Understanding Chemical Reactivity in Extended Systems：Exploring Models of Chemical Softness in Carbon Nanotubes

Chemical reactivity towards electron transfer is captured by the Fukui function.However,this is not well defined when the system or its ions have degenerate or pseudo-degenerate ground states.In such a case,the first-order chemical response is not independent of the perturbation and the correct response has to be computed using the mathematical formalism of perturbation theory for degenerate states.Spatialpseudo-degeneracy is ubiquitous in nanostructures with high symmetry and totally extended systems.Given the size of these systems,using degenerate-state perturbation theory is impractical because it requires the calculation of many excited states.Here we present an alternative to compute the chemical response of extended systems using models of local softness in terms of the local density of states.The local softness is approximately equal to the density of states at the Fermi level.However,such approximation leaves out the contribution of inner states.In order to include and weight the contribution of the states around the Fermi level,a model inspired by the long-range behavior of the local softness is presented.Single wall capped carbon nanotubes(SWCCNT) illustrate the limitation of the frontier orbital theory in extended systems.Thus,we have used a C360 SWCCNT to test the proposed model and how it compares with available models based on the local density of states.Interestingly,a simple Hü ckel approximation captures the main features of chemical response of these systems.Our results suggest that density-of-states models of the softness along simple tight binding Hamiltonians could be used to explore the chemical reactivity of more complex system,such a surfaces and nanoparticles.

Supervised local and non-local structure preserving projections with application to just-in-time learning for adaptive soft sensor

In soft sensor field, just-in-time learning(JITL) is an effective approach to model nonlinear and time varying processes. However, most similarity criterions in JITL are computed in the input space only while ignoring important output information, which may lead to inaccurate construction of relevant sample set. To solve this problem, we propose a novel supervised feature extraction method suitable for the regression problem called supervised local and non-local structure preserving projections(SLNSPP), in which both input and output information can be easily and effectively incorporated through a newly defined similarity index. The SLNSPP can not only retain the virtue of locality preserving projections but also prevent faraway points from nearing after projection,which endues SLNSPP with powerful discriminating ability. Such two good properties of SLNSPP are desirable for JITL as they are expected to enhance the accuracy of similar sample selection. Consequently, we present a SLNSPP-JITL framework for developing adaptive soft sensor, including a sparse learning strategy to limit the scale and update the frequency of database. Finally, two case studies are conducted with benchmark datasets to evaluate the performance of the proposed schemes. The results demonstrate the effectiveness of LNSPP and SLNSPP.

Soft Locally Compact Spaces and Soft Paracompact Spaces

The concept of soft topological space was introduced by some authors. In the present paper, we investigate some basic notions of soft topological spaces by using new soft point concept. Later we give soft locally compact space and the relationships between them are discussed in detail. Finally, we define soft paracompactness and explore some of its basic properties.

Joint training with local soft attention and dual cross-neighbor label smoothing for unsupervised person re-identification

Existing unsupervised person re-identification approaches fail to fully capture thefine-grained features of local regions,which can result in people with similar appearances and different identities being assigned the same label after clustering.The identity-independent information contained in different local regions leads to different levels of local noise.To address these challenges,joint training with local soft attention and dual cross-neighbor label smoothing(DCLS)is proposed in this study.First,the joint training is divided into global and local parts,whereby a soft attention mechanism is proposed for the local branch to accurately capture the subtle differences in local regions,which improves the ability of the re-identification model in identifying a person’s local significant features.Second,DCLS is designed to progressively mitigate label noise in different local regions.The DCLS uses global and local similarity metrics to semantically align the global and local regions of the person and further determines the proximity association between local regions through the cross information of neighboring regions,thereby achieving label smoothing of the global and local regions throughout the training process.In extensive experiments,the proposed method outperformed existing methods under unsupervised settings on several standard person re-identification datasets.

Theoretical investigation of the stereoselectivity of some Diels-Alder reactions involving cyclopentadiene

The stereoselectivity of some Diels-Alder reactions was investigated by means of ABEEM-oTr model. Combined with local hard-soft and acid-base （HSAB） principle, we made reasonable explanation by calculating local softness of atom and bond regions for the stereoselectivity of four Diels-Alder reactions involving cyclopentadiene.

A novel multimode process monitoring method integrating LDRSKM with Bayesian inference

A local discriminant regularized soft k-means （LDRSKM） method with Bayesian inference is proposed for multimode process monitoring. LDRSKM extends the regularized soft k-means algorithm by exploiting the local and non-local geometric information of the data and generalized linear discriminant analysis to provide a better and more meaningful data partition. LDRSKM can perform clustering and subspace selection simultaneously, enhancing the separability of data residing in different clusters. With the data partition obtained, kernel support vector data description （KSVDD） is used to establish the monitoring statistics and control limits. Two Bayesian inference based global fault detection indicators are then developed using the local monitoring results associated with principal and residual subspaces. Based on clustering analysis, Bayesian inference and manifold learning methods, the within and cross-mode correlations, and local geometric information can be exploited to enhance monitoring performances for nonlinear and non-Gaussian processes. The effectiveness and efficiency of the proposed method are evaluated using the Tennessee Eastman benchmark process.