Energy Technology Data Exchange (ETDEWEB)
Cullen, D E
1998-11-22
TART98 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. TART98 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. TART98 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. TART98 completely supersedes all older versions of TART, and it is strongly recommended that users only use the most recent version of TART98 and its data files.
An improved combinatorial geometry model for arbitrary geometry in DSMC
Kargaran, H.; Minuchehr, A.; Zolfaghari, A.
2017-03-01
This paper focuses on a new direct simulation Monte Carlo (DSMC) code based on combinatorial geometry (CG) for simulation of any rarefied gas flow. The developed code, called DgSMC-A, has been supplied with an improved CG modeling able to significantly optimize the particle-tracking process, resulting in a highly reduced runtime compared to the conventional codes. The improved algorithm inserts a grid over the geometry and saves those grid elements containing some part of the geometry border. Since only a small part of a grid is engaged with the geometry border, significant time can be saved using the proposed algorithm. Embedding the modified algorithm in the DgSMC-A resulted in a fast, robust and self-governing code needless to any mesh generator. The code completely handles complex geometries created with first-and second-order surfaces. In addition, we developed a new surface area calculator in the CG methodology for complex geometries based on the Monte Carlo method with acceptable accuracy. Several well-known test cases are examined to indicate the code ability to deal with a wide range of realistic problems. Results are also found to be in good agreement with references and experimental data.
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.
TART97 a coupled neutron-photon 3-D, combinatorial geometry Monte Carlo transport code
Energy Technology Data Exchange (ETDEWEB)
Cullen, D.E.
1997-11-22
TART97 is a coupled neutron-photon, 3 Dimensional, combinatorial geometry, time dependent Monte Carlo transport code. This code can on any modern computer. It is a complete system to assist you with input preparation, running Monte Carlo calculations, and analysis of output results. TART97 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. TART97 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. TART97 completely supersedes all older versions of TART, and it is strongly recommended that users only use the most recent version of TART97 and its data riles.
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.
Combinatorial optimization tolerances calculated in linear time
Goldengorin, Boris; Sierksma, Gerard
2003-01-01
For a given optimal solution to a combinatorial optimization problem, we show, under very natural conditions, the equality of the minimal values of upper and lower tolerances, where the upper tolerances are calculated for the given optimal solution and the lower tolerances outside the optimal
Combinatorial optimization tolerances calculated in linear time
Goldengorin, Boris; Sierksma, Gerard
2003-01-01
For a given optimal solution to a combinatorial optimization problem, we show, under very natural conditions, the equality of the minimal values of upper and lower tolerances, where the upper tolerances are calculated for the given optimal solution and the lower tolerances outside the optimal soluti
Geometry of Psychological Time
Saniga, M
2003-01-01
The paper reviews the most illustrative cases of the "peculiar/anomalous" experiences of time (and, to a lesser extent, also space) and discusses a simple algebraic geometrical model accounting for the most pronounced of them.
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.
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.
Geometry of Minkowski Space-Time
Catoni, Francesco; Cannata, Roberto; Catoni, Vincenzo; Zampetti, Paolo
2011-01-01
This book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences of special relativity are merely a manifestation of space-time geometry. The book is written with the intention of providing students (and teachers) of the first years of University courses with a tool which is easy to be applied and allows the solution of any problem of relativistic kinematics at the same time. The book treats in a rigorous way, but using a non-sophisticated mathematics, the Kinematics of Special Relativity. As an example, the famous "Twin Paradox" is completely solved for all kinds of motions. The novelty of the presentation in this book consists in the extensive use of hyperbolic numbers, the simplest extension of complex numbers, for a complete formalization of the kinematics in the Minkowski space-time. Moreover, from this formalization the understanding of gravity co...
Geometry of Time and Dimensionality of Space
Saniga, M
2003-01-01
One of the most distinguished features of our algebraic geometrical, pencil concept of space-time is the fact that spatial dimensions and time stand, as far as their intrinsic structure is concerned, on completely different footings: the former being represented by pencils of lines, the latter by a pencil of conics. As a consequence, we argue that even at the classical (macroscopic) level there exists a much more intricate and profound coupling between space and time than that dictated by (general) relativity theory. It is surmised that this coupling can be furnished by so-called Cremona (or birational) transformations between two projective spaces of three dimensions, being fully embodied in the structure of configurations of their fundamental elements. We review properties of some of the simplest Cremona transformations and show that the corresponding "fundamental" space-times exhibit an intimate connection between the extrinsic geometry of time dimension and the dimensionality of space. Moreover, these Cre...
Measuring Space-Time Geometry over the Ages
Stebbins, Albert
2012-01-01
Theorists are often told to express things in the "observational plane". One can do this for space-time geometry, considering "visual" observations of matter in our universe by a single observer over time, with no assumptions about isometries, initial conditions, nor any particular relation between matter and geometry, such as Einstein's equations. Using observables as coordinates naturally leads to a parametrization of space-time geometry in terms of other observables, which in turn prescrib...
Wang, Qian; Huang, Hanyang; Wei, Kang; Zhao, Yi
2016-10-01
Mechanical stretching and topographical cues are both effective mechanical stimulations for regulating cell morphology, orientation, and behaviors. The competition of these two mechanical stimulations remains largely underexplored. Previous studies have suggested that a small cyclic mechanical strain is not able to reorient cells that have been pre-aligned by relatively large linear microstructures, but can reorient those pre-aligned by small linear micro/nanostructures if the characteristic dimension of these structures is below a certain threshold. Likewise, for micro/nanostructures with a given characteristic dimension, the strain must exceed a certain magnitude to overrule the topographic cues. There are however no in-depth investigations of such "thresholds" due to the lack of close examination of dynamic cell orientation during and shortly after the mechanical loading. In this study, the time-dependent combinatory effects of active and passive mechanical stimulations on cell orientation are investigated by developing a micromechanical stimulator. The results show that the cells pre-aligned by linear micro/nanostructures can be altered by cyclic in-plane strain, regardless of the structure size. During the loading, the micro/nanostructures can resist the reorientation effects by cyclic in-plane strain while the resistive capability (measured by the mean orientation angle change and the reorientation speed) increases with the increasing characteristic dimension. The micro/nanostructures also can recover the cell orientation after the cessation of cyclic in-plane strain, while the recovering capability increases with the characteristic dimension. The previously observed thresholds are largely dependent on the observation time points. In order to accurately evaluate the combinatory effects of the two mechanical stimulations, observations during the active loading with a short time interval or endpoint observations shortly after the loading are preferred. This
The Geometry of Noncommutative Space-Time
Mendes, R. Vilela
2016-10-01
Stabilization, by deformation, of the Poincaré-Heisenberg algebra requires both the introduction of a fundamental lentgh and the noncommutativity of translations which is associated to the gravitational field. The noncommutative geometry structure that follows from the deformed algebra is studied both for the non-commutative tangent space and the full space with gravity. The contact points of this approach with the work of David Finkelstein are emphasized.
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....
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....
Differential Geometry of Time-Dependent Mechanics
Giachetta, G; Sardanashvily, G
1997-01-01
The usual formulations of time-dependent mechanics start from a given splitting $Y=R\\times M$ of the coordinate bundle $Y\\to R$. From physical viewpoint, this splitting means that a reference frame has been chosen. Obviously, such a splitting is broken under reference frame transformations and time-dependent canonical transformations. Our goal is to formulate time-dependent mechanics in gauge-invariant form, i.e., independently of any reference frame. The main ingredient in this formulation is a connection on the bundle $Y\\to R$ which describes an arbitrary reference frame. We emphasize the following peculiarities of this approach to time-dependent mechanics. A phase space does not admit any canonical contact or presymplectic structure which would be preserved under reference frame transformations, whereas the canonical Poisson structure is degenerate. A Hamiltonian fails to be a function on a phase space. In particular, it can not participate in a Poisson bracket so that the evolution equation is not reduced...
Trugenberger, Carlo A
2016-01-01
In a recently developed approach, geometry is modelled as an emergent property of random networks. Here I show that one of these models I proposed is exactly quantum gravity defined in terms of the combinatorial Ricci curvature recently derived by Ollivier. Geometry in the weak (classical) gravity regime arises in a phase transition driven by the condensation of short graph cycles. The strong (quantum) gravity regime corresponds to "small world" random graphs with logarithmic distance scaling.
Time Complexity of Evolutionary Algorithms for Combinatorial Optimization: A Decade of Results
Institute of Scientific and Technical Information of China (English)
Pietro S. Oliveto; Jun He; Xin Yao
2007-01-01
Computational time complexity analyzes of evolutionary algorithms (EAs) have been performed since the mid-nineties. The first results were related to very simple algorithms, such as the (1+1)-EA, on toy problems. These efforts produced a deeper understanding of how EAs perform on different kinds of fitness landscapes and general mathematical tools that may be extended to the analysis of more complicated EAs on more realistic problems. In fact, in recent years, it has been possible to analyze the (1+1)-EA on combinatorial optimization problems with practical applications and more realistic population-based EAs on structured toy problems. This paper presents a survey of the results obtained in the last decade along these two research lines. The most common mathematical techniques are introduced, the basic ideas behind them are discussed and their elective applications are highlighted. Solved problems that were still open are enumerated as are those still awaiting for a solution. New questions and problems arisen in the meantime are also considered.
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
Measuring Space-Time Geometry over the Ages
Energy Technology Data Exchange (ETDEWEB)
Stebbins, Albert; /Fermilab
2012-05-01
Theorists are often told to express things in the 'observational plane'. One can do this for space-time geometry, considering 'visual' observations of matter in our universe by a single observer over time, with no assumptions about isometries, initial conditions, nor any particular relation between matter and geometry, such as Einstein's equations. Using observables as coordinates naturally leads to a parametrization of space-time geometry in terms of other observables, which in turn prescribes an observational program to measure the geometry. Under the assumption of vorticity-free matter flow we describe this observational program, which includes measurements of gravitational lensing, proper motion, and redshift drift. Only 15% of the curvature information can be extracted without long time baseline observations, and this increases to 35% with observations that will take decades. The rest would likely require centuries of observations. The formalism developed is exact, non-perturbative, and more general than the usual cosmological analysis.
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.
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
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).
DEFF Research Database (Denmark)
1997-01-01
The invention provides a method for the production of a combinatorial library of compound of general formula (I) using solid phase methodologies. The cleavage of the array of immobilised compounds of the phthalimido type from the solid support matrix is accomplished by using an array of dinucleop......The invention provides a method for the production of a combinatorial library of compound of general formula (I) using solid phase methodologies. The cleavage of the array of immobilised compounds of the phthalimido type from the solid support matrix is accomplished by using an array...... of dinucleophiles, e.g. hydrazines (hydrazinolysis) or N-hydroxylamines, whereby a combinatorial dimension is introduced in the cleavage step. The invention also provides a compound library....
Chvátal, V
2011-01-01
This book is a collection of six articles arising from the meeting of the NATO Advanced Study Institute (ASI) "Combinatorial Optimization: Methods and Applications," which was held at the University of Montreal in June 2006. This ASI consisted of seven series of five one-hour lectures and one series of four one-hour lectures. It was attended by some sixty students of graduate or postdoctoral level from fifteen countries worldwide. It includes topics such as: integer and mixed integer programming, facility location, branching on split disjunctions, convexity in combinatorial optimizat
Exact holographic mapping and emergent space-time geometry
Qi, Xiao-Liang
2013-01-01
In this paper, we propose an {\\it exact holographic mapping} which is a unitary mapping from the Hilbert space of a lattice system in flat space (boundary) to that of another lattice system in one higher dimension (bulk). By defining the distance in the bulk system from two-point correlation functions, we obtain an emergent bulk space-time geometry that is determined by the boundary state and the mapping. As a specific example, we study the exact holographic mapping for $(1+1)$-dimensional lattice Dirac fermions and explore the emergent bulk geometry corresponding to different boundary states including massless and massive states at zero temperature, and the massless system at finite temperature. We also study two entangled one-dimensional chains and show that the corresponding bulk geometry consists of two asymptotic regions connected by a worm-hole. The quantum quench of the coupled chains is mapped to dynamics of the worm-hole. In the end we discuss the general procedure of applying this approach to intera...
Combinatorial Reciprocity Theorems
Beck, Matthias
2012-01-01
A common theme of enumerative combinatorics is formed by counting functions that are polynomials evaluated at positive integers. In this expository paper, we focus on four families of such counting functions connected to hyperplane arrangements, lattice points in polyhedra, proper colorings of graphs, and $P$-partitions. We will see that in each instance we get interesting information out of a counting function when we evaluate it at a \\emph{negative} integer (and so, a priori the counting function does not make sense at this number). Our goals are to convey some of the charm these "alternative" evaluations of counting functions exhibit, and to weave a unifying thread through various combinatorial reciprocity theorems by looking at them through the lens of geometry, which will include some scenic detours through other combinatorial concepts.
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.
Dieleman, Peter; Waitukaitis, Scott; van Hecke, Martin
To design rigidly foldable quadrilateral meshes one generally needs to solve a complicated set of constraints. Here we present a systematic, combinatorial approach to create rigidly foldable quadrilateral meshes with a limited number of different vertices. The number of discrete, 1 degree-of-freedom folding branches for some of these meshes scales exponentially with the number of vertices on the edge, whilst other meshes generated this way only have two discrete folding branches, regardless of mesh size. We show how these two different behaviours both emerge from the two folding branches present in a single generic 4-vertex. Furthermore, we model generic 4-vertices as a spherical linkage and exploit a previously overlooked symmetry to create non-developable origami patterns using the same combinatorial framework.
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.
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
Entropy Bounds in $R\\times S^3$ Geometries
Brevik, I; Odintsov, S D; Brevik, Iver; Milton, Kimball A.; Odintsov, Sergei D.
2002-01-01
Exact calculations are given for the Casimir energy for various fields in $R\\times S^3$ geometry. The Green's function method naturally gives a result in a form convenient in the high-temperature limit, while the statistical mechanical approach gives a form convenient for low temperatures. The equivalence of these two representations is demonstrated. Some discrepancies with previous work are noted. In no case, even for ${\\cal N}=4$ SUSY, is the ratio of entropy to energy found to be bounded. This deviation, however, occurs for low temperature, where the equilibrium approach may not be relevant. The same methods are used to calculate the energy and free energy for the TE modes in a half-Einstein universe bounded by a perfectly conducting 2-sphere.
Institute of Scientific and Technical Information of China (English)
S.M.Zadeh; D.M.W Powers; K. Sammut; A.M. Yazdani
2016-01-01
Autonomous Underwater Vehicles (AUVs) are capable of conducting various underwater missions and marine tasks over long periods of time. In this study, a novel conflict-free motion-planning framework is introduced. This framework enhances AUV mission performance by completing the 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 advantage of the Biogeography- Based Optimization (BBO) algorithm to satisfy the objectives of both higher- and lower-level motion planners and guarantee the maximization of mission productivity for a single vehicle operation. The performance of the model is investigated under different scenarios, including cost constraints in time-varying operating fields. To demonstrate the reliability of the proposed model, the performance of each motion planner is separately assessed and statistical analysis is conducted to evaluate the total performance of the entire model. The simulation results indicate the stability of the proposed model and the feasibility of its application to real-time experiments.
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.
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.
Time integration of the shallow water equations in spherical geometry
D. Lanser; J.G. Blom (Joke); J.G. Verwer (Jan)
2000-01-01
textabstractThe shallow water equations in spherical geometry provide a prototype for developing and testing numerical algorithms for atmospheric circulation models. In a previous paper we have studied a spatial discretization of these equations based on an Osher-type finite-volume method on stereog
Time integration of the shallow water equations in spherical geometry
Lanser, D.; Blom, J.G.; Verwer, J.G.
2000-01-01
The shallow water equations in spherical geometry provide a prototype for developing and testing numerical algorithms for atmospheric circulation models. In a previous paper we have studied a spatial discretization of these equations based on an Osher-type finite-volume method on stereographic and l
Combinatorial materials synthesis
Directory of Open Access Journals (Sweden)
Ichiro Takeuchi
2005-10-01
Full Text Available The pace at which major technological changes take place is often dictated by the rate at which new materials are discovered, and the timely arrival of new materials has always played a key role in bringing advances to our society. It is no wonder then that the so-called combinatorial or high-throughput strategy has been embraced by practitioners of materials science in virtually every field. High-throughput experimentation allows simultaneous synthesis and screening of large arrays of different materials. Pioneered by the pharmaceutical industry, the combinatorial method is now widely considered to be a watershed in accelerating the discovery and optimization of new materials1–5.
Algorithmic Strategies in Combinatorial Chemistry
Energy Technology Data Exchange (ETDEWEB)
GOLDMAN,DEBORAH; ISTRAIL,SORIN; LANCIA,GIUSEPPE; PICCOLBONI,ANTONIO; WALENZ,BRIAN
2000-08-01
Combinatorial Chemistry is a powerful new technology in drug design and molecular recognition. It is a wet-laboratory methodology aimed at ``massively parallel'' screening of chemical compounds for the discovery of compounds that have a certain biological activity. The power of the method comes from the interaction between experimental design and computational modeling. Principles of ``rational'' drug design are used in the construction of combinatorial libraries to speed up the discovery of lead compounds with the desired biological activity. This paper presents algorithms, software development and computational complexity analysis for problems arising in the design of combinatorial libraries for drug discovery. The authors provide exact polynomial time algorithms and intractability results for several Inverse Problems-formulated as (chemical) graph reconstruction problems-related to the design of combinatorial libraries. These are the first rigorous algorithmic results in the literature. The authors also present results provided by the combinatorial chemistry software package OCOTILLO for combinatorial peptide design using real data libraries. The package provides exact solutions for general inverse problems based on shortest-path topological indices. The results are superior both in accuracy and computing time to the best software reports published in the literature. For 5-peptoid design, the computation is rigorously reduced to an exhaustive search of about 2% of the search space; the exact solutions are found in a few minutes.
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
Staircase-free finite-difference time-domain formulation for general materials in complex geometries
DEFF Research Database (Denmark)
Dridi, Kim; Hesthaven, J.S.; Ditkowski, A.
2001-01-01
A stable Cartesian grid staircase-free finite-difference time-domain formulation for arbitrary material distributions in general geometries is introduced. It is shown that the method exhibits higher accuracy than the classical Yee scheme for complex geometries since the computational representation...
Jet-Ricci Geometry of Time-Dependent Human Biomechanics
Ivancevic, Tijana T
2009-01-01
We propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds derived from the extended musculo-skeletal configuration manifold. The corresponding Riemannian geometrical evolution follows the Ricci flow diffusion. In particular, we show that the exponential-like decay of total biomechanical energy (due to exhaustion of biochemical resources) is closely related to the Ricci flow on the biomechanical configuration manifold. Keywords: Time-dependent biomechanics, extended configuration manifold, configuration bundle, jet manifolds, Ricci flow diffusion
Towards an axiomatic noncommutative geometry of quantum space and time
Kiselev, Arthemy V
2013-01-01
By exploring a possible physical realisation of the geometric concept of noncommutative tangent bundle, we outline an axiomatic quantum picture of space as topological manifold and time as a count of its reconfiguration events.
Jet-Ricci Geometry of Time-Dependent Human Biomechanics
Ivancevic, Tijana T.
2009-01-01
We propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds derived from the extended musculo-skeletal configuration manifold. The corresponding Riemannian geometrical evolution follows the Ricci flow diffusion. In particular, we show that the exponential-like decay of total biomechanical energy (due to exh...
Massey, Doreen, Power-geometries and the politics of space-time / [rezensiert von] Wolfgang Aschauer
Aschauer, Wolfgang
2008-01-01
Rezensiertes Werk: Power-geometries and the politics of space-time : Hettner-Lecture 1998 / with Doreen Massey. - Heidelberg : Dep. of Geography, Univ., 1999. - 112 S. : Ill. - (Hettner-Lectures ; 2) ISBN 3-88570-502-8
Noncommutative geometry, symmetries and quantum structure of space-time
Energy Technology Data Exchange (ETDEWEB)
Govindarajan, T R [Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113 (India); Gupta, Kumar S [Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064 (India); Harikumar, E [School of Physics, University of Hyderabad, Hyderabad 500046 (India); Meljanac, S, E-mail: trg@imsc.res.in, E-mail: kumars.gupta@saha.ac.in, E-mail: harisp@uohyd.ernet.in, E-mail: meljanac@irb.hr [Rudjer Botkovic Institute, Bijenicka c.54, HR-10002 Zagreb (Croatia)
2011-07-08
We discuss how space-time noncommutativity affects the symmetry groups and particle statistics. Assuming that statistics is superselected under a symmetry transformation, we argue that the corresponding flip operator must be twisted. It is argued that the twisted statistics naturally leads to a deformed oscillator algebra for scalar fields in such a background.
Boosted Horizon of a Boosted Space-Time Geometry
Battista, Emmanuele; Scudellaro, Paolo; Tramontano, Francesco
2015-01-01
We apply the ultrarelativistic boosting procedure to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface, by exploiting the picture of the embedding of an hyperboloid in a five-dimensional Minkowski spacetime. After reverting to the usual four-dimensional formalism, we also solve the geodesic equation and evaluate the Riemann curvature tensor of the boosted Schwarzschild-de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Eventually, the analysis of the Kretschmann invariant (and of the geodesic equation) shows the global structure of space- time, as we demonstrate the presence of a "scalar curvature singularity" within a 3-sphere and find that it is also possible to define what we have called "boosted horizon", a sort of elastic wall where all particles are surprisingly pushe...
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.
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.
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...
Emergent Hyperbolic Network Geometry
Bianconi, Ginestra; Rahmede, Christoph
2017-02-01
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry.
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
Fuzzy Geometry via the Spinor Bundle, with Applications to Holographic Space-time and Matrix Theory
Banks, Tom
2011-01-01
We present a new framework for defining fuzzy approximations to geometry in terms of a cutoff on the spectrum of the Dirac operator, and a generalization of it that we call the Dirac-Flux operator. This framework does not require a symplectic form on the manifold, and is completely rotation invariant on an arbitrary n-sphere. The framework is motivated by the formalism of Holographic Space-Time (HST), whose fundamental variables are sections of the spinor bundle over a compact Euclidean manifold. The strong holographic principle (SHP) requires the space of these sections to be finite dimensional. We discuss applications of fuzzy spinor geometry to HST and to Matrix Theory.
Directory of Open Access Journals (Sweden)
Wilhelm F. Maier
2004-10-01
Full Text Available Two recently published books examine combinatorial materials synthesis, high-throughput screening of libraries, and the design of successful experiments. Both are a must for those interested in materials development and discovery, says Wilhelm F. Maier
de Silva, Vin; Salamon, Dietmar
2012-01-01
We define combinatorial Floer homology of a transverse pair of noncontractibe nonisotopic embedded loops in an oriented 2-manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology.
Normal Order: Combinatorial Graphs
Solomon, A I; Blasiak, P; Horzela, A; Penson, K A; Solomon, Allan I.; Duchamp, Gerard; Blasiak, Pawel; Horzela, Andrzej; Penson, Karol A.
2004-01-01
A conventional context for supersymmetric problems arises when we consider systems containing both boson and fermion operators. In this note we consider the normal ordering problem for a string of such operators. In the general case, upon which we touch briefly, this problem leads to combinatorial numbers, the so-called Rook numbers. Since we assume that the two species, bosons and fermions, commute, we subsequently restrict ourselves to consideration of a single species, single-mode boson monomials. This problem leads to elegant generalisations of well-known combinatorial numbers, specifically Bell and Stirling numbers. We explicitly give the generating functions for some classes of these numbers. In this note we concentrate on the combinatorial graph approach, showing how some important classical results of graph theory lead to transparent representations of the combinatorial numbers associated with the boson normal ordering problem.
Analysis of airplane boarding via space-time geometry and random matrix theory
Bachmat, E; Skiena, S S; Stolyarov, N; Berend, D; Bachmat, Eitan; Sapir, Luba; Skiena, Steven; Stolyarov, Natan; berend, Daniel
2005-01-01
We show that airplane boarding can be asymptotically modeled by 2-dimensional Lorentzian geometry. Boarding time is given by the maximal proper time among curves in the model. Discrepancies between the model and simulation results are closely related to random matrix theory. We then show how such models can be used to explain why some commonly practiced airline boarding policies are ineffective and even detrimental.
Space versus Time: Unimodular versus Non-Unimodular Projective Ring Geometries?
Saniga, Metod
2008-01-01
Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to be unleashed for physics. There exist specific rings over which the projective spaces feature two principally distinct kinds of basic constituents (points and/or higher-rank linear subspaces), intricately interwoven with each other -- unimodular and non-unimodular. We conjecture that these two projective "degrees of freedom" can rudimentary be associated with spatial and temporal dimensions of physics, respectively. Our hypothesis is illustrated on the projective line over the smallest ring of ternions. Both the fundamental difference and intricate connection between time and space are demonstrated, and even the ring geometrical germs of the observed macroscopic dimensionality (3+1) of space-time and the arrow of time are outlined. Some other conceptual implications of this ...
Quantum Mechanics in the Geometry of Space-Time Elementary Theory
Boudet, Roger
2011-01-01
This book continues the fundamental work of Arnold Sommerfeld and David Hestenes formulating theoretical physics in terms of Minkowski space-time geometry. We see how the standard matrix version of the Dirac equation can be reformulated in terms of a real space-time algebra, thus revealing a geometric meaning for the “number i” in quantum mechanics. Next, it is examined in some detail how electroweak theory can be integrated into the Dirac theory and this way interpreted in terms of space-time geometry. Finally, some implications for quantum electrodynamics are considered.The presentation of real quantum electromagnetism is expressed in an addendum. The book covers both the use of the complex and the real languages and allows the reader acquainted with the first language to make a step by step translation to the second one.
High-resolution, real-time simultaneous 3D surface geometry and temperature measurement.
An, Yatong; Zhang, Song
2016-06-27
This paper presents a method to simultaneously measure three-dimensional (3D) surface geometry and temperature in real time. Specifically, we developed 1) a holistic approach to calibrate both a structured light system and a thermal camera under exactly the same world coordinate system even though these two sensors do not share the same wavelength; and 2) a computational framework to determine the sub-pixel corresponding temperature for each 3D point as well as discard those occluded points. Since the thermal 2D imaging and 3D visible imaging systems do not share the same spectrum of light, they can perform sensing simultaneously in real time: we developed a hardware system that can achieve real-time 3D geometry and temperature measurement at 26 Hz with 768 × 960 points per frame.
Samimi, Peyman
The relatively low oxidation resistance and subsequent surface embrittlement have often limited the use of titanium alloys in elevated temperature structural applications. Although extensive effort is spent to investigate the high temperature oxidation performance of titanium alloys, the studies are often constrained to complex technical titanium alloys and neither the mechanisms associated with evolution of the oxide scale nor the effect of oxygen ingress on the microstructure of the base metal are well-understood. In addition lack of systematic oxidation studies across a wider domain of the alloy composition has complicated the determination of composition-mechanism-property relationships. Clearly, it would be ideal to assess the influence of composition and exposure time on the oxidation resistance, independent of experimental variabilities regarding time, temperature and atmosphere as the potential source of error. Such studies might also provide a series of metrics (e.g., hardness, scale, etc) that could be interpreted together and related to the alloy composition. In this thesis a novel combinatorial approach was adopted whereby a series of compositionally graded specimens, (Ti-xMo, Ti-xCr, Ti-xAl and Ti-xW) were prepared using Laser Engineered Net Shaping (LENS(TM)) technology and exposed to still-air at 650 °C. (Abstract shortened by ProQuest.).
Late-time tails in a stationary axisymmetric EMDA black hole geometry
Institute of Scientific and Technical Information of China (English)
Pan Qi-Yuan; Jing Ji-Liang
2005-01-01
The late-time tails of massless and self-interacting (SI) (massive) scalar fields are investigated analytically in a stationary axisymmetric Einstein-Maxwell dilaton-axion (EMDA) black hole geometry. It is shown that the asymptotic behaviour of massless perturbations is dominated by an inverse power-law decaying tail and the intermediate asymptotic behaviour of SI (massive) perturbations is dominated by an oscillatory one.
Zero Geometry, Zero Space Time, The Seeds of The Final Theory
Kambiz Afrasiabi
2011-01-01
Problem statement: Lack of understanding And scientific formulation of zero geometry and zero space-time and the truth about initiation conditions would continue to keep us all in dark and we would continue to create more theories defining our observations about the known universe which could Indeed be part of our illusionary perception of reality And as long as they continue to align themselves with our observations we will continue to obey and propagate them. Approach: Second law of thermod...
DEFF Research Database (Denmark)
Larsen, Jesper Abildgaard; Wisniewski, Rafal; Grunnet, Jacob Deleuran
2008-01-01
As initially suggested by E. Sontag, it is possible to approximate an arbitrary nonlinear system by a set of piecewise linear systems. In this work we concentrate on how to control a system given by a set of piecewise linear systems defined on simplices. By using the results of L. Habets and J. van...... Schuppen, it is possible to find a controller for the system on each of the simplices thus guaranteeing that the system flow on the simplex only will leave the simplex through a subset of its faces. Motivated by R. Forman, on the triangulated state space we define a combinatorial vector field, which...... 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...
Methods from Differential Geometry in Polytope Theory
Adiprasito, Karim Alexander
2014-01-01
The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in connection with (discrete) differential geometry, geometric group theory and low-dimensional topology.
Analytic solutions for seismic travel time and ray path geometry through simple velocity models.
Energy Technology Data Exchange (ETDEWEB)
Ballard, Sanford
2007-12-01
The geometry of ray paths through realistic Earth models can be extremely complex due to the vertical and lateral heterogeneity of the velocity distribution within the models. Calculation of high fidelity ray paths and travel times through these models generally involves sophisticated algorithms that require significant assumptions and approximations. To test such algorithms it is desirable to have available analytic solutions for the geometry and travel time of rays through simpler velocity distributions against which the more complex algorithms can be compared. Also, in situations where computational performance requirements prohibit implementation of full 3D algorithms, it may be necessary to accept the accuracy limitations of analytic solutions in order to compute solutions that satisfy those requirements. Analytic solutions are described for the geometry and travel time of infinite frequency rays through radially symmetric 1D Earth models characterized by an inner sphere where the velocity distribution is given by the function V (r) = A-Br{sup 2}, optionally surrounded by some number of spherical shells of constant velocity. The mathematical basis of the calculations is described, sample calculations are presented, and results are compared to the Taup Toolkit of Crotwell et al. (1999). These solutions are useful for evaluating the fidelity of sophisticated 3D travel time calculators and in situations where performance requirements preclude the use of more computationally intensive calculators. It should be noted that most of the solutions presented are only quasi-analytic. Exact, closed form equations are derived but computation of solutions to specific problems generally require application of numerical integration or root finding techniques, which, while approximations, can be calculated to very high accuracy. Tolerances are set in the numerical algorithms such that computed travel time accuracies are better than 1 microsecond.
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…
Directory of Open Access Journals (Sweden)
Mohsen Sadighi Moshkenani
2007-06-01
Full Text Available This paper presents a novel modeling method for distributed real-time control systems. The method uses function blocks model of IEC 61499 standard related to industrial control systems in combination with object-oriented approach for software production. The new modeling technique is named OO+FB. This method models distribution characteristics and real-time constraints accurately and provides a proper background for analysis and design of controllers. The new methodology, gives a complete framework for facing with modern industrial processes, using the good characteristics of both fundamental method. In this paper, different steps of OO+FB is described and advantages of using such a model is discussed, so a reliable approach is introduced for modeling.
DEFF Research Database (Denmark)
Alstrøm, Tommy Sonne; Sørensen, Mads Peter; Pedersen, Niels Falsig
2010-01-01
The time-dependent Ginzburg-Landau equation is solved numerically for type-II superconductors of complex geometry using the finite element method. The geometry has a marked influence on the magnetic vortex distribution and the vortex dynamics. We have observed generation of giant vortices...
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
2012-10-01
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(2)O(2)) 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 significant in host defences against these pathogenic yeasts.
Research on universal combinatorial coding.
Lu, Jun; Zhang, Zhuo; Mo, Juan
2014-01-01
The conception of universal combinatorial coding is proposed. Relations exist more or less in many coding methods. It means that a kind of universal coding method is objectively existent. It can be a bridge connecting many coding methods. Universal combinatorial coding is lossless and it is based on the combinatorics theory. The combinational and exhaustive property make it closely related with the existing code methods. Universal combinatorial coding does not depend on the probability statistic characteristic of information source, and it has the characteristics across three coding branches. It has analyzed the relationship between the universal combinatorial coding and the variety of coding method and has researched many applications technologies of this coding method. In addition, the efficiency of universal combinatorial coding is analyzed theoretically. The multicharacteristic and multiapplication of universal combinatorial coding are unique in the existing coding methods. Universal combinatorial coding has theoretical research and practical application value.
Barral, N.; Olivier, G.; Alauzet, F.
2017-02-01
Anisotropic metric-based mesh adaptation has proved its efficiency to reduce the CPU time of steady and unsteady simulations while improving their accuracy. However, its extension to time-dependent problems with body-fitted moving geometries is far from straightforward. This paper establishes a well-founded framework for multiscale mesh adaptation of unsteady problems with moving boundaries. This framework is based on a novel space-time analysis of the interpolation error, within the continuous mesh theory. An optimal metric field, called ALE metric field, is derived, which takes into account the movement of the mesh during the adaptation. Based on this analysis, the global fixed-point adaptation algorithm for time-dependent simulations is extended to moving boundary problems, within the range of body-fitted moving meshes and ALE simulations. Finally, three dimensional adaptive simulations with moving boundaries are presented to validate the proposed approach.
Pseudorandomness and Combinatorial Constructions
2006-01-01
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or unknown. In computer science, probabilistic algorithms are sometimes simpler and more efficient than the best known deterministic algorithms for the same problem. Despite this evidence for the power of random choices, the computational theory of pseudorandom...
Lyndon, Roger C
2001-01-01
From the reviews: "This book (...) defines the boundaries of the subject now called combinatorial group theory. (...)it is a considerable achievement to have concentrated a survey of the subject into 339 pages. This includes a substantial and useful bibliography; (over 1100 ÄitemsÜ). ...the book is a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews, AMS, 1979.
A Hybrid Nodal Method for Time-Dependent Incompressible Flow in Two-Dimensional Arbitrary Geometries
Energy Technology Data Exchange (ETDEWEB)
Toreja, A J; Uddin, R
2002-10-21
A hybrid nodal-integral/finite-analytic method (NI-FAM) is developed for time-dependent, incompressible flow in two-dimensional arbitrary geometries. In this hybrid approach, the computational domain is divided into parallelepiped and wedge-shaped space-time nodes (cells). The conventional nodal integral method (NIM) is applied to the interfaces between adjacent parallelepiped nodes (cells), while a finite analytic approach is applied to the interfaces between parallelepiped and wedge-shaped nodes (cells). In this paper, the hybrid method is formally developed and an application of the NI-FAM to fluid flow in an enclosed cavity is presented. Results are compared with those obtained using a commercial computational fluid dynamics code.
Zero Geometry, Zero Space Time, The Seeds of The Final Theory
Directory of Open Access Journals (Sweden)
Kambiz Afrasiabi
2011-01-01
Full Text Available Problem statement: Lack of understanding And scientific formulation of zero geometry and zero space-time and the truth about initiation conditions would continue to keep us all in dark and we would continue to create more theories defining our observations about the known universe which could Indeed be part of our illusionary perception of reality And as long as they continue to align themselves with our observations we will continue to obey and propagate them. Approach: Second law of thermodynamics which is considered to be the most fundamental law governing The known universe and its behavior and at all levels from micro to macro cosmos is itself subject to such flaws simply because it is nonexistent in zero space-time and it reaches infinity at leap out of zero state bordered by infinity wall (the outermost border of the leap universe in no time. This law dictates that in the known universe/post big bang universe which is around 13.4 billion light years old the index of instability which inversely correlates with free energy incessantly increases following its inception, though we are in dark regarding the initiation condition of the known universe and the relation of initiation condition with entropy and This needs to be understood, dissected and formulated Into the new physics on an urgent basis. Results: Big bang which has been proposed to give rise to the known universe presumably is the product of collision of two p-branes and this collision is expected to be similar in nature to the collision of biological p-branes In which case one p-brane impregnates the other and I have alluded to that in my previous publications; Following collision of cosmic p-branes the free energy of the impregnated p-brane increases from zero to infinity in no time and because the cosmic p-branes are the residents of zero geometry and zero space-time in which all the values are zero , i.e., free energy and entropy are paradoxically both zero and because p
Capturing geometry in real-time using a tracked Microsoft Kinect
Tenedorio, Daniel; Fecho, Marlena; Schwartzhaupt, Jorge; Pardridge, Robert; Lue, James; Schulze, Jürgen P.
2012-03-01
We investigate the suitability of the Microsoft Kinect device for capturing real-world objects and places. Our new geometry scanning system permits the user to obtain detailed triangle models of non-moving objects with a tracked Kinect. The system generates a texture map for the triangle mesh using video frames from the Kinect's color camera and displays a continually-updated preview of the textured model in real-time, allowing the user to re-scan the scene from any direction to fill holes or increase the texture resolution. We also present filtering methods to maintain a high-quality model of reasonable size by removing overlapping or low-precision range scans. Our approach works well in the presence of degenerate geometry or when closing loops about the scanned subject. We demonstrate the ability of our system to acquire 3D models at human scale with a prototype implementation in the StarCAVE, a virtual reality environment at the University of California, San Diego. We designed the capturing algorithm to support the scanning of large areas, provided that accurate tracking is available.
Microbatteries for Combinatorial Studies of Conventional Lithium-Ion Batteries
West, William; Whitacre, Jay; Bugga, Ratnakumar
2003-01-01
Integrated arrays of microscopic solid-state batteries have been demonstrated in a continuing effort to develop microscopic sources of power and of voltage reference circuits to be incorporated into low-power integrated circuits. Perhaps even more importantly, arrays of microscopic batteries can be fabricated and tested in combinatorial experiments directed toward optimization and discovery of battery materials. The value of the combinatorial approach to optimization and discovery has been proven in the optoelectronic, pharmaceutical, and bioengineering industries. Depending on the specific application, the combinatorial approach can involve the investigation of hundreds or even thousands of different combinations; hence, it is time-consuming and expensive to attempt to implement the combinatorial approach by building and testing full-size, discrete cells and batteries. The conception of microbattery arrays makes it practical to bring the advantages of the combinatorial approach to the development of batteries.
Information Geometry in Time Dependent Quantum Systems and the Geometric Phase
Dey, Anshuman; Roy, Pratim; Sarkar, Tapobrata
2016-01-01
We study information theoretic geometry in time dependent quantum mechanical systems. First, we discuss global properties of the parameter manifold for two level systems exemplified by i) Rabi oscillations and ii) quenching dynamics of the XY spin chain in a transverse magnetic field, when driven across anisotropic criticality. Next, we comment upon the nature of the geometric phase from classical holonomy analyses of such parameter manifolds. In the context of the transverse XY model in the thermodynamic limit, our results are in contradiction to those in the existing literature, and we argue why the issue deserves a more careful analysis. Finally, we speculate on a novel geometric phase in the model, when driven across a quantum critical line.
Combinatorial auctions for electronic business
Indian Academy of Sciences (India)
Y Narahari; Pankaj Dayama
2005-04-01
Combinatorial auctions (CAs) have recently generated signiﬁcant interest as an automated mechanism for buying and selling bundles of goods. They are proving to be extremely useful in numerous e-business applications such as eselling, e-procurement, e-logistics, and B2B exchanges. In this article, we introduce combinatorial auctions and bring out important issues in the design of combinatorial auctions. We also highlight important contributions in current research in this area. This survey emphasizes combinatorial auctions as applied to electronic business situations.
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...... define an explicit combinatorial analytic modelspace, which is sufficiently abstract that it can serve as a go-between for proving that other sets such as the parabolic Mandelbrot set M1 has the same combinatorial structure as M. As an immediate application we use here the combinatorial-analytic model...
Real-time inversions for finite fault slip models and rupture geometry based on high-rate GPS data
Minson, Sarah E.; Murray, Jessica R.; Langbein, John O.; Gomberg, Joan S.
2015-01-01
We present an inversion strategy capable of using real-time high-rate GPS data to simultaneously solve for a distributed slip model and fault geometry in real time as a rupture unfolds. We employ Bayesian inference to find the optimal fault geometry and the distribution of possible slip models for that geometry using a simple analytical solution. By adopting an analytical Bayesian approach, we can solve this complex inversion problem (including calculating the uncertainties on our results) in real time. Furthermore, since the joint inversion for distributed slip and fault geometry can be computed in real time, the time required to obtain a source model of the earthquake does not depend on the computational cost. Instead, the time required is controlled by the duration of the rupture and the time required for information to propagate from the source to the receivers. We apply our modeling approach, called Bayesian Evidence-based Fault Orientation and Real-time Earthquake Slip, to the 2011 Tohoku-oki earthquake, 2003 Tokachi-oki earthquake, and a simulated Hayward fault earthquake. In all three cases, the inversion recovers the magnitude, spatial distribution of slip, and fault geometry in real time. Since our inversion relies on static offsets estimated from real-time high-rate GPS data, we also present performance tests of various approaches to estimating quasi-static offsets in real time. We find that the raw high-rate time series are the best data to use for determining the moment magnitude of the event, but slightly smoothing the raw time series helps stabilize the inversion for fault geometry.
Geometry from Information Geometry
Caticha, Ariel
2015-01-01
We use the method of maximum entropy to model physical space as a curved statistical manifold. It is then natural to use information geometry to explain the geometry of space. We find that the resultant information metric does not describe the full geometry of space but only its conformal geometry -- the geometry up to local changes of scale. Remarkably, this is precisely what is needed to model "physical" space in general relativity.
Introduction to combinatorial analysis
Riordan, John
2002-01-01
This introduction to combinatorial analysis defines the subject as ""the number of ways there are of doing some well-defined operation."" Chapter 1 surveys that part of the theory of permutations and combinations that finds a place in books on elementary algebra, which leads to the extended treatment of generation functions in Chapter 2, where an important result is the introduction of a set of multivariable polynomials.Chapter 3 contains an extended treatment of the principle of inclusion and exclusion which is indispensable to the enumeration of permutations with restricted position given
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...... of knownresults fromfirst-order infinitary rewriting and infinitary ¿-calculus to iCRSs. In particular, for fully-extended, left-linear iCRSs we prove the well-known compression property, and for orthogonal iCRSs we prove that (1) if a set of redexes U has a complete development, then all complete developments...
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...
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...
Institute of Scientific and Technical Information of China (English)
陈晨; 谭忠
2005-01-01
In this paper, we derive the continuous dependence on the initial-time geometry for the solution of a parabolic equation from dynamo theory. The forward in time problem and backward in time problem are considered. An explicit continuous dependence inequality is obtained even with different prescribed data.
Sensitivity Kernels for Flows in Time-Distance Helioseismology: Extension to Spherical Geometry
Böning, Vincent G A; Zima, Wolfgang; Birch, Aaron C; Gizon, Laurent
2016-01-01
We extend an existing Born approximation method for calculating the linear sensitivity of helioseismic travel times to flows from Cartesian to spherical geometry. This development is necessary for using the Born approximation for inferring large-scale flows in the deep solar interior. In a first sanity check, we compare two $f-$mode kernels from our spherical method and from an existing Cartesian method. The horizontal and total integrals agree to within 0.3 %. As a second consistency test, we consider a uniformly rotating Sun and a travel distance of 42 degrees. The analytical travel-time difference agrees with the forward-modelled travel-time difference to within 2 %. In addition, we evaluate the impact of different choices of filter functions on the kernels for a meridional travel distance of 42 degrees. For all filters, the sensitivity is found to be distributed over a large fraction of the convection zone. We show that the kernels depend on the filter function employed in the data analysis process. If mo...
Simple Combinatorial Optimisation Cost Games
van Velzen, S.
2005-01-01
In this paper we introduce the class of simple combinatorial optimisation cost games, which are games associated to {0, 1}-matrices.A coalitional value of a combinatorial optimisation game is determined by solving an integer program associated with this matrix and the characteristic vector of the
Polyhedral Techniques in Combinatorial Optimization
Aardal, K.I.; van Hoesel, S.
1995-01-01
Combinatorial optimization problems arise in several areas ranging from management to mathematics and graph theory. Most combinatorial optimization problems are compu- tationally hard due to the restriction that a subset of the variables have to take integral values. During the last two decades
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...
Stepniak, Katarzyna; Bock, Olivier; Wielgosz, Pawel
2017-04-01
The goal of this work is to determine the most accurate and homogeneous processing strategy to reprocess ground-based GNSS data from national networks for precise positioning and climate monitoring applications. We investigate the influence of the network geometry design strategy on the estimated coordinates of permanent stations and Zenith Total Delay (ZTD) time series. Three variants of processing were carried out and analyzed: 1) pre-defined network which usually contains baseline skeletons of reference stations and baselines to secondary stations forming a star-like structures with the main nodes connected to the reference skeleton; 2) the standard "obs-max" strategy available in Bernese GNSS Software; 3) a newly developed baselines design strategy optimized for ZTD estimation. The study shows that the network design has a strong impact especially on the quality and continuity of ZTD estimates. In case of sub-daily gaps in the measurements at reference stations, small clusters of stations can be disconnected from the main network in the first network strategy. This has little impact on coordinates, but offsets of a few centimeters in ZTD estimates and spikes in their formal errors can appear at all stations of the disconnected cluster. It is also responsible for significant discontinuities in the estimated ZTD series. Using the new developed network design strategy the reprocessed ZTD time series as well as time series of station positions are much more continuous and homogeneous in comparison to the standard approaches. Moreover, a post-processing screening procedure applied for ZTD and coordinates was applied to remove remaining outliers in time series. As a final screening and validation step, GNSS ZTD estimates were compared to ERA-Interim. The agreement between GNSS and ERA-Interim results with the new baseline design strategy and screening show a significant improvement.
An explicit combinatorial design
Ma, Xiongfeng
2011-01-01
A combinatorial design is a family of sets that are almost disjoint, which is applied in pseudo random number generations and randomness extractions. The parameter, $\\rho$, quantifying the overlap between the sets within the family, is directly related to the length of a random seed needed and the efficiency of an extractor. Nisan and Wigderson proposed an explicit construction of designs in 1994. Later in 2003, Hartman and Raz proved a bound of $\\rho\\le e^2$ for the Nisan-Wigderson construction. In this work, we prove a tighter bound of $\\rho
Combinatorial Maps with Normalized Knot
Zeps, Dainis
2010-01-01
We consider combinatorial maps with fixed combinatorial knot numbered with augmenting numeration called normalized knot. We show that knot's normalization doesn't affect combinatorial map what concerns its generality. Knot's normalization leads to more concise numeration of corners in maps, e.g., odd or even corners allow easy to follow distinguished cycles in map caused by the fixation of the knot. Knot's normalization may be applied to edge structuring knot too. If both are normalized then one is fully and other partially normalized mutually.
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 fractal Brownian motion model
Institute of Scientific and Technical Information of China (English)
朱炬波; 梁甸农
2000-01-01
To solve the problem of how to determine the non-scaled interval when processing radar clutter using fractal Brownian motion (FBM) model, a concept of combinatorial FBM model is presented. Since the earth (or sea) surface varies diversely with space, a radar clutter contains several fractal structures, which coexist on all scales. Taking the combination of two FBMs into account, via theoretical derivation we establish a combinatorial FBM model and present a method to estimate its fractal parameters. The correctness of the model and the method is proved by simulation experiments and computation of practial data. Furthermore, we obtain the relationship between fractal parameters when processing combinatorial model with a single FBM model. Meanwhile, by theoretical analysis it is concluded that when combinatorial model is observed on different scales, one of the fractal structures is more obvious.
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...
Stochastic integrals: a combinatorial approach
Rota, Gian-Carlo; Wallstrom, Timothy C.
1997-01-01
A combinatorial definition of multiple stochastic integrals is given in the setting of random measures. It is shown that some properties of such stochastic integrals, formerly known to hold in special cases, are instances of combinatorial identities on the lattice of partitions of a set. The notion of stochastic sequences of binomial type is introduced as a generalization of special polynomial sequences occuring in stochastic integration, such as Hermite, Poisson–Charlier an...
Combinatorial chemistry in the agrosciences.
Lindell, Stephen D; Pattenden, Lisa C; Shannon, Jonathan
2009-06-15
Combinatorial chemistry and high throughput screening have had a profound effect upon the way in which agrochemical companies conduct their lead discovery research. The article reviews recent applications of combinatorial synthesis in the lead discovery process for new fungicides, herbicides and insecticides. The role and importance of bioavailability guidelines, natural products, privileged structures, virtual screening and X-ray crystallographic protein structures on the design of solid- and solution-phase compound libraries is discussed and illustrated.
Dynamical System Approaches to Combinatorial Optimization
DEFF Research Database (Denmark)
Starke, Jens
2013-01-01
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....... Many of them are investigated analytically, and the costs of the solutions are compared numerically with those of solutions obtained by simulated annealing and the costs of a global optimal solution. Using dynamical systems, a solution to the combinatorial optimization problem emerges in the limit...... 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...
Saleem, Zain Hamid
In this thesis we study a special class of black hole geometries called subtracted geometries. Subtracted geometry black holes are obtained when one omits certain terms from the warp factor of the metric of general charged rotating black holes. The omission of these terms allows one to write the wave equation of the black hole in a completely separable way and one can explicitly see that the wave equation of a massless scalar field in this slightly altered background of a general multi-charged rotating black hole acquires an SL(2, R) x SL(2, R) x SO(3) symmetry. The "subtracted limit" is considered an appropriate limit for studying the internal structure of the non-subtracted black holes because new 'subtracted' black holes have the same horizon area and periodicity of the angular and time coordinates in the near horizon regions as the original black hole geometry it was constructed from. The new geometry is asymptotically conical and is physically similar to that of a black hole in an asymptotically confining box. We use the different nice properties of these geometries to understand various classically and quantum mechanically important features of general charged rotating black holes.
An improved space-time ETAS model for inverting the rupture geometry from seismicity triggering
Guo, Y.; Zhuang, J.; Zhou, S.; Gao, Y.
2015-12-01
This study incorporates the rupture geometry of big earthquakes in the formulation of theEpidemic-Type Aftershock Sequence (ETAS) model, which is a point process model widely applied in thestudy of spatiotemporal seismicity, rather than regarding every earthquake occurring at a point in space andtime. We apply the new model to the catalog from Sichuan province, China, between 1990 and 2013, duringwhich the Wenchuan Mw7.9 earthquake occurred in May 2008. Our results show that the modified modelhas better performance in both data fitting and aftershock simulation, confirming that the elliptic aftershockzone is caused by the superposition of the isotropic triggering effect from each patch of the rupture zone.Moreover, using the technique of stochastic reconstruction, we inverted the fault geometry and verifiedthat direct aftershocks of the main shock more likely occur in the transitive parts from high-slip parts tolow/median slip parts of the main shock fault area.
Petersen, Latrisha K; Chavez-Santoscoy, Ana V; Narasimhan, Balaji
2012-09-06
Polyanhydrides are a class of biomaterials with excellent biocompatibility and drug delivery capabilities. While they have been studied extensively with conventional one-sample-at-a-time synthesis techniques, a more recent high-throughput approach has been developed enabling the synthesis and testing of large libraries of polyanhydrides(1). This will facilitate more efficient optimization and design process of these biomaterials for drug and vaccine delivery applications. The method in this work describes the combinatorial synthesis of biodegradable polyanhydride film and nanoparticle libraries and the high-throughput detection of protein release from these libraries. In this robotically operated method (Figure 1), linear actuators and syringe pumps are controlled by LabVIEW, which enables a hands-free automated protocol, eliminating user error. Furthermore, this method enables the rapid fabrication of micro-scale polymer libraries, reducing the batch size while resulting in the creation of multivariant polymer systems. This combinatorial approach to polymer synthesis facilitates the synthesis of up to 15 different polymers in an equivalent amount of time it would take to synthesize one polymer conventionally. In addition, the combinatorial polymer library can be fabricated into blank or protein-loaded geometries including films or nanoparticles upon dissolution of the polymer library in a solvent and precipitation into a non-solvent (for nanoparticles) or by vacuum drying (for films). Upon loading a fluorochrome-conjugated protein into the polymer libraries, protein release kinetics can be assessed at high-throughput using a fluorescence-based detection method (Figures 2 and 3) as described previously(1). This combinatorial platform has been validated with conventional methods(2) and the polyanhydride film and nanoparticle libraries have been characterized with (1)H NMR and FTIR. The libraries have been screened for protein release kinetics, stability and
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.
Pitts, J Brian
2015-01-01
Klein-Gordon gravity, 1920s-30s particle physics, and 1890s Neumann-Seeliger modified gravity suggest a "graviton mass term" *algebraic* in the potential. Unlike Nordstr\\"om's "massless" theory, massive scalar gravity is invariant under the Poincar\\'e group but not the 15-parameter conformal group. It thus exhibits the whole Minkowski space-time structure, indirectly for volumes. Massive scalar gravity is plausible as a field theory, but violates Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide: matter sees a conformally flat metric due to universal coupling, but gravity sees the rest of the flat metric (on long distances) in the mass term. What is the `true' geometry, in line with Poincar\\'e's modal conventionality argument? Infinitely many theories exhibit this bimetric `geometry,' all with the total stress-energy's trace as source; geometry does not explain the field equations. The irrelevance of the Ehlers-Pirani-Schild construction to conven...
Theoretical modelling of the AGN iron-line/continuum time-lags in the lamp-post geometry
Epitropakis, A; Dovčiak, M; Pecháček, Tomáš; Emmanoulopoulos, D; Karas, V; McHardy, I M
2016-01-01
Context: Theoretical modelling of time-lags between variations in the Fe K$\\alpha$ emission and the X-ray continuum has the potential of shedding light on the physics and geometry of the X-ray emitting region in active galaxies (AGN) and X-ray binaries. In this work, we present the results from a systematic analysis of time-lags between variations in two energy bands ($5-7$ versus $2-4\\,\\mathrm{keV}$) for seven X-ray bright and variable AGN. Aims: To estimate time-lags as accurately as possible, and fit them with theoretical models, in the context of the `lamp-post' geometry, to constrain the geometry of the X-ray emitting region in AGN. Methods: We used all available archival \\textit{XMM-Newton} data for the sources in our sample and extracted light curves in the $5-7$ and $2-4\\,\\mathrm{keV}$ energy bands. We used these light curves and applied a thoroughly tested (through extensive numerical simulations) recipe in order to estimate time-lags which have minimal bias, approximately follow a Gaussian distribut...
Dorschner, B; Chikatamarla, S S; Karlin, I V
2017-06-01
Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work [B. Dorschner, S. Chikatamarla, F. Bösch, and I. Karlin, J. Comput. Phys. 295, 340 (2015)JCTPAH0021-999110.1016/j.jcp.2015.04.017] as well as for three-dimensional one-way coupled simulations of engine-type geometries in B. Dorschner, F. Bösch, S. Chikatamarla, K. Boulouchos, and I. Karlin [J. Fluid Mech. 801, 623 (2016)JFLSA70022-112010.1017/jfm.2016.448] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends the methodology to three-dimensional cases, including two-way coupling between fluid and structure and then turbulence and deforming geometries. To cover this wide range of applications, the classical benchmark of a sedimenting sphere is chosen first to validate the general two-way coupling algorithm. Increasing the complexity, we subsequently consider the simulation of a plunging SD7003 airfoil in the transitional regime at a Reynolds number of Re=40000 and, finally, to access the model's performance for deforming geometries, we conduct a two-way coupled simulation of a self-propelled anguilliform swimmer. These simulations confirm the viability of the new fluid-structure interaction lattice Boltzmann algorithm to simulate flows of engineering relevance.
Dorschner, B.; Chikatamarla, S. S.; Karlin, I. V.
2017-06-01
Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work [B. Dorschner, S. Chikatamarla, F. Bösch, and I. Karlin, J. Comput. Phys. 295, 340 (2015), 10.1016/j.jcp.2015.04.017] as well as for three-dimensional one-way coupled simulations of engine-type geometries in B . Dorschner, F. Bösch, S. Chikatamarla, K. Boulouchos, and I. Karlin [J. Fluid Mech. 801, 623 (2016), 10.1017/jfm.2016.448] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends the methodology to three-dimensional cases, including two-way coupling between fluid and structure and then turbulence and deforming geometries. To cover this wide range of applications, the classical benchmark of a sedimenting sphere is chosen first to validate the general two-way coupling algorithm. Increasing the complexity, we subsequently consider the simulation of a plunging SD7003 airfoil in the transitional regime at a Reynolds number of Re =40 000 and, finally, to access the model's performance for deforming geometries, we conduct a two-way coupled simulation of a self-propelled anguilliform swimmer. These simulations confirm the viability of the new fluid-structure interaction lattice Boltzmann algorithm to simulate flows of engineering relevance.
Discrete quantum geometries and their effective dimension
Thürigen, 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 ef...
Universally Balanced Combinatorial Optimization Games
Directory of Open Access Journals (Sweden)
Xiaotie Deng
2010-09-01
Full Text Available This article surveys studies on universally balanced properties of cooperative games defined in a succinct form. In particular, we focus on combinatorial optimization games in which the values to coalitions are defined through linear optimization programs, possibly combinatorial, that is subject to integer constraints. In economic settings, the integer requirement reflects some forms of indivisibility. We are interested in the classes of games that guarantee a non-empty core no matter what are the admissible values assigned to the parameters defining these programs. We call such classes universally balanced. We present characterization and complexity results on the universally balancedness property for some classes of interesting combinatorial optimization games. In particular, we focus on the algorithmic properties for identifying universally balancedness for the games under discussion.
Combinatorial optimization theory and algorithms
Korte, Bernhard
2002-01-01
Combinatorial optimization is one of the youngest and most active areas of discrete mathematics, and is probably its driving force today. This book describes the most important ideas, theoretical results, and algorithms of this field. It is conceived as an advanced graduate text, and it can also be used as an up-to-date reference work for current research. The book includes the essential fundamentals of graph theory, linear and integer programming, and complexity theory. It covers classical topics in combinatorial optimization as well as very recent ones. The emphasis is on theoretical results and algorithms with provably good performance. Some applications and heuristics are mentioned, too.
Combinatorial synthesis of natural products
DEFF Research Database (Denmark)
Nielsen, John
2002-01-01
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 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...
On an Extension of a Combinatorial Identity
Indian Academy of Sciences (India)
M Rana; A K Agarwal
2009-02-01
Using Frobenius partitions we extend the main results of [4]. This leads 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.
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 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 reasoning to solve problems
Coenen, Tom; Hof, Frits; Verhoef, Nellie
2016-01-01
This study reports combinatorial reasoning to solve problems. We observed the mathematical thinking of students aged 14-16. We study the variation of the students’ solution strategies in the context of emergent modelling. The results show that the students are tempted to begin the problem solving pr
The evolution of combinatorial phonology
Zuidema, Willem; de Boer, Bart
2009-01-01
A fundamental, universal property of human language is that its phonology is combinatorial. That is, one can identify a set of basic, distinct units (phonemes, syllables) that can be productively combined in many different ways. In this paper, we develop a methodological framework based on evolution
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...
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 ...
A Set of Questions in Combinatorial and Metric Geometry
Nandakumar, R.
2013-01-01
We briefly introduce several problems: (1) a generalization of the convex fair partition conjecture, (2) on non-trivial invariants among polyhedrons that can be formed from the same set of face polygons, (3) two questions on assembling rectangular tiles to form larger rectangles and (4) on convex regions which maximize and minimize the diameter for specified area and perimeter. For each question, we discuss partial solutions and indicate aspects that to our knowledge, await exploration.
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.
Geometry of historical epoch, the Alexandrov's problem and non-G\\"odel quantum time machine
Guts, Alexander K
2016-01-01
The new quantum principle of a time machine that is not using a smooth timelike loops in Lorentz manifolds is described. The proposed time machine is based on the destruction of interference of quantum superposition states in the Wheeler superspace.
Energy Technology Data Exchange (ETDEWEB)
Siketić, Zdravko; Skukan, Natko; Bogdanović Radović, Iva [Ruđer Bošković Institute, Bijenička cesta 54, 10000 Zagreb (Croatia)
2015-08-15
In this paper, time-of-flight elastic recoil detection analysis spectrometer with a newly constructed gas ionization detector for energy detection is presented. The detector is designed in the axial (Bragg) geometry with a 3 × 3 array of 50 nm thick Si{sub 3}N{sub 4} membranes as an entrance window. 40 mbar isobutane gas was sufficient to stop a 30 MeV primary iodine beam as well as all recoils in the detector volume. Spectrometer and detector performances were determined showing significant improvement in the mass and energy resolution, respectively, comparing to the spectrometer with a standard silicon particle detector for an energy measurement.
The priming of basic combinatory responses in MEG.
Blanco-Elorrieta, Esti; Ferreira, Victor S; Del Prato, Paul; Pylkkänen, Liina
2017-09-21
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
Advances in differential geometry and topology
Institute for Scientific Interchange. Turin
1990-01-01
The aim of this volume is to offer a set of high quality contributions on recent advances in Differential Geometry and Topology, with some emphasis on their application in physics.A broad range of themes is covered, including convex sets, Kaehler manifolds and moment map, combinatorial Morse theory and 3-manifolds, knot theory and statistical mechanics.
Combinatorial Multiobjective Optimization Using Genetic Algorithms
Crossley, William A.; Martin. Eric T.
2002-01-01
The research proposed in this document investigated multiobjective optimization approaches based upon the Genetic Algorithm (GA). Several versions of the GA have been adopted for multiobjective design, but, prior to this research, there had not been significant comparisons of the most popular strategies. The research effort first generalized the two-branch tournament genetic algorithm in to an N-branch genetic algorithm, then the N-branch GA was compared with a version of the popular Multi-Objective Genetic Algorithm (MOGA). Because the genetic algorithm is well suited to combinatorial (mixed discrete / continuous) optimization problems, the GA can be used in the conceptual phase of design to combine selection (discrete variable) and sizing (continuous variable) tasks. Using a multiobjective formulation for the design of a 50-passenger aircraft to meet the competing objectives of minimizing takeoff gross weight and minimizing trip time, the GA generated a range of tradeoff designs that illustrate which aircraft features change from a low-weight, slow trip-time aircraft design to a heavy-weight, short trip-time aircraft design. Given the objective formulation and analysis methods used, the results of this study identify where turboprop-powered aircraft and turbofan-powered aircraft become more desirable for the 50 seat passenger application. This aircraft design application also begins to suggest how a combinatorial multiobjective optimization technique could be used to assist in the design of morphing aircraft.
Cryptographic Combinatorial Clock-Proxy Auctions
Parkes, David C.; Rabin, Michael O.; Thorpe, Christopher
We present a cryptographic protocol for conducting efficient, provably correct and secrecy-preserving combinatorial clock-proxy auctions. The “clock phase” functions as a trusted auction despite price discovery: bidders submit encrypted bids, and prove for themselves that they meet activity rules, and can compute total demand and thus verify price increases without revealing any information about individual demands. In the sealed-bid “proxy phase”, all bids are revealed the auctioneer via time-lapse cryptography and a branch-and-bound algorithm is used to solve the winner-determination problem. Homomorphic encryption is used to prove the correctness of the solution, and establishes the correctness of the solution to any interested party. Still an NP-hard optimization problem, the use of homomorphic encryption imposes additional computational time on winner-determination that is linear in the size of the branch-and-bound search tree, and thus roughly linear in the original (search-based) computational time. The result is a solution that avoids, in the usual case, the exponential complexity of previous cryptographically-secure combinatorial auctions.
The time distribution of aftershock magnitudes, fault geometry and aftershock prediction
Bhattacharya, Pathikrit; Chakrabarti, B K
2009-01-01
We have analyzed, for the first time, the time cumulant of magnitudes of an aftershock sequence since the mainshock. This comes out to be a remarkable straight line whose slope is characteristic of the fault zone. This will provide an useful tool in understanding the temporal distribution of aftershocks after a specific mainshock.
Energy in the Kantowski–Sachs space-time using teleparallel geometry
Indian Academy of Sciences (India)
Anuradha Das Purkayastha
2013-04-01
The purpose of this paper is to examine the energy content of the inflationary Universe described by Kantowski–Sachs space-time in quasilocal approach of teleparallel gravity and in the Hamiltonian structure of the teleparallel equivalent of general relativity. The teleparallel versions of field equations are also derived in such a space-time.
Theoretical modelling of the AGN iron line vs. continuum time-lags in the lamp-post geometry
Epitropakis, A.; Papadakis, I. E.; Dovčiak, M.; Pecháček, T.; Emmanoulopoulos, D.; Karas, V.; McHardy, I. M.
2016-10-01
Context. Theoretical modelling of time-lags between variations in the Fe Kα emission and the X-ray continuum might shed light on the physics and geometry of the X-ray emitting region in active galaxies (AGN) and X-ray binaries. We here present the results from a systematic analysis of time-lags between variations in two energy bands (5-7 vs. 2-4 keV) for seven X-ray bright and variable AGN. Aims: We estimate time-lags as accurately as possible and fit them with theoretical models in the context of the lamp-post geometry. We also constrain the geometry of the X-ray emitting region in AGN. Methods: We used all available archival XMM-Newton data for the sources in our sample and extracted light curves in the 5-7 and 2-4 keV energy bands. We used these light curves and applied a thoroughly tested (through extensive numerical simulations) recipe to estimate time-lags that have minimal bias, approximately follow a Gaussian distribution, and have known errors. Using traditional χ2 minimisation techniques, we then fitted the observed time-lags with two different models: a phenomenological model where the time-lags have a power-law dependence on frequency, and a physical model, using the reverberation time-lags expected in the lamp-post geometry. The latter were computed assuming a point-like primary X-ray source above a black hole surrounded by a neutral and prograde accretion disc with solar iron abundance. We took all relativistic effects into account for various X-ray source heights, inclination angles, and black hole spin values. Results: Given the available data, time-lags between the two energy bands can only be reliably measured at frequencies between ~5 × 10-5 Hz and ~10-3 Hz. The power-law and reverberation time-lag models can both fit the data well in terms of formal statistical characteristics. When fitting the observed time-lags to the lamp-post reverberation scenario, we can only constrain the height of the X-ray source. The data require, or are consistent
Collective dynamics of time-delay-coupled phase oscillators in a frustrated geometry
Thakur, Bhumika; Sharma, Devendra; Sen, Abhijit; Johnston, George L.
2017-01-01
We study the effect of time delay on the dynamics of a system of repulsively coupled nonlinear oscillators that are configured as a geometrically frustrated network. In the absence of time delay, frustrated systems are known to possess a high degree of multistability among a large number of coexisting collective states except for the fully synchronized state that is normally obtained for attractively coupled systems. Time delay in the coupling is found to remove this constraint and to lead to such a synchronized ground state over a range of parameter values. A quantitative study of the variation of frustration in a system with the amount of time delay has been made and a universal scaling behavior is found. The variation in frustration as a function of the product of time delay and the collective frequency of the system is seen to lie on a characteristic curve that is common for all natural frequencies of the identical oscillators and coupling strengths. Thus time delay can be used as a tuning parameter to control the amount of frustration in a system and thereby influence its collective behavior. Our results can be of potential use in a host of practical applications in physical and biological systems in which frustrated configurations and time delay are known to coexist.
Energy Technology Data Exchange (ETDEWEB)
Williamson, Adam [X-FAB Semiconductor Foundries AG, Erfurt (Germany); Technische Universitaet Ilmenau (Germany); Voerckel, Andreas [X-FAB Semiconductor Foundries AG, Erfurt (Germany)
2010-07-01
Nano-structured silicon has received a growing and serious amount of interest in industrial technology and university research, particularly in regard to the possibility of such nanostructures in optics, with the primary interest here being black silicon as an anti-reflective coating (ARC) for photodiodes. Current literature now contains a wealth of morphological information to influence structure growth and shape in fluorine-based plasma etching in the presence of oxide-forming or fluorocarbon gas inhibitors. Using the computationally efficient grid-based differential time-domain numerical modeling of the finite-difference time-domain (FDTD) method, approximations to Maxwell's equations are solved to model the optical properties of crystalline black silicon. Multiple geometries, from pillars to more pyramid and needle-like structures, are considered and results are correlated to actual scanning electron microscope (SEM) pictures with corresponding reflection measurements taken in a Cary 5000 UV*VIS spectrophotometer with accompanying integrating (Ulbricht) sphere from 200 nm to 800 nm to evaluate both diffuse and specular reflection from the silicon surface. Optimal geometries are simulated and the consequences for photodiode applications are discussed.
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 Properties of Finite Models
Hubicka, Jan
2010-01-01
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite presentation). Extending classical work of Rado (for the random graph), we find a finite presentation for each of the following classes: homogeneous undirected graphs, homogeneous tournaments and homogeneous partially ordered sets. We also give a finite presentation of the rational Urysohn metric space and some homogeneous directed graphs. We survey well known structures that are finitely presented. We focus on structures endowed with natural partial orders and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism orders for various combinatorial objects. We give a new combinatorial proof of the existence of embedding-universal objects for homomorphism-defined...
Stem cells and combinatorial science.
Fang, Yue Qin; Wong, Wan Qing; Yap, Yan Wen; Orner, Brendan P
2007-09-01
Stem cell-based technologies have the potential to help cure a number of cell degenerative diseases. Combinatorial and high throughput screening techniques could provide tools to control and manipulate the self-renewal and differentiation of stem cells. This review chronicles historic and recent progress in the stem cell field involving both pluripotent and multipotent cells, and it highlights relevant cellular signal transduction pathways. This review further describes screens using libraries of soluble, small-molecule ligands, and arrays of molecules immobilized onto surfaces while proposing future trends in similar studies. It is hoped that by reviewing both the stem cell and the relevant high throughput screening literature, this paper can act as a resource to the combinatorial science community.
The Psychopathological Fabric of Time (and Space) and Its Underpinning Pencil-Borne Geometries
Saniga, M; Saniga, Metod; Buccheri, Rosolino
2003-01-01
The paper presents, to our knowledge, a first fairly comprehensive and mathematically well-underpinned classification of the psychopathology of time (and space). After reviewing the most illustrative first-person accounts of "anomalous/peculiar" experiences of time (and, to a lesser degree, also space) we introduce and describe in detail their algebraic geometrical model. The model features six qualitatively different types of the internal structure of time dimension and four types of that of space. As for time, the most pronounced are the ordinary "past-present-future," "present-only" ("eternal/everlasting now") and "no-present" (time "standing still") patterns; the remaining types represent an intriguing superposition of the three. Concerning space, the most elementary are the ordinary, i.e. "here-and-there," mode and the "here-only" one ("omnipresence"); the remaining two cases are again a specific mixture of the former two. We then show what the admissible combinations of temporal and spatial psycho-patte...
Combinatorial Approach of Associative Classification
P. R. Pal; R.C. Jain
2010-01-01
Association rule mining and classification are two important techniques of data mining in knowledge discovery process. Integration of these two has produced class association rule mining or associative classification techniques, which in many cases have shown better classification accuracy than conventional classifiers. Motivated by this study we have explored and applied the combinatorial mathematics in class association rule mining in this paper. Our algorithm is based on producing co...
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.
Geometry of Time, Axiom of Choice and Neuro-Biological Quantum Zeno Effect
Modgil, Moninder Singh
2007-01-01
Role of axiom of choice in quantum measurement is highlighted by suggesting that the conscious observer chooses the outcome from a mixed state. Further, in a periodically repeating universe, these outcomes must be pre-recorded within the non-physical conscious observers, which precludes free will. Free will however exists in a universe with open time, It is suggested that psychology's binding problem is connected with Cantor's original definition of set. Influence of consciousness on material outcome through quantum processes is discussed and interesting constraints derived. For example, it is predicted that quantum mechanical brain states should get frozen if monitored at sufficiently small space-time intervals - a neuro-biological version of the so called quantum zeno effect, which has been verified in domain of micro-physics. Existence of a very small micro-mini-black-hole in brain is predicted as a space-time structural interface between consciousness and brain, whose vaporization explains mass-loss repor...
A Lie-Algebra model for a noncommutative space time geometry
Doerfel, B D
2002-01-01
We propose a Lie-algebra model for noncommutative coordinate and momentum space . Based on a rigid commutation relation for the commutators of space time operators the model is quite constrained if one tries to keep Lorentz invariance as much as possible. We discuss the question of invariants esp. the definition of a mass.
Institute of Scientific and Technical Information of China (English)
Lu Haibo; Liu Weiqiang
2013-01-01
This paper focuses on the usage of the forward-facing cavity and opposing jet combinatorial configuration as the thermal protection system (TPS) for hypersonic vehicles.A hemispherecone nose-tip with the combinatorial configuration is investigated numerically in hypersonic free stream.Some numerical results are validated by experiments.The flow field parameters,aerodynamic force and surface heat flux distribution are obtained.The influence of the opposing jet stagnation pressure on cooling efficiency of the combinatorial TPS is discussed.The detailed numerical results show that the aerodynamic heating is reduced remarkably by the combinatorial system.The recirculation region plays a pivotal role for the reduction of heat flux.The larger the stagnation pressure of opposing jet is,the more the heating reduction is.This kind of combinatorial system is suitable to be the TPS for the high-speed vehicles which need long-range and long time flight.
Geometry and space-time extent of pion emission region at FCC energies
Okorokov, V A
2016-01-01
The energy dependence is investigated for a wide set of space-time characteristics derived from Bose - Einstein correlations of secondary pion pairs produced in proton-proton and nucleus-nucleus interactions. Analytic functions suggested for smooth approximations of energy dependence of emission region parameters demonstrate reasonable agreement with all available experimental results for proton-proton collisions while the approximations correspond to the most of experimental data for nucleus-nucleus collisions at energies above 5 GeV. Estimations for wide set of space-time quantities are obtained for energies of various mode for the Future Circular Collider (FCC) project based on the smooth approximations. The space particle densities at freeze-out are derived also from estimations for volume of emission region and for total multiplicity at FCC energies. Estimations for charged particle density and its critical value allow the possibility of lasing behavior for secondary pions in nucleus-nucleus collisions a...
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.
Bizi, Nadir; Besnard, Fabien
2016-01-01
An analogy with real Clifford algebras on even-dimensional vector spaces suggests to assign a space dimension and a time dimension (modulo 8) to an algebra (represented over a complex Hilbert space) containing two self-adjoint involutions and an anti-unitary operator with specific commutation relations. It is shown that this assignment is compatible with the tensor product, in the sense that a tensor product of such algebras corresponds to the addition of the space and time dimensions. This could provide an interpretation of the presence of such algebras in PT-symmetric Hamiltonians or the description of topological matter. This construction is used to build the tensor product of Lorentzian (and more generally pseudo-Riemannian) spectral triples, defined over a Krein space. The application to the standard model of particles suggests the identity of the time and space dimensions of the total (manifold+finite algebra) spectral triple. It also suggests the emergence of the pseudo-orthogonal group SO(4,6) in a gr...
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.
A geometry-based approach to determining time-temperature superposition shifts in aging experiments
Energy Technology Data Exchange (ETDEWEB)
Maiti, Amitesh
2015-12-21
A powerful way to expand the time and frequency range of material properties is through a method called time-temperature superposition (TTS). Traditionally, TTS has been applied to the dynamical mechanical and flow properties of thermo-rheologically simple materials, where a well-defined master curve can be objectively and accurately obtained by appropriate shifts of curves at different temperatures. However, TTS analysis can also be useful in many other situations where there is scatter in the data and where the principle holds only approximately. In such cases, shifting curves can become a subjective exercise and can often lead to significant errors in the long-term prediction. This mandates the need for an objective method of determining TTS shifts. Here, we adopt a method based on minimizing the “arc length” of the master curve, which is designed to work in situations where there is overlapping data at successive temperatures. We examine the accuracy of the method as a function of increasing noise in the data, and explore the effectiveness of data smoothing prior to TTS shifting. We validate the method using existing experimental data on the creep strain of an aramid fiber and the powder coarsening of an energetic material.
Geometry and Space-Time Extent of Pion Emission Region at FCC Energies
Directory of Open Access Journals (Sweden)
V. A. Okorokov
2016-01-01
Full Text Available The energy dependence is investigated for a wide set of space-time characteristics derived from Bose–Einstein correlations of secondary pion pairs produced in proton-proton and nucleus-nucleus interactions. Analytic functions suggested for smooth approximations of the energy dependence of emission region parameters demonstrate reasonable agreement with all available experimental results for proton-proton collisions while the approximations correspond to most of experimental data for nucleus-nucleus collisions at energies above 5 GeV. Estimations for a wide set of space-time quantities are obtained for energies for the Future Circular Collider (FCC project based on the smooth approximations. The space particle densities at freeze-out are derived also from estimations for the volume of the emission region and for total multiplicity at FCC energies. Estimations for charged particle density and its critical value allow the possibility of lasing behavior for secondary pions in nucleus-nucleus collisions at FCC energy. The mathematical formalism is presented for study of the peak shape of correlation function for general case of central-symmetrical Lévy–Feldheim distribution.
Some polyhedral results in combinatorial optimization
Xiao, Han; 肖汉
2016-01-01
Many combinatorial optimization problems can be conceived of as optimizing a linear function over a polyhedron. Investigating properties of the associated polyhedron has been evidenced to be a powerful schema for solving combinatorial optimization problems, especially for characterizing min-max relations. Three different topics in combinatorial optimization are explored in this thesis, which fall within a unified characterization: integrality of polyhedra. Various min-max relations in com...
Geometric and Combinatorial Structure of Hypersurface Coamoebas
Nisse, Mounir
2009-01-01
Let $V$ be a complex algebraic hypersurface defined by a polynomial $f$ with Newton polytope $\\Delta$. It is well known that the spine of its amoeba has a structure of a tropical hypersurface. We prove in this paper that there exists a complex tropical hypersurface $V_{\\infty, f}$ such that its coamoeba is homeomorphic to the closure in the real torus of the coamoeba of $V$. Moreover, the coamoeba of $V_{\\infty, f}$ contains an arrangement of $(n-1)$-torus depending only on the geometry of $\\Delta$ and the coefficients of $f$. In addition, we can consider this arrangement, as a weighted codual hyperplanes arrangement in the universal covering of the real torus, and the balancing condition (the analogous to that of tropical hypersurfaces) is satisfied. This codual hyperplanes arrangement is called the {\\em shell} of the complex coamoeba (the cousin of the spine of the complex amoeba). %(or the {\\em average contour} of the complex coamoeba). Using this combinatorial coamoebas structure, we show that the amoebas...
Dynamic Combinatorial Libraries : From Exploring Molecular Recognition to Systems Chemistry
Li, Jianwei; Nowak, Piotr; Otto, Sijbren
2013-01-01
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
Discrete quantum geometries and their effective dimension
Energy Technology Data Exchange (ETDEWEB)
Thuerigen, Johannes
2015-07-02
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.
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
Statistical mechanics of combinatorial auctions
Galla, Tobias; Leone, Michele; Marsili, Matteo; Sellitto, Mauro; Weigt, Martin; Zecchina, Riccardo
2006-05-01
Combinatorial auctions are formulated as frustrated lattice gases on sparse random graphs, allowing the determination of the optimal revenue by methods of statistical physics. Transitions between computationally easy and hard regimes are found and interpreted in terms of the geometric structure of the space of solutions. We introduce an iterative algorithm to solve intermediate and large instances, and discuss competing states of optimal revenue and maximal number of satisfied bidders. The algorithm can be generalized to the hard phase and to more sophisticated auction protocols.
Fairness in Combinatorial Auctioning Systems
Saini, Megha
2008-01-01
One of the Multi-Agent Systems that is widely used by various government agencies, buyers and sellers in a market economy, in such a manner so as to attain optimized resource allocation, is the Combinatorial Auctioning System (CAS). We study another important aspect of resource allocations in CAS, namely fairness. We present two important notions of fairness in CAS, extended fairness and basic fairness. We give an algorithm that works by incorporating a metric to ensure fairness in a CAS that uses the Vickrey-Clark-Groves (VCG) mechanism, and uses an algorithm of Sandholm to achieve optimality. Mathematical formulations are given to represent measures of extended fairness and basic fairness.
Cubature formulas on combinatorial graphs
Pesenson, Isaac Z
2011-01-01
Many contemporary applications, for example, cataloging of galaxies, document analysis, face recognition, learning theory, image processing, operate with a large amount of data which is often represented as a graph embedded into a high dimensional Euclidean space. The variety of problems arising in contemporary data processing requires development on graphs such topics of the classical harmonic analysis as Shannon sampling, splines, wavelets, cubature formulas. The goal of the paper is to establish cubature formulas on finite combinatorial graphs. The results have direct applications to problems that arise in connection with data filtering, data denoising and data dimension reduction.
Nakonieczna, Anna
2015-01-01
There does not exist a notion of time which could be transferred straightforwardly from classical to quantum gravity. For this reason, a method of time quantification which would be appropriate for gravity quantization is being sought. One of the existing proposals is using the evolving matter as an intrinsic `clock' while investigating the dynamics of gravitational systems. The objective of our research was to check whether scalar fields can serve as time variables during a dynamical evolution of a coupled multi-component matter-geometry system. For this purpose, we investigated a gravitational collapse of a self-interacting complex and real scalar fields in the Brans-Dicke theory using the 2+2 spacetime foliation. We focused mainly on the region of high curvature appearing nearby the emerging singularity, which is essential from the perspective of quantum gravity. We investigated several formulations of the theory for various values of the Brans-Dicke coupling constant and the coupling between the Brans-Dic...
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.
Combinatorial algorithms for the seriation problem
Seminaroti, Matteo
2016-01-01
In this thesis we study the seriation problem, a combinatorial problem arising in data analysis, which asks to sequence a set of objects in such a way that similar objects are ordered close to each other. We focus on the combinatorial structure and properties of Robinsonian matrices, a special class
Combinatorial Interpretation of General Eulerian Numbers
Directory of Open Access Journals (Sweden)
Tingyao Xiong
2014-01-01
Full Text Available Since the 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,….
Combinatorial Solutions to Normal Ordering of Bosons
Blasiak, P; Horzela, A; Penson, K A; Solomon, A I
2005-01-01
We present a combinatorial method of constructing solutions to the normal ordering of boson operators. Generalizations of standard combinatorial notions - the Stirling and Bell numbers, Bell polynomials and Dobinski relations - lead to calculational tools which allow to find explicitly normally ordered forms for a large class of operator functions.
Combinatorial Properties of Finite Models
Hubicka, Jan
2010-09-01
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite presentation). Extending classical work of Rado (for the random graph), we find a finite presentation for each of the following classes: homogeneous undirected graphs, homogeneous tournaments and homogeneous partially ordered sets. We also give a finite presentation of the rational Urysohn metric space and some homogeneous directed graphs. We survey well known structures that are finitely presented. We focus on structures endowed with natural partial orders and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism orders for various combinatorial objects. We give a new combinatorial proof of the existence of embedding-universal objects for homomorphism-defined classes of structures. This relates countable embedding-universal structures to homomorphism dualities (finite homomorphism-universal structures) and Urysohn metric spaces. Our explicit construction also allows us to show several properties of these structures.
Neural computation via neural geometry: a place code for inter-whisker timing in the barrel cortex?
Wilson, Stuart P; Bednar, James A; Prescott, Tony J; Mitchinson, Ben
2011-10-01
The place theory proposed by Jeffress (1948) is still the dominant model of how the brain represents the movement of sensory stimuli between sensory receptors. According to the place theory, delays in signalling between neurons, dependent on the distances between them, compensate for time differences in the stimulation of sensory receptors. Hence the location of neurons, activated by the coincident arrival of multiple signals, reports the stimulus movement velocity. Despite its generality, most evidence for the place theory has been provided by studies of the auditory system of auditory specialists like the barn owl, but in the study of mammalian auditory systems the evidence is inconclusive. We ask to what extent the somatosensory systems of tactile specialists like rats and mice use distance dependent delays between neurons to compute the motion of tactile stimuli between the facial whiskers (or 'vibrissae'). We present a model in which synaptic inputs evoked by whisker deflections arrive at neurons in layer 2/3 (L2/3) somatosensory 'barrel' cortex at different times. The timing of synaptic inputs to each neuron depends on its location relative to sources of input in layer 4 (L4) that represent stimulation of each whisker. Constrained by the geometry and timing of projections from L4 to L2/3, the model can account for a range of experimentally measured responses to two-whisker stimuli. Consistent with that data, responses of model neurons located between the barrels to paired stimulation of two whiskers are greater than the sum of the responses to either whisker input alone. The model predicts that for neurons located closer to either barrel these supralinear responses are tuned for longer inter-whisker stimulation intervals, yielding a topographic map for the inter-whisker deflection interval across the surface of L2/3. This map constitutes a neural place code for the relative timing of sensory stimuli.
Nakonieczna, Anna
2016-01-01
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 meas...
Students Discovering Spherical Geometry Using Dynamic Geometry Software
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Students Discovering Spherical Geometry Using Dynamic Geometry Software
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
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....
Energy Technology Data Exchange (ETDEWEB)
Nakonieczna, Anna [Institute of Physics, Maria Curie-Skłodowska University,Plac Marii Curie-Skłodowskiej 1, 20-031 Lublin (Poland); Institute of Agrophysics, Polish Academy of Sciences, Doświadczalna 4, 20-290 Lublin (Poland); Yeom, Dong-han [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University,No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan (China)
2016-02-08
There does not exist a notion of time which could be transferred straightforwardly from classical to quantum gravity. For this reason, a method of time quantification which would be appropriate for gravity quantization is being sought. One of the existing proposals is using the evolving matter as an intrinsic ‘clock’ while investigating the dynamics of gravitational systems. The objective of our research was to check whether scalar fields can serve as time variables during a dynamical evolution of a coupled multi-component matter-geometry system. We concentrated on a neutral case, which means that the elaborated system was not charged electrically nor magnetically. For this purpose, we investigated a gravitational collapse of a self-interacting complex and real scalar fields in the Brans-Dicke theory using the 2+2 spacetime foliation. We focused mainly on the region of high curvature appearing nearby the emerging singularity, which is essential from the perspective of quantum gravity. We investigated several formulations of the theory for various values of the Brans-Dicke coupling constant and the coupling between the Brans-Dicke field and the matter sector of the theory. The obtained results indicated that the evolving scalar fields can be treated as time variables in close proximity of the singularity due to the following reasons. The constancy hypersurfaces of the Brans-Dicke field are spacelike in the vicinity of the singularity apart from the case, in which the equation of motion of the field reduces to the wave equation due to a specific choice of free evolution parameters. The hypersurfaces of constant complex and real scalar fields are spacelike in the regions nearby the singularities formed during the examined process. The values of the field functions change monotonically in the areas, in which the constancy hypersurfaces are spacelike.
Genetic Algorithm Based Combinatorial Auction Method for Multi-Robot Task Allocation
Institute of Scientific and Technical Information of China (English)
GONG Jian-wei; HUANG Wan-ning; XIONG Guang-ming; MAN Yi-ming
2007-01-01
An improved genetic algorithm is proposed to solve the problem of bad real-time performance or inability to get a global optimal/better solution when applying single-item auction (SIA) method or combinatorial auction method to multi-robot task allocation.The genetic algorithm based combinatorial auction (GACA) method which combines the basic-genetic algorithm with a new concept of ringed chromosome is used to solve the winner determination problem (WDP) of combinatorial auction.The simulation experiments are conducted in OpenSim, a multi-robot simulator.The results show that GACA can get a satisfying solution in a reasonable shot time, and compared with SIA or parthenogenesis algorithm combinatorial auction (PGACA) method, it is the simplest and has higher search efficiency, also, GACA can get a global better/optimal solution and satisfy the high real-time requirement of multi-robot task allocation.
Structure-based design of combinatorial mutagenesis libraries.
Verma, Deeptak; Grigoryan, Gevorg; Bailey-Kellogg, Chris
2015-05-01
The development of protein variants with improved properties (thermostability, binding affinity, catalytic activity, etc.) has greatly benefited from the application of high-throughput screens evaluating large, diverse combinatorial libraries. At the same time, since only a very limited portion of sequence space can be experimentally constructed and tested, an attractive possibility is to use computational protein design to focus libraries on a productive portion of the space. We present a general-purpose method, called "Structure-based Optimization of Combinatorial Mutagenesis" (SOCoM), which can optimize arbitrarily large combinatorial mutagenesis libraries directly based on structural energies of their constituents. SOCoM chooses both positions and substitutions, employing a combinatorial optimization framework based on library-averaged energy potentials in order to avoid explicitly modeling every variant in every possible library. In case study applications to green fluorescent protein, β-lactamase, and lipase A, SOCoM optimizes relatively small, focused libraries whose variants achieve energies comparable to or better than previous library design efforts, as well as larger libraries (previously not designable by structure-based methods) whose variants cover greater diversity while still maintaining substantially better energies than would be achieved by representative random library approaches. By allowing the creation of large-scale combinatorial libraries based on structural calculations, SOCoM promises to increase the scope of applicability of computational protein design and improve the hit rate of discovering beneficial variants. While designs presented here focus on variant stability (predicted by total energy), SOCoM can readily incorporate other structure-based assessments, such as the energy gap between alternative conformational or bound states.
Connell, Paul
2015-04-01
The origin of high energy electrons which contribute to the Relativistic Runaway Electron Avalanche of a TGF are not precisely known, or yet observed, though the most obvious source would seem to be the products of cosmic ray showers, or electron avalanches generated in the high electric field near the tips of lightning leaders. With our new TGF simulation software package LEPTRACK we can now easily create any electric field geometry to be expected in stormclouds, any kind of electron source, and are investigating scenarios of TGF ignition, which may or may not be runaway, and in any direction - not just vertical. Vidoes, lightcurves and spectra, presenting the detailed density structure and time evolution of TGF photon, electron, neucleon and ionization trails were presented for the first time at the AGU Fall Meeting in 2014 - showing the complicated effects of changing electric field strength and air density - and the as yet unrecognized importance of the earth magnetic field in trapping electrons and positrons in the upper atmosphere at the magnetic equator - possibly giving rise to the hard tail seen in some TGF spectra observed by AGILE. We will present here an extension of this work to show the dynamics of TGF ignition scenarios of current interest - upward, downward and randomly directed - both from free electrons and from combinations of lightning leader micro-fields producing electron avalanches, which are then input to the macro-fields expected at or above thunderstorm cloudtops. We will show the spatial shape and time evolution of TGF particle structures, along with their optical and gamma ray spectra emitted, and bring to life their essential physics.
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.
Cheng, Xiaogan; Chen, Hanlin; Lin, Xiubin; Yang, Shufeng; Chen, Shenqiang; Zhang, Fenfen; Li, Kang; Liu, Zelin
2016-09-01
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.
Ashikaga, Hiroshi; Omens, Jeffrey H; Covell, James W
2004-11-01
To test the hypothesis that the abnormal ventricular geometry in failing hearts may be accounted for by regionally selective remodeling of myocardial laminae or sheets, we investigated remodeling of the transmural architecture in chronic volume overload induced by an aortocaval shunt. We determined three-dimensional finite deformation at apical and basal sites in left ventricular anterior wall of six dogs with the use of biplane cineradiography of implanted markers. Myocardial strains at end diastole were measured at a failing state referred to control to describe remodeling of myofibers and sheet structures over time. After 9 +/- 2 wk (means +/- SE) of volume overload, the myocardial volume within the marker sets increased by >20%. At 2 wk, the basal site had myofiber elongation (0.099 +/- 0.030; P architecture is regionally heterogeneous in chronic volume overload. The early differences in fiber elongation seem most likely due to a regional gradient in diastolic wall stress, whereas the late differences in wall thickness are most likely related to regional differences in the laminar architecture of the wall. These results suggest that the temporal progression of ventricular remodeling may be anatomically designed at the level of regional laminar architecture.
Guggenheimer, Heinrich W
1977-01-01
This is a text of local differential geometry considered as an application of advanced calculus and linear algebra. The discussion is designed for advanced undergraduate or beginning graduate study, and presumes of readers only a fair knowledge of matrix algebra and of advanced calculus of functions of several real variables. The author, who is a Professor of Mathematics at the Polytechnic Institute of New York, begins with a discussion of plane geometry and then treats the local theory of Lie groups and transformation groups, solid differential geometry, and Riemannian geometry, leading to a
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
EDITORIAL: Combinatorial and High-Throughput Materials Research
Potyrailo, Radislav A.; Takeuchi, Ichiro
2005-01-01
The success of combinatorial and high-throughput methodologies relies greatly on the availability of various characterization tools with new and improved capabilities [1]. Indeed, how useful can a combinatorial library of 250, 400, 25 000 or 2 000 000 compounds be [2-5] if one is unable to characterize its properties of interest fairly quickly? How useful can a set of thousands of spectra or chromatograms be if one is unable to analyse them in a timely manner? For these reasons, the development of new approaches for materials characterization is one of the most active areas in combinatorial materials science. The importance of this aspect of research in the field has been discussed in numerous conferences including the Pittsburgh Conferences, the American Chemical Society Meetings, the American Physical Society Meetings, the Materials Research Society Symposia and various Gordon Research Conferences. Naturally, the development of new measurement instrumentation attracts the attention not only of practitioners of combinatorial materials science but also of those who design new software for data manipulation and mining. Experimental designs of combinatorial libraries are pursued with available and realistic synthetic and characterization capabilities in mind. It is becoming increasingly critical to link the design of new equipment for high-throughput parallel materials synthesis with integrated measurement tools in order to enhance the efficacy of the overall experimental strategy. We have received an overwhelming response to our proposal and call for papers for this Special Issue on Combinatorial Materials Science. The papers in this issue of Measurement Science and Technology are a very timely collection that captures the state of modern combinatorial materials science. They demonstrate the significant advances that are taking place in the field. In some cases, characterization tools are now being operated in the factory mode. At the same time, major challenges
Combinatorial Chemistry for Optical Sensing Applications
Díaz-García, M. E.; Luis, G. Pina; Rivero-Espejel, I. A.
The recent interest in combinatorial chemistry for the synthesis of selective recognition materials for optical sensing applications is presented. The preparation, screening, and applications of libraries of ligands and chemosensors against molecular species and metal ions are first considered. Included in this chapter are also the developments involving applications of combinatorial approaches to the discovery of sol-gel and acrylic-based imprinted materials for optical sensing of antibiotics and pesticides, as well as libraries of doped sol-gels for high-throughput optical sensing of oxygen. The potential of combinatorial chemistry applied to the discovery of new sensing materials is highlighted.
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
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.
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.
Foundations of algebraic geometry
Weil, A
1946-01-01
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
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...
Winkler, Gates R; Winkler, Jay R
2011-11-01
Combinatorial approaches for targeted discovery of new materials require rapid screening systems to evaluate large numbers of new material compositions. High-throughput combinatorial materials discovery is a capital-intensive undertaking requiring sophisticated robotic sample preparation and rapid screening assays. A distributed approach to combinatorial materials discovery can achieve similar goals by increasing the breadth of participation and reducing the size of the capital investment. The discovery of new photoactive materials for solar fuels production demands a screening device to probe materials for electrochemical current production upon irradiation with visible light. We have developed a system that uses an array of pulsed light-emitting diodes (LEDs) synchronized with a two-electrode potentiostat that can measure the photoelectrochemical responses of combinatorial sample arrays deposited on conducting glass plates. Compared to raster scanning methods, this LED system trades spatial resolution for a substantial reduction in scan time. © 2011 American Institute of Physics
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...
Hybrid Genetic Algorithm with PSO Effect for Combinatorial Optimisation Problems
Directory of Open Access Journals (Sweden)
M. H. Mehta
2012-12-01
Full Text Available In engineering field, many problems are hard to solve in some definite interval of time. These problems known as “combinatorial optimisation problems” are of the category NP. These problems are easy to solve in some polynomial time when input size is small but as input size grows problems become toughest to solve in some definite interval of time. Long known conventional methods are not able to solve the problems and thus proper heuristics is necessary. Evolutionary algorithms based on behaviours of different animals and species have been invented and studied for this purpose. Genetic Algorithm is considered a powerful algorithm for solving combinatorial optimisation problems. Genetic algorithms work on these problems mimicking the human genetics. It follows principle of “survival of the fittest” kind of strategy. Particle swarm optimisation is a new evolutionary approach that copies behaviour of swarm in nature. However, neither traditional genetic algorithms nor particle swarm optimisation alone has been completely successful for solving combinatorial optimisation problems. Here a hybrid algorithm is proposed in which strengths of both algorithms are merged and performance of proposed algorithm is compared with simple genetic algorithm. Results show that proposed algorithm works definitely better than the simple genetic algorithm.
Accessing Specific Peptide Recognition by Combinatorial Chemistry
DEFF Research Database (Denmark)
Li, Ming
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...... was studied with this hook peptide library via the beadbead adhesion screening approach. The recognition pairs interlocked and formed a complex. (chapter 8) During accessing peptide molecular recognition by combinatorial chemistry, we faced several problems, which were solved by a range of analytical...
Combinatorial Discovery and Optimization of New Materials
Institute of Scientific and Technical Information of China (English)
Gao Chen; Zhang Xinyi; Yan Dongsheng
2001-01-01
The concept of the combinatorial discovery and optimization of new materials, and its background,importance, and application, as well as its current status in the world, are briefly reviewed in this paper.
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.
A product formula and combinatorial field theory
Horzela, A; Duchamp, G H E; Penson, K A; Solomon, A I
2004-01-01
We treat the problem of normally ordering expressions involving the standard boson operators a, a* where [a,a*]=1. We show that a simple product formula for formal power series - essentially an extension of the Taylor expansion - leads to a double exponential formula which enables a powerful graphical description of the generating functions of the combinatorial sequences associated with such functions - in essence, a combinatorial field theory. We apply these techniques to some examples related to specific physical Hamiltonians.
A drop-on-demand ink-jet printer for combinatorial libraries and functionally graded ceramics.
Mohebi, Mohammad Masoud; Evans, Julian R G
2002-01-01
A printer has been designed and built for the preparation of combinatorial libraries of ceramics and for solid freeforming of functionally graded ceramics with three-dimensionally programmable spatial variation in composition. Several ceramic suspensions (as inks) can be subjected to micromixing behind the nozzle and printed at precise positions. Both mixing and positioning are computer-controlled. The machine consists of an XY table to control the geometry, a set of electromagnetic valves that manage the mixing, a combined electromagnetic valve and sapphire nozzle that form the print head, and a computer that controls the whole system. The mixing valves can eject as little as 1 mg/s ink into the mixing chamber. The printer has been controlled, run, calibrated and tested; the composition and geometry of printed mixtures can be controlled precisely. This method for the controlled mixing of powders facilitates the advance of combinatorial methods within the materials sciences.
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
Graustein, William C
2006-01-01
This first course in differential geometry presents the fundamentals of the metric differential geometry of curves and surfaces in a Euclidean space of three dimensions. Written by an outstanding teacher and mathematician, it explains the material in the most effective way, using vector notation and technique. It also provides an introduction to the study of Riemannian geometry.Suitable for advanced undergraduates and graduate students, the text presupposes a knowledge of calculus. The first nine chapters focus on the theory, treating the basic properties of curves and surfaces, the mapping of
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...
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.
Eum, Jun-Ho; Kim, Sung-Hoon; Yi, Soung Soo; Jang, Kiwan
2012-05-01
Carbon coils could be synthesized using C2H2/H2 as source gases and SF6 as an incorporated additive gas under thermal chemical vapor deposition system. Nickel catalyst layer deposition and then hydrogen plasma pretreatment were performed prior to the carbon coils deposition reaction. According to the different reaction processes, the injection time of SF6 gas flow was varied. The characteristics (formation density, morphology, and geometry) of the deposited carbon coils on the substrates were investigated according to the different reaction processes. Finally, the large-scale synthesis of carbon coils and their geometry control could be achieved merely by manipulating SF6 gas flow injection time. Three cases growth aspects were proposed according to SF6 gas flow injection time in association with the fluorine's characteristics for etching the materials or enhancing the nucleation sites.
Combinatorial study of ceramic tape-casting slurries.
Liu, Zhifu; Wang, Yiling; Li, Yongxiang
2012-03-12
Ceramic tape-casting slurries are complex systems composed of ceramic powder, solvent, and a number of organic components. Conventionally, the development of ceramic tape-casting slurries is time-consuming and of low efficiency. In this work, combinatorial approaches were applied to screen the ethanol and ethyl-acetate binary solvent based slurry for ceramic green tape-casting. The combinatorial libraries were designed considering the variation of the amount of PVB (Poly vinyl-butyral) binder, polyethylene-400, and butyl-benzyl-phthalate plasticizers, and glyceryl triacetate dispersant. A parallel magnetic stirring process was used to make the combinatorial slurry library. The properties mapping of the slurry library was obtained by investigating the sedimentation and rheological characteristics of the slurries. The slurry composition was refined by scaling up the experiments and comparing the microstructure, mechanical property, and sintering behavior of green tapes made from the selected slurries. Finally, a kind of ethanol-ethyl acetate binary solvent based slurry system suitable for making X7R dielectric ceramic green tapes was achieved.
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.
Similarity searching in large combinatorial chemistry spaces
Rarey, Matthias; Stahl, Martin
2001-06-01
We present a novel algorithm, called Ftrees-FS, for similarity searching in large chemistry spaces based on dynamic programming. Given a query compound, the algorithm generates sets of compounds from a given chemistry space that are similar to the query. The similarity search is based on the feature tree similarity measure representing molecules by tree structures. This descriptor allows handling combinatorial chemistry spaces as a whole instead of looking at subsets of enumerated compounds. Within few minutes of computing time, the algorithm is able to find the most similar compound in very large spaces as well as sets of compounds at an arbitrary similarity level. In addition, the diversity among the generated compounds can be controlled. A set of 17 000 fragments of known drugs, generated by the RECAP procedure from the World Drug Index, was used as the search chemistry space. These fragments can be combined to more than 1018 compounds of reasonable size. For validation, known antagonists/inhibitors of several targets including dopamine D4, histamine H1, and COX2 are used as queries. Comparison of the compounds created by Ftrees-FS to other known actives demonstrates the ability of the method to jump between structurally unrelated molecule classes.
Dynamic combinatorial libraries of artificial repeat proteins.
Eisenberg, Margarita; Shumacher, Inbal; Cohen-Luria, Rivka; Ashkenasy, Gonen
2013-06-15
Repeat proteins are found in almost all cellular systems, where they are involved in diverse molecular recognition processes. Recent studies have suggested that de novo designed repeat proteins may serve as universal binders, and might potentially be used as practical alternative to antibodies. We describe here a novel chemical methodology for producing small libraries of repeat proteins, and screening in parallel the ligand binding of library members. The first stage of this research involved the total synthesis of a consensus-based three-repeat tetratricopeptide (TPR) protein (~14 kDa), via sequential attachment of the respective peptides. Despite the effectiveness of the synthesis and ligation steps, this method was found to be too demanding for the production of proteins containing variable number of repeats. Additionally, the analysis of binding of the individual proteins was time consuming. Therefore, we designed and prepared novel dynamic combinatorial libraries (DCLs), and show that their equilibration can facilitate the formation of TPR proteins containing up to eight repeating units. Interestingly, equilibration of the library building blocks in the presence of the biologically relevant ligands, Hsp90 and Hsp70, induced their oligomerization into forming more of the proteins with large recognition surfaces. We suggest that this work presents a novel simple and rapid tool for the simultaneous screening of protein mixtures with variable binding surfaces, and for identifying new binders for ligands of interest.
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,
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
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
Rahaman, Farook; Sharma, Ranjan; Tiwari, Rishi Kumar
2014-01-01
We report a 3D charged black hole solution in an anti desetter space inspired by noncommutative geometry.In this construction,the black hole exhibits two horizon which turn into a single horizon in the extreme case.We investigate the impacts of the electromagnetic field on the location of the event horizon,mass and thermodynamic properties such as Hawking temperature,entropy and heat capacity of the black hole.The geodesics of the charged black hole are also analyzed.
Santo, J
1999-01-01
The ALICE Geometry Database project consists of the development of a set of data structures to store the geometrical information of the ALICE Detector. This Database will be used in Simulation, Reconstruction and Visualisation and will interface with existing CAD systems and Geometrical Modellers.At the present time, we are able to read a complete GEANT3 geometry, to store it in our database and to visualise it. On disk, we store different geometry files in hierarchical fashion, and all the nodes, materials, shapes, configurations and transformations distributed in this tree structure. The present status of the prototype and its future evolution will be presented.
Partition functions and graphs: A combinatorial approach
Solomon, A I; Duchamp, G; Horzela, A; Penson, K A; Solomon, Allan I.; Blasiak, Pawel; Duchamp, Gerard; Horzela, Andrzej; Penson, Karol A.
2004-01-01
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the partition function, for example, is essentially a combinatorial problem. In this talk we shall show that one approach is via the normal ordering of the second quantized operators appearing in the partition function. This in turn leads to a combinatorial graphical description, giving essentially Feynman-type graphs associated with the theory. We illustrate this methodology by the explicit calculation of two model examples, the free boson gas and a superfluid boson model. We show how the calculation of partition functions can be facilitated by knowledge of the combinatorics of the boson normal ordering problem; this naturally gives rise to the Bell numbers of combinatorics. The associated graphical representation of these numbers gives a perturbation expansion in terms of a sequen...
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...
Space-efficient parallel algorithms for combinatorial search problems
DEFF Research Database (Denmark)
Pietrcaprina, Andrea; Pucci, Geppino; Silvestri, Francesco;
2015-01-01
We present space-efficient parallel strategies for two fundamental combinatorial search problems, namely, backtrack search and branch-and-bound , both involving the visit of an n-node tree of height h under the assumption that a node can be accessed only through its father or its children. For both...... problems we propose efficient algorithms that run on a p-processor distributed-memory machine. For backtrack search, we give a deterministic algorithm running in O(n/p+hlogp) time, and a Las Vegas algorithm requiring optimal O(n/p+h) time, with high probability. Building on the backtrack search algorithm...
Pottmann, Helmut; Eigensatz, Michael; Vaxman, A.; Wallner, Johannes
2015-01-01
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
Pottmann, Helmut; Eigensatz, Michael; Vaxman, A.; Wallner, Johannes
2015-01-01
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
Combinatorial study of colored Hurwitz polyz\\^etas
Enjalbert, Jean-Yves; Minh, Hoang Ngoc
2012-01-01
A combinatorial study discloses two surjective morphisms between generalized shuffle algebras and algebras generated by the colored Hurwitz polyz\\^etas. The combinatorial aspects of the products and co-products involved in these algebras will be examined.
Combinatorial set theory partition relations for cardinals
Erdös, P; Hajnal, A; Rado, P
2011-01-01
This work presents the most important combinatorial ideas in partition calculus and discusses ordinary partition relations for cardinals without the assumption of the generalized continuum hypothesis. A separate section of the book describes the main partition symbols scattered in the literature. A chapter on the applications of the combinatorial methods in partition calculus includes a section on topology with Arhangel''skii''s famous result that a first countable compact Hausdorff space has cardinality, at most continuum. Several sections on set mappings are included as well as an account of
Toward Chemical Implementation of Encoded Combinatorial Libraries
DEFF Research Database (Denmark)
Nielsen, John; Janda, Kim D.
1994-01-01
by existing methodologies. Here we detail the synthesis of several matrices and the necessary chemistry to implement the conceptual scheme. In addition, we disclose how this novel technology permits a controlled ′dendritic" display of the chemical libraries. © 1994 Academic Press. All rights reserved.......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...
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…
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...
Kreyszig, Erwin
1991-01-01
An introductory textbook on the differential geometry of curves and surfaces in three-dimensional Euclidean space, presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the theoretical and practical importance of the different concepts, methods and results involved. With problems at the end of each section, and solutions listed at the end of the book. Includes 99 illustrations.
Elementary differential geometry
Pressley, Andrew
2001-01-01
Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there The book will provide an invaluable resource to all those taking a first course in differential geometry, for their lecture...
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
Polyhredral techniques in combinatorial optimization I: theory
Aardal, K.; Hoesel, S. van
2001-01-01
Combinatorial optimization problems appear in many disciplines ranging from management and logistics to mathematics, physics, and chemistry. These problems are usually relatively easy to formulate mathematically, but most of them are computationally hard due to the restriction that a subset of the v
Grobner Basis Approach to Some Combinatorial Problems
Directory of Open Access Journals (Sweden)
Victor Ufnarovski
2012-10-01
Full Text Available We consider several simple combinatorial problems and discuss different ways to express them using polynomial equations and try to describe the \\GB of the corresponding ideals. The main instruments are complete symmetric polynomials that help to express different conditions in rather compact way.
Grobner Basis Approach to Some Combinatorial Problems
2012-01-01
We consider several simple combinatorial problems and discuss different ways to express them using polynomial equations and try to describe the \\GB of the corresponding ideals. The main instruments are complete symmetric polynomials that help to express different conditions in rather compact way.
Infinitary Combinatory Reduction Systems: Normalising Reduction Strategies
Ketema, Jeroen; 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 fi
Erratum to Ordered Partial Combinatory Algebras
Hofstra, P.; Oosten, J. van
2003-01-01
To our regret the paper Ordered Partial Combinatory Algebras contains a mistake which we correct here The flaw concerns the definition of compu tational density definition 3.5 which appeared in section 3.3 page 451 This definition is too rigid and as a consequence Lemma 3.6 on page 452
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…
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…
Recent developments in dynamic combinatorial chemistry
Otto, Sijbren; Furlan, Ricardo L.E.; Sanders, Jeremy K.M.
2002-01-01
Generating combinatorial libraries under equilibrium conditions has the important advantage that the libraries are adaptive (i.e. they can respond to exterior influences in the form of molecular recognition events). Thus, a ligand will direct and amplify the formation of its ideal receptor and vice
Boltzmann Samplers for Colored Combinatorial Objects
Bodini, Olivier
2009-01-01
In this paper, we give a general framework for the Boltzmann generation of colored objects belonging to combinatorial constructible classes. We propose an intuitive notion called profiled objects which allows the sampling of size-colored objects (and also of k-colored objects) although the corresponding class cannot be described by an analytic ordinary generating function.
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
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....
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...
Zhai, G.; Shirzaei, M.
2015-12-01
The Kilauea volcano, Hawaii Island, is one of the most active volcanoes worldwide. Its complex system, including magma reservoirs and rift zones, provides a unique opportunity to investigate the dynamics of magma transport and supply. The models explaining the system are yet limited to the first order analytical solutions with fixed geometry. To obtain a 4D map of the volume changes at the Kilauea summit magmatic system (KSMS), we implement a novel geometry-free time-dependent inverse modeling scheme, using a distribution of point center of dilatations (PCDs). The model is constrained using high resolution surface deformation data, which are obtained through InSAR time series analysis of well populated SAR data sets acquired at two overlapping tracks of Envisat satellite during 2003 and 2011. Principal Component Analysis (PCA) of the 4D maps of volume change identifies five major active reservoir beneath Kilauea caldera. The southern caldera reservoir (SCR) gains volume slowly till 2006 before its rapid inflation during 2006 - mid-2007, followed by deflation until the start of re-inflation in mid-2010. Other reservoirs show episodic temporal correlation and anti-correlation with SCR. We found that the top-down relation between reservoirs at the Kilauea summit is not necessarily valid at all time scales. Identifying statistically significant PCDs through Chi-square test, we develop and apply a boundary element modeling scheme to solve for the volume change time series and complex geometry of the summit magmatic system. Availability of such models allows realistic estimates of volume change and associated seismic hazard and enhance the forecast models.
DEFF Research Database (Denmark)
Kongstad, Kenneth Thermann; Andersen-Ranberg, Johan; Hamberger, Björn Robert
In this work, the analytical technique, HPLC-HRMS-SPE-NMR was used for the first time in combination with combinatorial biosynthetic investigations in N. benthamiana. This efficient setup allowed for identification of several diterpene synthase (diTPS) combinations responsible for stereospecific ......In this work, the analytical technique, HPLC-HRMS-SPE-NMR was used for the first time in combination with combinatorial biosynthetic investigations in N. benthamiana. This efficient setup allowed for identification of several diterpene synthase (diTPS) combinations responsible for...
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.
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 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)
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
Combinatorial Chemical Bath Deposition of CdS Contacts for Chalcogenide Photovoltaics.
Mokurala, Krishnaiah; Baranowski, Lauryn L; de Souza Lucas, Francisco W; Siol, Sebastian; van Hest, Maikel F A M; Mallick, Sudhanshu; Bhargava, Parag; Zakutayev, Andriy
2016-09-12
Contact layers play an important role in thin film solar cells, but new material development and optimization of its thickness is usually a long and tedious process. A high-throughput experimental approach has been used to accelerate the rate of research in photovoltaic (PV) light absorbers and transparent conductive electrodes, however the combinatorial research on contact layers is less common. Here, we report on the chemical bath deposition (CBD) of CdS thin films by combinatorial dip coating technique and apply these contact layers to Cu(In,Ga)Se2 (CIGSe) and Cu2ZnSnSe4 (CZTSe) light absorbers in PV devices. Combinatorial thickness steps of CdS thin films were achieved by removal of the substrate from the chemical bath, at regular intervals of time, and in equal distance increments. The trends in the photoconversion efficiency and in the spectral response of the PV devices as a function of thickness of CdS contacts were explained with the help of optical and morphological characterization of the CdS thin films. The maximum PV efficiency achieved for the combinatorial dip-coating CBD was similar to that for the PV devices processed using conventional CBD. The results of this study lead to the conclusion that combinatorial dip-coating can be used to accelerate the optimization of PV device performance of CdS and other candidate contact layers for a wide range of emerging absorbers.
Combinatorial Chemical Bath Deposition of CdS Contacts for Chalcogenide Photovoltaics
Energy Technology Data Exchange (ETDEWEB)
Mokurala, Krishnaiah; Baranowski, Lauryn L.; de Souza Lucas, Francisco W.; Siol, Sebastian; van Hest, Maikel F. A. M.; Mallick, Sudhanshu; Bhargava, Parag; Zakutayev, Andriy
2016-09-12
Contact layers play an important role in thin film solar cells, but new material development and optimization of its thickness is usually a long and tedious process. A high-throughput experimental approach has been used to accelerate the rate of research in photovoltaic (PV) light absorbers and transparent conductive electrodes, however the combinatorial research on contact layers is less common. Here, we report on the chemical bath deposition (CBD) of CdS thin films by combinatorial dip coating technique and apply these contact layers to Cu(In,Ga)Se2 (CIGSe) and Cu2ZnSnSe4 (CZTSe) light absorbers in PV devices. Combinatorial thickness steps of CdS thin films were achieved by removal of the substrate from the chemical bath, at regular intervals of time, and in equal distance increments. The trends in the photoconversion efficiency and in the spectral response of the PV devices as a function of thickness of CdS contacts were explained with the help of optical and morphological characterization of the CdS thin films. The maximum PV efficiency achieved for the combinatorial dip-coating CBD was similar to that for the PV devices processed using conventional CBD. The results of this study lead to the conclusion that combinatorial dip-coating can be used to accelerate the optimization of PV device performance of CdS and other candidate contact layers for a wide range of emerging absorbers.
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 distributions 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 generalization of Newton's gravitational scalar potential exterior to the spherical mass or pressure distribution under consideration.
McAteer, R. T. J.
2013-06-01
When Mandelbrot, the father of modern fractal geometry, made this seemingly obvious statement he was trying to show that we should move out of our comfortable Euclidean space and adopt a fractal approach to geometry. The concepts and mathematical tools of fractal geometry provides insight into natural physical systems that Euclidean tools cannot do. The benet from applying fractal geometry to studies of Self-Organized Criticality (SOC) are even greater. SOC and fractal geometry share concepts of dynamic n-body interactions, apparent non-predictability, self-similarity, and an approach to global statistics in space and time that make these two areas into naturally paired research techniques. Further, the iterative generation techniques used in both SOC models and in fractals mean they share common features and common problems. This chapter explores the strong historical connections between fractal geometry and SOC from both a mathematical and conceptual understanding, explores modern day interactions between these two topics, and discusses how this is likely to evolve into an even stronger link in the near future.
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
Bambi, Cosimo
2012-01-01
Astrophysical black hole candidates are thought to be the Kerr black holes predicted by General Relativity, but there is not yet a clear evidence that the geometry of the space-time around these objects is really described by the Kerr metric. In order to confirm the Kerr black hole hypothesis, we have to observe strong gravity features and check they are in agreement with the ones predicted by General Relativity. In this paper, I study what kind of information can be extracted by analyzing the broad K$\\alpha$ iron line, which is often seen in the X-ray spectrum of both stellar-mass and super-massive black hole candidates and whose shape is supposed to be strongly affected by the space-time geometry. I extend previous studies in the literature. It turns out that there is a strong degeneracy between the spin parameter and the deformation parameter; that is, the line emitted around a Kerr black hole with a certain spin can be very similar to the one coming from the space-time around a non-Kerr object with a quit...
Wetterich, C
2012-01-01
In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes the "physical geometry"? We resolve this "metric ambiguity" by an investigation of the most general form of the quantum effective action for several metrics. In the long-distance limit the physical metric is universal and accounts for a massless graviton. Other degrees of freedom contained in the various metric candidates describe very massive scalars and symmetric second rank tensors. They only play a role at microscopic distances, typically around the Planck length. The universality of geometry at long distances extends to the vierbein and the connection. On the other hand, for distances and time intervals of Planck size geometry looses its universal meaning. Time is born with the big bang.
Krimer, Daniel; Costa, Fidel
2017-01-01
Volcano petrologists and geochemists increasingly use time-scale determinations of magmatic processes from modeling the chemical zoning patterns in crystals. Most determinations are done using one-dimensional traverses across a two-dimensional crystal section. However, crystals are three-dimensional objects with complex shapes, and diffusion and re-equilibration occurs in multiple dimensions. Given that we can mainly study the crystals in two-dimensional petrographic thin sections, the determined time-scales could be in error if multiple dimensional and geometrical effects are not identified and accounted for. Here we report the results of a numerical study where we investigate the role of multiple dimensions, geometry, and initial conditions of Fe-Mg diffusion in an orthopyroxene crystal with the view towards proper determinations of time scales from modeling natural crystals. We found that merging diffusion fronts (i.e. diffusion from multiple directions) causes 'additional' diffusion that has the greatest influence close to the crystal's corners (i.e. where two crystal faces meet), and with longer times the affected area widens. We also found that the one-dimensional traverses that can lead to the most accurate calculated time-scales from natural crystals are along the b- crystallographic axis on the ab-plane when model inputs (concentration and zoning geometry) are taken as measured (rather than inferred from other observations). More specifically, accurate time-scales are obtained if the compositional traverses are highly symmetrical and contain a concentration plateau measured through the crystal center. On the other hand, for two-dimensional models the ab- and ac-planes are better suited if the initial (pre-diffusion) concentration and zoning geometry inputs are known or can be estimated, although these are a priory unknown, and thus, may be difficult to use in practical terms. We also found that under certain conditions, a combined one-dimensional and two
Cubic Curves, Finite Geometry and Cryptography
Bruen, A A; Wehlau, D L
2011-01-01
Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational points are also surveyed. A possible strengthening of the security of elliptic curve cryptography is proposed using a `shared secret' related to the group law. Cubic curves are also used in a new way to construct sets of points having various combinatorial and geometric properties that are of particular interest in finite Desarguesian planes.
On Range Searching in the Group Model and Combinatorial Discrepancy
DEFF Research Database (Denmark)
Larsen, Kasper Green
2011-01-01
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 $t_ut_q = Omega(disc^2/lg n)$ where...... $t_u$ is the worst case update time, $t_q$ 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:begin{itemize}item For half space range searching in $d$-dimensional space, we get a lower bound of $t_u t_q = Omega(n^{1-1/d}/lg n)$. This comes within a $lg n lg lg n$ factor of the best known upper bound. item For orthogonal range searching in $d...
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...
Single-Parameter Combinatorial Auctions with Partially Public Valuations
Goel, Gagan; Karande, Chinmay; Wang, Lei
We consider the problem of designing truthful auctions, when the bidders' valuations have a public and a private component. In particular, we consider combinatorial auctions where the valuation of an agent i for a set S of items can be expressed as v i f(S), where v i is a private single parameter of the agent, and the function f is publicly known. Our motivation behind studying this problem is two-fold: (a) Such valuation functions arise naturally in the case of ad-slots in broadcast media such as Television and Radio. For an ad shown in a set S of ad-slots, f(S) is, say, the number of unique viewers reached by the ad, and v i is the valuation per-unique-viewer. (b) From a theoretical point of view, this factorization of the valuation function simplifies the bidding language, and renders the combinatorial auction more amenable to better approximation factors. We present a general technique, based on maximal-in-range mechanisms, that converts any α-approximation non-truthful algorithm (α ≤ 1) for this problem into Ω(α/log{n}) and Ω(α)-approximate truthful mechanisms which run in polynomial time and quasi-polynomial time, respectively.
Models of optimum discrete signals on the vector combinatorial configurations
Directory of Open Access Journals (Sweden)
V. V. Riznyk
2016-06-01
Full Text Available Method for construction of optimum discrete signals, based on a new conceptual combinatorial model of the systems - Ideal Ring Vector sequences (clusters of the IRV is proposed. IRV clusters are cyclic ordered sequences of t- integer sub-sequences of sequence, which form perfect relationships of t-dimensional partitions over a virtual t-dimensional lattice covered surface of a finite space interval. The sums of connected sub-sequences of an IRV enumerate the set of t- coordinates specified with respect to cyclic frame reference exactly R-times. This property makes IRVs useful in applications, which need to partition multidimensional objects with the smallest possible number of intersections. There are discover a great class of new two- and multidimensional combinatorial constructions, which being in excess classic models of discrete systems with respect to number and combinatorial varieties with theoretically non-limited values of upper boundaries on order of dimensionality –IRV. It shows that remarkable properties of IRVs encoded in fine structure of torus circular symmetry. There are regarded basic properties these models and made shortest comparative analysis of the models with classical models. Indicate that the IRVs to be in exceed of difference sets multiply, and set of the classical difference sets is subset of the IRVs. Some of useful examples for constructing of the optimum discrete signals, error-correcting codes, and ring monolithic optimum vector codes using IRVs are considered. The problem statement involves development the regular method for construction of the optimum discrete signals using two- and multidimensional IRVs. The favorable technical merits of IRVs sets named “Gloria to Ukraine Stars”, which remarkable properties hold for the same set of the IRVs in varieties permutations of its terms is demonstrated, and method for design of two- or multidimensional vector signals coded based on the optimum binary monolithic
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 ...
Three Syntactic Theories for Combinatory Graph Reduction
DEFF Research Database (Denmark)
Danvy, Olivier; Zerny, Ian
2011-01-01
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...... of term graphs in the sense of Barendregt et al. The corresponding storeless abstract machine and natural semantics follow mutatis mutandis. We then interpret let expressions as operations over a global store (thus shifting, in Strachey's words, from denotable entities to storable entities), resulting...
Three Syntactic Theories for Combinatory Graph Reduction
DEFF Research Database (Denmark)
Danvy, Olivier; Zerny, Ian
2013-01-01
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...... of combinatory term graphs. We then recast let bindings as bindings in a global store, thus shifting, in Strachey's words, from denotable entities to storable entities. The store-based terms can still be interpreted as term graphs. We express this third syntactic theory, which we prove equivalent to the second...
Dynamic combinatorial self-replicating systems.
Moulin, Emilie; Giuseppone, Nicolas
2012-01-01
Thanks to their intrinsic network topologies, dynamic combinatorial libraries (DCLs) represent new tools for investigating fundamental aspects related to self-organization and adaptation processes. Very recently the first examples integrating self-replication features within DCLs have pushed even further the idea of implementing dynamic combinatorial chemistry (DCC) towards minimal systems capable of self-construction and/or evolution. Indeed, feedback loop processes - in particular in the form of autocatalytic reactions - are keystones to build dynamic supersystems which could possibly approach the roots of "Darwinian" evolvability at mesoscale. This topic of current interest also shows significant potentialities beyond its fundamental character, because truly smart and autonomous materials for the future will have to respond to changes of their environment by selecting and by exponentially amplifying their fittest constituents.
Stochastic Combinatorial Optimization under Probabilistic Constraints
Agrawal, Shipra; Ye, Yinyu
2008-01-01
In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center problem and the set cover problem, with uncertainty characterized by a probability distribution over set of points or elements to be covered. We consider these problems under adaptive and non-adaptive settings, and present efficient approximation algorithms for the case when underlying distribution is a product distribution. In contrast to the expected cost model prevalent in stochastic optimization literature, our problem definitions support restrictions on the probability distributions of the total costs, via incorporating constraints that bound the probability with which the incurred costs may exceed a given threshold.
Assessment of structural diversity in combinatorial synthesis.
Fergus, Suzanne; Bender, Andreas; Spring, David R
2005-06-01
This article covers the combinatorial synthesis of small molecules with maximal structural diversity to generate a collection of pure compounds that are attractive for lead generation in a phenotypic, high-throughput screening approach. Nature synthesises diverse small molecules, but there are disadvantages with using natural product sources. The efficient chemical synthesis of structural diversity (and complexity) is the aim of diversity-oriented synthesis, and recent progress is reviewed. Specific highlights include a discussion of strategies to obtain structural diversity and an analysis of molecular descriptors used to classify compounds. The assessment of how successful one synthesis is versus another is subjective, therefore we test-drive software to assess structural diversity in combinatorial synthesis, which is freely available via a web interface.
Memetic firefly algorithm for combinatorial optimization
Fister, Iztok; Fister, Iztok; Brest, Janez
2012-01-01
Firefly algorithms belong to modern meta-heuristic algorithms inspired by nature that can be successfully applied to continuous optimization problems. In this paper, we have been applied the firefly algorithm, hybridized with local search heuristic, to combinatorial optimization problems, where we use graph 3-coloring problems as test benchmarks. The results of the proposed memetic firefly algorithm (MFFA) were compared with the results of the Hybrid Evolutionary Algorithm (HEA), Tabucol, and the evolutionary algorithm with SAW method (EA-SAW) by coloring the suite of medium-scaled random graphs (graphs with 500 vertices) generated using the Culberson random graph generator. The results of firefly algorithm were very promising and showed a potential that this algorithm could successfully be applied in near future to the other combinatorial optimization problems as well.
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.
High throughput combinatorial screening of semiconductor materials
Mao, Samuel S.
2011-11-01
This article provides an overview of an advanced combinatorial material discovery platform developed recently for screening semiconductor materials with properties that may have applications ranging from radiation detectors to solar cells. Semiconductor thin-film libraries, each consisting of 256 materials of different composition arranged into a 16×16 matrix, were fabricated using laser-assisted evaporation process along with a combinatorial mechanism to achieve variations. The composition and microstructure of individual materials on each thin-film library were characterized with an integrated scanning micro-beam x-ray fluorescence and diffraction system, while the band gaps were determined by scanning optical reflection and transmission of the libraries. An ultrafast ultraviolet photon-induced charge probe was devised to measure the mobility and lifetime of individual thin-film materials on semiconductor libraries. Selected results on the discovery of semiconductors with desired band gaps and transport properties are illustrated.
COMBINATORIAL DESIGN APPROACHES FOR TEST GENERATION
Institute of Scientific and Technical Information of China (English)
Shi Liang; Xu Baowen; Nie Changhai
2005-01-01
The n-way combination testing is a specification-based testing criterion, which requires that for a system consisted of a few parameters, every combination of valid values of arbitrary n(n ≥ 2) parameters be covered by at least one test. This letter proposed two different test generation algorithms based on combinatorial design for the n-way coverage criterion. The automatic test generators are implemented and some valuable empirical results are obtained.
Switched Systems and Motion Coordination: Combinatorial Challenges
Sadovsky, Alexander V.
2016-01-01
Problems of routing commercial air traffic in a terminal airspace encounter different constraints: separation assurance, aircraft performance limitations, regulations. The general setting of these problems is that of a switched control system. Such a system combines the differentiable motion of the aircraft with the combinatorial choices of choosing precedence when traffic routes merge and choosing branches when the routes diverge. This presentation gives an overview of the problem, the ATM context, related literature, and directions for future research.
A combinatorial approach to metamaterials discovery
Plum, E; Chen, W T; Fedotov, V A; Tsai, D P; Zheludev, N I
2010-01-01
We report a high through-put combinatorial approach to photonic metamaterial optimization. The new approach is based on parallel synthesis and consecutive optical characterization of large numbers of spatially addressable nano-fabricated metamaterial samples (libraries) with quasi-continuous variation of design parameters under real manufacturing conditions. We illustrate this method for Fano-resonance plasmonic nanostructures arriving at explicit recipes for high quality factors needed for switching and sensing applications.
One-parameter groups and combinatorial physics
Duchamp, G; Solomon, A I; Horzela, A; Blasiak, P; Duchamp, Gerard; Penson, Karol A.; Solomon, Allan I.; Horzela, Andrej; Blasiak, Pawel
2004-01-01
In this communication, we consider the normal ordering of sums of elements of the form (a*^r a a*^s), where a* and a are boson creation and annihilation operators. We discuss the integration of the associated one-parameter groups and their combinatorial by-products. In particular, we show how these groups can be realized as groups of substitutions with prefunctions.
The Combinatorial Retention Auction Mechanism (CRAM)
Coughlan, Peter; Gates, William (Bill); Myung, Noah
2013-01-01
Approved for public release; distribution is unlimited. Revised version We propose a reverse uniform price auction called Combinatorial Retention Auction Mechanism (CRAM) that integrates both monetary and non-monetary incentives (NMIs). CRAM computes the cash bonus and NMIs to a single cost parameter, retains the lowest cost employees and provides them with compensation equal to the cost of the first excluded employee. CRAM is dominant strategy incentive compatible. We provide optimal b...
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.
Methods for combinatorial and parallel library design.
Schnur, Dora M; Beno, Brett R; Tebben, Andrew J; Cavallaro, Cullen
2011-01-01
Diversity has historically played a critical role in design of combinatorial libraries, screening sets and corporate collections for lead discovery. Large library design dominated the field in the 1990s with methods ranging anywhere from purely arbitrary through property based reagent selection to product based approaches. In recent years, however, there has been a downward trend in library size. This was due to increased information about the desirable targets gleaned from the genomics revolution and to the ever growing availability of target protein structures from crystallography and homology modeling. Creation of libraries directed toward families of receptors such as GPCRs, kinases, nuclear hormone receptors, proteases, etc., replaced the generation of libraries based primarily on diversity while single target focused library design has remained an important objective. Concurrently, computing grids and cpu clusters have facilitated the development of structure based tools that screen hundreds of thousands of molecules. Smaller "smarter" combinatorial and focused parallel libraries replaced those early un-focused large libraries in the twenty-first century drug design paradigm. While diversity still plays a role in lead discovery, the focus of current library design methods has shifted to receptor based methods, scaffold hopping/bio-isostere searching, and a much needed emphasis on synthetic feasibility. Methods such as "privileged substructures based design" and pharmacophore based design still are important methods for parallel and small combinatorial library design. This chapter discusses some of the possible design methods and presents examples where they are available.
Spacetime and Euclidean Geometry
Brill, D R; Brill, Dieter; Jacobson, Ted
2004-01-01
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".
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.
DEFF Research Database (Denmark)
Kongstad, Kenneth Thermann; Andersen-Ranberg, Johan; Hamberger, Björn Robert;
In this work, the analytical technique, HPLC-HRMS-SPE-NMR was used for the first time in combination with combinatorial biosynthetic investigations in N. benthamiana. This efficient setup allowed for identification of several diterpene synthase (diTPS) combinations responsible for stereospecific...
Guido, Ciro A; Knecht, Stefan; Kongsted, Jacob; Mennucci, Benedetta
2013-05-14
We analyze potentials and limits of the Time-Dependent Density Functional Theory (TD-DFT) approach for the determination of excited-state geometries of organic molecules in gas-phase and in solution. Three very popular DFT exchange-correlation functionals, two hybrids (B3LYP and PBE0) and one long-range corrected (CAM-B3LYP), are here investigated, and the results are compared to the correlated RI-CC2 wave function approach. Solvent effects are further analyzed by means of a polarizable continuum model. A total of 15 organic chromophores (including both small molecules and larger push-pull systems) are considered as prototypes of n → π* and π → π* singlet excitations. Our analysis allows to point out specific correlations between the accuracy of the various functionals and the type of excitation and/or the type of chemical bonds involved. We find that while the best ground-state geometries are obtained with PBE0 and B3LYP, CAM-B3LYP yields the most accurate description of electronic and geometrical characteristics of excited states, both in gas-phase and in solution.
Liang, Jun; Guan, Zhi-Hua; Liu, Yan-Chun; Liu, Bo
2017-02-01
The P- v criticality and phase transition in the extended phase space of a noncommutative geometry inspired Reissner-Nordström (RN) black hole in Anti-de Sitter (AdS) space-time are studied, where the cosmological constant appears as a dynamical pressure and its conjugate quantity is thermodynamic volume of the black hole. It is found that the P- v criticality and the small black hole/large black hole phase transition appear for the noncommutative RN-AdS black hole. Numerical calculations indicate that the noncommutative parameter affects the phase transition as well as the critical temperature, horizon radius, pressure and ratio. The critical ratio is no longer universal, which is different from the result in the van de Waals liquid-gas system. The nature of phase transition at the critical point is also discussed. Especially, for the noncommutative geometry inspired RN-AdS black hole, a new thermodynamic quantity Ψ conjugate to the noncommutative parameter θ has to be defined further, which is required for consistency of both the first law of thermodynamics and the corresponding Smarr relation.
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...
Pavlenko, E.; Andreev, M.; Babina, Y.; Malanushenko, V.
2013-01-01
Attempts to estimate the time of a spin-orbital synchronization for asynchronous polar BY Cam have been made many times since 1994 year. However the estimates obtained did not coincide in a wide region, varying from 150 years (Piirola et al. 1994) up to >3500 years (Kafka et al. 2005). We have undertaken photometric observations of BY Cam over 8.1 years (2004 - 2012) and collected an array of data covering 998 hours during 178 nights. Analyzing the data, we have obtained the most reliable estimate of the spin-orbital time synchronization, Ts = 250±20 years, which agrees very well with both Ts = 150- 290 yrs for asynchronous polar V1500 Cyg (Pavlenko & Pelt 1991); (Stockman et al. 1988) and the theoretically predicted Ts < 1000 yr for asynchronous polars as a whole (Andronov 1987). We also found that the accretion stream switches between two dipole magnetic poles and the equatorial magnetic poles during a synodic ˜ 15-d cycle; the number of switching and their phases can be kept during neighbor cycles but varies on a scale of years. Probably this may depend on the phase of the long-term ˜ 1500 day periodicity (Andreev et al. 2012).
Antenna geometry strategy with prior information for direction-finding MIMO radars
Institute of Scientific and Technical Information of China (English)
Weidong Jiang; Haowen Chen; Xiang Li
2015-01-01
The antenna geometry strategy for direction finding (DF) with multiple-input multiple-output (MIMO) radars is studied. One case, usual y encountered is practical applications, is consi-dered. For a directional antenna geometry with a prior direction, the trace-optimal (TO) criterion (minimizing the trace) on the av-erage Cram ´er-Rao bound (CRB) matrix is employed. A qualitative explanation for antenna geometry is provided, which is a combi-natorial optimization problem. In the numerical example section, it is shown that the antenna geometries, designed by the proposed strategy, outperform the representative DF antenna geometries.
Combinatorial arrays and parallel screening for positive electrode discovery
Spong, A. D.; Vitins, G.; Guerin, S.; Hayden, B. E.; Russell, A. E.; Owen, John R.
Combinatorial techniques have been applied to the preparation and screening of positive electrode candidates for lithium batteries. This work describes the automated parallel synthesis of 64-electrode arrays using a Packard Multiprobe II liquid handling system. A cell was constructed with a single lithium reference-counter electrode and 64, three-millimeter-diameter working electrodes containing Li xMn 2O 4 active material, PVdF-HFP binder and carbon black as a conducting additive. Eight duplicate electrodes, each of eight respective compositions, were deposited on the array and the mass fraction of carbon was varied in steps from 1 to 25%. The results showed a rapid increase in capacity at the percolation limit of 3% for most cells. Some groups of nominally identical cells showed random variations in capacity, especially at low carbon loadings. The overall result is a demonstration of advantages of the combinatorial concept, which were time-saving and an improved statistical significance of the results compared with on-off experiments.
Combinatorial particle swarm optimization for solving blocking flowshop scheduling problem
Directory of Open Access Journals (Sweden)
Mansour Eddaly
2016-10-01
Full Text Available This paper addresses to the flowshop scheduling problem with blocking constraints. The objective is to minimize the makespan criterion. We propose a hybrid combinatorial particle swarm optimization algorithm (HCPSO as a resolution technique for solving this problem. At the initialization, different priority rules are exploited. Experimental study and statistical analysis were performed to select the most adapted one for this problem. Then, the swarm behavior is tested for solving a combinatorial optimization problem such as a sequencing problem under constraints. Finally, an iterated local search algorithm based on probabilistic perturbation is sequentially introduced to the particle swarm optimization algorithm for improving the quality of solution. The computational results show that our approach is able to improve several best known solutions of the literature. In fact, 76 solutions among 120 were improved. Moreover, HCPSO outperforms the compared methods in terms of quality of solutions in short time requirements. Also, the performance of the proposed approach is evaluated according to a real-world industrial problem.
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.
Novel Combinatorial Immunotherapy for Melanoma
2015-10-01
Molecular Genetics hosts weekly seminar given by invited external speakers, who present cutting edge research related to Tumor Immunology and Cancer ...reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching...existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments
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...
Rębilas, Krzysztof
2014-01-01
Starting from the classical Newton's second law which, according to our assumption, is valid in any instantaneous inertial rest frame of body that moves in Minkowskian space-time we get the relativistic equation of motion $\\vec{F}=d\\vec{p}/dt$, where $\\vec{p}$ is the relativistic momentum. The relativistic momentum is then derived without referring to any additional assumptions concerning elastic collisions of bodies. Lorentz-invariance of the relativistic law is proved without tensor formalism. Some new method of force transformation is also presented.
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).
Generalized topological spaces in evolutionary theory and combinatorial chemistry.
Stadler, Bärbel M R; Stadler, Peter F
2002-01-01
The search spaces in combinatorial chemistry as well as the sequence spaces underlying (molecular) evolution are conventionally thought of as graphs. Recombination, however, implies a nongraphical structure of the combinatorial search spaces. These structures, and their implications for search process itself, are heretofore not well understood in general. In this contribution we review a very general formalism from point set topology and discuss its application to combinatorial search spaces, fitness landscapes, evolutionary trajectories, and artificial chemistries.
Polanco, J D; Ujevic, M; Polanco, Jose D.; Letelier, Patricio S.; Ujevic, Maximiliano
2004-01-01
A numerical solution of Einstein field equations for a spherical symmetric and stationary system of identical and auto-gravitating particles in phase transition is presented. The fluid possess a perfect fluid energy momentum tensor, and the internal interactions of the system are represented by a van der Walls like equation of state able to describe a first order phase transition of the type gas-liquid. We find that the space-time curvature, the radial component of the metric, and the pressure and density show discontinuities in their radial derivatives in the phase coexistence region. This region is found to be a spherical surface concentric with the star and the system can be thought as a foliation of acronal, concentric and isobaric surfaces in which the coexistence of phases occurs in only one of these surfaces. This kind of system can be used to represent a star with a high energy density core and low energy density mantle in hydrodynamic equilibrium.
Advanced Aqueous Phase Catalyst Development using Combinatorial Methods Project
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...
Uniform generation of combinatorial structures
Energy Technology Data Exchange (ETDEWEB)
Zito, M.; Pu, I.; Amos, M.; Gibbons, A. [Univ. of Warwick, Coventry (United Kingdom)
1996-12-31
We describe several RNC algorithms for generating graphs and subgraphs uniformly at random. For example, unlabelled undirected graphs are generated in O(log{sup 3} n lg lg n) time using O({epsilon}n{sup 1.5}/lg{sup 3} n lg lg n) processors if their number is n lg lg n known in advance and in O(lg n) time using O ({epsilon}n{sup 2}/lg n) processors otherwise. In both cases the error probability is the inverse of a polynomial in {epsilon}. Thus {epsilon} may be chosen to trade-off processors for error probability. Also, for an arbitrary graph, we describe RNC algorithms for the uniform generation of its subgraphs that are either non-simple paths or spanning trees. The work measure for the subgraph algorithms is essentially determined by the transitive closure bottleneck. As for sequential algorithms, the general notion of constructing generators from counters also applies to parallel algorithms although this approach is not employed by all the algorithms of this paper.
PCB Drill Path Optimization by Combinatorial Cuckoo Search Algorithm
Directory of Open Access Journals (Sweden)
Wei Chen Esmonde Lim
2014-01-01
Full Text Available Optimization of drill path can lead to significant reduction in machining time which directly improves productivity of manufacturing systems. In a batch production of a large number of items to be drilled such as printed circuit boards (PCB, the travel time of the drilling device is a significant portion of the overall manufacturing process. To increase PCB manufacturing productivity and to reduce production costs, a good option is to minimize the drill path route using an optimization algorithm. This paper reports a combinatorial cuckoo search algorithm for solving drill path optimization problem. The performance of the proposed algorithm is tested and verified with three case studies from the literature. The computational experience conducted in this research indicates that the proposed algorithm is capable of efficiently finding the optimal path for PCB holes drilling process.
PCB drill path optimization by combinatorial cuckoo search algorithm.
Lim, Wei Chen Esmonde; Kanagaraj, G; Ponnambalam, S G
2014-01-01
Optimization of drill path can lead to significant reduction in machining time which directly improves productivity of manufacturing systems. In a batch production of a large number of items to be drilled such as printed circuit boards (PCB), the travel time of the drilling device is a significant portion of the overall manufacturing process. To increase PCB manufacturing productivity and to reduce production costs, a good option is to minimize the drill path route using an optimization algorithm. This paper reports a combinatorial cuckoo search algorithm for solving drill path optimization problem. The performance of the proposed algorithm is tested and verified with three case studies from the literature. The computational experience conducted in this research indicates that the proposed algorithm is capable of efficiently finding the optimal path for PCB holes drilling process.
Cusp geometry of fibered 3-manifolds
Futer, David
2011-01-01
Let F be a surface and suppose that \\phi: F -> F is a pseudo-Anosov homeomorphism fixing a puncture p of F. The mapping torus M = M_\\phi\\ is hyperbolic and contains a maximal cusp C about the puncture p. We show that the area and height of the cusp torus bounding C are equal, up to explicit multiplicative error, to the stable translation distance of \\phi\\ acting on the arc complex A(F,p). Our proofs rely on elementary facts about the hyperbolic geometry of pleated surfaces. In particular, we do not use any deep results in Teichmueller theory, Kleinian group theory, or the coarse geometry of A(F,p). A similar result holds for quasi-Fuchsian manifolds N = (F x R). In that setting, we prove a combinatorial estimate on the area and height of the cusp annulus in the convex core of N and give explicit multiplicative and additive errors.
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).
Criticality and parallelism in combinatorial optimization
Energy Technology Data Exchange (ETDEWEB)
Macready, W.G.; Kauffman, S.A. [Santa Fe Institute, NM (United States); Siapas, A.G. [Massachusetts Institute of Technology, Cambridge, MA (United States)
1996-01-05
Local search methods constitute one of the most successful approaches to solving large-scale combinatorial optimization problems. As these methods are increasingly parallelized, optimization performance initially improves, but then abruptly degrades to no matter than that of random search beyond a certain point. The existence of this transition is demonstrated for a family of generalized spin-glass models and the traveling salesman problem. Finite-size scaling is used to characterize size-dependent effects near the transition, and analytical insight is obtained through a mean-field approximation. 17 refs., 5 figs.
Algebraic and combinatorial Brill-Noether theory
Caporaso, Lucia
2011-01-01
The interplay between algebro-geometric and combinatorial Brill-Noether theory is studied. The Brill-Noether variety of a graph shown to be non-empty if the Brill-Noether number is non-negative, as a consequence of the analogous fact for smooth projective curves. Similarly, the existence of a graph for which the Brill-Noether variety is empty implies the emptiness of the corresponding Brill-Noether variety for a general curve. The main tool is a refinement of Baker's Specialization Lemma.
Method and apparatus for combinatorial chemistry
Foote, Robert S.
2007-02-20
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.
Apparatus for combinatorial screening of electrochemical materials
A high throughput combinatorial screening method and apparatus for the evaluation of electrochemical materials using a single voltage source is disclosed wherein temperature changes arising from the application of an electrical load to a cell array are used to evaluate the relative electrochemical efficiency of the materials comprising the array. The apparatus may include an array of electrochemical cells that are connected to each other in parallel or in series, an electronic load for applying a voltage or current to the electrochemical cells , and a device , external to the cells, for monitoring the relative temperature of each cell when the load is applied.
2009-12-15
A high throughput combinatorial screening method and apparatus for the evaluation of electrochemical materials using a single voltage source (2) is disclosed wherein temperature changes arising from the application of an electrical load to a cell array (1) are used to evaluate the relative electrochemical efficiency of the materials comprising the array. The apparatus may include an array of electrochemical cells (1) that are connected to each other in parallel or in series, an electronic load (2) for applying a voltage or current to the electrochemical cells (1), and a device (3), external to the cells, for monitoring the relative temperature of each cell when the load is applied.
Combinatorial level densities for practical applications
Directory of Open Access Journals (Sweden)
Sin M.
2010-03-01
Full Text Available We review our calculated energy-, spin- and parity-dependent nuclear level densities based on the microscopic combinatorial model described in ref. [1]. We show that this model predicts the experimental sand p-wave neutron resonance spacings with a degree of accuracy comparable to that of the best global models available and also provides reasonable description of low energies cumulative number of levels as well as of the experimental data obtained by the Oslo group [2]. We also provide a renormalization recipe which enables to play with the tabulated results for practical applications. Finally, we study the impact of temperature dependent calculation on s-wave neutron resonance spacings.
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
Combinatorial nuclear level-density model
Energy Technology Data Exchange (ETDEWEB)
Moller, Peter [Los Alamos National Laboratory; Aberg, Sven [LUND SWEDEN; Uhrenhoit, Henrik [LUND SWEDEN; Ickhikawa, Takatoshi [RIKEN
2008-01-01
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: neutron separation energy level spacings, data on total level-density functions from the Oslo method and data on parity ratios.
Jang, Min-Kyoung; Kim, Yun-Jeong; Kim, Dae-Hee; Kang, Duk-Hyun; Song, Jae-Kwan
2010-01-01
Background and Objectives Right ventricle (RV) remodeling can determine tricuspid valve (TV) geometry and the severity of functional tricuspid regurgitation (TR). Subjects and Methods In 53 patients with various degrees of functional TR and in sinus rhythm, RV and TV geometries were analyzed using real-time 3-dimensional echocardiography, including tenting angles of 3 leaflets, septal-lateral and antero-posterior tricuspid annulus diameters and inlet RV dimensions, mid-RV septal-lateral dimension, and the distance between annulus and apex. A mid-systole frame when the TV tenting is smallest was selected for the analysis. RV end-diastolic and end-systolic volumes were measured. The severity of functional TR was determined by distal jet area. Results TR distal jet area was mainly determined by septal-lateral annulus diameter (p<0.001) RV inlet dimension (p=0.015), RV end-systolic volume (p=0.010), septal (p=0.019), and anterior leaflet tenting angles (p=0.045) by multiple stepwise linear regression analysis. Leaflet tenting angles were mainly determined by septal-lateral RV inlet dimension. Septal-lateral annulus diameter was determined by septal-lateral RV inlet dimension (p<0.001) and mid RV dimension (p=0.033), whereas antero-posterior annulus diameter was determined by antero-posterior RV inlet dimension (p<0.001). Conclusion Functional TR severity is determined by septal-lateral annulus and RV dilation, and tenting of septal and anterior leaflets. TV leaflet tenting is mainly determined by septal-lateral RV inlet dilation, and tricuspid annulus dilation is closely linked with inlet RV dilation. PMID:20967146
Tong, Wei
2017-04-01
Combinatorial material research offers fast and efficient solutions to identify promising and advanced materials. It has revolutionized the pharmaceutical industry and now is being applied to accelerate the discovery of other new compounds, e.g. superconductors, luminescent materials, catalysts etc. Differing from the traditional trial-and-error process, this approach allows for the synthesis of a large number of compositionally diverse compounds by varying the combinations of the components and adjusting the ratios. It largely reduces the cost of single-sample synthesis/characterization, along with the turnaround time in the material discovery process, therefore, could dramatically change the existing paradigm for discovering and commercializing new materials. This talk outlines the use of combinatorial materials approach in the material discovery in transportation sector. It covers the general introduction to the combinatorial material concept, state of art for its application in energy-related research. At the end, LBNL capabilities in combinatorial materials synthesis and high throughput characterization that are applicable for material discovery research will be highlighted.
Ding, Yuzhe; Li, Jiannan; Xiao, Wenwu; Xiao, Kai; Lee, Joyce; Bhardwaj, Urvashi; Zhu, Zijie; Digiglio, Philip; Yang, Gaomai; Lam, Kit S; Pan, Tingrui
2015-10-20
Since the 1960s, combination chemotherapy has been widely utilized as a standard method to treat cancer. However, because of the potentially enormous number of drug candidates and combinations, conventional identification methods of the effective drug combinations are usually associated with significantly high operational costs, low throughput screening, laborious and time-consuming procedures, and ethical concerns. In this paper, we present a low-cost, high-efficiency microfluidic print-to-screen (P2S) platform, which integrates combinatorial screening with biomolecular printing for high-throughput screening of anticancer drug combinations. This P2S platform provides several distinct advantages and features, including automatic combinatorial printing, high-throughput parallel drug screening, modular disposable cartridge, and biocompatibility, which can potentially speed up the entire discovery cycle of potent drug combinations. Microfluidic impact printing utilizing plug-and-play microfluidic cartridges is experimentally characterized with controllable droplet volume and accurate positioning. Furthermore, the combinatorial print-to-screen assay is demonstrated in a proof-of-concept biological experiment which can identify the positive hits among the entire drug combination library in a parallel and rapid manner. Overall, this microfluidic print-to-screen platform offers a simple, low-cost, high-efficiency solution for high-throughput large-scale combinatorial screening and can be applicable for various emerging applications in drug cocktail discovery.
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....
Self-encoding resin beads of combinatorial library screening
Lei, Du; Zhao, Yuandi; Cheng, Tongsheng; Zeng, Shaoqun; Luo, Qingming
2003-07-01
The latest self-encoding resin bead is a novel technology for solid phase synthesis combinatorial library screening. A new encode-positional deconvolution strategy which was based on that technology been illustrated compared with positional scanning and iterative strategies. The self-encoding resin beads technology provides an efficient method for improving the high-throughput screening of combinatorial library.
Development of Combinatorial Methods for Alloy Design and Optimization
Energy Technology Data Exchange (ETDEWEB)
Pharr, George M.; George, Easo P.; Santella, Michael L
2005-07-01
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
Green, Martin L.; Takeuchi, Ichiro; Hattrick-Simpers, Jason R.
2013-06-01
High throughput (combinatorial) materials science methodology is a relatively new research paradigm that offers the promise of rapid and efficient materials screening, optimization, and discovery. The paradigm started in the pharmaceutical industry but was rapidly adopted to accelerate materials research in a wide variety of areas. High throughput experiments are characterized by synthesis of a "library" sample that contains the materials variation of interest (typically composition), and rapid and localized measurement schemes that result in massive data sets. Because the data are collected at the same time on the same "library" sample, they can be highly uniform with respect to fixed processing parameters. This article critically reviews the literature pertaining to applications of combinatorial materials science for electronic, magnetic, optical, and energy-related materials. It is expected that high throughput methodologies will facilitate commercialization of novel materials for these critically important applications. Despite the overwhelming evidence presented in this paper that high throughput studies can effectively inform commercial practice, in our perception, it remains an underutilized research and development tool. Part of this perception may be due to the inaccessibility of proprietary industrial research and development practices, but clearly the initial cost and availability of high throughput laboratory equipment plays a role. Combinatorial materials science has traditionally been focused on materials discovery, screening, and optimization to combat the extremely high cost and long development times for new materials and their introduction into commerce. Going forward, combinatorial materials science will also be driven by other needs such as materials substitution and experimental verification of materials properties predicted by modeling and simulation, which have recently received much attention with the advent of the Materials Genome
Kabe, Koustubh
2010-01-01
A spin (dependent) system treatment of gravity is adopted akin to the Sen-Ashtekar treatment. Time is reinserted into the space ``fluid'' at the quantum Level. This time - the Lorentzian one- is shown to be a vorticity of a ``fluid particle'' of the space and the effect is integrated over all the fluid particles to incorporate time in quantum gravity. This spacetime is viewed as a fluid of future light cones called the SU(2) dipoles of causality here in the paper.The future light cone structure is soldered internally to the new variables derived in this paper to accomodate a background free physics of quantum strings. The emergence of spacetime is shown to be a first order phase transition and that of separation of gravity from the unified field to be a second order phase transition. For the former case the cosmic time is chosen as the order parameter and for the latter case the angular momentum is chosen as the order parameter. A quantum blackhole thus nucleates at transition temperature which is the Planck ...
Combinatorial Clustering and the Beta Negative Binomial Process.
Broderick, Tamara; Mackey, Lester; Paisley, John; Jordan, Michael I
2015-02-01
We develop a Bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual. We introduce a combinatorial stochastic process known as the negative binomial process ( NBP ) as an infinite-dimensional prior appropriate for such problems. We show that the NBP is conjugate to the beta process, and we characterize the posterior distribution under the beta-negative binomial process ( BNBP) and hierarchical models based on the BNBP (the HBNBP). We study the asymptotic properties of the BNBP and develop a three-parameter extension of the BNBP that exhibits power-law behavior. We derive MCMC algorithms for posterior inference under the HBNBP , and we present experiments using these algorithms in the domains of image segmentation, object recognition, and document analysis.
A combinatorial morphospace for angiosperm pollen
Mander, Luke
2016-04-01
The morphology of angiosperm (flowering plant) pollen is extraordinarily diverse. This diversity results from variations in the morphology of discrete anatomical components. These components include the overall shape of a pollen grain, the stratification of the exine, the number and form of any apertures, the type of dispersal unit, and the nature of any surface ornamentation. Different angiosperm pollen morphotypes reflect different combinations of these discrete components. In this talk, I ask the following question: given the anatomical components of angiosperm pollen that are known to exist in the plant kingdom, how many unique biologically plausible combinations of these components are there? I explore this question from the perspective of enumerative combinatorics using an algorithm I have written in the Python programming language. This algorithm (1) calculates the number of combinations of these components; (2) enumerates those combinations; and (3) graphically displays those combinations. The result is a combinatorial morphospace that reflects an underlying notion that the process of morphogenesis in angiosperm pollen can be thought of as an n choose k counting problem. I compare the morphology of extant and fossil angiosperm pollen grains to this morphospace, and suggest that from a combinatorial point of view angiosperm pollen is not as diverse as it could be, which may be a result of developmental constraints.
Combinatorial design of textured mechanical metamaterials.
Coulais, Corentin; Teomy, Eial; de Reus, Koen; Shokef, Yair; van Hecke, Martin
2016-07-28
The structural complexity of metamaterials is limitless, but, in practice, most designs comprise periodic architectures that lead to materials with spatially homogeneous features. More advanced applications in soft robotics, prosthetics and wearable technology involve spatially textured mechanical functionality, which requires aperiodic architectures. However, a naive implementation of such structural complexity invariably leads to geometrical frustration (whereby local constraints cannot be satisfied everywhere), which prevents coherent operation and impedes functionality. Here we introduce a combinatorial strategy for the design of aperiodic, yet frustration-free, mechanical metamaterials that exhibit spatially textured functionalities. We implement this strategy using cubic building blocks-voxels-that deform anisotropically, a local stacking rule that allows cooperative shape changes by guaranteeing that deformed building blocks fit together as in a three-dimensional jigsaw puzzle, and three-dimensional printing. These aperiodic metamaterials exhibit long-range holographic order, whereby the two-dimensional pixelated surface texture dictates the three-dimensional interior voxel arrangement. They also act as programmable shape-shifters, morphing into spatially complex, but predictable and designable, shapes when uniaxially compressed. Finally, their mechanical response to compression by a textured surface reveals their ability to perform sensing and pattern analysis. Combinatorial design thus opens up a new avenue towards mechanical metamaterials with unusual order and machine-like functionalities.
Combinatorial design of textured mechanical metamaterials
Coulais, Corentin; Teomy, Eial; de Reus, Koen; Shokef, Yair; van Hecke, Martin
2016-07-01
The structural complexity of metamaterials is limitless, but, in practice, most designs comprise periodic architectures that lead to materials with spatially homogeneous features. More advanced applications in soft robotics, prosthetics and wearable technology involve spatially textured mechanical functionality, which requires aperiodic architectures. However, a naive implementation of such structural complexity invariably leads to geometrical frustration (whereby local constraints cannot be satisfied everywhere), which prevents coherent operation and impedes functionality. Here we introduce a combinatorial strategy for the design of aperiodic, yet frustration-free, mechanical metamaterials that exhibit spatially textured functionalities. We implement this strategy using cubic building blocks—voxels—that deform anisotropically, a local stacking rule that allows cooperative shape changes by guaranteeing that deformed building blocks fit together as in a three-dimensional jigsaw puzzle, and three-dimensional printing. These aperiodic metamaterials exhibit long-range holographic order, whereby the two-dimensional pixelated surface texture dictates the three-dimensional interior voxel arrangement. They also act as programmable shape-shifters, morphing into spatially complex, but predictable and designable, shapes when uniaxially compressed. Finally, their mechanical response to compression by a textured surface reveals their ability to perform sensing and pattern analysis. Combinatorial design thus opens up a new avenue towards mechanical metamaterials with unusual order and machine-like functionalities.
Locating Minimal Fault Interaction in Combinatorial Testing
Directory of Open Access Journals (Sweden)
Wei Zheng
2016-01-01
Full Text Available Combinatorial testing (CT technique could significantly reduce testing cost and increase software system quality. By using the test suite generated by CT as input to conduct black-box testing towards a system, we are able to detect interactions that trigger the system’s faults. Given a test case, there may be only part of all its parameters relevant to the defects in system and the interaction constructed by those partial parameters is key factor of triggering fault. If we can locate those parameters accurately, this will facilitate the software diagnosing and testing process. This paper proposes a novel algorithm named complete Fault Interaction Location (comFIL to locate those interactions that cause system’s failures and meanwhile obtains the minimal set of target interactions in test suite produced by CT. By applying this method, testers can analyze and locate the factors relevant to defects of system more precisely, thus making the process of software testing and debugging easier and more efficient. The results of our empirical study indicate that comFIL performs better compared with known fault location techniques in combinatorial testing because of its improved effectiveness and precision.
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.
Rasmussen, N. G.; Simeoni, G. G.; Lefmann, K.
2016-04-01
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 (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.
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.
Combinatorics, geometry, and mathematical physics
Energy Technology Data Exchange (ETDEWEB)
Chen, W.Y.C.; Louck, J.D.
1998-11-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Combinatorics and geometry have been among the most active areas of mathematics over the past few years because of newly discovered inter-relations between them and their potential for applications. In this project, the authors set out to identify problems in physics, chemistry, and biology where these methods could impact significantly. In particular, the experience suggested that the areas of unitary symmetry and discrete dynamical systems could be brought more strongly under the purview of combinatorial methods. Unitary symmetry deals with the detailed description of the quantum mechanics of many-particle systems, and discrete dynamical systems with chaotic systems. The depth and complexity of the mathematics in these physical areas of research suggested that not only could significant advances be made in these areas, but also that here would be a fertile feedback of concept and structure to enrich combinatorics itself by setting new directions. During the three years of this project, the goals have been realized beyond expectation, and in this report the authors set forth these advancements and justify their optimism.
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.
Energy Technology Data Exchange (ETDEWEB)
Itoh, Yoshiaki [Institute of Statistical Mathematics and the Graduate University for Advanced Studies, 4-6-7 Minami-Azabu Minatoku, Tokyo 106-8569 (Japan)], E-mail: itoh@ism.ac.jp
2009-01-16
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
Adler, Irving
1967-01-01
This richly detailed overview surveys the development and evolution of geometrical ideas and concepts from ancient times to the present. In addition to the relationship between physical and mathematical spaces, it examines the interactions of geometry, algebra, and calculus. The text proves many significant theorems and employs several important techniques. Chapters on non- Euclidean geometry and projective geometry form brief, self-contained treatments.More than 100 exercises with answers and 200 diagrams illuminate the text. Teachers, students (particularly those majoring in mathematics educa
Bär, Christian; Schwarz, Matthias
2012-01-01
This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.
Cukier, Mimi; Asdourian, Tony; Thakker, Anand
2012-01-01
Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…
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, ...
DEFF Research Database (Denmark)
Denton, Paul W.; Søgaard, Ole Schmeltz; Tolstrup, Martin
2016-01-01
regard the anatomical locations and cell subsets that harbor persistent HIV. Combinatorial research challenges pertain to the order of administration, timing of administration and specific combinations of compounds to be administered during HIV eradication therapy. Overcoming these challenges...... 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....
Juan, Angel A.; Javier Faulin; Scott E. Grasman; Markus Rabe; Gonçalo Figueira
2015-01-01
Many combinatorial optimization problems (COPs) encountered in real-world logistics, transportation, production, healthcare, financial, telecommunication, and computing applications are NP-hard in nature. These real-life COPs are frequently characterized by their large-scale sizes and the need for obtaining high-quality solutions in short computing times, thus requiring the use of metaheuristic algorithms. Metaheuristics benefit from different random-search and parallelization paradigms, but ...
Wood, M.; Neal, J. C.; Hostache, R.; Corato, G.; Bates, P. D.; Chini, M.; Giustarini, L.; Matgen, P.; Wagener, T.
2014-12-01
The objective of this work is to calibrate channel depth and roughness parameters of the LISFLOOD-FP Sub-Grid 2D hydraulic model using SAR image-derived flood extent maps. The aim is to reduce uncertainty in flood model predictions for those rivers where channel geometry is unknown and/or cannot be easily measured. In particular we consider the effectiveness of using real SAR data for calibration and whether the number and timings of SAR acquisitions is of benefit to the final result. Terrain data are processed from 2m LiDAR images and inflows to the model are taken from gauged data. As a test case we applied the method to the River Severn between Worcester and Tewkesbury. We firstly applied the automatic flood mapping algorithm of Giustarini[1] et al. (2013) to ENVISAT ASAR (wide swath mode) flood images; generating a series of flood maps. We then created an ensemble of flood extent maps with the hydraulic model (each model representing a unique parameter set). Where there is a favourable comparison between the modelled flood map and the SAR obtained flood map we may suggest an optimal parameter set. Applying the method to a sequence of SAR acquisitions provides insight into the advantages, disadvantages and limitations of using series of acquired images. To complete the investigation we simultaneously explore parameter 'identifiabilty' within a sequence of available satellite observations by adopting the DYNIA method proposed by Wagener[2] et al. (2003). We show where we might most easily detect the depth and roughness parameters within the SAR acquisition sequence. [1] Giustarini. 2013. 'A Change Detection Approach to Flood Mapping in Urban Areas Using TerraSAR-X'. IEEE Transactions on Geoscience and Remote Sensing, vol. 51, no. 4. [2] Wagener. 2003. 'Towards reduced uncertainty in conceptual rainfall-runoff modelling: Dynamic identifiability analysis'. Hydrol. Process. 17, 455-476.
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.
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...
Combinatorial polynomials as moments, Hankel transforms and exponential Riordan arrays
Barry, Paul
2011-01-01
In the case of two combinatorial polynomials, we show that they can exhibited as moments of paramaterized families of orthogonal polynomials, and hence derive their Hankel transforms. Exponential Riordan arrays are the main vehicles used for this.
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...
Advanced Aqueous Phase Catalyst Development using Combinatorial Methods Project
National Aeronautics and Space Administration — The use of combinatorial methods is proposed to rapidly screen catalyst formulations for the advanced development of aqueous phase oxidation catalysts with greater...
New opioid peptides, peptidomimetics, and heterocyclic compounds from combinatorial libraries.
Dooley, C T; Houghten, R A
1999-01-01
Here we review the use of combinatorial libraries in opioid receptor assays. Following a brief description of the history of the combinatorial field, methods for the generation of synthetic libraries and the deconvolution of mixture-based libraries are presented. Case studies involving opioid assays used to demonstrate the viability of combinatorial libraries are described. The identification of new opioid peptides from combinatorial libraries is reviewed. The peptides found are composed of L-amino acids, D-amino acids, or L-, D-, and unnatural amino acids, and range from tetrapeptides to decapeptides. Likewise, new opioid compounds identified from peptidomimetic libraries, such as peptoids and alkylated dipeptides, and those identified from acyclic (e.g., polyamine, urea) and heterocyclic (e.g., bicyclic guanidine) libraries, are reviewed.
Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory
Tanasa, Adrian
2010-01-01
We briefly review the r\\^ole played by algebraic structures like combinatorial Hopf algebras in the renormalizability of (noncommutative) quantum field theory. After sketching the commutative case, we analyze the noncommutative Grosse-Wulkenhaar model.
Combinatorial and high-throughput screening approaches for strain engineering.
Liu, Wenshan; Jiang, Rongrong
2015-03-01
Microbes have long been used in the industry to produce valuable biochemicals. Combinatorial engineering approaches, new strain engineering tools derived from inverse metabolic engineering, have started to attract attention in recent years, including genome shuffling, error-prone DNA polymerase, global transcription machinery engineering (gTME), random knockout/overexpression libraries, ribosome engineering, multiplex automated genome engineering (MAGE), customized optimization of metabolic pathways by combinatorial transcriptional engineering (COMPACTER), and library construction of "tunable intergenic regions" (TIGR). Since combinatorial approaches and high-throughput screening methods are fundamentally interconnected, color/fluorescence-based, growth-based, and biosensor-based high-throughput screening methods have been reviewed. We believe that with the help of metabolic engineering tools and new combinatorial approaches, plus effective high-throughput screening methods, researchers will be able to achieve better results on improving microorganism performance under stress or enhancing biochemical yield.
Reinvigorating natural product combinatorial biosynthesis with synthetic biology.
Kim, Eunji; Moore, Bradley S; Yoon, Yeo Joon
2015-09-01
Natural products continue to play a pivotal role in drug-discovery efforts and in the understanding if human health. The ability to extend nature's chemistry through combinatorial biosynthesis--altering functional groups, regiochemistry and scaffold backbones through the manipulation of biosynthetic enzymes--offers unique opportunities to create natural product analogs. Incorporating emerging synthetic biology techniques has the potential to further accelerate the refinement of combinatorial biosynthesis as a robust platform for the diversification of natural chemical drug leads. Two decades after the field originated, we discuss the current limitations, the realities and the state of the art of combinatorial biosynthesis, including the engineering of substrate specificity of biosynthetic enzymes and the development of heterologous expression systems for biosynthetic pathways. We also propose a new perspective for the combinatorial biosynthesis of natural products that could reinvigorate drug discovery by using synthetic biology in combination with synthetic chemistry.
Dynamic Combinatorial Libraries of Disulfide Cages in Water
West, Kevin R.; Bake, Kyle D.; Otto, Sijbren
2005-01-01
Dynamic combinatorial libraries (DCLs) containing water-soluble disulfide-linked cages (alongside macrocyclic structures) have been generated and characterized. Unlike most other strategies for generating molecular cages, the structures are held together by covalent bonds, which are formed under
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.
Mahé, Louis; Roy, Marie-Françoise
1992-01-01
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...
Variational Splines and Paley--Wiener Spaces on Combinatorial Graphs
Pesenson, Isaac
2011-01-01
Notions of interpolating variational splines and Paley-Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator onG. The existence and uniqueness of interpolating variational splines on a graph is shown. As an application of variational splines, the paper presents a reconstruction algorithm of Paley-Wiener functions on graphs from their uniqueness sets.
Variational Splines and Paley--Wiener Spaces on Combinatorial Graphs
Pesenson, Isaac
2011-01-01
Notions of interpolating variational splines and Paley-Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator onG. The existence and uniqueness of interpolating variational splines on a graph is shown. As an application of variational splines, the paper presents a reconstruction algorithm of Paley-Wiener functions on graphs from their uniqueness sets.
TARCMO: Theory and Algorithms for Robust, Combinatorial, Multicriteria Optimization
2016-11-28
magnitude in computational experiments on portfolio optimization problems. The research on this topic has been published as [CG15a], where details can...AFRL-AFOSR-UK-TR-2017-0001 TARCMO: Theory and Algorithms for Robust, Combinatorial, Multicriteria Optimization Horst Hamacher Technische Universität...To) 15 May 2013 to 12 May 2016 4. TITLE AND SUBTITLE TARCMO: Theory and Algorithms for Robust, Combinatorial, Multicriteria Optimization 5a. CONTRACT
Sampling, Filtering and Sparse Approximations on Combinatorial Graphs
Pesenson, Isaac Z
2011-01-01
In this paper we address sampling and approximation of functions on combinatorial graphs. We develop filtering on graphs by using Schr\\"odinger's group of operators generated by combinatorial Laplace operator. Then we construct a sampling theory by proving Poincare and Plancherel-Polya-type inequalities for functions on graphs. These results lead to a theory of sparse approximations on graphs and have potential applications to filtering, denoising, data dimension reduction, image processing, image compression, computer graphics, visualization and learning theory.
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.
Combinatorial Dyson-Schwinger equations and inductive data types
Kock, Joachim
2015-01-01
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 co...
The application of combinatorial approach to the optimization of dielectric/ferroelectric materials
Chang, Hauyee
Combinatorial approaches are methods developed to facilitate the rapid discovery and optimization of materials by the simultaneous synthesis and screening of a large number of compounds within a short period of time. This work describes its application to dielectric and ferroelectric thin film materials, in particular, (Ba,SrCa)TiO3. New methods and instruments for thin film fabrication and measurement are developed to handle the synthesis and analysis of up to thousands of samples simultaneously. Thin films are fabricated with a novel multilayer precursor method. Precursors of the various elemental components within the target compound, such as BaF 2 and TiO2 for BaTiO3, are deposited at room temperature as separate layers. These multilayers are thermally processed under a two step procedure. A low temperature treatment over a period of days interdiffuses the layers to form a homogeneous amorphous intermediate. This is followed by a high temperature crystallization step, which forms the final crystalline product. Effects of dopants on the dielectric constant and loss of (BaSr)TiO 3 are studied with the discrete combinatorial approach, where up to thousands of discrete thin film samples are fabricated on an individual single crystal substrate. A continuous combinatorial sample resembling a ternary phase diagram of (Ba,Sr,Ca)TiO3 is also fabricated in search of the lowest loss compositions that are useful for various applications such as the storage node capacitors in dynamic random access memories. These combinatorial samples of (BaSr,Ca)TiO3 are measured with the newly developed scanning evanescent microwave microscope (SEMM). This instrument is capable of rapid and accurate non-contact characterization of the thin film dielectric constants and losses. The measured results show good agreement with results from more conventional methods such as the interdigital electrodes measurements. Various issues concerning the combinatorial approach in materials science are
Instability of supersymmetric microstate geometries
Eperon, Felicity C; Santos, Jorge E
2016-01-01
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
Molecular motion in restricted geometries
Indian Academy of Sciences (India)
Siddharth Gautam; S Mitra; R Mukhopadhyay
2008-10-01
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 scales involved in the motion and the geometry of motion can be studied using QENS. Molecular dynamics (MD) simulation not only provides insight into the details of the different types of motion possible but also does not suffer limitations of the experimental set-up. Here we report the effect of confinement on molecular dynamics in various restricted geometries as studied by QENS and MD simulations: An example where the QENS technique provided direct evidence of phase transition associated with change in the dynamical behaviour of the molecules is also discussed.
Instability of supersymmetric microstate geometries
Energy Technology Data Exchange (ETDEWEB)
Eperon, Felicity C.; Reall, Harvey S.; Santos, Jorge E. [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2016-10-07
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an “evanescent ergosurface”: a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
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.
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.
Digital Differential Geometry Processing
Institute of Scientific and Technical Information of China (English)
Xin-Guo Liu; Hu-Jun Bao; Qun-Sheng Peng
2006-01-01
The theory and methods of digital geometry processing has been a hot research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient,Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.
A Combinatorial Geometry Computer Description of the M578 Light Recovery Vehicle
1984-05-01
41.5647 RIGHT 51.9534 0.0000 23.BIO1 0.0000 34.2901 0.0000 FIST TABLE 4-1. M*7« LIGHT "> ECOV £«>Y VEHICLE SOLID TABLE (CONTINUED) a* o...5 -A06 w« 7 -877 -878 -879 HEAD LOWER 872 872 -8T -876 -8P8 0 0 0 0 0 NECK TABLE A-2. M578 LI GHT » ECOV ftRY 7CH TCLE REGTT IN TABLE
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.
Interactions between Digital Geometry and Combinatorics on Words
Brlek, Srečko
2011-01-01
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.
Combinatorial Problems of Applied Discrete Mathematics.
1979-12-01
Attenuated Spaces, Utilitas Mathematica, 15(1979) , 3—29. 6. Characterization of Projective Incidence Structures, Geometria Dedicata, 5 (1976), 361—376. 7...Pj rtia l geometries, generalized quadrang les and strong/v regular graf t/ us , • Att i dcl Convegno di Geometria Combinatoria e sue app
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...
Institute of Scientific and Technical Information of China (English)
GUO Enli; MO Xiaohuan
2006-01-01
In this paper,a survey on Riemann-Finsler geometry is given.Non-trivial examples of Finsler metrics satisfying different curvature conditions are presented.Local and global results in Finsler geometry are analyzed.
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
Combinatorial Approximation Algorithms for MaxCut using Random Walks
Kale, Satyen
2010-01-01
We give the first combinatorial approximation algorithm for Maxcut that beats the trivial 0.5 factor by a constant. The main partitioning procedure is very intuitive, natural, and easily described. It essentially performs a number of random walks and aggregates the information to provide the partition. We can control the running time to get an approximation factor-running time tradeoff. We show that for any constant b > 1.5, there is an O(n^{b}) algorithm that outputs a (0.5+delta)-approximation for Maxcut, where delta = delta(b) is some positive constant. One of the components of our algorithm is a weak local graph partitioning procedure that may be of independent interest. Given a starting vertex $i$ and a conductance parameter phi, unless a random walk of length ell = O(log n) starting from i mixes rapidly (in terms of phi and ell), we can find a cut of conductance at most phi close to the vertex. The work done per vertex found in the cut is sublinear in n.
Conventionalism and integrable Weyl geometry
Pucheu, M. L.
2015-03-01
Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.
Combinatorial investigation of rare-earth free permanent magnets
Fackler, Sean Wu
The combinatorial high throughput method allows one to rapidly study a large number of samples with systematically changing parameters. We apply this method to study Fe-Co-V alloys as alternatives to rare-earth permanent magnets. Rare-earth permanent magnets derive their unmatched magnetic properties from the hybridization of Fe and Co with the f-orbitals of rare-earth elements, which have strong spin-orbit coupling. It is predicted that Fe and Co may also have strong hybridization with 4d and 5d refractory transition metals with strong spin-orbit coupling. Refractory transition metals like V also have the desirable property of high temperature stability, which is important for permanent magnet applications in traction motors. In this work, we focus on the role of crystal structure, composition, and secondary phases in the origin of competitive permanent magnetic properties of a particular Fe-Co-V alloy. Fe38Co52V10, compositions are known as Vicalloys. Fe-CoV composition spreads were sputtered onto three-inch silicon wafers and patterned into discrete sample pads forming a combinatorial library. We employed highthroughput screening methods using synchrotron X-rays, wavelength dispersive spectroscopy, and magneto-optical Kerr effect (MOKE) to rapidly screen crystal structure, composition, and magnetic properties, respectively. We found that in-plane magnetic coercive fields of our Vicalloy thin films agree with known bulk values (300 G), but found a remarkable eight times increase of the out-of-plane coercive fields (˜2,500 G). To explain this, we measured the switching fields between in-plane and out-of-plane thin film directions which revealed that the Kondorsky model of 180° domain wall reversal was responsible for Vicalloy's enhanced out-of-plane coercive field and possibly its permanent magnetic properties. The Kondorsky model suggests that domain-wall pinning is the origin of Vicalloy's permanent magnetic properties, in contrast to strain, shape, or
Covariant Macroscopic Quantum Geometry
Hogan, Craig J
2012-01-01
A covariant noncommutative algebra of position operators is presented, and interpreted as the macroscopic limit of a geometry that describes a collective quantum behavior of the positions of massive bodies in a flat emergent space-time. The commutator defines a quantum-geometrical relationship between world lines that depends on their separation and relative velocity, but on no other property of the bodies, and leads to a transverse uncertainty of the geometrical wave function that increases with separation. The number of geometrical degrees of freedom in a space-time volume scales holographically, as the surface area in Planck units. Ongoing branching of the wave function causes fluctuations in transverse position, shared coherently among bodies with similar trajectories. The theory can be tested using appropriately configured Michelson interferometers.
Neural blackboard architectures of combinatorial structures in cognition.
van der Velde, Frank; de Kamps, Marc
2006-02-01
Human cognition is unique in the way in which it relies on combinatorial (or compositional) structures. Language provides ample evidence for the existence of combinatorial structures, but they can also be found in visual cognition. To understand the neural basis of human cognition, it is therefore essential to understand how combinatorial structures can be instantiated in neural terms. In his recent book on the foundations of language, Jackendoff described four fundamental problems for a neural instantiation of combinatorial structures: the massiveness of the binding problem, the problem of 2, the problem of variables, and the transformation of combinatorial structures from working memory to long-term memory. This paper aims to show that these problems can be solved by means of neural "blackboard" architectures. For this purpose, a neural blackboard architecture for sentence structure is presented. In this architecture, neural structures that encode for words are temporarily bound in a manner that preserves the structure of the sentence. It is shown that the architecture solves the four problems presented by Jackendoff. The ability of the architecture to instantiate sentence structures is illustrated with examples of sentence complexity observed in human language performance. Similarities exist between the architecture for sentence structure and blackboard architectures for combinatorial structures in visual cognition, derived from the structure of the visual cortex. These architectures are briefly discussed, together with an example of a combinatorial structure in which the blackboard architectures for language and vision are combined. In this way, the architecture for language is grounded in perception. Perspectives and potential developments of the architectures are discussed.
Geometry, topology, and string theory
Energy Technology Data Exchange (ETDEWEB)
Varadarajan, Uday
2003-07-10
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 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
Introduction to projective geometry
Wylie, C R
2008-01-01
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include w
Affine and Projective Geometry
Bennett, M K
1995-01-01
An important new perspective on AFFINE AND PROJECTIVE GEOMETRY. This innovative book treats math majors and math education students to a fresh look at affine and projective geometry from algebraic, synthetic, and lattice theoretic points of view. Affine and Projective Geometry comes complete with ninety illustrations, and numerous examples and exercises, covering material for two semesters of upper-level undergraduate mathematics. The first part of the book deals with the correlation between synthetic geometry and linear algebra. In the second part, geometry is used to introduce lattice theory
Symplectic geometries on supermanifolds
Lavrov, P M
2007-01-01
Extension of symplectic geometry on manifolds to the supersymmetric case is considered. In the even case it leads to the even symplectic geometry (or, equivalently, to the geometry on supermanifolds endowed with an non-degenerate Poisson bracket) or to the geometry on an even Fedosov supermanifolds. It is proven that in the odd case there are two different scalar symplectic structures (namely, an odd closed differential 2-form and the antibracket) which can be used for construction of different symplectic geometries on supermanifolds.
Mapping the Materials Genome through Combinatorial Informatics
Rajan, Krishna
2012-02-01
The recently announced White House Materials Genome Initiative provides an exciting challenge to the materials science community. To meet that challenge one needs to address a critical question, namely what is the materials genome? Some guide on how to the answer this question can be gained by recognizing that a ``gene'' is a carrier of information. In the biological sciences, discovering how to manipulate these genes has generated exciting discoveries in fundamental molecular biology as well as significant advances in biotechnology. Scaling that up to molecular, cellular length scales and beyond, has spawned from genomics, fields such as proteomics, metabolomics and essentially systems biology. The ``omics'' approach requires that one needs to discover and track these ``carriers of information'' and then correlate that information to predict behavior. A similar challenge lies in materials science, where there is a diverse array of modalities of materials ``discovery'' ranging from new materials chemistries and molecular arrangements with novel properties, to the development and design of new micro- and mesoscale structures. Hence to meaningfully adapt the spirit of ``genomics'' style research in materials science, we need to first identify and map the ``genes'' across different materials science applications On the experimental side, combinatorial experiments have opened a new approach to generate data in a high throughput manner, but without a clear way to link that to models, the full value of that data is not realized. Hence along with experimental and computational materials science, we need to add a ``third leg'' to our toolkit to make the ``Materials Genome'' a reality, the science of Materials Informatics. In this presentation we provide an overview of how information science coupled to materials science can in fact achieve the goal of mapping the ``Materials Genome''.
Data-Driven Online and Real-Time Combinatorial Optimization
2013-10-30
Problem , the online Traveling Salesman Problem , and variations of the online Quota Hamil- tonian Path Problem and the online Traveling ...has the lowest competitive ratio among all algorithms of this kind. Second, we consider the Online Traveling Salesman Problem , and consider randomized...matroid secretary problem on a partition matroid. 6. Jaillet, P. and X. Lu. “Online Traveling Salesman Problems with Rejection Options”, submitted
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...... be demonstrated. The resulting library of model compounds was verified by LC-MS analysis. (C) 1997 Elsevier Science Ltd....
Gualtieri, Marco
2010-01-01
Generalized Kahler geometry is the natural analogue of Kahler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible with a metric so that it defines a second generalized complex structure. We explore the fundamental aspects of this geometry, including its equivalence with the bi-Hermitian geometry on the target of a 2-dimensional sigma model with (2,2) supersymmetry, as well as the relation to holomorphic Dirac geometry and the resulting derived deformation theory. We also explore the analogy between pre-quantum line bundles and gerbes in the context of generalized Kahler geometry.
Methods for euclidean geometry
Byer, Owen; Smeltzer, Deirdre L
2010-01-01
Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.
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.
Combinatorial Mutagenesis and Selection to Understand and Improve Yeast Promoters
Directory of Open Access Journals (Sweden)
Laila Berg
2013-01-01
Full Text Available Microbial promoters are important targets both for understanding the global gene expression and developing genetic tools for heterologous expression of proteins and complex biosynthetic pathways. Previously, we have developed and used combinatorial mutagenesis methods to analyse and improve bacterial expression systems. Here, we present for the first time an analogous strategy for yeast. Our model promoter is the strong and inducible promoter in methylotrophic Pichia pastoris. The Zeocin resistance gene was applied as a valuable reporter for mutant promoter activity, and we used an episomal plasmid vector to ensure a constant reporter gene dosage in the yeast host cells. This novel design enabled direct selection for colonies of recombinant cells with altered Zeocin tolerance levels originating solely from randomly introduced point mutations in the promoter DNA sequence. We demonstrate that this approach can be used to select for promoter variants with abolished glucose repression in large mutant libraries. We also selected promoter variants with elevated expression level under induced conditions. The properties of the selected promoter variants were confirmed by expressing luciferase as an alternative reporter gene. The tools developed here should be useful for effective screening, characterization, and improvement of any yeast promoters.
Combinatorial effects on clumped isotopes and their significance in biogeochemistry
Yeung, Laurence Y.
2016-01-01
The arrangement of isotopes within a collection of molecules records their physical and chemical histories. Clumped-isotope analysis interrogates these arrangements, i.e., how often rare isotopes are bound together, which in many cases can be explained by equilibrium and/or kinetic isotope fractionation. However, purely combinatorial effects, rooted in the statistics of pairing atoms in a closed system, are also relevant, and not well understood. Here, I show that combinatorial isotope effects are most important when two identical atoms are neighbors on the same molecule (e.g., O2, N2, and D-D clumping in CH4). When the two halves of an atom pair are either assembled with different isotopic preferences or drawn from different reservoirs, combinatorial effects cause depletions in clumped-isotope abundance that are most likely between zero and -1‰, although they could potentially be -10‰ or larger for D-D pairs. These depletions are of similar magnitude, but of opposite sign, to low-temperature equilibrium clumped-isotope effects for many small molecules. Enzymatic isotope-pairing reactions, which can have site-specific isotopic fractionation factors and atom reservoirs, should express this class of combinatorial isotope effect, although it is not limited to biological reactions. Chemical-kinetic isotope effects, which are related to a bond-forming transition state, arise independently and express second-order combinatorial effects related to the abundance of the rare isotope. Heteronuclear moeties (e.g., Csbnd O and Csbnd H), are insensitive to direct combinatorial influences, but secondary combinatorial influences are evident. In general, both combinatorial and chemical-kinetic factors are important for calculating and interpreting clumped-isotope signatures of kinetically controlled reactions. I apply this analytical framework to isotope-pairing reactions relevant to geochemical oxygen, carbon, and nitrogen cycling that may be influenced by combinatorial
Invention as a combinatorial process: evidence from US patents.
Youn, Hyejin; Strumsky, Deborah; Bettencourt, Luis M A; Lobo, José
2015-05-06
Invention has been commonly conceptualized as a search over a space of combinatorial possibilities. Despite the existence of a rich literature, spanning a variety of disciplines, elaborating on the recombinant nature of invention, we lack a formal and quantitative characterization of the combinatorial process underpinning inventive activity. Here, we use US patent records dating from 1790 to 2010 to formally characterize invention as a combinatorial process. To do this, we treat patented inventions as carriers of technologies and avail ourselves of the elaborate system of technology codes used by the United States Patent and Trademark Office to classify the technologies responsible for an invention's novelty. We find that the combinatorial inventive process exhibits an invariant rate of 'exploitation' (refinements of existing combinations of technologies) and 'exploration' (the development of new technological combinations). This combinatorial dynamic contrasts sharply with the creation of new technological capabilities-the building blocks to be combined-that has significantly slowed down. We also find that, notwithstanding the very reduced rate at which new technologies are introduced, the generation of novel technological combinations engenders a practically infinite space of technological configurations.
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.
Dynamic Combinatorial Chemistry with Diselenides, Disulfides, Imines and Metal Coordination
DEFF Research Database (Denmark)
Sørensen, Anne
The design and preparation of strong and selective artificial receptors, especially biomi-metic receptors that function in aqueous solution, has proved truly challenging. In this thesis it will be described how the strengths of dynamic combinatorial chemistry can be used to great advantage...... in this field. The aim of this project has therefore been to develop new ways of using dynamic combinatorial libraries for molecular recognition in aqueous media. The focus has been on using what has been learned from the well-established di-sulfide exchange chemistry to incorporate a new reaction into dynamic...... 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...
Combinatorial Evolution and Forecasting of Communication Protocol ZigBee
Levin, Mark Sh; Kistler, Rolf; Klapproth, Alexander
2012-01-01
The article addresses combinatorial evolution and forecasting of communication protocol for wireless sensor networks (ZigBee). Morphological tree structure (a version of and-or tree) is used as a hierarchical model for the protocol. Three generations of ZigBee protocol are examined. A set of protocol change operations is generated and described. The change operations are used as items for forecasting based on combinatorial problems (e.g., clustering, knapsack problem, multiple choice knapsack problem). Two kinds of preliminary forecasts for the examined communication protocol are considered: (i) direct expert (expert judgment) based forecast, (ii) computation of the forecast(s) (usage of multicriteria decision making and combinatorial optimization problems). Finally, aggregation of the obtained preliminary forecasts is considered (two aggregation strategies are used).
Combinatorial Constructions for Sifting Primes and Enumerating the Rationals
Gnang, Edinah K
2012-01-01
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that such mappings achieve much more than enumeration of rooted trees. We discuss two related structural bijections. The first corresponds to a bijective map between integers and rooted trees. The first bijection also suggests a new algorithm for sifting primes. The second bijection extends the first one in order to map rational numbers to a family of rooted trees. The second bijection suggests a new combinatorial construction for generating reduced rational numbers, thereby producing refinements of the output of the Wilf-Calkin[1] Algorithm.
Combinatorial Selection and Least Absolute Shrinkage via the CLASH Algorithm
Kyrillidis, Anastasios
2012-01-01
The least absolute shrinkage and selection operator (LASSO) for linear regression exploits the geometric interplay of the $\\ell_2$-data error objective and the $\\ell_1$-norm constraint to arbitrarily select sparse models. Guiding this uninformed selection process with sparsity models has been precisely the center of attention over the last decade in order to improve learning performance. To this end, we alter the selection process of LASSO to explicitly leverage combinatorial sparsity models (CSMs) via the combinatorial selection and least absolute shrinkage (CLASH) operator. We provide concrete guidelines how to leverage combinatorial constraints within CLASH, and characterize CLASH's guarantees as a function of the set restricted isometry constants of the sensing matrix. Finally, our experimental results show that CLASH can outperform both LASSO and model-based compressive sensing in sparse estimation.
Key Updating Methods for Combinatorial Design Based Key Management Schemes
Directory of Open Access Journals (Sweden)
Chonghuan Xu
2014-01-01
Full Text Available Wireless sensor network (WSN has become one of the most promising network technologies for many useful applications. However, for the lack of resources, it is different but important to ensure the security of the WSNs. Key management is a corner stone on which to build secure WSNs for it has a fundamental role in confidentiality, authentication, and so on. Combinatorial design theory has been used to generate good-designed key rings for each sensor node in WSNs. A large number of combinatorial design based key management schemes have been proposed but none of them have taken key updating into consideration. In this paper, we point out the essence of key updating for the unital design based key management scheme and propose two key updating methods; then, we conduct performance analysis on the two methods from three aspects; at last, we generalize the two methods to other combinatorial design based key management schemes and enhance the second method.
Combinatorial realizations of crystals via torus actions on quiver varieties
Sam, Steven V
2012-01-01
Consider Kashiwara's crystal associated to a highest weight representation of a symmetric Kac--Moody algebra. There is a geometric realization of this object using Nakajima's quiver varieties. In many particular cases it can also be realized by elementary combinatorial methods. Here we propose a framework for extracting combinatorial realizations from the geometric picture: we construct certain torus actions on the quiver varieties and use Morse theory to index the irreducible components by connected components of the subvariety of torus fixed points. We then discuss the case of affine sl(n). There the fixed point components are just points, and are naturally indexed by multi-partitions. There is some choice in our construction, leading to a family of combinatorial realizations for each highest weight crystal. In the case of the crystal of the fundamental representation we recover a family of realizations which was recently constructed by Fayers. This gives a more conceptual proof of Fayers' result as well as...
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.
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
General Construction of Tubular Geometry
Mukhopadhyay, Partha
2016-01-01
We consider the problem of locally describing tubular geometry around a submanifold embedded in a (pseudo)Riemannian manifold in its general form. Given the geometry of ambient space in an arbitrary coordinate system and equations determining the submanifold in the same system, we compute the tubular expansion coefficients in terms of this {\\it a priori data}. This is done by using an indirect method that crucially applies the tubular expansion theorem for vielbein previously derived. With an explicit construction involving the relevant coordinate and non-coordinate frames we verify consistency of the whole method up to quadratic order in vielbein expansion. Furthermore, we perform certain (long and tedious) higher order computation which verifies the first non-trivial spin connection term in the expansion for the first time. Earlier a similar method was used to compute tubular geometry in loop space. We explain this work in the light of our general construction.
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.
Improving Combinatorial Ambiguities of ttbar Events Using Neural Networks
Shim, Ji Hyun
2014-01-01
We present a method for resolving the combinatorial issues in the \\ttbar lepton+jets events occurring at the Tevatron collider. By incorporating multiple information into an artificial neural network, we introduce a novel event reconstruction method for such events. We find that this method significantly reduces the number of combinatorial ambiguities. Compared to the classical reconstruction method, our method provides significantly higher purity with same efficiency. We illustrate the reconstructed observables for the realistic top-quark mass and the forward-backward asymmetry measurements. A Monte Carlo study shows that our method provides meaningful improvements in the top-quark measurements using same amount of data as other methods.
Revisiting Combinatorial Ambiguities at Hadron Colliders with MT2
Baringer, Philip; McCaskey, Mathew; Noonan, Daniel
2011-01-01
We present a method to resolve combinatorial issues in multi-particle final states at hadron colliders. The use of kinematic variables such as MT2 and invariant mass significantly reduces combinatorial ambiguities in the signal, but at a cost of losing statistics. We illustrate this idea with gluino pair production leading to 4 jets $+\\met$ in the final state as well as $t\\bar{t}$ production in the dilepton channel. Compared to results in recent studies, our method provides greater efficiency with similar purity
Combinatorial theory of Macdonald polynomials I: Proof of Haglund's formula
Haglund, J.; Haiman, M.; Loehr, N
2005-01-01
Haglund recently proposed a combinatorial interpretation of the modified Macdonald polynomials H̃μ. We give a combinatorial proof of this conjecture, which establishes the existence and integrality of H̃μ. As corollaries, we obtain the cocharge formula of Lascoux and Schützenberger for Hall–Littlewood polynomials, a formula of Sahi and Knop for Jack's symmetric functions, a generalization of this result to the integral Macdonald polynomials Jμ, a formula for H̃μ in terms of Lascoux–Leclerc–Th...
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
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.
Euclidean geometry and transformations
Dodge, Clayton W
1972-01-01
This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
Introduction to finite geometries
Kárteszi, F
1976-01-01
North-Holland Texts in Advanced Mathematics: Introduction to Finite Geometries focuses on the advancements in finite geometries, including mapping and combinatorics. The manuscript first offers information on the basic concepts on finite geometries and Galois geometries. Discussions focus on linear mapping of a given quadrangle onto another given quadrangle; point configurations of order 2 on a Galois plane of even order; canonical equation of curves of the second order on the Galois planes of even order; and set of collineations mapping a Galois plane onto itself. The text then ponders on geo
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.
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...
A Relationship between Geometry and Algebra
Bejarano, Jose Ricardo Arteaga
2011-01-01
The three key documents for study geometry are: 1) "The Elements" of Euclid, 2) the lecture by B. Riemann at G\\"ottingen in 1854 entitled "\\"Uber die Hypothesen welche der Geometrie zu Grunde liegen" (On the hypotheses which underlie geometry) and 3) the "Erlangen Program", a document written by F. Klein (1872) on his income as professor at the Faculty of Philosophy and the Senate of the Erlangen University. The latter document F. Klein introduces the concept of group as a tool to study geometry. The concept of a group of transformations of space was known at the time. The purpose of this informative paper is to show a relationship between geometry and algebra through an example, the projective plane. Erlangen program until today continues being a guideline of how to study geometry.
Euclidean Geometry via Programming.
Filimonov, Rossen; Kreith, Kurt
1992-01-01
Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability and compares it to…
Supersymmetric Sigma Model Geometry
Ulf Lindström
2012-01-01
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.
Supersymmetric Sigma Model geometry
Lindström, Ulf
2012-01-01
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.
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.
Bergshoeff, Eric A.; Riccioni, Fabio; Alvarez-Gaumé, L.
2011-01-01
We probe doubled geometry with dual fundamental branes. i.e. solitons. Restricting ourselves first to solitonic branes with more than two transverse directions we find that the doubled geometry requires an effective wrapping rule for the solitonic branes which is dual to the wrapping rule for fundam
Leading log expansion of combinatorial Dyson Schwinger equations
Delage, Lucas
2016-01-01
We study combinatorial Dyson Schwinger equations, expressed in the Hopf algebra of words with a quasi shuffle product. We map them into an algebra of polynomials in one indeterminate L and show that the leading log expansion one obtains with such a mapping are simple power law like expression
Dynamic Combinatorial Libraries of Disulfide Cages in Water
West, Kevin R.; Bake, Kyle D.; Otto, Sijbren
2005-01-01
Dynamic combinatorial libraries (DCLs) containing water-soluble disulfide-linked cages (alongside macrocyclic structures) have been generated and characterized. Unlike most other strategies for generating molecular cages, the structures are held together by covalent bonds, which are formed under the
A Synthetic Receptor for Nicotine from a Dynamic Combinatorial Library
Hamieh, Saleh; Ludlow, R. Frederick; Perraud, Olivier; West, Kevin R.; Mattia, Elio; Otto, Sijbren
2012-01-01
Designing synthetic receptors that bind biologically relevant guests in an aqueous solution remains a considerable challenge. We now report a new synthetic receptor for nicotine, selected from a dynamic combinatorial library, that binds this guest in water at neutral pH through a combination of hydr
Combinatorial conditions for low rank solutions in semidefinite programming
Varvitsiotis, A.
2013-01-01
In this thesis we investigate combinatorial conditions that guarantee the existence of low-rank optimal solutions to semidefinite programs. Results of this type are important for approximation algorithms and for the study of geometric representations of graphs. The structure of the thesis is as
Combinatorial conditions for low rank solutions in semidefinite programming
A. Varvitsiotis (Antonios)
2013-01-01
htmlabstractIn this thesis we investigate combinatorial conditions that guarantee the existence of low-rank optimal solutions to semidefinite programs. Results of this type are important for approximation algorithms and for the study of geometric representations of graphs. The structure of the
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 f
Identities for Generalized Fibonacci Numbers: A Combinatorial Approach
Plaza, A.; Falcon, S.
2008-01-01
This note shows a combinatorial approach to some identities for generalized Fibonacci numbers. While it is a straightforward task to prove these identities with induction, and also by arithmetical manipulations such as rearrangements, the approach used here is quite simple to follow and eventually reduces the proof to a counting problem. (Contains…
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.
A graphical formalism for mixed multi-unit combinatorial auctions
Gionvannucci, A.; Cerquides, J.; Endriss, U.; Rodríguez-Aguilar, J.A.
2010-01-01
Mixed multi-unit combinatorial auctions are auctions that allow participants to bid for bundles of goods to buy, for bundles of goods to sell, and for transformations of goods. The intuitive meaning of a bid for a transformation is that the bidder is offering to produce a set of output goods after h
Solids: a combinatorial auction for a housing corporation
Goossens, D.R.; Onderstal, S.; Spieksma, F.C.R.; Coles, P.; Das, S.; Lahaie, S.; Szymanski, B.
2012-01-01
On May 7, 2011, over one hundred bidders took part in a combinatorial auction for housing space in a newly erected building in Amsterdam (the Netherlands). This paper describes the development of this auction. We sketch our collaboration with the housing corporation that resulted in design choices
Combinatorial Model Involving Stochastic Choices of Destination, Mode and Route
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Traffic assignment models are one of the basic tools for the analysis and design of transportation systems. However, the existing models have some defects. Considering the characteristics of Chinese urban mixed traffic and the randomness of transportation information, the author develops a combinatorial model involving stochastic choices of destination, mode and route. Its uniqueness and equivalance are also proved by the optimization theory.
Dithioacetal Exchange: A New Reversible Reaction for Dynamic Combinatorial Chemistry.
Orrillo, A Gastón; Escalante, Andrea M; Furlan, Ricardo L E
2016-05-10
Reversibility of dithioacetal bond formation is reported under acidic mild conditions. Its utility for dynamic combinatorial chemistry was explored by combining it with orthogonal disulfide exchange. In such a setup, thiols are positioned at the intersection of both chemistries, constituting a connecting node between temporally separated networks.
Automated Combinatorial Chemistry in the Organic Chemistry Majors Laboratory
Nichols, Christopher J.; Hanne, Larry F.
2010-01-01
A multidisciplinary experiment has been developed in which students each synthesize a combinatorial library of 48 hydrazones with the aid of a liquid-handling robot. Each product is then subjected to a Kirby-Bauer disk diffusion assay to assess its antibacterial activity. Students gain experience working with automation and at the…
Synthetic receptors for ammonium ions using dynamic combinatorial chemistry
Hamieh, Saleh
2015-01-01
The general topic of this dissertation is the development of synthetic receptors for organic ammonium ions in near physiological conditions using disulfide dynamic combinatorial chemistry (DCC). Chapter 1 explains the importance of this development and the associated difficulties when using the conv
Combinatorial conditions for low rank solutions in semidefinite programming
Varvitsiotis, A.
2013-01-01
In this thesis we investigate combinatorial conditions that guarantee the existence of low-rank optimal solutions to semidefinite programs. Results of this type are important for approximation algorithms and for the study of geometric representations of graphs. The structure of the thesis is as foll
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 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
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...
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...
Geometry-Experiment Algorithm for Steiner Minimal Tree Problem
Directory of Open Access Journals (Sweden)
Zong-Xiao Yang
2013-01-01
Full Text Available It is well known that the Steiner minimal tree problem is one of the classical nonlinear combinatorial optimization problems. A visualization experiment approach succeeds in generating Steiner points automatically and showing the system shortest path, named Steiner minimum tree, physically and intuitively. However, it is difficult to form stabilized system shortest path when the number of given points is increased and irregularly distributed. Two algorithms, geometry algorithm and geometry-experiment algorithm (GEA, are constructed to solve system shortest path using the property of Delaunay diagram and basic philosophy of Geo-Steiner algorithm and matching up with the visualization experiment approach (VEA when the given points increase. The approximate optimizing results are received by GEA and VEA for two examples. The validity of GEA was proved by solving practical problems in engineering, experiment, and comparative analysis. And the global shortest path can be obtained by GEA successfully with several actual calculations.
Lee, Jonathan A.
2005-01-01
High-throughput measurement techniques are reviewed for solid phase transformation from materials produced by combinatorial methods, which are highly efficient concepts to fabricate large variety of material libraries with different compositional gradients on a single wafer. Combinatorial methods hold high potential for reducing the time and costs associated with the development of new materials, as compared to time-consuming and labor-intensive conventional methods that test large batches of material, one- composition at a time. These high-throughput techniques can be automated to rapidly capture and analyze data, using the entire material library on a single wafer, thereby accelerating the pace of materials discovery and knowledge generation for solid phase transformations. The review covers experimental techniques that are applicable to inorganic materials such as shape memory alloys, graded materials, metal hydrides, ferric materials, semiconductors and industrial alloys.
Some combinatorial problems on binary rooted trees occurring in population genetics
Disanto, Filippo
2011-01-01
Models in evolutionary biology are intimately linked to the tree paradigm. Given a direction by time, ancestry relationship between species, individuals, alleles or cells can be depicted as a rooted tree. Of particular interest are binary rooted unordered trees. These can be further classified into shape trees, phylogenetic trees, ranked trees and labelled ranked trees. In this work we want to focus on several combinatorial aspects concerning these classes of trees. We consider numerations and probabilistic properties of these trees when generated under the random coalescent process. We derive several summary statistics which serve to characterize 'typical' trees.
Immobilized OBOC combinatorial bead array to facilitate multiplicative screening.
Xiao, Wenwu; Bononi, Fernanda C; Townsend, Jared; Li, Yuanpei; Liu, Ruiwu; Lam, Kit S
2013-07-01
One-bead-one-compound (OBOC) combinatorial library screening has been broadly utilized for the last two decades to identify small molecules, peptides or peptidomimetics targeting variable screening probes such as cell surface receptors, bacteria, protein kinases, phosphatases, proteases etc. In previous screening methods, library beads were suspended in solution and screened against one single probe. Only the positive beads were tracked and isolated for additional screens and finally selected for chemical decoding. During this process, the remaining negative beads were not tracked and discarded. Here we report a novel bead immobilization method such that a bead library array can be conveniently prepared and screened in its entirety, sequentially many times with a series of distinct probes. This method not only allows us to increase the screening efficiency but also permits us to determine the binding profile of each and every library bead against a large number of target receptors. As proof of concept, we serially screened a random OBOC disulfide containing cyclic heptapeptide library with three water soluble dyes as model probes: malachite green, bromocresol purple and indigo carmine. This multiplicative screening approach resulted in a rapid determination of the binding profile of each and every bead respective to each of the three dyes. Beads that interacted with malachite green only, bromocresol purple only, or both indigo carmine and bromocresol purple were isolated, and their peptide sequences were determined with microsequencer. Ultimately, the novel OBOC multiplicative screening approach could play a key role in the enhancement of existing on-bead assays such as whole cell binding, bacteria binding, protein binding, posttranslational modifications etc. with increased efficiency, capacity, and specificity.
Microfluidic platform for combinatorial synthesis in picolitre droplets.
Theberge, Ashleigh B; Mayot, Estelle; El Harrak, Abdeslam; Kleinschmidt, Felix; Huck, Wilhelm T S; Griffiths, Andrew D
2012-04-07
This paper presents a droplet-based microfluidic platform for miniaturized combinatorial synthesis. As a proof of concept, a library of small molecules for early stage drug screening was produced. We present an efficient strategy for producing a 7 × 3 library of potential thrombin inhibitors that can be utilized for other combinatorial synthesis applications. Picolitre droplets containing the first type of reagent (reagents A(1), A(2), …, A(m)) were formed individually in identical microfluidic chips and then stored off chip with the aid of stabilizing surfactants. These droplets were then mixed to form a library of droplets containing reagents A(1-m), each individually compartmentalized, which was reinjected into a second microfluidic chip and combinatorially fused with picolitre droplets containing the second reagent (reagents B(1), B(2), …, B(n)) that were formed on chip. The concept was demonstrated with a three-component Ugi-type reaction involving an amine (reagents A(1-3)), an aldehyde (reagents B(1-7)), and an isocyanide (held constant), to synthesize a library of small molecules with potential thrombin inhibitory activity. Our technique produced 10(6) droplets of each reaction at a rate of 2.3 kHz. Each droplet had a reaction volume of 3.1 pL, at least six orders of magnitude lower than conventional techniques. The droplets can then be divided into aliquots for different downstream screening applications. In addition to medicinal chemistry applications, this combinatorial droplet-based approach holds great potential for other applications that involve sampling large areas of chemical parameter space with minimal reagent consumption; such an approach could be beneficial when optimizing reaction conditions or performing combinatorial reactions aimed at producing novel materials.
Riemann-Finsler Geometry with Applications to Information Geometry
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Information geometry is a new branch in mathematics, originated from the applications of differential geometry to statistics. In this paper we briefly introduce RiemannFinsler geometry, by which we establish Information Geometry on a much broader base,so that the potential applications of Information Geometry will be beyond statistics.
Ariwahjoedi, Seramika; Kosasih, Jusak Sali; Rovelli, Carlo; Zen, Freddy Permana
2016-01-01
Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, restrictions are given to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.
Bonola, Roberto
2010-01-01
This is an excellent historical and mathematical view by a renowned Italian geometer of the geometries that have risen from a rejection of Euclid's parallel postulate. Students, teachers and mathematicians will find here a ready reference source and guide to a field that has now become overwhelmingly important.Non-Euclidean Geometry first examines the various attempts to prove Euclid's parallel postulate-by the Greeks, Arabs, and mathematicians of the Renaissance. Then, ranging through the 17th, 18th and 19th centuries, it considers the forerunners and founders of non-Euclidean geometry, such
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 a
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
Simultaneous Disulfide and Boronic Acid Ester Exchange in Dynamic Combinatorial Libraries
DEFF Research Database (Denmark)
Diemer, Sanna L.; Kristensen, Morten; Rasmussen, Brian
2015-01-01
Dynamic combinatorial chemistry has emerged as a promising tool for the discovery of complex receptors in supramolecular chemistry. At the heart of dynamic combinatorial chemistry are the reversible reactions that enable the exchange of building blocks between library members in dynamic combinato......Dynamic combinatorial chemistry has emerged as a promising tool for the discovery of complex receptors in supramolecular chemistry. At the heart of dynamic combinatorial chemistry are the reversible reactions that enable the exchange of building blocks between library members in dynamic...... combinatorial libraries (DCLs) ensuring thermodynamic control over the system. If more than one reversible reaction operates in a single dynamic combinatorial library, the complexity of the system increases dramatically, and so does its possible applications. One can imagine two reversible reactions...... that operate simultaneously or two reversible reactions that operate independently. Both these scenarios have advantages and disadvantages. In this contribution, we show how disulfide exchange and boronic ester transesterification can function simultaneous in dynamic combinatorial libraries under appropriate...
Speziale, Simone
2013-01-01
We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with space-like faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalims are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, abelian geometric picture. It can be described by an Euclidean singular structure on the 2-dimensional space-like surface defined by a foliation of space-time by null hypersurfaces. This geometric structure is na...
Geometries from field theories
Aoki, Sinya; Kikuchi, Kengo; Onogi, Tetsuya
2015-10-01
We propose a method to define a d+1-dimensional geometry from a d-dimensional quantum field theory in the 1/N expansion. We first construct a d+1-dimensional field theory from the d-dimensional one via the gradient-flow equation, whose flow time t represents the energy scale of the system such that trArr 0 corresponds to the ultraviolet and trArr infty to the infrared. We then define the induced metric from d+1-dimensional field operators. We show that the metric defined in this way becomes classical in the large-N limit, in the sense that quantum fluctuations of the metric are suppressed as 1/N due to the large-N factorization property. As a concrete example, we apply our method to the O(N) nonlinear σ model in two dimensions. We calculate the 3D induced metric, which is shown to describe an anti-de Sitter space in the massless limit. Finally, we discuss several open issues for future studies.
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
Chern, Shiing-Shen
1990-01-01
Discussed are the major historical developments of geometry. Euclid, Descartes, Klein's Erlanger Program, Gaus and Riemann, globalization, topology, Elie Cartan, and an application to molecular biology are included as topics. (KR)
Kumaresan, S
2005-01-01
Including Affine and projective classification of Conics, 2 point homogeneity's of the planes, essential isometrics, non euclidean plan geometrics, in this book, the treatment of Geometry goes beyond the Kleinian views.
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...
Emenaker, Charles E.
1999-01-01
Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)
Geometry of differential equations
Khovanskiĭ, A; Vassiliev, V
1998-01-01
This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.
Facilitating Understandings of Geometry.
Pappas, Christine C.; Bush, Sara
1989-01-01
Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)
Melzak, Z A
2008-01-01
Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. 1983 edition.
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.
Derived logarithmic geometry I
Steffen, Sagave; Timo, Schurg; Gabriele, Vezzosi
2016-01-01
In order to develop the foundations of logarithmic derived geometry, we introduce a model category of logarithmic simplicial rings and a notion of derived log \\'etale maps and use this to define derived log stacks.
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.
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...
Hohmann, Manuel
2014-01-01
From general relativity we have learned the principles of general covariance and local Lorentz invariance, which follow from the fact that we consider observables as tensors on a spacetime manifold whose geometry is modeled by a Lorentzian metric. Approaches to quantum gravity, however, hint towards a breaking of these symmetries and the possible existence of more general, non-tensorial geometric structures. Possible implications of these approaches are non-tensorial transformation laws between different observers and an observer-dependent notion of geometry. In this work we review two different frameworks for observer dependent geometries, which may provide hints towards a quantization of gravity and possible explanations for so far unexplained phenomena: Finsler spacetimes and Cartan geometry on observer space. We discuss their definitions, properties and applications to observers, field theories and gravity.
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
Schreiber, Urs
2016-01-01
This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution to this problem exists in higher differential geometry. In section 2 we survey examples and problems of interest. In section 3 we survey the abstract cohesive homotopy theory that serves to make all this precise and tractable.
Punzi, Raffaele; Wohlfarth, Mattias N R
2008-01-01
We reveal the non-metric geometry underlying omega-->0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking constrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.
Energy Technology Data Exchange (ETDEWEB)
Punzi, Raffaele [Zentrum fuer Mathematische Physik und II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)], E-mail: raffaele.punzi@desy.de; Schuller, Frederic P. [Max Planck Institut fuer Gravitationsphysik, Albert Einstein Institut, Am Muehlenberg 1, 14467 Potsdam (Germany)], E-mail: fps@aei.mpg.de; Wohlfarth, Mattias N.R. [Zentrum fuer Mathematische Physik und II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)], E-mail: mattias.wohlfarth@desy.de
2008-12-11
We reveal the non-metric geometry underlying {omega}{yields}0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking contrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.
Layton, Donovan S; Trinh, Cong T
2016-08-01
Volatile organic acids are byproducts of fermentative metabolism, for example, anaerobic digestion of lignocellulosic biomass or organic wastes, and are often times undesired inhibiting cell growth and reducing directed formation of the desired products. Here, we devised a general framework for upgrading these volatile organic acids to high-value esters that can be used as flavors, fragrances, solvents, and biofuels. This framework employs the acid-to-ester modules, consisting of an AAT (alcohol acyltransferase) plus ACT (acyl CoA transferase) submodule and an alcohol submodule, for co-fermentation of sugars and organic acids to acyl CoAs and alcohols to form a combinatorial library of esters. By assembling these modules with the engineered Escherichia coli modular chassis cell, we developed microbial manufacturing platforms to perform the following functions: (i) rapid in vivo screening of novel AATs for their catalytic activities; (ii) expanding combinatorial biosynthesis of unique fermentative esters; and (iii) upgrading volatile organic acids to esters using single or mixed cell cultures. To demonstrate this framework, we screened for a set of five unique and divergent AATs from multiple species, and were able to determine their novel activities as well as produce a library of 12 out of the 13 expected esters from co-fermentation of sugars and (C2-C6) volatile organic acids. We envision the developed framework to be valuable for in vivo characterization of a repertoire of not-well-characterized natural AATs, expanding the combinatorial biosynthesis of fermentative esters, and upgrading volatile organic acids to high-value esters. Biotechnol. Bioeng. 2016;113: 1764-1776. © 2016 Wiley Periodicals, Inc.
An algebraic geometry approach to protein structure determination from NMR data.
Wang, Lincong; Mettu, Ramgopal R; Donald, Bruce Randall
2005-01-01
Our paper describes the first provably-efficient algorithm for determining protein structures de novo, solely from experimental data. We show how the global nature of a certain kind of NMR data provides quantifiable complexity-theoretic benefits, allowing us to classify our algorithm as running in polynomial time. While our algorithm uses NMR data as input, it is the first polynomial-time algorithm to compute high-resolution structures de novo using any experimentally-recorded data, from either NMR spectroscopy or X-Ray crystallography. Improved algorithms for protein structure determination are needed, because currently, the process is expensive and time-consuming. For example, an area of intense research in NMR methodology is automated assignment of nuclear Overhauser effect (NOE) restraints, in which structure determination sits in a tight inner-loop (cycle) of assignment/refinement. These algorithms are very time-consuming, and typically require a large cluster. Thus, algorithms for protein structure determination that are known to run in polynomial time and provide guarantees on solution accuracy are likely to have great impact in the long-term. Methods stemming from a technique called "distance geometry embedding" do come with provable guarantees, but the NP-hardness of these problem formulations implies that in the worst case these techniques cannot run in polynomial time. We are able to avoid the NP-hardness by (a) some mild assumptions about the protein being studied, (b) the use of residual dipolar couplings (RDCs) instead of a dense network of NOEs, and (c) novel algorithms and proofs that exploit the biophysical geometry of (a) and (b), drawing on a variety of computer science, computational geometry, and computational algebra techniques. In our algorithm, RDC data, which gives global restraints on the orientation of internuclear bond vectors, is used in conjunction with very sparse NOE data to obtain a polynomial-time algorithm for protein structure
Kanazawa, Takahiko; Yasuda, Keiichiro
Metaheuristics is a new paradigm that aims to obtain an approximate solution within a feasible computation time. To design the effective metaheuristics, strategies of intensification and diversification are essential. This paper proposes an algorithm that has long term policy for realizing intensification and diversification based on higher level structure in solution space. In order to verify the performance, the proposed algorithm is applied to some traveling salesman problems which are typical combinatorial optimization problems.
Communities of minima in local optima networks of combinatorial spaces
Daolio, Fabio; Tomassini, Marco; Vérel, Sébastien; Ochoa, Gabriela
2011-05-01
In this work, we present a new methodology to study the structure of the configuration spaces of hard combinatorial problems. It consists in building the network that has as nodes the locally optimal configurations and as edges the weighted oriented transitions between their basins of attraction. We apply the approach to the detection of communities in the optima networks produced by two different classes of instances of a hard combinatorial optimization problem: the quadratic assignment problem (QAP). We provide evidence indicating that the two problem instance classes give rise to very different configuration spaces. For the so-called real-like class, the networks possess a clear modular structure, while the optima networks belonging to the class of random uniform instances are less well partitionable into clusters. This is convincingly supported by using several statistical tests. Finally, we briefly discuss the consequences of the findings for heuristically searching the corresponding problem spaces.
Parsing Combinatory Categorial Grammar with Answer Set Programming: Preliminary Report
Lierler, Yuliya
2011-01-01
Combinatory categorial grammar (CCG) is a grammar formalism used for natural language parsing. CCG assigns structured lexical categories to words and uses a small set of combinatory rules to combine these categories to parse a sentence. In this work we propose and implement a new approach to CCG parsing that relies on a prominent knowledge representation formalism, answer set programming (ASP) - a declarative programming paradigm. We formulate the task of CCG parsing as a planning problem and use an ASP computational tool to compute solutions that correspond to valid parses. Compared to other approaches, there is no need to implement a specific parsing algorithm using such a declarative method. Our approach aims at producing all semantically distinct parse trees for a given sentence. From this goal, normalization and efficiency issues arise, and we deal with them by combining and extending existing strategies. We have implemented a CCG parsing tool kit - AspCcgTk - that uses ASP as its main computational mean...
Laguerre-type derivatives: Dobinski relations and combinatorial identities
Penson, K A; Horzela, A; Solomon, A I; Duchamp, G H E
2009-01-01
We consider properties of the operators D(r,M)=a^r(a^\\dag a)^M (which we call generalized Laguerre-type derivatives), with r=1,2,..., M=0,1,..., where a and a^\\dag are boson annihilation and creation operators respectively, satisfying [a,a^\\dag]=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 which 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.
Combinatorial Gene Regulation through Kinetic Control of the Transcription Cycle.
Scholes, Clarissa; DePace, Angela H; Sánchez, Álvaro
2017-01-25
Cells decide when, where, and to what level to express their genes by "computing" information from transcription factors (TFs) binding to regulatory DNA. How is the information contained in multiple TF-binding sites integrated to dictate the rate of transcription? The dominant conceptual and quantitative model is that TFs combinatorially recruit one another and RNA polymerase to the promoter by direct physical interactions. Here, we develop a quantitative framework to explore kinetic control, an alternative model in which combinatorial gene regulation can result from TFs working on different kinetic steps of the transcription cycle. Kinetic control can generate a wide range of analog and Boolean computations without requiring the input TFs to be simultaneously bound to regulatory DNA. We propose experiments that will illuminate the role of kinetic control in transcription and discuss implications for deciphering the cis-regulatory "code."
Quasi-combinatorial energy landscapes for nanoalloy structure optimisation.
Schebarchov, D; Wales, D J
2015-11-14
We formulate nanoalloy structure prediction as a mixed-variable optimisation problem, where the homotops can be associated with an effective, quasi-combinatorial energy landscape in permutation space. We survey this effective landscape for a representative set of binary systems modelled by the Gupta potential. In segregating systems with small lattice mismatch, we find that homotops have a relatively straightforward landscape with few local optima - a scenario well-suited for local (combinatorial) optimisation techniques that scale quadratically with system size. Combining these techniques with multiple local-neighbourhood structures yields a search for multiminima, and we demonstrate that generalised basin-hopping with a metropolis acceptance criterion in the space of multiminima can then be effective for global optimisation of binary and ternary nanoalloys.
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.
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.
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...... including MSNT-mediated esterification of both support-bound alcohols and carboxylic acids has been implemented successfully. Copyright (C) 1996 Elsevier Science Ltd....
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...... including MSNT-mediated esterification of both support-bound alcohols and carboxylic acids has been implemented successfully. Copyright (C) 1996 Elsevier Science Ltd....
Immobilized OBOC combinatorial bead array to facilitate multiplicative screening
Xiao, Wenwu; Bononi, Fernanda C.; Townsend, Jared; Li, Yuanpei; Liu, Ruiwu; Lam, Kit S.
2013-01-01
One-bead-one-compound (OBOC) combinatorial library screening has been broadly utilized for the last two decades to identify small molecules, peptides or peptidomimetics targeting variable screening probes such as cell surface receptors, bacteria, protein kinases, phosphatases, proteases etc. In previous screening methods, library beads were suspended in solution and screened against one single probe. Only the positive beads were tracked and isolated for additional screens and finally selected...
The evolution of combinatorial gene regulation in fungi.
Tuch, Brian B.; Galgoczy, David J.; Hernday, Aaron D.; Hao Li; Johnson, Alexander D.
2008-01-01
It is widely suspected that gene regulatory networks are highly plastic. The rapid turnover of transcription factor binding sites has been predicted on theoretical grounds and has been experimentally demonstrated in closely related species. We combined experimental approaches with comparative genomics to focus on the role of combinatorial control in the evolution of a large transcriptional circuit in the fungal lineage. Our study centers on Mcm1, a transcriptional regulator that, in combinati...
A Combinatorial interpretation of Hofstadter's G-sequence
Rahman, Mustazee
2011-01-01
We give a combinatorial interpretation of a classical meta-Fibonacci sequence defined by G(n) = n - G(G(n-1)) with the initial condition G(1) = 1, which appears in Hofstadter's 'Godel, Escher, Bach: An Eternal Golden Braid'. The interpretation is in terms of an infinite labelled tree. We then show a few corollaries about the behaviour of the sequence G(n) directly from the interpretation.
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.
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.
Controlling Combinatorial Complexity in Software and Malware Behavior Computation
Energy Technology Data Exchange (ETDEWEB)
Pleszkoch, Mark G [ORNL; Linger, Richard C [ORNL
2015-01-01
Virtually all software is out of intellectual control in that no one knows its full behavior. Software Behavior Computation (SBC) is a new technology for understanding everything software does. SBC applies the mathematics of denotational semantics implemented by function composition in Functional Trace Tables (FTTs) to compute the behavior of programs, expressed as disjoint cases of conditional concurrent assignments. In some circumstances, combinatorial explosions in the number of cases can occur when calculating the behavior of sequences of multiple branching structures. This paper describes computational methods that avoid combinatorial explosions. The predicates that control branching structures such as ifthenelses can be organized into three categories: 1) Independent, resulting in no behavior case explosion, 2) Coordinated, resulting in two behavior cases, or 3) Goaloriented, with potential exponential growth in the number of cases. Traditional FTT-based behavior computation can be augmented by two additional computational methods, namely, Single-Value Function Abstractions (SVFAs) and, introduced in this paper, Relational Trace Tables (RTTs). These methods can be applied to the three predicate categories to avoid combinatorial growth in behavior cases while maintaining mathematical correctness.
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
Emergent Complex Network Geometry
Wu, Zhihao; Rahmede, Christoph; Bianconi, Ginestra
2014-01-01
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geo...
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...
Supersymmetry and noncommutative geometry
Beenakker, Wim; Suijlekom, Walter D van
2016-01-01
In this work the question whether noncommutative geometry allows for supersymmetric theories is addressed. Noncommutative geometry has seen remarkable applications in high energy physics, viz. the geometrical interpretation of the Standard Model, however such a question has not been answered in a conclusive way so far. The book starts with a systematic analysis of the possibilities for so-called almost-commutative geometries on a 4-dimensional, flat background to exhibit not only a particle content that is eligible for supersymmetry, but also have a supersymmetric action. An approach is proposed in which the basic `building blocks' of potentially supersymmetric theories and the demands for their action to be supersymmetric are identified. It is then described how a novel kind of soft supersymmetry breaking Lagrangian arises naturally from the spectral action. Finally, the above formalism is applied to explore the existence of a noncommutative version of the minimal supersymmetric Standard Model. This book is ...
Cecil, Thomas E
2015-01-01
This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hy...
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...
Integral Geometry and Holography
Czech, Bartlomiej; McCandlish, Samuel; Sully, James
2015-01-01
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS$_3$/CFT$_2$ correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we...
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.
Quanta of Geometry and Unification
Chamseddine, Ali H
2016-01-01
This is a tribute to Abdus Salam's memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in space-time (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.
The Geometry of Conventionality
Weatherall, James Owen
2013-01-01
Hans Reichenbach famously argued that the geometry of spacetime is conventional in relativity theory, in the sense that one can freely choose the spacetime metric so long as one is willing to postulate a "universal force field". Here we make precise a sense in which the field Reichenbach defines fails to be a "force". We then argue that there is an interesting and perhaps tenable sense in which geometry is conventional in classical spacetimes. We conclude with a no-go result showing that the variety of conventionalism available in classical spacetimes does not extend to relativistic spacetimes.
Bowyer, Adrian
1983-01-01
A Programmer's Geometry provides a guide in programming geometric shapes. The book presents formulas and examples of computer representation and coding of geometry. Each of the nine chapters of the text deals with the representation and solution of a specific geometrical problem, such as areas, vectors, and volumes. The last chapter provides a brief discussion on generating image through a computer. The codes presented in the book are written in FORTRAN 77. The text will be of great use to programmers who are working on projects that involve geometric calculations.
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
Eisenhart, L P
1927-01-01
The use of the differential geometry of a Riemannian space in the mathematical formulation of physical theories led to important developments in the geometry of such spaces. The concept of parallelism of vectors, as introduced by Levi-Civita, gave rise to a theory of the affine properties of a Riemannian space. Covariant differentiation, as developed by Christoffel and Ricci, is a fundamental process in this theory. Various writers, notably Eddington, Einstein and Weyl, in their efforts to formulate a combined theory of gravitation and electromagnetism, proposed a simultaneous generalization o
Skorupska, Katarzyna; Maggard, Paul A; Eichberger, Rainer; Schwarzburg, Klaus; Shahbazi, Paria; Zoellner, Brandon; Parkinson, Bruce A
2015-12-14
High-throughput combinatorial methods have been useful in identifying new oxide semiconductors with the potential to be applied to solar water splitting. Most of these techniques have been limited to producing and screening oxide phases formed at temperatures below approximately 550 °C. We report the development of a combinatorial approach to discover and optimize high temperature phases for photoelectrochemical water splitting. As a demonstration material, we chose to produce thin films of high temperature CuNb oxide phases by inkjet printing on two different substrates: fluorine-doped tin oxide and crystalline Si, which required different sample pyrolysis procedures. The selection of pyrolysis parameters, such as temperature/time programs, and the use of oxidizing, nonreactive or reducing atmospheres determines the composition of the thin film materials and their photoelectrochemical performance. XPS, XRD, and SEM analyses were used to determine the composition and oxidation states within the copper niobium oxide phases and to then guide the production of target Cu(1+)Nb(5+)-oxide phases. The charge carrier dynamics of the thin films produced by the inkjet printing are compared with pure CuNbO3 microcrystalline material obtained from inorganic bulk synthesis.
Large-scale prediction of microRNA-disease associations by combinatorial prioritization algorithm
Yu, Hua; Chen, Xiaojun; Lu, Lu
2017-03-01
Identification of the associations between microRNA molecules and human diseases from large-scale heterogeneous biological data is an important step for understanding the pathogenesis of diseases in microRNA level. However, experimental verification of microRNA-disease associations is expensive and time-consuming. To overcome the drawbacks of conventional experimental methods, we presented a combinatorial prioritization algorithm to predict the microRNA-disease associations. Importantly, our method can be used to predict microRNAs (diseases) associated with the diseases (microRNAs) without the known associated microRNAs (diseases). The predictive performance of our proposed approach was evaluated and verified by the internal cross-validations and external independent validations based on standard association datasets. The results demonstrate that our proposed method achieves the impressive performance for predicting the microRNA-disease association with the Area Under receiver operation characteristic Curve (AUC), 86.93%, which is indeed outperform the previous prediction methods. Particularly, we observed that the ensemble-based method by integrating the predictions of multiple algorithms can give more reliable and robust prediction than the single algorithm, with the AUC score improved to 92.26%. We applied our combinatorial prioritization algorithm to lung neoplasms and breast neoplasms, and revealed their top 30 microRNA candidates, which are in consistent with the published literatures and databases.
Large-scale prediction of microRNA-disease associations by combinatorial prioritization algorithm
Yu, Hua; Chen, Xiaojun; Lu, Lu
2017-01-01
Identification of the associations between microRNA molecules and human diseases from large-scale heterogeneous biological data is an important step for understanding the pathogenesis of diseases in microRNA level. However, experimental verification of microRNA-disease associations is expensive and time-consuming. To overcome the drawbacks of conventional experimental methods, we presented a combinatorial prioritization algorithm to predict the microRNA-disease associations. Importantly, our method can be used to predict microRNAs (diseases) associated with the diseases (microRNAs) without the known associated microRNAs (diseases). The predictive performance of our proposed approach was evaluated and verified by the internal cross-validations and external independent validations based on standard association datasets. The results demonstrate that our proposed method achieves the impressive performance for predicting the microRNA-disease association with the Area Under receiver operation characteristic Curve (AUC), 86.93%, which is indeed outperform the previous prediction methods. Particularly, we observed that the ensemble-based method by integrating the predictions of multiple algorithms can give more reliable and robust prediction than the single algorithm, with the AUC score improved to 92.26%. We applied our combinatorial prioritization algorithm to lung neoplasms and breast neoplasms, and revealed their top 30 microRNA candidates, which are in consistent with the published literatures and databases. PMID:28317855
Nonlinearity measurements of solar cells with an LED-based combinatorial flux addition method.
Hamadani, Behrang H; Shore, Andrew; Roller, John; Yoon, Howard W; Campanelli, Mark
2016-02-01
We present a light emitting diode (LED)-based system utilizing a combinatorial flux addition method to investigate the nonlinear relationship in solar cells between the output current of the cell and the incident irradiance level. The magnitude of the light flux is controlled by the supplied currents to two LEDs (or two sets of them) in a combinatorial fashion. The signals measured from the cell are arranged within a related overdetermined linear system of equations derived from an appropriately chosen N(th) degree polynomial representing the relationship between the measured signals and the incident fluxes. The flux values and the polynomial coefficients are then solved for by linear least squares to obtain the best fit. The technique can be applied to any solar cell, under either monochromatic or broadband spectrum. For the unscaled solution, no reference detectors or prior calibrations of the light flux are required. However, if at least one calibrated irradiance value is known, then the entire curve can be scaled to an appropriate spectral responsivity value. Using this technique, a large number of data points can be obtained in a relatively short time scale over a large signal range.
Directory of Open Access Journals (Sweden)
Mirna Radin Sabadoš
2011-10-01
Full Text Available The proposal that the world is made of sequences of zeros and ones, overtly expressed in DeLillo’s early novel Ratner’s Star (1976, marks the first time in DeLillo’s fiction that he introduces the idea that the (creation of reality is of mathematical nature. The “zero-oneness” of the world thirty odd years later, although it still may be an uncommon thought in literature, is ubiquitous in the visual arts, in film and in architecture, and binary code has become the basis of our digitally enhanced reality. Looking at DeLillo’s Millennial novels, this paper seeks to explore models of the space-time continuum of the fictional reality that DeLillo constructs; focusing on Ratner’s Star as a literary exploration of a three-dimensional space and on the novel Body Artist as an investigation of the fourth dimension, pondering time, we hope to register the “sum total of one’s data” (WN as the only palpable texture of DeLillo’s reality.
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
Noncommutative geometry, Lorentzian structures and causality
Franco, Nicolas
2014-01-01
The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However, noncommutative geometry has mainly been developed using the Euclidean signature, and the typical Lorentzian aspects of space-time, the causal structure in particular, are not taken into account. We present an extension of noncommutative geometry \\`a la Connes suitable the for accommodation of Lorentzian structures. In this context, we show that it is possible to recover the notion of causality from purely algebraic data. We explore the causal structure of a simple toy model based on an almost commutative geometry and we show that the coupling between the space-time and an internal noncommutative space establishes a new `speed of light constraint'.
Universal correlators from geometry
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, Robbert [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Temuerhan, Mine; Sinkovics, Annamaria [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)]. E-mail: sinkovic@science.uva.nl
2004-11-01
Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion. (author)
Universal Correlators from Geometry
Dijkgraaf, Robbert; Sinkovics, Annamaria; Temurhan, Mine
2004-11-01
Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion.
Universal Correlators from Geometry
Dijkgraaf, R; Temurhan, M; Dijkgraaf, Robbert; Sinkovics, Annamaria; Temurhan, Mine
2004-01-01
Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion.
Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740
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.