Matrix expression of finite orthogonal wavelet transform of finite impulse response signal is more valuable for theoretical analysis and understanding. However, clear deduction for matrix expression has not been provi...Matrix expression of finite orthogonal wavelet transform of finite impulse response signal is more valuable for theoretical analysis and understanding. However, clear deduction for matrix expression has not been provided yet. In this paper, the formulation to generate the re-lated matrix is put forward and the theorem on the orthogonality of this matrix proved. This effort deploys a basis for more deeper and wider applications in chemical processes. *展开更多
Huntington’s disease(HD)is a fatal neurodegenerative disorder characterized by a triad of behavioral symptoms:involuntary movement,emotional change,and cognitive dysfunction.Although alterations in WNT signaling have...Huntington’s disease(HD)is a fatal neurodegenerative disorder characterized by a triad of behavioral symptoms:involuntary movement,emotional change,and cognitive dysfunction.Although alterations in WNT signaling have been reported in HD,its precise role in pathogenesis remains unclear.In this study,we found that astrocytic WNT5B mRNA and protein levels are elevated in the striatum of both HD patients and HD model mice.The noncanonical WNT5B signaling pathway induced sustained expression of matrix metallopeptidase 14(MMP14),an extracellular matrix(ECM)-degrading enzyme,via activation of the NFATc2 transcription factor in both human and primary mouse astrocytes.Robust upregulation of MMP14 led to ECM degradation,medium spiny neuron(MSN)damage,and increased mutant huntingtin aggregation in N171-82Q HD transgenic mice.Furthermore,WNT5B gain-offunction exacerbated neuropathology,impaired motor coordination,and shortened the lifespan of N171-82Q mice.We further demonstrated that the overexpression of the estrogen receptorα(ERα)suppresses NFATc2 transcriptional activity in vitro.A targeted therapy for the WNT5B-NFATc2-MMP14 signaling pathway by genistein,a phytoestrogen,reduced MMP14 transcription by antagonizing NFATc2 activity and preventing ECM degradation in N171-82Q mice.Genistein treatment also ameliorated neuropathology and motor deficits and prolonged the lifespan of HD mice.Together,these findings define a molecular pathological mechanism in which astrocytic MMP14 transcription,driven by the noncanonical WNT5B signaling pathway,promotes ECM degradation and MSN damage and accelerates neurodegeneration in HD.Modulation of the noncell-autonomous WNT5BNFATc2-MMP14 signaling pathway by genistein may serve as a potential therapeutic strategy for mitigating HD pathogenesis.展开更多
This paper gives a matrix expression of logic. Under the matrix expression, a general description of the logical operators is proposed. Using the semi-tensor product of matrices, the proofs of logical equivalences, im...This paper gives a matrix expression of logic. Under the matrix expression, a general description of the logical operators is proposed. Using the semi-tensor product of matrices, the proofs of logical equivalences, implications, etc., can be simplified a lot. Certain general properties are revealed. Then, based on matrix expression, the logical operators are extended to multi-valued logic, which provides a foundation for fuzzy logical inference. Finally, we propose a new type of logic, called mix-valued logic, and a new design technique, called logic-based fuzzy control. They provide a numerically computable framework for the application of fuzzy logic for the control of fuzzy systems.展开更多
An equivalent definition of hypermatrices is introduced.The matrix expression of hypermatrices is proposed.Using permu-tation matrices,the conversion between different matrix expressions is revealed.The various kinds ...An equivalent definition of hypermatrices is introduced.The matrix expression of hypermatrices is proposed.Using permu-tation matrices,the conversion between different matrix expressions is revealed.The various kinds of contracted products of hypermatrices are realized by semi-tensor products(STP)of matrices via matrix expressions of hypermatrices.展开更多
In this paper, a new necessary and sufficient condition for the existence of a Hermitian solution as well as a new expression of the general Hermitian solution to the system of matrix equations A1X = C1 and A3XB3 = C3...In this paper, a new necessary and sufficient condition for the existence of a Hermitian solution as well as a new expression of the general Hermitian solution to the system of matrix equations A1X = C1 and A3XB3 = C3 are derived. The max-min ranks and inertias of these Hermitian solutions with some interesting applications are shown. In particular, the max-min ranks and inertias of the Hermitian part of the general solution to this system are presented.展开更多
The algorithmic tangent modulus at finite strains in current configuration plays an important role in the nonlinear finite element method. In this work, the exact tensorial forms of the algorithmic tangent modulus at ...The algorithmic tangent modulus at finite strains in current configuration plays an important role in the nonlinear finite element method. In this work, the exact tensorial forms of the algorithmic tangent modulus at finite strains are derived in the principal space and their corresponding matrix expressions are also presented. The algorithmic tangent modulus consists of two terms. The first term depends on a specific yield surface, while the second term is independent of the specific yield surface. The elastoplastic matrix in the principal space associated with the specific yield surface is derived by the logarithmic strains in terms of the local multiplicative decomposition. The Drucker-Prager yield function of elastoplastic material is used as a numerical example to verify the present algorithmic tangent modulus at finite strains.展开更多
A biclustering algorithm extends conventional clustering techniques to extract all of the meaningful subgroups of genes and conditions in the expression matrix of a microarray dataset. However, such algorithms are ver...A biclustering algorithm extends conventional clustering techniques to extract all of the meaningful subgroups of genes and conditions in the expression matrix of a microarray dataset. However, such algorithms are very sensitive to input parameters and show poor scalability. This paper proposes a scalable unsupervised biclustering framework, SUBic, to find high quality constant-row biclusters in an expression matrix effectively. A one-dimensional clustering algorithm is proposed to partition the attributes, that is, columns of an expression matrix into disjoint groups based on the similarity of expression values. These groups form a set of short transactions and are used to discover a set of frequent itemsets each of which corresponds to a bicluster. However, a bicluster may include any attribute whose expression value is not similar enough to others, so a bicluster refinement is used to enhance the quality of a bicluster by removing those attributes based on its distribution of expression values. The performance of the proposed method is comparatively analyzed through a series of experiments on synthetic and real datasets.展开更多
文摘Matrix expression of finite orthogonal wavelet transform of finite impulse response signal is more valuable for theoretical analysis and understanding. However, clear deduction for matrix expression has not been provided yet. In this paper, the formulation to generate the re-lated matrix is put forward and the theorem on the orthogonality of this matrix proved. This effort deploys a basis for more deeper and wider applications in chemical processes. *
基金funded by multiple grants from the National Research Foundation of Korea(NRF),supported by the Ministry of Education,Science and Technology,including the Sejong Science Fellowship(2021R1C1C2095827,S.J.H.)grants 2020M3E5D9079742,2021M3A9G1015618,and RS-2022-NR070632 awarded to H.R+3 种基金Additional support was provided through the Korea Dementia Research Project(RS2023-KH137130 to H.R.)under the Korea Dementia Research Center(KDRC),funded by the Ministry of Health&Welfare and the Ministry of Science and ICTThis work was also partially supported by the Korea Institute of Science and Technology(KIST)through grants 2E33701,2E33722,2Z07276,and 2Z07368(H.R.)We further acknowledge support from the U.S.National Institutes of Health(NIH R01NS109537,J.L.)English language and stylistic editing were assisted by AI-based proofreading tools(ChatGPT,OpenAI).
文摘Huntington’s disease(HD)is a fatal neurodegenerative disorder characterized by a triad of behavioral symptoms:involuntary movement,emotional change,and cognitive dysfunction.Although alterations in WNT signaling have been reported in HD,its precise role in pathogenesis remains unclear.In this study,we found that astrocytic WNT5B mRNA and protein levels are elevated in the striatum of both HD patients and HD model mice.The noncanonical WNT5B signaling pathway induced sustained expression of matrix metallopeptidase 14(MMP14),an extracellular matrix(ECM)-degrading enzyme,via activation of the NFATc2 transcription factor in both human and primary mouse astrocytes.Robust upregulation of MMP14 led to ECM degradation,medium spiny neuron(MSN)damage,and increased mutant huntingtin aggregation in N171-82Q HD transgenic mice.Furthermore,WNT5B gain-offunction exacerbated neuropathology,impaired motor coordination,and shortened the lifespan of N171-82Q mice.We further demonstrated that the overexpression of the estrogen receptorα(ERα)suppresses NFATc2 transcriptional activity in vitro.A targeted therapy for the WNT5B-NFATc2-MMP14 signaling pathway by genistein,a phytoestrogen,reduced MMP14 transcription by antagonizing NFATc2 activity and preventing ECM degradation in N171-82Q mice.Genistein treatment also ameliorated neuropathology and motor deficits and prolonged the lifespan of HD mice.Together,these findings define a molecular pathological mechanism in which astrocytic MMP14 transcription,driven by the noncanonical WNT5B signaling pathway,promotes ECM degradation and MSN damage and accelerates neurodegeneration in HD.Modulation of the noncell-autonomous WNT5BNFATc2-MMP14 signaling pathway by genistein may serve as a potential therapeutic strategy for mitigating HD pathogenesis.
基金the National Natural Science Foundation of China (No.60274010, 60343001, 60221301, 60334040)
文摘This paper gives a matrix expression of logic. Under the matrix expression, a general description of the logical operators is proposed. Using the semi-tensor product of matrices, the proofs of logical equivalences, implications, etc., can be simplified a lot. Certain general properties are revealed. Then, based on matrix expression, the logical operators are extended to multi-valued logic, which provides a foundation for fuzzy logical inference. Finally, we propose a new type of logic, called mix-valued logic, and a new design technique, called logic-based fuzzy control. They provide a numerically computable framework for the application of fuzzy logic for the control of fuzzy systems.
基金This work was supported partly by the National Natural Science Foundation of China(NSFC)(Nos.62073315,62103305)the Shanghai Pujiang Program(No.21PJ 1413100)China Postdoctoral Science Foundation(Nos.2021M703423,2022T150686).
文摘An equivalent definition of hypermatrices is introduced.The matrix expression of hypermatrices is proposed.Using permu-tation matrices,the conversion between different matrix expressions is revealed.The various kinds of contracted products of hypermatrices are realized by semi-tensor products(STP)of matrices via matrix expressions of hypermatrices.
文摘In this paper, a new necessary and sufficient condition for the existence of a Hermitian solution as well as a new expression of the general Hermitian solution to the system of matrix equations A1X = C1 and A3XB3 = C3 are derived. The max-min ranks and inertias of these Hermitian solutions with some interesting applications are shown. In particular, the max-min ranks and inertias of the Hermitian part of the general solution to this system are presented.
基金Project supported by the National Natural Science Foundation of China(Nos.41172116,U1261212,and 51134005)
文摘The algorithmic tangent modulus at finite strains in current configuration plays an important role in the nonlinear finite element method. In this work, the exact tensorial forms of the algorithmic tangent modulus at finite strains are derived in the principal space and their corresponding matrix expressions are also presented. The algorithmic tangent modulus consists of two terms. The first term depends on a specific yield surface, while the second term is independent of the specific yield surface. The elastoplastic matrix in the principal space associated with the specific yield surface is derived by the logarithmic strains in terms of the local multiplicative decomposition. The Drucker-Prager yield function of elastoplastic material is used as a numerical example to verify the present algorithmic tangent modulus at finite strains.
基金supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Education,Science and Technology (MEST) of Korea under Grant No. 2011-0016648
文摘A biclustering algorithm extends conventional clustering techniques to extract all of the meaningful subgroups of genes and conditions in the expression matrix of a microarray dataset. However, such algorithms are very sensitive to input parameters and show poor scalability. This paper proposes a scalable unsupervised biclustering framework, SUBic, to find high quality constant-row biclusters in an expression matrix effectively. A one-dimensional clustering algorithm is proposed to partition the attributes, that is, columns of an expression matrix into disjoint groups based on the similarity of expression values. These groups form a set of short transactions and are used to discover a set of frequent itemsets each of which corresponds to a bicluster. However, a bicluster may include any attribute whose expression value is not similar enough to others, so a bicluster refinement is used to enhance the quality of a bicluster by removing those attributes based on its distribution of expression values. The performance of the proposed method is comparatively analyzed through a series of experiments on synthetic and real datasets.
