Overlapping Resonances in Open Quantum Systems

An $N$-level quantum system is coupled to a bosonic heat reservoir at positive temperature. We analyze the system-reservoir dynamics in the following regime: The strength $\lambda$ of the system-reservoir coupling is fixed and small, but larger than the spacing $\sigma$ of system energy levels. For vanishing $\sigma$ there is a manifold of invariant system-reservoir states and for $\sigma>0$ the only invariant state is the joint equilibrium. The manifold is invariant for $\sigma=0$ but becomes quasi-invariant for $\sigma>0$. Namely, on a first time-scale of the order $1/\lambda^2$, initial states approach the manifold. Then they converge to the joint equilibrium state on a much larger time-scale of the order $\lambda^2/\sigma^2$. We give a detailed expansion of the system-reservoir evolution showing the above scenario.Comment: Annales Henri Poincare 201

Multiscale dynamics of open three-level quantum systems with two quasi-degenerate levels

We consider a three-level quantum system interacting with a bosonic thermal reservoir. Two energy levels of the system are nearly degenerate but well separated from the third one. The system-reservoir interaction constant is larger than the energy difference of the degenerate levels, but it is smaller than the separation between the latter and the remaining level. We show that the quasi-degeneracy of energy levels leads to the existence of a manifold of quasi-stationary states, and the dynamics exhibits two characteristic time scales. On the first, shorter one, initial states approach the quasi-stationary manifold. Then, on the much longer second time scale, the final unique equilibrium is reached.Comment: Final text as publishe

The Application of Analytic Hierarchy Process in Supplier Selection for Specialty Paper Making Company, A case study in Anhui Welbon Gaosen Paper Co.,Ltd

Majority of enterprises choose to implement JIT procurement model to face the marketing fierce competition in recent decades. Single sourcing supplier is the main characteristic in JIT procurement, thence, selecting a suitable supplier become increasingly important. The purpose of the research is to select the most suitable supplier for the case company. More specifical, to identify supplier selection criteria for the case company, then exploiting a flexible analytic model which is AHP to help the case company choose a suitable supplier for implementing JIT Procurement, finally suggestions are given for case company in supplier relationship management, which based on implementing JIT Procurement. The study begins with literature review of purchasing behavior, supplier related theory and AHP method. Afterwards, qualitative research method of interview and quantitative research method of questionnaires were utilized to identify evaluation criteria and collect pair-wise comparison data for judgment matrixes. Finally, eigenvectors and eigenvalues of judgment matrixes were calculated for ranking priorities and all vectors were passed by consistency verification. Based on the result from previous research, supplier with the total highest score becomes the most suitable alternative. In addition, suggestions of supplier relationship management are given for the sake of success further implementation of JIT procurement in the case company.fi=Opinnäytetyö kokotekstinä PDF-muodossa.|en=Thesis fulltext in PDF format.|sv=Lärdomsprov tillgängligt som fulltext i PDF-format

Learning Active Basis Models by EM-Type Algorithms

EM algorithm is a convenient tool for maximum likelihood model fitting when the data are incomplete or when there are latent variables or hidden states. In this review article we explain that EM algorithm is a natural computational scheme for learning image templates of object categories where the learning is not fully supervised. We represent an image template by an active basis model, which is a linear composition of a selected set of localized, elongated and oriented wavelet elements that are allowed to slightly perturb their locations and orientations to account for the deformations of object shapes. The model can be easily learned when the objects in the training images are of the same pose, and appear at the same location and scale. This is often called supervised learning. In the situation where the objects may appear at different unknown locations, orientations and scales in the training images, we have to incorporate the unknown locations, orientations and scales as latent variables into the image generation process, and learn the template by EM-type algorithms. The E-step imputes the unknown locations, orientations and scales based on the currently learned template. This step can be considered self-supervision, which involves using the current template to recognize the objects in the training images. The M-step then relearns the template based on the imputed locations, orientations and scales, and this is essentially the same as supervised learning. So the EM learning process iterates between recognition and supervised learning. We illustrate this scheme by several experiments.Comment: Published in at http://dx.doi.org/10.1214/09-STS281 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Traveling waves for a diffusive SIR-B epidemic model with multiple transmission pathways

In this work, we consider a diffusive SIR-B epidemic model with multiple transmission pathways and saturating incidence rates. We first present the explicit formula of the basic reproduction number R0. Then we show that if R0 > 1, there exists a constant c ∗ > 0 such that the system admits traveling wave solutions connecting the disease-free equilibrium and endemic equilibrium with speed c if and only if c ≥ c Since the system does not admit the comparison principle, we appeal to the standard Schauder’s fixed point theorem to prove the existence of traveling waves. Moreover, a suitable Lyapunov function is constructed to prove the upward convergence of traveling waves