A recent line of works established a remarkable connection for antiferromagnetic 2-spin systems, including the Ising and hard-core models, showing that the computational complexity of approximating the partition function for graphs with maximum degree \Delta undergoes a computational transition that coincides with the statistical physics uniqueness/non-uniqueness phase transition on the infinite \Delta-regular tree. Despite this clear picture for 2-spin systems, there is little known for multi-spin systems. We present the first analog of the above inapproximability results for multi-spin systems. The main difficulty in previous inapproximability results was analyzing the behavior of the model on random \Delta-regular bipartite graphs, which served as the gadget in the reduction. To this end one needs to understand the moments of the partition function. Our key contribution is connecting: (i) induced matrix norms, (ii) maxima of the expectation of the partition function, and (iii) attractive fixed points of the associated tree recursions (belief propagation). We thus obtain a generic analysis of the Gibbs distribution of any multi-spin system on random regular bipartite graphs. We also treat in depth the k-colorings and the q-state antiferromagnetic Potts models. Based on these findings, we prove that for \Delta constant and even k<\Delta, it is NP-hard to approximate within an exponential factor the number of k-colorings on triangle-free \Delta-regular graphs. We also prove an analogous statement for the antiferromagnetic Potts model. Our hardness results for these models complement the conjectured regime where the models are believed to have efficient approximation schemes. We systematize the approach to obtain a general theorem for the computational hardness of counting in antiferromagnetic spin systems, which we ultimately use to obtain the inapproximability results for the k-colorings and q-state antiferromagnetic Potts models, as well as (the previously known results for) antiferromagnetic 2-spin systems. The criterion captures in an appropriate way the statistical physics uniqueness phase transition on the tree.

Physiologically based pharmacokinetic (PBPK) modeling is a tool used in drug discovery and human health risk assessment. PBPK models are mathematical representations of the anatomy, physiology and biochemistry of an organism. PBPK models, using both compound and physiologic inputs, are used to predict a drug’s pharmacokinetics in various situations. Tissue to plasma partition coefficients (Kp), a key PBPK model input, define the steady state concentration differential between the tissue and plasma and are used to predict the volume of distribution. Experimental determination of these parameters once limited the development of PBPK models however in silico prediction methods were introduced to overcome this issue. The developed algorithms vary in input parameters and prediction accuracy and none are considered standard, warranting further research. Chapter 2 presents a newly developed Kp prediction algorithm that requires only readily available input parameters. Using a test dataset, this Kp prediction algorithm demonstrated good prediction accuracy and greater prediction accuracy than preexisting algorithms. Chapter 3 introduced a decision tree based Kp prediction method. In this novel approach, six previously published algorithms, including the one developed in Chapter 2, were utilized. The aim of the developed classifier was to identify the most accurate tissue-specific Kp prediction algorithm for a new drug. A dataset consisting of 122 drugs was used to train the classifier and identify the most accurate Kp prediction algorithm for a certain physico-chemical space. Three versions of tissue specific classifiers were developed and were dependent on the necessary inputs. The use of the classifier resulted in a better prediction accuracy as compared to the use of any single Kp prediction algorithm for all tissues; the current mode of use in PBPK model building. With built-in estimation equations for those input parameters not necessarily available, this Kp prediction tool will provide Kp prediction when only limited input parameters are available. The two presented innovative methods will improve tissue distribution prediction accuracy thus enhancing the confidence in PBPK modeling outputs.

Thesis (M.S.)--Ohio University, August, 1997. / Title from PDF t.p.

Thesis (doctoral)--Universität Breslau.

Stuttgart, Univ., Studienarb., 2003.

University, Diss., 2000--Dortmund. / Dateiformat: PDF.

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 362-371). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 194-205). Available also in a digital version from Dissertation Abstracts.

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