions for approximately 25% and 50% of the synthetic and real-world instances, respectively. FR or FR+BCD provided similar or better solutions in less CPU time than CPLEX for 73% of the difficult real-world instances.