Introduction to combinatorial geometry
International Nuclear Information System (INIS)
Gabriel, T.A.; Emmett, M.B.
1985-01-01
The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity
International Nuclear Information System (INIS)
Cullen, D.E
2000-01-01
TART2000 is a coupled neutron-photon, 3 Dimensional, combinatorial geometry, time dependent Monte Carlo radiation transport code. This code can run on any modern computer. It is a complete system to assist you with input Preparation, running Monte Carlo calculations, and analysis of output results. TART2000 is also incredibly FAST; if you have used similar codes, you will be amazed at how fast this code is compared to other similar codes. Use of the entire system can save you a great deal of time and energy. TART2000 is distributed on CD. This CD contains on-line documentation for all codes included in the system, the codes configured to run on a variety of computers, and many example problems that you can use to familiarize yourself with the system. TART2000 completely supersedes all older versions of TART, and it is strongly recommended that users only use the most recent version of TART2000 and its data files
Cullen, D
2000-01-01
TART2000 is a coupled neutron-photon, 3 Dimensional, combinatorial geometry, time dependent Monte Carlo radiation transport code. This code can run on any modern computer. It is a complete system to assist you with input Preparation, running Monte Carlo calculations, and analysis of output results. TART2000 is also incredibly FAST; if you have used similar codes, you will be amazed at how fast this code is compared to other similar codes. Use of the entire system can save you a great deal of time and energy. TART2000 is distributed on CD. This CD contains on-line documentation for all codes included in the system, the codes configured to run on a variety of computers, and many example problems that you can use to familiarize yourself with the system. TART2000 completely supersedes all older versions of TART, and it is strongly recommended that users only use the most recent version of TART2000 and its data files.
Combinatorial geometry in the plane
Hadwiger, Hugo; Klee, Victor
2014-01-01
Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa
MIFT: GIFT Combinatorial Geometry Input to VCS Code
1977-03-01
r-w w-^ H ^ß0318is CQ BRL °RCUMr REPORT NO. 1967 —-S: ... MIFT: GIFT COMBINATORIAL GEOMETRY INPUT TO VCS CODE Albert E...TITLE (and Subtitle) MIFT: GIFT Combinatorial Geometry Input to VCS Code S. TYPE OF REPORT & PERIOD COVERED FINAL 6. PERFORMING ORG. REPORT NUMBER...Vehicle Code System (VCS) called MORSE was modified to accept the GIFT combinatorial geometry package. GIFT , as opposed to the geometry package
Combinatorial algebraic geometry selected papers from the 2016 apprenticeship program
Sturmfels, Bernd
2017-01-01
This volume consolidates selected articles from the 2016 Apprenticeship Program at the Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that ran from July through December of 2016. Written primarily by junior mathematicians, the articles cover a range of topics in combinatorial algebraic geometry including curves, surfaces, Grassmannians, convexity, abelian varieties, and moduli spaces. This book bridges the gap between graduate courses and cutting-edge research by connecting historical sources, computation, explicit examples, and new results.
From combinatorial optimization to real algebraic geometry and back
Directory of Open Access Journals (Sweden)
Janez Povh
2014-12-01
Full Text Available In this paper, we explain the relations between combinatorial optimization and real algebraic geometry with a special focus to the quadratic assignment problem. We demonstrate how to write a quadratic optimization problem over discrete feasible set as a linear optimization problem over the cone of completely positive matrices. The latter formulation enables a hierarchy of approximations which rely on results from polynomial optimization, a sub-eld of real algebraic geometry.
Parameterized combinatorial geometry modeling in Moritz
International Nuclear Information System (INIS)
Van Riper, K.A.
2005-01-01
We describe the use of named variables as surface and solid body coefficients in the Moritz geometry editing program. Variables can also be used as material numbers, cell densities, and transformation values. A variable is defined as a constant or an arithmetic combination of constants and other variables. A variable reference, such as in a surface coefficient, can be a single variable or an expression containing variables and constants. Moritz can read and write geometry models in MCNP and ITS ACCEPT format; support for other codes will be added. The geometry can be saved with either the variables in place, for modifying the models in Moritz, or with the variables evaluated for use in the transport codes. A program window shows a list of variables and provides fields for editing them. Surface coefficients and other values that use a variable reference are shown in a distinctive style on object property dialogs; associated buttons show fields for editing the reference. We discuss our use of variables in defining geometry models for shielding studies in PET clinics. When a model is parameterized through the use of variables, changes such as room dimensions, shielding layer widths, and cell compositions can be quickly achieved by changing a few numbers without requiring knowledge of the input syntax for the transport code or the tedious and error prone work of recalculating many surface or solid body coefficients. (author)
Combinatorial geometry domain decomposition strategies for Monte Carlo simulations
Energy Technology Data Exchange (ETDEWEB)
Li, G.; Zhang, B.; Deng, L.; Mo, Z.; Liu, Z.; Shangguan, D.; Ma, Y.; Li, S.; Hu, Z. [Institute of Applied Physics and Computational Mathematics, Beijing, 100094 (China)
2013-07-01
Analysis and modeling of nuclear reactors can lead to memory overload for a single core processor when it comes to refined modeling. A method to solve this problem is called 'domain decomposition'. In the current work, domain decomposition algorithms for a combinatorial geometry Monte Carlo transport code are developed on the JCOGIN (J Combinatorial Geometry Monte Carlo transport INfrastructure). Tree-based decomposition and asynchronous communication of particle information between domains are described in the paper. Combination of domain decomposition and domain replication (particle parallelism) is demonstrated and compared with that of MERCURY code. A full-core reactor model is simulated to verify the domain decomposition algorithms using the Monte Carlo particle transport code JMCT (J Monte Carlo Transport Code), which has being developed on the JCOGIN infrastructure. Besides, influences of the domain decomposition algorithms to tally variances are discussed. (authors)
Combinatorial geometry domain decomposition strategies for Monte Carlo simulations
International Nuclear Information System (INIS)
Li, G.; Zhang, B.; Deng, L.; Mo, Z.; Liu, Z.; Shangguan, D.; Ma, Y.; Li, S.; Hu, Z.
2013-01-01
Analysis and modeling of nuclear reactors can lead to memory overload for a single core processor when it comes to refined modeling. A method to solve this problem is called 'domain decomposition'. In the current work, domain decomposition algorithms for a combinatorial geometry Monte Carlo transport code are developed on the JCOGIN (J Combinatorial Geometry Monte Carlo transport INfrastructure). Tree-based decomposition and asynchronous communication of particle information between domains are described in the paper. Combination of domain decomposition and domain replication (particle parallelism) is demonstrated and compared with that of MERCURY code. A full-core reactor model is simulated to verify the domain decomposition algorithms using the Monte Carlo particle transport code JMCT (J Monte Carlo Transport Code), which has being developed on the JCOGIN infrastructure. Besides, influences of the domain decomposition algorithms to tally variances are discussed. (authors)
KENO-IV/CG, the combinatorial geometry version of the KENO Monte Carlo criticality safety program
International Nuclear Information System (INIS)
West, J.T.; Petrie, L.M.; Fraley, S.K.
1979-09-01
KENO-IV/CG was developed to merge the simple geometry input description utilized by combinatorial geometry with the repeating lattice feature of the original KENO geometry package. The result is a criticality code with the ability to model a complex system of repeating rectangular lattices inside a complicated three-dimensional geometry system. Furthermore, combinatorial geometry was modified to differentiate between combinatorial zones describing a particular KENO BOX to be repeated in a KENO array and those combinatorial zones describing geometry external to an array. This allows the user to maintain a simple coordinate system without any geometric conflict due to spatial overlap. Several difficult criticality design problems have been solved with the new geometry package in KENO-IV/CG, thus illustrating the power of the code to model difficult geometries with a minimum of effort
International Nuclear Information System (INIS)
Azmy, Y. Y.
2004-01-01
An approach is developed for solving the neutron diffusion equation on combinatorial geometry computational cells, that is computational cells composed by combinatorial operations involving simple-shaped component cells. The only constraint on the component cells from which the combinatorial cells are assembled is that they possess a legitimate discretization of the underlying diffusion equation. We use the Finite Difference (FD) approximation of the x, y-geometry diffusion equation in this work. Performing the same combinatorial operations involved in composing the combinatorial cell on these discrete-variable equations yields equations that employ new discrete variables defined only on the combinatorial cell's volume and faces. The only approximation involved in this process, beyond the truncation error committed in discretizing the diffusion equation over each component cell, is a consistent-order Legendre series expansion. Preliminary results for simple configurations establish the accuracy of the solution to the combinatorial geometry solution compared to straight FD as the system dimensions decrease. Furthermore numerical results validate the consistent Legendre-series expansion order by illustrating the second order accuracy of the combinatorial geometry solution, the same as standard FD. Nevertheless the magnitude of the error for the new approach is larger than FD's since it incorporates the additional truncated series approximation. (authors)
International Nuclear Information System (INIS)
Burns, T.J.
1992-01-01
A graphical-based code system is being developed at ORNL to manipulate combinatorial geometries for radiation transport and shielding applications. The current version (basically a combinatorial geometry debugger) consists of two parts: a FORTRAN-based ''view'' generator and a Microsoft Windows application for displaying the geometry. Options and features of both modules are discussed. Examples illustrating the various options available are presented. The potential for utilizing the images produced using the debugger as a visualization tool for the output of the radiation transport codes is discussed as is the future direction of the development
COGEDIF - automatic TORT and DORT input generation from MORSE combinatorial geometry models
International Nuclear Information System (INIS)
Castelli, R.A.; Barnett, D.A.
1992-01-01
COGEDIF is an interactive utility which was developed to automate the preparation of two and three dimensional geometrical inputs for the ORNL-TORT and DORT discrete ordinates programs from complex three dimensional models described using the MORSE combinatorial geometry input description. The program creates either continuous or disjoint mesh input based upon the intersections of user defined meshing planes and the MORSE body definitions. The composition overlay of the combinatorial geometry is used to create the composition mapping of the discretized geometry based upon the composition found at the centroid of each of the mesh cells. This program simplifies the process of using discrete orthogonal mesh cells to represent non-orthogonal geometries in large models which require mesh sizes of the order of a million cells or more. The program was specifically written to take advantage of the new TORT disjoint mesh option which was developed at ORNL
Semiclassical quantum gravity: statistics of combinatorial Riemannian geometries
International Nuclear Information System (INIS)
Bombelli, L.; Corichi, A.; Winkler, O.
2005-01-01
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at ''quantum scales'' and continuum, classical geometries at large scales. Such a correspondence can be meaningfully established when one has a ''semiclassical'' state in the underlying quantum gravity theory, and the uncertainties in the correspondence arise both from quantum fluctuations in this state and from the kinematical procedure of matching a smooth geometry to a discrete one. We focus on the latter type of uncertainty, and suggest the use of statistical geometry as a way to quantify it. With a cell complex as an example of discrete structure, we discuss how to construct quantities that define a smooth geometry, and how to estimate the associated uncertainties. We also comment briefly on how to combine our results with uncertainties in the underlying quantum state, and on their use when considering phenomenological aspects of quantum gravity. (Abstract Copyright [2005], Wiley Periodicals, Inc.)
Solar proton exposure of an ICRU sphere within a complex structure Part I: Combinatorial geometry.
Wilson, John W; Slaba, Tony C; Badavi, Francis F; Reddell, Brandon D; Bahadori, Amir A
2016-06-01
The 3DHZETRN code, with improved neutron and light ion (Z≤2) transport procedures, was recently developed and compared to Monte Carlo (MC) simulations using simplified spherical geometries. It was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in general combinatorial geometry. A more complex shielding structure with internal parts surrounding a tissue sphere is considered and compared against MC simulations. It is shown that even in the more complex geometry, 3DHZETRN agrees well with the MC codes and maintains a high degree of computational efficiency. Published by Elsevier Ltd.
Solar Proton Transport within an ICRU Sphere Surrounded by a Complex Shield: Combinatorial Geometry
Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.
2015-01-01
The 3DHZETRN code, with improved neutron and light ion (Z (is) less than 2) transport procedures, was recently developed and compared to Monte Carlo (MC) simulations using simplified spherical geometries. It was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in general combinatorial geometry. A more complex shielding structure with internal parts surrounding a tissue sphere is considered and compared against MC simulations. It is shown that even in the more complex geometry, 3DHZETRN agrees well with the MC codes and maintains a high degree of computational efficiency.
Directory of Open Access Journals (Sweden)
Daniel Khoshnoudirad
2015-11-01
Full Text Available The aim of this work is to provide a complete characterization of a (m,n-cube. The latter are the pieces of discrete planes appearing in Theoretical Computer Science, Discrete Geometry and Combinatorics. This characterization in three dimensions is the exact equivalent of the preimage for a discrete segment as it has been introduced by McIlroy. Further this characterization, which avoids the redundancies, reduces the combinatorial problem of determining the cardinality of the (m,n-cubes to a new combinatorial problem consisting of determining the volumic regions formed by the crossing of planes. This work can find applications in Imaging, Vision, and pattern recognition for instance.
A Combinatorial Approach to Time Asymmetry
Directory of Open Access Journals (Sweden)
Martin Tamm
2016-03-01
Full Text Available In this paper, simple models for the multiverse are analyzed. Each universe is viewed as a path in a graph, and by considering very general statistical assumptions, essentially originating from Boltzmann, we can make the set of all such paths into a finite probability space. We can then also attempt to compute the probabilities for different kinds of behavior and in particular under certain conditions argue that an asymmetric behavior of the entropy should be much more probable than a symmetric one. This offers an explanation for the asymmetry of time as a broken symmetry in the multiverse. The focus here is on simple models which can be analyzed using methods from combinatorics. Although the computational difficulties rapidly become enormous when the size of the model grows, this still gives hints about how a full-scale model should behave.
Energy Technology Data Exchange (ETDEWEB)
Nakagawa, Takahiro; Ochiai, Katsuharu [Plant and System Planning Department, Toshiba Corporation, Yokohama, Kanagawa (Japan); Uematsu, Mikio; Hayashida, Yoshihisa [Department of Nuclear Engineering, Toshiba Engineering Corporation, Yokohama, Kanagawa (Japan)
2000-03-01
A boiling water reactor (BWR) plant has a single loop coolant system, in which main steam generated in the reactor core proceeds directly into turbines. Consequently, radioactive {sup 16}N (6.2 MeV photon emitter) contained in the steam contributes to gamma-ray skyshine dose in the vicinity of the BWR plant. The skyshine dose analysis is generally performed with the line-beam method code SKYSHINE, in which calculational geometry consists of a rectangular turbine building and a set of isotropic point sources corresponding to an actual distribution of {sup 16}N sources. For the purpose of upgrading calculational accuracy, the SKYSHINE-CG code has been developed by incorporating the combinatorial geometry (CG) routine into the SKYSHINE code, so that shielding effect of in-building equipment can be properly considered using a three-dimensional model composed of boxes, cylinders, spheres, etc. Skyshine dose rate around a 500 MWe BWR plant was calculated with both SKYSHINE and SKYSHINE-CG codes, and the calculated results were compared with measured data obtained with a NaI(Tl) scintillation detector. The C/E values for SKYSHINE-CG calculation were scattered around 4.0, whereas the ones for SKYSHINE calculation were as large as 6.0. Calculational error was found to be reduced by adopting three-dimensional model based on the combinatorial geometry method. (author)
International Nuclear Information System (INIS)
Greenman, G.M.; O'Brien, M.J.; Procassini, R.J.; Joy, K.I.
2009-01-01
Two enhancements to the combinatorial geometry (CG) particle tracker in the Mercury Monte Carlo transport code are presented. The first enhancement is a hybrid particle tracker wherein a mesh region is embedded within a CG region. This method permits efficient calculations of problems with contain both large-scale heterogeneous and homogeneous regions. The second enhancement relates to the addition of parallelism within the CG tracker via spatial domain decomposition. This permits calculations of problems with a large degree of geometric complexity, which are not possible through particle parallelism alone. In this method, the cells are decomposed across processors and a particles is communicated to an adjacent processor when it tracks to an interprocessor boundary. Applications that demonstrate the efficacy of these new methods are presented
The Cherenkov correlated timing detector: materials, geometry and timing constraints
International Nuclear Information System (INIS)
Aronstein, D.; Bergfeld, T.; Horton, D.; Palmer, M.; Selen, M.; Thayer, G.; Boyer, V.; Honscheid, K.; Kichimi, H.; Sugaya, Y.; Yamaguchi, H.; Yoshimura, Y.; Kanda, S.; Olsen, S.; Ueno, K.; Tamura, N.; Yoshimura, K.; Lu, C.; Marlow, D.; Mindas, C.; Prebys, E.; Pomianowski, P.
1996-01-01
The key parameters of Cherenkov correlated timing (CCT) detectors are discussed. Measurements of radiator geometry, optical properties of radiator and coupling materials, and photon detector timing performance are presented. (orig.)
Relativity in Combinatorial Gravitational Fields
Directory of Open Access Journals (Sweden)
Mao Linfan
2010-04-01
Full Text Available A combinatorial spacetime $(mathscr{C}_G| uboverline{t}$ is a smoothly combinatorial manifold $mathscr{C}$ underlying a graph $G$ evolving on a time vector $overline{t}$. As we known, Einstein's general relativity is suitable for use only in one spacetime. What is its disguise in a combinatorial spacetime? Applying combinatorial Riemannian geometry enables us to present a combinatorial spacetime model for the Universe and suggest a generalized Einstein gravitational equation in such model. Forfinding its solutions, a generalized relativity principle, called projective principle is proposed, i.e., a physics law ina combinatorial spacetime is invariant under a projection on its a subspace and then a spherically symmetric multi-solutions ofgeneralized Einstein gravitational equations in vacuum or charged body are found. We also consider the geometrical structure in such solutions with physical formations, and conclude that an ultimate theory for the Universe maybe established if all such spacetimes in ${f R}^3$. Otherwise, our theory is only an approximate theory and endless forever.
Statistical geometry and space-time
International Nuclear Information System (INIS)
Grauert, H.
1976-01-01
In this paper I try to construct a mathematical tool by which the full structure of Lorentz geometry to space time can be given, but beyond that the background - to speak pictorially - the subsoil for electromagnetic and matter waves, too. The tool could be useful to describe the connections between various particles, electromagnetism and gravity and to compute observables which were not theoretically related, up to now. Moreover, the tool is simpler than the Riemann tensor: it consists just of a set S of line segments in space time, briefly speaking. (orig.) [de
DEFF Research Database (Denmark)
Nielsen, John
1994-01-01
An overview of combinatorial chemistry is presented. Combinatorial chemistry, sometimes referred to as `irrational drug design,' involves the generation of molecular diversity. The resulting chemical library is then screened for biologically active compounds.......An overview of combinatorial chemistry is presented. Combinatorial chemistry, sometimes referred to as `irrational drug design,' involves the generation of molecular diversity. The resulting chemical library is then screened for biologically active compounds....
Prediction and Geometry of Chaotic Time Series
National Research Council Canada - National Science Library
Leonardi, Mary
1997-01-01
This thesis examines the topic of chaotic time series. An overview of chaos, dynamical systems, and traditional approaches to time series analysis is provided, followed by an examination of state space reconstruction...
Sossinsky, A B
2012-01-01
The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...
Indian Academy of Sciences (India)
. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...
Special relativity and space-time geometry.
Molski, M.
An attempt has been made to formulate the special theory of relativity in a space-time that is explicitly absolute and strictly determines the kinematical characteristics of a particle in uniform translational motion. The approach developed is consistent with Einstein's relativity and permits explanation of the inertia phenomenon.
Prasolov, V V
2015-01-01
This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.
Introduction to combinatorial designs
Wallis, WD
2007-01-01
Combinatorial theory is one of the fastest growing areas of modern mathematics. Focusing on a major part of this subject, Introduction to Combinatorial Designs, Second Edition provides a solid foundation in the classical areas of design theory as well as in more contemporary designs based on applications in a variety of fields. After an overview of basic concepts, the text introduces balanced designs and finite geometries. The author then delves into balanced incomplete block designs, covering difference methods, residual and derived designs, and resolvability. Following a chapter on the e
Antolini, Ermete
2017-02-13
Combinatorial chemistry and high-throughput screening represent an innovative and rapid tool to prepare and evaluate a large number of new materials, saving time and expense for research and development. Considering that the activity and selectivity of catalysts depend on complex kinetic phenomena, making their development largely empirical in practice, they are prime candidates for combinatorial discovery and optimization. This review presents an overview of recent results of combinatorial screening of low-temperature fuel cell electrocatalysts for methanol oxidation. Optimum catalyst compositions obtained by combinatorial screening were compared with those of bulk catalysts, and the effect of the library geometry on the screening of catalyst composition is highlighted.
Pedoe, Dan
1988-01-01
""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he
Combinatorial methods with computer applications
Gross, Jonathan L
2007-01-01
Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinatorial methods course or in a combined graph theory and combinatorics course.After an introduction to combinatorics, the book explores six systematic approaches within a comprehensive framework: sequences, solving recurrences, evaluating summation exp
Empirical intrinsic geometry for nonlinear modeling and time series filtering.
Talmon, Ronen; Coifman, Ronald R
2013-07-30
In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.
Interacting particle systems in time-dependent geometries
Ali, A.; Ball, R. C.; Grosskinsky, S.; Somfai, E.
2013-09-01
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be described effectively by space-time trajectories of interacting particles, such as domain boundaries in two-dimensional growth or river networks. We study trajectories embedded in time-dependent geometries, and the main focus is on uniformly expanding or decreasing domains for which we obtain an exact mapping to simple fixed domain systems while preserving the local scale invariance properties. This approach was recently introduced in Ali et al (2013 Phys. Rev. E 87 020102(R)) and here we provide a detailed discussion on its applicability for self-affine Markovian models, and how it can be adapted to self-affine models with memory or explicit time dependence. The mapping corresponds to a nonlinear time transformation which converges to a finite value for a large class of trajectories, enabling an exact analysis of asymptotic properties in expanding domains. We further provide a detailed discussion of different particle interactions and generalized geometries. All our findings are based on exact computations and are illustrated numerically for various examples, including Lévy processes and fractional Brownian motion.
Space-Time Geometry of Quark and Strange Quark Matter
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We study quark and strange quark matter in the context of general relativity. For this purpose, we solve Einstein's field equations for quark and strange quark matter in spherical symmetric space-times. We analyze strange quark matter for the different equations of state (EOS) in the spherical symmetric space-times, thus we are able to obtain the space-time geometries of quark and strange quark matter. Also, we discuss die features of the obtained solutions. The obtained solutions are consistent with the results of Brookhaven Laboratory, i.e. the quark-gluon plasma has a vanishing shear (i.e. quark-gluon plasma is perfect).
The algebraic approach to space-time geometry
International Nuclear Information System (INIS)
Heller, M.; Multarzynski, P.; Sasin, W.
1989-01-01
A differential manifold can be defined in terms of smooth real functions carried by it. By rejecting the postulate, in such a definition, demanding the local diffeomorphism of a manifold to the Euclidean space, one obtains the so-called differential space concept. Every subset of R n turns out to be a differential space. Extensive parts of differential geometry on differential spaces, developed by Sikorski, are reviewed and adapted to relativistic purposes. Differential space as a new model of space-time is proposed. The Lorentz structure and Einstein's field equations on differential spaces are discussed. 20 refs. (author)
Founding Gravitation in 4D Euclidean Space-Time Geometry
International Nuclear Information System (INIS)
Winkler, Franz-Guenter
2010-01-01
The Euclidean interpretation of special relativity which has been suggested by the author is a formulation of special relativity in ordinary 4D Euclidean space-time geometry. The natural and geometrically intuitive generalization of this view involves variations of the speed of light (depending on location and direction) and a Euclidean principle of general covariance. In this article, a gravitation model by Jan Broekaert, which implements a view of relativity theory in the spirit of Lorentz and Poincare, is reconstructed and shown to fulfill the principles of the Euclidean approach after an appropriate reinterpretation.
Cosmological solutions and finite time singularities in Finslerian geometry
Paul, Nupur; de, S. S.; Rahaman, Farook
2018-03-01
We consider a very general scenario of our universe where its geometry is characterized by the Finslerian structure on the underlying spacetime manifold, a generalization of the Riemannian geometry. Now considering a general energy-momentum tensor for matter sector, we derive the gravitational field equations in such spacetime. Further, to depict the cosmological dynamics in such spacetime proposing an interesting equation of state identified by a sole parameter γ which for isotropic limit is simply the barotropic equation of state p = (γ ‑ 1)ρ (γ ∈ ℝ being the barotropic index), we solve the background dynamics. The dynamics offers several possibilities depending on this sole parameter as follows: (i) only an exponential expansion, or (ii) a finite time past singularity (big bang) with late accelerating phase, or (iii) a nonsingular universe exhibiting an accelerating scenario at late time which finally predicts a big rip type singularity. We also discuss several energy conditions and the possibility of cosmic bounce. Finally, we establish the first law of thermodynamics in such spacetime.
Cubical version of combinatorial differential forms
DEFF Research Database (Denmark)
Kock, Anders
2010-01-01
The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry.......The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry....
Algorithms in combinatorial design theory
Colbourn, CJ
1985-01-01
The scope of the volume includes all algorithmic and computational aspects of research on combinatorial designs. Algorithmic aspects include generation, isomorphism and analysis techniques - both heuristic methods used in practice, and the computational complexity of these operations. The scope within design theory includes all aspects of block designs, Latin squares and their variants, pairwise balanced designs and projective planes and related geometries.
Space–time and spatial geodesic orbits in Schwarzschild geometry
Resca, Lorenzo
2018-05-01
Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit equations for a proper spatial submanifold of Schwarzschild metric at any given coordinate-time correspond to an unphysical gravitational repulsion in the non-relativistic limit. This demonstrates at a basic level the centrality and critical role of relativistic time and its intimate pseudo-Riemannian connection with space. Correspondingly, a commonly popularised depiction of geodesic orbits of planets as resulting from the curvature of space produced by the Sun, represented as a rubber sheet dipped in the middle by the weighing of that massive body, is mistaken and misleading for the essence of relativity, even in the non-relativistic limit.
Ng, Marlee K; Cheung, Peter
2016-02-01
It has been over 50 years since Allfrey et al. proposed that histone acetylation regulates RNA synthesis, and the study of histone modifications has progressed at an extraordinary pace for the past two decades. In this review, we provide a perspective on some key events and advances in our understanding of histone modifications. We also highlight reagents and tools from past to present that facilitated progress in this research field. Using histone H3 phosphorylation as an underlying thread, we review the rationale that led to the proposal of the histone code hypothesis, as well as examples that illustrate the concepts of combinatorial histone modifications and cross-talk pathways. We further highlight the importance of investigating these mechanisms in the context of nucleosomes rather than just at the histone level and present current and developing approaches for such studies. Overall, research on histone modifications has yielded great mechanistic insights into the regulation of genomic functions, and extending these studies using nucleosomes will further elucidate the complexity of these pathways in a more physiologically relevant context.
Geometry of time-spaces non-commutative algebraic geometry, applied to quantum theory
Landau, Olav Arnfinn
2011-01-01
This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory o
Zadeh, S. M.; Powers, D. M. W.; Sammut, K.; Yazdani, A. M.
2016-12-01
Autonomous Underwater Vehicles (AUVs) are capable of spending long periods of time for carrying out various underwater missions and marine tasks. In this paper, a novel conflict-free motion planning framework is introduced to enhance underwater vehicle's mission performance by completing maximum number of highest priority tasks in a limited time through a large scale waypoint cluttered operating field, and ensuring safe deployment during the mission. The proposed combinatorial route-path planner model takes the advantages of the Biogeography-Based Optimization (BBO) algorithm toward satisfying objectives of both higher-lower level motion planners and guarantees maximization of the mission productivity for a single vehicle operation. The performance of the model is investigated under different scenarios including the particular cost constraints in time-varying operating fields. To show the reliability of the proposed model, performance of each motion planner assessed separately and then statistical analysis is undertaken to evaluate the total performance of the entire model. The simulation results indicate the stability of the contributed model and its feasible application for real experiments.
Fiber bundle geometry and space-time structure
International Nuclear Information System (INIS)
Nascimento, J.C.
1977-01-01
Within the framework of the geometric formulation of Gauge theories in fiber bundles, the general relation between the bundle connection (Gauge field) and the geometry of the base space is obtained. A possible Gauge theory for gravitation is presented [pt
Applications of combinatorial optimization
Paschos, Vangelis Th
2013-01-01
Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aims to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization. "Applications of Combinatorial Optimization" is presenting a certain number among the most common and well-known applications of Combinatorial Optimization.
Geometry modeling for SAM-CE Monte Carlo calculations
International Nuclear Information System (INIS)
Steinberg, H.A.; Troubetzkoy, E.S.
1980-01-01
Three geometry packages have been developed and incorporated into SAM-CE, for representing in three dimensions the transport medium. These are combinatorial geometry - a general (non-lattice) system, complex combinatorial geometry - a very general system with lattice capability, and special reactor geometry - a special purpose system for light water reactor geometries. Their different attributes are described
Sane, Sharad S
2013-01-01
This is a basic text on combinatorics that deals with all the three aspects of the discipline: tricks, techniques and theory, and attempts to blend them. The book has several distinctive features. Probability and random variables with their interconnections to permutations are discussed. The theme of parity has been specially included and it covers applications ranging from solving the Nim game to the quadratic reciprocity law. Chapters related to geometry include triangulations and Sperner's theorem, classification of regular polytopes, tilings and an introduction to the Eulcidean Ramsey theory. Material on group actions covers Sylow theory, automorphism groups and a classification of finite subgroups of orthogonal groups. All chapters have a large number of exercises with varying degrees of difficulty, ranging from material suitable for Mathematical Olympiads to research.
Concepts of combinatorial optimization
Paschos, Vangelis Th
2014-01-01
Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aim to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization.Concepts of Combinatorial Optimization, is divided into three parts:- On the complexity of combinatorial optimization problems, presenting basics about worst-case and randomi
Spinor Field Nonlinearity and Space-Time Geometry
Saha, Bijan
2018-03-01
Within the scope of Bianchi type VI,VI0,V, III, I, LRSBI and FRW cosmological models we have studied the role of nonlinear spinor field on the evolution of the Universe and the spinor field itself. It was found that due to the presence of non-trivial non-diagonal components of the energy-momentum tensor of the spinor field in the anisotropic space-time, there occur some severe restrictions both on the metric functions and on the components of the spinor field. In this report we have considered a polynomial nonlinearity which is a function of invariants constructed from the bilinear spinor forms. It is found that in case of a Bianchi type-VI space-time, depending of the sign of self-coupling constants, the model allows either late time acceleration or oscillatory mode of evolution. In case of a Bianchi VI 0 type space-time due to the specific behavior of the spinor field we have two different scenarios. In one case the invariants constructed from bilinear spinor forms become trivial, thus giving rise to a massless and linear spinor field Lagrangian. This case is equivalent to the vacuum solution of the Bianchi VI 0 type space-time. The second case allows non-vanishing massive and nonlinear terms and depending on the sign of coupling constants gives rise to accelerating mode of expansion or the one that after obtaining some maximum value contracts and ends in big crunch, consequently generating space-time singularity. In case of a Bianchi type-V model there occur two possibilities. In one case we found that the metric functions are similar to each other. In this case the Universe expands with acceleration if the self-coupling constant is taken to be a positive one, whereas a negative coupling constant gives rise to a cyclic or periodic solution. In the second case the spinor mass and the spinor field nonlinearity vanish and the Universe expands linearly in time. In case of a Bianchi type-III model the space-time remains locally rotationally symmetric all the time
Geometry and dynamics with time-dependent constraints
Evans, Jonathan M.; Jonathan M Evans; Philip A Tuckey
1995-01-01
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which require time-dependent gauge fixing conditions in order to reduce them to their physical degrees of freedom. To illustrate our results we discuss the gauge-fixing of relativistic particles and strings moving in arbitrary background electromagnetic and antisymmetric tensor fields.
Geometry of finite deformations and time-incremental analysis
Czech Academy of Sciences Publication Activity Database
Fiala, Zdeněk
2016-01-01
Roč. 81, May (2016), s. 230-244 ISSN 0020-7462 Institutional support: RVO:68378297 Keywords : solid mechanics * finite deformations * time-incremental analysis * Lagrangian system * evolution equation of Lie type Subject RIV: BE - Theoretical Physics Impact factor: 2.074, year: 2016 http://www.sciencedirect.com/science/article/pii/S0020746216000330
Computational Complexity of Combinatorial Surfaces
Vegter, Gert; Yap, Chee K.
1990-01-01
We investigate the computational problems associated with combinatorial surfaces. Specifically, we present an algorithm (based on the Brahana-Dehn-Heegaard approach) for transforming the polygonal schema of a closed triangulated surface into its canonical form in O(n log n) time, where n is the
Cryptographic Combinatorial Securities Exchanges
Thorpe, Christopher; Parkes, David C.
We present a useful new mechanism that facilitates the atomic exchange of many large baskets of securities in a combinatorial exchange. Cryptography prevents information about the securities in the baskets from being exploited, enhancing trust. Our exchange offers institutions who wish to trade large positions a new alternative to existing methods of block trading: they can reduce transaction costs by taking advantage of other institutions’ available liquidity, while third party liquidity providers guarantee execution—preserving their desired portfolio composition at all times. In our exchange, institutions submit encrypted orders which are crossed, leaving a “remainder”. The exchange proves facts about the portfolio risk of this remainder to third party liquidity providers without revealing the securities in the remainder, the knowledge of which could also be exploited. The third parties learn either (depending on the setting) the portfolio risk parameters of the remainder itself, or how their own portfolio risk would change if they were to incorporate the remainder into a portfolio they submit. In one setting, these third parties submit bids on the commission, and the winner supplies necessary liquidity for the entire exchange to clear. This guaranteed clearing, coupled with external price discovery from the primary markets for the securities, sidesteps difficult combinatorial optimization problems. This latter method of proving how taking on the remainder would change risk parameters of one’s own portfolio, without revealing the remainder’s contents or its own risk parameters, is a useful protocol of independent interest.
SAM-CE, Time-Dependent 3-D Neutron Transport, Gamma Transport in Complex Geometry by Monte-Carlo
International Nuclear Information System (INIS)
2003-01-01
1 - Nature of physical problem solved: The SAM-CE system comprises two Monte Carlo codes, SAM-F and SAM-A. SAM-F supersedes the forward Monte Carlo code, SAM-C. SAM-A is an adjoint Monte Carlo code designed to calculate the response due to fields of primary and secondary gamma radiation. The SAM-CE system is a FORTRAN Monte Carlo computer code designed to solve the time-dependent neutron and gamma-ray transport equations in complex three-dimensional geometries. SAM-CE is applicable for forward neutron calculations and for forward as well as adjoint primary gamma-ray calculations. In addition, SAM-CE is applicable for the gamma-ray stage of the coupled neutron-secondary gamma ray problem, which may be solved in either the forward or the adjoint mode. Time-dependent fluxes, and flux functionals such as dose, heating, count rates, etc., are calculated as functions of energy, time and position. Multiple scoring regions are permitted and these may be either finite volume regions or point detectors or both. Other scores of interest, e.g., collision and absorption densities, etc., are also made. 2 - Method of solution: A special feature of SAM-CE is its use of the 'combinatorial geometry' technique which affords the user geometric capabilities exceeding those available with other commonly used geometric packages. All nuclear interaction cross section data (derived from the ENDF for neutrons and from the UNC-format library for gamma-rays) are tabulated in point energy meshes. The energy meshes for neutrons are internally derived, based on built-in convergence criteria and user- supplied tolerances. Tabulated neutron data for each distinct nuclide are in unique and appropriate energy meshes. Both resolved and unresolved resonance parameters from ENDF data files are treated automatically, and extremely precise and detailed descriptions of cross section behaviour is permitted. Such treatment avoids the ambiguities usually associated with multi-group codes, which use flux
Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes
2014-01-01
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
Pottmann, Helmut
2014-11-26
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Combinatorial designs a tribute to Haim Hanani
Hartman, A
1989-01-01
Haim Hanani pioneered the techniques for constructing designs and the theory of pairwise balanced designs, leading directly to Wilson''s Existence Theorem. He also led the way in the study of resolvable designs, covering and packing problems, latin squares, 3-designs and other combinatorial configurations.The Hanani volume is a collection of research and survey papers at the forefront of research in combinatorial design theory, including Professor Hanani''s own latest work on Balanced Incomplete Block Designs. Other areas covered include Steiner systems, finite geometries, quasigroups, and t-designs.
Combinatorial commutative algebra
Miller, Ezra
2005-01-01
Offers an introduction to combinatorial commutative algebra, focusing on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determined rings. The chapters in this work cover topics ranging from homological invariants of monomial ideals and their polyhedral resolutions, to tools for studying algebraic varieties.
Dynamic combinatorial chemistry
Otto, Sijbren; Furlan, Ricardo L.E.; Sanders, Jeremy K.M.
2002-01-01
A combinatorial library that responds to its target by increasing the concentration of strong binders at the expense of weak binders sounds ideal. Dynamic combinatorial chemistry has the potential to achieve exactly this. In this review, we will highlight the unique features that distinguish dynamic
DEFF Research Database (Denmark)
Larsen, Peter Gorm; Lausdahl, Kenneth; Battle, Nick
2010-01-01
by forgotten preconditions as well as broken invariants and post-conditions. Trace definitions are defined as regular expressions describing possible sequences of operation calls, and are conceptually similar to UML sequence diagrams. In this paper we present a tool enabling test automation based on VDM traces......Abstract—Combinatorial testing in VDM involves the automatic generation and execution of a large collection of test cases derived from templates provided in the form of trace definitions added to a VDM specification. The main value of this is the rapid detection of run-time errors caused......, and explain how it is possible to reduce large collections of test cases in different ways. Its use is illustrated with a small case study....
Integer and combinatorial optimization
Nemhauser, George L
1999-01-01
Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION ""This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best and most complete texts on combinatorial optimization . . . available. [And] with more than 700 entries, [it] has quite an exhaustive reference list.""-Optima ""A unifying approach to optimization problems is to formulate them like linear programming problems, while restricting some or all of the variables to the integers. This book is an encyclopedic resource for such f
Nonparametric combinatorial sequence models.
Wauthier, Fabian L; Jordan, Michael I; Jojic, Nebojsa
2011-11-01
This work considers biological sequences that exhibit combinatorial structures in their composition: groups of positions of the aligned sequences are "linked" and covary as one unit across sequences. If multiple such groups exist, complex interactions can emerge between them. Sequences of this kind arise frequently in biology but methodologies for analyzing them are still being developed. This article presents a nonparametric prior on sequences which allows combinatorial structures to emerge and which induces a posterior distribution over factorized sequence representations. We carry out experiments on three biological sequence families which indicate that combinatorial structures are indeed present and that combinatorial sequence models can more succinctly describe them than simpler mixture models. We conclude with an application to MHC binding prediction which highlights the utility of the posterior distribution over sequence representations induced by the prior. By integrating out the posterior, our method compares favorably to leading binding predictors.
DEFF Research Database (Denmark)
Larsen, Jesper Abildgaard; Wisniewski, Rafal; Grunnet, Jacob Deleuran
2008-01-01
indicates for a given face the future simplex. In the suggested definition we allow nondeterminacy in form of splitting and merging of solution trajectories. The combinatorial vector field gives rise to combinatorial counterparts of most concepts from dynamical systems, such as duals to vector fields, flow......, flow lines, fixed points and Lyapunov functions. Finally it will be shown how this theory extends to switched dynamical systems and an algorithmic overview of how to do supervisory control will be shown towards the end....
Torus actions, combinatorial topology, and homological algebra
International Nuclear Information System (INIS)
Bukhshtaber, V M; Panov, T E
2000-01-01
This paper is a survey of new results and open problems connected with fundamental combinatorial concepts, including polytopes, simplicial complexes, cubical complexes, and arrangements of subspaces. Attention is concentrated on simplicial and cubical subdivisions of manifolds, and especially on spheres. Important constructions are described that enable one to study these combinatorial objects by using commutative and homological algebra. The proposed approach to combinatorial problems is based on the theory of moment-angle complexes recently developed by the authors. The crucial construction assigns to each simplicial complex K with m vertices a T m -space Z K with special bigraded cellular decomposition. In the framework of this theory, well-known non-singular toric varieties arise as orbit spaces of maximally free actions of subtori on moment-angle complexes corresponding to simplicial spheres. It is shown that diverse invariants of simplicial complexes and related combinatorial-geometric objects can be expressed in terms of bigraded cohomology rings of the corresponding moment-angle complexes. Finally, it is shown that the new relationships between combinatorics, geometry, and topology lead to solutions of some well-known topological problems
Performance evaluation of novel LaBr3(Ce) scintillator geometries for fast-timing applications
International Nuclear Information System (INIS)
Vedia, V.; Carmona-Gallardo, M.; Fraile, L.M.; Mach, H.; Udías, J.M.
2017-01-01
We evaluate the performance of two LaBr 3 (Ce) crystals that were produced with special geometries, aimed at enhancing the scintillation light collection and thus the time resolution. Their design was motivated by the construction of high-performance fast-timing arrays like the FAst TIMing array for DESPEC (FATIMA), which demands a high packing factor in addition to good time and energy resolutions. Energy resolution and efficiency were measured using standard calibration sources. Timing measurements were performed at 60 Co and 22 Na γ-energies against a fast BaF 2 reference detector. The time resolution was optimized by the choice of the photomultiplier bias voltage and the fine tuning of the constant fraction discriminator parameters. Monte Carlo simulations using the Geant4 toolkit were performed in order to achieve a better understanding of how the new geometries affect the light transport and thus the performance of the crystals. It is found that the conical-shaped LaBr 3 (Ce) crystals are optimal for fast-timing applications and for the construction of arrays such as FATIMA.
Motivation for Using Generalized Geometry in the Time Dependent Transport Code TDKENO
Energy Technology Data Exchange (ETDEWEB)
Dustin Popp; Zander Mausolff; Sedat Goluoglu
2016-04-01
We are proposing to use the code, TDKENO, to model TREAT. TDKENO solves the time dependent, three dimensional Boltzmann transport equation with explicit representation of delayed neutrons. Instead of directly integrating this equation, the neutron flux is factored into two components – a rapidly varying amplitude equation and a slowly varying shape equation and each is solved separately on different time scales. The shape equation is solved using the 3D Monte Carlo transport code KENO, from Oak Ridge National Laboratory’s SCALE code package. Using the Monte Carlo method to solve the shape equation is still computationally intensive, but the operation is only performed when needed. The amplitude equation is solved deterministically and frequently, so the solution gives an accurate time-dependent solution without having to repeatedly We have modified TDKENO to incorporate KENO-VI so that we may accurately represent the geometries within TREAT. This paper explains the motivation behind using generalized geometry, and provides the results of our modifications. TDKENO uses the Improved Quasi-Static method to accomplish this. In this method, the neutron flux is factored into two components. One component is a purely time-dependent and rapidly varying amplitude function, which is solved deterministically and very frequently (small time steps). The other is a slowly varying flux shape function that weakly depends on time and is only solved when needed (significantly larger time steps).
Exirifard, Qasem
2013-01-01
We present a phenomenological model for the nature in the Finsler and Randers space-time geometries. We show that the parity-odd light speed anisotropy perpendicular to the gravitational equipotential surfaces encodes the deviation from the Riemann geometry toward the Randers geometry. We utilize an asymmetrical ring resonator and propose a setup in order to directly measure this deviation. We address the constraints that the current technology will impose on the deviation should the anisotro...
Infinitary Combinatory Reduction Systems
DEFF Research Database (Denmark)
Ketema, Jeroen; Simonsen, Jakob Grue
2011-01-01
We define infinitary Combinatory Reduction Systems (iCRSs), thus providing the first notion of infinitary higher-order rewriting. The systems defined are sufficiently general that ordinary infinitary term rewriting and infinitary ¿-calculus are special cases. Furthermore,we generalise a number...
Manipulating Combinatorial Structures.
Labelle, Gilbert
This set of transparencies shows how the manipulation of combinatorial structures in the context of modern combinatorics can easily lead to interesting teaching and learning activities at every level of education from elementary school to university. The transparencies describe: (1) the importance and relations of combinatorics to science and…
Combinatorial stresses kill pathogenic Candida species
Kaloriti, Despoina; Tillmann, Anna; Cook, Emily; Jacobsen, Mette; You, Tao; Lenardon, Megan; Ames, Lauren; Barahona, Mauricio; Chandrasekaran, Komelapriya; Coghill, George; Goodman, Daniel; Gow, Neil A. R.; Grebogi, Celso; Ho, Hsueh-Lui; Ingram, Piers; McDonagh, Andrew; De Moura, Alessandro P. S.; Pang, Wei; Puttnam, Melanie; Radmaneshfar, Elahe; Romano, Maria Carmen; Silk, Daniel; Stark, Jaroslav; Stumpf, Michael; Thiel, Marco; Thorne, Thomas; Usher, Jane; Yin, Zhikang; Haynes, Ken; Brown, Alistair J. P.
2012-01-01
Pathogenic microbes exist in dynamic niches and have evolved robust adaptive responses to promote survival in their hosts. The major fungal pathogens of humans, Candida albicans and Candida glabrata, are exposed to a range of environmental stresses in their hosts including osmotic, oxidative and nitrosative stresses. Significant efforts have been devoted to the characterization of the adaptive responses to each of these stresses. In the wild, cells are frequently exposed simultaneously to combinations of these stresses and yet the effects of such combinatorial stresses have not been explored. We have developed a common experimental platform to facilitate the comparison of combinatorial stress responses in C. glabrata and C. albicans. This platform is based on the growth of cells in buffered rich medium at 30°C, and was used to define relatively low, medium and high doses of osmotic (NaCl), oxidative (H 2O2) and nitrosative stresses (e.g., dipropylenetriamine (DPTA)-NONOate). The effects of combinatorial stresses were compared with the corresponding individual stresses under these growth conditions. We show for the first time that certain combinations of combinatorial stress are especially potent in terms of their ability to kill C. albicans and C. glabrata and/or inhibit their growth. This was the case for combinations of osmotic plus oxidative stress and for oxidative plus nitrosative stress. We predict that combinatorial stresses may be highly signif cant in host defences against these pathogenic yeasts. PMID:22463109
Specific features of time-dependent Psub(N) approximations in spherical geometry
International Nuclear Information System (INIS)
Peltzer, P.; Pucker, N.
1979-01-01
Approximations to the time-dependent linear transport equation can result in more serious distortions in the description of the actual physical situation than in the stationary problem. This is demonstrated in detail for the case of a neutron pulse in spherical geometry, treated within a P 1 approximation. One has to pay special attention to the singularity at r = 0 and to the effect of the boundary conditions. Effects similar to those shown here are also to be expected in connection with Psub(N) approximations of higher order. (Auth.)
Li, Bofeng; Feng, Yanming; Shen, Yunzhong; Wang, Charles
2010-11-01
Real-time kinematic (RTK) GPS techniques have been extensively developed for applications including surveying, structural monitoring, and machine automation. Limitations of the existing RTK techniques that hinder their applications for geodynamics purposes are twofold: (1) the achievable RTK accuracy is on the level of a few centimeters and the uncertainty of vertical component is 1.5-2 times worse than those of horizontal components and (2) the RTK position uncertainty grows in proportional to the base-to-rover distances. The key limiting factor behind the problems is the significant effect of residual tropospheric errors on the positioning solutions, especially on the highly correlated height component. This paper develops the geometry-specified troposphere decorrelation strategy to achieve the subcentimeter kinematic positioning accuracy in all three components. The key is to set up a relative zenith tropospheric delay (RZTD) parameter to absorb the residual tropospheric effects and to solve the established model as an ill-posed problem using the regularization method. In order to compute a reasonable regularization parameter to obtain an optimal regularized solution, the covariance matrix of positional parameters estimated without the RZTD parameter, which is characterized by observation geometry, is used to replace the quadratic matrix of their "true" values. As a result, the regularization parameter is adaptively computed with variation of observation geometry. The experiment results show that new method can efficiently alleviate the model's ill condition and stabilize the solution from a single data epoch. Compared to the results from the conventional least squares method, the new method can improve the long-range RTK solution precision from several centimeters to the subcentimeter in all components. More significantly, the precision of the height component is even higher. Several geosciences applications that require subcentimeter real-time solutions can
Quantum Resonance Approach to Combinatorial Optimization
Zak, Michail
1997-01-01
It is shown that quantum resonance can be used for combinatorial optimization. The advantage of the approach is in independence of the computing time upon the dimensionality of the problem. As an example, the solution to a constraint satisfaction problem of exponential complexity is demonstrated.
Local differential geometry of null curves in conformally flat space-time
International Nuclear Information System (INIS)
Urbantke, H.
1989-01-01
The conformally invariant differential geometry of null curves in conformally flat space-times is given, using the six-vector formalism which has generalizations to higher dimensions. This is then paralleled by a twistor description, with a twofold merit: firstly, sometimes the description is easier in twistor terms, sometimes in six-vector terms, which leads to a mutual enlightenment of both; and secondly, the case of null curves in timelike pseudospheres or 2+1 Minkowski space we were only able to treat twistorially, making use of an invariant differential found by Fubini and Cech. The result is the expected one: apart from stated exceptional cases there is a conformally invariant parameter and two conformally invariant curvatures which, when specified in terms of this parameter, serve to characterize the curve up to conformal transformations. 12 refs. (Author)
Analytic theory of the energy and time independent particle transport in the plane geometry
International Nuclear Information System (INIS)
Simovic, R.D.
2001-01-01
An analytic investigation of the energy and time independent particle transport in the plane geometry described by a common anisotropic scattering function is carried out. Regarding the particles with specific diffusion histories in the infinite or the semi-infinite medium, new exact solutions of the corresponding transport equations are analytically derived by means of the Fourier inversion technique. Two particular groups of particles scattered after each successive collision into the directions μ 0, were considered. Its Fourier transformed transport equations have solutions without logarithmic singular points, in the upper part or the lower part of the complex k-plane. The Fourier inversion of solutions are carried out analytically and the obtained formulae represents valid generalization of the expressions for the flux of once scattered particles. (author)
Digital atom interferometer with single particle control on a discretized space-time geometry.
Steffen, Andreas; Alberti, Andrea; Alt, Wolfgang; Belmechri, Noomen; Hild, Sebastian; Karski, Michał; Widera, Artur; Meschede, Dieter
2012-06-19
Engineering quantum particle systems, such as quantum simulators and quantum cellular automata, relies on full coherent control of quantum paths at the single particle level. Here we present an atom interferometer operating with single trapped atoms, where single particle wave packets are controlled through spin-dependent potentials. The interferometer is constructed from a sequence of discrete operations based on a set of elementary building blocks, which permit composing arbitrary interferometer geometries in a digital manner. We use this modularity to devise a space-time analogue of the well-known spin echo technique, yielding insight into decoherence mechanisms. We also demonstrate mesoscopic delocalization of single atoms with a separation-to-localization ratio exceeding 500; this result suggests their utilization beyond quantum logic applications as nano-resolution quantum probes in precision measurements, being able to measure potential gradients with precision 5 x 10(-4) in units of gravitational acceleration g.
Variation in computer time with geometry prescription in monte carlo code KENO-IV
International Nuclear Information System (INIS)
Gopalakrishnan, C.R.
1988-01-01
In most studies, the Monte Carlo criticality code KENO-IV has been compared with other Monte Carlo codes, but evaluation of its performance with different box descriptions has not been done so far. In Monte Carlo computations, any fractional savings of computing time is highly desirable. Variation in computation time with box description in KENO for two different fast reactor fuel subassemblies of FBTR and PFBR is studied. The K eff of an infinite array of fuel subassemblies is calculated by modelling the subassemblies in two different ways (i) multi-region, (ii) multi-box. In addition to these two cases, excess reactivity calculations of FBTR are also performed in two ways to study this effect in a complex geometry. It is observed that the K eff values calculated by multi-region and multi-box models agree very well. However the increase in computation time from the multi-box to the multi-region is considerable, while the difference in computer storage requirements for the two models is negligible. This variation in computing time arises from the way the neutron is tracked in the two cases. (author)
Some results from the combinatorial approach to quantum logic
International Nuclear Information System (INIS)
Greechie, R.J.
1976-01-01
The combinatorial approach to quantum logic focuses on certain interconnections between graphs, combinatorial designs, and convex sets as applied to a quantum logic. This article is concerned only with orthomodular lattices and associated structures. A class of complete atomic irreducible semimodular orthomodular lattices is derived which may not be represented as linear subspaces of a vector space over a division ring. Each of these lattices is a proposition system of dimension three. These proposition systems form orthocomplemented non-Desarguesian projective geometries. (B.R.H.)
Directory of Open Access Journals (Sweden)
Igor V. Protasov
2013-09-01
$\\Delta(A=\\{g\\in G:|gA\\cap A|=\\infty\\}$. The mapping $\\Delta:\\mathcal{P}_G\\rightarrow\\mathcal{P}_G$, $A\\mapsto\\Delta(A$, is called a combinatorial derivation and can be considered as an analogue of the topological derivation $d:\\mathcal{P}_X\\rightarrow\\mathcal{P}_X$, $A\\mapsto A^d$, where $X$ is a topological space and $A^d$ is the set of all limit points of $A$. Content: elementary properties, thin and almost thin subsets, partitions, inverse construction and $\\Delta$-trajectories, $\\Delta$ and $d$.
Dynamic Combinatorial Chemistry
DEFF Research Database (Denmark)
Lisbjerg, Micke
This thesis is divided into seven chapters, which can all be read individually. The first chapter, however, contains a general introduction to the chemistry used in the remaining six chapters, and it is therefore recommended to read chapter one before reading the other chapters. Chapter 1...... is a general introductory chapter for the whole thesis. The history and concepts of dynamic combinatorial chemistry are described, as are some of the new and intriguing results recently obtained. Finally, the properties of a broad range of hexameric macrocycles are described in detail. Chapter 2 gives...
Introduction to tropical geometry
Maclagan, Diane
2015-01-01
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...
International Nuclear Information System (INIS)
Gurevich, L.Eh.; Gliner, Eh.B.
1978-01-01
Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding
cDREM: inferring dynamic combinatorial gene regulation.
Wise, Aaron; Bar-Joseph, Ziv
2015-04-01
Genes are often combinatorially regulated by multiple transcription factors (TFs). Such combinatorial regulation plays an important role in development and facilitates the ability of cells to respond to different stresses. While a number of approaches have utilized sequence and ChIP-based datasets to study combinational regulation, these have often ignored the combinational logic and the dynamics associated with such regulation. Here we present cDREM, a new method for reconstructing dynamic models of combinatorial regulation. cDREM integrates time series gene expression data with (static) protein interaction data. The method is based on a hidden Markov model and utilizes the sparse group Lasso to identify small subsets of combinatorially active TFs, their time of activation, and the logical function they implement. We tested cDREM on yeast and human data sets. Using yeast we show that the predicted combinatorial sets agree with other high throughput genomic datasets and improve upon prior methods developed to infer combinatorial regulation. Applying cDREM to study human response to flu, we were able to identify several combinatorial TF sets, some of which were known to regulate immune response while others represent novel combinations of important TFs.
Spectral dimension of quantum geometries
International Nuclear Information System (INIS)
Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes
2014-01-01
The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)
Boltzmann Oracle for Combinatorial Systems
Pivoteau , Carine; Salvy , Bruno; Soria , Michèle
2008-01-01
International audience; Boltzmann random generation applies to well-deﬁned systems of recursive combinatorial equations. It relies on oracles giving values of the enumeration generating series inside their disk of convergence. We show that the combinatorial systems translate into numerical iteration schemes that provide such oracles. In particular, we give a fast oracle based on Newton iteration.
Jumarie, Guy
2013-04-01
By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way.
On the impact of GNSS ambiguity resolution: geometry, ionosphere, time and biases
Khodabandeh, A.; Teunissen, P. J. G.
2018-06-01
Integer ambiguity resolution (IAR) is the key to fast and precise GNSS positioning and navigation. Next to the positioning parameters, however, there are several other types of GNSS parameters that are of importance for a range of different applications like atmospheric sounding, instrumental calibrations or time transfer. As some of these parameters may still require pseudo-range data for their estimation, their response to IAR may differ significantly. To infer the impact of ambiguity resolution on the parameters, we show how the ambiguity-resolved double-differenced phase data propagate into the GNSS parameter solutions. For that purpose, we introduce a canonical decomposition of the GNSS network model that, through its decoupled and decorrelated nature, provides direct insight into which parameters, or functions thereof, gain from IAR and which do not. Next to this qualitative analysis, we present for the GNSS estimable parameters of geometry, ionosphere, timing and instrumental biases closed-form expressions of their IAR precision gains together with supporting numerical examples.
Mitjana, Margarida
2018-01-01
This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five series of lectures. The first series is dedicated to the study of several matrix classes defined combinatorially, and was delivered by Richard A. Brualdi. The second one, given by Pauline van den Driessche, is concerned with the study of spectral properties of matrices with a given sign pattern. Dragan Stevanović delivered the third one, devoted to describing the spectral radius of a graph as a tool to provide bounds of parameters related with properties of a graph. The fourth lecture was delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.
Worth Longest, P; Hindle, Michael; Das Choudhuri, Suparna
2009-06-01
For most newly developed spray aerosol inhalers, the generation time is a potentially important variable that can be fully controlled. The objective of this study was to determine the effects of spray aerosol generation time on transport and deposition in a standard induction port (IP) and more realistic mouth-throat (MT) geometry. Capillary aerosol generation (CAG) was selected as a representative system in which spray momentum was expected to significantly impact deposition. Sectional and total depositions in the IP and MT geometries were assessed at a constant CAG flow rate of 25 mg/sec for aerosol generation times of 1, 2, and 4 sec using both in vitro experiments and a previously developed computational fluid dynamics (CFD) model. Both the in vitro and numerical results indicated that extending the generation time of the spray aerosol, delivered at a constant mass flow rate, significantly reduced deposition in the IP and more realistic MT geometry. Specifically, increasing the generation time of the CAG system from 1 to 4 sec reduced the deposition fraction in the IP and MT geometries by approximately 60 and 33%, respectively. Furthermore, the CFD predictions of deposition fraction were found to be in good agreement with the in vitro results for all times considered in both the IP and MT geometries. The numerical results indicated that the reduction in deposition fraction over time was associated with temporal dissipation of what was termed the spray aerosol "burst effect." Based on these results, increasing the spray aerosol generation time, at a constant mass flow rate, may be an effective strategy for reducing deposition in the standard IP and in more realistic MT geometries.
Spinning geometry = Twisted geometry
International Nuclear Information System (INIS)
Freidel, Laurent; Ziprick, Jonathan
2014-01-01
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)
Combinatorial optimization games
Energy Technology Data Exchange (ETDEWEB)
Deng, X. [York Univ., North York, Ontario (Canada); Ibaraki, Toshihide; Nagamochi, Hiroshi [Kyoto Univ. (Japan)
1997-06-01
We introduce a general integer programming formulation for a class of combinatorial optimization games, which immediately allows us to improve the algorithmic result for finding amputations in the core (an important solution concept in cooperative game theory) of the network flow game on simple networks by Kalai and Zemel. An interesting result is a general theorem that the core for this class of games is nonempty if and only if a related linear program has an integer optimal solution. We study the properties for this mathematical condition to hold for several interesting problems, and apply them to resolve algorithmic and complexity issues for their cores along the line as put forward in: decide whether the core is empty; if the core is empty, find an imputation in the core; given an imputation x, test whether x is in the core. We also explore the properties of totally balanced games in this succinct formulation of cooperative games.
On an extension of a combinatorial identity
Indian Academy of Sciences (India)
to an infinite family of 4-way combinatorial identities. In some particular cases we get even 5-way combinatorial identities which give us four new combinatorial versions of. Göllnitz–Gordon identities. Keywords. n-Color partitions; lattice paths; Frobenius partitions; Göllnitz–Gordon identities; combinatorial interpretations. 1.
INdAM conference "CoMeTA 2013 - Combinatorial Methods in Topology and Algebra"
Delucchi, Emanuele; Moci, Luca
2015-01-01
Combinatorics plays a prominent role in contemporary mathematics, due to the vibrant development it has experienced in the last two decades and its many interactions with other subjects. This book arises from the INdAM conference "CoMeTA 2013 - Combinatorial Methods in Topology and Algebra,'' which was held in Cortona in September 2013. The event brought together emerging and leading researchers at the crossroads of Combinatorics, Topology and Algebra, with a particular focus on new trends in subjects such as: hyperplane arrangements; discrete geometry and combinatorial topology; polytope theory and triangulations of manifolds; combinatorial algebraic geometry and commutative algebra; algebraic combinatorics; and combinatorial representation theory. The book is divided into two parts. The first expands on the topics discussed at the conference by providing additional background and explanations, while the second presents original contributions on new trends in the topics addressed by the conference.
Combinatorial Nano-Bio Interfaces.
Cai, Pingqiang; Zhang, Xiaoqian; Wang, Ming; Wu, Yun-Long; Chen, Xiaodong
2018-06-08
Nano-bio interfaces are emerging from the convergence of engineered nanomaterials and biological entities. Despite rapid growth, clinical translation of biomedical nanomaterials is heavily compromised by the lack of comprehensive understanding of biophysicochemical interactions at nano-bio interfaces. In the past decade, a few investigations have adopted a combinatorial approach toward decoding nano-bio interfaces. Combinatorial nano-bio interfaces comprise the design of nanocombinatorial libraries and high-throughput bioevaluation. In this Perspective, we address challenges in combinatorial nano-bio interfaces and call for multiparametric nanocombinatorics (composition, morphology, mechanics, surface chemistry), multiscale bioevaluation (biomolecules, organelles, cells, tissues/organs), and the recruitment of computational modeling and artificial intelligence. Leveraging combinatorial nano-bio interfaces will shed light on precision nanomedicine and its potential applications.
Combinatorial designs constructions and analysis
Stinson, Douglas R
2004-01-01
Created to teach students many of the most important techniques used for constructing combinatorial designs, this is an ideal textbook for advanced undergraduate and graduate courses in combinatorial design theory. The text features clear explanations of basic designs, such as Steiner and Kirkman triple systems, mutual orthogonal Latin squares, finite projective and affine planes, and Steiner quadruple systems. In these settings, the student will master various construction techniques, both classic and modern, and will be well-prepared to construct a vast array of combinatorial designs. Design theory offers a progressive approach to the subject, with carefully ordered results. It begins with simple constructions that gradually increase in complexity. Each design has a construction that contains new ideas or that reinforces and builds upon similar ideas previously introduced. A new text/reference covering all apsects of modern combinatorial design theory. Graduates and professionals in computer science, applie...
Combinatorial Mathematics: Research into Practice
Sriraman, Bharath; English, Lyn D.
2004-01-01
Implications and suggestions for using combinatorial mathematics in the classroom through a survey and synthesis of numerous research studies are presented. The implications revolve around five major themes that emerge from analysis of these studies.
Number systems and combinatorial problems
Yordzhev, Krasimir
2014-01-01
The present work has been designed for students in secondary school and their teachers in mathematics. We will show how with the help of our knowledge of number systems we can solve problems from other fields of mathematics for example in combinatorial analysis and most of all when proving some combinatorial identities. To demonstrate discussed in this article method we have chosen several suitable mathematical tasks.
Directory of Open Access Journals (Sweden)
Mac-Thiong Jean-Marc
2009-02-01
Full Text Available Abstract Background The correction of trunk deformity is crucial in scoliosis surgery, especially for the patient's self-image. However, direct visualization of external scoliotic trunk deformity during surgical correction is difficult due to the covering draping sheets. Methods An optoelectronic camera system with 10 passive markers is used to track the trunk geometry of 5 scoliotic patients during corrective surgery. The position of 10 anatomical landmarks and 5 trunk indices computed from the position of the passive markers are compared during and after instrumentation of the spine. Results Internal validation of the accuracy of tracking was evaluated at 0.41 +/- 0.05 mm RMS. Intra operative tracking during surgical maneuvers shows improvement of the shoulder balance during and after correction of the spine. Improvement of the overall patient balance is observed. At last, a minor increase of the spinal length can be noticed. Conclusion Tracking of the external geometry of the trunk during surgical correction is useful to monitor changes occurring under the sterile draping sheets. Moreover, this technique can used be used to reach the optimal configuration on the operating frame before proceeding to surgery. The current tracking technique was able to detect significant changes in trunk geometry caused by posterior instrumentation of the spine despite significant correction of the spinal curvature. It could therefore become relevant for computer-assisted guidance of surgical maneuvers when performing posterior instrumentation of the scoliotic spine, provide important insights during positioning of patients.
International Nuclear Information System (INIS)
Henderson, D.L.
1987-01-01
Time-dependent integral transport equation flux and current kernels for plane and spherical geometry are derived for homogeneous media. Using the multiple collision formalism, isotropic sources that are delta distributions in time are considered for four different problems. The plane geometry flux kernel is applied to a uniformly distributed source within an infinite medium and to a surface source in a semi-infinite medium. The spherical flux kernel is applied to a point source in an infinite medium and to a point source at the origin of a finite sphere. The time-dependent first-flight leakage rates corresponding to the existing steady state first-flight escape probabilities are computed by the Laplace transform technique assuming a delta distribution source in time. The case of a constant source emitting neutrons over a time interval, Δt, for a spatially uniform source is obtained for a slab and a sphere. Time-dependent first-flight leakage rates are also determined for the general two region spherical medium problem for isotropic sources with a delta distribution in time uniformly distributed throughout both the inner and outer regions. The time-dependent collision rates due to the uncollided neutrons are computed for a slab and a sphere using the time-dependent first-flight leakage rates and the time-dependent continuity equation. The case of a constant source emitting neutrons over a time interval, Δt, is also considered
Combinatorial synthesis of natural products
DEFF Research Database (Denmark)
Nielsen, John
2002-01-01
Combinatorial syntheses allow production of compound libraries in an expeditious and organized manner immediately applicable for high-throughput screening. Natural products possess a pedigree to justify quality and appreciation in drug discovery and development. Currently, we are seeing a rapid...... increase in application of natural products in combinatorial chemistry and vice versa. The therapeutic areas of infectious disease and oncology still dominate but many new areas are emerging. Several complex natural products have now been synthesised by solid-phase methods and have created the foundation...... for preparation of combinatorial libraries. In other examples, natural products or intermediates have served as building blocks or scaffolds in the synthesis of complex natural products, bioactive analogues or designed hybrid molecules. Finally, structural motifs from the biologically active parent molecule have...
Combinatorial optimization theory and algorithms
Korte, Bernhard
2018-01-01
This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics (paths, flows, matching, matroids, NP-completeness, approximation algorithms) in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Throughout, it contains complete but concise proofs, and also provides numerous exercises and references. This sixth edition has again been updated, revised, and significantly extended. Among other additions, there are new sections on shallow-light trees, submodular function maximization, smoothed analysis of the knapsack problem, the (ln 4+ɛ)-approximation for Steiner trees, and the VPN theorem. Thus, this book continues to represent the state of the art of combinatorial opti...
Effect of the Implicit Combinatorial Model on Combinatorial Reasoning in Secondary School Pupils.
Batanero, Carmen; And Others
1997-01-01
Elementary combinatorial problems may be classified into three different combinatorial models: (1) selection; (2) partition; and (3) distribution. The main goal of this research was to determine the effect of the implicit combinatorial model on pupils' combinatorial reasoning before and after instruction. Gives an analysis of variance of the…
Performance evaluation of novel LaBr{sub 3}(Ce) scintillator geometries for fast-timing applications
Energy Technology Data Exchange (ETDEWEB)
Vedia, V., E-mail: mv.vedia@ucm.es [Grupo de Física Nuclear, Facultad de CC. Físicas, Universidad Complutense, CEI Moncloa, 28040 Madrid (Spain); Carmona-Gallardo, M.; Fraile, L.M. [Grupo de Física Nuclear, Facultad de CC. Físicas, Universidad Complutense, CEI Moncloa, 28040 Madrid (Spain); Mach, H. [Grupo de Física Nuclear, Facultad de CC. Físicas, Universidad Complutense, CEI Moncloa, 28040 Madrid (Spain); National Centre for Nuclear Research, Division for Nuclear Physics, BP1, Warsaw (Poland); Udías, J.M. [Grupo de Física Nuclear, Facultad de CC. Físicas, Universidad Complutense, CEI Moncloa, 28040 Madrid (Spain)
2017-06-11
We evaluate the performance of two LaBr{sub 3}(Ce) crystals that were produced with special geometries, aimed at enhancing the scintillation light collection and thus the time resolution. Their design was motivated by the construction of high-performance fast-timing arrays like the FAst TIMing array for DESPEC (FATIMA), which demands a high packing factor in addition to good time and energy resolutions. Energy resolution and efficiency were measured using standard calibration sources. Timing measurements were performed at {sup 60}Co and {sup 22}Na γ-energies against a fast BaF{sub 2} reference detector. The time resolution was optimized by the choice of the photomultiplier bias voltage and the fine tuning of the constant fraction discriminator parameters. Monte Carlo simulations using the Geant4 toolkit were performed in order to achieve a better understanding of how the new geometries affect the light transport and thus the performance of the crystals. It is found that the conical-shaped LaBr{sub 3}(Ce) crystals are optimal for fast-timing applications and for the construction of arrays such as FATIMA.
Geometry Helps to Compare Persistence Diagrams
Energy Technology Data Exchange (ETDEWEB)
Kerber, Michael; Morozov, Dmitriy; Nigmetov, Arnur
2015-11-16
Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement geometric variants of the Hopcroft--Karp algorithm for bottleneck matching (based on previous work by Efrat el al.), and of the auction algorithm by Bertsekas for Wasserstein distance computation. Both implementations use k-d trees to replace a linear scan with a geometric proximity query. Our interest in this problem stems from the desire to compute distances between persistence diagrams, a problem that comes up frequently in topological data analysis. We show that our geometric matching algorithms lead to a substantial performance gain, both in running time and in memory consumption, over their purely combinatorial counterparts. Moreover, our implementation significantly outperforms the only other implementation available for comparing persistence diagrams.
Graphical debugging of combinational geometry
International Nuclear Information System (INIS)
Burns, T.J.; Smith, M.S.
1992-01-01
A graphical debugger for combinatorial geometry being developed at Oak Ridge National Laboratory is described. The prototype debugger consists of two parts: a FORTRAN-based ''view'' generator and a Microsoft Windows application for displaying the geometry. Options and features of both modules are discussed. Examples illustrating the various options available are presented. The potential for utilizing the images produced using the debugger as a visualization tool for the output of the radiation transport codes is discussed as is the future direction of the development
Pitts, J. Brian
2016-02-01
What if gravity satisfied the Klein-Gordon equation? Both particle physics from the 1920-30s and the 1890s Neumann-Seeliger modification of Newtonian gravity with exponential decay suggest considering a "graviton mass term" for gravity, which is algebraic in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman-Cunningham conformal group. It therefore exhibits the whole of Minkowski space-time structure, albeit only indirectly concerning volumes. Massive scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity(s): matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric (barely or on long distances) in the mass term. What is the 'true' geometry, one might wonder, in line with Poincaré's modal conventionality argument? Infinitely many theories exhibit this bimetric 'geometry,' all with the total stress-energy's trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers-Pirani-Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities-indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein's equations along the lines of Einstein's newly re-appreciated "physical strategy" and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity (massless spin 2, Pauli and Fierz
Combinatorial differential geometry and ideal Bianchi-Ricci identities
Czech Academy of Sciences Publication Activity Database
Janyška, J.; Markl, Martin
2011-01-01
Roč. 11, č. 3 (2011), s. 509-540 ISSN 1615-715X R&D Projects: GA ČR GA201/08/0397 Institutional research plan: CEZ:AV0Z10190503 Keywords : Natural operator * linear connection * reduction theorem Subject RIV: BA - General Mathematics Impact factor: 0.338, year: 2011 http://www.degruyter.com/view/j/advg.2011.11.issue-3/advgeom.2011.017/advgeom.2011.017. xml
Combinatorial differential geometry and ideal Bianchi-Ricci identities
Czech Academy of Sciences Publication Activity Database
Janyška, J.; Markl, Martin
2011-01-01
Roč. 11, č. 3 (2011), s. 509-540 ISSN 1615-715X R&D Projects: GA ČR GA201/08/0397 Institutional research plan: CEZ:AV0Z10190503 Keywords : Natural operator * linear connection * reduction theorem Subject RIV: BA - General Mathematics Impact factor: 0.338, year: 2011 http://www.degruyter.com/view/j/advg.2011.11.issue-3/advgeom.2011.017/advgeom.2011.017.xml
Combinatorial optimization networks and matroids
Lawler, Eugene
2011-01-01
Perceptively written text examines optimization problems that can be formulated in terms of networks and algebraic structures called matroids. Chapters cover shortest paths, network flows, bipartite matching, nonbipartite matching, matroids and the greedy algorithm, matroid intersections, and the matroid parity problems. A suitable text or reference for courses in combinatorial computing and concrete computational complexity in departments of computer science and mathematics.
Combinatorial synthesis of ceramic materials
Lauf, Robert J.; Walls, Claudia A.; Boatner, Lynn A.
2006-11-14
A combinatorial library includes a gelcast substrate defining a plurality of cavities in at least one surface thereof; and a plurality of gelcast test materials in the cavities, at least two of the test materials differing from the substrate in at least one compositional characteristic, the two test materials differing from each other in at least one compositional characteristic.
Combinatorial auctions for electronic business
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
(6) Information feedback: An auction protocol may be a direct mechanism or an .... transparency of allocation decisions arise in resolving these ties. .... bidding, however more recently, combinatorial bids are allowed [50] making ...... Also, truth revelation and other game theoretic considerations are not taken into account.
Combinatorial Proofs and Algebraic Proofs
Indian Academy of Sciences (India)
Permanent link: https://www.ias.ac.in/article/fulltext/reso/018/07/0630-0645. Keywords. Combinatorial proof; algebraic proof; binomial identity; recurrence relation; composition; Fibonacci number; Fibonacci identity; Pascal triangle. Author Affiliations. Shailesh A Shirali1. Sahyadri School Tiwai Hill, Rajgurunagar Pune 410 ...
Morphological Constraints on Cerebellar Granule Cell Combinatorial Diversity.
Gilmer, Jesse I; Person, Abigail L
2017-12-13
Combinatorial expansion by the cerebellar granule cell layer (GCL) is fundamental to theories of cerebellar contributions to motor control and learning. Granule cells (GrCs) sample approximately four mossy fiber inputs and are thought to form a combinatorial code useful for pattern separation and learning. We constructed a spatially realistic model of the cerebellar GCL and examined how GCL architecture contributes to GrC combinatorial diversity. We found that GrC combinatorial diversity saturates quickly as mossy fiber input diversity increases, and that this saturation is in part a consequence of short dendrites, which limit access to diverse inputs and favor dense sampling of local inputs. This local sampling also produced GrCs that were combinatorially redundant, even when input diversity was extremely high. In addition, we found that mossy fiber clustering, which is a common anatomical pattern, also led to increased redundancy of GrC input combinations. We related this redundancy to hypothesized roles of temporal expansion of GrC information encoding in service of learned timing, and we show that GCL architecture produces GrC populations that support both temporal and combinatorial expansion. Finally, we used novel anatomical measurements from mice of either sex to inform modeling of sparse and filopodia-bearing mossy fibers, finding that these circuit features uniquely contribute to enhancing GrC diversification and redundancy. Our results complement information theoretic studies of granule layer structure and provide insight into the contributions of granule layer anatomical features to afferent mixing. SIGNIFICANCE STATEMENT Cerebellar granule cells are among the simplest neurons, with tiny somata and, on average, just four dendrites. These characteristics, along with their dense organization, inspired influential theoretical work on the granule cell layer as a combinatorial expander, where each granule cell represents a unique combination of inputs
Dynamical System Approaches to Combinatorial Optimization
DEFF Research Database (Denmark)
Starke, Jens
2013-01-01
of large times as an asymptotically stable point of the dynamics. The obtained solutions are often not globally optimal but good approximations of it. Dynamical system and neural network approaches are appropriate methods for distributed and parallel processing. Because of the parallelization......Several dynamical system approaches to combinatorial optimization problems are described and compared. These include dynamical systems derived from penalty methods; the approach of Hopfield and Tank; self-organizing maps, that is, Kohonen networks; coupled selection equations; and hybrid methods...... thereof can be used as models for many industrial problems like manufacturing planning and optimization of flexible manufacturing systems. This is illustrated for an example in distributed robotic systems....
Ruler of the plane - Games of geometry
Beekhuis, S.; Buchin, K.; Castermans, T.; Hurks, T.; Sonke, W.; Aronov, B.; Katz, M.J.
2017-01-01
Ruler of the Plane is a set of games illustrating concepts from combinatorial and computational geometry. The games are based on the art gallery problem, ham-sandwich cuts, the Voronoi game, and geometric network connectivity problems like the Euclidean minimum spanning tree and traveling
CUNY Graduate Center Workshops on Combinatorial and Additive Number Theory
2017-01-01
Based on talks from the 2015 and 2016 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 19 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003, the workshop series surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, primality testing, and cryptography are among the topics featured in this volume. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. Researchers and graduate students interested in the current progress in number theory will find this selection of articles relevant and compelling. .
International Nuclear Information System (INIS)
Hill, T. R.; Reed, W. H.
1980-01-01
1 - Description of problem or function: TIMEX solves the time- dependent, one-dimensional multigroup transport equation with delayed neutrons in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective, periodic, white, albedo or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted. 2 - Method of solution: The discrete ordinates approximation for the angular variable is used with the diamond (central) difference approximation for the angular extrapolation in curved geometries. A linear discontinuous finite element representation for the angular flux in each spatial mesh cell is used. Negative fluxes are eliminated by a local set-to-zero and correct algorithm. The time variable is differenced by an explicit technique that is unconditionally stable so that arbitrarily large time-steps can be taken. Two acceleration methods, exponential extrapolation and re-balance, are utilized to improve the accuracy of the time differencing scheme. 3 - Restrictions on the complexity of the problem: Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXCOR can be accommodated. In addition, the CDC version permits the use of extended core storage less than MAXECS
International Nuclear Information System (INIS)
Murphy, T.J.; Lerche, R.A.; Bennett, C.; Howe, G.
1995-01-01
A geometry-compensated neutron time-of-flight detector has been constructed and used on Nova to measure ion temperatures from indirectly driven implosions with yields between 2.5 and 5x10 9 DD neutrons. The detector, which has an estimated respond time of 250 ps, was located 150 cm from the targets. Due to the long decay time of the scintillator, the time-of-flight signal must be unfolded from the measured detector signal. Several methods for determining the width of the neutron energy spectrum from the data have been developed and give similar results. Scattered x rays continue to be a problem for low yield shots, but should be brought under control with adequate shielding
International Nuclear Information System (INIS)
Murphy, T.J.; Lerche, R.A.; Bennett, C.; Howe, G.
1994-05-01
A geometry-compensated neutron time-of-flight detector has been constructed and used on Nova to measure ion temperatures from indirectly-driven implosions with yields between 2.5 and 5 x 10 9 DD neutrons. The detector, which has an estimated response time of 250 ps, was located 150 cm from the targets. Due to the long decay time of the scintillator, the time-of-flight signal must be unfolded from the measured detector signal. Several methods for determining the width of the neutron energy spectrum from the data have been developed and give similar results. Scattered x rays continue to be a problem for low yield shots, but should be brought under control with adequate shielding
The priming of basic combinatory responses in MEG.
Blanco-Elorrieta, Esti; Ferreira, Victor S; Del Prato, Paul; Pylkkänen, Liina
2018-01-01
Priming has been a powerful tool for the study of human memory and especially the memory representations relevant for language. However, although it is well established that lexical access can be primed, we do not know exactly what types of computations can be primed above the word level. This work took a neurobiological approach and assessed the ways in which the complex representation of a minimal combinatory phrase, such as red boat, can be primed, as evidenced by the spatiotemporal profiles of magnetoencephalography (MEG) signals. Specifically, we built upon recent progress on the neural signatures of phrasal composition and tested whether the brain activities implicated for the basic combination of two words could be primed. In two experiments, MEG was recorded during a picture naming task where the prime trials were designed to replicate previously reported combinatory effects and the target trials to test whether those combinatory effects could be primed. The manipulation of the primes was successful in eliciting larger activity for adjective-noun combinations than single nouns in left anterior temporal and ventromedial prefrontal cortices, replicating prior MEG studies on parallel contrasts. Priming of similarly timed activity was observed during target trials in anterior temporal cortex, but only when the prime and target shared an adjective. No priming in temporal cortex was observed for single word repetition and two control tasks showed that the priming effect was not elicited if the prime pictures were simply viewed but not named. In sum, this work provides evidence that very basic combinatory operations can be primed, with the necessity for some lexical overlap between prime and target suggesting combinatory conceptual, as opposed to syntactic processing. Both our combinatory and priming effects were early, onsetting between 100 and 150ms after picture onset and thus are likely to reflect the very earliest planning stages of a combinatory message
Combinatorial Speculations and the Combinatorial Conjecture for Mathematics
Mao, Linfan
2006-01-01
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to find combinatorial behavior for objectives. Recently, such research works appeared on journals for mathematics and theoretical physics on cosmos. The main purpose of this paper is to survey these thinking and ideas for mathematics and cosmological physics, s...
Markov's theorem and algorithmically non-recognizable combinatorial manifolds
International Nuclear Information System (INIS)
Shtan'ko, M A
2004-01-01
We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial n-dimensional manifold for every n≥4. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all n≥4. We use Borisov's group with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem
Geometry and time scales of self-consistent orbits in a modified SU(2) model
International Nuclear Information System (INIS)
Jezek, D.M.; Hernandez, E.S.; Solari, H.G.
1986-01-01
We investigate the time-dependent Hartree-Fock flow pattern of a two-level many fermion system interacting via a two-body interaction which does not preserve the parity symmetry of standard SU(2) models. The geometrical features of the time-dependent Hartree-Fock energy surface are analyzed and a phase instability is clearly recognized. The time evolution of one-body observables along self-consistent and exact trajectories are examined together with the overlaps between both orbits. Typical time scales for the determinantal motion can be set and the validity of the time-dependent Hartree-Fock approach in the various regions of quasispin phase space is discussed
International Nuclear Information System (INIS)
Murphy, T.J.; Lerche, R.A.
1992-01-01
Current-mode neutron time-of-flight detectors are used on Nova for neutron yield, ion temperature, and neutron emission time measurements. Currently used detectors are limited by the time response of the microchannel plate photomultiplier tubes used with the scintillators, scintillator decay time, scintillator thickness, and oscilloscope response time. A change in the geometry of the scintillator allows one to take advantage of the increased time resolution made possible by more advanced transient recorders and microchannel plate photomultiplier tubes. A prototype detector has been designed to incorporate these changes, and could potentially yield time resolution of less than 150 ps. Experimental results are presented demonstrating an ion temperature measurement of a direct-drive DT implosion on Nova
Bai, Chao-ying; He, Lei-yu; Li, Xing-wang; Sun, Jia-yu
2018-05-01
To conduct forward and simultaneous inversion in a complex geological model, including an irregular topography (or irregular reflector or velocity anomaly), we in this paper combined our previous multiphase arrival tracking method (referred as triangular shortest-path method, TSPM) in triangular (2D) or tetrahedral (3D) cell model and a linearized inversion solver (referred to as damped minimum norms and constrained least squares problem solved using the conjugate gradient method, DMNCLS-CG) to formulate a simultaneous travel time inversion method for updating both velocity and reflector geometry by using multiphase arrival times. In the triangular/tetrahedral cells, we deduced the partial derivative of velocity variation with respective to the depth change of reflector. The numerical simulation results show that the computational accuracy can be tuned to a high precision in forward modeling and the irregular velocity anomaly and reflector geometry can be accurately captured in the simultaneous inversion, because the triangular/tetrahedral cell can be easily used to stitch the irregular topography or subsurface interface.
Combinatorial algebra syntax and semantics
Sapir, Mark V
2014-01-01
Combinatorial Algebra: Syntax and Semantics provides a comprehensive account of many areas of combinatorial algebra. It contains self-contained proofs of more than 20 fundamental results, both classical and modern. This includes Golod–Shafarevich and Olshanskii's solutions of Burnside problems, Shirshov's solution of Kurosh's problem for PI rings, Belov's solution of Specht's problem for varieties of rings, Grigorchuk's solution of Milnor's problem, Bass–Guivarc'h theorem about the growth of nilpotent groups, Kleiman's solution of Hanna Neumann's problem for varieties of groups, Adian's solution of von Neumann-Day's problem, Trahtman's solution of the road coloring problem of Adler, Goodwyn and Weiss. The book emphasize several ``universal" tools, such as trees, subshifts, uniformly recurrent words, diagrams and automata. With over 350 exercises at various levels of difficulty and with hints for the more difficult problems, this book can be used as a textbook, and aims to reach a wide and diversified...
Combinatorial aspects of covering arrays
Directory of Open Access Journals (Sweden)
Charles J. Colbourn
2004-11-01
Full Text Available Covering arrays generalize orthogonal arrays by requiring that t -tuples be covered, but not requiring that the appearance of t -tuples be balanced.Their uses in screening experiments has found application in software testing, hardware testing, and a variety of fields in which interactions among factors are to be identified. Here a combinatorial view of covering arrays is adopted, encompassing basic bounds, direct constructions, recursive constructions, algorithmic methods, and applications.
Wieberger, Florian; Kolb, Tristan; Neuber, Christian; Ober, Christopher K; Schmidt, Hans-Werner
2013-04-08
In this article we present several developed and improved combinatorial techniques to optimize processing conditions and material properties of organic thin films. The combinatorial approach allows investigations of multi-variable dependencies and is the perfect tool to investigate organic thin films regarding their high performance purposes. In this context we develop and establish the reliable preparation of gradients of material composition, temperature, exposure, and immersion time. Furthermore we demonstrate the smart application of combinations of composition and processing gradients to create combinatorial libraries. First a binary combinatorial library is created by applying two gradients perpendicular to each other. A third gradient is carried out in very small areas and arranged matrix-like over the entire binary combinatorial library resulting in a ternary combinatorial library. Ternary combinatorial libraries allow identifying precise trends for the optimization of multi-variable dependent processes which is demonstrated on the lithographic patterning process. Here we verify conclusively the strong interaction and thus the interdependency of variables in the preparation and properties of complex organic thin film systems. The established gradient preparation techniques are not limited to lithographic patterning. It is possible to utilize and transfer the reported combinatorial techniques to other multi-variable dependent processes and to investigate and optimize thin film layers and devices for optical, electro-optical, and electronic applications.
Directory of Open Access Journals (Sweden)
Hans-Werner Schmidt
2013-04-01
Full Text Available In this article we present several developed and improved combinatorial techniques to optimize processing conditions and material properties of organic thin films. The combinatorial approach allows investigations of multi-variable dependencies and is the perfect tool to investigate organic thin films regarding their high performance purposes. In this context we develop and establish the reliable preparation of gradients of material composition, temperature, exposure, and immersion time. Furthermore we demonstrate the smart application of combinations of composition and processing gradients to create combinatorial libraries. First a binary combinatorial library is created by applying two gradients perpendicular to each other. A third gradient is carried out in very small areas and arranged matrix-like over the entire binary combinatorial library resulting in a ternary combinatorial library. Ternary combinatorial libraries allow identifying precise trends for the optimization of multi-variable dependent processes which is demonstrated on the lithographic patterning process. Here we verify conclusively the strong interaction and thus the interdependency of variables in the preparation and properties of complex organic thin film systems. The established gradient preparation techniques are not limited to lithographic patterning. It is possible to utilize and transfer the reported combinatorial techniques to other multi-variable dependent processes and to investigate and optimize thin film layers and devices for optical, electro-optical, and electronic applications.
Space Versus Time: Unimodular Versus Non-Unimodular Projective Ring Geometries?
Czech Academy of Sciences Publication Activity Database
Saniga, M.; Pracna, Petr
2010-01-01
Roč. 4, - (2010), s. 719-735 ISSN 2159-063X Institutional research plan: CEZ:AV0Z40400503 Keywords : projective ring lines * smallest ring of ternions * Germas: of space-time Subject RIV: CF - Physical ; Theoretical Chemistry http://journalofcosmology.com/Multiverse4.html
Fenz, Wolfgang; Dirnberger, Johannes
2015-03-01
Providing suitable training for aspiring neurosurgeons is becoming more and more problematic. The increasing popularity of the endovascular treatment of intracranial aneurysms leads to a lack of simple surgical situations for clipping operations, leaving mainly the complex cases, which present even experienced surgeons with a challenge. To alleviate this situation, we have developed a training simulator with haptic interaction allowing trainees to practice virtual clipping surgeries on real patient-specific vessel geometries. By using specialized finite element (FEM) algorithms (fast finite element method, matrix condensation) combined with GPU acceleration, we can achieve the necessary frame rate for smooth real-time interaction with the detailed models needed for a realistic simulation of the vessel wall deformation caused by the clamping with surgical clips. Vessel wall geometries for typical training scenarios were obtained from 3D-reconstructed medical image data, while for the instruments (clipping forceps, various types of clips, suction tubes) we use models provided by manufacturer Aesculap AG. Collisions between vessel and instruments have to be continuously detected and transformed into corresponding boundary conditions and feedback forces, calculated using a contact plane method. After a training, the achieved result can be assessed based on various criteria, including a simulation of the residual blood flow into the aneurysm. Rigid models of the surgical access and surrounding brain tissue, plus coupling a real forceps to the haptic input device further increase the realism of the simulation.
International Nuclear Information System (INIS)
Fujii, A; Hayashi, S; Fujii, S; Yanagi, K
2014-01-01
This paper deals with the functional performance of optical surface texture measuring instruments on the market. It is well known that their height response curves against certain referential geometry are not always identical to each other. So, a more precise study on the optical instrument's characteristics is greatly needed. Firstly, we developed a new simulation tool using a finite-difference time-domain technique, which enables the prediction of the height response curve against the fundamental surface geometry in the case of the confocal laser scanning microscope. Secondly, by utilizing this new simulation tool, measurement results, including outliers, were compared with the analytical simulation results. The comparison showed the consistency, which indicates that necessary conditions of surface measurement standards for verifying the instrument performance can be established. Consequently, we suggest that the maximum measurable slope angle must be added to evaluation subjects as significant metrological characteristics of measuring instruments, along with the lateral period limit. Finally, we propose a procedure to determine the lateral period limit in an ISO standard. (paper)
Real-time geometry-aware augmented reality in minimally invasive surgery.
Chen, Long; Tang, Wen; John, Nigel W
2017-10-01
The potential of augmented reality (AR) technology to assist minimally invasive surgery (MIS) lies in its computational performance and accuracy in dealing with challenging MIS scenes. Even with the latest hardware and software technologies, achieving both real-time and accurate augmented information overlay in MIS is still a formidable task. In this Letter, the authors present a novel real-time AR framework for MIS that achieves interactive geometric aware AR in endoscopic surgery with stereo views. The authors' framework tracks the movement of the endoscopic camera and simultaneously reconstructs a dense geometric mesh of the MIS scene. The movement of the camera is predicted by minimising the re-projection error to achieve a fast tracking performance, while the three-dimensional mesh is incrementally built by a dense zero mean normalised cross-correlation stereo-matching method to improve the accuracy of the surface reconstruction. The proposed system does not require any prior template or pre-operative scan and can infer the geometric information intra-operatively in real time. With the geometric information available, the proposed AR framework is able to interactively add annotations, localisation of tumours and vessels, and measurement labelling with greater precision and accuracy compared with the state-of-the-art approaches.
Geometry Survey of the Time-of-Flight Neutron-Elastic Scattering (Antonella) Experiment
Energy Technology Data Exchange (ETDEWEB)
Oshinowo, Babatunde O. [Fermilab; Izraelevitch, Federico [Buenos Aires U.
2016-10-17
The Antonella experiment is a measurement of the ionization efficiency of nuclear recoils in silicon at low energies [1]. It is a neutron elastic scattering experiment motivated by the search for dark matter particles. In this experiment, a proton beam hits a lithium target and neutrons are produced. The neutron shower passes through a collimator that produces a neutron beam. The beam illuminates a silicon detector. With a certain probability, a neutron interacts with a silicon nucleus of the detector producing elastic scattering. After the interaction, a fraction of the neutron energy is transferred to the silicon nucleus which acquires kinetic energy and recoils. This kinetic energy is then dissipated in the detector producing ionization and thermal energy. The ionization produced is measured with the silicon detector electronics. On the other hand, the neutron is scattered out of the beam. A neutron-detector array (made of scintillator bars) registers the neutron arrival time and the scattering angle to reconstruct the kinematics of the neutron-nucleus interaction with the time-of-flight technique [2]. In the reconstruction equations, the energy of the nuclear recoil is a function of the scattering angle with respect to the beam direction, the time-of-flight of the neutron and the geometric distances between components of the setup (neutron-production target, silicon detector, scintillator bars). This paper summarizes the survey of the different components of the experiment that made possible the off-line analysis of the collected data. Measurements were made with the API Radian Laser Tracker and I-360 Probe Wireless. The survey was completed at the University of Notre Dame, Indiana, USA in February 2015.
Time-dependent recovery from Hell film boiling: confined geometry case
International Nuclear Information System (INIS)
Filippov, Yu.P.; Sergeev, I.A.
1991-01-01
Experiment results for transient cooldown of a solid in saturated superfluid helium after heat load switch-off are reported. The fluid space restriction in the vicinity of a heater is a specific feature of the tested heat transfer configuration. In this case the recovery duration is found to be set as ≅70% by the stage of film boiling received by the end of heat generation, as ≅20% -by the value of bulk fluid temperature, as ≅15% - by the confinement degree. The sample orientation does not affect the recovery time directly. The investigation has been performed at the Particle Physics Laboratory, JINR
International Nuclear Information System (INIS)
Mahnken, Andreas H.; Jost, Gregor; Seidensticker, Peter; Kuhl, Christiane; Pietsch, Hubertus
2012-01-01
Objective: To assess the effect of low-osmolar, monomeric contrast media with different iodine concentrations on bolus shape in aortic CT angiography. Materials and methods: Repeated sequential computed tomography scanning of the descending aorta of eight beagle dogs (5 male, 12.7 ± 3.1 kg) was performed without table movement with a standardized CT scan protocol. Iopromide 300 (300 mg I/mL), iopromide 370 (370 mg I/mL) and iomeprol 400 (400 mg I/mL) were administered via a foreleg vein with an identical iodine delivery rate of 1.2 g I/s and a total iodine dose of 300 mg I/kg body weight. Time-enhancement curves were computed and analyzed. Results: Iopromide 300 showed the highest peak enhancement (445.2 ± 89.1 HU), steepest up-slope (104.2 ± 17.5 HU/s) and smallest full width at half maximum (FWHM; 5.8 ± 1.0 s). Peak enhancement, duration of FWHM, enhancement at FWHM and up-slope differed significantly between iopromide 300 and iomeprol 400 (p 0.05). Conclusions: Low viscous iopromide 300 results in a better defined bolus with a significantly higher peak enhancement, steeper up-slope and smaller FWHM when compared to iomeprol 400. These characteristics potentially affect contrast timing.
Discrete quantum geometries and their effective dimension
International Nuclear Information System (INIS)
Thuerigen, Johannes
2015-01-01
In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.
More on the rainbow chain: entanglement, space-time geometry and thermal states
International Nuclear Information System (INIS)
Rodríguez-Laguna, Javier; Dubail, Jérôme; Ramírez, Giovanni; Calabrese, Pasquale; Sierra, Germán
2017-01-01
The rainbow chain is an inhomogenous exactly solvable local spin model that, in its ground state, displays a half-chain entanglement entropy growing linearly with the system size. Although many exact results about the rainbow chain are known, the structure of the underlying quantum field theory has not yet been unraveled. Here we show that the universal scaling features of this model are captured by a massless Dirac fermion in a curved space-time with constant negative curvature R = − h "2 ( h is the amplitude of the inhomogeneity). This identification allows us to use recently developed techniques to study inhomogeneous conformal systems and to analytically characterise the entanglement entropies of more general bipartitions. These results are carefully tested against exact numerical calculations. Finally, we study the entanglement entropies of the rainbow chain in thermal states, and find that there is a non-trivial interplay between the rainbow effective temperature T_R and the physical temperature T . (paper)
Efficient Algorithms for Real-Time GPU Volumetric Cloud Rendering with Enhanced Geometry
Directory of Open Access Journals (Sweden)
Carlos Jiménez de Parga
2018-04-01
Full Text Available This paper presents several new techniques for volumetric cloud rendering using efficient algorithms and data structures based on ray-tracing methods for cumulus generation, achieving an optimum balance between realism and performance. These techniques target applications such as flight simulations, computer games, and educational software, even with conventional graphics hardware. The contours of clouds are defined by implicit mathematical expressions or triangulated structures inside which volumetric rendering is performed. Novel techniques are used to reproduce the asymmetrical nature of clouds and the effects of light-scattering, with low computing costs. The work includes a new method to create randomized fractal clouds using a recursive grammar. The graphical results are comparable to those produced by state-of-the-art, hyper-realistic algorithms. These methods provide real-time performance, and are superior to particle-based systems. These outcomes suggest that our methods offer a good balance between realism and performance, and are suitable for use in the standard graphics industry.
Iversen, Birger
1992-01-01
Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics
SABRINA, Geometry Plot Program for MCNP
International Nuclear Information System (INIS)
SEIDL, Marcus
2003-01-01
1 - Description of program or function: SABRINA is an interactive, three-dimensional, geometry-modeling code system, primarily for use with CCC-200/MCNP. SABRINA's capabilities include creation, visualization, and verification of three-dimensional geometries specified by either surface- or body-base combinatorial geometry; display of particle tracks are calculated by MCNP; and volume fraction generation. 2 - Method of solution: Rendering is performed by ray tracing or an edge and intersection algorithm. Volume fraction calculations are made by ray tracing. 3 - Restrictions on the complexity of the problem: A graphics display with X Window capability is required
van den Broek, P.M.
1984-01-01
The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.
Dynamic combinatorial libraries : new opportunities in systems chemistry
Hunt, Rosemary A. R.; Otto, Sijbren; Hunt, Rosemary A.R.
2011-01-01
Combinatorial chemistry is a tool for selecting molecules with special properties. Dynamic combinatorial chemistry started off aiming to be just that. However, unlike ordinary combinatorial chemistry, the interconnectedness of dynamic libraries gives them an extra dimension. An understanding of
The Yoccoz Combinatorial Analytic Invariant
DEFF Research Database (Denmark)
Petersen, Carsten Lunde; Roesch, Pascale
2008-01-01
In this paper we develop a combinatorial analytic encoding of the Mandelbrot set M. The encoding is implicit in Yoccoz' proof of local connectivity of M at any Yoccoz parameter, i.e. any at most finitely renormalizable parameter for which all periodic orbits are repelling. Using this encoding we ...... to reprove that the dyadic veins of M are arcs and that more generally any two Yoccoz parameters are joined by a unique ruled (in the sense of Douady-Hubbard) arc in M....
Probabilistic methods in combinatorial analysis
Sachkov, Vladimir N
2014-01-01
This 1997 work explores the role of probabilistic methods for solving combinatorial problems. These methods not only provide the means of efficiently using such notions as characteristic and generating functions, the moment method and so on but also let us use the powerful technique of limit theorems. The basic objects under investigation are nonnegative matrices, partitions and mappings of finite sets, with special emphasis on permutations and graphs, and equivalence classes specified on sequences of finite length consisting of elements of partially ordered sets; these specify the probabilist
Log-balanced combinatorial sequences
Directory of Open Access Journals (Sweden)
Tomislav Došlic
2005-01-01
Full Text Available We consider log-convex sequences that satisfy an additional constraint imposed on their rate of growth. We call such sequences log-balanced. It is shown that all such sequences satisfy a pair of double inequalities. Sufficient conditions for log-balancedness are given for the case when the sequence satisfies a two- (or more- term linear recurrence. It is shown that many combinatorially interesting sequences belong to this class, and, as a consequence, that the above-mentioned double inequalities are valid for all of them.
Nasir Mahmood, Muhammad; Schmidt, Christian; Trauth, Nico
2017-04-01
Stream morphological features, in combination with hydrological variability play a key role in water and solute exchange across surface and subsurface waters. Meanders are prominent morphological features within stream systems which exhibit unique hydrodynamics. The water surface elevation difference across the inner bank of a meander induces lateral hyporheic exchange within the intra-meander region. This hyporheic flow is characterized by considerably prolonged flow paths and residence times (RT) compared to smaller scales of hyporheic exchange. In this study we examine the impact of different meander geometries on the intra-meander hyporheic flow field and solute mobilization under both steady state and transient flow conditions. We developed a number of artificial meander shape scenarios, representing various meander evolution stages, ranging from a typical initial to advanced stage (near cut off ) meander. Three dimensional steady state numerical groundwater flow simulations including the unsaturated zone were performed for the intra-meander region. The meandering stream was implemented in the model by adjusting the top layers of the modelling domain to the streambed elevation and assigning linearly decreasing head boundary conditions to the streambed cells. Residence times for the intra-meander region were computed by advective particle tracking across the inner bank of meander. Selected steady state cases were extended to transient flow simulations to evaluate the impact of stream discharge events on the temporal behavior of the water exchange and solute transport in the intra-meander region. The transient stream discharge was simulated for a number of discharge events of variable duration and peak height using the surface water model HEC-RAS. Transient hydraulic heads obtained from the surface water model were applied as transient head boundary conditions to the streambed cells of the groundwater model. A solute concentration source was added in the
Combinatorial optimization on a Boltzmann machine
Korst, J.H.M.; Aarts, E.H.L.
1989-01-01
We discuss the problem of solving (approximately) combinatorial optimization problems on a Boltzmann machine. It is shown for a number of combinatorial optimization problems how they can be mapped directly onto a Boltzmann machine by choosing appropriate connection patterns and connection strengths.
Combinatorial Interpretation of General Eulerian Numbers
Tingyao Xiong; Jonathan I. Hall; Hung-Ping Tsao
2014-01-01
Since 1950s, mathematicians have successfully interpreted the traditional Eulerian numbers and $q-$Eulerian numbers combinatorially. In this paper, the authors give a combinatorial interpretation to the general Eulerian numbers defined on general arithmetic progressions { a, a+d, a+2d,...}.
Fourier analysis in combinatorial number theory
International Nuclear Information System (INIS)
Shkredov, Il'ya D
2010-01-01
In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.
Fourier analysis in combinatorial number theory
Energy Technology Data Exchange (ETDEWEB)
Shkredov, Il' ya D [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)
2010-09-16
In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.
Toward Chemical Implementation of Encoded Combinatorial Libraries
DEFF Research Database (Denmark)
Nielsen, John; Janda, Kim D.
1994-01-01
The recent application of "combinatorial libraries" to supplement existing drug screening processes might simplify and accelerate the search for new lead compounds or drugs. Recently, a scheme for encoded combinatorial chemistry was put forward to surmount a number of the limitations possessed...
Nakonieczna, Anna; Yeom, Dong-han
2016-05-01
Investigating the dynamics of gravitational systems, especially in the regime of quantum gravity, poses a problem of measuring time during the evolution. One of the approaches to this issue is using one of the internal degrees of freedom as a time variable. The objective of our research was to check whether a scalar field or any other dynamical quantity being a part of a coupled multi-component matter-geometry system can be treated as a `clock' during its evolution. We investigated a collapse of a self-gravitating electrically charged scalar field in the Einstein and Brans-Dicke theories using the 2+2 formalism. Our findings concentrated on the spacetime region of high curvature existing in the vicinity of the emerging singularity, which is essential for the quantum gravity applications. We investigated several values of the Brans-Dicke coupling constant and the coupling between the Brans-Dicke and the electrically charged scalar fields. It turned out that both evolving scalar fields and a function which measures the amount of electric charge within a sphere of a given radius can be used to quantify time nearby the singularity in the dynamical spacetime part, in which the apparent horizon surrounding the singularity is spacelike. Using them in this respect in the asymptotic spacetime region is possible only when both fields are present in the system and, moreover, they are coupled to each other. The only nonzero component of the Maxwell field four-potential cannot be used to quantify time during the considered process in the neighborhood of the whole central singularity. None of the investigated dynamical quantities is a good candidate for measuring time nearby the Cauchy horizon, which is also singular due to the mass inflation phenomenon.
Combinatorial nanomedicines for colon cancer therapy.
Anitha, A; Maya, S; Sivaram, Amal J; Mony, U; Jayakumar, R
2016-01-01
Colon cancer is one of the major causes of cancer deaths worldwide. Even after surgical resection and aggressive chemotherapy, 50% of colorectal carcinoma patients develop recurrent disease. Thus, the rationale of developing new therapeutic approaches to improve the current chemotherapeutic regimen would be highly recommended. There are reports on the effectiveness of combination chemotherapy in colon cancer and it has been practiced in clinics for long time. These approaches are associated with toxic side effects. Later, the drug delivery research had shown the potential of nanoencapsulation techniques and active targeting as an effective method to improve the effectiveness of chemotherapy with less toxicity. This current focus article provides a brief analysis of the ongoing research in the colon cancer area using the combinatorial nanomedicines and its outcome. © 2015 Wiley Periodicals, Inc.
International Nuclear Information System (INIS)
Hadad, Kamal; Pirouzmand, Ahmad; Ayoobian, Navid
2008-01-01
This paper describes the application of a multilayer cellular neural network (CNN) to model and solve the time dependent one-speed neutron transport equation in slab geometry. We use a neutron angular flux in terms of the Chebyshev polynomials (T N ) of the first kind and then we attempt to implement the equations in an equivalent electrical circuit. We apply this equivalent circuit to analyze the T N moments equation in a uniform finite slab using Marshak type vacuum boundary condition. The validity of the CNN results is evaluated with numerical solution of the steady state T N moments equations by MATLAB. Steady state, as well as transient simulations, shows a very good comparison between the two methods. We used our CNN model to simulate space-time response of total flux and its moments for various c (where c is the mean number of secondary neutrons per collision). The complete algorithm could be implemented using very large-scale integrated circuit (VLSI) circuitry. The efficiency of the calculation method makes it useful for neutron transport calculations
DEFF Research Database (Denmark)
Tong, Glenn; Nielsen, John
1996-01-01
The actinomycin antibiotics bind to nucleic acids via both intercalation and hydrogen bonding. We found this 'double-action attack' mechanism very attractive in our search for a novel class of nucleic acid binders. A highly convergent, solid-phase synthetic strategy has been developed for a class...... with the requirements for combinatorial synthesis and furthermore, the final segment condensation allows, for the first time, double-combinatorial chemistry to be performed where two combinatorial libraries can be reacted with each other. Copyright (C) 1996 Elsevier Science Ltd....
Movable geometry and eigenvalue search capability in the MC21 Monte Carlo code
International Nuclear Information System (INIS)
Gill, D. F.; Nease, B. R.; Griesheimer, D. P.
2013-01-01
A description of a robust and flexible movable geometry implementation in the Monte Carlo code MC21 is described along with a search algorithm that can be used in conjunction with the movable geometry capability to perform eigenvalue searches based on the position of some geometric component. The natural use of the combined movement and search capability is searching to critical through variation of control rod (or control drum) position. The movable geometry discussion provides the mathematical framework for moving surfaces in the MC21 combinatorial solid geometry description. A discussion of the interface between the movable geometry system and the user is also described, particularly the ability to create a hierarchy of movable groups. Combined with the hierarchical geometry description in MC21 the movable group framework provides a very powerful system for inline geometry modification. The eigenvalue search algorithm implemented in MC21 is also described. The foundations of this algorithm are a regula falsi search though several considerations are made in an effort to increase the efficiency of the algorithm for use with Monte Carlo. Specifically, criteria are developed to determine after each batch whether the Monte Carlo calculation should be continued, the search iteration can be rejected, or the search iteration has converged. These criteria seek to minimize the amount of time spent per iteration. Results for the regula falsi method are shown, illustrating that the method as implemented is indeed convergent and that the optimizations made ultimately reduce the total computational expense. (authors)
Movable geometry and eigenvalue search capability in the MC21 Monte Carlo code
Energy Technology Data Exchange (ETDEWEB)
Gill, D. F.; Nease, B. R.; Griesheimer, D. P. [Bettis Atomic Power Laboratory, PO Box 79, West Mifflin, PA 15122 (United States)
2013-07-01
A description of a robust and flexible movable geometry implementation in the Monte Carlo code MC21 is described along with a search algorithm that can be used in conjunction with the movable geometry capability to perform eigenvalue searches based on the position of some geometric component. The natural use of the combined movement and search capability is searching to critical through variation of control rod (or control drum) position. The movable geometry discussion provides the mathematical framework for moving surfaces in the MC21 combinatorial solid geometry description. A discussion of the interface between the movable geometry system and the user is also described, particularly the ability to create a hierarchy of movable groups. Combined with the hierarchical geometry description in MC21 the movable group framework provides a very powerful system for inline geometry modification. The eigenvalue search algorithm implemented in MC21 is also described. The foundations of this algorithm are a regula falsi search though several considerations are made in an effort to increase the efficiency of the algorithm for use with Monte Carlo. Specifically, criteria are developed to determine after each batch whether the Monte Carlo calculation should be continued, the search iteration can be rejected, or the search iteration has converged. These criteria seek to minimize the amount of time spent per iteration. Results for the regula falsi method are shown, illustrating that the method as implemented is indeed convergent and that the optimizations made ultimately reduce the total computational expense. (authors)
Rodger, Alison
1995-01-01
Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and trans
Cheng, Xiaogan; Chen, Hanlin; Lin, Xiubin; Yang, Shufeng; Chen, Shenqiang; Zhang, Fenfen; Li, Kang; Liu, Zelin
2016-12-01
The Pamir region, located to the northwest of the Tibetan Plateau, provides important information that can aid the understanding of the plateau's tectonic evolution. Here we present new findings on the deformation geometry and timing of the Wupoer thrust belt at the northeastern margin of Pamir. Field investigations and interpretations of seismic profiles indicate that the eastern portion of the Wupoer thrust belt is dominated by an underlying foreland basin and an overlying piggy-back basin. A regional unconformity occurs between the Pliocene (N2) and the underlying Miocene (N1) or Paleogene (Pg) strata associated with two other local unconformities between Lower Pleistocene (Q1) and N2 and between Middle Pleistocene (Q2-4) and Q1 strata. Results of structural restorations suggest that compressional deformation was initiated during the latest Miocene to earliest Pliocene, contributing a total shortening magnitude of 48.6 km with a total shortening rate of 48.12%, most of which occurred in the period from the latest Miocene to earliest Pliocene. These results, combined with previous studies on the Kongur and Tarshkorgan extensional system, suggest an interesting picture of strong piedmont compressional thrusting activity concurrent with interorogen extensional rifting. Combining these results with previously published work on the lithospheric architecture of the Pamir, we propose that gravitational collapse drove the formation of simultaneous extensional and compressional structures with a weak, ductile middle crustal layer acting as a décollement along which both the extensional and compressional faults merged.
Secomb, Timothy W
2016-12-01
A novel theoretical method is presented for simulating the spatially resolved convective and diffusive transport of reacting solutes between microvascular networks and the surrounding tissues. The method allows for efficient computational solution of problems involving convection and non-linear binding of solutes in blood flowing through microvascular networks with realistic 3D geometries, coupled with transvascular exchange and diffusion and reaction in the surrounding tissue space. The method is based on a Green's function approach, in which the solute concentration distribution in the tissue is expressed as a sum of fields generated by time-varying distributions of discrete sources and sinks. As an example of the application of the method, the washout of an inert diffusible tracer substance from a tissue region perfused by a network of microvessels is simulated, showing its dependence on the solute's transvascular permeability and tissue diffusivity. Exponential decay of the washout concentration is predicted, with rate constants that are about 10-30% lower than the rate constants for a tissue cylinder model with the same vessel length, vessel surface area and blood flow rate per tissue volume. © The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Laplacians on discrete and quantum geometries
International Nuclear Information System (INIS)
Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes
2013-01-01
We extend discrete calculus for arbitrary (p-form) fields on embedded lattices to abstract discrete geometries based on combinatorial complexes. We then provide a general definition of discrete Laplacian using both the primal cellular complex and its combinatorial dual. The precise implementation of geometric volume factors is not unique and, comparing the definition with a circumcentric and a barycentric dual, we argue that the latter is, in general, more appropriate because it induces a Laplacian with more desirable properties. We give the expression of the discrete Laplacian in several different sets of geometric variables, suitable for computations in different quantum gravity formalisms. Furthermore, we investigate the possibility of transforming from position to momentum space for scalar fields, thus setting the stage for the calculation of heat kernel and spectral dimension in discrete quantum geometries. (paper)
International Nuclear Information System (INIS)
Robinson, I.; Trautman, A.
1988-01-01
The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem
O'Leary, Michael
2010-01-01
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull
Developments in special geometry
International Nuclear Information System (INIS)
Mohaupt, Thomas; Vaughan, Owen
2012-01-01
We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.
Configuration spaces geometry, topology and representation theory
Cohen, Frederick; Concini, Corrado; Feichtner, Eva; Gaiffi, Giovanni; Salvetti, Mario
2016-01-01
This book collects the scientific contributions of a group of leading experts who took part in the INdAM Meeting held in Cortona in September 2014. With combinatorial techniques as the central theme, it focuses on recent developments in configuration spaces from various perspectives. It also discusses their applications in areas ranging from representation theory, toric geometry and geometric group theory to applied algebraic topology.
Grassmannian geometry of scattering amplitudes
Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav
2016-01-01
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...
Groups and Geometries : Siena Conference
Kantor, William; Lunardon, Guglielmo; Pasini, Antonio; Tamburini, Maria
1998-01-01
On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of f...
Geometry of multihadron production
Energy Technology Data Exchange (ETDEWEB)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.
Geometry of multihadron production
International Nuclear Information System (INIS)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions
Obfuscation Framework Based on Functionally Equivalent Combinatorial Logic Families
2008-03-01
of Defense, or the United States Government . AFIT/GCS/ENG/08-12 Obfuscation Framework Based on Functionally Equivalent Combinatorial Logic Families...time, United States policy strongly encourages the sale and transfer of some military equipment to foreign governments and makes it easier for...Proceedings of the International Conference on Availability, Reliability and Security, 2007. 14. McDonald, J. Todd and Alec Yasinsac. “Of unicorns and random
Maor, Eli
2014-01-01
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur
Tumor-targeting peptides from combinatorial libraries*
Liu, Ruiwu; Li, Xiaocen; Xiao, Wenwu; Lam, Kit S.
2018-01-01
Cancer is one of the major and leading causes of death worldwide. Two of the greatest challenges infighting cancer are early detection and effective treatments with no or minimum side effects. Widespread use of targeted therapies and molecular imaging in clinics requires high affinity, tumor-specific agents as effective targeting vehicles to deliver therapeutics and imaging probes to the primary or metastatic tumor sites. Combinatorial libraries such as phage-display and one-bead one-compound (OBOC) peptide libraries are powerful approaches in discovering tumor-targeting peptides. This review gives an overview of different combinatorial library technologies that have been used for the discovery of tumor-targeting peptides. Examples of tumor-targeting peptides identified from each combinatorial library method will be discussed. Published tumor-targeting peptide ligands and their applications will also be summarized by the combinatorial library methods and their corresponding binding receptors. PMID:27210583
Combinatorial Micro-Macro Dynamical Systems
Diaz, Rafael; Villamarin, Sergio
2015-01-01
The second law of thermodynamics states that the entropy of an isolated system is almost always increasing. We propose combinatorial formalizations of the second law and explore their conditions of possibilities.
Conferences on Combinatorial and Additive Number Theory
2014-01-01
This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems, and future challenges in number theory.
Jack superpolynomials: physical and combinatorial definitions
International Nuclear Information System (INIS)
Desrosiers, P.; Mathieu, P.; Lapointe, L.
2004-01-01
Jack superpolynomials are eigenfunctions of the supersymmetric extension of the quantum trigonometric Calogero-Moser-Sutherland Hamiltonian. They are orthogonal with respect to the scalar product, dubbed physical, that is naturally induced by this quantum-mechanical problem. But Jack superpolynomials can also be defined more combinatorially, starting from the multiplicative bases of symmetric superpolynomials, enforcing orthogonality with respect to a one-parameter deformation of the combinatorial scalar product. Both constructions turn out to be equivalent. (author)
Kemnitz, Arnfried
Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.
Lefschetz, Solomon
2005-01-01
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz
2017-01-01
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...
Programme for test generation for combinatorial and sequential systems
International Nuclear Information System (INIS)
Tran Huy Hoan
1973-01-01
This research thesis reports the computer-assisted search for tests aimed at failure detection in combinatorial and sequential logic circuits. As he wants to deal with complex circuits with many modules such as those met in large scale integrated circuits (LSI), the author used propagation paths. He reports the development of a method which is valid for combinatorial systems and for several sequential circuits comprising elementary logic modules and JK and RS flip-flops. This method is developed on an IBM 360/91 computer in PL/1 language. The used memory space is limited and adjustable with respect to circuit dimension. Computing time is short when compared to that needed by other programmes. The solution is practical and efficient for failure test and localisation
Combinatorial Optimization in Project Selection Using Genetic Algorithm
Dewi, Sari; Sawaluddin
2018-01-01
This paper discusses the problem of project selection in the presence of two objective functions that maximize profit and minimize cost and the existence of some limitations is limited resources availability and time available so that there is need allocation of resources in each project. These resources are human resources, machine resources, raw material resources. This is treated as a consideration to not exceed the budget that has been determined. So that can be formulated mathematics for objective function (multi-objective) with boundaries that fulfilled. To assist the project selection process, a multi-objective combinatorial optimization approach is used to obtain an optimal solution for the selection of the right project. It then described a multi-objective method of genetic algorithm as one method of multi-objective combinatorial optimization approach to simplify the project selection process in a large scope.
Non-unique factorizations algebraic, combinatorial and analytic theory
Geroldinger, Alfred
2006-01-01
From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, Non-Unique Factorizations: Algebraic, Combinatorial, and Analytic Theory offers a look at the present state of the theory in a single, unified resource.Taking a broad look at the algebraic, combinatorial, and analytic fundamentals, this book derives factorization results and applies them in concrete arithmetical situations using appropriate transfer principles. It begins with a basic introduction that can be understood with knowledge of standard basic algebra. The authors then move to the algebraic theory of monoids, arithmetic theory of monoids, the structure of sets of lengths, additive group theory, arithmetical invariants, and the arithmetic of Krull monoids. They also provide a s...
Exact combinatorial approach to finite coagulating systems
Fronczak, Agata; Chmiel, Anna; Fronczak, Piotr
2018-02-01
This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.
Distributing the computation in combinatorial optimization experiments over the cloud
Directory of Open Access Journals (Sweden)
Mario Brcic
2017-12-01
Full Text Available Combinatorial optimization is an area of great importance since many of the real-world problems have discrete parameters which are part of the objective function to be optimized. Development of combinatorial optimization algorithms is guided by the empirical study of the candidate ideas and their performance over a wide range of settings or scenarios to infer general conclusions. Number of scenarios can be overwhelming, especially when modeling uncertainty in some of the problem’s parameters. Since the process is also iterative and many ideas and hypotheses may be tested, execution time of each experiment has an important role in the efficiency and successfulness. Structure of such experiments allows for significant execution time improvement by distributing the computation. We focus on the cloud computing as a cost-efficient solution in these circumstances. In this paper we present a system for validating and comparing stochastic combinatorial optimization algorithms. The system also deals with selection of the optimal settings for computational nodes and number of nodes in terms of performance-cost tradeoff. We present applications of the system on a new class of project scheduling problem. We show that we can optimize the selection over cloud service providers as one of the settings and, according to the model, it resulted in a substantial cost-savings while meeting the deadline.
Burello, E.; Bologa, C.; Frecer, V.; Miertus, S.
Combinatorial chemistry and technologies have been developed to a stage where synthetic schemes are available for generation of a large variety of organic molecules. The innovative concept of combinatorial design assumes that screening of a large and diverse library of compounds will increase the probability of finding an active analogue among the compounds tested. Since the rate at which libraries are screened for activity currently constitutes a limitation to the use of combinatorial technologies, it is important to be selective about the number of compounds to be synthesized. Early experience with combinatorial chemistry indicated that chemical diversity alone did not result in a significant increase in the number of generated lead compounds. Emphasis has therefore been increasingly put on the use of computer assisted combinatorial chemical techniques. Computational methods are valuable in the design of virtual libraries of molecular models. Selection strategies based on computed physicochemical properties of the models or of a target compound are introduced to reduce the time and costs of library synthesis and screening. In addition, computational structure-based library focusing methods can be used to perform in silico screening of the activity of compounds against a target receptor by docking the ligands into the receptor model. Three case studies are discussed dealing with the design of targeted combinatorial libraries of inhibitors of HIV-1 protease, P. falciparum plasmepsin and human urokinase as potential antivirial, antimalarial and anticancer drugs. These illustrate library focusing strategies.
Energy Technology Data Exchange (ETDEWEB)
Grotz, Andreas
2011-10-07
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
International Nuclear Information System (INIS)
Grotz, Andreas
2011-01-01
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Intrinsic information carriers in combinatorial dynamical systems
Harmer, Russ; Danos, Vincent; Feret, Jérôme; Krivine, Jean; Fontana, Walter
2010-09-01
Many proteins are composed of structural and chemical features—"sites" for short—characterized by definite interaction capabilities, such as noncovalent binding or covalent modification of other proteins. This modularity allows for varying degrees of independence, as the behavior of a site might be controlled by the state of some but not all sites of the ambient protein. Independence quickly generates a startling combinatorial complexity that shapes most biological networks, such as mammalian signaling systems, and effectively prevents their study in terms of kinetic equations—unless the complexity is radically trimmed. Yet, if combinatorial complexity is key to the system's behavior, eliminating it will prevent, not facilitate, understanding. A more adequate representation of a combinatorial system is provided by a graph-based framework of rewrite rules where each rule specifies only the information that an interaction mechanism depends on. Unlike reactions, which deal with molecular species, rules deal with patterns, i.e., multisets of molecular species. Although the stochastic dynamics induced by a collection of rules on a mixture of molecules can be simulated, it appears useful to capture the system's average or deterministic behavior by means of differential equations. However, expansion of the rules into kinetic equations at the level of molecular species is not only impractical, but conceptually indefensible. If rules describe bona fide patterns of interaction, molecular species are unlikely to constitute appropriate units of dynamics. Rather, we must seek aggregate variables reflective of the causal structure laid down by the rules. We call these variables "fragments" and the process of identifying them "fragmentation." Ideally, fragments are aspects of the system's microscopic population that the set of rules can actually distinguish on average; in practice, it may only be feasible to identify an approximation to this. Most importantly, fragments are
Intrinsic information carriers in combinatorial dynamical systems.
Harmer, Russ; Danos, Vincent; Feret, Jérôme; Krivine, Jean; Fontana, Walter
2010-09-01
Many proteins are composed of structural and chemical features--"sites" for short--characterized by definite interaction capabilities, such as noncovalent binding or covalent modification of other proteins. This modularity allows for varying degrees of independence, as the behavior of a site might be controlled by the state of some but not all sites of the ambient protein. Independence quickly generates a startling combinatorial complexity that shapes most biological networks, such as mammalian signaling systems, and effectively prevents their study in terms of kinetic equations-unless the complexity is radically trimmed. Yet, if combinatorial complexity is key to the system's behavior, eliminating it will prevent, not facilitate, understanding. A more adequate representation of a combinatorial system is provided by a graph-based framework of rewrite rules where each rule specifies only the information that an interaction mechanism depends on. Unlike reactions, which deal with molecular species, rules deal with patterns, i.e., multisets of molecular species. Although the stochastic dynamics induced by a collection of rules on a mixture of molecules can be simulated, it appears useful to capture the system's average or deterministic behavior by means of differential equations. However, expansion of the rules into kinetic equations at the level of molecular species is not only impractical, but conceptually indefensible. If rules describe bona fide patterns of interaction, molecular species are unlikely to constitute appropriate units of dynamics. Rather, we must seek aggregate variables reflective of the causal structure laid down by the rules. We call these variables "fragments" and the process of identifying them "fragmentation." Ideally, fragments are aspects of the system's microscopic population that the set of rules can actually distinguish on average; in practice, it may only be feasible to identify an approximation to this. Most importantly, fragments are
Burdette, A C
1971-01-01
Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st
Berger, Marcel
2010-01-01
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,
Robinson, Gilbert de B
2011-01-01
This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom
Connes, Alain
1994-01-01
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat
Zhao, Yongguang; Li, Chuanrong; Ma, Lingling; Tang, Lingli; Wang, Ning; Zhou, Chuncheng; Qian, Yonggang
2017-10-01
Time series of satellite reflectance data have been widely used to characterize environmental phenomena, describe trends in vegetation dynamics and study climate change. However, several sensors with wide spatial coverage and high observation frequency are usually designed to have large field of view (FOV), which cause variations in the sun-targetsensor geometry in time-series reflectance data. In this study, on the basis of semiempirical kernel-driven BRDF model, a new semi-empirical model was proposed to normalize the sun-target-sensor geometry of remote sensing image. To evaluate the proposed model, bidirectional reflectance under different canopy growth conditions simulated by Discrete Anisotropic Radiative Transfer (DART) model were used. The semi-empirical model was first fitted by using all simulated bidirectional reflectance. Experimental result showed a good fit between the bidirectional reflectance estimated by the proposed model and the simulated value. Then, MODIS time-series reflectance data was normalized to a common sun-target-sensor geometry by the proposed model. The experimental results showed the proposed model yielded good fits between the observed and estimated values. The noise-like fluctuations in time-series reflectance data was also reduced after the sun-target-sensor normalization process.
Indian Academy of Sciences (India)
mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.
Geometry -----------~--------------RESONANCE
Indian Academy of Sciences (India)
Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.
DEFF Research Database (Denmark)
Rasmussen, N. G.; Simeoni, G. G.; Lefmann, K.
2016-01-01
A dedicated beam-focusing device has been designed for the direct geometry thermal-cold neutron time-of-flight spectrometer TOFTOF at the neutron facility FRM II (Garching, Germany). The prototype, based on the compressed Archimedes' mirror concept, benefits from the adaptive-optics technology (a...... than 3.5 would have only marginal influence on the optimal behaviour, whereas comparable spectrometers could take advantage of longer focusing segments, with particular impact for the thermal region of the neutron spectrum....
Energy Technology Data Exchange (ETDEWEB)
Boo, Bong Hyun; Kwak, Hae Ran; Hong, Seung Ki [Chungnam National University, Daejeon (Korea, Republic of); Park, Chan Jo [Korea Research Institute of Chemical Technology, Daejeon (Korea, Republic of); No, Kwang Hyun [Sookmyung Womens University, Seoul (Korea, Republic of)
2010-08-15
We have searched low-lying conformers of calix[4]arene and found one global minimum having a cone shape, together with three conformers such as partial cone-shape conformers. We then elucidated the thermodynamics for the conformational changes by performing density-functional theory (DFT) calculations. The time-dependent DFT calculation enabled us to assign the absorption spectrum and to reveal a variation of the excitation energies with geometry.
C. M. Scoby; P. Musumeci; J. T. Moody; M. S. Gutierrez
2010-01-01
In this paper we study a new geometry setup for electro-optic sampling (EOS) where the electron beam runs parallel to the ⟨110⟩ face of a ZnTe crystal and the probe laser is perpendicular to it and to the beam path. The simple setup is used to encode the time-of-arrival information of a 3.5 MeV
International Nuclear Information System (INIS)
Schenck, Peter K.; Bassim, Nabil D.; Otani, Makoto; Oguchi, Hiroyuki; Green, Martin L.
2007-01-01
The goal of the design of pulsed laser deposition (PLD) combinatorial library films is to optimize the compositional coverage of the films while maintaining a uniform thickness. The deposition pattern of excimer laser PLD films can be modeled with a bimodal cos n distribution. Deposited films were characterized using a spectroscopic reflectometer (250-1000 nm) to map the thickness of both single composition calibration films and combinatorial library films. These distribution functions were used to simulate the composition and thickness of multiple target combinatorial library films. The simulations were correlated with electron-probe microanalysis wavelength-dispersive spectroscopy (EPMA-WDS) composition maps. The composition and thickness of the library films can be fine-tuned by adjusting the laser spot size, fluence, background gas pressure, target geometry and other processing parameters which affect the deposition pattern. Results from compositionally graded combinatorial library films of the ternary system Al 2 O 3 -HfO 2 -Y 2 O 3 are discussed
Local formulae for combinatorial Pontryagin classes
International Nuclear Information System (INIS)
Gaifullin, Alexander A
2004-01-01
Let p(|K|) be the characteristic class of a combinatorial manifold K given by a polynomial p in the rational Pontryagin classes of K. We prove that for any polynomial p there is a function taking each combinatorial manifold K to a cycle z p (K) in its rational simplicial chains such that: 1) the Poincare dual of z p (K) represents the cohomology class p(|K|); 2) the coefficient of each simplex Δ in the cycle z p (K) is determined solely by the combinatorial type of linkΔ. We explicitly describe all such functions for the first Pontryagin class. We obtain estimates for the denominators of the coefficients of the simplices in the cycles z p (K)
Accessing Specific Peptide Recognition by Combinatorial Chemistry
DEFF Research Database (Denmark)
Li, Ming
Molecular recognition is at the basis of all processes for life, and plays a central role in many biological processes, such as protein folding, the structural organization of cells and organelles, signal transduction, and the immune response. Hence, my PhD project is entitled “Accessing Specific...... Peptide Recognition by Combinatorial Chemistry”. Molecular recognition is a specific interaction between two or more molecules through noncovalent bonding, such as hydrogen bonding, metal coordination, van der Waals forces, π−π, hydrophobic, or electrostatic interactions. The association involves kinetic....... Combinatorial chemistry was invented in 1980s based on observation of functional aspects of the adaptive immune system. It was employed for drug development and optimization in conjunction with high-throughput synthesis and screening. (chapter 2) Combinatorial chemistry is able to rapidly produce many thousands...
A quark interpretation of the combinatorial hierarchy
International Nuclear Information System (INIS)
Enqvist, Kari.
1979-01-01
We propose a physical interpretation of the second level of the combinatorial hierarchy in terms of three quarks, three antiquarks and the vacuum. This interpretation allows us to introduce a new quantum number, which measures electromagnetic mass splitting of the quarks. We extend our argument by analogue to baryons, and find some SU(3) and some new mass formulas for baryons. The generalization of our approach to other hierarchy levels is discussed. We present also an empirical mass formula for baryons, which seems to be loosely connected with the combinatorial hierarchy. (author)
Petersen, Peter
2016-01-01
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...
International Nuclear Information System (INIS)
Strominger, A.
1990-01-01
A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)
Dynamic combinatorial chemistry with diselenides and disulfides in water
DEFF Research Database (Denmark)
Rasmussen, Brian; Sørensen, Anne; Gotfredsen, Henrik
2014-01-01
Diselenide exchange is introduced as a reversible reaction in dynamic combinatorial chemistry in water. At neutral pH, diselenides are found to mix with disulfides and form dynamic combinatorial libraries of diselenides, disulfides, and selenenylsulfides. This journal is......Diselenide exchange is introduced as a reversible reaction in dynamic combinatorial chemistry in water. At neutral pH, diselenides are found to mix with disulfides and form dynamic combinatorial libraries of diselenides, disulfides, and selenenylsulfides. This journal is...
Functional completeness of the mixed λ-calculus and combinatory logic
DEFF Research Database (Denmark)
Nielson, Hanne Riis; Nielson, Flemming
1990-01-01
Functional completeness of the combinatory logic means that every lambda-expression may be translated into an equivalent combinator expression and this is the theoretical basis for the implementation of functional languages on combinator-based abstract machines. To obtain efficient implementations...... it is important to distinguish between early and late binding times, i.e. to distinguish between compile-time and run-time computations. The authors therefore introduce a two-level version of the lambda-calculus where this distinction is made in an explicit way. Turning to the combinatory logic they generate...
International Nuclear Information System (INIS)
Esquivel E, J.; Alonso V, G.; Del Valle G, E.
2015-09-01
The solution of the neutron diffusion equation either for reactors in steady state or time dependent, is obtained through approximations generated by implementing of nodal methods such as RTN-0 (Raviart-Thomas-Nedelec of zero index), which is used in this study. Since the nodal methods are applied in quadrangular geometries, in this paper a technique in which the hexagonal geometry through the transfinite interpolation of Gordon-Hall becomes the appropriate geometry to make use of the nodal method RTN-0 is presented. As a result, a computer program was developed, whereby is possible to obtain among other results the neutron multiplication effective factor (k eff ), and the distribution of radial and/or axial power. To verify the operation of the code, was applied to three benchmark problems: in the first two reactors VVER and FBR, results k eff and power distribution are obtained, considering the steady state case of reactor; while the third problem a type VVER is analyzed, in its case dependent of time, which qualitative results are presented on the behavior of the reactor power. (Author)
International Nuclear Information System (INIS)
Pirouzmand, Ahmad; Hadad, Kamal
2011-01-01
Highlights: → This paper describes the solution of time-independent neutron transport equation. → Using a novel method based on cellular neural networks (CNNs) coupled with P N method. → Utilize the CNN model to simulate spatial scalar flux distribution in steady state. → The accuracy, stability, and capabilities of CNN model are examined in x-y geometry. - Abstract: This paper describes a novel method based on using cellular neural networks (CNN) coupled with spherical harmonics method (P N ) to solve the time-independent neutron transport equation in x-y geometry. To achieve this, an equivalent electrical circuit based on second-order form of neutron transport equation and relevant boundary conditions is obtained using CNN method. We use the CNN model to simulate spatial response of scalar flux distribution in the steady state condition for different order of spherical harmonics approximations. The accuracy, stability, and capabilities of CNN model are examined in 2D Cartesian geometry for fixed source and criticality problems.
A New Approach for Proving or Generating Combinatorial Identities
Gonzalez, Luis
2010-01-01
A new method for proving, in an immediate way, many combinatorial identities is presented. The method is based on a simple recursive combinatorial formula involving n + 1 arbitrary real parameters. Moreover, this formula enables one not only to prove, but also generate many different combinatorial identities (not being required to know them "a…
Asessing for Structural Understanding in Childrens' Combinatorial Problem Solving.
English, Lyn
1999-01-01
Assesses children's structural understanding of combinatorial problems when presented in a variety of task situations. Provides an explanatory model of students' combinatorial understandings that informs teaching and assessment. Addresses several components of children's structural understanding of elementary combinatorial problems. (Contains 50…
General Geometry and Geometry of Electromagnetism
Shahverdiyev, Shervgi S.
2002-01-01
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...
Combinatorial biosynthesis of medicinal plant secondary metabolites
Julsing, Mattijs K.; Koulman, Albert; Woerdenbag, Herman J.; Quax, Wim J.; Kayser, Oliver
2006-01-01
Combinatorial biosynthesis is a new tool in the generation of novel natural products and for the production of rare and expensive natural products. The basic concept is combining metabolic pathways in different organisms on a genetic level. As a consequence heterologous organisms provide precursors
Infinitary Combinatory Reduction Systems: Normalising Reduction Strategies
Ketema, J.; Simonsen, Jakob Grue
2010-01-01
We study normalising reduction strategies for infinitary Combinatory Reduction Systems (iCRSs). We prove that all fair, outermost-fair, and needed-fair strategies are normalising for orthogonal, fully-extended iCRSs. These facts properly generalise a number of results on normalising strategies in
PIPERIDINE OLIGOMERS AND COMBINATORIAL LIBRARIES THEREOF
DEFF Research Database (Denmark)
1999-01-01
The present invention relates to piperidine oligomers, methods for the preparation of piperidine oligomers and compound libraries thereof, and the use of piperidine oligomers as drug substances. The present invention also relates to the use of combinatorial libraries of piperidine oligomers...... in libraries (arrays) of compounds especially suitable for screening purposes....
Dendrimer-based dynamic combinatorial libraries
Chang, T.; Meijer, E.W.
2005-01-01
The aim of this project is to create water-sol. dynamic combinatorial libraries based upon dendrimer-guest complexes. The guest mols. are designed to bind to dendrimers using multiple secondary interactions, such as electrostatics and hydrogen bonding. We have been able to incorporate various guest
Gian-Carlos Rota and Combinatorial Math.
Kolata, Gina Bari
1979-01-01
Presents the first of a series of occasional articles about mathematics as seen through the eyes of its prominent scholars. In an interview with Gian-Carlos Rota of the Massachusetts Institute of Technology he discusses how combinatorial mathematics began as a field and its future. (HM)
A Model of Students' Combinatorial Thinking
Lockwood, Elise
2013-01-01
Combinatorial topics have become increasingly prevalent in K-12 and undergraduate curricula, yet research on combinatorics education indicates that students face difficulties when solving counting problems. The research community has not yet addressed students' ways of thinking at a level that facilitates deeper understanding of how students…
Combinatorial Aspects of the Generalized Euler's Totient
Directory of Open Access Journals (Sweden)
Nittiya Pabhapote
2010-01-01
Full Text Available A generalized Euler's totient is defined as a Dirichlet convolution of a power function and a product of the Souriau-Hsu-Möbius function with a completely multiplicative function. Two combinatorial aspects of the generalized Euler's totient, namely, its connections to other totients and its relations with counting formulae, are investigated.
Logging to Facilitate Combinatorial System Testing
Kruse, P.M.; Prasetya, I.S.W.B.; Hage, J; Elyasov, Alexander
2014-01-01
Testing a web application is typically very complicated. Imposing simple coverage criteria such as function or line coverage is often not sufficient to uncover bugs due to incorrect components integration. Combinatorial testing can enforce a stronger criterion, while still allowing the
Ciarlet, Philippe G
2007-01-01
This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a selfcontained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and
On Some Algebraic and Combinatorial Properties of Dunkl Elements
Kirillov, Anatol N.
2013-06-01
We introduce and study a certain class of nonhomogeneous quadratic algebras together with the special set of mutually commuting elements inside of each, the so-called Dunkl elements. We describe relations among the Dunkl elements. This result is a further generalization of similar results obtained in [S. Fomin and A. N. Kirillov, Quadratic algebras, Dunkl elements and Schubert calculus, in Advances in Geometry (eds. J.-S. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, Boston, 1995), pp. 147-182, A. Postnikov, On a quantum version of Pieri's formula, in Advances in Geometry (eds. J.-S. Brylinski, R. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, 1995), pp. 371-383 and A. N. Kirillov and T. Maenor, A Note on Quantum K-Theory of Flag Varieties, preprint]. As an application we describe explicitly the set of relations among the Gaudin elements in the group ring of the symmetric group, cf. [E. Mukhin, V. Tarasov and A. Varchenko, Bethe Subalgebras of the Group Algebra of the Symmetric Group, preprint arXiv:1004.4248]. Also we describe a few combinatorial properties of some special elements in the associative quasi-classical Yang-Baxter algebra in a connection with the values of the β-Grothendieck polynomials for some special permutations, and on the other hand, with the Ehrhart polynomial of the Chan-Robbins polytope.
Proceedings of the 8th Nordic Combinatorial Conference
DEFF Research Database (Denmark)
Geil, Olav; Andersen, Lars Døvling
The Nordic Combinatorial Conferences were initiated in 1981 by mathematicians from Stavanger. Held approximately every three years since then, the conferences have been able to sustain the interest from combinatorialists all over the Nordic countries. In 2004 the 8th conference is held in Aalborg......, Denmark. We are pleased that so many people have chosen to attend, and that lectures were offered from more participants than we had originally reserved time for. We asked two mathematicians to give special lectures and are happy that both accepted immediately. Andries Brouwer from the Technical...
Design of diversity and focused combinatorial libraries in drug discovery.
Young, S Stanley; Ge, Nanxiang
2004-05-01
Using well-characterized chemical reactions and readily available monomers, chemists are able to create sets of compounds, termed libraries, which are useful in drug discovery processes. The design of combinatorial chemical libraries can be complex and there has been much information recently published offering suggestions on how the design process can be carried out. This review focuses on literature with the goal of organizing current thinking. At this point in time, it is clear that benchmarking of current suggested methods is required as opposed to further new methods.
Physical interpretation of the combinatorial hierarchy
International Nuclear Information System (INIS)
Bastin, T.; Noyes, H.P.
1978-01-01
The combinatorial hierarchy model for base particle processes is compared and contrasted with the Ur-theory as developed at the Tutzing Conferences. It agrees with Ur-theory about a finite basis, the ''fixed past--uncertain future'' aspects of physics, and the necessity of dropping Bohr's requirement of reduction to the haptic language of commonsense and classical physics. However, it retains a constructive, hierarchial approach with can yield only an approximate and discrete ''space time'', and introduces the observation metaphysic at the start. Concrete interpretation of the four levels of the hierarchy (with cardinals 3, 7, 127, 2 127 -1 approx. =10 38 ) associates the three levels which map up and down with three absolute conservation laws (charge, baryon number, lepton number) and the spin dichotomy. The first level represents +, -, and +- unit charge. The second has the quantum nubmers of a baryon--antibaryon pair and associated charged meson (e.g., n anti n, p anti n, p anti p, n anti p, π + , π 0 , π - ). The third level associates this pair, now including four spin states as well as four charge states, with a neutral lepton--antilepton pair (e anti e or ν anti ν) in four spin states (total, 64 states): three charged spinless, three charged spin-1, and neutral spin-1 mesons (15 states), and a neutral vector boson associated with the leptons; this gives 3 + 15 + 3 x 15 = 63 possible boson states, so a total correct count of 63 + 64 = 127 states. Something like SU 2 X SU 3 and other indications of quark quantum numbers can occur as substructures at the fourth (unstable) level. A slight extension gives the usual static approximation to the building energy of the hydrogen atom, α 2 m/sub e/c 2 . Cosmological implications of the theory are in accord with current experience. A beginning in the physical interpretation of a theory which could eventually encompass all branches of physics was made. 3 figures, 6 tables
Combinatorial explosion in model gene networks
Edwards, R.; Glass, L.
2000-09-01
The explosive growth in knowledge of the genome of humans and other organisms leaves open the question of how the functioning of genes in interacting networks is coordinated for orderly activity. One approach to this problem is to study mathematical properties of abstract network models that capture the logical structures of gene networks. The principal issue is to understand how particular patterns of activity can result from particular network structures, and what types of behavior are possible. We study idealized models in which the logical structure of the network is explicitly represented by Boolean functions that can be represented by directed graphs on n-cubes, but which are continuous in time and described by differential equations, rather than being updated synchronously via a discrete clock. The equations are piecewise linear, which allows significant analysis and facilitates rapid integration along trajectories. We first give a combinatorial solution to the question of how many distinct logical structures exist for n-dimensional networks, showing that the number increases very rapidly with n. We then outline analytic methods that can be used to establish the existence, stability and periods of periodic orbits corresponding to particular cycles on the n-cube. We use these methods to confirm the existence of limit cycles discovered in a sample of a million randomly generated structures of networks of 4 genes. Even with only 4 genes, at least several hundred different patterns of stable periodic behavior are possible, many of them surprisingly complex. We discuss ways of further classifying these periodic behaviors, showing that small mutations (reversal of one or a few edges on the n-cube) need not destroy the stability of a limit cycle. Although these networks are very simple as models of gene networks, their mathematical transparency reveals relationships between structure and behavior, they suggest that the possibilities for orderly dynamics in such
Combinatorial structures to modeling simple games and applications
Molinero, Xavier
2017-09-01
We connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures. First, we characterize simple games as influence games using influence graphs. It let us to modeling simple games as combinatorial structures (from the viewpoint of structures or graphs). Second, we formally define molecules as combinations of atoms. It let us to modeling molecules as combinatorial structures (from the viewpoint of combinations). It is open to generate such combinatorial structures using some specific techniques as genetic algorithms, (meta-)heuristics algorithms and parallel programming, among others.
Directory of Open Access Journals (Sweden)
Chifu E. N.
2009-07-01
Full Text Available Here, we present a profound and complete analytical solution to Einstein’s gravitational field equations exterior to astrophysically real or hypothetical time varying distribu- tions of mass or pressure within regions of spherical geometry. The single arbitrary function f in our proposed exterior metric tensor and constructed field equations makes our method unique, mathematically less combersome and astrophysically satisfactory. The obtained solution of Einstein’s gravitational field equations tends out to be a gen- eralization of Newton’s gravitational scalar potential exterior to the spherical mass or pressure distribution under consideration
Directory of Open Access Journals (Sweden)
Dutta Bhaskar
2010-12-01
Full Text Available Abstract Background In this study, we investigated the individual and combinatorial effect of elevated CO2 conditions and salinity stress on the dynamics of both the transcriptional and metabolic physiology of Arabidopsis thaliana liquid hydroponic cultures over the first 30 hours of continuous treatment. Both perturbations are of particular interest in plant and agro-biotechnological applications. Moreover, within the timeframe of this experiment, they are expected to affect plant growth to opposite directions. Thus, a major objective was to investigate whether this expected "divergence" was valid for the individual perturbations and to study how it is manifested under the combined stress at two molecular levels of cellular function, using high-throughput analyses. Results We observed that a high salinity has stronger effect than elevated CO2 at both the transcriptional and metabolic levels, b the transcriptional responses to the salinity and combined stresses exhibit strong similarity, implying a robust transcriptional machinery acting to the salinity stress independent of the co-occurrence of elevated CO2, c the combinatorial effect of the two perturbations on the metabolic physiology is milder than of the salinity stress alone. Metabolomic analysis suggested that the beneficial role of elevated CO2 on salt-stressed plants within the timeframe of this study should be attributed to the provided additional resources; these allow the plants to respond to high salinity without having to forfeit other major metabolic functions, and d 9 h-12 h and 24 h of treatment coincide with significant changes in the metabolic physiology under any of the investigated stresses. Significant differences between the acute and longer term responses were observed at both molecular levels. Conclusions This study contributes large-scale dynamic omic data from two levels of cellular function for a plant system under various stresses. It provides an additional example
International Nuclear Information System (INIS)
Jonsson, Rickard; Westman, Hans
2006-01-01
We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity
Geometry on the space of geometries
International Nuclear Information System (INIS)
Christodoulakis, T.; Zanelli, J.
1988-06-01
We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs
International Nuclear Information System (INIS)
Clifton, P.M.
1985-03-01
This study examines the sensitivity of the travel time distribution predicted by a reference case model to (1) scale of representation of the model parameters, (2) size of the model domain, (3) correlation range of log-transmissivity, and (4) cross correlations between transmissivity and effective thickness. The basis for the reference model is the preliminary stochastic travel time model previously documented by the Basalt Waste Isolation Project. Results of this study show the following. The variability of the predicted travel times can be adequately represented when the ratio between the size of the zones used to represent the model parameters and the log-transmissivity correlation range is less than about one-fifth. The size of the model domain and the types of boundary conditions can have a strong impact on the distribution of travel times. Longer log-transmissivity correlation ranges cause larger variability in the predicted travel times. Positive cross correlation between transmissivity and effective thickness causes a decrease in the travel time variability. These results demonstrate the need for a sound conceptual model prior to conducting a stochastic travel time analysis
CEXE INCEXE, 1 Group 3-D Time-Dependent Xe Oscillations in X-Y-Z Geometry with Feedback
International Nuclear Information System (INIS)
Kern, R.; Pacino, S.
1973-01-01
1 - Description of problem or function: CEXE solves the three- dimensional xyz time-dependent xenon spatial oscillation problem using a modified one energy group theory and a nodal representation. 2 - Method of solution: CEXE solves for the spatial neutron source distribution with coupled Doppler and moderator temperature feedbacks. The time dependence of the iodine and xenon concentrations are based on the assumption of constant power during each time-step interval. 3 - Restrictions on the complexity of the problem: Maximum reactor core size representation is restricted to a nodal configuration of 19 x 19 x 10 in the x, y, z directions, respectively
ON range searching in the group model and combinatorial discrepancy
DEFF Research Database (Denmark)
Larsen, Kasper Green
2014-01-01
In this paper we establish an intimate connection between dynamic range searching in the group model and combinatorial discrepancy. Our result states that, for a broad class of range searching data structures (including all known upper bounds), it must hold that $t_u t_q=\\Omega(\\mbox{disc}^2......)$, where $t_u$ is the worst case update time, $t_q$ is the worst case query time, and disc is the combinatorial discrepancy of the range searching problem in question. This relation immediately implies a whole range of exceptionally high and near-tight lower bounds for all of the basic range searching...... problems. We list a few of them in the following: (1) For $d$-dimensional halfspace range searching, we get a lower bound of $t_u t_q=\\Omega(n^{1-1/d})$. This comes within an lg lg $n$ factor of the best known upper bound. (2) For orthogonal range searching, we get a lower bound of $t_u t...
Combinatorial therapy discovery using mixed integer linear programming.
Pang, Kaifang; Wan, Ying-Wooi; Choi, William T; Donehower, Lawrence A; Sun, Jingchun; Pant, Dhruv; Liu, Zhandong
2014-05-15
Combinatorial therapies play increasingly important roles in combating complex diseases. Owing to the huge cost associated with experimental methods in identifying optimal drug combinations, computational approaches can provide a guide to limit the search space and reduce cost. However, few computational approaches have been developed for this purpose, and thus there is a great need of new algorithms for drug combination prediction. Here we proposed to formulate the optimal combinatorial therapy problem into two complementary mathematical algorithms, Balanced Target Set Cover (BTSC) and Minimum Off-Target Set Cover (MOTSC). Given a disease gene set, BTSC seeks a balanced solution that maximizes the coverage on the disease genes and minimizes the off-target hits at the same time. MOTSC seeks a full coverage on the disease gene set while minimizing the off-target set. Through simulation, both BTSC and MOTSC demonstrated a much faster running time over exhaustive search with the same accuracy. When applied to real disease gene sets, our algorithms not only identified known drug combinations, but also predicted novel drug combinations that are worth further testing. In addition, we developed a web-based tool to allow users to iteratively search for optimal drug combinations given a user-defined gene set. Our tool is freely available for noncommercial use at http://www.drug.liuzlab.org/. zhandong.liu@bcm.edu Supplementary data are available at Bioinformatics online.
International Nuclear Information System (INIS)
Clifton, P.M.
1984-12-01
The deep basalt formations beneath the Hanford Site are being investigated for the Department of Energy (DOE) to assess their suitability as a host medium for a high level nuclear waste repository. Predicted performance of the proposed repository is an important part of the investigation. One of the performance measures being used to gauge the suitability of the host medium is pre-waste-emplacement groundwater travel times to the accessible environment. Many deterministic analyses of groundwater travel times have been completed by Rockwell and other independent organizations. Recently, Rockwell has completed a preliminary stochastic analysis of groundwater travel times. This document presents analyses that show the sensitivity of the results from the previous stochastic travel time study to: (1) scale of representation of model parameters, (2) size of the model domain, (3) correlation range of log-transmissivity, and (4) cross-correlation between transmissivity and effective thickness. 40 refs., 29 figs., 6 tabs
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
International Nuclear Information System (INIS)
Konopleva, N.P.
2009-01-01
The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
International Nuclear Information System (INIS)
Khaneja, Navin; Brockett, Roger; Glaser, Steffen J.
2002-01-01
Radio-frequency pulses are used in nuclear-magnetic-resonance spectroscopy to produce unitary transfer of states. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation, and to optimize the sensitivity of the experiments. Many coherence-transfer experiments in NMR, involving a network of coupled spins, use temporary spin decoupling to produce desired effective Hamiltonians. In this paper, we demonstrate that significant time can be saved in producing an effective Hamiltonian if spin decoupling is avoided. We provide time-optimal pulse sequences for producing an important class of effective Hamiltonians in three-spin networks. These effective Hamiltonians are useful for coherence-transfer experiments in three-spin systems and implementation of indirect swap and Λ 2 (U) gates in the context of NMR quantum computing. It is shown that computing these time-optimal pulses can be reduced to geometric problems that involve computing sub-Riemannian geodesics. Using these geometric ideas, explicit expressions for the minimum time required for producing these effective Hamiltonians, transfer of coherence, and implementation of indirect swap gates, in a three-spin network are derived (Theorems 1 and 2). It is demonstrated that geometric control techniques provide a systematic way of finding time-optimal pulse sequences for transferring coherence and synthesizing unitary transformations in quantum networks, with considerable time savings (e.g., 42.3% for constructing indirect swap gates)
Quantum fields and processes a combinatorial approach
Gough, John
2018-01-01
Wick ordering of creation and annihilation operators is of fundamental importance for computing averages and correlations in quantum field theory and, by extension, in the Hudson-Parthasarathy theory of quantum stochastic processes, quantum mechanics, stochastic processes, and probability. This book develops the unified combinatorial framework behind these examples, starting with the simplest mathematically, and working up to the Fock space setting for quantum fields. Emphasizing ideas from combinatorics such as the role of lattice of partitions for multiple stochastic integrals by Wallstrom-Rota and combinatorial species by Joyal, it presents insights coming from quantum probability. It also introduces a 'field calculus' which acts as a succinct alternative to standard Feynman diagrams and formulates quantum field theory (cumulant moments, Dyson-Schwinger equation, tree expansions, 1-particle irreducibility) in this language. Featuring many worked examples, the book is aimed at mathematical physicists, quant...
Gems of combinatorial optimization and graph algorithms
Skutella, Martin; Stiller, Sebastian; Wagner, Dorothea
2015-01-01
Are you looking for new lectures for your course on algorithms, combinatorial optimization, or algorithmic game theory? Maybe you need a convenient source of relevant, current topics for a graduate student or advanced undergraduate student seminar? Or perhaps you just want an enjoyable look at some beautiful mathematical and algorithmic results, ideas, proofs, concepts, and techniques in discrete mathematics and theoretical computer science? Gems of Combinatorial Optimization and Graph Algorithms is a handpicked collection of up-to-date articles, carefully prepared by a select group of international experts, who have contributed some of their most mathematically or algorithmically elegant ideas. Topics include longest tours and Steiner trees in geometric spaces, cartograms, resource buying games, congestion games, selfish routing, revenue equivalence and shortest paths, scheduling, linear structures in graphs, contraction hierarchies, budgeted matching problems, and motifs in networks. This ...
Quantum fields and processes a combinatorial approach
Gough, John
2018-01-01
Wick ordering of creation and annihilation operators is of fundamental importance for computing averages and correlations in quantum field theory and, by extension, in the Hudson–Parthasarathy theory of quantum stochastic processes, quantum mechanics, stochastic processes, and probability. This book develops the unified combinatorial framework behind these examples, starting with the simplest mathematically, and working up to the Fock space setting for quantum fields. Emphasizing ideas from combinatorics such as the role of lattice of partitions for multiple stochastic integrals by Wallstrom–Rota and combinatorial species by Joyal, it presents insights coming from quantum probability. It also introduces a 'field calculus' which acts as a succinct alternative to standard Feynman diagrams and formulates quantum field theory (cumulant moments, Dyson–Schwinger equation, tree expansions, 1-particle irreducibility) in this language. Featuring many worked examples, the book is aimed at mathematical physicists,...
Three Syntactic Theories for Combinatory Graph Reduction
DEFF Research Database (Denmark)
Danvy, Olivier; Zerny, Ian
2011-01-01
in a third syntactic theory. The structure of the store-based abstract machine corresponding to this third syntactic theory oincides with that of Turner's original reduction machine. The three syntactic theories presented here The three syntactic heories presented here therefore have the following......We present a purely syntactic theory of graph reduction for the canonical combinators S, K, and I, where graph vertices are represented with evaluation contexts and let expressions. We express this syntactic theory as a reduction semantics, which we refocus into the first storeless abstract machine...... for combinatory graph reduction, which we refunctionalize into the first storeless natural semantics for combinatory graph reduction.We then factor out the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand, resulting in a second syntactic theory, this one...
Three Syntactic Theories for Combinatory Graph Reduction
DEFF Research Database (Denmark)
Danvy, Olivier; Zerny, Ian
2013-01-01
, as a store-based reduction semantics of combinatory term graphs. We then refocus this store-based reduction semantics into a store-based abstract machine. The architecture of this store-based abstract machine coincides with that of Turner's original reduction machine. The three syntactic theories presented......We present a purely syntactic theory of graph reduction for the canonical combinators S, K, and I, where graph vertices are represented with evaluation contexts and let expressions. We express this rst syntactic theory as a storeless reduction semantics of combinatory terms. We then factor out...... the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand . The factored terms can be interpreted as term graphs in the sense of Barendregt et al. We express this second syntactic theory, which we prove equivalent to the rst, as a storeless reduction semantics...
DNA-Encoded Dynamic Combinatorial Chemical Libraries.
Reddavide, Francesco V; Lin, Weilin; Lehnert, Sarah; Zhang, Yixin
2015-06-26
Dynamic combinatorial chemistry (DCC) explores the thermodynamic equilibrium of reversible reactions. Its application in the discovery of protein binders is largely limited by difficulties in the analysis of complex reaction mixtures. DNA-encoded chemical library (DECL) technology allows the selection of binders from a mixture of up to billions of different compounds; however, experimental results often show low a signal-to-noise ratio and poor correlation between enrichment factor and binding affinity. Herein we describe the design and application of DNA-encoded dynamic combinatorial chemical libraries (EDCCLs). Our experiments have shown that the EDCCL approach can be used not only to convert monovalent binders into high-affinity bivalent binders, but also to cause remarkably enhanced enrichment of potent bivalent binders by driving their in situ synthesis. We also demonstrate the application of EDCCLs in DNA-templated chemical reactions. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Exploiting Quantum Resonance to Solve Combinatorial Problems
Zak, Michail; Fijany, Amir
2006-01-01
Quantum resonance would be exploited in a proposed quantum-computing approach to the solution of combinatorial optimization problems. In quantum computing in general, one takes advantage of the fact that an algorithm cannot be decoupled from the physical effects available to implement it. Prior approaches to quantum computing have involved exploitation of only a subset of known quantum physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of tensor-product decomposability of unitary evolution of many-particle quantum systems for physically simulating solutions to NP-complete problems (a class of problems that are intractable with respect to classical methods of computation). In this approach, reinforcement and selection of a desired solution would be executed by means of quantum resonance. Classes of NP-complete problems that are important in practice and could be solved by the proposed approach include planning, scheduling, search, and optimal design.
Sources of hyperbolic geometry
Stillwell, John
1996-01-01
This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...
Solar Proton Transport Within an ICRU Sphere Surrounded by a Complex Shield: Ray-trace Geometry
Slaba, Tony C.; Wilson, John W.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.
2015-01-01
A computationally efficient 3DHZETRN code with enhanced neutron and light ion (Z is less than or equal to 2) propagation was recently developed for complex, inhomogeneous shield geometry described by combinatorial objects. Comparisons were made between 3DHZETRN results and Monte Carlo (MC) simulations at locations within the combinatorial geometry, and it was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in ray-trace geometry. This latest extension enables the code to be used within current engineering design practices utilizing fully detailed vehicle and habitat geometries. Through convergence testing, it is shown that fidelity in an actual shield geometry can be maintained in the discrete ray-trace description by systematically increasing the number of discrete rays used. It is also shown that this fidelity is carried into transport procedures and resulting exposure quantities without sacrificing computational efficiency.
Combinatorial Cis-regulation in Saccharomyces Species
Directory of Open Access Journals (Sweden)
Aaron T. Spivak
2016-03-01
Full Text Available Transcriptional control of gene expression requires interactions between the cis-regulatory elements (CREs controlling gene promoters. We developed a sensitive computational method to identify CRE combinations with conserved spacing that does not require genome alignments. When applied to seven sensu stricto and sensu lato Saccharomyces species, 80% of the predicted interactions displayed some evidence of combinatorial transcriptional behavior in several existing datasets including: (1 chromatin immunoprecipitation data for colocalization of transcription factors, (2 gene expression data for coexpression of predicted regulatory targets, and (3 gene ontology databases for common pathway membership of predicted regulatory targets. We tested several predicted CRE interactions with chromatin immunoprecipitation experiments in a wild-type strain and strains in which a predicted cofactor was deleted. Our experiments confirmed that transcription factor (TF occupancy at the promoters of the CRE combination target genes depends on the predicted cofactor while occupancy of other promoters is independent of the predicted cofactor. Our method has the additional advantage of identifying regulatory differences between species. By analyzing the S. cerevisiae and S. bayanus genomes, we identified differences in combinatorial cis-regulation between the species and showed that the predicted changes in gene regulation explain several of the species-specific differences seen in gene expression datasets. In some instances, the same CRE combinations appear to regulate genes involved in distinct biological processes in the two different species. The results of this research demonstrate that (1 combinatorial cis-regulation can be inferred by multi-genome analysis and (2 combinatorial cis-regulation can explain differences in gene expression between species.
The Combinatorial Trace Method in Action
Krebs, Mike; Martinez, Natalie C.
2013-01-01
On any finite graph, the number of closed walks of length k is equal to the sum of the kth powers of the eigenvalues of any adjacency matrix. This simple observation is the basis for the combinatorial trace method, wherein we attempt to count (or bound) the number of closed walks of a given length so as to obtain information about the graph's…
A combinatorial framework to quantify peak/pit asymmetries in complex dynamics
Hasson, Uri; Iacovacci, Jacopo; Davis, Ben; Flanagan, Ryan; Tagliazucchi, E.; Laufs, Helmut; Lacasa, Lucas
2018-01-01
We explore a combinatorial framework which efficiently quantifies the asymmetries between minima and maxima in local fluctuations of time series. We first showcase its performance by applying it to a battery of synthetic cases. We find rigorous results on some canonical dynamical models (stochastic
Juste, B; Miro, R; Gallardo, S; Santos, A; Verdu, G
2006-01-01
The present work has simulated the photon and electron transport in a Theratron 780 (MDS Nordion) (60)Co radiotherapy unit, using the Monte Carlo transport code, MCNP (Monte Carlo N-Particle), version 5. In order to become computationally more efficient in view of taking part in the practical field of radiotherapy treatment planning, this work is focused mainly on the analysis of dose results and on the required computing time of different tallies applied in the model to speed up calculations.
Neural Meta-Memes Framework for Combinatorial Optimization
Song, Li Qin; Lim, Meng Hiot; Ong, Yew Soon
In this paper, we present a Neural Meta-Memes Framework (NMMF) for combinatorial optimization. NMMF is a framework which models basic optimization algorithms as memes and manages them dynamically when solving combinatorial problems. NMMF encompasses neural networks which serve as the overall planner/coordinator to balance the workload between memes. We show the efficacy of the proposed NMMF through empirical study on a class of combinatorial problem, the quadratic assignment problem (QAP).
Topics in combinatorial pattern matching
DEFF Research Database (Denmark)
Vildhøj, Hjalte Wedel
Problem. Given m documents of total length n, we consider the problem of finding a longest string common to at least d ≥ 2 of the documents. This problem is known as the longest common substring (LCS) problem and has a classic O(n) space and O(n) time solution (Weiner [FOCS’73], Hui [CPM’92]). However...
Molecular motion in restricted geometries
Indian Academy of Sciences (India)
Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...
Use of combinatorial chemistry to speed drug discovery.
Rádl, S
1998-10-01
IBC's International Conference on Integrating Combinatorial Chemistry into the Discovery Pipeline was held September 14-15, 1998. The program started with a pre-conference workshop on High-Throughput Compound Characterization and Purification. The agenda of the main conference was divided into sessions of Synthesis, Automation and Unique Chemistries; Integrating Combinatorial Chemistry, Medicinal Chemistry and Screening; Combinatorial Chemistry Applications for Drug Discovery; and Information and Data Management. This meeting was an excellent opportunity to see how big pharma, biotech and service companies are addressing the current bottlenecks in combinatorial chemistry to speed drug discovery. (c) 1998 Prous Science. All rights reserved.
Advanced Aqueous Phase Catalyst Development using Combinatorial Methods, Phase II
National Aeronautics and Space Administration — Combinatorial methods are proposed to develop advanced Aqueous Oxidation Catalysts (AOCs) with the capability to mineralize organic contaminants present in effluents...
Effects of Suboptimal Bidding in Combinatorial Auctions
Schneider, Stefan; Shabalin, Pasha; Bichler, Martin
Though the VCG auction assumes a central place in the mechanism design literature, there are a number of reasons for favoring iterative combinatorial auction designs. Several promising ascending auction formats have been developed throughout the past few years based on primal-dual and subgradient algorithms and linear programming theory. Prices are interpreted as a feasible dual solution and the provisional allocation is interpreted as a feasible primal solution. iBundle( 3) (Parkes and Ungar 2000), dVSV (de Vries et al. 2007) and the Ascending Proxy auction (Ausubel and Milgrom 2002) result in VCG payoffs when the coalitional value function satisfies the buyer submodularity condition and bidders bid straightforward, which is an expost Nash equilibrium in that case. iBEA and CreditDebit auctions (Mishra and Parkes 2007) do not even require the buyer submodularity condition and achieve the same properties for general valuations. In many situations, however, one cannot assume bidders to bid straightforward and it is not clear from the theory how these non-linear personalized price auctions (NLPPAs) perform in this case. Robustness of auctions with respect to different bidding behavior is therefore a critical issue for any application. We have conducted a large number of computational experiments to analyze the performance of NLPPA designs with respect to different bidding strategies and different valuation models. We compare the results of NLPPAs to those of the VCG auction and those of iterative combinatorial auctions with approximate linear prices, such as ALPS (Bichler et al. 2009) and the Combinatorial Clock auction (Porter et al. 2003).
Recursive deconvolution of combinatorial chemical libraries.
Erb, E; Janda, K D; Brenner, S
1994-01-01
A recursive strategy that solves for the active members of a chemical library is presented. A pentapeptide library with an alphabet of Gly, Leu, Phe, and Tyr (1024 members) was constructed on a solid support by the method of split synthesis. One member of this library (NH2-Tyr-Gly-Gly-Phe-Leu) is a native binder to a beta-endorphin antibody. A variation of the split synthesis approach is used to build the combinatorial library. In four vials, a member of the library's alphabet is coupled to a...
Quantum resonance for simulating combinatorial problems
International Nuclear Information System (INIS)
Zak, Michail; Fijany, Amir
2005-01-01
Quantum computing by simulations is based upon similarity between mathematical formalism of a quantum phenomenon and phenomena to be analyzed. In this Letter, the mathematical formalism of quantum resonance combined with tensor product decomposability of unitary evolutions is mapped onto a class of NP-complete combinatorial problems. It has been demonstrated that nature has polynomial resources for solving NP-complete problems and that will help to develop a new strategy for artificial intelligence, as well as to re-evaluate the role of natural selection in biological evolution
Automatic generation of combinatorial test data
Zhang, Jian; Ma, Feifei
2014-01-01
This book reviews the state-of-the-art in combinatorial testing, with particular emphasis on the automatic generation of test data. It describes the most commonly used approaches in this area - including algebraic construction, greedy methods, evolutionary computation, constraint solving and optimization - and explains major algorithms with examples. In addition, the book lists a number of test generation tools, as well as benchmarks and applications. Addressing a multidisciplinary topic, it will be of particular interest to researchers and professionals in the areas of software testing, combi
Method and apparatus for combinatorial chemistry
Foote, Robert S [Oak Ridge, TN
2012-06-05
A method and apparatus are provided for performing light-directed reactions in spatially addressable channels within a plurality of channels. One aspect of the invention employs photoactivatable reagents in solutions disposed into spatially addressable flow streams to control the parallel synthesis of molecules immobilized within the channels. The reagents may be photoactivated within a subset of channels at the site of immobilized substrate molecules or at a light-addressable site upstream from the substrate molecules. The method and apparatus of the invention find particularly utility in the synthesis of biopolymer arrays, e.g., oligonucleotides, peptides and carbohydrates, and in the combinatorial synthesis of small molecule arrays for drug discovery.
Quantum annealing for combinatorial clustering
Kumar, Vaibhaw; Bass, Gideon; Tomlin, Casey; Dulny, Joseph
2018-02-01
Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of within-the-cluster distances between points. The straightforward approach involves examining all the possible assignments of points to each of the clusters. This approach guarantees the solution will be a global minimum; however, the number of possible assignments scales quickly with the number of data points and becomes computationally intractable even for very small datasets. In order to circumvent this issue, cost function minima are found using popular local search-based heuristic approaches such as k-means and hierarchical clustering. Due to their greedy nature, such techniques do not guarantee that a global minimum will be found and can lead to sub-optimal clustering assignments. Other classes of global search-based techniques, such as simulated annealing, tabu search, and genetic algorithms, may offer better quality results but can be too time-consuming to implement. In this work, we describe how quantum annealing can be used to carry out clustering. We map the clustering objective to a quadratic binary optimization problem and discuss two clustering algorithms which are then implemented on commercially available quantum annealing hardware, as well as on a purely classical solver "qbsolv." The first algorithm assigns N data points to K clusters, and the second one can be used to perform binary clustering in a hierarchical manner. We present our results in the form of benchmarks against well-known k-means clustering and discuss the advantages and disadvantages of the proposed techniques.
On Definitions and Existence of Combinatorial Entropy of 2d Fields
DEFF Research Database (Denmark)
Forchhammer, Søren Otto; Shtarkov, Yuri; Justesen, Jørn
1998-01-01
Different definitions of combinatorial entropy is presented and conditions for their existence examined.......Different definitions of combinatorial entropy is presented and conditions for their existence examined....
Silva, Alessandro
1993-01-01
The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.
Eisenhart, Luther Pfahler
2005-01-01
This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.
Combinatorial Quantum Field Theory and Gluing Formula for Determinants
Reshetikhin, N.; Vertman, B.
2015-01-01
We define the combinatorial Dirichlet-to-Neumann operator and establish a gluing formula for determinants of discrete Laplacians using a combinatorial Gaussian quantum field theory. In case of a diagonal inner product on cochains we provide an explicit local expression for the discrete
Combinatorial Libraries of Bis-Heterocyclic Compounds with Skeletal Diversity
Soural, Miroslav; Bouillon, Isabelle; Krchňák, Viktor
2009-01-01
Combinatorial solid-phase synthesis of bis-heterocyclic compounds, characterized by the presence of two heterocyclic cores connected by a spacer of variable length/structure, provided structurally heterogeneous libraries with skeletal diversity. Both heterocyclic rings were assembled on resin in a combinatorial fashion. PMID:18811208
Combinatorial Libraries of Bis-Heterocyclic Compounds with Skeletal Diversity
Soural, Miroslav; Bouillon, Isabelle; Krchňák, Viktor
2008-01-01
Combinatorial solid-phase synthesis of bis-heterocyclic compounds, characterized by the presence of two heterocyclic cores connected by a spacer of variable length/structure, provided structurally heterogeneous libraries with skeletal diversity. Both heterocyclic rings were assembled on resin in a combinatorial fashion.
Combinatorial identities for tenth order mock theta functions
Indian Academy of Sciences (India)
44
which lead us to one 4-way and one 3-way combinatorial identity. ... mock theta functions, partition identities and different combinatorial parameters, see for ... 3. Example 1.1. There are twelve (n + 1)–color partitions of 2: 21, 21 + 01, 11 + 11, ...
Development of Combinatorial Methods for Alloy Design and Optimization
International Nuclear Information System (INIS)
Pharr, George M.; George, Easo P.; Santella, Michael L
2005-01-01
The primary goal of this research was to develop a comprehensive methodology for designing and optimizing metallic alloys by combinatorial principles. Because conventional techniques for alloy preparation are unavoidably restrictive in the range of alloy composition that can be examined, combinatorial methods promise to significantly reduce the time, energy, and expense needed for alloy design. Combinatorial methods can be developed not only to optimize existing alloys, but to explore and develop new ones as well. The scientific approach involved fabricating an alloy specimen with a continuous distribution of binary and ternary alloy compositions across its surface--an ''alloy library''--and then using spatially resolved probing techniques to characterize its structure, composition, and relevant properties. The three specific objectives of the project were: (1) to devise means by which simple test specimens with a library of alloy compositions spanning the range interest can be produced; (2) to assess how well the properties of the combinatorial specimen reproduce those of the conventionally processed alloys; and (3) to devise screening tools which can be used to rapidly assess the important properties of the alloys. As proof of principle, the methodology was applied to the Fe-Ni-Cr ternary alloy system that constitutes many commercially important materials such as stainless steels and the H-series and C-series heat and corrosion resistant casting alloys. Three different techniques were developed for making alloy libraries: (1) vapor deposition of discrete thin films on an appropriate substrate and then alloying them together by solid-state diffusion; (2) co-deposition of the alloying elements from three separate magnetron sputtering sources onto an inert substrate; and (3) localized melting of thin films with a focused electron-beam welding system. Each of the techniques was found to have its own advantages and disadvantages. A new and very powerful technique for
A Robust Parallel Algorithm for Combinatorial Compressed Sensing
Mendoza-Smith, Rodrigo; Tanner, Jared W.; Wechsung, Florian
2018-04-01
In previous work two of the authors have shown that a vector $x \\in \\mathbb{R}^n$ with at most $k Parallel-$\\ell_0$ decoding algorithm, where $\\mathrm{nnz}(A)$ denotes the number of nonzero entries in $A \\in \\mathbb{R}^{m \\times n}$. In this paper we present the Robust-$\\ell_0$ decoding algorithm, which robustifies Parallel-$\\ell_0$ when the sketch $Ax$ is corrupted by additive noise. This robustness is achieved by approximating the asymptotic posterior distribution of values in the sketch given its corrupted measurements. We provide analytic expressions that approximate these posteriors under the assumptions that the nonzero entries in the signal and the noise are drawn from continuous distributions. Numerical experiments presented show that Robust-$\\ell_0$ is superior to existing greedy and combinatorial compressed sensing algorithms in the presence of small to moderate signal-to-noise ratios in the setting of Gaussian signals and Gaussian additive noise.
Exact model reduction of combinatorial reaction networks
Directory of Open Access Journals (Sweden)
Fey Dirk
2008-08-01
Full Text Available Abstract Background Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models. Results We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs to a model with 87 ODEs. Conclusion The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks.
Optical geometry across the horizon
International Nuclear Information System (INIS)
Jonsson, Rickard
2006-01-01
In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework
Heterogenous phase as a mean in combinatorial chemistry
International Nuclear Information System (INIS)
Abdel-Hamid, S.G.
2007-01-01
Combinatorial chemistry is a rapid and inexpensive technique for the synthesis of hundreds of thousands of organic compounds of potential medicinal activity. In the past few decades a large number of combinatorial libraries have been constructed, and significantly supplement the chemical diversity of the traditional collections of the potentially active medicinal compounds. Solid phase synthesis was used to enrich the combinatorial chemistry libraries, through the use of solid supports (resins) and their modified forms. Most of the new libraries of compounds appeared recently, were synthesized by the use of solid-phase. Solid-phase combinatorial chemistry (SPCC) is now considered as an outstanding branch in pharmaceutical chemistry research and used extensively as a tool for drug discovery within the context of high-throughput chemical synthesis. The best pure libraries synthesized by the use of solid phase combinatorial chemistry (SPCC) may well be those of intermediate complexity that are free of artifact-causing nuisance compounds. (author)
Directory of Open Access Journals (Sweden)
C. M. Scoby
2010-02-01
Full Text Available In this paper we study a new geometry setup for electro-optic sampling (EOS where the electron beam runs parallel to the ⟨110⟩ face of a ZnTe crystal and the probe laser is perpendicular to it and to the beam path. The simple setup is used to encode the time-of-arrival information of a 3.5 MeV<10 pC electron bunch on the spatial profile of the laser pulse. The electric field lines inside the dielectric bend at an angle due to a relatively large (n∼3 index of refraction of the ZnTe crystal. We found theoretically and experimentally that the EOS signal can be maximized with a proper choice of incoming laser polarization angle. We achieved single-shot nondestructive measurement of the relative time of arrival between the pump and the probe beams thus improving the temporal resolution of ultrafast relativistic electron diffraction experiments.
International Nuclear Information System (INIS)
Hull, C.M.
1993-01-01
The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)
Random vs. Combinatorial Methods for Discrete Event Simulation of a Grid Computer Network
Kuhn, D. Richard; Kacker, Raghu; Lei, Yu
2010-01-01
This study compared random and t-way combinatorial inputs of a network simulator, to determine if these two approaches produce significantly different deadlock detection for varying network configurations. Modeling deadlock detection is important for analyzing configuration changes that could inadvertently degrade network operations, or to determine modifications that could be made by attackers to deliberately induce deadlock. Discrete event simulation of a network may be conducted using random generation, of inputs. In this study, we compare random with combinatorial generation of inputs. Combinatorial (or t-way) testing requires every combination of any t parameter values to be covered by at least one test. Combinatorial methods can be highly effective because empirical data suggest that nearly all failures involve the interaction of a small number of parameters (1 to 6). Thus, for example, if all deadlocks involve at most 5-way interactions between n parameters, then exhaustive testing of all n-way interactions adds no additional information that would not be obtained by testing all 5-way interactions. While the maximum degree of interaction between parameters involved in the deadlocks clearly cannot be known in advance, covering all t-way interactions may be more efficient than using random generation of inputs. In this study we tested this hypothesis for t = 2, 3, and 4 for deadlock detection in a network simulation. Achieving the same degree of coverage provided by 4-way tests would have required approximately 3.2 times as many random tests; thus combinatorial methods were more efficient for detecting deadlocks involving a higher degree of interactions. The paper reviews explanations for these results and implications for modeling and simulation.
Combinatorial Pooling Enables Selective Sequencing of the Barley Gene Space
Lonardi, Stefano; Duma, Denisa; Alpert, Matthew; Cordero, Francesca; Beccuti, Marco; Bhat, Prasanna R.; Wu, Yonghui; Ciardo, Gianfranco; Alsaihati, Burair; Ma, Yaqin; Wanamaker, Steve; Resnik, Josh; Bozdag, Serdar; Luo, Ming-Cheng; Close, Timothy J.
2013-01-01
For the vast majority of species – including many economically or ecologically important organisms, progress in biological research is hampered due to the lack of a reference genome sequence. Despite recent advances in sequencing technologies, several factors still limit the availability of such a critical resource. At the same time, many research groups and international consortia have already produced BAC libraries and physical maps and now are in a position to proceed with the development of whole-genome sequences organized around a physical map anchored to a genetic map. We propose a BAC-by-BAC sequencing protocol that combines combinatorial pooling design and second-generation sequencing technology to efficiently approach denovo selective genome sequencing. We show that combinatorial pooling is a cost-effective and practical alternative to exhaustive DNA barcoding when preparing sequencing libraries for hundreds or thousands of DNA samples, such as in this case gene-bearing minimum-tiling-path BAC clones. The novelty of the protocol hinges on the computational ability to efficiently compare hundred millions of short reads and assign them to the correct BAC clones (deconvolution) so that the assembly can be carried out clone-by-clone. Experimental results on simulated data for the rice genome show that the deconvolution is very accurate, and the resulting BAC assemblies have high quality. Results on real data for a gene-rich subset of the barley genome confirm that the deconvolution is accurate and the BAC assemblies have good quality. While our method cannot provide the level of completeness that one would achieve with a comprehensive whole-genome sequencing project, we show that it is quite successful in reconstructing the gene sequences within BACs. In the case of plants such as barley, this level of sequence knowledge is sufficient to support critical end-point objectives such as map-based cloning and marker-assisted breeding. PMID:23592960
Combinatorial pooling enables selective sequencing of the barley gene space.
Directory of Open Access Journals (Sweden)
Stefano Lonardi
2013-04-01
Full Text Available For the vast majority of species - including many economically or ecologically important organisms, progress in biological research is hampered due to the lack of a reference genome sequence. Despite recent advances in sequencing technologies, several factors still limit the availability of such a critical resource. At the same time, many research groups and international consortia have already produced BAC libraries and physical maps and now are in a position to proceed with the development of whole-genome sequences organized around a physical map anchored to a genetic map. We propose a BAC-by-BAC sequencing protocol that combines combinatorial pooling design and second-generation sequencing technology to efficiently approach denovo selective genome sequencing. We show that combinatorial pooling is a cost-effective and practical alternative to exhaustive DNA barcoding when preparing sequencing libraries for hundreds or thousands of DNA samples, such as in this case gene-bearing minimum-tiling-path BAC clones. The novelty of the protocol hinges on the computational ability to efficiently compare hundred millions of short reads and assign them to the correct BAC clones (deconvolution so that the assembly can be carried out clone-by-clone. Experimental results on simulated data for the rice genome show that the deconvolution is very accurate, and the resulting BAC assemblies have high quality. Results on real data for a gene-rich subset of the barley genome confirm that the deconvolution is accurate and the BAC assemblies have good quality. While our method cannot provide the level of completeness that one would achieve with a comprehensive whole-genome sequencing project, we show that it is quite successful in reconstructing the gene sequences within BACs. In the case of plants such as barley, this level of sequence knowledge is sufficient to support critical end-point objectives such as map-based cloning and marker-assisted breeding.
Combinatorial pooling enables selective sequencing of the barley gene space.
Lonardi, Stefano; Duma, Denisa; Alpert, Matthew; Cordero, Francesca; Beccuti, Marco; Bhat, Prasanna R; Wu, Yonghui; Ciardo, Gianfranco; Alsaihati, Burair; Ma, Yaqin; Wanamaker, Steve; Resnik, Josh; Bozdag, Serdar; Luo, Ming-Cheng; Close, Timothy J
2013-04-01
For the vast majority of species - including many economically or ecologically important organisms, progress in biological research is hampered due to the lack of a reference genome sequence. Despite recent advances in sequencing technologies, several factors still limit the availability of such a critical resource. At the same time, many research groups and international consortia have already produced BAC libraries and physical maps and now are in a position to proceed with the development of whole-genome sequences organized around a physical map anchored to a genetic map. We propose a BAC-by-BAC sequencing protocol that combines combinatorial pooling design and second-generation sequencing technology to efficiently approach denovo selective genome sequencing. We show that combinatorial pooling is a cost-effective and practical alternative to exhaustive DNA barcoding when preparing sequencing libraries for hundreds or thousands of DNA samples, such as in this case gene-bearing minimum-tiling-path BAC clones. The novelty of the protocol hinges on the computational ability to efficiently compare hundred millions of short reads and assign them to the correct BAC clones (deconvolution) so that the assembly can be carried out clone-by-clone. Experimental results on simulated data for the rice genome show that the deconvolution is very accurate, and the resulting BAC assemblies have high quality. Results on real data for a gene-rich subset of the barley genome confirm that the deconvolution is accurate and the BAC assemblies have good quality. While our method cannot provide the level of completeness that one would achieve with a comprehensive whole-genome sequencing project, we show that it is quite successful in reconstructing the gene sequences within BACs. In the case of plants such as barley, this level of sequence knowledge is sufficient to support critical end-point objectives such as map-based cloning and marker-assisted breeding.
International Nuclear Information System (INIS)
Yamazaki, Rie; Nishioka, Seiko; Date, Hiroyuki; Shirato, Hiroki; Koike, Takao; Nishioka, Takeshi
2012-01-01
The use of stereotactic body radiotherapy (SBRT) is rapidly increasing. Presently, the most accurate method uses fiducial markers implanted near the tumor. A shortcoming of this method is that the beams turn off during the majority of the respiratory cycle, resulting in a prolonged treatment time. Recent advances in collimation technology have enabled continuous irradiation to a moving tumor. However, the lung is a dynamic organ characterized by inhalation exhalation cycles, during which marker/tumor geometry may change (i.e., misalignment), resulting in under-dosing to the tumor. Eight patients with lung cancer who were candidates for stereotactic radiotherapy were examined with 4D high-resolution CT. As a marker surrogate, virtual bronchoscopy using the pulmonary artery (VBPA) was conducted. To detect possible marker/tumor misalignment during the respiration cycle, the distance between the peripheral bronchus, where a marker could be implanted, and the center of gravity of a tumor were calculated for each respiratory phase. When the respiration cycle was divided into 10 phases, the median value was significantly larger for the 30%-70% respiratory phases compared to that for the 10% respiratory phase (P<0.05, Mann–Whitney U-test). These results demonstrate that physiological aspect must be considered when continuous tumor tracking is applied to a moving tumor. To minimize an “additional” internal target volume (ITV) margin, a marker should be placed approximately 2.5 cm from the tumor
Energy Technology Data Exchange (ETDEWEB)
Rasmussen, N.G. [Nanoscience Center, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø (Denmark); Simeoni, G.G., E-mail: ggsimeoni@outlook.com [Heinz Maier-Leibnitz Zentrum (MLZ) and Physics Department, Technical University of Munich, D-85748 Garching (Germany); Lefmann, K. [Nanoscience Center, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø (Denmark)
2016-04-21
A dedicated beam-focusing device has been designed for the direct geometry thermal-cold neutron time-of-flight spectrometer TOFTOF at the neutron facility FRM II (Garching, Germany). The prototype, based on the compressed Archimedes' mirror concept, benefits from the adaptive-optics technology (adjustable supermirror curvature) and the compact size (only 0.5 m long). We have simulated the neutron transport across the entire guide system. We present a detailed computer characterization of the existing device, along with the study of the factors mostly influencing the future improvement. We have optimized the simulated prototype as a function of the neutron wavelength, accounting also for all relevant features of a real instrument like the non-reflecting side edges. The results confirm the “chromatic” displacement of the focal point (flux density maximum) at fixed supermirror curvature, and the ability of a variable curvature to keep the focal point at the sample position. Our simulations are in excellent agreement with theoretical predictions and the experimentally measured beam profile. With respect to the possibility of a further upgrade, we find that supermirror coatings with m-values higher than 3.5 would have only marginal influence on the optimal behaviour, whereas comparable spectrometers could take advantage of longer focusing segments, with particular impact for the thermal region of the neutron spectrum.
International Nuclear Information System (INIS)
Itoh, Yoshiaki
2009-01-01
The combinatorial method is useful to obtain conserved quantities for some nonlinear integrable systems, as an alternative to the Lax representation method. Here we extend the combinatorial method and introduce an elementary geometry to show the vanishing of the Poisson brackets of the Hamiltonian structure for a Lotka-Volterra system of competing species. We associate a set of points on a circle with a set of species of the Lotka-Volterra system, where the dominance relations between points are given by the dominance relations between the species. We associate each term of the conserved quantities with a subset of points on the circle, which simplifies to show the vanishing of the Poisson brackets
Fallow), Stray
2009-01-01
Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and
Solar proton exposure of an ICRU sphere within a complex structure part II: Ray-trace geometry.
Slaba, Tony C; Wilson, John W; Badavi, Francis F; Reddell, Brandon D; Bahadori, Amir A
2016-06-01
A computationally efficient 3DHZETRN code with enhanced neutron and light ion (Z ≤ 2) propagation was recently developed for complex, inhomogeneous shield geometry described by combinatorial objects. Comparisons were made between 3DHZETRN results and Monte Carlo (MC) simulations at locations within the combinatorial geometry, and it was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in ray-trace geometry. This latest extension enables the code to be used within current engineering design practices utilizing fully detailed vehicle and habitat geometries. Through convergence testing, it is shown that fidelity in an actual shield geometry can be maintained in the discrete ray-trace description by systematically increasing the number of discrete rays used. It is also shown that this fidelity is carried into transport procedures and resulting exposure quantities without sacrificing computational efficiency. Published by Elsevier Ltd.
Bifurcation-based approach reveals synergism and optimal combinatorial perturbation.
Liu, Yanwei; Li, Shanshan; Liu, Zengrong; Wang, Ruiqi
2016-06-01
Cells accomplish the process of fate decisions and form terminal lineages through a series of binary choices in which cells switch stable states from one branch to another as the interacting strengths of regulatory factors continuously vary. Various combinatorial effects may occur because almost all regulatory processes are managed in a combinatorial fashion. Combinatorial regulation is crucial for cell fate decisions because it may effectively integrate many different signaling pathways to meet the higher regulation demand during cell development. However, whether the contribution of combinatorial regulation to the state transition is better than that of a single one and if so, what the optimal combination strategy is, seem to be significant issue from the point of view of both biology and mathematics. Using the approaches of combinatorial perturbations and bifurcation analysis, we provide a general framework for the quantitative analysis of synergism in molecular networks. Different from the known methods, the bifurcation-based approach depends only on stable state responses to stimuli because the state transition induced by combinatorial perturbations occurs between stable states. More importantly, an optimal combinatorial perturbation strategy can be determined by investigating the relationship between the bifurcation curve of a synergistic perturbation pair and the level set of a specific objective function. The approach is applied to two models, i.e., a theoretical multistable decision model and a biologically realistic CREB model, to show its validity, although the approach holds for a general class of biological systems.
Characterizing the combinatorial beam angle selection problem
Bangert, Mark; Ziegenhein, Peter; Oelfke, Uwe
2012-10-01
The beam angle selection (BAS) problem in intensity-modulated radiation therapy is often interpreted as a combinatorial optimization problem, i.e. finding the best combination of η beams in a discrete set of candidate beams. It is well established that the combinatorial BAS problem may be solved efficiently with metaheuristics such as simulated annealing or genetic algorithms. However, the underlying parameters of the optimization process, such as the inclusion of non-coplanar candidate beams, the angular resolution in the space of candidate beams, and the number of evaluated beam ensembles as well as the relative performance of different metaheuristics have not yet been systematically investigated. We study these open questions in a meta-analysis of four strategies for combinatorial optimization in order to provide a reference for future research related to the BAS problem in intensity-modulated radiation therapy treatment planning. We introduce a high-performance inverse planning engine for BAS. It performs a full fluence optimization for ≈3600 treatment plans per hour while handling up to 50 GB of dose influence data (≈1400 candidate beams). For three head and neck patients, we compare the relative performance of a genetic, a cross-entropy, a simulated annealing and a naive iterative algorithm. The selection of ensembles with 5, 7, 9 and 11 beams considering either only coplanar or all feasible candidate beams is studied for an angular resolution of 5°, 10°, 15° and 20° in the space of candidate beams. The impact of different convergence criteria is investigated in comparison to a fixed termination after the evaluation of 10 000 beam ensembles. In total, our simulations comprise a full fluence optimization for about 3000 000 treatment plans. All four combinatorial BAS strategies yield significant improvements of the objective function value and of the corresponding dose distributions compared to standard beam configurations with equi
Identification and Interrogation of Combinatorial Histone Modifications
Directory of Open Access Journals (Sweden)
Kelly R Karch
2013-12-01
Full Text Available Histone proteins are dynamically modified to mediate a variety of cellular processes including gene transcription, DNA damage repair, and apoptosis. Regulation of these processes occurs through the recruitment of non-histone proteins to chromatin by specific combinations of histone post-translational modifications (PTMs. Mass spectrometry has emerged as an essential tool to discover and quantify histone PTMs both within and between samples in an unbiased manner. Developments in mass spectrometry that allow for characterization of large histone peptides or intact protein has made it possible to determine which modifications occur simultaneously on a single histone polypeptide. A variety of techniques from biochemistry, biophysics, and chemical biology have been employed to determine the biological relevance of discovered combinatorial codes. This review first describes advancements in the field of mass spectrometry that have facilitated histone PTM analysis and then covers notable approaches to probe the biological relevance of these modifications in their nucleosomal context.
Characterizing the combinatorial beam angle selection problem
International Nuclear Information System (INIS)
Bangert, Mark; Ziegenhein, Peter; Oelfke, Uwe
2012-01-01
The beam angle selection (BAS) problem in intensity-modulated radiation therapy is often interpreted as a combinatorial optimization problem, i.e. finding the best combination of η beams in a discrete set of candidate beams. It is well established that the combinatorial BAS problem may be solved efficiently with metaheuristics such as simulated annealing or genetic algorithms. However, the underlying parameters of the optimization process, such as the inclusion of non-coplanar candidate beams, the angular resolution in the space of candidate beams, and the number of evaluated beam ensembles as well as the relative performance of different metaheuristics have not yet been systematically investigated. We study these open questions in a meta-analysis of four strategies for combinatorial optimization in order to provide a reference for future research related to the BAS problem in intensity-modulated radiation therapy treatment planning. We introduce a high-performance inverse planning engine for BAS. It performs a full fluence optimization for ≈3600 treatment plans per hour while handling up to 50 GB of dose influence data (≈1400 candidate beams). For three head and neck patients, we compare the relative performance of a genetic, a cross-entropy, a simulated annealing and a naive iterative algorithm. The selection of ensembles with 5, 7, 9 and 11 beams considering either only coplanar or all feasible candidate beams is studied for an angular resolution of 5°, 10°, 15° and 20° in the space of candidate beams. The impact of different convergence criteria is investigated in comparison to a fixed termination after the evaluation of 10 000 beam ensembles. In total, our simulations comprise a full fluence optimization for about 3000 000 treatment plans. All four combinatorial BAS strategies yield significant improvements of the objective function value and of the corresponding dose distributions compared to standard beam configurations with equi
Combinatorial nuclear level-density model
International Nuclear Information System (INIS)
Uhrenholt, H.; Åberg, S.; Dobrowolski, A.; Døssing, Th.; Ichikawa, T.; Möller, P.
2013-01-01
A microscopic nuclear level-density model is presented. The model is a completely combinatorial (micro-canonical) model based on the folded-Yukawa single-particle potential and includes explicit treatment of pairing, rotational and vibrational states. The microscopic character of all states enables extraction of level-distribution functions with respect to pairing gaps, parity and angular momentum. The results of the model are compared to available experimental data: level spacings at neutron separation energy, data on total level-density functions from the Oslo method, cumulative level densities from low-lying discrete states, and data on parity ratios. Spherical and deformed nuclei follow basically different coupling schemes, and we focus on deformed nuclei
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
On the Cut-off Point for Combinatorial Group Testing
DEFF Research Database (Denmark)
Fischer, Paul; Klasner, N.; Wegener, I.
1999-01-01
is answered by 1 if Q contains at least one essential object and by 0 otherwise. In the statistical setting the objects are essential, independently of each other, with a given probability p combinatorial setting the number k ... group testing is equal to p* = 12(3 - 5), i.e., the strategy of testing each object individually minimizes the average number of queries iff p >= p* or n = 1. In the combinatorial setting the worst case number of queries is of interest. It has been conjectured that the cut-off point of combinatorial...
Maximization of Tsallis entropy in the combinatorial formulation
International Nuclear Information System (INIS)
Suyari, Hiroki
2010-01-01
This paper presents the mathematical reformulation for maximization of Tsallis entropy S q in the combinatorial sense. More concretely, we generalize the original derivation of Maxwell-Boltzmann distribution law to Tsallis statistics by means of the corresponding generalized multinomial coefficient. Our results reveal that maximization of S 2-q under the usual expectation or S q under q-average using the escort expectation are naturally derived from the combinatorial formulations for Tsallis statistics with respective combinatorial dualities, that is, one for additive duality and the other for multiplicative duality.
Luo, Li; Luo, Le; Zhang, Xinli; He, Xiaoli
2017-07-10
Accurate forecasting of hospital outpatient visits is beneficial for the reasonable planning and allocation of healthcare resource to meet the medical demands. In terms of the multiple attributes of daily outpatient visits, such as randomness, cyclicity and trend, time series methods, ARIMA, can be a good choice for outpatient visits forecasting. On the other hand, the hospital outpatient visits are also affected by the doctors' scheduling and the effects are not pure random. Thinking about the impure specialty, this paper presents a new forecasting model that takes cyclicity and the day of the week effect into consideration. We formulate a seasonal ARIMA (SARIMA) model on a daily time series and then a single exponential smoothing (SES) model on the day of the week time series, and finally establish a combinatorial model by modifying them. The models are applied to 1 year of daily visits data of urban outpatients in two internal medicine departments of a large hospital in Chengdu, for forecasting the daily outpatient visits about 1 week ahead. The proposed model is applied to forecast the cross-sectional data for 7 consecutive days of daily outpatient visits over an 8-weeks period based on 43 weeks of observation data during 1 year. The results show that the two single traditional models and the combinatorial model are simplicity of implementation and low computational intensiveness, whilst being appropriate for short-term forecast horizons. Furthermore, the combinatorial model can capture the comprehensive features of the time series data better. Combinatorial model can achieve better prediction performance than the single model, with lower residuals variance and small mean of residual errors which needs to be optimized deeply on the next research step.
The World of Combinatorial Fuzzy Problems and the Efficiency of Fuzzy Approximation Algorithms
Yamakami, Tomoyuki
2015-01-01
We re-examine a practical aspect of combinatorial fuzzy problems of various types, including search, counting, optimization, and decision problems. We are focused only on those fuzzy problems that take series of fuzzy input objects and produce fuzzy values. To solve such problems efficiently, we design fast fuzzy algorithms, which are modeled by polynomial-time deterministic fuzzy Turing machines equipped with read-only auxiliary tapes and write-only output tapes and also modeled by polynomia...
The geometry of on-shell diagrams
Franco, Sebastián; Galloni, Daniele; Mariotti, Alberto
2014-08-01
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such as the Grassmannian. We perform a detailed investigation of the combinatorial and geometric objects associated to these graphs. We mainly focus on their relation to polytopes and toric geometry, the Grassmannian and its stratification. Our work extends the current understanding of these connections along several important fronts, most notably eliminating restrictions imposed by planarity, positivity, reducibility and edge removability. We illustrate our ideas with several explicit examples and introduce concrete methods that considerably simplify computations. We consider it highly likely that the structures unveiled in this article will arise in the on-shell study of scattering amplitudes beyond the planar limit. Our results can be conversely regarded as an expansion in the understanding of the Grassmannian in terms of bipartite graphs.
Implementation of a combinatorial cleavage and deprotection scheme
DEFF Research Database (Denmark)
Nielsen, John; Rasmussen, Palle H.
1996-01-01
Phthalhydrazide libraries are synthesized in solution from substituted hydrazines and phthalimides in several different library formats including single compounds, indexed sub-libraries and a full library. When carried out during solid-phase synthesis, this combinatorial cleavage and deprotection...
ON 3-WAY COMBINATORIAL IDENTITIES A. K. AGARWAL MEGHA ...
Indian Academy of Sciences (India)
36
∗Corresponding author: Department of Basic and Applied Sciences, University College of Engineering,. Punjabi ... In this paper we provide combinatorial meanings to two generalized basic ... 2010 Mathematics Subject Classification. 05A15 ...
Analysis and design of algorithms for combinatorial problems
Ausiello, G
1985-01-01
Combinatorial problems have been from the very beginning part of the history of mathematics. By the Sixties, the main classes of combinatorial problems had been defined. During that decade, a great number of research contributions in graph theory had been produced, which laid the foundations for most of the research in graph optimization in the following years. During the Seventies, a large number of special purpose models were developed. The impressive growth of this field since has been strongly determined by the demand of applications and influenced by the technological increases in computing power and the availability of data and software. The availability of such basic tools has led to the feasibility of the exact or well approximate solution of large scale realistic combinatorial optimization problems and has created a number of new combinatorial problems.
Olefin Metathesis in Peptidomimetics, Dynamic Combinatorial Chemistry, and Molecular Imprinting
National Research Council Canada - National Science Library
Low, Tammy K
2006-01-01
.... Our research goals consisted of employing olefin metathesis in the synthesis of peptidomimetics, and studying the feasibility of this method in dynamic combinatorial chemistry and molecular imprinting of nerve agents...
Dynamic combinatorial libraries: from exploring molecular recognition to systems chemistry.
Li, Jianwei; Nowak, Piotr; Otto, Sijbren
2013-06-26
Dynamic combinatorial chemistry (DCC) is a subset of combinatorial chemistry where the library members interconvert continuously by exchanging building blocks with each other. Dynamic combinatorial libraries (DCLs) are powerful tools for discovering the unexpected and have given rise to many fascinating molecules, ranging from interlocked structures to self-replicators. Furthermore, dynamic combinatorial molecular networks can produce emergent properties at systems level, which provide exciting new opportunities in systems chemistry. In this perspective we will highlight some new methodologies in this field and analyze selected examples of DCLs that are under thermodynamic control, leading to synthetic receptors, catalytic systems, and complex self-assembled supramolecular architectures. Also reviewed are extensions of the principles of DCC to systems that are not at equilibrium and may therefore harbor richer functional behavior. Examples include self-replication and molecular machines.
Novel Combinatorial Chemistry-Derived Inhibitors of Oncogenic Phosphatases
National Research Council Canada - National Science Library
Lazo, John
1999-01-01
Our overall goal of this US Army Breast Cancer Grant entitled "Novel Combinatorial Chemistry-Derived Inhibitors of Oncogenic Phosphatases" is to identity and develop novel therapeutic agents for human breast cancer...
Directory of Open Access Journals (Sweden)
Fushing Hsieh
2016-11-01
Full Text Available Discrete combinatorial optimization problems in real world are typically defined via an ensemble of potentially high dimensional measurements pertaining to all subjects of a system under study. We point out that such a data ensemble in fact embeds with system's information content that is not directly used in defining the combinatorial optimization problems. Can machine learning algorithms extract such information content and make combinatorial optimizing tasks more efficient? Would such algorithmic computations bring new perspectives into this classic topic of Applied Mathematics and Theoretical Computer Science? We show that answers to both questions are positive. One key reason is due to permutation invariance. That is, the data ensemble of subjects' measurement vectors is permutation invariant when it is represented through a subject-vs-measurement matrix. An unsupervised machine learning algorithm, called Data Mechanics (DM, is applied to find optimal permutations on row and column axes such that the permuted matrix reveals coupled deterministic and stochastic structures as the system's information content. The deterministic structures are shown to facilitate geometry-based divide-and-conquer scheme that helps optimizing task, while stochastic structures are used to generate an ensemble of mimicries retaining the deterministic structures, and then reveal the robustness pertaining to the original version of optimal solution. Two simulated systems, Assignment problem and Traveling Salesman problem, are considered. Beyond demonstrating computational advantages and intrinsic robustness in the two systems, we propose brand new robust optimal solutions. We believe such robust versions of optimal solutions are potentially more realistic and practical in real world settings.
The Combinatorial Rigidity Conjecture is False for Cubic Polynomials
DEFF Research Database (Denmark)
Henriksen, Christian
2003-01-01
We show that there exist two cubic polynomials with connected Julia sets which are combinatorially equivalent but not topologically conjugate on their Julia sets. This disproves a conjecture by McMullen from 1995.......We show that there exist two cubic polynomials with connected Julia sets which are combinatorially equivalent but not topologically conjugate on their Julia sets. This disproves a conjecture by McMullen from 1995....
Distributing the computation in combinatorial optimization experiments over the cloud
Mario Brcic; Nikica Hlupic; Nenad Katanic
2017-01-01
Combinatorial optimization is an area of great importance since many of the real-world problems have discrete parameters which are part of the objective function to be optimized. Development of combinatorial optimization algorithms is guided by the empirical study of the candidate ideas and their performance over a wide range of settings or scenarios to infer general conclusions. Number of scenarios can be overwhelming, especially when modeling uncertainty in some of the problem’s parameters....
Enabling high performance computational science through combinatorial algorithms
International Nuclear Information System (INIS)
Boman, Erik G; Bozdag, Doruk; Catalyurek, Umit V; Devine, Karen D; Gebremedhin, Assefaw H; Hovland, Paul D; Pothen, Alex; Strout, Michelle Mills
2007-01-01
The Combinatorial Scientific Computing and Petascale Simulations (CSCAPES) Institute is developing algorithms and software for combinatorial problems that play an enabling role in scientific and engineering computations. Discrete algorithms will be increasingly critical for achieving high performance for irregular problems on petascale architectures. This paper describes recent contributions by researchers at the CSCAPES Institute in the areas of load balancing, parallel graph coloring, performance improvement, and parallel automatic differentiation
On the combinatorial foundations of Regge-calculus
International Nuclear Information System (INIS)
Budach, L.
1989-01-01
Lipschitz-Killing curvatures of piecewise flat spaces are combinatorial analogues of Lipschitz-Killing curvatures of Riemannian manifolds. In the following paper rigorous combinatorial representations and proofs of all basic results for Lipschitz-Killing curvatures not using analytic arguments are given. The principal tools for an elementary representation of Regge calculus can be developed by means of basic properties of dihedral angles. (author)
Immune-Stimulating Combinatorial Therapy for Prostate Cancer
2016-10-01
Overlap: None 20 90061946 (Drake) Title: Epigenetic Drugs and Immuno Therapy for Prostate Cancer (EDIT-PC) Effort: 1.2 calendar months (10% effort...AWARD NUMBER: W81XWH-15-1-0667 TITLE: Immune-Stimulating Combinatorial Therapy for Prostate Cancer PRINCIPAL INVESTIGATOR: Robert Ivkov...Stimulating Combinatorial Therapy for Prostate Cancer 5a. CONTRACT NUMBER 5b. GRANT NUMBER W81XWH-15-1-0667 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S
Enabling high performance computational science through combinatorial algorithms
Energy Technology Data Exchange (ETDEWEB)
Boman, Erik G [Discrete Algorithms and Math Department, Sandia National Laboratories (United States); Bozdag, Doruk [Biomedical Informatics, and Electrical and Computer Engineering, Ohio State University (United States); Catalyurek, Umit V [Biomedical Informatics, and Electrical and Computer Engineering, Ohio State University (United States); Devine, Karen D [Discrete Algorithms and Math Department, Sandia National Laboratories (United States); Gebremedhin, Assefaw H [Computer Science and Center for Computational Science, Old Dominion University (United States); Hovland, Paul D [Mathematics and Computer Science Division, Argonne National Laboratory (United States); Pothen, Alex [Computer Science and Center for Computational Science, Old Dominion University (United States); Strout, Michelle Mills [Computer Science, Colorado State University (United States)
2007-07-15
The Combinatorial Scientific Computing and Petascale Simulations (CSCAPES) Institute is developing algorithms and software for combinatorial problems that play an enabling role in scientific and engineering computations. Discrete algorithms will be increasingly critical for achieving high performance for irregular problems on petascale architectures. This paper describes recent contributions by researchers at the CSCAPES Institute in the areas of load balancing, parallel graph coloring, performance improvement, and parallel automatic differentiation.
Combinatorial Dyson-Schwinger equations and inductive data types
Kock, Joachim
2016-06-01
The goal of this contribution is to explain the analogy between combinatorial Dyson-Schwinger equations and inductive data types to a readership of mathematical physicists. The connection relies on an interpretation of combinatorial Dyson-Schwinger equations as fixpoint equations for polynomial functors (established elsewhere by the author, and summarised here), combined with the now-classical fact that polynomial functors provide semantics for inductive types. The paper is expository, and comprises also a brief introduction to type theory.
Interactions between Digital Geometry and Combinatorics on Words
Directory of Open Access Journals (Sweden)
Srečko Brlek
2011-08-01
Full Text Available We review some recent results in digital geometry obtained by using a combinatorics on words approach to discrete geometry. Motivated on the one hand by the well-known theory of Sturmian words which model conveniently discrete lines in the plane, and on the other hand by the development of digital geometry, this study reveals strong links between the two fields. Discrete figures are identified with polyominoes encoded by words. The combinatorial tools lead to elegant descriptions of geometrical features and efficient algorithms. Among these, radix-trees are useful for efficiently detecting path intersection, Lyndon and Christoffel words appear as the main tools for describing digital convexity; equations on words allow to better understand tilings by translations.
3-D world modeling based on combinatorial geometry for autonomous robot navigation
International Nuclear Information System (INIS)
Goldstein, M.; Pin, F.G.; De Saussure, G.; Weisbin, C.R.
1987-01-01
In applications of robotics to surveillance and mapping at nuclear facilities the scene to be described is three-dimensional. Using range data a 3-D model of the environment can be built. First, each measured point on the object surface is surrounded by a solid sphere with a radius determined by the range to that point. Then the 3-D shapes of the visible surfaces are obtained by taking the (Boolean) union of the spheres. Using this representation distances to boundary surfaces can be efficiently calculated. This feature is particularly useful for navigation purposes. The efficiency of the proposed approach is illustrated by a simulation of a spherical robot navigating in a 3-D room with static obstacles
Combinatorial differential geometry and ideal Bianchi-Ricci identities II - the torsion case
Czech Academy of Sciences Publication Activity Database
Janyška, J.; Markl, Martin
2012-01-01
Roč. 48, č. 1 (2012), s. 61-80 ISSN 0044-8753 R&D Projects: GA ČR GA201/08/0397 Institutional support: RVO:67985840 Keywords : natural operator * linear connection * torsion Subject RIV: BA - General Mathematics http://www.dml.cz/handle/10338.dmlcz/142092
Meyer, Walter J
2006-01-01
Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...
Indian Academy of Sciences (India)
algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.
International Nuclear Information System (INIS)
Sloane, Peter
2007-01-01
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
Energy Technology Data Exchange (ETDEWEB)
Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)
2007-09-15
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
Combinatorial approaches to evaluate nanodiamond uptake and induced cellular fate
Eldawud, Reem; Reitzig, Manuela; Opitz, Jörg; Rojansakul, Yon; Jiang, Wenjuan; Nangia, Shikha; Zoica Dinu, Cerasela
2016-02-01
Nanodiamonds (NDs) are an emerging class of engineered nanomaterials that hold great promise for the next generation of bionanotechnological products to be used for drug and gene delivery, or for bio-imaging and biosensing. Previous studies have shown that upon their cellular uptake, NDs exhibit high biocompatibility in various in vitro and in vivo set-ups. Herein we hypothesized that the increased NDs biocompatibility is a result of minimum membrane perturbations and their reduced ability to induce disruption or damage during cellular translocation. Using multi-scale combinatorial approaches that simulate ND-membrane interactions, we correlated NDs real-time cellular uptake and kinetics with the ND-induced membrane fluctuations to derive energy requirements for the uptake to occur. Our discrete and real-time analyses showed that the majority of NDs internalization occurs within 2 h of cellular exposure, however, with no effects on cellular viability, proliferation or cellular behavior. Furthermore, our simulation analyses using coarse-grained models identified key changes in the energy profile, membrane deformation and recovery time, all functions of the average ND or ND-based agglomerate size. Understanding the mechanisms responsible for ND-cell membrane interactions could possibly advance their implementation in various biomedical applications.
Combinatorial approaches to evaluate nanodiamond uptake and induced cellular fate
Eldawud, Reem; Reitzig, Manuela; Opitz, Jörg; Rojansakul, Yon; Jiang, Wenjuan; Nangia, Shikha; Dinu, Cerasela Zoica
2016-01-01
Nanodiamonds (NDs) are an emerging class of engineered nanomaterials that hold great promise for the next generation of bionanotechnological products to be used for drug and gene delivery, or for bio-imaging and biosensing. Previous studies have shown that upon their cellular uptake, NDs exhibit high biocompatibility in various in vitro and in vivo set-ups. Herein we hypothesized that the increased NDs biocompatibility is a result of minimum membrane perturbations and their reduced ability to induce disruption or damage during cellular translocation. Using multi-scale combinatorial approaches that simulate ND-membrane interactions, we correlated NDs real-time cellular uptake and kinetics with the ND-induced membrane fluctuations to derive energy requirements for the uptake to occur. Our discrete and real-time analyses showed that the majority of NDs internalization occurs within 2 h of cellular exposure, however, with no effects on cellular viability, proliferation or cellular behavior. Furthermore, our simulation analyses using coarse-grained models identified key changes in the energy profile, membrane deformation and recovery time, all functions of the average ND or ND-based agglomerate size. Understanding the mechanisms responsible for ND-cell membrane interactions could possibly advance their implementation in various biomedical applications. PMID:26820775
Combinatorial approaches to evaluate nanodiamond uptake and induced cellular fate
International Nuclear Information System (INIS)
Eldawud, Reem; Dinu, Cerasela Zoica; Reitzig, Manuela; Opitz, Jörg; Rojansakul, Yon; Jiang, Wenjuan; Nangia, Shikha
2016-01-01
Nanodiamonds (NDs) are an emerging class of engineered nanomaterials that hold great promise for the next generation of bionanotechnological products to be used for drug and gene delivery, or for bio-imaging and biosensing. Previous studies have shown that upon their cellular uptake, NDs exhibit high biocompatibility in various in vitro and in vivo set-ups. Herein we hypothesized that the increased NDs biocompatibility is a result of minimum membrane perturbations and their reduced ability to induce disruption or damage during cellular translocation. Using multi-scale combinatorial approaches that simulate ND-membrane interactions, we correlated NDs real-time cellular uptake and kinetics with the ND-induced membrane fluctuations to derive energy requirements for the uptake to occur. Our discrete and real-time analyses showed that the majority of NDs internalization occurs within 2 h of cellular exposure, however, with no effects on cellular viability, proliferation or cellular behavior. Furthermore, our simulation analyses using coarse-grained models identified key changes in the energy profile, membrane deformation and recovery time, all functions of the average ND or ND-based agglomerate size. Understanding the mechanisms responsible for ND-cell membrane interactions could possibly advance their implementation in various biomedical applications. (paper)
Combinatorial approaches to evaluate nanodiamond uptake and induced cellular fate.
Eldawud, Reem; Reitzig, Manuela; Opitz, Jörg; Rojansakul, Yon; Jiang, Wenjuan; Nangia, Shikha; Dinu, Cerasela Zoica
2016-02-26
Nanodiamonds (NDs) are an emerging class of engineered nanomaterials that hold great promise for the next generation of bionanotechnological products to be used for drug and gene delivery, or for bio-imaging and biosensing. Previous studies have shown that upon their cellular uptake, NDs exhibit high biocompatibility in various in vitro and in vivo set-ups. Herein we hypothesized that the increased NDs biocompatibility is a result of minimum membrane perturbations and their reduced ability to induce disruption or damage during cellular translocation. Using multi-scale combinatorial approaches that simulate ND-membrane interactions, we correlated NDs real-time cellular uptake and kinetics with the ND-induced membrane fluctuations to derive energy requirements for the uptake to occur. Our discrete and real-time analyses showed that the majority of NDs internalization occurs within 2 h of cellular exposure, however, with no effects on cellular viability, proliferation or cellular behavior. Furthermore, our simulation analyses using coarse-grained models identified key changes in the energy profile, membrane deformation and recovery time, all functions of the average ND or ND-based agglomerate size. Understanding the mechanisms responsible for ND-cell membrane interactions could possibly advance their implementation in various biomedical applications.
A combinatorial approach to angiosperm pollen morphology.
Mander, Luke
2016-11-30
Angiosperms (flowering plants) are strikingly diverse. This is clearly expressed in the morphology of their pollen grains, which are characterized by enormous variety in their shape and patterning. In this paper, I approach angiosperm pollen morphology from the perspective of enumerative combinatorics. This involves generating angiosperm pollen morphotypes by algorithmically combining character states and enumerating the results of these combinations. I use this approach to generate 3 643 200 pollen morphotypes, which I visualize using a parallel-coordinates plot. This represents a raw morphospace. To compare real-world and theoretical morphologies, I map the pollen of 1008 species of Neotropical angiosperms growing on Barro Colorado Island (BCI), Panama, onto this raw morphospace. This highlights that, in addition to their well-documented taxonomic diversity, Neotropical rainforests also represent an enormous reservoir of morphological diversity. Angiosperm pollen morphospace at BCI has been filled mostly by pollen morphotypes that are unique to single plant species. Repetition of pollen morphotypes among higher taxa at BCI reflects both constraint and convergence. This combinatorial approach to morphology addresses the complexity that results from large numbers of discrete character combinations and could be employed in any situation where organismal form can be captured by discrete morphological characters. © 2016 The Author(s).
Scalable Combinatorial Tools for Health Disparities Research
Directory of Open Access Journals (Sweden)
Michael A. Langston
2014-10-01
Full Text Available Despite staggering investments made in unraveling the human genome, current estimates suggest that as much as 90% of the variance in cancer and chronic diseases can be attributed to factors outside an individual’s genetic endowment, particularly to environmental exposures experienced across his or her life course. New analytical approaches are clearly required as investigators turn to complicated systems theory and ecological, place-based and life-history perspectives in order to understand more clearly the relationships between social determinants, environmental exposures and health disparities. While traditional data analysis techniques remain foundational to health disparities research, they are easily overwhelmed by the ever-increasing size and heterogeneity of available data needed to illuminate latent gene x environment interactions. This has prompted the adaptation and application of scalable combinatorial methods, many from genome science research, to the study of population health. Most of these powerful tools are algorithmically sophisticated, highly automated and mathematically abstract. Their utility motivates the main theme of this paper, which is to describe real applications of innovative transdisciplinary models and analyses in an effort to help move the research community closer toward identifying the causal mechanisms and associated environmental contexts underlying health disparities. The public health exposome is used as a contemporary focus for addressing the complex nature of this subject.
Combinatorial effects of odorants on mouse behavior
Saraiva, Luis R.; Kondoh, Kunio; Ye, Xiaolan; Yoon, Kyoung-hye; Hernandez, Marcus; Buck, Linda B.
2016-01-01
The mechanisms by which odors induce instinctive behaviors are largely unknown. Odor detection in the mouse nose is mediated by >1, 000 different odorant receptors (ORs) and trace amine-associated receptors (TAARs). Odor perceptions are encoded combinatorially by ORs and can be altered by slight changes in the combination of activated receptors. However, the stereotyped nature of instinctive odor responses suggests the involvement of specific receptors and genetically programmed neural circuits relatively immune to extraneous odor stimuli and receptor inputs. Here, we report that, contrary to expectation, innate odor-induced behaviors can be context-dependent. First, different ligands for a given TAAR can vary in behavioral effect. Second, when combined, some attractive and aversive odorants neutralize one another’s behavioral effects. Both a TAAR ligand and a common odorant block aversion to a predator odor, indicating that this ability is not unique to TAARs and can extend to an aversive response of potential importance to survival. In vitro testing of single receptors with binary odorant mixtures indicates that behavioral blocking can occur without receptor antagonism in the nose. Moreover, genetic ablation of a single receptor prevents its cognate ligand from blocking predator odor aversion, indicating that the blocking requires sensory input from the receptor. Together, these findings indicate that innate odor-induced behaviors can depend on context, that signals from a single receptor can block innate odor aversion, and that instinctive behavioral responses to odors can be modulated by interactions in the brain among signals derived from different receptors. PMID:27208093
International Nuclear Information System (INIS)
Al Issa, Suleiman; Macián-Juan, Rafael
2017-01-01
Highlights: • CCFL characteristics are investigated in PWR large-scale hot-leg pipe geometry. • Image processing of air-water interface produced time-averaged interface distributions. • Time-averages provide a comparative method of CCFL characteristics among different studies. • CCFL correlations depend upon the range of investigated water delivery for Dh ≫ 50 mm. • 1D codes are incapable of investigating CCFL because of lack of interface distribution. - Abstract: Countercurrent Flow Limitation (CCFL) was experimentally investigated in a 1/3.9 downscaled COLLIDER facility with a 190 mm pipe’s diameter using air/water at 1 atmospheric pressure. Previous investigations provided knowledge over the onset of CCFL mechanisms. In current article, CCFL characteristics at the COLLIDER facility are measured and discussed along with time-averaged distributions of the air/water interface for a selected matrix of liquid/gas velocities. The article demonstrates the time-averaged interface as a useful method to identify CCFL characteristics at quasi-stationary flow conditions eliminating variations that appears in single images, and showing essential comparative flow features such as: the degree of restriction at the bend, the extension and the intensity of the two-phase mixing zones, and the average water level within the horizontal part and the steam generator. Consequently, making it possible to compare interface distributions obtained at different investigations. The distributions are also beneficial for CFD validations of CCFL as the instant chaotic gas/liquid interface is impossible to reproduce in CFD simulations. The current study shows that final CCFL characteristics curve (and the corresponding CCFL correlation) depends upon the covered measuring range of water delivery. It also shows that a hydraulic diameter should be sufficiently larger than 50 mm in order to obtain CCFL characteristics comparable to the 1:1 scale data (namely the UPTF data). Finally
Geometry essentials for dummies
Ryan, Mark
2011-01-01
Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque
Geometry, topology, and string theory
Energy Technology Data Exchange (ETDEWEB)
Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Geometry, topology, and string theory
International Nuclear Information System (INIS)
Varadarajan, Uday
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated
Arithmetic noncommutative geometry
Marcolli, Matilde
2005-01-01
Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...
"One-sample concept" micro-combinatory for high throughput TEM of binary films.
Sáfrán, György
2018-04-01
Phases of thin films may remarkably differ from that of bulk. Unlike to the comprehensive data files of Binary Phase Diagrams [1] available for bulk, complete phase maps for thin binary layers do not exist. This is due to both the diverse metastable, non-equilibrium or instable phases feasible in thin films and the required volume of characterization work with analytical techniques like TEM, SAED and EDS. The aim of the present work was to develop a method that remarkably facilitates the TEM study of the diverse binary phases of thin films, or the creation of phase maps. A micro-combinatorial method was worked out that enables both preparation and study of a gradient two-component film within a single TEM specimen. For a demonstration of the technique thin Mn x Al 1- x binary samples with evolving concentration from x = 0 to x = 1 have been prepared so that the transition from pure Mn to pure Al covers a 1.5 mm long track within the 3 mm diameter TEM grid. The proposed method enables the preparation and study of thin combinatorial samples including all feasible phases as a function of composition or other deposition parameters. Contrary to known "combinatorial chemistry", in which a series of different samples are deposited in one run, and investigated, one at a time, the present micro-combinatorial method produces a single specimen condensing a complete library of a binary system that can be studied, efficiently, within a single TEM session. That provides extremely high throughput for TEM characterization of composition-dependent phases, exploration of new materials, or the construction of phase diagrams of binary films. Copyright © 2018 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Kubo, Momoji; Ando, Minako; Sakahara, Satoshi; Jung, Changho; Seki, Kotaro; Kusagaya, Tomonori; Endou, Akira; Takami, Seiichi; Imamura, Akira; Miyamoto, Akira
2004-01-01
Recently, we have proposed a new concept called 'combinatorial computational chemistry' to realize a theoretical, high-throughput screening of catalysts and materials. We have already applied our combinatorial, computational-chemistry approach, mainly based on static first-principles calculations, to various catalysts and materials systems and its applicability to the catalysts and materials design was strongly confirmed. In order to realize more effective and efficient combinatorial, computational-chemistry screening, a high-speed, chemical-reaction-dynamics simulator based on quantum-chemical, molecular-dynamics method is essential. However, to the best of our knowledge, there is no chemical-reaction-dynamics simulator, which has an enough high-speed ability to perform a high-throughput screening. In the present study, we have succeeded in the development of a chemical-reaction-dynamics simulator based on our original, tight-binding, quantum-chemical, molecular-dynamics method, which is more than 5000 times faster than the regular first-principles, molecular-dynamics method. Moreover, its applicability and effectiveness to the atomistic clarification of the methanol-synthesis dynamics at reaction temperature were demonstrated
Azimi, Sayyed M; Sheridan, Steven D; Ghannad-Rezaie, Mostafa; Eimon, Peter M; Yanik, Mehmet Fatih
2018-05-01
Identification of optimal transcription-factor expression patterns to direct cellular differentiation along a desired pathway presents significant challenges. We demonstrate massively combinatorial screening of temporally-varying mRNA transcription factors to direct differentiation of neural progenitor cells using a dynamically-reconfigurable magnetically-guided spotting technology for localizing mRNA, enabling experiments on millimetre size spots. In addition, we present a time-interleaved delivery method that dramatically reduces fluctuations in the delivered transcription-factor copy-numbers per cell. We screened combinatorial and temporal delivery of a pool of midbrain-specific transcription factors to augment the generation of dopaminergic neurons. We show that the combinatorial delivery of LMX1A, FOXA2 and PITX3 is highly effective in generating dopaminergic neurons from midbrain progenitors. We show that LMX1A significantly increases TH -expression levels when delivered to neural progenitor cells either during proliferation or after induction of neural differentiation, while FOXA2 and PITX3 increase expression only when delivered prior to induction, demonstrating temporal dependence of factor addition. © 2018, Azimi et al.
The design of geometry teaching: learning from the geometry textbooks of Godfrey and Siddons
Fujita, Taro; Jones, Keith
2002-01-01
Deciding how to teach geometry remains a demanding task with one of major arguments being about how to combine the intuitive and deductive aspects of geometry into an effective teaching design. In order to try to obtain an insight into tackling this issue, this paper reports an analysis of innovative geometry textbooks which were published in the early part of the 20th Century, a time when significant efforts were being made to improve the teaching and learning of geometry. The analysis sugge...
Energy Technology Data Exchange (ETDEWEB)
Parsons, Brendon A.; Pinkerton, David K.; Wright, Bob W.; Synovec, Robert E.
2016-04-01
The illicit chemical alteration of petroleum fuels is of scientific interest, particularly to regulatory agencies which set fuel specifications, or excises based on those specifications. One type of alteration is the reaction of diesel fuel with concentrated sulfuric acid. Such reactions are known to subtly alter the chemical composition of the fuel, particularly the aromatic species native to the fuel. Comprehensive two-dimensional gas chromatography coupled with time-of-flight mass spectrometry (GC × GC–TOFMS) is ideally suited for the analysis of diesel fuel, but may provide the analyst with an overwhelming amount of data, particularly in sample-class comparison experiments comprised of many samples. The tile-based Fisher-ratio (F-ratio) method reduces the abundance of data in a GC × GC–TOFMS experiment to only the peaks which significantly distinguish the unaltered and acid altered sample classes. Three samples of diesel fuel from different filling stations were each altered to discover chemical features, i.e., analyte peaks, which were consistently changed by the acid reaction. Using different fuels prioritizes the discovery of features which are likely to be robust to the variation present between fuel samples and which will consequently be useful in determining whether an unknown sample has been acid altered. The subsequent analysis confirmed that aromatic species are removed by the acid alteration, with the degree of removal consistent with predicted reactivity toward electrophilic aromatic sulfonation. Additionally, we observed that alkenes and alkynes were also removed from the fuel, and that sulfur dioxide or compounds that degrade to sulfur dioxide are generated by the acid alteration. In addition to applying the previously reported tile-based F-ratio method, this report also expands null distribution analysis to algorithmically determine an F-ratio threshold to confidently select only the features which are sufficiently class-distinguishing. When
Parsons, Brendon A; Pinkerton, David K; Wright, Bob W; Synovec, Robert E
2016-04-01
The illicit chemical alteration of petroleum fuels is of keen interest, particularly to regulatory agencies that set fuel specifications, or taxes/credits based on those specifications. One type of alteration is the reaction of diesel fuel with concentrated sulfuric acid. Such reactions are known to subtly alter the chemical composition of the fuel, particularly the aromatic species native to the fuel. Comprehensive two-dimensional gas chromatography coupled with time-of-flight mass spectrometry (GC×GC-TOFMS) is well suited for the analysis of diesel fuel, but may provide the analyst with an overwhelming amount of data, particularly in sample-class comparison experiments comprised of many samples. Tile-based Fisher-ratio (F-ratio) analysis reduces the abundance of data in a GC×GC-TOFMS experiment to only the peaks which significantly distinguish the unaltered and acid altered sample classes. Three samples of diesel fuel from differently branded filling stations were each altered to discover chemical features, i.e., analyte peaks, which were consistently changed by the acid reaction. Using different fuels prioritizes the discovery of features likely to be robust to the variation present between fuel samples and may consequently be useful in determining whether an unknown sample has been acid altered. The subsequent analysis confirmed that aromatic species are removed by the acid alteration, with the degree of removal consistent with predicted reactivity toward electrophilic aromatic sulfonation. Additionally, we observed that alkenes and alkynes were also removed from the fuel, and that sulfur dioxide or compounds that degrade to sulfur dioxide are generated by the acid alteration. In addition to applying the previously reported tile-based F-ratio method, this report also expands null distribution analysis to algorithmically determine an F-ratio threshold to confidently select only the features which are sufficiently class-distinguishing. When applied to the acid
Solid-Phase Synthesis of Small Molecule Libraries using Double Combinatorial Chemistry
DEFF Research Database (Denmark)
Nielsen, John; Jensen, Flemming R.
1997-01-01
The first synthesis of a combinatorial library using double combinatorial chemistry is presented. Coupling of unprotected Fmoc-tyrosine to the solid support was followed by Mitsunobu O-alkylation. Introduction of a diacid linker yields a system in which the double combinatorial step can be demons......The first synthesis of a combinatorial library using double combinatorial chemistry is presented. Coupling of unprotected Fmoc-tyrosine to the solid support was followed by Mitsunobu O-alkylation. Introduction of a diacid linker yields a system in which the double combinatorial step can...
Individualized Pixel Synthesis and Characterization of Combinatorial Materials Chips
Directory of Open Access Journals (Sweden)
Xiao-Dong Xiang
2015-06-01
Full Text Available Conventionally, an experimentally determined phase diagram requires studies of phase formation at a range of temperatures for each composition, which takes years of effort from multiple research groups. Combinatorial materials chip technology, featuring high-throughput synthesis and characterization, is able to determine the phase diagram of an entire composition spread of a binary or ternary system at a single temperature on one materials library, which, though significantly increasing efficiency, still requires many libraries processed at a series of temperatures in order to complete a phase diagram. In this paper, we propose a “one-chip method” to construct a complete phase diagram by individually synthesizing each pixel step by step with a progressive pulse of energy to heat at different temperatures while monitoring the phase evolution on the pixel in situ in real time. Repeating this process pixel by pixel throughout the whole chip allows the entire binary or ternary phase diagram to be mapped on one chip in a single experiment. The feasibility of this methodology is demonstrated in a study of a Ge-Sb-Te ternary alloy system, on which the amorphous-crystalline phase boundary is determined.
Combinatorial Models for Assembly and Decomposition of Products
Directory of Open Access Journals (Sweden)
A. N. Bojko
2015-01-01
Full Text Available The paper discusses the most popular combinatorial models that are used for the synthesis of design solutions at the stage of the assembly process flow preparation. It shows that while assembling the product the relations of parts can be represented as a structure of preferences, which is formed on the basis of objective design restrictions put in at the stage of the product design. This structure is a binary preference relation pre-order. Its symmetrical part is equivalence and describes the entry of parts into the assembly unit. The asymmetric part is a partial order. It specifies part- ordering time in in the course of the assembly process. The structure of preferences is a minimal description of the restrictions and constraints in the assembly process. It can serve as a source for generating multiple assembly sequences of a product and its components, which are allowed by design. This multiplicity increases the likelihood of rational choice under uncertainty, unpredictable changes in the properties of technological or industrial systems.Incomplete dominance relation gives grounds for further examination and better understanding of the project situation. Operation field of the study is limited to a set of disparate elements of the partial order. Different strategies for processing the disparate elements may be offered, e.g. selection of the most informative pairs, comparison of which foremost linearizes the original partial order.
Bárány, Imre; Vilcu, Costin
2016-01-01
This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.
General Relativity: Geometry Meets Physics
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
Fundamental concepts of geometry
Meserve, Bruce E
1983-01-01
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.
Dayside merging and cusp geometry
International Nuclear Information System (INIS)
Crooker, N.U.
1979-01-01
Geometrical considerations are presented to show that dayside magnetic merging when constrained to act only where the fields are antiparallel results in lines of merging that converge at the polar cusps. An important consequence of this geometry is that no accelerated flows are predicted across the dayside magnetopause. Acceleration owing to merging acts in opposition to the magnetosheath flow at the merging point and produces the variably directed, slower-than-magnetosheath flows observed in the entry layer. Another consequence of the merging geometry is that much of the time closed field lines constitute the subsolar region of the magnetopause. The manner in which the polar cap convection patterns predicted by the proposed geometry change as the interplanetary field is rotated through 360 0 provides a unifying description of how the observed single circular vortex and the crescent-shaped double vortex patterns mutually evolve under the influence of a single operating principle
Balancing focused combinatorial libraries based on multiple GPCR ligands
Soltanshahi, Farhad; Mansley, Tamsin E.; Choi, Sun; Clark, Robert D.
2006-08-01
G-Protein coupled receptors (GPCRs) are important targets for drug discovery, and combinatorial chemistry is an important tool for pharmaceutical development. The absence of detailed structural information, however, limits the kinds of combinatorial design techniques that can be applied to GPCR targets. This is particularly problematic given the current emphasis on focused combinatorial libraries. By linking an incremental construction method (OptDesign) to the very fast shape-matching capability of ChemSpace, we have created an efficient method for designing targeted sublibraries that are topomerically similar to known actives. Multi-objective scoring allows consideration of multiple queries (actives) simultaneously. This can lead to a distribution of products skewed towards one particular query structure, however, particularly when the ligands of interest are quite dissimilar to one another. A novel pivoting technique is described which makes it possible to generate promising designs even under those circumstances. The approach is illustrated by application to some serotonergic agonists and chemokine antagonists.
Summation on the basis of combinatorial representation of equal powers
Directory of Open Access Journals (Sweden)
Alexander I. Nikonov
2016-03-01
Full Text Available In the paper the conclusion of combinatorial expressions for the sums of members of several sequences is considered. Conclusion is made on the basis of combinatorial representation of the sum of the weighted equal powers. The weighted members of a geometrical progression, the simple arithmetic-geometrical and combined progressions are subject to summation. One of principal places in the given conclusion occupies representation of members of each of the specified progressions in the form of matrix elements. The row of this matrix is formed with use of a gang of equal powers with the set weight factor. Besides, in work formulas of combinatorial identities with participation of free components of the sums of equal powers, and also separate power-member of sequence of equal powers or a geometrical progression are presented. All presented formulas have the general basis-components of the sums of equal powers.
Combinatorial vector fields and the valley structure of fitness landscapes.
Stadler, Bärbel M R; Stadler, Peter F
2010-12-01
Adaptive (downhill) walks are a computationally convenient way of analyzing the geometric structure of fitness landscapes. Their inherently stochastic nature has limited their mathematical analysis, however. Here we develop a framework that interprets adaptive walks as deterministic trajectories in combinatorial vector fields and in return associate these combinatorial vector fields with weights that measure their steepness across the landscape. We show that the combinatorial vector fields and their weights have a product structure that is governed by the neutrality of the landscape. This product structure makes practical computations feasible. The framework presented here also provides an alternative, and mathematically more convenient, way of defining notions of valleys, saddle points, and barriers in landscape. As an application, we propose a refined approximation for transition rates between macrostates that are associated with the valleys of the landscape.
Yan, Zongkai; Zhang, Xiaokun; Li, Guang; Cui, Yuxing; Jiang, Zhaolian; Liu, Wen; Peng, Zhi; Xiang, Yong
2018-01-01
The conventional methods for designing and preparing thin film based on wet process remain a challenge due to disadvantages such as time-consuming and ineffective, which hinders the development of novel materials. Herein, we present a high-throughput combinatorial technique for continuous thin film preparation relied on chemical bath deposition (CBD). The method is ideally used to prepare high-throughput combinatorial material library with low decomposition temperatures and high water- or oxygen-sensitivity at relatively high-temperature. To check this system, a Cu(In, Ga)Se (CIGS) thin films library doped with 0-19.04 at.% of antimony (Sb) was taken as an example to evaluate the regulation of varying Sb doping concentration on the grain growth, structure, morphology and electrical properties of CIGS thin film systemically. Combined with the Energy Dispersive Spectrometer (EDS), X-ray Photoelectron Spectroscopy (XPS), automated X-ray Diffraction (XRD) for rapid screening and Localized Electrochemical Impedance Spectroscopy (LEIS), it was confirmed that this combinatorial high-throughput system could be used to identify the composition with the optimal grain orientation growth, microstructure and electrical properties systematically, through accurately monitoring the doping content and material composition. According to the characterization results, a Sb2Se3 quasi-liquid phase promoted CIGS film-growth model has been put forward. In addition to CIGS thin film reported here, the combinatorial CBD also could be applied to the high-throughput screening of other sulfide thin film material systems.
Cartailler, Jerome; Kwon, Taekyung; Yuste, Rafael; Holcman, David
2018-03-07
Most synaptic excitatory connections are made on dendritic spines. But how the voltage in spines is modulated by its geometry remains unclear. To investigate the electrical properties of spines, we combine voltage imaging data with electro-diffusion modeling. We first present a temporal deconvolution procedure for the genetically encoded voltage sensor expressed in hippocampal cultured neurons and then use electro-diffusion theory to compute the electric field and the current-voltage conversion. We extract a range for the neck resistances of 〈R〉=100±35MΩ. When a significant current is injected in a spine, the neck resistance can be inversely proportional to its radius, but not to the radius square, as predicted by Ohm's law. We conclude that the postsynaptic voltage cannot only be modulated by changing the number of receptors, but also by the spine geometry. Thus, spine morphology could be a key component in determining synaptic transduction and plasticity. Copyright © 2018 Elsevier Inc. All rights reserved.
Recent advances in combinatorial biosynthesis for drug discovery
Directory of Open Access Journals (Sweden)
Sun H
2015-02-01
Full Text Available Huihua Sun,1,* Zihe Liu,1,* Huimin Zhao,1,2 Ee Lui Ang1 1Metabolic Engineering Research Laboratory, Institute of Chemical and Engineering Sciences, Agency for Science, Technology and Research, Singapore; 2Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA *These authors contributed equally to this work Abstract: Because of extraordinary structural diversity and broad biological activities, natural products have played a significant role in drug discovery. These therapeutically important secondary metabolites are assembled and modified by dedicated biosynthetic pathways in their host living organisms. Traditionally, chemists have attempted to synthesize natural product analogs that are important sources of new drugs. However, the extraordinary structural complexity of natural products sometimes makes it challenging for traditional chemical synthesis, which usually involves multiple steps, harsh conditions, toxic organic solvents, and byproduct wastes. In contrast, combinatorial biosynthesis exploits substrate promiscuity and employs engineered enzymes and pathways to produce novel “unnatural” natural products, substantially expanding the structural diversity of natural products with potential pharmaceutical value. Thus, combinatorial biosynthesis provides an environmentally friendly way to produce natural product analogs. Efficient expression of the combinatorial biosynthetic pathway in genetically tractable heterologous hosts can increase the titer of the compound, eventually resulting in less expensive drugs. In this review, we will discuss three major strategies for combinatorial biosynthesis: 1 precursor-directed biosynthesis; 2 enzyme-level modification, which includes swapping of the entire domains, modules and subunits, site-specific mutagenesis, and directed evolution; 3 pathway-level recombination. Recent examples of combinatorial biosynthesis employing these
Harańczyk, Maciej; Gutowski, Maciej
2007-01-01
We describe a procedure of finding low-energy tautomers of a molecule. The procedure consists of (i) combinatorial generation of a library of tautomers, (ii) screening based on the results of geometry optimization of initial structures performed at the density functional level of theory, and (iii) final refinement of geometry for the top hits at the second-order Möller-Plesset level of theory followed by single-point energy calculations at the coupled cluster level of theory with single, double, and perturbative triple excitations. The library of initial structures of various tautomers is generated with TauTGen, a tautomer generator program. The procedure proved to be successful for these molecular systems for which common chemical knowledge had not been sufficient to predict the most stable structures.
Combinatorial methods for advanced materials research and development
Energy Technology Data Exchange (ETDEWEB)
Cremer, R.; Dondorf, S.; Hauck, M.; Horbach, D.; Kaiser, M.; Krysta, S.; Kyrylov, O.; Muenstermann, E.; Philipps, M.; Reichert, K.; Strauch, G. [Rheinisch-Westfaelische Technische Hochschule Aachen (Germany). Lehrstuhl fuer Theoretische Huettenkunde
2001-10-01
The applicability of combinatorial methods in developing advanced materials is illustrated presenting four examples for the deposition and characterization of one- and two-dimensionally laterally graded coatings, which were deposited by means of (reactive) magnetron sputtering and plasma-enhanced chemical vapor deposition. To emphasize the advantages of combinatorial approaches, metastable hard coatings like (Ti,Al)N and (Ti,Al,Hf)N respectively, as well as Ge-Sb-Te based films for rewritable optical data storage were investigated with respect to the relations between structure, composition, and the desired materials properties. (orig.)
Combinatorial reasoning an introduction to the art of counting
DeTemple, Duane
2014-01-01
Written by well-known scholars in the field, this book introduces combinatorics alongside modern techniques, showcases the interdisciplinary aspects of the topic, and illustrates how to problem solve with a multitude of exercises throughout. The authors' approach is very reader-friendly and avoids the ""scholarly tone"" found in many books on this topic. Combinatorial Reasoning: An Introduction to the Art of Counting: Focuses on enumeration and combinatorial thinking as a way to develop a variety of effective approaches to solving counting problemsIncludes brief summaries of basic concepts f
Mitigation of Control Channel Jamming via Combinatorial Key Distribution
Falahati, Abolfazl; Azarafrooz, Mahdi
The problem of countering control channel jamming against internal adversaries in wireless ad hoc networks is addressed. Using combinatorial key distribution, a new method to secure the control channel access is introduced. This method, utilizes the established keys in the key establishment phase to hide the location of control channels without the need for a secure BS. This is in obtained by combination of a collision free one-way function and a combinatorial key establishment method. The proposed scheme can be considered as a special case of the ALOHA random access schemes which uses the common established keys as its seeds to generate the pattern of transmission.
Polyhedral and semidefinite programming methods in combinatorial optimization
Tunçel, Levent
2010-01-01
Since the early 1960s, polyhedral methods have played a central role in both the theory and practice of combinatorial optimization. Since the early 1990s, a new technique, semidefinite programming, has been increasingly applied to some combinatorial optimization problems. The semidefinite programming problem is the problem of optimizing a linear function of matrix variables, subject to finitely many linear inequalities and the positive semidefiniteness condition on some of the matrix variables. On certain problems, such as maximum cut, maximum satisfiability, maximum stable set and geometric r
On some interconnections between combinatorial optimization and extremal graph theory
Directory of Open Access Journals (Sweden)
Cvetković Dragoš M.
2004-01-01
Full Text Available The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set. While in combinatorial optimization the point is in developing efficient algorithms and heuristics for solving specified types of problems, the extremal graph theory deals with finding bounds for various graph invariants under some constraints and with constructing extremal graphs. We analyze by examples some interconnections and interactions of the two theories and propose some conclusions.
Fast Combinatorial Algorithm for the Solution of Linearly Constrained Least Squares Problems
Van Benthem, Mark H.; Keenan, Michael R.
2008-11-11
A fast combinatorial algorithm can significantly reduce the computational burden when solving general equality and inequality constrained least squares problems with large numbers of observation vectors. The combinatorial algorithm provides a mathematically rigorous solution and operates at great speed by reorganizing the calculations to take advantage of the combinatorial nature of the problems to be solved. The combinatorial algorithm exploits the structure that exists in large-scale problems in order to minimize the number of arithmetic operations required to obtain a solution.
1996-01-01
Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.
Morris, Barbara H.
2004-01-01
This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…
Numerically robust geometry engine for compound solid geometries
International Nuclear Information System (INIS)
Vlachoudis, V.; Sinuela-Pastor, D.
2013-01-01
Monte Carlo programs heavily rely on a fast and numerically robust solid geometry engines. However the success of solid modeling, depends on facilities for specifying and editing parameterized models through a user-friendly graphical front-end. Such a user interface has to be fast enough in order to be interactive for 2D and/or 3D displays, but at the same time numerically robust in order to display possible modeling errors at real time that could be critical for the simulation. The graphical user interface Flair for FLUKA currently employs such an engine where special emphasis has been given on being fast and numerically robust. The numerically robustness is achieved by a novel method of estimating the floating precision of the operations, which dynamically adapts all the decision operations accordingly. Moreover a predictive caching mechanism is ensuring that logical errors in the geometry description are found online, without compromising the processing time by checking all regions. (authors)
Methods of information geometry
Amari, Shun-Ichi
2000-01-01
Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...
Solid-Phase Synthesis of Small Molecule Libraries using Double Combinatorial Chemistry
DEFF Research Database (Denmark)
Nielsen, John; Jensen, Flemming R.
1997-01-01
The first synthesis of a combinatorial library using double combinatorial chemistry is presented. Coupling of unprotected Fmoc-tyrosine to the solid support was followed by Mitsunobu O-alkylation. Introduction of a diacid linker yields a system in which the double combinatorial step can be demons...
Flag varieties an interplay of geometry, combinatorics, and representation theory
Lakshmibai, V
2009-01-01
Flag varieties are important geometric objects and their study involves an interplay of geometry, combinatorics, and representation theory. This book is detailed account of this interplay. In the area of representation theory, the book presents a discussion of complex semisimple Lie algebras and of semisimple algebraic groups; in addition, the representation theory of symmetric groups is also discussed. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Because of the connections with root systems, many of the geometric results admit elegant combinatorial description, a typical example being the description of the singular locus of a Schubert variety. This is shown to be a consequence of standard monomial theory (abbreviated SMT). Thus the book includes SMT and some important applications - singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert variet...
Increasing insightful thinking in analytic geometry
Timmer, Mark; Verhoef, Neeltje Cornelia
Elsewhere in this issue Ferdinand Verhulst described the discussion of the interaction of analysis and geometry in the 19th century. In modern times such discussions come up again and again. As of 2014, synthetic geometry will not be part of the Dutch 'vwo - mathematics B' programme anymore.
Curvature tensor copies in affine geometry
International Nuclear Information System (INIS)
Srivastava, P.P.
1981-01-01
The sets of space-time and spin-connections which give rise to the same curvature tensor are constructed. The corresponding geometries are compared. Results are illustrated by an explicit calculation and comment on the copies in Einstein-Cartan and Weyl-Cartan geometries. (Author) [pt
Sums over geometries and improvements on the mean field approximation
International Nuclear Information System (INIS)
Sacksteder, Vincent E. IV
2007-01-01
The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian was originally proposed as a tool for calculating systematic corrections to the Bethe approximation, a mean-field approximation which is important in statistical mechanics, glasses, coding theory, and combinatorial optimization. Detailed analysis shows that the trivial saddle point generates a sum over geometries reminiscent of dynamically triangulated quantum gravity, which suggests new possibilities to design sums over geometries for the specific purpose of obtaining improved mean-field approximations to D-dimensional theories. In the case of the Efetov theory, the dominant geometries are locally treelike, and the sum over geometries diverges in a way that is similar to quantum gravity's divergence when all topologies are included. Expertise from the field of dynamically triangulated quantum gravity about sums over geometries may be able to remedy these defects and fulfill the Efetov theory's original promise. The other saddle points of the Efetov Lagrangian are also analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which is unusual for bosonic theories. The standard formula for Gaussian integrals is generalized to nonnormal kernels
Theory of site-specific interactions of the combinatorial transcription factors with DNA
International Nuclear Information System (INIS)
Murugan, R
2010-01-01
We derive a functional relationship between the mean first passage time associated with the concurrent binding of multiple transcription factors (TFs) at their respective combinatorial cis-regulatory module sites (CRMs) and the number n of TFs involved in the regulation of the initiation of transcription of a gene of interest. Our results suggest that the overall search time τ s that is required by the n TFs to locate their CRMs which are all located on the same DNA chain scales with n as τ s ∼n α where α ∼ (2/5). When the jump size k that is associated with the dynamics of all the n TFs along DNA is higher than that of the critical jump size k c that scales with the size of DNA N as k c ∼ N 2/3 , we observe a similar power law scaling relationship and also the exponent α. When k c , α shows a strong dependence on both n and k. Apparently there is a critical number of combinatorial TFs n c ∼ 20 that is required to efficiently regulate the initiation of transcription of a given gene below which (2/5) 1. These results seem to be independent of the initial distances between the TFs and their corresponding CRMs and also suggest that the maximum number of TFs involved in a given combinatorial regulation of the initiation of transcription of a gene of interest seems to be restricted by the degree of condensation of the genomic DNA. The optimum number m opt of roadblock protein molecules per genome at which the search time associated with these n TFs to locate their binding sites is a minimum seems to scale as m opt ∼Ln α/2 where L is the sliding length of TFs whose maximum value seems to be such that L ≤ 10 4 bps for the E. coli bacterial genome.
Isocyanide based multi component reactions in combinatorial chemistry.
Dömling, A.
1998-01-01
Although usually regarded as a recent development, the combinatorial approach to the synthesis of libraries of new drug candidates was first described as early as 1961 using the isocyanide-based one-pot multicomponent Ugi reaction. Isocyanide-based multi component reactions (MCR's) markedly differ
Dynamic Combinatorial Chemistry with Diselenides, Disulfides, Imines and Metal Coordination
DEFF Research Database (Denmark)
Sørensen, Anne
combinatorial chemistry, namely the reversible diselenide exchange reaction. The first part of the thesis describes the development of a thermally induced OAr → SeAr migration reaction. Here, it was proven possible to rearrange a variety of substituted O-aryl selenocarbamates into the corresponding Se...
Dynamic combinatorial chemistry at the phospholipid bilayer interface
Mansfeld, Friederike M.; Au-Yeung, Ho Yu; Sanders, Jeremy K.M.; Otto, Sijbren
2010-01-01
Background: Molecular recognition at the environment provided by the phospholipid bilayer interface plays an important role in biology and is subject of intense investigation. Dynamic combinatorial chemistry is a powerful approach for exploring molecular recognition, but has thus far not been
Confluence of an extension of combinatory logic by Boolean constants
DEFF Research Database (Denmark)
Czajka, Łukasz
2017-01-01
We show confluence of a conditional term rewriting system CL-pc1, which is an extension of Combinatory Logic by Boolean constants. This solves problem 15 from the RTA list of open problems. The proof has been fully formalized in the Coq proof assistant....
Combinatorial Solid-Phase Synthesis of Balanol Analogues
DEFF Research Database (Denmark)
Nielsen, John; Lyngsø, Lars Ole
1996-01-01
The natural product balanol has served as a template for the design and synthesis of a combinatorial library using solid-phase chemistry. Using a retrosynthetic analysis, the structural analogues have been assembled from three relatively accessible building blocks. The solid-phase chemistry inclu...
Combinatorial algorithms enabling computational science: tales from the front
International Nuclear Information System (INIS)
Bhowmick, Sanjukta; Boman, Erik G; Devine, Karen; Gebremedhin, Assefaw; Hendrickson, Bruce; Hovland, Paul; Munson, Todd; Pothen, Alex
2006-01-01
Combinatorial algorithms have long played a crucial enabling role in scientific and engineering computations. The importance of discrete algorithms continues to grow with the demands of new applications and advanced architectures. This paper surveys some recent developments in this rapidly changing and highly interdisciplinary field
Combinatorial structures and processing in neural blackboard architectures
van der Velde, Frank; van der Velde, Frank; de Kamps, Marc; Besold, Tarek R.; d'Avila Garcez, Artur; Marcus, Gary F.; Miikkulainen, Risto
2015-01-01
We discuss and illustrate Neural Blackboard Architectures (NBAs) as the basis for variable binding and combinatorial processing the brain. We focus on the NBA for sentence structure. NBAs are based on the notion that conceptual representations are in situ, hence cannot be copied or transported.
Combinatorial chemistry approach to development of molecular plastic solar cells
Godovsky, Dmitri; Inganäs, Olle; Brabec, Christoph J.; Sariciftci, N. Serdar; Hummelen, Jan C.; Janssen, Rene A.J.; Prato, M.; Maggini, M.; Segura, Jose; Martin, Nazario
1999-01-01
We used a combinatorial chemistry approach to develop the molecular plastic solar cells based on soluble fullerene derivatives or solubilized TCNQ molecules in combination with conjugated polymers. Profiles, formed by the diffusion of low molecular weight component in the spin-cast polymer host were
Angelin, Marcus; Larsson, Rikard; Vongvilai, Pornrapee; Ramstrom, Olof
2010-01-01
In this laboratory experiment, college students are introduced to dynamic combinatorial chemistry (DCC) and apply it to determine the substrate selectivity of acetylcholinesterase (AChE). Initially, the students construct a chemical library of dynamically interchanging thioesters and thiols. Then, AChE is added and allowed to select and hydrolyze…
Dynamic combinatorial libraries based on hydrogen-bonde molecular boxes
Kerckhoffs, J.M.C.A.; Mateos timoneda, Miguel; Reinhoudt, David; Crego Calama, Mercedes
2007-01-01
This article describes two different types of dynamic combinatorial libraries of host and guest molecules. The first part of this article describes the encapsulation of alizarin trimer 2 a3 by dynamic mixtures of up to twenty different self-assembled molecular receptors together with the
Anti-termite efficacy of Capparis decidua and its combinatorial ...
African Journals Online (AJOL)
Michael Horsfall
ABSTRACT: Capparis deciduas and its combinatorial mixtures were evaluated to observe the anti-termite efficacy against Indian white termite Odontotermes obesus. These have shown very high termiticidal activity and wood protection in the soil. It is proved by very low LD50 values i.e. 0.0218mg/g and 0.021mg/g obtained ...
Combinatorial algorithms enabling computational science: tales from the front
Energy Technology Data Exchange (ETDEWEB)
Bhowmick, Sanjukta [Mathematics and Computer Science Division, Argonne National Laboratory (United States); Boman, Erik G [Discrete Algorithms and Math Department, Sandia National Laboratories (United States); Devine, Karen [Discrete Algorithms and Math Department, Sandia National Laboratories (United States); Gebremedhin, Assefaw [Computer Science Department, Old Dominion University (United States); Hendrickson, Bruce [Discrete Algorithms and Math Department, Sandia National Laboratories (United States); Hovland, Paul [Mathematics and Computer Science Division, Argonne National Laboratory (United States); Munson, Todd [Mathematics and Computer Science Division, Argonne National Laboratory (United States); Pothen, Alex [Computer Science Department, Old Dominion University (United States)
2006-09-15
Combinatorial algorithms have long played a crucial enabling role in scientific and engineering computations. The importance of discrete algorithms continues to grow with the demands of new applications and advanced architectures. This paper surveys some recent developments in this rapidly changing and highly interdisciplinary field.
Some Combinatorial Interpretations and Applications of Fuss-Catalan Numbers
Lin, Chin-Hung
2011-01-01
Fuss-Catalan number is a family of generalized Catalan numbers. We begin by two definitions of Fuss-Catalan numbers and some basic properties. And we give some combinatorial interpretations different from original Catalan numbers. Finally we generalize the Jonah's theorem as its applications.
A Combinatorial Proof of a Result on Generalized Lucas Polynomials
Directory of Open Access Journals (Sweden)
Laugier Alexandre
2016-09-01
Full Text Available We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉 = 2; 〈1〉= s, respectively.
Some experience of shielding calculations by combinatorial method
International Nuclear Information System (INIS)
Korobejnikov, V.V.; Oussanov, V.I.
1996-01-01
Some aspects of the compound systems shielding calculations by a combinatorial approach are discussed. The effectiveness of such an approach is based on the fundamental characteristic of a compound system: if some element of the system have in itself mathematical or physical properties favorable for calculation, these properties may be used in a combinatorial approach and are lost when the system is being calculated in the whole by a direct approach. The combinatorial technique applied is well known. A compound system are being splitting for two or more auxiliary subsystems (so that calculation each of them is a more simple problem than calculation of the original problem (or at last is a soluble problem if original one is not). Calculation of every subsystem are carried out by suitable method and code, the coupling being made through boundary conditions or boundary source. The special consideration in the paper is given to a fast reactor shielding combinatorial analysis and to the testing of the results received. (author)
A combinatorial approximation algorithm for CDMA downlink rate allocation
Boucherie, Richardus J.; Bumb, A.F.; Endrayanto, A.I.; Woeginger, Gerhard; Raghavan, S.; Anandalingam, G.
2006-01-01
This paper presents a combinatorial algorithm for downlink rate allocation in Code Division Multiple Access (CDMA) mobile networks. By discretizing the coverage area into small segments, the transmit power requirements are characterized via a matrix representation that separates user and system
A combinatorial approximation algorithm for CDMA downlink rate allocation
Boucherie, Richardus J.; Bumb, A.F.; Endrayanto, A.I.; Woeginger, Gerhard
2004-01-01
This paper presents a combinatorial algorithm for downlink rate allocation in Code Division Multiple Access (CDMA) mobile networks. By discretizing the coverage area into small segments, the transmit power requirements are characterized via a matrix representation that separates user and system
A combinatorial enumeration problem of RNA secondary structures
African Journals Online (AJOL)
use
2011-12-21
Dec 21, 2011 ... interesting combinatorial questions (Chen et al., 2005;. Liu, 2006; Schmitt and Waterman 1994; Stein and. Waterman 1978). The research on the enumeration of. RNA secondary structures becomes one of the hot topics in Computational Molecular Biology. An RNA molecule is described by its sequences of.
Complex and symplectic geometry
Medori, Costantino; Tomassini, Adriano
2017-01-01
This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.
Kulczycki, Stefan
2008-01-01
This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff
Energy Technology Data Exchange (ETDEWEB)
Berkolaiko, G. [Department of Mathematics, Texas A and M University, College Station, Texas 77843-3368 (United States); Kuipers, J. [Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg (Germany)
2013-12-15
Electronic transport through chaotic quantum dots exhibits universal behaviour which can be understood through the semiclassical approximation. Within the approximation, calculation of transport moments reduces to codifying classical correlations between scattering trajectories. These can be represented as ribbon graphs and we develop an algorithmic combinatorial method to generate all such graphs with a given genus. This provides an expansion of the linear transport moments for systems both with and without time reversal symmetry. The computational implementation is then able to progress several orders further than previous semiclassical formulae as well as those derived from an asymptotic expansion of random matrix results. The patterns observed also suggest a general form for the higher orders.
DEFF Research Database (Denmark)
Denton, Paul W.; Søgaard, Ole Schmeltz; Tolstrup, Martin
2016-01-01
Research challenges associated with understanding HIV persistence during antiretroviral therapy can be categorized as temporal, spatial and combinatorial. Temporal research challenges relate to the timing of events during establishment and maintenance of HIV persistence. Spatial research challeng...... for directly addressing these research challenges. The aim of this manuscript is to provide a comprehensive review of these recent translational advances made in animal models of HIV persistence....... will improve our understanding of HIV persistence and move the field closer to achieving eradication of persistent HIV. Given that humanized mice and non-human primate HIV models permit rigorous control of experimental conditions, these models have been used extensively as in vivo research platforms...
Paths and partitions: Combinatorial descriptions of the parafermionic states
Mathieu, Pierre
2009-09-01
The Zk parafermionic conformal field theories, despite the relative complexity of their modes algebra, offer the simplest context for the study of the bases of states and their different combinatorial representations. Three bases are known. The classic one is given by strings of the fundamental parafermionic operators whose sequences of modes are in correspondence with restricted partitions with parts at distance k -1 differing at least by 2. Another basis is expressed in terms of the ordered modes of the k -1 different parafermionic fields, which are in correspondence with the so-called multiple partitions. Both types of partitions have a natural (Bressoud) path representation. Finally, a third basis, formulated in terms of different paths, is inherited from the solution of the restricted solid-on-solid model of Andrews-Baxter-Forrester. The aim of this work is to review, in a unified and pedagogical exposition, these four different combinatorial representations of the states of the Zk parafermionic models. The first part of this article presents the different paths and partitions and their bijective relations; it is purely combinatorial, self-contained, and elementary; it can be read independently of the conformal-field-theory applications. The second part links this combinatorial analysis with the bases of states of the Zk parafermionic theories. With the prototypical example of the parafermionic models worked out in detail, this analysis contributes to fix some foundations for the combinatorial study of more complicated theories. Indeed, as we briefly indicate in ending, generalized versions of both the Bressoud and the Andrews-Baxter-Forrester paths emerge naturally in the description of the minimal models.
Planetary Image Geometry Library
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
Roe, John
2003-01-01
Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...
Lectures on Symplectic Geometry
Silva, Ana Cannas
2001-01-01
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...
Kollár, János
1997-01-01
This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.
DEFF Research Database (Denmark)
Kokkendorff, Simon Lyngby
2002-01-01
The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...
Busemann, Herbert
2005-01-01
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
Tabachnikov, Serge
2005-01-01
Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...
Rudiments of algebraic geometry
Jenner, WE
2017-01-01
Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
2013-01-01
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
Intermediate algebra & analytic geometry
Gondin, William R
1967-01-01
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system
Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio
2013-01-01
We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.
International Nuclear Information System (INIS)
Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J
2014-01-01
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
Software Geometry in Simulations
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
Global aspects of complex geometry
Catanese, Fabrizio; Huckleberry, Alan T
2006-01-01
Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.
Exact combinatorial reliability analysis of dynamic systems with sequence-dependent failures
International Nuclear Information System (INIS)
Xing Liudong; Shrestha, Akhilesh; Dai Yuanshun
2011-01-01
Many real-life fault-tolerant systems are subjected to sequence-dependent failure behavior, in which the order in which the fault events occur is important to the system reliability. Such systems can be modeled by dynamic fault trees (DFT) with priority-AND (pAND) gates. Existing approaches for the reliability analysis of systems subjected to sequence-dependent failures are typically state-space-based, simulation-based or inclusion-exclusion-based methods. Those methods either suffer from the state-space explosion problem or require long computation time especially when results with high degree of accuracy are desired. In this paper, an analytical method based on sequential binary decision diagrams is proposed. The proposed approach can analyze the exact reliability of non-repairable dynamic systems subjected to the sequence-dependent failure behavior. Also, the proposed approach is combinatorial and is applicable for analyzing systems with any arbitrary component time-to-failure distributions. The application and advantages of the proposed approach are illustrated through analysis of several examples. - Highlights: → We analyze the sequence-dependent failure behavior using combinatorial models. → The method has no limitation on the type of time-to-failure distributions. → The method is analytical and based on sequential binary decision diagrams (SBDD). → The method is computationally more efficient than existing methods.
Physical meaning of the optical reference geometry
International Nuclear Information System (INIS)
Abramowicz, M.A.
1990-09-01
I show that contrary to a popular misconception the optical reference geometry, introduced a few years ago as a formally possible metric of a 3-space corresponding to a static spacetime, is quite satisfactory also from the physical point of view. The optical reference geometry has a clear physical meaning, as it may be constructed experimentally by measuring light round travel time between static observers. Distances and directions in the optical reference geometry are more strongly connected to experiment than distances and directions in the widely used directly projected metric (discussed e.g. in Landau and Lifshitz textbook. In addition, the optical reference geometry is more natural and convenient than the directly projected one in application to dynamics. In the optical geometry dynamical behaviour of matter is described by concepts and formulae identical to those well known in Newtonian dynamics on a given two dimensional (curved) surface. (author). 22 refs
MONTE CARLO ANALYSES OF THE YALINA THERMAL FACILITY WITH SERPENT STEREOLITHOGRAPHY GEOMETRY MODEL
Energy Technology Data Exchange (ETDEWEB)
Talamo, A.; Gohar, Y.
2015-01-01
This paper analyzes the YALINA Thermal subcritical assembly of Belarus using two different Monte Carlo transport programs, SERPENT and MCNP. The MCNP model is based on combinatorial geometry and universes hierarchy, while the SERPENT model is based on Stereolithography geometry. The latter consists of unstructured triangulated surfaces defined by the normal and vertices. This geometry format is used by 3D printers and it has been created by: the CUBIT software, MATLAB scripts, and C coding. All the Monte Carlo simulations have been performed using the ENDF/B-VII.0 nuclear data library. Both MCNP and SERPENT share the same geometry specifications, which describe the facility details without using any material homogenization. Three different configurations have been studied with different number of fuel rods. The three fuel configurations use 216, 245, or 280 fuel rods, respectively. The numerical simulations show that the agreement between SERPENT and MCNP results is within few tens of pcms.
Computational synthetic geometry
Bokowski, Jürgen
1989-01-01
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
Zheng, Fangyang
2002-01-01
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...
Bioinspired computation in combinatorial optimization: algorithms and their computational complexity
DEFF Research Database (Denmark)
Neumann, Frank; Witt, Carsten
2012-01-01
Bioinspired computation methods, such as evolutionary algorithms and ant colony optimization, are being applied successfully to complex engineering and combinatorial optimization problems, and it is very important that we understand the computational complexity of these algorithms. This tutorials...... problems. Classical single objective optimization is examined first. They then investigate the computational complexity of bioinspired computation applied to multiobjective variants of the considered combinatorial optimization problems, and in particular they show how multiobjective optimization can help...... to speed up bioinspired computation for single-objective optimization problems. The tutorial is based on a book written by the authors with the same title. Further information about the book can be found at www.bioinspiredcomputation.com....
An Atlas of Combinatorial Transcriptional Regulation in Mouse and Man
Ravasi, Timothy; Suzuki, Harukazu; Cannistraci, Carlo; Katayama, Shintaro; Bajic, Vladimir B.; Tan, Kai; Akalin, Altuna; Schmeier, Sebastian; Kanamori-Katayama, Mutsumi; Bertin, Nicolas; Carninci, Piero; Daub, Carsten O.; Forrest, Alistair R.R.; Gough, Julian; Grimmond, Sean; Han, Jung-Hoon; Hashimoto, Takehiro; Hide, Winston; Hofmann, Oliver; Kamburov, Atanas; Kaur, Mandeep; Kawaji, Hideya; Kubosaki, Atsutaka; Lassmann, Timo; van Nimwegen, Erik; MacPherson, Cameron Ross; Ogawa, Chihiro; Radovanovic, Aleksandar; Schwartz, Ariel; Teasdale, Rohan D.; Tegné r, Jesper; Lenhard, Boris; Teichmann, Sarah A.; Arakawa, Takahiro; Ninomiya, Noriko; Murakami, Kayoko; Tagami, Michihira; Fukuda, Shiro; Imamura, Kengo; Kai, Chikatoshi; Ishihara, Ryoko; Kitazume, Yayoi; Kawai, Jun; Hume, David A.; Ideker, Trey; Hayashizaki, Yoshihide
2010-01-01
Combinatorial interactions among transcription factors are critical to directing tissue-specific gene expression. To build a global atlas of these combinations, we have screened for physical interactions among the majority of human and mouse DNA-binding transcription factors (TFs). The complete networks contain 762 human and 877 mouse interactions. Analysis of the networks reveals that highly connected TFs are broadly expressed across tissues, and that roughly half of the measured interactions are conserved between mouse and human. The data highlight the importance of TF combinations for determining cell fate, and they lead to the identification of a SMAD3/FLI1 complex expressed during development of immunity. The availability of large TF combinatorial networks in both human and mouse will provide many opportunities to study gene regulation, tissue differentiation, and mammalian evolution.
Laguerre-type derivatives: Dobinski relations and combinatorial identities
International Nuclear Information System (INIS)
Penson, K. A.; Blasiak, P.; Horzela, A.; Duchamp, G. H. E.; Solomon, A. I.
2009-01-01
We consider properties of the operators D(r,M)=a r (a † a) M (which we call generalized Laguerre-type derivatives), with r=1,2,..., M=0,1,..., where a and a † are boson annihilation and creation operators, respectively, satisfying [a,a † ]=1. We obtain explicit formulas for the normally ordered form of arbitrary Taylor-expandable functions of D(r,M) with the help of an operator relation that generalizes the Dobinski formula. Coherent state expectation values of certain operator functions of D(r,M) turn out to be generating functions of combinatorial numbers. In many cases the corresponding combinatorial structures can be explicitly identified.
An Atlas of Combinatorial Transcriptional Regulation in Mouse and Man
Ravasi, Timothy
2010-03-01
Combinatorial interactions among transcription factors are critical to directing tissue-specific gene expression. To build a global atlas of these combinations, we have screened for physical interactions among the majority of human and mouse DNA-binding transcription factors (TFs). The complete networks contain 762 human and 877 mouse interactions. Analysis of the networks reveals that highly connected TFs are broadly expressed across tissues, and that roughly half of the measured interactions are conserved between mouse and human. The data highlight the importance of TF combinations for determining cell fate, and they lead to the identification of a SMAD3/FLI1 complex expressed during development of immunity. The availability of large TF combinatorial networks in both human and mouse will provide many opportunities to study gene regulation, tissue differentiation, and mammalian evolution.
Combinatorial nuclear level density by a Monte Carlo method
International Nuclear Information System (INIS)
Cerf, N.
1994-01-01
We present a new combinatorial method for the calculation of the nuclear level density. It is based on a Monte Carlo technique, in order to avoid a direct counting procedure which is generally impracticable for high-A nuclei. The Monte Carlo simulation, making use of the Metropolis sampling scheme, allows a computationally fast estimate of the level density for many fermion systems in large shell model spaces. We emphasize the advantages of this Monte Carlo approach, particularly concerning the prediction of the spin and parity distributions of the excited states,and compare our results with those derived from a traditional combinatorial or a statistical method. Such a Monte Carlo technique seems very promising to determine accurate level densities in a large energy range for nuclear reaction calculations
Rapakoulia, Trisevgeni
2017-08-09
Motivation: Drug combination therapy for treatment of cancers and other multifactorial diseases has the potential of increasing the therapeutic effect, while reducing the likelihood of drug resistance. In order to reduce time and cost spent in comprehensive screens, methods are needed which can model additive effects of possible drug combinations. Results: We here show that the transcriptional response to combinatorial drug treatment at promoters, as measured by single molecule CAGE technology, is accurately described by a linear combination of the responses of the individual drugs at a genome wide scale. We also find that the same linear relationship holds for transcription at enhancer elements. We conclude that the described approach is promising for eliciting the transcriptional response to multidrug treatment at promoters and enhancers in an unbiased genome wide way, which may minimize the need for exhaustive combinatorial screens.
Yale, Paul B
2012-01-01
This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi
The geometry of special relativity
International Nuclear Information System (INIS)
Parizet, Jean
2008-01-01
This book for students in mathematics or physics shows the interest of geometry to understand special relativity as a consequence of invariance of Maxwell equations and of constancy of the speed of light. Space-time is actually provided with a geometrical structure and a physical interpretation: at each observer are associated his own time and his own physical space in which occur events he is concerned with. This leads to a natural approach to special relativity. The Lorentz group and its algebra are then studied by using matrices and the Pauli algebra. Quaternions are also addressed
Combinatorial drug screening identifies Ewing sarcoma-specific sensitivities
Radic-Sarikas, Branka; Tsafou, Kalliopi P.; Emdal, Kristina B.; Papamarkou, Theodore; Huber, Kilian V.M.; Mutz, Cornelia; Toretsky, Jeffrey A.; Bennett, Keiryn L.; Olsen, Jesper V.; Brunak, Søren; Kovar, Heinrich; Superti-Furga, Giulio
2017-01-01
Improvements in survival for Ewing sarcoma pediatric and adolescent patients have been modest over the past 20 years. Combinations of anticancer agents endure as an option to overcome resistance to single treatments caused by compensatory pathways. Moreover, combinations are thought to lessen any associated adverse side effects through reduced dosing, which is particularly important in childhood tumors. Using a parallel phenotypic combinatorial screening approach of cells derived from three p...
Rapid mapping of protein functional epitopes by combinatorial alanine scanning
Weiss, GA; Watanabe, CK; Zhong, A; Goddard, A; Sidhu, SS
2000-01-01
A combinatorial alanine-scanning strategy was used to determine simultaneously the functional contributions of 19 side chains buried at the interface between human growth hormone and the extracellular domain of its receptor. A phage-displayed protein library was constructed in which the 19 side chains were preferentially allowed to vary only as the wild type or alanine. The library pool was subjected to binding selections to isolate functional clones, and DNA sequencing was used to determine ...
Combinatorial Models for Assembly and Decomposition of Products
A. N. Bojko
2015-01-01
The paper discusses the most popular combinatorial models that are used for the synthesis of design solutions at the stage of the assembly process flow preparation. It shows that while assembling the product the relations of parts can be represented as a structure of preferences, which is formed on the basis of objective design restrictions put in at the stage of the product design. This structure is a binary preference relation pre-order. Its symmetrical part is equivalence and describes the...
A binary plasmid system for shuffling combinatorial antibody libraries.
Collet, T A; Roben, P; O'Kennedy, R; Barbas, C F; Burton, D R; Lerner, R A
1992-01-01
We have used a binary system of replicon-compatible plasmids to test the potential for promiscuous recombination of heavy and light chains within sets of human Fab fragments isolated from combinatorial antibody libraries. Antibody molecules showed a surprising amount of promiscuity in that a particular heavy chain could recombine with multiple light chains with retention of binding to a protein antigen. The degree to which a given heavy chain productively paired with any light chain to bind a...
View discovery in OLAP databases through statistical combinatorial optimization
Energy Technology Data Exchange (ETDEWEB)
Hengartner, Nick W [Los Alamos National Laboratory; Burke, John [PNNL; Critchlow, Terence [PNNL; Joslyn, Cliff [PNNL; Hogan, Emilie [PNNL
2009-01-01
OnLine Analytical Processing (OLAP) is a relational database technology providing users with rapid access to summary, aggregated views of a single large database, and is widely recognized for knowledge representation and discovery in high-dimensional relational databases. OLAP technologies provide intuitive and graphical access to the massively complex set of possible summary views available in large relational (SQL) structured data repositories. The capability of OLAP database software systems to handle data complexity comes at a high price for analysts, presenting them a combinatorially vast space of views of a relational database. We respond to the need to deploy technologies sufficient to allow users to guide themselves to areas of local structure by casting the space of 'views' of an OLAP database as a combinatorial object of all projections and subsets, and 'view discovery' as an search process over that lattice. We equip the view lattice with statistical information theoretical measures sufficient to support a combinatorial optimization process. We outline 'hop-chaining' as a particular view discovery algorithm over this object, wherein users are guided across a permutation of the dimensions by searching for successive two-dimensional views, pushing seen dimensions into an increasingly large background filter in a 'spiraling' search process. We illustrate this work in the context of data cubes recording summary statistics for radiation portal monitors at US ports.
A combinatorial perspective of the protein inference problem.
Yang, Chao; He, Zengyou; Yu, Weichuan
2013-01-01
In a shotgun proteomics experiment, proteins are the most biologically meaningful output. The success of proteomics studies depends on the ability to accurately and efficiently identify proteins. Many methods have been proposed to facilitate the identification of proteins from peptide identification results. However, the relationship between protein identification and peptide identification has not been thoroughly explained before. In this paper, we devote ourselves to a combinatorial perspective of the protein inference problem. We employ combinatorial mathematics to calculate the conditional protein probabilities (protein probability means the probability that a protein is correctly identified) under three assumptions, which lead to a lower bound, an upper bound, and an empirical estimation of protein probabilities, respectively. The combinatorial perspective enables us to obtain an analytical expression for protein inference. Our method achieves comparable results with ProteinProphet in a more efficient manner in experiments on two data sets of standard protein mixtures and two data sets of real samples. Based on our model, we study the impact of unique peptides and degenerate peptides (degenerate peptides are peptides shared by at least two proteins) on protein probabilities. Meanwhile, we also study the relationship between our model and ProteinProphet. We name our program ProteinInfer. Its Java source code, our supplementary document and experimental results are available at: >http://bioinformatics.ust.hk/proteininfer.
View Discovery in OLAP Databases through Statistical Combinatorial Optimization
Energy Technology Data Exchange (ETDEWEB)
Joslyn, Cliff A.; Burke, Edward J.; Critchlow, Terence J.
2009-05-01
The capability of OLAP database software systems to handle data complexity comes at a high price for analysts, presenting them a combinatorially vast space of views of a relational database. We respond to the need to deploy technologies sufficient to allow users to guide themselves to areas of local structure by casting the space of ``views'' of an OLAP database as a combinatorial object of all projections and subsets, and ``view discovery'' as an search process over that lattice. We equip the view lattice with statistical information theoretical measures sufficient to support a combinatorial optimization process. We outline ``hop-chaining'' as a particular view discovery algorithm over this object, wherein users are guided across a permutation of the dimensions by searching for successive two-dimensional views, pushing seen dimensions into an increasingly large background filter in a ``spiraling'' search process. We illustrate this work in the context of data cubes recording summary statistics for radiation portal monitors at US ports.
Energy Technology Data Exchange (ETDEWEB)
Chu, Young Hwan [Department of New Energy.Resource Engineering, College of Science and Engineering, Sangji University, 124, Sangjidae-gil, Wonju-si, Gangwon-Do 220-702 (Korea); Shul, Yong Gun [Department of Chemical and Biomolecular Engineering, Yonsei University, 134, Shinchon-Dong, Seodaemun-Gu, Seoul 120-749 (Korea)
2010-10-15
Low-temperature direct alcohol fuel cells fed with different kinds of alcohol (methanol, ethanol and 2-propanol) have been investigated by employing ternary electrocatalysts (Pt-Ru-Sn) as anode catalysts. Combinatorial chemistry has been applied to screen the 66-PtRuSn-anode arrays at the same time to reduce cost, time, and effort when we select the optimum composition of electrocatalysts for DAFCs (Direct Alcohol Fuel Cells). PtRuSn (80:20:0) showed the lowest onset potential for methanol electro-oxidation, PtRuSn (50:0:50) for ethanol, and PtRuSn (20:70:10) for 2-propanol in CV results respectively, and single cell performance test indicated that Ru is more suitable for direct methanol fuel cell system, Sn for direct ethanol fuel cell system, and 2-propanol could be applied as fuel with low platinum composition anode electrocatalyst. The single cell performance results and electrochemical results (CV) were well matched with the combinatorial electrochemical results. As a result, we could verify the availability of combinatorial chemistry by comparing the results of each extreme electrocatalysts compositions as follows: PtRuSn (80:20:0) for methanol, PtRuSn (50:0:50) for ethanol and PtRuSn (20:70:10) for 2-propanol. (author)
Directory of Open Access Journals (Sweden)
Kikinis Ron
2006-03-01
Full Text Available Abstract Introduction Mitral Valve (MV 3D structural data can be easily obtained using standard transesophageal echocardiography (TEE devices but quantitative pre- and intraoperative volume analysis of the MV is presently not feasible in the cardiac operation room (OR. Finite element method (FEM modelling is necessary to carry out precise and individual volume analysis and in the future will form the basis for simulation of cardiac interventions. Method With the present retrospective pilot study we describe a method to transfer MV geometric data to 3D Slicer 2 software, an open-source medical visualization and analysis software package. A newly developed software program (ROIExtract allowed selection of a region-of-interest (ROI from the TEE data and data transformation for use in 3D Slicer. FEM models for quantitative volumetric studies were generated. Results ROI selection permitted the visualization and calculations required to create a sequence of volume rendered models of the MV allowing time-based visualization of regional deformation. Quantitation of tissue volume, especially important in myxomatous degeneration can be carried out. Rendered volumes are shown in 3D as well as in time-resolved 4D animations. Conclusion The visualization of the segmented MV may significantly enhance clinical interpretation. This method provides an infrastructure for the study of image guided assessment of clinical findings and surgical planning. For complete pre- and intraoperative 3D MV FEM analysis, three input elements are necessary: 1. time-gated, reality-based structural information, 2. continuous MV pressure and 3. instantaneous tissue elastance. The present process makes the first of these elements available. Volume defect analysis is essential to fully understand functional and geometrical dysfunction of but not limited to the valve. 3D Slicer was used for semi-automatic valve border detection and volume-rendering of clinical 3D echocardiographic
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Multiplicity in difference geometry
Tomasic, Ivan
2011-01-01
We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \\sigma-finite morphism between difference curves are all of the same size, when counted with correct multiplicities.
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm
2011-01-01
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...
Diophantine geometry an introduction
Hindry, Marc
2000-01-01
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
Boyer, Carl B
2012-01-01
Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.
Coxeter, HSM
1965-01-01
This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.
International Nuclear Information System (INIS)
Ezin, J.P.
1988-08-01
The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs
Hartshorne, Robin
2000-01-01
In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...
Frydel, Derek; Rice, Stuart A
2007-12-01
We report a hydrodynamic analysis of the long-time behavior of the linear and angular velocity autocorrelation functions of an isolated colloid particle constrained to have quasi-two-dimensional motion, and compare the predicted behavior with the results of lattice-Boltzmann simulations. Our analysis uses the singularity method to characterize unsteady linear motion of an incompressible fluid. For bounded fluids we construct an image system with a discrete set of fundamental solutions of the Stokes equation from which we extract the long-time decay of the velocity. For the case that there are free slip boundary conditions at walls separated by H particle diameters, the time evolution of the parallel linear velocity and the perpendicular rotational velocity following impulsive excitation both correspond to the time evolution of a two-dimensional (2D) fluid with effective density rho_(2D)=rhoH. For the case that there are no slip boundary conditions at the walls, the same types of motion correspond to 2D fluid motions with a coefficient of friction xi=pi(2)nu/H(2) modulo a prefactor of order 1, with nu the kinematic viscosity. The linear particle motion perpendicular to the walls also experiences an effective frictional force, but the time dependence is proportional to t(-2) , which cannot be related to either pure 3D or pure 2D fluid motion. Our incompressible fluid model predicts correct self-diffusion constants but it does not capture all of the effects of the fluid confinement on the particle motion. In particular, the linear motion of a particle perpendicular to the walls is influenced by coupling between the density flux and the velocity field, which leads to damped velocity oscillations whose frequency is proportional to c_(s)/H , with c_(s) the velocity of sound. For particle motion parallel to no slip walls there is a slowing down of a density flux that spreads diffusively, which generates a long-time decay proportional to t(-1) .
International Nuclear Information System (INIS)
Abedinia, O.; Amjady, N.; Shafie-khah, M.; Catalão, J.P.S.
2015-01-01
Highlights: • Presenting a Combinatorial Neural Network. • Suggesting a new stochastic search method. • Adapting the suggested method as a training mechanism. • Proposing a new forecast strategy. • Testing the proposed strategy on real-world electricity markets. - Abstract: Electricity price forecast is key information for successful operation of electricity market participants. However, the time series of electricity price has nonlinear, non-stationary and volatile behaviour and so its forecast method should have high learning capability to extract the complex input/output mapping function of electricity price. In this paper, a Combinatorial Neural Network (CNN) based forecasting engine is proposed to predict the future values of price data. The CNN-based forecasting engine is equipped with a new training mechanism for optimizing the weights of the CNN. This training mechanism is based on an efficient stochastic search method, which is a modified version of chemical reaction optimization algorithm, giving high learning ability to the CNN. The proposed price forecast strategy is tested on the real-world electricity markets of Pennsylvania–New Jersey–Maryland (PJM) and mainland Spain and its obtained results are extensively compared with the results obtained from several other forecast methods. These comparisons illustrate effectiveness of the proposed strategy.
Doerr, Timothy; Alves, Gelio; Yu, Yi-Kuo
2006-03-01
Typical combinatorial optimizations are NP-hard; however, for a particular class of cost functions the corresponding combinatorial optimizations can be solved in polynomial time. This suggests a way to efficiently find approximate solutions - - find a transformation that makes the cost function as similar as possible to that of the solvable class. After keeping many high-ranking solutions using the approximate cost function, one may then re-assess these solutions with the full cost function to find the best approximate solution. Under this approach, it is important to be able to assess the quality of the solutions obtained, e.g., by finding the true ranking of kth best approximate solution when all possible solutions are considered exhaustively. To tackle this statistical issue, we provide a systematic method starting with a scaling function generated from the fininte number of high- ranking solutions followed by a convergent iterative mapping. This method, useful in a variant of the directed paths in random media problem proposed here, can also provide a statistical significance assessment for one of the most important proteomic tasks - - peptide sequencing using tandem mass spectrometry data.
Generating an Automated Test Suite by Variable Strength Combinatorial Testing for Web Services
Directory of Open Access Journals (Sweden)
Yin Li
2016-09-01
Full Text Available Testing Web Services has become the spotlight of software engineering as an important means to assure the quality of Web application. Due to lacking of graphic interface and source code, Web services need an automated testing method, which is an important part in efficiently designing and generating test suite. However, the existing testing methods may lead to the redundancy of test suite and the decrease of fault-detecting ability since it cannot handle scenarios where the strengths of the different interactions are not uniform. With the purpose of solving this problem, firstly the formal tree model based on WSDL is constructed and the actual interaction relationship of each node is made sufficient consideration into, then the combinatorial testing is proposed to generate variable strength combinatorial test suite based on One-test-at-a-time strategy. At last test cases are minimized according to constraint rules. The results show that compared with conventional random testing, the proposed approach can detect more errors with the same amount of test cases which turning out to be more ideal than existing ones in size.
Directory of Open Access Journals (Sweden)
Armand Paauw
Full Text Available Horizontal gene transfer is a key step in the evolution of Enterobacteriaceae. By acquiring virulence determinants of foreign origin, commensals can evolve into pathogens. In Enterobacteriaceae, horizontal transfer of these virulence determinants is largely dependent on transfer by plasmids, phages, genomic islands (GIs and genomic modules (GMs. The High Pathogenicity Island (HPI is a GI encoding virulence genes that can be transferred between different Enterobacteriaceae. We investigated the HPI because it was present in an Enterobacter hormaechei outbreak strain (EHOS. Genome sequence analysis showed that the EHOS contained an integration site for mobile elements and harbored two GIs and three putative GMs, including a new variant of the HPI (HPI-ICEEh1. We demonstrate, for the first time, that combinatorial transfers of GIs and GMs between Enterobacter cloacae complex isolates must have occurred. Furthermore, the excision and circularization of several combinations of the GIs and GMs was demonstrated. Because of its flexibility, the multiple integration site of mobile DNA can be considered an integration hotspot (IHS that increases the genomic plasticity of the bacterium. Multiple combinatorial transfers of diverse combinations of the HPI and other genomic elements among Enterobacteriaceae may accelerate the generation of new pathogenic strains.
International Nuclear Information System (INIS)
Setsuhara, Yuichi; Cho, Ken; Takenaka, Kosuke; Shiratani, Masaharu; Sekine, Makoto; Hori, Masaru
2010-01-01
A plasma-process analyzer has been developed on the basis of combinatorial method, in which process examinations with continuous variations of plasma-process conditions can be carried out on a substrate holder with an inclined distribution of process parameters. Combinatorial plasma-process analyses have been demonstrated for examinations of plasma-polymer interactions in terms of etching characteristics and surface morphologies in order to show feasibility and effectiveness of the methodology as advanced research and development for next-generation plasma nano processes. The etching properties and surface morphologies have been investigated for polyethylene terephthalate (PET) films exposed to argon-oxygen mixture plasmas. The etching depth data obtained from three independent batches of the experiments showed universal and almost linear dependence with increasing product of (ion saturation current) x (exposure time); i.e. ion dose. Surface roughness of the polymer slightly increased with increasing ion dose, while the mean spacing after plasma exposure was found to decrease monotonically with increasing ion dose but was saturated at the level of approximately 250 nm.
Concept of combinatorial de novo design of drug-like molecules by particle swarm optimization.
Hartenfeller, Markus; Proschak, Ewgenij; Schüller, Andreas; Schneider, Gisbert
2008-07-01
We present a fast stochastic optimization algorithm for fragment-based molecular de novo design (COLIBREE, Combinatorial Library Breeding). The search strategy is based on a discrete version of particle swarm optimization. Molecules are represented by a scaffold, which remains constant during optimization, and variable linkers and side chains. Different linkers represent virtual chemical reactions. Side-chain building blocks were obtained from pseudo-retrosynthetic dissection of large compound databases. Here, ligand-based design was performed using chemically advanced template search (CATS) topological pharmacophore similarity to reference ligands as fitness function. A weighting scheme was included for particle swarm optimization-based molecular design, which permits the use of many reference ligands and allows for positive and negative design to be performed simultaneously. In a case study, the approach was applied to the de novo design of potential peroxisome proliferator-activated receptor subtype-selective agonists. The results demonstrate the ability of the technique to cope with large combinatorial chemistry spaces and its applicability to focused library design. The technique was able to perform exploitation of a known scheme and at the same time explorative search for novel ligands within the framework of a given molecular core structure. It thereby represents a practical solution for compound screening in the early hit and lead finding phase of a drug discovery project.
IκBα mediates prostate cancer cell death induced by combinatorial targeting of the androgen receptor
International Nuclear Information System (INIS)
Carter, Sarah Louise; Centenera, Margaret Mary; Tilley, Wayne Desmond; Selth, Luke Ashton; Butler, Lisa Maree
2016-01-01
Combining different clinical agents to target multiple pathways in prostate cancer cells, including androgen receptor (AR) signaling, is potentially an effective strategy to improve outcomes for men with metastatic disease. We have previously demonstrated that sub-effective concentrations of an AR antagonist, bicalutamide, and the histone deacetylase inhibitor, vorinostat, act synergistically when combined to cause death of AR-dependent prostate cancer cells. In this study, expression profiling of human prostate cancer cells treated with bicalutamide or vorinostat, alone or in combination, was employed to determine the molecular mechanisms underlying this synergistic action. Cell viability assays and quantitative real time PCR were used to validate identified candidate genes. A substantial proportion of the genes modulated by the combination of bicalutamide and vorinostat were androgen regulated. Independent pathway analysis identified further pathways and genes, most notably NFKBIA (encoding IκBα, an inhibitor of NF-κB and p53 signaling), as targets of this combinatorial treatment. Depletion of IκBα by siRNA knockdown enhanced apoptosis of prostate cancer cells, while ectopic overexpression of IκBα markedly suppressed cell death induced by the combination of bicalutamide and vorinostat. These findings implicate IκBα as a key mediator of the apoptotic action of this combinatorial AR targeting strategy and a promising new therapeutic target for prostate cancer. The online version of this article (doi:10.1186/s12885-016-2188-2) contains supplementary material, which is available to authorized users
Counting in Lattices: Combinatorial Problems from Statistical Mechanics.
Randall, Dana Jill
In this thesis we consider two classical combinatorial problems arising in statistical mechanics: counting matchings and self-avoiding walks in lattice graphs. The first problem arises in the study of the thermodynamical properties of monomers and dimers (diatomic molecules) in crystals. Fisher, Kasteleyn and Temperley discovered an elegant technique to exactly count the number of perfect matchings in two dimensional lattices, but it is not applicable for matchings of arbitrary size, or in higher dimensional lattices. We present the first efficient approximation algorithm for computing the number of matchings of any size in any periodic lattice in arbitrary dimension. The algorithm is based on Monte Carlo simulation of a suitable Markov chain and has rigorously derived performance guarantees that do not rely on any assumptions. In addition, we show that these results generalize to counting matchings in any graph which is the Cayley graph of a finite group. The second problem is counting self-avoiding walks in lattices. This problem arises in the study of the thermodynamics of long polymer chains in dilute solution. While there are a number of Monte Carlo algorithms used to count self -avoiding walks in practice, these are heuristic and their correctness relies on unproven conjectures. In contrast, we present an efficient algorithm which relies on a single, widely-believed conjecture that is simpler than preceding assumptions and, more importantly, is one which the algorithm itself can test. Thus our algorithm is reliable, in the sense that it either outputs answers that are guaranteed, with high probability, to be correct, or finds a counterexample to the conjecture. In either case we know we can trust our results and the algorithm is guaranteed to run in polynomial time. This is the first algorithm for counting self-avoiding walks in which the error bounds are rigorously controlled. This work was supported in part by an AT&T graduate fellowship, a University of
International Nuclear Information System (INIS)
Flachenecker, G.; Materny, A.
2004-01-01
We present femtosecond time-resolved pump-probe experiments on iodine molecules enclosed into well-defined cages and channels of different crystalline SiO 2 modifications of zeolites. The new experimental results obtained from iodine in TON (Silica-ZSM-22), FER (Silica-Ferrierit), and MFI (Silicalit-1) porosils are compared with data published earlier on the iodine/DDR (Decadodecasil 3R) porosil system [Flachenecker et al., Phys. Chem. Chem. Phys. 5, 865 (2003)]. A summary of all findings is given. The processes analyzed by means of the ultrafast spectroscopy are the vibrational relaxation as well as the dissociation and recombination reactions, which are caused by the interaction of the photo-excited iodine molecules with the cavity walls of the porosils. A clear dependence of the observed dynamics on the geometry of the surrounding lattice structure can be seen. These measurements are supported by temperature-dependent experiments. Making use of a theoretical model which is based on the classical Langevin equation, an analysis of the geometry-reaction relation is performed. The Brownian dynamics simulations show that in contrast to the vibrational relaxation the predissociation dynamics are independent of the frequency of collisions with the surroundings. From the results obtained in the different surroundings, we conclude that mainly local fields are responsible for the crossing from the bound B state to the repulsive a/a ' states of the iodine molecules
Rapoport, Diego L.
2011-01-01
In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further related to the commutator of the True and False operators of matrix logic, still with a quantum superposed state related to a Moebius surface, and as the physical field at the basis of Spencer-Brown's primitive distinction in the protologic of the calculus of distinction. In this setting, paradox, self-reference, depth, time and space, higher-order non-dual logic, perception, spin and a time operator, the Klein bottle, hypernumbers due to Musès which include non-trivial square roots of ±1 and in particular non-trivial nilpotents, quantum field operators, the transformation of cognition to spin for two-state quantum systems, are found to be keenly interwoven in a world conception compatible with the philosophical approach taken for basis of this article. The Klein bottle is found not only to be the topological in-formation for self-reference and paradox whose logical counterpart in the calculus of indications are the paradoxical imaginary time waves, but also a classical-quantum transformer (Hadamard's gate in quantum computation) which is indispensable to be able to obtain a complete multivalued logical system, and still to generate the matrix extension of classical connective Boolean logic. We further find that the multivalued logic that stems from considering the paradoxical equation in the calculus of distinctions, and in particular, the imaginary solutions to this equation
Childress, Stephen; Gilbert, Andrew D.
2018-02-01
A theory of an eroding ‘hairpin’ vortex dipole structure in three-dimensions is developed, extending our previous study of an axisymmetric eroding dipole without swirl. The axisymmetric toroidal dipole was found to lead to maximal growth of vorticity, as {t}4/3. The hairpin is here similarly proposed as a model to produce large ‘self-stretching’ of vorticity, with the possibility of finite-time blow-up. We derive a system of partial differential equations of ‘generalized’ form, involving contour averaging of a locally two-dimensional Euler flow. We do not attempt here to solve the system exactly, but point out that non-existence of physically acceptable solutions would most probably be a result of the axial flow. Because of the axial flow the vorticity distribution within the dipole eddies is no longer of the simple Sadovskii type (vorticity constant over a cross-section) obtained in the axisymmetric problem. Thus the solution of the system depends upon the existence of a larger class of propagating two-dimensional dipoles. The hairpin model is obtained by formal asymptotic analysis. As in the axisymmetric problem a local transformation to ‘shrinking’ coordinates is introduced, but now in a self-similar form appropriate to the study of a possible finite-time singularity. We discuss some properties of the model, including a study of the helicity and a first step in iterating toward a solution from the Sadovskii structure. We also present examples of two-dimensional propagating dipoles not previously studied, which have a vorticity profile consistent with our model. Although no rigorous results can be given, and analysis of the system is only partial, the formal calculations are consistent with the possibility of a finite time blowup of vorticity at a point of vanishing circulation of the dipole eddies, but depending upon the existence of the necessary two-dimensional propagating dipole. Our results also suggest that conservation of kinetic energy as
Network geometry with flavor: From complexity to quantum geometry
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but
Programming system for analytic geometry
International Nuclear Information System (INIS)
Raymond, Jacques
1970-01-01
After having outlined the characteristics of computing centres which do not comply with engineering tasks, notably the time required by all different tasks to be performed when developing a software (assembly, compilation, link edition, loading, run), and identified constraints specific to engineering, the author identifies the characteristics a programming system should have to suit engineering tasks. He discussed existing conversational systems and their programming language, and their main drawbacks. Then, he presents a system which aims at facilitating programming and addressing problems of analytic geometry and trigonometry
Geometry of supersymmetric gauge theories
International Nuclear Information System (INIS)
Gieres, F.
1988-01-01
This monograph gives a detailed and pedagogical account of the geometry of rigid superspace and supersymmetric Yang-Mills theories. While the core of the text is concerned with the classical theory, the quantization and anomaly problem are briefly discussed following a comprehensive introduction to BRS differential algebras and their field theoretical applications. Among the treated topics are invariant forms and vector fields on superspace, the matrix-representation of the super-Poincare group, invariant connections on reductive homogeneous spaces and the supermetric approach. Various aspects of the subject are discussed for the first time in textbook and are consistently presented in a unified geometric formalism
Multivariate calculus and geometry
Dineen, Seán
2014-01-01
Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
Transformational plane geometry
Umble, Ronald N
2014-01-01
Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...
Multilevel geometry optimization
Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.
2000-02-01
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.
Multilevel geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)
2000-02-15
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.
Riisager, Peter; Knight, Kim B.; Baker, Joel A.; Ukstins Peate, Ingrid; Al-Kadasi, Mohamed; Al-Subbary, Abdulkarim; Renne, Paul R.
2005-09-01
A combined paleomagnetic and 40Ar / 39Ar study was carried out along eight stratigraphically overlapping sections in the Oligocene Afro-Arabian flood volcanic province in Yemen (73 sites). The composite section covers the entire volcanic stratigraphy in the sampling region and represents five polarity zones that are correlated to the geomagnetic polarity time scale based on 40Ar / 39Ar ages from this and previous studies. The resulting magnetostratigraphy is similar to that of the conjugate margin in Ethiopia. The earliest basaltic volcanism took place in a reverse polarity chron that appears to correspond to C11r, while the massive rhyolitic ignimbrite eruptions correlated to ash layers in Oligocene Indian Ocean sediment 2700 km away from the Afro-Arabian traps, appear to have taken place during magnetochron C11n. The youngest ignimbrite was emplaced during magnetochron C9n. Both 40Ar / 39Ar and paleomagnetic data suggest rapid Red Sea. By analyzing Afro-Arabian paleomagnetic data in conjunction with contemporaneous paleomagnetic poles available from different latitudes we argue that the Oligocene paleomagnetic field was dominated by the axial dipole with insignificant non-dipole field contributions.
Krauss, Lawrence M.; Turner, Michael S.
1999-01-01
The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
International Nuclear Information System (INIS)
Lepora, N.; Kibble, T.
1999-01-01
We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the scalar sector, and a squashed metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbative features of Weinberg-Salam theory. (author)
Integral geometry and valuations
Solanes, Gil
2014-01-01
Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...
CBM RICH geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration
2016-07-01
The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.
Introducing geometry concept based on history of Islamic geometry
Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.
2018-01-01
Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.
Quantum Adiabatic Optimization and Combinatorial Landscapes
Smelyanskiy, V. N.; Knysh, S.; Morris, R. D.
2003-01-01
In this paper we analyze the performance of the Quantum Adiabatic Evolution (QAE) algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, gamma = M / N. We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (verses only energy) is used, and are able to show the existence of a dynamic threshold gamma = gammad, beyond which QAE should take an exponentially long time to find a solution. We compare the results for extended and simplified sets of landscapes and provide numerical evidence in support of our universality ansatz.
Combinatorial constructions in ergodic theory and dynamics
Katok, Anatole
2003-01-01
Ergodic theory studies measure-preserving transformations of measure spaces. These objects are intrinsically infinite and the notion of an individual point or an orbit makes no sense. Still there is a variety of situations when a measure-preserving transformation (and its asymptotic behavior) can be well described as a limit of certain finite objects (periodic processes). In the first part of this book this idea is developed systematically, genericity of approximation in various categories is explored, and numerous applications are presented, including spectral multiplicity and properties of the maximal spectral type. The second part of the book contains a treatment of various constructions of cohomological nature with an emphasis on obtaining interesting asymptotic behavior from approximate pictures at different time scales. The book presents a view of ergodic theory not found in other expository sources and is suitable for graduate students familiar with measure theory and basic functional analysis.
Moritz enhancements for visualization of complicated geometry models
International Nuclear Information System (INIS)
Van Riper, K. A.
2009-01-01
We describe new features implemented in the Moritz geometry editing and visualization program to enhance the accuracy and efficiency of viewing complex geometry models. The 3D display is based on OpenGL and requires conversion of the combinatorial surface and solid body geometry used by MCNP and other transport codes to a set of polygons. Calculation of those polygons can take many minutes for complex models. Once calculated, the polygons can be saved to a file and reused when the same or a derivative model is loaded; the file can be read and processed in under a second. A cell can be filled with a collection of other cells constituting a universe. A new option bypasses use of the filled cell's boundaries when calculating the polygons for the filling universe. This option, when applicable, speeds processing, improves the 3D image, and permits reuse of the universe's polygons when other cells are filled with transformed instances of the universe. Surfaces and solid bodies used in a cell description must be converted to polygons before calculating the polygonal representation of a cell; this conversion requires truncation of infinite surfaces. A new method for truncating transformed surfaces ensures the finite surface intersects the entire model. When a surface or solid body is processed in a cell description, an optional test detects when that object does not contribute additional polygons; if so, that object May be extraneous for the cell description. (authors)
Two lectures on D-geometry and noncommutative geometry
International Nuclear Information System (INIS)
Douglas, M.R.
1999-01-01
This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)
Combinatorial effects of arginine and fluoride on oral bacteria.
Zheng, X; Cheng, X; Wang, L; Qiu, W; Wang, S; Zhou, Y; Li, M; Li, Y; Cheng, L; Li, J; Zhou, X; Xu, X
2015-02-01
Dental caries is closely associated with the microbial disequilibrium between acidogenic/aciduric pathogens and alkali-generating commensal residents within the dental plaque. Fluoride is a widely used anticaries agent, which promotes tooth hard-tissue remineralization and suppresses bacterial activities. Recent clinical trials have shown that oral hygiene products containing both fluoride and arginine possess a greater anticaries effect compared with those containing fluoride alone, indicating synergy between fluoride and arginine in caries management. Here, we hypothesize that arginine may augment the ecological benefit of fluoride by enriching alkali-generating bacteria in the plaque biofilm and thus synergizes with fluoride in controlling dental caries. Specifically, we assessed the combinatory effects of NaF/arginine on planktonic and biofilm cultures of Streptococcus mutans, Streptococcus sanguinis, and Porphyromonas gingivalis with checkerboard microdilution assays. The optimal NaF/arginine combinations were selected, and their combinatory effects on microbial composition were further examined in single-, dual-, and 3-species biofilm using bacterial species-specific fluorescence in situ hybridization and quantitative polymerase chain reaction. We found that arginine synergized with fluoride in suppressing acidogenic S. mutans in both planktonic and biofilm cultures. In addition, the NaF/arginine combination synergistically reduced S. mutans but enriched S. sanguinis within the multispecies biofilms. More importantly, the optimal combination of NaF/arginine maintained a "streptococcal pressure" against the potential growth of oral anaerobe P. gingivalis within the alkalized biofilm. Taken together, we conclude that the combinatory application of fluoride and arginine has a potential synergistic effect in maintaining a healthy oral microbial equilibrium and thus represents a promising ecological approach to caries management. © International & American
Estimating meme fitness in adaptive memetic algorithms for combinatorial problems.
Smith, J E
2012-01-01
Among the most promising and active research areas in heuristic optimisation is the field of adaptive memetic algorithms (AMAs). These gain much of their reported robustness by adapting the probability with which each of a set of local improvement operators is applied, according to an estimate of their current value to the search process. This paper addresses the issue of how the current value should be estimated. Assuming the estimate occurs over several applications of a meme, we consider whether the extreme or mean improvements should be used, and whether this aggregation should be global, or local to some part of the solution space. To investigate these issues, we use the well-established COMA framework that coevolves the specification of a population of memes (representing different local search algorithms) alongside a population of candidate solutions to the problem at hand. Two very different memetic algorithms are considered: the first using adaptive operator pursuit to adjust the probabilities of applying a fixed set of memes, and a second which applies genetic operators to dynamically adapt and create memes and their functional definitions. For the latter, especially on combinatorial problems, credit assignment mechanisms based on historical records, or on notions of landscape locality, will have limited application, and it is necessary to estimate the value of a meme via some form of sampling. The results on a set of binary encoded combinatorial problems show that both methods are very effective, and that for some problems it is necessary to use thousands of variables in order to tease apart the differences between different reward schemes. However, for both memetic algorithms, a significant pattern emerges that reward based on mean improvement is better than that based on extreme improvement. This contradicts recent findings from adapting the parameters of operators involved in global evolutionary search. The results also show that local reward schemes
The second immanant of some combinatorial matrices
Directory of Open Access Journals (Sweden)
R. B. Bapat
2015-06-01
Full Text Available Let $A = (a_{i,j}_{1 leq i,j leq n}$ be an $n times n$ matrix where $n geq 2$. Let $dt(A$, its second immanant be the immanant corresponding to the partition $lambda_2 = 2,1^{n-2}$. Let $G$ be a connected graph with blocks $B_1, B_2, ldots B_p$ and with $q$-exponential distance matrix $ED_G$. We given an explicit formula for $dt(ED_G$ which shows that $dt(ED_G$ is independent of the manner in which the blocks are connected. Our result is similar in form to the result of Graham, Hoffman and Hosoya and in spirit to that of Bapat, Lal and Pati who show that $det ED_T$ where $T$ is a tree is independent of the structure of $T$ and only its number of vertices. Our result extends more generally to a product distance matrix associated to a connected graph $G$. Similar results are shown for the $q$-analogue of $T$'s laplacian and a suitably defined matrix for arbitrary connected graphs.
Combinatorial interpretations of binomial coefficient analogues related to Lucas sequences
Sagan, Bruce; Savage, Carla
2009-01-01
Let s and t be variables. Define polynomials {n} in s, t by {0}=0, {1}=1, and {n}=s{n-1}+t{n-2} for n >= 2. If s, t are integers then the corresponding sequence of integers is called a Lucas sequence. Define an analogue of the binomial coefficients by C{n,k}={n}!/({k}!{n-k}!) where {n}!={1}{2}...{n}. It is easy to see that C{n,k} is a polynomial in s and t. The purpose of this note is to give two combinatorial interpretations for this polynomial in terms of statistics on integer partitions in...
First steps in combinatorial optimization on graphons: matchings
Czech Academy of Sciences Publication Activity Database
Doležal, Martin; Hladký, J.; Hu, P.; Piguet, Diana
2017-01-01
Roč. 61, August (2017), s. 359-365 ISSN 1571-0653 R&D Projects: GA ČR GA16-07378S; GA ČR GJ16-07822Y EU Projects: European Commission(XE) 628974 - PAECIDM Institutional support: RVO:67985840 ; RVO:67985807 Keywords : graphon * graph limits * matching * combinatorial optimization Subject RIV: BA - General Mathematics ; BA - General Mathematics (UIVT-O) OBOR OECD: Pure mathematics ; Pure mathematics (UIVT-O) http://www.sciencedirect.com/science/article/pii/S1571065317301452
Combinatorial synthesis of oxazol-thiazole bis-heterocyclic compounds.
Murru, Siva; Nefzi, Adel
2014-01-13
A combinatorial library of novel oxazol-thiazole bis-heterocycles was synthesized in good to excellent overall yields with high purity using a solution and solid-phase parallel synthesis approach. Oxazole amino acids, prepared from serine methyl ester and amino acids via coupling and cyclodehydration, were treated with Fmoc-NCS and α-haloketones for the parallel synthesis of diverse bis-heterocycles. Fmoc-isothiocyanate is used as a traceless reagent for thiazole formation. Oxazole diversity can be achieved by using variety of amino acids, whereas thiazole diversity is produced with various haloketones.
Advances in bio-inspired computing for combinatorial optimization problems
Pintea, Camelia-Mihaela
2013-01-01
Advances in Bio-inspired Combinatorial Optimization Problems' illustrates several recent bio-inspired efficient algorithms for solving NP-hard problems.Theoretical bio-inspired concepts and models, in particular for agents, ants and virtual robots are described. Large-scale optimization problems, for example: the Generalized Traveling Salesman Problem and the Railway Traveling Salesman Problem, are solved and their results are discussed.Some of the main concepts and models described in this book are: inner rule to guide ant search - a recent model in ant optimization, heterogeneous sensitive a
Combinatorial interpretation of Haldane-Wu fractional exclusion statistics.
Aringazin, A K; Mazhitov, M I
2002-08-01
Assuming that the maximal allowed number of identical particles in a state is an integer parameter, q, we derive the statistical weight and analyze the associated equation that defines the statistical distribution. The derived distribution covers Fermi-Dirac and Bose-Einstein ones in the particular cases q=1 and q--> infinity (n(i)/q-->1), respectively. We show that the derived statistical weight provides a natural combinatorial interpretation of Haldane-Wu fractional exclusion statistics, and present exact solutions of the distribution equation.
What Diagrams Argue in Late Imperial Chinese Combinatorial Texts.
Bréard, Andrea
2015-01-01
Attitudes towards diagrammatic reasoning and visualization in mathematics were seldom spelled out in texts from pre-modern China, although illustrations figure prominently in mathematical literature since the eleventh century. Taking the sums of finite series and their combinatorial interpretation as a case study, this article investigates the epistemological function of illustrations from the eleventh to the nineteenth century that encode either the mathematical objects themselves or represent their related algorithms. It particularly focuses on the two illustrations given in Wang Lai's (1768-1813) Mathematical Principles of Sequential Combinations, arguing that they reflect a specific mode of nineteenth-century mathematical argumentative practice and served as a heuristic model for later authors.
First steps in combinatorial optimization on graphons: matchings
Czech Academy of Sciences Publication Activity Database
Doležal, Martin; Hladký, J.; Hu, P.; Piguet, Diana
2017-01-01
Roč. 61, August (2017), s. 359-365 ISSN 1571-0653 R&D Projects: GA ČR GA16-07378S; GA ČR GJ16-07822Y EU Projects: European Commission(XE) 628974 - PAECIDM Institutional support: RVO:67985840 ; RVO:67985807 Keywords : graphon * graph limits * matching * combinatorial optimization Subject RIV: BA - General Mathematics; BA - General Mathematics (UIVT-O) OBOR OECD: Pure mathematics; Pure mathematics (UIVT-O) http://www.sciencedirect.com/science/article/pii/S1571065317301452
International Nuclear Information System (INIS)
Hook, D W
2008-01-01
A geometric framework for quantum mechanics arose during the mid 1970s when authors such as Cantoni explored the notion of generalized transition probabilities, and Kibble promoted the idea that the space of pure quantum states provides a natural quantum mechanical analogue for classical phase space. This central idea can be seen easily since the projection of Schroedinger's equation from a Hilbert space into the space of pure spaces is a set of Hamilton's equations. Over the intervening years considerable work has been carried out by a variety of authors and a mature description of quantum mechanics in geometric terms has emerged with many applications. This current offering would seem ideally placed to review the last thirty years of progress and relate this to the most recent work in quantum entanglement. Bengtsson and Zyczkowski's beautifully illustrated volume, Geometry of Quantum States (referred to as GQS from now on) attempts to cover considerable ground in its 466 pages. Its topics range from colour theory in Chapter 1 to quantum entanglement in Chapter 15-to say that this is a whirlwind tour is, perhaps, no understatement. The use of the work 'introduction' in the subtitle of GQS, might suggest to the reader that this work be viewed as a textbook and I think that this interpretation would be incorrect. The authors have chosen to present a survey of different topics with the specific aim to introduce entanglement in geometric terms-the book is not intended as a pedagogical introduction to the geometric approach to quantum mechanics. Each of the fifteen chapters is a short, and mostly self-contained, essay on a particular aspect or application of geometry in the context of quantum mechanics with entanglement being addressed specifically in the final chapter. The chapters fall into three classifications: those concerned with the mathematical background, those which discuss quantum theory and the foundational aspects of the geometric framework, and
Functional integration over geometries
International Nuclear Information System (INIS)
Mottola, E.
1995-01-01
The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted
Development of GIFT-PC: the software with multi-drawing functions of three dimensional geometries
International Nuclear Information System (INIS)
Tsuda, Shuichi; Yamaguchi, Yasuhiro
2001-05-01
The Combinatorial Geometry (CG) is a general-purpose geometry package used on radiation transport simulation codes. It is quite useful to illustrate the CG geometries on a simulation code because the visible information of the CG geometries used in a calculation can avoid some mistakes in the case of complicated data, and make it easier to understand the calculation models in the case of presentations. GIFT code (Geographic Information For Target) hsa been developed at Ballistic Research Laboratory, US, for the purpose of illustrating the components of a target from any point of view, calculating a projected area or volume and checking the correctness of the geometry description. Using the drawing functions of GIFT code, perspective or isometric views of a target can be obtained from various points of view. The present report describes the overview of GIFT code and the development of GIFT-PC. GIFT-PC, based on GIFT code, has been developed for easier drawings of three-dimensional geometries using the GUI (Graphical User Interface) system of personal computers, and can be used in various fields as a useful drawing tool for CG geometries. (author)
Dooner, David B
2012-01-01
Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat
Flegg, H Graham
2001-01-01
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Torsional heterotic geometries
International Nuclear Information System (INIS)
Becker, Katrin; Sethi, Savdeep
2009-01-01
We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. We propose the existence of a much larger landscape of compact torsional geometries using string duality. Finally, we present some quantum exact metrics that correspond to NS5-branes placed on an elliptic space. These metrics describe how torus isometries are broken by NS flux.
Geometrie verstehen: statisch - kinematisch
Kroll, Ekkehard
Dem Allgemeinen steht begrifflich das Besondere gegenüber. In diesem Sinne sind allgemeine Überlegungen zum Verstehen von Mathematik zu ergänzen durch Untersuchungen hinsichtlich des Verstehens der einzelnen mathematischen Disziplinen, insbesondere der Geometrie. Hier haben viele Schülerinnen und Schüler Probleme. Diese rühren hauptsächlich daher, dass eine fertige geometrische Konstruktion in ihrer statischen Präsentation auf Papier nicht mehr die einzelnen Konstruktionsschritte erkennen lässt; zum Nachvollzug müssen sie daher ergänzend in einer Konstruktionsbeschreibung festgehalten werden.
Kendig, Keith
2015-01-01
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
Abhyankar, Shreeram Shankar
1964-01-01
This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from
Akopyan, A V
2007-01-01
The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confoca
2015-01-01
This stimulating volume offers a broad collection of the principles of geometry and trigonometry and contains colorful diagrams to bring mathematical principles to life. Subjects are enriched by references to famous mathematicians and their ideas, and the stories are presented in a very comprehensible way. Readers investigate the relationships of points, lines, surfaces, and solids. They study construction methods for drawing figures, a wealth of facts about these figures, and above all, methods to prove the facts. They learn about triangle measure for circular motion, sine and cosine, tangent
REA, The Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric
On relational nature of geometry of microphysics
International Nuclear Information System (INIS)
Chylinski, Z.
1985-11-01
A relativity principle and a curiosity of Galilei space-time is described. An internal space-time of R 4 relation is presented. Lorentz limit of R 4 geometry and a field theory is given. The sources of the effects of R 4 hypothesis are characterized. The completeness of quantum description is discussed. 32 refs. (A.S.)
Graded geometry and Poisson reduction
Cattaneo, A S; Zambon, M
2009-01-01
The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics
Enumeration of Combinatorial Classes of Single Variable Complex Polynomial Vector Fields
DEFF Research Database (Denmark)
Dias, Kealey
A vector field in the space of degree d monic, centered single variable complex polynomial vector fields has a combinatorial structure which can be fully described by a combinatorial data set consisting of an equivalence relation and a marked subset on the integers mod 2d-2, satisfying certain...
Combinatorial enzyme technology for the conversion of agricultural fibers to functional properties
The concept of combinatorial chemistry has received little attention in agriculture and food research, although its applications in this area were described more than fifteen years ago (1, 2). More recently, interest in the use of combinatorial chemistry in agrochemical discovery has been revitalize...