35,628 research outputs found
High-dimensional limits of eigenvalue distributions for general Wishart process
In this article, we obtain an equation for the high-dimensional limit measure
of eigenvalues of generalized Wishart processes, and the results is extended to
random particle systems that generalize SDEs of eigenvalues. We also introduce
a new set of conditions on the coefficient matrices for the existence and
uniqueness of a strong solution for the SDEs of eigenvalues. The equation of
the limit measure is further discussed assuming self-similarity on the
eigenvalues.Comment: 28 page
Thermodynamical property of entanglement entropy and deconfinement phase transition
We analyze the holographic entanglement entropy in a soliton background with
Wilson lines and derive a relation analogous to the first law of
thermodynamics. The confinement/deconfinement phase transition occurs due to
the competition of two minimal surfaces. The entropic c function probes the
confinement/deconfinement phase transition. It is sensitive to the degrees of
freedom (DOF) smaller than the size of a spatial circle. When the Wilson line
becomes large, the entropic c function becomes non-monotonic as a function of
the size and does not satisfy the usual c-theorem. We analyze the entanglement
entropy for a small subregion and the relation analogous to the first law of
thermodynamics. For the small amount of Wilson lines, the excited amount of the
entanglement entropy decreases from the ground state. It reflects that
confinement decreases degrees of freedom. We finally discuss the second order
correction of the holographic entanglement entropy.Comment: 25 pages, 5 figures; v2 minor changes, references adde
DNA sequences classification and computation scheme based on the symmetry principle
The DNA sequences containing multifarious novel symmetrical structure frequently play crucial role in how genomes work. Here we present a new scheme for understanding the structural features and potential mathematical rules of symmetrical DNA sequences using a method containing stepwise classification and recursive computation. By defining the symmetry of DNA sequences, we classify all sequences and conclude a series of recursive equations for computing the quantity of all classes of sequences existing theoretically; moreover, the symmetries of the typical sequences at different levels are analyzed. The classification and quantitative relation demonstrate that DNA sequences have recursive and nested properties. The scheme may help us better discuss the formation and the growth mechanism of DNA sequences because it has a capability of educing the information about structure and quantity of longer sequences according to that of shorter sequences by some recursive rules. Our scheme may provide a new stepping stone to the theoretical characterization, as well as structural analysis, of DNA sequences
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