Use Multilevel Graph Partitioning Scheme to solve traveling salesman problem

The traveling salesman problem is although looking very simple problem but it is an important combinatorial problem. In this thesis I have tried to find the shortest distance tour in which each city is visited exactly one time and return to the starting city. I have tried to solve traveling salesman problem using multilevel graph partitioning approach.Although traveling salesman problem itself very difficult as this problem is belong to the NP-Complete problems but I have tried my best to solve this problem using multilevel graph partitioning it also belong to the NP-Complete problems. I have solved this thesis by using the k-mean partitioning algorithm which divides the problem into multiple partitions and solving each partition separately and its solution is used to improve the overall tour by applying Lin Kernighan algorithm on it. Through all this I got optimal solution which proofs that solving traveling salesman problem through graph partition scheme is good for this NP-Problem and through this we can solved this intractable problem within few minutes.Keywords: Graph Partitioning Scheme, Traveling Salesman Problem.

Localization in splitting of matter waves

In this paper we present an analysis of how matter waves, guided as propagating modes in potential structures, are split under adiabatic conditions. The description is formulated in terms of localized states obtained through a unitary transformation acting on the mode functions. The mathematical framework results in coupled propagation equations that are decoupled in the asymptotic regions as well before as after the split. The resulting states have the advantage of describing propagation in situations, for instance matter-wave interferometers, where local perturbations make the transverse modes of the guiding potential unsuitable as a basis. The different regimes of validity of adiabatic propagation schemes based on localized versus delocalized basis states are also outlined. Nontrivial dynamics for superposition states propagating through split potential structures is investigated through numerical simulations. For superposition states the influence of longitudinal wave-packet extension on the localization is investigated and shown to be accurately described in quantitative terms using the adiabatic formulations presented here.

Biomarkers of extracellular matrix metabolism (MMP-9 and TIMP-1) and risk of stroke, myocardial infarction and cause-specific mortality : cohort study

Objective: Turnover of the extracellular matrix in all solid organs is governed mainly by a balance between the degrading matrix metalloproteinases (MMPs) and their tissue inhibitors (TIMPs). An altered extracellular matrix metabolism has been implicated in a variety of diseases. We investigated relations of serum levels of MMP-9 and TIMP-1 to mortality risk from an etiological perspective. Design: The prospective Uppsala Longitudinal Study of Adult Men (ULSAM) cohort, followed from 1991–1995 for up to 18.1 years. A random population-based sample of 1,082 71-year-old men, no loss to follow-up. Endpoints were all-cause (n = 628), cardiovascular (n = 230), non-cardiovascular (n = 398) and cancer mortality (n = 178), and fatal or non-fatal myocardial infarction (n = 138) or stroke (n = 163). Results: Serum MMP-9 and TIMP-1 levels were associated with risk of all-cause mortality (Cox proportional hazard ratio [HR] per standard deviation 1.10, 95% confidence interval [CI] 1.03–1.19; and 1.11, 1.02–1.20; respectively). TIMP-1 levels were mainly related to risks of cardiovascular mortality and stroke (HR per standard deviation 1.22, 95% CI 1.09–1.37; and 1.18, 1.04–1.35; respectively). All relations except those of TIMP-1 to stroke risk were attenuated by adjustment for cardiovascular disease risk factors. Relations in a subsample without cardiovascular disease or cancer were similar to those in the total sample. Conclusion: In this community-based cohort of elderly men, serum MMP-9 and TIMP-1 levels were related to mortality risk. An altered extracellular matrix metabolism may be involved in several detrimental pathways, and circulating MMP-9 or TIMP-1 levels may be relevant markers thereof.

Estimation of Parameters in Random Effect Models with Incidence Matrix Uncertainty

Random effect models have been widely applied in many fields of research. However, models with uncertain design matrices for random effects have been little investigated before. In some applications with such problems, an expectation method has been used for simplicity. This method does not include the extra information of uncertainty in the design matrix is not included. The closed solution for this problem is generally difficult to attain. We therefore propose an two-step algorithm for estimating the parameters, especially the variance components in the model. The implementation is based on Monte Carlo approximation and a Newton-Raphson-based EM algorithm. As an example, a simulated genetics dataset was analyzed. The results showed that the proportion of the total variance explained by the random effects was accurately estimated, which was highly underestimated by the expectation method. By introducing heuristic search and optimization methods, the algorithm can possibly be developed to infer the 'model-based' best design matrix and the corresponding best estimates.

Assessing the physical environment of older people’s residential care facilities: development of the Swedish version of the Sheffield Care Environment Assessment Matrix (S-SCEAM)

Background There is emerging evidence that the physical environment is important for health, quality of life and care, but there is a lack of valid instruments to assess health care environments. The Sheffield Care Environment Assessment Matrix (SCEAM), developed in the United Kingdom, provides a comprehensive assessment of the physical environment of residential care facilities for older people. This paper reports on the translation and adaptation of SCEAM for use in Swedish residential care facilities for older people, including information on its validity and reliability. Methods SCEAM was translated into Swedish and back-translated into English, and assessed for its relevance by experts using content validity index (CVI) together with qualitative data. After modification, the validity assessments were repeated and followed by test-retest and inter-rater reliability tests in six units within a Swedish residential care facility that varied in terms of their environmental characteristics. Results Translation and back translation identified linguistic and semantic related issues. The results of the first content validity analysis showed that more than one third of the items had item-CVI (I-CVI) values less than the critical value of 0.78.  After modifying the instrument, the second content validation analysis resulted in I-CVI scores above 0.78, the suggested criteria for excellent content validity. Test-retest reliability showed high stability (96% and 95% for two independent raters respectively), and inter-rater reliability demonstrated high levels of agreement (95% and 94% on two separate rating occasions). Kappa values were very good for test-retest (κ= 0.903 and 0.869) and inter-rater reliability (κ= 0.851 and 0.832). Conclusions Adapting an instrument to a domestic context is a complex and time-consuming process, requiring an understanding of the culture where the instrument was developed and where it is to be used. A team, including the instrument’s developers, translators, and researchers is necessary to ensure a valid translation and adaption. This study showed preliminary validity and reliability evidence for the Swedish version (S-SCEAM) when used in a Swedish context. Further, we believe that the S-SCEAM has improved compared to the original instrument and suggest that it can be used as a foundation for future developments of the SCEAM model.