426 research outputs found
Reply to Hagen & Sudarshan's Comment
We show that the argument in Phys Rev Lett 70 (1993) 1360 is correct and
consistent, and that Hagen & Sudarshan's solution has inconsistency leading to
non-vanishing commutators of and even in physical
states. This proves that many of HS's statements in their Comment are based
merely on incorrect guess, but not on careful algebra.Comment: one page, UMN-TH-1245/9
Inferring gene regulatory networks from gene expression data by a dynamic Bayesian network-based model
Enabled by recent advances in bioinformatics, the inference of gene regulatory networks (GRNs) from gene expression data has garnered much interest from researchers. This is due to the need of researchers to understand the dynamic behavior and uncover the vast information lay hidden within the networks. In this regard, dynamic Bayesian network (DBN) is extensively used to infer GRNs due to its ability to handle time-series microarray data and modeling feedback loops. However, the efficiency of DBN in inferring GRNs is often hampered by missing values in expression data, and excessive computation time due to the large search space whereby DBN treats all genes as potential regulators for a target gene. In this paper, we proposed a DBN-based model with missing values imputation to improve inference efficiency, and potential regulators detection which aims to lessen computation time by limiting potential regulators based on expression changes. The performance of the proposed model is assessed by using time-series expression data of yeast cell cycle. The experimental results showed reduced computation time and improved efficiency in detecting gene-gene relationships
Inferring gene regulatory networks from gene expression data by a dynamic Bayesian network-based model
Enabled by recent advances in bioinformatics, the inference of gene regulatory networks (GRNs) from gene expression data has garnered much interest from researchers. This is due to the need of researchers to understand the dynamic behavior and uncover the vast information lay hidden within the networks. In this regard, dynamic Bayesian network (DBN) is extensively used to infer GRNs due to its ability to handle time-series microarray data and modeling feedback loops. However, the efficiency of DBN in inferring GRNs is often hampered by missing values in expression data, and excessive computation time due to the large search space whereby DBN treats all genes as potential regulators for a target gene. In this paper, we proposed a DBN-based model with missing values imputation to improve inference efficiency, and potential regulators detection which aims to lessen computation time by limiting potential regulators based on expression changes. The performance of the proposed model is assessed by using time-series expression data of yeast cell cycle. The experimental results showed reduced computation time and improved efficiency in detecting gene-gene relationships
Unequal Intra-layer Coupling in a Bilayer Driven Lattice Gas
The system under study is a twin-layered square lattice gas at half-filling,
being driven to non-equilibrium steady states by a large, finite `electric'
field. By making intra-layer couplings unequal we were able to extend the phase
diagram obtained by Hill, Zia and Schmittmann (1996) and found that the
tri-critical point, which separates the phase regions of the stripped (S) phase
(stable at positive interlayer interactions J_3), the filled-empty (FE) phase
(stable at negative J_3) and disorder (D), is shifted even further into the
negative J_3 region as the coupling traverse to the driving field increases.
Many transient phases to the S phase at the S-FE boundary were found to be
long-lived. We also attempted to test whether the universality class of D-FE
transitions under a drive is still Ising. Simulation results suggest a value of
1.75 for the exponent gamma but a value close to 2.0 for the ratio gamma/nu. We
speculate that the D-FE second order transition is different from Ising near
criticality, where observed first-order-like transitions between FE and its
"local minimum" cousin occur during each simulation run.Comment: 29 pages, 19 figure
Low Catalyst Loadings in Olefin Metathesis: Synthesis of Nitrogen Heterocycles by Ring-Closing Metathesis
A series of ruthenium catalysts have been screened under ring-closing metathesis (RCM) conditions to produce five-, six-, and seven-membered carbamate-protected cyclic amines. Many of these catalysts demonstrated excellent RCM activity and yields with as low as 500 ppm catalyst loadings. RCM of the five-membered carbamate series could be run neat, the six-membered carbamate series could be run at 1.0 M, and the seven-membered carbamate series worked best at 0.2−0.05 M
Shape invariance in prepotential approach to exactly solvable models
100學年度研究獎補助論文[[abstract]]In supersymmetric quantum mechanics, exact-solvability of one-dimensional quantum systems can be classified only with an additional assumption of integrability, the so-called shape invariance condition. In this paper we show that in the prepotential approach we proposed previously, shape invariance is automatically satisfied and needs not be assumed.[[journaltype]]國外[[incitationindex]]SCI[[booktype]]紙本[[countrycodes]]US
Planar Dirac Electron in Coulomb and Magnetic Fields: a Bethe ansatz approach
The Dirac equation for an electron in two spatial dimensions in the Coulomb
and homogeneous magnetic fields is an example of the so-called quasi-exactly
solvable models. The solvable parts of its spectrum was previously solved from
the recursion relations. In this work we present a purely algebraic solution
based on the Bethe ansatz equations. It is realised that, unlike the
corresponding problems in the Schr\"odinger and the Klein-Gordon case, here the
unknown parameters to be solved for in the Bethe ansatz equations include not
only the roots of wave function assumed, but also a parameter from the relevant
operator. We also show that the quasi-exactly solvable differential equation
does not belong to the classes based on the algebra .Comment: LaTex, 12 pages, no figure
Charged particles in external fields as physical examples of quasi-exactly solvable models: a unified treatment
We present a unified treatment of three cases of quasi-exactly solvable
problems, namely, charged particle moving in Coulomb and magnetic fields, for
both the Schr\"odinger and the Klein-Gordon case, and the relative motion of
two charged particles in an external oscillator potential. We show that all
these cases are reducible to the same basic equation, which is quasi-exactly
solvable owing to the existence of a hidden algebraic structure. A
systematic and unified algebraic solution to the basic equation using the
method of factorization is given. Analytic expressions of the energies and the
allowed frequencies for the three cases are given in terms of the roots of one
and the same set of Bethe ansatz equations.Comment: RevTex, 15 pages, no figure
Finite-dimensional Schwinger basis, deformed symmetries, Wigner function, and an algebraic approach to quantum phase
Schwinger's finite (D) dimensional periodic Hilbert space representations are
studied on the toroidal lattice {\ee Z}_{D} \times {\ee Z}_{D} with specific
emphasis on the deformed oscillator subalgebras and the generalized
representations of the Wigner function. These subalgebras are shown to be
admissible endowed with the non-negative norm of Hilbert space vectors. Hence,
they provide the desired canonical basis for the algebraic formulation of the
quantum phase problem. Certain equivalence classes in the space of labels are
identified within each subalgebra, and connections with area-preserving
canonical transformations are examined. The generalized representations of the
Wigner function are examined in the finite-dimensional cyclic Schwinger basis.
These representations are shown to conform to all fundamental conditions of the
generalized phase space Wigner distribution. As a specific application of the
Schwinger basis, the number-phase unitary operator pair in {\ee Z}_{D} \times
{\ee Z}_{D} is studied and, based on the admissibility of the underlying
q-oscillator subalgebra, an {\it algebraic} approach to the unitary quantum
phase operator is established. This being the focus of this work, connections
with the Susskind-Glogower- Carruthers-Nieto phase operator formalism as well
as standard action-angle Wigner function formalisms are examined in the
infinite-period limit. The concept of continuously shifted Fock basis is
introduced to facilitate the Fock space representations of the Wigner function.Comment: 19 pages, no figure
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