In this paper, we show that two Toeplitz operators Tf and Tg on the Hardy space of the polydisk can commute if and only if the Berezin transform of the commutator [Tf, Tg] is n-harmonic.
Proteasomes are responsible for the production of the majority of cytotoxic T lymphocyte(CTL) epitopes.Hence,it is important to identify correctly which peptides will be generated by proteasomes from an unknown protein.However,the pool of proteasome cleavage data used in the prediction algorithms,whether from major histocompatibility complex(MHC) I ligand or in vitro digestion data,is not identical to in vivo proteasomal digestion products.Therefore,the accuracy and reliability of these models still need to be improved.In this paper,three types of proteasomal cleavage data,constitutive proteasome(cCP),immunoproteasome(iCP) in vitro cleavage,and MHC I ligand data,were used for training cleave-site predictive methods based on the kernel-function stabilized matrix method(KSMM).The predictive accuracies of the KSMM+pair coefficients were 75.0%,72.3%,and 83.1% for cCP,iCP,and MHC I ligand data,respectively,which were comparable to the results from support vector machine(SVM).The three proteasomal cleavage methods were combined in turn with MHC I-peptide binding predictions to model MHC I-peptide processing and the presentation pathway.These integrations markedly improved MHC I peptide identification,increasing area under the receiver operator characteristics(ROC) curve(AUC) values from 0.82 to 0.91.The results suggested that both MHC I ligand and proteasomal in vitro degradation data can give an exact simulation of in vivo processed digestion.The information extracted from cCP and iCP in vitro cleavage data demonstrated that both cCP and iCP are selective in their usage of peptide bonds for cleavage.
In this paper, we characterize the symbols for （semi-）commuting dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space. We show that for φ ,ψ ∈ W1, ∞, SφSψ = SψSφ on （Dh）⊥ if and only if φ and ψ satisfy one of the following conditions： （1） Both φ and ψ are harmonic functions; （2） There exist complex constants α and β, not both O, such that φ = αφ＋β.
In this paper,we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C.We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.Meanwhile,we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.
