Reconstructing the relaxation dynamics induced by an unknown heat bath

In quantum state tomography, one potential source of error is uncontrolled contact of the system with a heat bath whose detailed properties are not known, and whose impact on the system moreover varies between different runs of the experiment. Precisely these variations provide a handle for reconstructing the system?s effective relaxation dynamics. I propose a pertinent estimation scheme which is based on a steepest-descent ansatz and maximum likelihood. After reconstructing the relaxation dynamics, the original quantum state of the system can be constrained to a curve in state space.     

Maximizing the mean subtree order

This article focuses on properties and structures of trees with maximum mean subtree order in a given family; such trees are called optimal in the family. Our main goal is to describe the structure of optimal trees in and , the families of all trees and caterpillars, respectively, of order . We begin by establishing a powerful tool called the Gluing Lemma, which is used to prove several of our main results. In particular, we show that if is an optimal tree in or for , then every leaf of is adjacent to a vertex of degree at least . We also use the Gluing Lemma to answer an open question of Jamison and to provide a conceptually simple proof of Jamison's result that the path has minimum mean subtree order among all trees of order . We prove that if is optimal in , then the number of leaves in is and that if is optimal in , then the number of leaves in is . Along the way, we describe the asymptotic structure of optimal trees in several narrower families of trees.     

A Tree-valued Markov Process Associated with an Admissible Family of Branching Mechanisms

Let E?R be an interval. By studying an admissible family of branching mechanisms{ψt,t ∈E} introduced in Li [Ann. Probab., 42, 41-79(2014)], we construct a decreasing Levy-CRT-valued process {Tt, t ∈ E} by pruning Lévy trees accordingly such that for each t ∈E, Tt is a ψt-Lévy tree. We also obtain an analogous process {Tt*,t ∈E} by pruning a critical Levy tree conditioned to be infinite. Under a regular condition on the admissible family of branching mechanisms, we show that the law of {Tt,t ∈E} at the ascension time A := inf{t ∈E;Tt is finite} can be represented by{Tt*,t∈E}.The results generalize those studied in Abraham and Delmas [Ann. Probab., 40, 1167-1211(2012)].     

Embedding hypertrees into steiner triple systems

In this paper, we are interested in the following question: given an arbitrary Steiner triple system on vertices and any 3‐uniform hypertree on vertices, is it necessary that contains as a subgraph provided ? We show the answer is positive for a class of hypertrees and conjecture that the answer is always positive.     

Logging damage and injured tree mortality in tropical forest management

Using insights from the forest ecology literature, we analyze the effect of injured trees on stand composition and carbon stored in above‐ground biomass and the implications for forest management decisions. Results from a Faustmann model with data for a tropical forest on Kalimantan show that up to 50% of the basal area of the stand before harvest can consist of injured trees. Considering injured trees leads to an increase in the amount of carbon in above‐ground biomass of up to 165%. These effects are larger under reduced impact logging than under conventional logging. The effects on land expectation value and cutting cycle are relatively small. The results suggest that considering injured trees in models for tropical forest management is important for the correct assessment of the potential of financial programs to store carbon and conserve forest ecosystem services in managed tropical forests, such as reducing emissions from deforestation and forest degradation and payment for ecosystem services. Recommendations for Resource Managers

• Considering the role of injured trees is important for managing tropical forests
• These trees can cover up to 50% of basal area and contain more than 50% of the carbon stored in above‐ground biomass
• Reduced impact logging leads to a larger basal area of injured trees and more carbon stored in injured trees than conventional logging
• Injured trees play an important role when assessing the potential for carbon storage in the context of payment for forest ecosystem services.

     

Quintic hyperbolic nonpolynomial spline and finite difference method for nonlinear second order differential equations and its application

An efficient numerical method based on quintic nonpolynomial spline basis and high order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of spline functions we derive consistency conditions and high order discretizations of the differential equation with the significant first order derivative. The error analysis of the new method is discussed briefly. The new method is analyzed for its efficiency using the physical problems. The order and accuracy of the proposed method have been analyzed in terms of maximum errors and root mean square errors.