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Uniform distributions in a class of convex polyhedrons with applications to drug combination studies

Guo-Liang Tian, Hong-Bin Fang, Ming Tan, Hong Qin, Man-Lai Tang
2009 Journal of Multivariate Analysis  
In addition, we develop methods for generating uniform distributions in a class of convex polyhedrons in n-dimensional Euclidean space R n .  ...  In particular, SRs for uniform distributions in regions with order restrictions are presented. We apply the proposed method to the experimental design for a drug combination study.  ...  Particular applications in a drug combination study are presented. The proposed methods could be extended to generating uniform distributions in other convex polyhedrons such as a hexahedron in R 3 .  ... 
doi:10.1016/j.jmva.2009.02.011 fatcat:aqe4wjcdavgj5k6bqlcfkibsya

Simulation of polyhedral convex contoured distributions

Wolf-Dieter Richter, Kay Schicker
2017 Journal of Statistical Distributions and Applications  
from the literature, and applied to drug combination studies.  ...  Based upon a stochastic representation, the method is extended to the general class of polyhedral convex contoured distributions of known dimension.  ...  Acknowledgement The authors are grateful to a referee who provided valuable suggestions on improving the paper and an additional recent reference, and declare that they have no competing interests in the  ... 
doi:10.1186/s40488-017-0055-6 fatcat:za36jv5qmveplkuh5czbqoge7a

Dose and Sample Size Determination for Multi-Drug Combination Studies

Ming T. Tan, Hong-Bin Fang, Guo-Liang Tian
2009 Statistics in Biopharmaceutical Research  
Using the general methodology, we derive the combinations and sample size specifically for a common class of drugs to derive the experimental design.  ...  In addition, we illustrate the method with the SAHA and Ara-C and Etoposide combination studies.  ...  Ross, MD, Ph.D. for inclusion of the SAHA combination study as an example.  ... 
doi:10.1198/sbr.2009.0029 fatcat:tlllzvjkhzc2ldvwf66je46sqq

''On the Shoulders of Giants'' A brief excursion into the history of mathematical programming

Rainer Tichatschke
2012 Discussiones Mathematicae Differential Inclusions Control and Optimization  
But, in contrast to other branches of mathematics, we don't have to dig too deeply into the past centuries to find their roots.  ...  Similar to many mathematical fields also the topic of mathematical programming has its origin in applied problems.  ...  Acknowledgement I would like to express my gratitude to V.F. Demyanov who provided me with some photos of Russian mathematicians from his collection Faces and Places.  ... 
doi:10.7151/dmdico.1140 fatcat:c2eeah57kbgddg35dqg4ftznbq

Spherical Distance Metrics Applied to Protein Structure Classification [article]

James DeFelice, Vicente M. Reyes
2015 arXiv   pre-print
Structural relationships among proteins are important in the study of their evolution as well as in drug design and development.  ...  In this respect, the combination of geometric models with MDI has been shown to be effective.  ...  Begin with a rhombic triacontahedron (convex polyhedron, 30 faces, each face a rhombus); 2. surround the polyhedron with a sphere; 3. recursively apply the following steps: (a) project all vertices of  ... 
arXiv:1602.08079v1 fatcat:znqtuf3ag5bwhfm73zhctiwku4

Static analysis for probabilistic programs

Sriram Sankaranarayanan, Aleksandar Chakarov, Sumit Gulwani
2013 Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation - PLDI '13  
Each path yields interval bounds that can be summed up with a "coverage" bound to yield an interval that encloses the probability of assertion for the program as a whole.  ...  The queries are evaluated over each path by a combination of symbolic execution and probabilistic volumebound computations.  ...  All opinions expressed are those of the authors and not necessarily of the NSF.  ... 
doi:10.1145/2491956.2462179 dblp:conf/pldi/SankaranarayananCG13 fatcat:5l7vkdhtgjhspn7r5ouitebhv4

Tropical Geometry of Phylogenetic Tree Space: A Statistical Perspective [article]

Anthea Monod, Bo Lin, Ruriko Yoshida, Qiwen Kang
2021 arXiv   pre-print
studies in probability and statistics.  ...  They are also objects of interest in pure mathematics, such as algebraic geometry and combinatorics, due to their discrete geometry.  ...  The authors would also like to acknowledge the GI-SAID EpiFlu TM initiative for making the data used in this study publicly available. R.Y. is supported in part by NSF DMS #1622369 and #1916037.  ... 
arXiv:1805.12400v7 fatcat:yf6mtwxxrff27lqttc7pzhcq3q

Machine learning approach for structure-based zeolite classification

D. Andrew Carr, Mohammed Lach-hab, Shujiang Yang, Iosif I. Vaisman, Estela Blaisten-Barojas
2009 Microporous and Mesoporous Materials  
The ZSP is able to obtain classification in this multitude of classes with more than 81% of correctly classified instances based on framework type.  ...  This study is aimed at combining computational geometry methods with machine learning algorithms for classification of inorganic solid materials of known structure.  ...  We acknowledge interesting discussions with Prof. John Schreifels of GMU. EBB acknowledges useful discussions with Dr. V. Karen of NIST.  ... 
doi:10.1016/j.micromeso.2008.07.027 fatcat:phizevczonfa3cfdza6np2gyty

Buckling-induced encapsulation of structured elastic shells under pressure

J. Shim, C. Perdigou, E. R. Chen, K. Bertoldi, P. M. Reis
2012 Proceedings of the National Academy of Sciences of the United States of America  
We are grateful to Zorana Zeravcic for helpful discussions, and to Harvard School of Engineering and Applied Sciences Academic Computing for their support.  ...  Mathematically, these mechanical constraints can be rephrased as follows: The skeleton of the Buckliball should (a′) be a convex uniform polyhedra, excluding the dihedral symmetry group (i.e., Platonic  ...  As an example, the Venus flytrap combines a swelling mechanism with buckling behavior to increase the speed of leaf motility (14, 15) .  ... 
doi:10.1073/pnas.1115674109 pmid:22451901 pmcid:PMC3341048 fatcat:6ubmqkuy75frveatcf6xt3a67i

Learning binary relations and total orders

S.A. Goldman, R.L. Rivest, R.E. Schapire
1989 30th Annual Symposium on Foundations of Computer Science  
according to a uniform probability distribution on the instance space.  ...  The problem of learning a binary relation between two sets of objects or between a set and itself is studied.  ...  algorithm based on approximate and probabilistic counting and also suggested the problem of learning a total order on n elements.  ... 
doi:10.1109/sfcs.1989.63454 dblp:conf/focs/GoldmanRS89 fatcat:47gaxdfpxzetpjf32aahfvgsyy

Learning Binary Relations and Total Orders

Sally A. Goldman, Ronald L. Rivest, Robert E. Schapire
1993 SIAM journal on computing (Print)  
according to a uniform probability distribution on the instance space.  ...  The problem of learning a binary relation between two sets of objects or between a set and itself is studied.  ...  algorithm based on approximate and probabilistic counting and also suggested the problem of learning a total order on n elements.  ... 
doi:10.1137/0222062 fatcat:foleasvsz5dwnbkt5dqqavi3km

Optical and mechanical properties of streptavidin-conjugated gold nanospheres through data mining techniques

Simone Peli, Andrea Ronchi, Giada Bianchetti, Francesco Rossella, Claudio Giannetti, Marcella Chiari, Pasqualantonio Pingue, Francesco Banfi, Gabriele Ferrini
2020 Scientific Reports  
The aim is to monitor their optical response in complex chemical environments that may be experienced in, e.g., photothermal therapy or drug delivery applications.  ...  Nanospheres with different surface densities have been deposited and exposed to a plasma treatment to modify their polymer binding chains.  ...  to uniform particle-in-polymer systems 56 .  ... 
doi:10.1038/s41598-020-72534-1 pmid:33004805 fatcat:s2wf2nvyxnbmhlqyjwspcdeuxu

Towards Human Cell Simulation [chapter]

Simone Spolaor, Marco Gribaudo, Mauro Iacono, Tomas Kadavy, Zuzana Komínková Oplatková, Giancarlo Mauri, Sabri Pllana, Roman Senkerik, Natalija Stojanovic, Esko Turunen, Adam Viktorin, Salvatore Vitabile (+2 others)
2019 Msphere  
Though, even with a candidate parameterization, the simulation of mechanistic models could be challenging due to the extreme computational effort required.  ...  Although mathematical models that describe the interactions among all biochemical processes in a cell are theoretically feasible, their simulation is generally hard because of a variety of reasons.  ...  This chapter is also based upon work from COST Action CA15140 "Improving Applicability of Nature-Inspired Optimisation by Joining Theory and Practice (ImAppNIO)" supported by COST.  ... 
doi:10.1007/978-3-030-16272-6_8 fatcat:qpkryzcgpbec7nsgyndw5xpj7q

Learning Binary Relations and Total Orders [chapter]

Sally A. Goldman, Ronald L. Rivest, Robert E. Schapire
1989 Proceedings of the Second Annual Workshop on Computational Learning Theory  
according to a uniform probability distribution on the instance space.  ...  We study the problem of learning a binary relation between two sets of objects or between a set and itself.  ...  idea of using an approximate halving algorithm based on approximate and probabilistic 5 We note that William Chen 7] has recently extended the projective geometry argument to obtain a lower bound of  ... 
doi:10.1016/b978-0-08-094829-4.50034-9 fatcat:4tgt2vcm7baipiwaovwuacyzde

Scalable computation of intracellular metabolite concentrations [article]

Amir Akbari, Bernhard O. Palsson
2020 arXiv   pre-print
These concentrations are constrained within physiologically possible ranges to enable an organism to grow in extreme conditions and adapt to its environment.  ...  We then compare their performance in two case studies, showing that the global-optimization formulation exhibits more desirable scaling properties than the random-sampling and polynomial-optimization formulation  ...  At each grid point, the volume is estimated by generating 10 8 random points with a uniform distribution in a bounding box.  ... 
arXiv:2008.05568v1 fatcat:cziscc2ulna2hhylpx6fqdvjtu
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