Lifting,superadditivity, mixed integer rounding and single node flow sets revisited

In this survey we attempt to give a unified presentation of a variety of results on the lifting of valid inequalities, as well as a standard procedure combining mixed integer rounding with lifting for the development of strong valid inequalities for knapsack and single node flow sets. Our hope is that the latter can be used in practice to generate cutting planes for mixed integer programs. The survey contains essentially two parts. In the first we present lifting in a very general way, emphasizing superadditive lifting which allows one to lift simultaneously different sets of variables. In the second, our procedure for generating strong valid inequalities consists of reduction to a knapsack set with a single continuous variable, construction of a mixed integer rounding inequality, and superadditive lifting. It is applied to several generalizations of the 0–1 single node flow set. This paper appeared in 4OR, 1, 173–208 (2003). The first author is supported by the FNRS as a chercheur qualifié. This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming. The scientific responsibility is assumed by the authors.     

Influence diagrams with super value nodes involving imprecise information

The concept of super value nodes was established to allow dynamic programming to be performed within the theory of influence diagrams and to reduce the computational complexity in solving problems by means of influence diagrams. This paper is focused on how influence diagrams with super value nodes are affected by the presence of imprecise information. We analyze how to reduce the complexity when evaluating an influence diagram in this framework by modelling these kinds of nodes and random magnitudes in terms of fuzzy random variables. Finally, an applied example of the theoretical results is developed.     

Level of nodes in increasing trees revisited

Simply generated families of trees are described by the equation T(z) = ϕ(T(z)) for their generating function. If a tree has n nodes, we say that it is increasing if each node has a label ∈ { 1,…,n}, no label occurs twice, and whenever we proceed from the root to a leaf, the labels are increasing. This leads to the concept of simple families of increasing trees. Three such families are especially important: recursive trees, heap ordered trees, and binary increasing trees. They belong to the subclass of very simple families of increasing trees, which can be characterized in 3 different ways. This paper contains results about these families as well as about polynomial families (the function ϕ(u) is just a polynomial). The random variable of interest is the level of the node (labelled) j, in random trees of size n ≥ j. For very simple families, this is independent of n, and the limiting distribution is Gaussian. For polynomial families, we can prove this as well for j,n → ∞ such that n − j is fixed. Additional results are also given. These results follow from the study of certain trivariate generating functions and Hwang's quasi power theorem. They unify and extend earlier results by Devroye, Mahmoud, and others. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

Evaluation of image quality of DWIBS versus DWI sequences in thoracic MRI at 3 T

Purpose

To compare diffusion weighted imaging with background suppression (DWIBS) sequence with classic spectral diffusion sequence (DWI) with and without respiratory gating in mediastinal lymph node analysis at 3 T.

Materials and methods

26 patients scheduled for mediastinoscopic lymph node analysis, prospectively undergone a thoracic 3 T MRI with DWIBS (FatSat = STIR; TR/TE = 6674.1/44.7 ms; IR = 260 ms) and DWI sequences (FatSat = SPIR; TR/TE = 1291/59.6 ms) (b = 0-400-800 s/mm2) with and without (free breathing) respiratory gating.Images at b = 800 were analyzed by two radiologists. They performed qualitative analysis of fat-sat homogeneity and motion artifacts, rated from 0 to 4, and quantitative evaluation by studying signal to background (STB) of lymph nodes.

Results

Quality of fat suppression was significantly higher for DWIBS than for DWI both for free-breathing (score 3.48 ± 0.65 vs. 1.76 ± 0.96, p < 0.0001) and respiratory-gated scans (3.17 ± 0.77 vs. 1.72 ± 0.73, p = 0.0001). Similarly, artifacts were reduced with DWIBS (3.16 ± 0.47 vs. 1.76 ± 0.59, p < 0.0001; 3.0 ± 0.73 vs. 2.04 ± 0.53, p = 0.0001). Quantitative analysis showed higher STB with DWIBS (3.26 ± 1.83 vs. 0.98 ± 0.44, p < 0.0001; 3.56 ±, 2.09 vs. 0.92 ± 0.59, p < 0.0001). Gating did not improve image quality and STB on DWIBS (p > 0.05).

Conclusion

In thoracic MRI, ungated DWIBS sequence improves fat-sat homogeneity, reduces motion artifacts and increases STB of lymph nodes. Respiratory gating does not improve DWIBS image quality.     

剪切弯曲下短深梁位移数值计算精度的研究

分析了短深梁位移的基本解，评述了有限元解法中关于高次分布力简化为节点力的问题。使用虚功原理和位移线性插值推导了满足二次分布力作用的精确节点力分配公式。通过矩形截面悬臂梁自由终端受集中载荷的算例，阐明了提高短深梁位移计算精度的途径。     

On Some Classical Methods to Improve Algebraic Curves and Surfaces

First, a modern presentation of the theory of the Halphen transform is given. This method associates to a plane projective curve C, once a general conic has been chosen, another birationally equivalent plane curve, whose singularities are simpler than those of C. Repeating, a curve is obtained whose only singularities are nodes. Next, it is studied how to apply this process to a family of plane curves. With this technique it is possible to transform a given family (with irreducible general member) into one where, generically, the curves are nodal. Finally, it is studied a similar process, called the Halphen–Picard transformation, for surfaces in three-space. By suitably reiterating this procedure, a surface can be transformed into a birationally equivalent one (in the same projective space), such that the sections with planes in a general pencil are, generically, nodal curves.     

Routing problems: A bibliography

This bibliography contains 500 references on four classical routing problems: the Traveling Salesman Problem, the Vehicle Routing Problem, the Chinese Postman Problem, and the Rural Postman Problem. References are presented alphabetically under a number of subheadings.     

Analysis of identification methods of key nodes in transportation network

The identification of key nodes plays an important role in improving the robustness of the transportation network. For different types of transportation networks, the effect of the same identification method may be different. It is of practical significance to study the key nodes identification methods corresponding to various types of transportation networks. Based on the knowledge of complex networks, the metro networks and the bus networks are selected as the objects, and the key nodes are identified by the node degree identification method, the neighbor node degree identification method, the weighted k-shell degree neighborhood identification method (KSD), the degree k-shell identification method (DKS), and the degree k-shell neighborhood identification method (DKSN). Take the network efficiency and the largest connected subgraph as the effective indicators. The results show that the KSD identification method that comprehensively considers the elements has the best recognition effect and has certain practical significance.     

Potential of magnetic resonance spectroscopy to detect metastasis in axillary lymph nodes in breast cancer

Focused pathological evaluation of axillary lymph nodes in breast cancer is gaining importance. Nuclear magnetic resonance (NMR) spectroscopy that assesses the whole of the specimen has the potential in evaluating micrometastases. The biochemical changes associated with breast cancer metastases in axillary nodes by in vitro NMR and its use in the detection of axillary metastases in a clinical setting in comparison with conventional histopathology is presented in this study. Eighty-eight lymph nodes obtained from 30 patients with breast cancer were investigated. Histopathology revealed metastases in 20 nodes from 11 patients, while in vitro NMR spectroscopy revealed metastases in 22 nodes. Out of these 22 nodes, 16 were the same, which showed metastases on histopathology, while 6 nodes have shown metastases only on in vitro magnetic resonance spectroscopy (MRS). These 6 nodes with suspicion of metastases on MRS were subjected to reevaluation with serial sectioning and immunohistochemistry, but no additional metastases were revealed. Forty metabolites could be identified from the MR spectrum of lymph nodes. The levels of the glycerophosphocholine-phosphocholine (GPC-PC), choline, lactate, alanine and uridine diphosphoglucose were elevated significantly in nodes with metastases. In addition, the intensity ratio of GPC-PC/threonine (Thr) was higher in nodes with metastases, and using this as marker, MRS detected the axillary metastases with a sensitivity, specificity and accuracy of 80%, 91% and 88%, respectively. Neoadjuvant chemotherapy (NACT) lowered the concentrations of GPC-PC and GPC-PC/Thr ratio. The accuracy of MRS in detecting metastases was 75% in patients who received NACT (n=9) as compared to 96% in those who did not (n=21). Our results demonstrate the potential of in vitro MRS in characterizing the metabolite profile of the axillary nodes with breast cancer metastases. It detected axillary metastases with reasonable accuracy and can be complementary to histopathological evaluation and immunohistochemistry.