With this work, we introduce a novel method for the unsupervised learning of conceptual hierarchies, or concept maps as they are sometimes called, which is aimed specifically for use with literary texts, as such disti...With this work, we introduce a novel method for the unsupervised learning of conceptual hierarchies, or concept maps as they are sometimes called, which is aimed specifically for use with literary texts, as such distinguishing itself from the majority of research literature on the topic which is primarily focused on building ontologies from a vast array of different types of data sources, both structured and unstructured, to support various forms of AI, in particular, the Semantic Web as envisioned by Tim Berners-Lee. We first elaborate on mutually informing disciplines of philosophy and computer science, or more specifically the relationship between metaphysics, epistemology, ontology, computing and AI, followed by a technically in-depth discussion of DEBRA, our dependency tree based concept hierarchy constructor, which as its name alludes to, constructs a conceptual map in the form of a directed graph which illustrates the concepts, their respective relations, and the implied ontological structure of the concepts as encoded in the text, decoded with standard Python NLP libraries such as spaCy and NLTK. With this work we hope to both augment the Knowledge Representation literature with opportunities for intellectual advancement in AI with more intuitive, less analytical, and well-known forms of knowledge representation from the cognitive science community, as well as open up new areas of research between Computer Science and the Humanities with respect to the application of the latest in NLP tools and techniques upon literature of cultural significance, shedding light on existing methods of computation with respect to documents in semantic space that effectively allows for, at the very least, the comparison and evolution of texts through time, using vector space math.展开更多
A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with sl(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613)...A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with sl(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613). Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra sl(4). In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.展开更多
The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokho...The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.展开更多
In this paper, nonlocal symmetries defined by bilinear B¨acklund transformation for bilinear potential Kd V(p Kd V)equation are obtained. By introducing an auxiliary variable which just satisfies the Schwartzian ...In this paper, nonlocal symmetries defined by bilinear B¨acklund transformation for bilinear potential Kd V(p Kd V)equation are obtained. By introducing an auxiliary variable which just satisfies the Schwartzian form of Kd V(SKd V)equation, the nonlocal symmetry is localized and the Levi transformation is presented. Besides, based on three different types of nonlocal symmetries for potential Kd V equation, three sets of negative p Kd V hierarchies along with their bilinear forms are constructed. An impressive result is that the coefficients of the third type of(bilinear) negative p Kd V hierarchy(N > 0) are variable, which are obtained via introducing an arbitrary parameter by considering the translation invariance of the p Kd V equation.展开更多
In the paper [Standard goal programming with fuzzy hierarchies: a sequential approach, Soft Computing, First online: 22 March 2015], it has been assumed that the normalized deviations should lie between zero and one. ...In the paper [Standard goal programming with fuzzy hierarchies: a sequential approach, Soft Computing, First online: 22 March 2015], it has been assumed that the normalized deviations should lie between zero and one. In some cases, this assumption may not be valid. Therefore, additional constraints must be incorporated into the model to ensure that the normalized deviations should not exceed one. This modification is illustrated by the given numerical example.展开更多
A new Lie algebra G and its two types of loop algebras (?)_1 and (?)2 are constructed.Basing on (?)_1 and(?)_2,two different isospectral problems are designed,furthermore,two Liouville integrable soiiton hierarchies a...A new Lie algebra G and its two types of loop algebras (?)_1 and (?)2 are constructed.Basing on (?)_1 and(?)_2,two different isospectral problems are designed,furthermore,two Liouville integrable soiiton hierarchies are obtainedrespectively under the framework of zero curvature equation,which is derived from the compatibility of the isospectralproblems expressed by Hirota operators.At the same time,we obtain the Hamiltonian structure of the first hierarchyand the bi-Hamiltonian structure of the second one with the help of the quadratic-form identity.展开更多
Unlike other balistids, grey triggerfish Batistes capriscus occur in social groups in subtropical reef assemblages andhave been noted to cooperate in capturing large crustacean prey. The objective of this study were t...Unlike other balistids, grey triggerfish Batistes capriscus occur in social groups in subtropical reef assemblages andhave been noted to cooperate in capturing large crustacean prey. The objective of this study were to determine the structure ofdominance hierarchies of these social groups and the factors that influence hierarchies of wild-caught grey triggerfish in a naturalisticsetting. From observations of four groups of triggerfish (n - 19 fish) in both dyad and group (4-5 fish) settings, we providea description of triggerfish behaviors and coloration patterns and an explanation of the social context in which suites of behaviorsare used by dominant, middle-ranking, and subordinate fish. Sixteen behaviors and nine coloration patterns were noted forgrey triggerfish. Grey triggerfish groups form linear hierarchies in both dyads and groups as measured by Landau's Index ofLinearity (h = 1.0 for Groups 1, 3, and 4 and h = 0.95 for Group 2 in dyads; h = 1.0 for all groups in group settings). Dyadic hierarchies,however, were not necessarily good predictors of the hierarchies found in larger group settings, as they only predictedtwo of the four group hierarchies. Sex played no role in influencing status or behavior. Size had the greatest influence on dominancestatus, with larger fish being more dominant than smaller fish. An individual's dominance ranking influenced both bodycoloration and posture. These results suggest that color patterns and body postures may also be used by observers as an indicatorof an individual's social status in展开更多
For the limit fractional Volterra(LFV)hierarchy,we construct the n-fold Darboux transformation and the soliton solutions.Furthermore,we extend the LFV hierarchy to the noncommutative LFV(NCLFV)hierarchy,and construct ...For the limit fractional Volterra(LFV)hierarchy,we construct the n-fold Darboux transformation and the soliton solutions.Furthermore,we extend the LFV hierarchy to the noncommutative LFV(NCLFV)hierarchy,and construct the Darboux transformation expressed by quasi determinant of the noncommutative version.Meanwhile,we establish the relationship between new and old solutions of the NCLFV hierarchy.Finally,the quasi determinant solutions of the NCLFV hierarchy are obtained.展开更多
文摘With this work, we introduce a novel method for the unsupervised learning of conceptual hierarchies, or concept maps as they are sometimes called, which is aimed specifically for use with literary texts, as such distinguishing itself from the majority of research literature on the topic which is primarily focused on building ontologies from a vast array of different types of data sources, both structured and unstructured, to support various forms of AI, in particular, the Semantic Web as envisioned by Tim Berners-Lee. We first elaborate on mutually informing disciplines of philosophy and computer science, or more specifically the relationship between metaphysics, epistemology, ontology, computing and AI, followed by a technically in-depth discussion of DEBRA, our dependency tree based concept hierarchy constructor, which as its name alludes to, constructs a conceptual map in the form of a directed graph which illustrates the concepts, their respective relations, and the implied ontological structure of the concepts as encoded in the text, decoded with standard Python NLP libraries such as spaCy and NLTK. With this work we hope to both augment the Knowledge Representation literature with opportunities for intellectual advancement in AI with more intuitive, less analytical, and well-known forms of knowledge representation from the cognitive science community, as well as open up new areas of research between Computer Science and the Humanities with respect to the application of the latest in NLP tools and techniques upon literature of cultural significance, shedding light on existing methods of computation with respect to documents in semantic space that effectively allows for, at the very least, the comparison and evolution of texts through time, using vector space math.
基金Project supported by the Natural Science Foundation of Shanghai (Grant No. 09ZR1410800)the Science Foundation of Key Laboratory of Mathematics Mechanization (Grant No. KLMM0806)+2 种基金the Shanghai Leading Academic Discipline Project (Grant No. J50101)the Key Disciplines of Shanghai Municipality (Grant No. S30104)the National Natural Science Foundation of China (Grant Nos. 61072147 and 11071159)
文摘A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with sl(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613). Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra sl(4). In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.
基金supported in part by NSFC(11975145 and 11972291)the Natural Science Foundation for Colleges and Universities in Jiangsu Province(17 KJB 110020)。
文摘The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.
基金supported by the Natural Science Foundation of Zhejiang Province,China(Grant No.LQ13A010014)the National Natural Science Foundation of China(Grant Nos.11326164,11401528,and 11275072)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120076110024)
文摘In this paper, nonlocal symmetries defined by bilinear B¨acklund transformation for bilinear potential Kd V(p Kd V)equation are obtained. By introducing an auxiliary variable which just satisfies the Schwartzian form of Kd V(SKd V)equation, the nonlocal symmetry is localized and the Levi transformation is presented. Besides, based on three different types of nonlocal symmetries for potential Kd V equation, three sets of negative p Kd V hierarchies along with their bilinear forms are constructed. An impressive result is that the coefficients of the third type of(bilinear) negative p Kd V hierarchy(N > 0) are variable, which are obtained via introducing an arbitrary parameter by considering the translation invariance of the p Kd V equation.
文摘In the paper [Standard goal programming with fuzzy hierarchies: a sequential approach, Soft Computing, First online: 22 March 2015], it has been assumed that the normalized deviations should lie between zero and one. In some cases, this assumption may not be valid. Therefore, additional constraints must be incorporated into the model to ensure that the normalized deviations should not exceed one. This modification is illustrated by the given numerical example.
基金Supported by the Natural Science Foundation of Shanghai under Grant No.09ZR1412800the Innovation Program of Shanghai Municipal Education Commission under Grant No.10ZZ131
基金supported by National Basic Research Program of China (973 Program) under Grant No.2007CB814800National Natural Science Foundation of China under Grant No.10601028the Natural Science Foundation of Fujian Province under Grant No.2008J0199
文摘我们第一分别地基于特徵函数对称减小和非标准的减小建议二种新多部件 BKP (mcBKP ) 层次。第一种与其宽松的代表被介绍的前後一致的来源一起包含 BKP 方程的二种类型。两个承认的二个 mcBKP 层次减小到抑制 k 的 BKP 层次并且到与前後一致的来源一起的维的层次，它包括二与前後一致的来源一起与前後一致的来源一起并且双向 SK 方程 SK 方程打的 integrable (1+1 ) 。
基金Supported by the Natural Science Foundation of Shanghai under Grant No.09ZR1410800the Science Foundation of Key Laboratory of Mathematics Mechanization under Grant No.KLMM0806
文摘A new Lie algebra G and its two types of loop algebras (?)_1 and (?)2 are constructed.Basing on (?)_1 and(?)_2,two different isospectral problems are designed,furthermore,two Liouville integrable soiiton hierarchies are obtainedrespectively under the framework of zero curvature equation,which is derived from the compatibility of the isospectralproblems expressed by Hirota operators.At the same time,we obtain the Hamiltonian structure of the first hierarchyand the bi-Hamiltonian structure of the second one with the help of the quadratic-form identity.
基金funded by a Research Enhancement Grant to KLL from Southwest Texas State University, San Marcos,TX, USA
文摘Unlike other balistids, grey triggerfish Batistes capriscus occur in social groups in subtropical reef assemblages andhave been noted to cooperate in capturing large crustacean prey. The objective of this study were to determine the structure ofdominance hierarchies of these social groups and the factors that influence hierarchies of wild-caught grey triggerfish in a naturalisticsetting. From observations of four groups of triggerfish (n - 19 fish) in both dyad and group (4-5 fish) settings, we providea description of triggerfish behaviors and coloration patterns and an explanation of the social context in which suites of behaviorsare used by dominant, middle-ranking, and subordinate fish. Sixteen behaviors and nine coloration patterns were noted forgrey triggerfish. Grey triggerfish groups form linear hierarchies in both dyads and groups as measured by Landau's Index ofLinearity (h = 1.0 for Groups 1, 3, and 4 and h = 0.95 for Group 2 in dyads; h = 1.0 for all groups in group settings). Dyadic hierarchies,however, were not necessarily good predictors of the hierarchies found in larger group settings, as they only predictedtwo of the four group hierarchies. Sex played no role in influencing status or behavior. Size had the greatest influence on dominancestatus, with larger fish being more dominant than smaller fish. An individual's dominance ranking influenced both bodycoloration and posture. These results suggest that color patterns and body postures may also be used by observers as an indicatorof an individual's social status in
基金supported by the National Natural Science Foundation of China under Grant No.12071237KC Wong Magna Fund in Ningbo University。
文摘For the limit fractional Volterra(LFV)hierarchy,we construct the n-fold Darboux transformation and the soliton solutions.Furthermore,we extend the LFV hierarchy to the noncommutative LFV(NCLFV)hierarchy,and construct the Darboux transformation expressed by quasi determinant of the noncommutative version.Meanwhile,we establish the relationship between new and old solutions of the NCLFV hierarchy.Finally,the quasi determinant solutions of the NCLFV hierarchy are obtained.
