407 research outputs found

    The Markov chain tree theorem and the state reduction algorithm in commutative semirings

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    We extend the Markov chain tree theorem to general commutative semirings, and we generalize the state reduction algorithm to commutative semifields. This leads to a new universal algorithm, whose prototype is the state reduction algorithm which computes the Markov chain tree vector of a stochastic matrix.Comment: 13 page

    Stability and Spectral Properties in the Max Algebra with Applications in Ranking Schemes

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    This thesis is concerned with the correspondence between the max algebra and non-negative linear algebra. It is motivated by the Perron-Frobenius theory as a powerful tool in ranking applications. Throughout the thesis, we consider max-algebraic versions of some standard results of non-negative linear algeb- ra. We are specifically interested in the spectral and stability properties of non-negative matrices. We see that many well-known theorems in this context extend to the max algebra. We also consider how we can relate these results to ranking applications in decision making problems. In particular, we focus on deriving ranking schemes for the Analytic Hierarchy Process (AHP). We start by describing fundamental concepts that will be used throughout the thesis after a general introduction. We also state well-known results in both non-negative linear algebra and the max algebra. We are next interested in the characterisation of the spectral properties of mat- rix polynomials. We analyse their relation to multi-step difference equations. We show how results for matrix polynomials in the conventional algebra carry over naturally to the max-algebraic setting. We also consider an extension of the so-called Fundamental Theorem of Demography to the max algebra. Using the concept of a multigraph, we prove that a number of inequalities related to the spectral radius of a matrix polynomial are also true for its largest max eigenvalue. We are next concerned with the asymptotic stability of non-negative matrices in the context of dynamical systems. We are motivated by the relation of P-matrices and positive stability of non-negative matrices. We discuss how equivalent conditions connected with this relation echo similar results over the max algebra. Moreover, we consider extensions of the properties of sets of P-matrices to the max algebra. In this direction, we highlight the central role of the max version of the generalised spectral radius. We then focus on ranking applications in multi-criteria decision making prob- lems. In particular, we consider the Analytic Hierarchy Process (AHP) which is a method to deal with these types of problems. We analyse the classical Eigenvalue Method (EM) for the AHP and its max-algebraic version for the single criterion case. We discuss how to treat multiple criteria within the max-algebraic framework. We address this generalisation by considering the multi-criteria AHP as a multi-objective optimisation problem. We consider three approaches within the framework of multi-objective optimisation, and use the optimal solution to provide an overall ranking scheme in each case. We also study the problem of constructing a ranking scheme using a combi- natorial approach. We are inspired by the so-called Matrix Tree Theorem for Markov Chains. It connects the spectral theory of non-negative matrices with directed spanning trees. We prove that a similar relation can be established over the max algebra. We consider its possible applications to decision making problems. Finally, we conclude with a summary of our results and suggestions for future extensions of these

    Predictive Importance of Ultrasonography and Anti-Thyroid Antibodies in the Management of Thyroid Nodules in Indeterminate Cytology

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    Objectives: The aim of this study is to examine the effects of ultrasonography and serum anti-thyroid antibody (ATAb)levels in predicting malignancy in cases where molecular tests cannot be performed in indeterminate thyroid nodules. Methods: Ultrasonographic features of the dominant thyroid nodule of a total of 228 patients who were operated for nodular goiter were analyzed and preoperative serum ATAb levels were examined. Especially in Bethesda category 3 nodules correlation of these parameters with malignancy rates and Hashimoto’s thyroiditis (HT) was investigated. Results: Malignancy was detected in 24.5% (12/49) Bethesda Category 3 nodules. Anti-thyroglobulin (Anti-TG) and-or anti-thyroid peroxidase (anti-TPO) positivity in serum 36.5% (72/197) was correlated with histopathologically proven HT (p=0.001). Poor prognostic factors were found to be less common in HT-associated papillary thyroid cancer (PTC). Ultrasonographic characteristics such as hypoechogenicity, microcalcification, and border irregularity were significant in predicting malignancy in indeterminate nodules (p=0.038- 0.003- 0.004, respectively). The central vascularization pattern remained in the background compared to other parameters (p=0.059). In the presence of ultrasonographic halo, 92.7% (51/55) of the nodules were benign (p=0.001). Conclusion: In the management of thyroid nodules in indeterminate cytology, suspicious ultrasonographic features and Hashimoto's thyroiditis should be encouraging in making the surgical decision

    Experience with 3-D composite grids

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    Experience with the three-dimensional (3-D), chimera grid embedding scheme is described. Applications of the inviscid version to a multiple-body configuration, a wind/body/tail configuration, and an estimate of wind tunnel wall interference are described. Applications to viscous flows include a 3-D cavity and another multi-body configuration. A variety of grid generators is used, and several embedding strategies are described

    On applications of chimera grid schemes to store separation

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    A finite difference scheme which uses multiple overset meshes to simulate the aerodynamics of aircraft/store interaction and store separation is described. In this chimera, or multiple mesh, scheme, a complex configuration is mapped using a major grid about the main component of the configuration, and minor overset meshes are used to map each additional component such as a store. As a first step in modeling the aerodynamics of store separation, two dimensional inviscid flow calculations were carried out in which one of the minor meshes is allowed to move with respect to the major grid. Solutions of calibrated two dimensional problems indicate that allowing one mesh to move with respect to another does not adversely affect the time accuracy of an unsteady solution. Steady, inviscid three dimensional computations demonstrate the capability to simulate complex configurations, including closely packed multiple bodies

    The Analytic Hierarchy Process, Max Algebra and Multi-objective Optimisation

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    The Analytic Hierarchy Process (AHP) is widely used for decision making involving multiple criteria. Elsner and van den Driessche introduced a max-algebraic approach to the single criterion AHP. We extend this to the multi-criteria AHP, by considering multi-objective generalisations of the single objective optimisation problem solved in these earlier papers. We relate the existence of globally optimal solutions to the commutativity properties of the associated matrices; we relate min-max optimal solutions to the generalised spectral radius; and we prove that Pareto optimal solutions are guaranteed to exist.Comment: 1 figur

    Platelet-lymphocyte ratio predicts poor prognosis in stage II / III colon and rectum cancer

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    Objective: There is an increasing number of studies in the literature reporting that serum platelet/lymphocyte ratio (PLR) can provide useful prognostic data for various cancers. In the present study, the effects of platelet-lymphocyte ratio on survival in stage II/III colorectal cancers (CRC) were examined. Material and Method:A total of 106 Stage II/III CRC patients who underwent curative surgery 2015-2020 were included in the study. Emergency cases and patients diagnosed with other than adenocarcinoma were excluded from the study. The demographic data of the patients, preoperative imaging and laboratory results, postoperative pathology reports, and patient follow-up examination data were obtained from hospital records. The relations between demographic, histopathological, hematological values and the prognosis was analyzed in terms of statistical significance. Results:Among the 106 patients, 62 (58.5%) were male and 44 (41.5%) were female. The mean age was 64.3±12.01 (23-89). The mean follow-up period was calculated as 24.6±15.8 (2-63) months. When the pathology reports were reviewed, it was found that the mean tumor diameter was 5.3±2.33 cm (2-17) and the mean metastatic lymph node was 1.8±2.4 (0-10). The PLR ratio was determined as a poor prognostic factor affecting survival in the cox regression analysis, in which preoperative complete blood count, c-reactive protein and albumin values, neutrophil-lymphocyte ratio (NLR), lymphocyte-monocyte ratio (LMR), and PLR were compared, and was separated from other variables (P=0.002 CI= 95%). When variables such as age, clinical stage, and tumor diameter were included in the model, PLR was similarly found to be an important predictive variable (P= 0.002). When only NLR, LMR, and PLR were evaluated, PLR again came to the forefront with a significance value of P=0.01. Also, high neutrophil count, increased platelet distribution volume (PDW), advanced age, and perineural invasion (PNI) were found to be significant factors in predicting poor prognosis. Conclusions: High PLR is a poor prognostic factor for CRC patients. For this reason, it may be necessary to follow a more aggressive strategy in the management of postoperative treatment in patients who have high PLR

    Summary Findings from the AVT-191 Project to Assess Sensitivity Analysis and Uncertainty Quantification Methods for Military Vehicle Design

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    A NATO symposium held in Greece in 2008 identified many promising sensitivity analysis and uncertainty quantification technologies, but the maturity and suitability of these methods for realistic applications was not clear. The NATO Science and Technology Organization, Task Group AVT-191 was established to evaluate the maturity and suitability of various sensitivity analysis and uncertainty quantification methods for application to realistic vehicle development problems. The program ran from 2011 to 2015, and the work was organized into four discipline-centric teams: external aerodynamics, internal aerodynamics, aeroelasticity, and hydrodynamics. This paper summarizes findings and lessons learned from the task group

    A Monte Carlo study of the three-dimensional Coulomb frustrated Ising ferromagnet

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    We have investigated by Monte-Carlo simulation the phase diagram of a three-dimensional Ising model with nearest-neighbor ferromagnetic interactions and small, but long-range (Coulombic) antiferromagnetic interactions. We have developed an efficient cluster algorithm and used different lattice sizes and geometries, which allows us to obtain the main characteristics of the temperature-frustration phase diagram. Our finite-size scaling analysis confirms that the melting of the lamellar phases into the paramgnetic phase is driven first-order by the fluctuations. Transitions between ordered phases with different modulation patterns is observed in some regions of the diagram, in agreement with a recent mean-field analysis.Comment: 14 pages, 10 figures, submitted to Phys. Rev.

    Digital Twin of a Wheeled Service Robot

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    Bakalářská práce se zabývá vytvořením digitálního dvojčete robotu. V úvodu je seznámení se stavebnicí Bioloid Robotis STEM a s jednotlivými kolovými roboty. Pokračuje vytvoření 3D modelu jednoho z robotů a vytvoření jeho zjednodušeného 3D modelu. K simulaci vzorové úlohy je využit program CoppeliaSim. Po přenesení modelů a přidání motorů a senzorů je robot naprogramován pro splnění úlohy, která se dále odzkouší na robotu sestaveném ze stavebnice, čím se porovná chování robotu v simulaci s realitou.The bachelor's thesis deals with the creation of a digital robot twin. The introduction introduces the Bioloid Robotis STEM kit and the individual wheeled robots. The creation of a 3D model of one of the robots and the creation of his simplified 3D model. CoppeliaSim is used to simulate a sample task. After transferring the models and adding motors and sensors, the robot is programmed to complete the task, which is further tested on a robot assembled from a kit, which helps as compare the behavior of the robot in the simulation with reality.354 - Katedra robotikydobř
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