Pair Model Research Articles

Long‐term photo‐identification study of fin whales in the Pelagos Sanctuary (NW Mediterranean) as a baseline for targeted conservation and mitigation measures

Abstract Historical abundance estimates are important for establishing baselines from which trends can be determined using more recent data. Long‐term studies based on photo‐identification were merged and used to estimate population size, survival rate and sex ratio (biopsy sampling) of fin whales in the North‐western Mediterranean. Merging four existing photo‐id catalogues yielded a Mediterranean catalogue with 507 individually identified fin whales. Ninety‐five (18.7%) individuals were resighted at least once during the study period (1990–2007): 71 whales were resighted in different years, 24 within the same season and 13 both in the same season and in different years. The number of resightings within‐season ranged from one to four, over periods from 1 to 90 days. Capture histories from these individuals were used in the capture–recapture analyses. Estimates of the animals present in the area each year between 1991 and 1995 through different modelling approaches were consistent: 900–1,000 from a POPAN open population model; 1,200 from a multi‐sample closed population model; and 900–1,100 from simple two‐sample closed population models for pairs of consecutive years, all with heavily overlapping 95% confidence intervals. The estimated apparent survival rate of 0.916 (95% CI = 0.773–0.972) was lower than expected, which may be linked to temporary or permanent emigration, or mortality possibly owing to ship strikes. Conservation and mitigation measures such as Important Marine Mammal Areas and Particularly Sensitive Sea Areas are presented and discussed.

Covariance predicts conserved protein residue interactions important for the emergence and continued evolution of SARS-CoV-2 as a human pathogen.

SARS-CoV-2 is one of three recognized coronaviruses (CoVs) that have caused epidemics or pandemics in the 21st century and that likely emerged from animal reservoirs. Differences in nucleotide and protein sequence composition within related β-coronaviruses are often used to better understand CoV evolution, host adaptation, and their emergence as human pathogens. Here we report the comprehensive analysis of amino acid residue changes that have occurred in lineage B β-coronaviruses that show covariance with each other. This analysis revealed patterns of covariance within conserved viral proteins that potentially define conserved interactions within and between core proteins encoded by SARS-CoV-2 related β-coronaviruses. We identified not only individual pairs but also networks of amino acid residues that exhibited statistically high frequencies of covariance with each other using an independent pair model followed by a tandem model approach. Using 149 different CoV genomes that vary in their relatedness, we identified networks of unique combinations of alleles that can be incrementally traced genome by genome within different phylogenic lineages. Remarkably, covariant residues and their respective regions most abundantly represented are implicated in the emergence of SARS-CoV-2 and are also enriched in dominant SARS-CoV-2 variants.

A commonality-based enhancement for sentence modeling with supervision

Sentence pair modeling is a fundamental yet challenging issue for feature mining in natural language processing (NLP) tasks. Recently, most works have generated feature and sentence representation based on the interactive attention mechanism. However, these models have two limitations: (1) they only consider global information through attention coefficient weighting, which makes insufficient utilization of critical features; (2) they only conduct internal training by fine-tuning network parameters, in which attention results are poorly explained. In this paper, inspired by human reasoning, we propose a Commonality Aggregated approach (CA) to enhance the lightweight interaction model by considering phrase features and contextual words. Specifically, we first fuse positional encoding and employ supervised training to extract critical phrase information from the text as the commonality of sentence pairs. Then, we deploy transfer learning and utilize interaction network to combine crucial phrase features, core word features, and positional encoding to enhance sentence pair modeling. Compared with the original network, extensive experiments on multiple benchmark datasets demonstrate the effectiveness of the proposed commonality aggregated method with stronger competitiveness. Further visual analysisanalysies validated the more explicit interpretability of attention, and extended experimental results indicate the excellent generalization of our approach.

Novel Prognosis and Therapeutic Response Model of Immune-Related lncRNA Pairs in Clear Cell Renal Cell Carcinoma.

Clear cell renal cell carcinoma (ccRCC) is the most common type of renal carcinoma. It is particularly important to accurately judge the prognosis of patients. Since most tumor prediction models depend on the specific expression level of related genes, a better model therefore needs to be constructed. To provide an immune-related lncRNA (irlncRNAs) tumor prognosis model that is independent of the specific gene expression levels, we first downloaded and sorted out the data on ccRCC in the TCGA database and screened irlncRNAs using co-expression analysis and then obtained the differently expressed irlncRNA (DEirlncRNA) pairs by means of univariate analysis. In addition, we modified LASSO penalized regression. Subsequently, the ROC curve was drawn, and we compared the area under the curve, calculated the Akaike information standard value of the 5-year receiver operating characteristic curve, and determined the cut-off point to establish the best model to distinguish the high- or low-disease-risk group of ccRCC. Subsequently, we reassessed the model from the perspectives of survival, clinic-pathological characteristics, tumor-infiltrating immune cells, chemotherapeutics efficacy, and immunosuppressed biomarkers. A total of 17 DEirlncRNAs pairs (AL031710.1|AC104984.5, AC020907.4|AC127-24.4,AC091185.1|AC005104.1, AL513218.1|AC079015.1, AC104564.3|HOXB-AS3, AC003070.1|LINC01355, SEMA6A-AS1|CR936218.1, AL513327.1|AS005785.1, AC084876.1|AC009704.2, IGFL2-AS1|PRDM16-DT, AC011462.4|MMP25-AS1, AL662844.3I|TGB2-AS1, ARHGAP27P1|AC116914.2, AC093788.1|AC007098.1, MCF2L-AS1|AC093001.1, SMIM25|AC008870.2, and AC027796.4|LINC00893) were identified, all of which were included in the Cox regression model. Using the cut-off point, we can better distinguish patients according to different factors, such as survival status, invasive clinic-pathological features, tumor immune infiltration, whether they are sensitive to chemotherapy or not, and expression of immunosuppressive biomarkers. We constructed the irlncRNA model by means of pairing, which can better eliminate the dependence on the expression level of the target genes. In other words, the signature established by pairing irlncRNA regardless of expression levels showed promising clinical prediction value.

High-spin levels, β− decay and monopole effects in A = 128 hole nuclei near 132Sn

The high-spin levels and β− decay in neutron-rich hole nuclei of A=128 are studied by large-scale shell-model calculations with the extended pairing plus multipole-multipole force model. The excited energy and logft values of β− decay are predicted in the final states of 128Ag, 128Cd, and 128In by the cascaded decays calculated in A=128 hole nuclei. The 16+ level of 128Cd is predicted as a spin-trap isomer feeding the existing high-spin 16+ of 128In by β− decay. The monopole effects are investigated carefully in the β− decay process from the ground state 0+ of 128Cd to the 1+ levels of 128In, while the half-life is affected by monopole corrections acting on the configuration of final states.

Efforts to Improve Teachers' Competence in Developing Learning Sources and Media With The Think Pair and Share Model Discussion

The general research objective is to determine the level of teacher skills in developing learning resources and media after supervision of the Think Pair and Share model. In particular, this study aims to improve the skills of teachers in developing learning resources and media through the supervision of the Think Pair and Share model.The research subjects were teachers of SD Negeri 1 Klego, Klego District, Boyolali Regency, totaling 7 people. The type of research is school action research. Data collection techniques used: questionnaires, observations, interviews, and documentation. The data analysis technique used descriptive qualitative.The results of the study concluded: (1) Think Pair and Share model was able to increase the active participation of teachers to exchange ideas and experiences, increase reciprocal interaction between teachers, increase openness among teachers, increase teacher understanding of the problems encountered in the learning process; (2) Think Pair and Share model is very effective to improve the skills of teachers in developing learning resources and media, because all teachers respond with high categories. In other words, the teacher feels that supervision with the Think Pair and Share model is very useful for improving learning resources and media.

Deformation and Response Analysis of Spur Gear Pairs with Flexible Ring Gears and Localized Spalling Faults

For the analysis on the deformation of flexible ring gears in spur gear pairs, the complete flexible ring is discretized, and the boundary condition is added to the connecting points to develop a calculation method for the flexible deformation. The ovality index is used to describe the deformation degree of flexible ring gears, then the influences of ring-gear width and the spalling defects on the flexible deformation of ring gears are discussed. The result shows that the flexible deformation of ring gears is caused by the gear pair meshing force, and the deformed shape is close to an ellipse. In the single-tooth meshing interval of gear pairs, the main form of deformation is being stretched, and while in the double-tooth meshes, the main form is bending deformation. When the width of the ring gear rims is increased, the flexible deformation of the ring gears can be effectively suppressed, and the vibration amplitude of the gear pairs can be reduced. Additionally, when there is a localized spalling fault on gear pairs, the sudden changes in the deformation of flexible ring gears are generated by the shock of the meshing force. Finally, through the finite element analysis model and the experiment, the mathematical model of gear pairs with flexible rings is confirmed.

Structure-Function Relationship between Cluster Mean Defect and Sector Peripapillary Retinal Nerve Fiber Layer Thickness in Primary Open Angle Glaucoma.

Purpose To determine the structure–function relationship between cluster mean defect (MD) offered by standard automated perimetry and corresponding sector peripapillary retinal nerve fiber layer thickness (pRNFLT) measured with optical coherence tomography (OCT) in primary open angle glaucoma (POAG). Method 39 healthy eyes (control group), 43 early POAG eyes (global MD ≤ 6 dB, early group), 30 moderate POAG eyes (global MD between 6 and 12 dB, moderate group), and 53 advanced POAG eyes (global MD > 12 dB, advanced group) underwent visual field (VF) examination with Octopus perimeter (dynamic strategy/G2 pattern) and peripapillary retinal nerve fiber layer thickness measurements with RTVue-100 FD-OCT. Spearman analysis was used to investigate the correlation between cluster MDs provided by Octopus perimeter and corresponding sector pRNFLT for the total sample and each subgroup, respectively. Then, linear (y = a+ bx) and curvilinear (quadratic, y = a+bx + cx2) regression analyses were employed to investigate the model for the cluster MD-sector pRNFLT pair with significant correlation. The strength of the relationship was characterized with correlation coefficient (ρ) and coefficient of determination (R2). For the cluster–sector pair that could be fitted by both models, Wilcoxon signed rank test of absolute residuals was used to compare the goodness of fit. Results Correlation between cluster MDs and corresponding sector pRNFLT was significant for all clusters in the total sample (ρ values: −0.572 to 0.832, P < 0.001) and in the POAG group (ρ values: −0.551 to −0.777, P < 0.001). The highest ρ values were found for cluster-sector pair 9 and pair 3, respectively. The curvilinear (quadratic) model provided better fit for all 10 cluster-sector pairs in the total sample (R2 values: 0.431–0.687, P < 0.001) and in the POAG group (R2 values: 0.364–0.594, P < 0.01). The highest R2 values were found also for cluster–sector pair 9 and pair 3, respectively. In the control group, no significant correlation was found for any cluster–sector pair (P > 0.01). In the early group, correlation was significant for cluster–sector pairs 3, 8, and 9 (ρ values: −0.449, −0.627, and −0.815, resp., P < 0.01). In the moderate group, correlation was significant for pairs 2, 3, 8, and 9 (ρ values: −0.703, −0.556, −0.680, and −0.637, resp., P < 0.01). In the advanced group, correlation was significant (P < 0.01) for all 10 pairs (ρ values: −0.395 to −0.699, P < 0.001) except for pairs 2, 3, and 8, and the highest ρ value was found for pair 1. For all cluster–sector pairs with significant correlation in the early, moderate, and advanced groups, only linear model could be fitted (P < 0.01), except for pair 9 in the early group and pair 5 in the advanced group. Conclusions Cluster MD of the Octopus visual field showed significant moderate-to-strong negative correlation and curvilinear (quadratic) relationship with the corresponding sector pRNFLT for POAG. This type of regional structure–function relationship varied according to the severity of POAG, and at each stage, the significantly correlated cluster–sector pairs mainly showed linear relationship. The results could provide guidance for better utilization of this regional structure–function method in the management of different stages of POAG.

Upaya Peningkatan Hasil Belajar Siswa Kelas V Dengan Menerapkan Model Paired Story Telling

The purpose of this study was to determine the increase in student learning outcomes in understanding light and its properties in the fifth grade science subject at SD Negeri 47 Lubuklinggau by using the paired story telling learning model. The method used in this research is the Classroom Action Research (CAR) method which begins with pre-action data and is carried out in two research cycles. The results showed that student learning outcomes in pre-cycle 9 students completed (33.33%) increased in cycle 1 to 18 students completed (66.67%) and in cycle 2 managed to increase to 24 students completed (88.89%). In conclusion, the Think Pair Share learning model can improve student learning outcomes on material about natural events.&#x0D; Keywords: Light, Paired Story Telling, PTK

Electron group localization in atoms and molecules.

Partitioning atomic and molecular charge densities in non-overlapping chemically significant regions is a challenging problem for quantum chemists. The present method aims to build a tool that enables the determination of "good boundaries" with the help of elementary statistical methods or information theory. This is done by minimizing an objective function with respect to the boundaries of the localization regions, the choice of this function being guided by a clarity requirement. With the sum of the indices of dispersion (ΣD) or the mutual information as the objective function, the method yields partitions in good agreement with the Aufbau rules for Li-Rn atoms and with Lewis's pairing model for molecules.

Magnetization recoil-curve overshoot and interaction plots in Co thin films

Recoil magnetization curves measured on Fe, Co and Ni films have recently been found to lie entirely and way outside the major hysteresis loop, a phenomenon referred to as a recoil-curve overshoot, RCO. A model of pairs of exchange-coupled grains with slightly-misaligned anisotropy axes has been able to reproduce key features of these films such as the collapse of the hard-magnetization axis with greatly enhanced remanent magnetization and coercivity, the RCO as well as kinks some major loops present near saturation. In the present work we employ an interaction plot technique in order to probe the nature of the interactions influencing the peculiar magnetization reversal. Our study on a 25-nm-thick magnetron-sputtered Co film reveals another unforeseen, in thin ferromagnetic films, features, disclosed in the vicinity of the collapsed hard axis where scissors-like magnetization reversal takes place—wholly negative interaction plots and hysteretic loops with positive recoil fields. Through model simulations we show that, contrary to the widespread notion, ferromagnetic intergrain coupling might be solely responsible for these puzzling features of ferromagnetic hysteresis.

Abstract 3110: Identification of the phosphorylation network in PDX and corresponding organoid (PDXO) models upon targeted therapy treatment using deep phosphoproteomic analysis[MB1

Abstract In precision medicine, genomic, transcriptomic, and proteomic data has contributed to the identification of novel driver genes and the molecular-level characterization of cancers. This data has led to a better understanding of drug modulation and resistance mechanisms. Patient-derived tumor models, including patient-derived xenograft (PDX) and organoid counterparts (PDXO), have been increasingly viewed as predictive preclinical cancer models. These models closely recapitulate tumor complexity, enabling the study of tumor identity for personalized medicine. Leveraging our large PDX collection models which are genomically and phenotypically annotated and validated, we have established and characterized a series of PDXO models to be used as scalable and high throughput compatible drug screening platforms. Here we conducted methodical analysis of drug response in paired PDX and PDXO models. In addition, trough deep whole- and phospho-proteomic analysis, we have analyzed and compared the effect of targeted therapies on protein expression and phosphorylation in both PDX and PDXO tumor models. Indeed, one of the most common post-translational modifications that is involved in cell regulation and intracellular signal transduction is reversible protein phosphorylation catalyzed by protein kinases. For this purpose, we have tested a KRAS inhibitor (AMG510), BCR-ABL TKI (Ponatinib) and EGFR TKI (Afatinib) respectively in lung NSCLC model carrying KRAS G12C mutation, colorectal model with RET fusion and Lung NSCLC model with EGFR exon 19 deletion. According to our historical data, a specific relationship between area under the curve value of organoid drug dose response and in vivo tumor growth has been observed, irrespective of the drug treatment. Furthermore, comparison between PDX and PDXO models deploying quantitative proteomic data enabled deep characterization of both global expression and signaling cascades modulated through small molecule inhibitors. Thus, we demonstrate the predictivity of organoid cultures to not only model in vivo drug responses but also to serve as a powerful platform to investigate target identification, mechanism of action and resistance mechanism via deep proteomics analysis. Citation Format: Xiaoxi Xu, Marco Tognetti, Yuehan Feng, Limei Shang, Leilei Chen, Jessie Wang, Roland Bruderer, Ludovic Bourré, Henry Li. Identification of the phosphorylation network in PDX and corresponding organoid (PDXO) models upon targeted therapy treatment using deep phosphoproteomic analysis[MB1] [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 3110.

Abstract 1595: Analysis of spatiotemporal phenotypic heterogeneity in chemoresistant triple negative breast cancer using imaging mass cytometry

Abstract Shifts in tumor cell phenotype in response to selective pressures (i.e. changing microenvironments, drug treatments) pose one of the biggest obstacles to successful breast cancer therapies. Phenotypically diverse breast tumor and stroma subpopulations, and interactions between them that alter tumor cell biology, represent unique and spatially distinct niches. We hypothesize that localized neighborhoods of breast tumor cells possess specialized phenotypes that mediate chemoresistance and represent novel therapeutic vulnerabilities. In order to assess these potential phenotypes, we utilized imaging mass cytometry (IMC), a highly multiplexed imaging modality that allows simultaneous measurement of 30-40 antigens while retaining the spatial architecture of the cancer tissue. We constructed an IMC antibody panel that combines markers for tissue architecture, tumor and stromal cell phenotyping, and signaling pathway activation. IMC was applied to patient-derived xenograft (PDX) models of triple negative breast cancer (TNBC).Our TNBC PDX collection was established from tumors obtained before and after neoadjuvant Adriamycin and cyclophosphamide (AC). IMC analysis of 18 PDX models representing eight patients revealed that stromal cell phenotypes were generally shared between all models, but tumor cell phenotypes were largely patient-specific. While every model was comprised primarily of a few major tumor cell phenotypes, we noted that each case also harbored several minor, unique populations, suggesting that specialized neighborhoods may exist within the tumor mass. Comparison of paired PDX models showed a wide range of phenotypic responses to chemotherapy, ranging from stable tumor composition to widespread changes in tumor phenotypes. These phenotypic changes arose despite relatively consistent genomic architecture. Vimentinhi fibroblasts were present more often in post-AC models, while SMAhi fibroblasts were unchanged after treatment. Comparison of pre-/post-AC PDX pairs revealed spatially constrained MAPK activation emerged after treatment. To capture acute changes in tumor phenotype, we treated treatment-naïve PDX models with AC and evaluated tumors by IMC. As tumors regressed and then regrew, we identified novel phenotypic shifts, again including increased MAPK signaling localized to discrete neighborhoods, suggesting this property may be a common feature of chemoresistant TNBC. Analysis of adjacent cells revealed seven distinct neighborhoods, and ongoing work is aimed at determining whether these neighborhoods are altered in response to chemotherapy treatment. Taken together, our findings suggest that distinct tumor phenotypes arise following treatment. Our goal is to determine whether these unique phenotypic niches functionally contribute to chemoresistance and if disruption of these niches enhances chemosensitivity. Citation Format: Amanda L. Rinkenbaugh, Vidya C. Sinha, Pankaj Singh, Yuan Qi, Jiansu Shao, Xiaomei Zhang, Gloria V. Echeverria, W. Fraser Symmans, Stacy L. Moulder, Helen Piwnica-Worms. Analysis of spatiotemporal phenotypic heterogeneity in chemoresistant triple negative breast cancer using imaging mass cytometry [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 1595.

Predicting the breeding hotspots of the southern right whale, Eubalaena australis (Cetartiodactyla: Mysticeti), along the southern Brazilian coastline

To predict the potential breeding hotspots of southern right whales in southern Brazil, we used a Maxent model with a “presence-only” dataset. The dataset was obtained from a systematic aerial survey and public records of the Programa de Monitoramento de Cetáceos da Bacia de Santos and Sistema de Apoio ao Monitoramento de Mamíferos Marinhos. Because of spatial autocorrelation, 528 records out of 3028 were used in the modelling process. The explanatory variables used in the models were coastal distance, linearity, slope and substrate type. The models were created separately for unaccompanied adults (Ad) and mother-calf pairs (Fe). Both models showed good accuracy according to their area under the curve values (Ad=0.974; Fe=0.958). Coastal distance was the most relevant explanatory variable for the unaccompanied adult model (54%), whereas coastal linearity was more relevant for the mother-calf pair model (82%). The estimated area for mother-calf pairs was more restricted to coastal areas than that for unaccompanied adults, possibly owing to the high number of shelter areas for calves near the coast. This is the first study to predict the potential breeding hotspots of southern right whales in Brazil and its results will allow for a more directed management of these whales and provide further research opportunities.

Individual scheduling approach for multi-class airline cabin crew with manpower requirement heterogeneity

The cabin crew pairing problem is one of the major challenges faced by airlines. Traditionally, multi-class cabin crews are scheduled on a team basis separated by aircraft types (families) as cockpit crews. However, the manpower requirements for cabin crew across aircraft types (families) are heterogeneous, which cannot be handled by the team scheduling approach. Thus, some airlines nowadays are adopting the individual scheduling approach to deal with the flight manpower requirement heterogeneity. Motivated by the emergence of the individual cabin crew pairing practice, we conduct an analytical study which aims at improving manpower utilization while reducing costs by utilizing a new individual cabin crew pairing generation approach. We also mathematically formulate crew substitution in the model which can help hedge against manpower requirement variations. The impacts of the relationship between manpower availability with requirement benchmarks on cabin crew scheduling strategies are investigated to derive deep insights. A column generation based solution approach is developed. Computational experiments based on small-scale real-world collected flight schedules are conducted to test the distinctive features of the proposed individual pairing model. In addition, a series of large hypothetical instances are employed to examine the advantages of the proposed model over the traditional team-based model in terms of manpower utilization improvement and cost reduction through a customized Genetic Algorithm.

Research on methods of tooth contact analysis and modification optimization for internal spur gear pair

Internal spur gear pair is widely used in industry. There is little current research on how to analyze and modify internal spur gear pairs that affect design and transmission performance. In this paper, a modeling method and an improved tooth contact analysis (TCA) method for internal spur gear pair are presented. The comparison between the improved TCA method and conventional TCA method is done, and the correctness and advantage of the improved TCA method are proved. The loaded tooth contact analysis (LTCA) method for spur gear pair is studied, and its feasibility is verified by Romax. Based on the method of penalty function, a modification optimization method of internal spur gear pair is proposed. Compared with the conventional particle swarm modification optimization, the proposed modification optimization method of internal spur gear pair is suitable for engineering application from the view of time-consuming and result. In order to facilitate modification, a modification parameter conversion method is proposed, and the conversion formulas from the modification length on tooth root of pinion to that on tooth tip of ring gear is derived. A dynamic model for internal spur gear pair is built, and dynamic simulation is carried out. The analysis results show that the optimization of the correction can significantly reduce the mean square value of the vibration acceleration. The research results supply a basis for the analysis and the modification optimization of internal spur gear pair.

Transitional patterns in the spherical mean-field plus quadrupole-quadrupole and pairing model within two-j shells

Patterns of transition between several terms in the spherical mean-field plus quadrupole-quadrupole and pairing model within two-j shells are studied. By analyzing the variational features of the quantities in the quadrupole-quadrupole term to pairing term, mean-field term to quadrupole-quadrupole term, and mean-field term to pairing term, we find that with the even-n cases, some observables such as low-lying energy level ratio E(41+)/E(21+), the overlap |〈41+;x0|41+;x〉| with x0=0 and x0=1, B(E2;41+→21+) and electric quadrupole moment value Q(41+), are sensitive with respect to a control parameter or the number of valence nucleons. The investigation also indicates that increasing the spacing of single-particle energy level can produce the significant transitional behavior.

Research on the meshing characteristics of asymmetric gears considering the tooth profile deviation

This paper establishes a time-varying meshing stiffness (TVMS) analytical model for asymmetric gear pair based on the potential energy principle to analyze the TVMS, transmission error, and load share ratio of asymmetric gears. The model considers the adjacent teeth' influence on the body deformation of the gear teeth and is verified the reasonableness by finite element analysis. The effect of tooth tip relief on the characteristics of asymmetric gear pairs is analyzed in this paper. Considering the tooth profile deviation due to tip relief and tooth profile error of the asymmetric gear can obtain results that are closer to the original meshing condition. The results show that the gear contact ratio decreases with the increase of one side of the gear pressure angle. Conversely, the TVMS of spur gear will increase in a certain extent. During modification section of tooth profile, some significant variations will happen on the behaviors of asymmetric gears such as TVMS, transmission error and load share ratio. Slight tooth profile errors on the surface produce conspicuous fluctuations in gear meshing characteristics.

Pairwise Compatibility for 2-Simple Minded Collections II: Preprojective Algebras and Semibrick Pairs of Full Rank

Let \(\Lambda \) be a finite-dimensional associative algebra over a field. A semibrick pair is a finite set of \(\Lambda \)-modules for which certain Hom- and Ext-sets vanish. A semibrick pair is completable if it can be enlarged so that a generating condition is satisfied. We prove that if \(\Lambda \) is \(\tau \)-tilting finite with at most three simple modules, then the completability of a semibrick pair can be characterized using conditions on pairs of modules. We then use the weak order to construct a combinatorial model for the semibrick pairs of preprojective algebras of type \(A_n\). From this model, we deduce that any semibrick pair of size n satisfies the generating condition, and that the dimension vectors of any semibrick pair form a subset of the column vectors of some c-matrix. Finally, we show that no “pairwise” criteria for completability exists for preprojective algebras of Dynkin diagrams with more than three vertices.

Vertex Nomination Between Graphs via Spectral Embedding and Quadratic Programming

Given a network and a subset of interesting vertices whose identities are only partially known, the vertex nomination problem seeks to rank the remaining vertices in such a way that the interesting vertices are ranked at the top of the list. An important variant of this problem is vertex nomination in the multiple graphs setting. Given two graphs G 1, G 2 with common vertices and a vertex of interest , we wish to rank the vertices of G 2 such that the vertices most similar to x are ranked at the top of the list. The current article addresses this problem and proposes a method that first applies adjacency spectral graph embedding to embed the graphs into a common Euclidean space, and then solves a penalized linear assignment problem to obtain the nomination lists. Since the spectral embedding of the graphs are only unique up to orthogonal transformations, we present two approaches to eliminate this potential nonidentifiability. One approach is based on orthogonal Procrustes and is applicable when there are enough vertices with known correspondence between the two graphs. Another approach uses adaptive point set registration and is applicable when there are few or no vertices with known correspondence. We show that our nomination scheme leads to accurate nomination under a generative model for pairs of random graphs that are approximately low-rank and possibly with pairwise edge correlations. We illustrate our algorithm’s performance through simulation studies on synthetic data as well as analysis of a high-school friendship network and analysis of transition rates between web pages on the Bing search engine. Supplementary materials for this article are available and include R code, data, and an appendix with detailed proofs.