Behavior of Graph Laplacians on Manifolds with Boundary

In manifold learning, algorithms based on graph Laplacians constructed from data have received considerable attention both in practical applications and theoretical analysis. In particular, the convergence of graph Laplacians obtained from sampled data to certain continuous operators has become an active research topic recently. Most of the existing work has been done under the assumption that the data is sampled from a manifold without boundary or that the functions of interests are evaluated at a point away from the boundary. However, the question of boundary behavior is of considerable practical and theoretical interest. In this paper we provide an analysis of the behavior of graph Laplacians at a point near or on the boundary, discuss their convergence rates and their implications and provide some numerical results. It turns out that while points near the boundary occupy only a small part of the total volume of a manifold, the behavior of graph Laplacian there has different scaling properties from its behavior elsewhere on the manifold, with global effects on the whole manifold, an observation with potentially important implications for the general problem of learning on manifolds

Necessary and sufficient conditions for local creation of quantum correlation

Quantum correlation can be created by a local operation from some initially classical states. We prove that the necessary and sufficient condition for a local trace-preserving channel to create quantum correlation is that it is not a commutativity-preserving channel. This condition is valid for arbitrary finite dimension systems. We also derive the explicit form of commutativity-preserving channels. For a qubit, a commutativity-preserving channel is either a completely decohering channel or a mixing channel. For a three-dimensional system (qutrit), a commutativity-preserving channel is either a completely decohering channel or an isotropic channel.Comment: Theorem 2 has been modifie

Combine Your “Will” and “Able”: Career Adaptability’s Influence on Performance

Adaptivity and adaptability are two key elements representing one’s “willingness” and “ability,” respectively, in the career construction theory (CCT) framework. On the basis of CCT and complemented by the visual of resources in the conservation of resources theory, this study combines career issues and performance and examines the joint effect of adaptivity and adaptability on career self-management which will lead to improved performance. Using a sample of Chinese employees (N = 232), the study first examines the mediating role that career self-management plays between career adaptability and performance and then tests the moderating role of proactive personality. Results show career adaptability positively predicts performance, with this relationship partially mediated by career self-management. The positive effect of career adaptability on career self-management is stronger among those who are more proactive than less proactive. Further, the indirect effect of career adaptability on performance is stronger among proactive employees than those with lower levels of proactive personality. These findings provide implications for both theories and practices

Exchange requirement-based delivery method of structural design information for collaborative design using industry foundation classes

In Architecture, engineering, and construction (AEC) collaboration, exchange requirements (ERs) vary in different projects with different platforms. In order to ensure the completeness and accuracy of data sharing and exchange for structural engineering in collaborative design, an ER-based delivery method was proposed to improve the delivery of structural design information. First, a process map of structural design was developed based on Information Delivery Manual (IDM). Within this process map, an ER Matrix of structural design was proposed to define information required by other disciplines at different stages. This matrix was composed of a set of required structural objects and their attributes, which were mapped to related Industry Foundation Classes (IFC) data. The mapping between the ER Matrix and IFC-based structural model data was implemented by an exchange model generation algorithm. Furthermore, a delivery tool was developed to define the ER Matrix in two ways, including user interface and XML-based language. A practical project was used to illustrate the utility of the proposed method. The results show that the proposed method using IFC is beneficial for structural information delivery

Analysis And Control Of Severe Vibration Of A Screw Compressor Outlet Piping System

The severe vibration of a screw compressor outlet piping system caused the fatigue failure of some thermowells and the unscheduled shut down of the system. The main reasons of the abnormal vibration in the outlet piping system were investigated by developing an acoustic model to simulate the gas pulsation and establishing two finite element models to conduct the mechanical vibration analyses. The acoustic analysis results showed that the pulsation amplitudes of most nodes in the outlet piping system exceeded the allowable values. The results of mechanical vibration analyses indicated that the insufficient stiffness of the outlet piping system and the first-order structure resonance occurred on thermowells were also the key factors inducing vibration. Several methods were put forward to attenuate vibration amplitude of the outlet piping system as well as the thermowells. A new pulsation attenuator was installed and the piping layout was rearranged to reduce pulsation amplitudes and shaking forces of all nodes in the outlet piping system. Several reasonable supports were added to improve the stiffness of the outlet piping system. After reinforcing the thermowells, the first-order natural frequency of the thermowells increased from 207.4Hz to 280.7Hz, away from the excitation frequency of 196.67Hz. The field measurement results showed that vibration amplitude and the vibration velocity decreased significantly after modifications

Receptor-Targeting Phthalocyanine Photosensitizer for Improving Antitumor Photocytotoxicity

Photodynamic therapy (PDT) is a promising therapeutic modality which uses a photosensitizer to capture visible light resulting in phototoxicity in the irradiated region. PDT has been used in a number of pathological indications, including tumor. A key desirable feature of the photosensitizer is the high phototoxicity on tumor cells but not on normal cells. In this study, we conjugate a gonadotropin-releasing hormone (GnRH) to a photosensitizer, Zinc phthalocyanine (ZnPc), in order to enhance its specificity to breast cancer, which over-expresses GnRH receptor. ZnPc has unique advantages over other photosensitizers, but is difficult to derivatize and purify as a single isomer. We previously developed a straight-forward way to synthesize mono-substituted β-carboxy-phthalocyanine zinc (ZnPc-COOH). Photophysical and photochemical parameters of this ZnPc-GnRH conjugate including fluorescence quantum yield (Фf), fluorescence decay time (τs) and singlet oxygen quantum yield (ФΔ) were evaluated and found comparable with that of ZnPc, indicating that addition of a GnRH peptide does not significantly alter the generation of singlet oxygen from ZnPc. Cellular uptakes and phototoxicities of this conjugate were tested and found significantly enhanced on human breast cancer cell lines overexpressing GnRH receptors (MDA-MB-231 and MCF-7 cells) compared to cells with low levels of GnRH receptors, such as human embryonic lung fibroblast (HELF) and human liver carcinoma (HepG2) cells. In addition, the cellular uptake of this conjugate toward MCF-7 cells were found clearly alleviated by a GnRH receptor blocker Cetrorelix, suggesting that the cellular uptake of this conjugate was GnRH receptor-mediated. Put together, these findings revealed that coupling ZnPc with GnRH analogue was an effective way to improve the selectivity of ZnPc towards tumors with over-expressed GnRH receptors

Quantum correlating power of local quantum channels

We define quantum-correlating power (QCP) of a local quantum channel acting on the left part of a bipartite quantum system as the maximum amount of left quantum correlation that can be created by this channel. We prove that for any local channel, the optimal input state, which corresponds to the maximum quantum correlation in the output state, must be a classical-classical state. Further, the single-qubit channels with maximum QCP can be found in the class of channels which take their optimal input states to rank-two quantum-classical states. A superactivation property of QCP, that is, two zero-QCP channels can constitute a positive-QCP channel, is observed and discussed for single-qubit phase damping channels. The analytic expression for QCP of single-qubit amplitude damping channel is obtained

NQE: N-ary Query Embedding for Complex Query Answering over Hyper-relational Knowledge Graphs

Complex query answering (CQA) is an essential task for multi-hop and logical reasoning on knowledge graphs (KGs). Currently, most approaches are limited to queries among binary relational facts and pay less attention to n-ary facts (n>=2) containing more than two entities, which are more prevalent in the real world. Moreover, previous CQA methods can only make predictions for a few given types of queries and cannot be flexibly extended to more complex logical queries, which significantly limits their applications. To overcome these challenges, in this work, we propose a novel N-ary Query Embedding (NQE) model for CQA over hyper-relational knowledge graphs (HKGs), which include massive n-ary facts. The NQE utilizes a dual-heterogeneous Transformer encoder and fuzzy logic theory to satisfy all n-ary FOL queries, including existential quantifiers, conjunction, disjunction, and negation. We also propose a parallel processing algorithm that can train or predict arbitrary n-ary FOL queries in a single batch, regardless of the kind of each query, with good flexibility and extensibility. In addition, we generate a new CQA dataset WD50K-NFOL, including diverse n-ary FOL queries over WD50K. Experimental results on WD50K-NFOL and other standard CQA datasets show that NQE is the state-of-the-art CQA method over HKGs with good generalization capability. Our code and dataset are publicly available.Comment: Accepted by the 37th AAAI Conference on Artificial Intelligence (AAAI-2023

Application of a nerve stereoscopic reconstruction technique based on ultrasonic images in the diagnosis of neuralgic amyotrophy

Objective: To propose a nerve stereoscopic reconstruction technique based on ultrasound imaging for site diagnosis, intuitive reflection of disease severity, and classification of neuralgic amyotrophy (NA).Methods: We enrolled 44 patients with NA who underwent high-frequency ultrasonography examination. Multiple sites on the normal side and the affected side were scanned to calculate the ratio of the cross-section area (CSA) of the affected side to the normal side at each location measured, i.e., the cross-section area swelling ratio (CSASR). The CSASR of 44 patients and 30 normal controls was analyzed to determine their threshold value for the diagnosis of NA. Then, ultrasound images of the cross-section were used to reconstruct the stereoscopic model of the nerve on the affected side and the normal side. Using the CSASR values in each measurement location, a CSASR stereoscopic model was developed.Results: The threshold value of CSASR for ultrasound diagnosis of NA was 1.55. The average diseased segments per patient was 2.49 ± 1.97, with an average overall length of 10.03 ± 7.95 cm. Nerve stereoscopic reconstruction could be conducted for swelling, torsion, incomplete constriction, and complete constriction.Conclusion: The ultrasound image reconstruction method proposed in this study can accurately determine the site, range, and type of neuropathies in patients with NA, and simultaneously provide complete and accurate data information and intuitive morphological information