A Structural Connection between Linear and 0-1 Integer Linear Formulations
ERIC Educational Resources Information Center
Adlakha, V.; Kowalski, K.
2007-01-01
The connection between linear and 0-1 integer linear formulations has attracted the attention of many researchers. The main reason triggering this interest has been an availability of efficient computer programs for solving pure linear problems including the transportation problem. Also the optimality of linear problems is easily verifiable…
Evaluating the impact of AND/OR search on 0-1 integer linear programming
Dechter, R.
2010-01-01
AND/OR search spaces accommodate advanced algorithmic schemes for graphical models which can exploit the structure of the model. We extend and evaluate the depth-first and best-first AND/OR search algorithms to solving 0-1 Integer Linear Programs (0-1 ILP) within this framework. We also include a class of dynamic variable ordering heuristics while exploring an AND/OR search tree for 0-1 ILPs. We demonstrate the effectiveness of these search algorithms on a variety of benchmarks, including real-world combinatorial auctions, random uncapacitated warehouse location problems and MAX-SAT instances. PMID:21052484
Investigating Integer Restrictions in Linear Programming
ERIC Educational Resources Information Center
Edwards, Thomas G.; Chelst, Kenneth R.; Principato, Angela M.; Wilhelm, Thad L.
2015-01-01
Linear programming (LP) is an application of graphing linear systems that appears in many Algebra 2 textbooks. Although not explicitly mentioned in the Common Core State Standards for Mathematics, linear programming blends seamlessly into modeling with mathematics, the fourth Standard for Mathematical Practice (CCSSI 2010, p. 7). In solving a…
Detection of code spread OFDM based on 0-1 integer quadratic programming
NASA Astrophysics Data System (ADS)
Elghariani, Ali; Zoltowski, Michael D.
2012-05-01
In this paper we introduce Integer Quadratic Programming (MIQP) approach to optimally detect QPSK Code Spread OFDM (CS-OFDM) by formulating the problem as a combinatorial optimization problem. The Branch and Bound (BB) algorithm is utilized to solve this integer quadratic programming problem. Furthermore, we propose combined preprocessing steps that can be applied prior to BB so that the computational complexity of the optimum receiver is reduced. The first step in this combination is to detect as much as possible symbols using procedures presented in [9], which is basically based on the gradient of quadratic function. The second step detects the undetected symbols from the first step using MMSE estimator. The result of the latter step will be used to predict the initial upper bound of the BB algorithm. Simulation results show that the proposed preprocessing combination when applied prior to BB provides optimal performance with a significantly reduced computational complexity.
Split diversity in constrained conservation prioritization using integer linear programming
Chernomor, Olga; Minh, Bui Quang; Forest, Félix; Klaere, Steffen; Ingram, Travis; Henzinger, Monika; von Haeseler, Arndt
2015-01-01
Phylogenetic diversity (PD) is a measure of biodiversity based on the evolutionary history of species. Here, we discuss several optimization problems related to the use of PD, and the more general measure split diversity (SD), in conservation prioritization. Depending on the conservation goal and the information available about species, one can construct optimization routines that incorporate various conservation constraints. We demonstrate how this information can be used to select sets of species for conservation action. Specifically, we discuss the use of species' geographic distributions, the choice of candidates under economic pressure, and the use of predator–prey interactions between the species in a community to define viability constraints. Despite such optimization problems falling into the area of NP hard problems, it is possible to solve them in a reasonable amount of time using integer programming. We apply integer linear programming to a variety of models for conservation prioritization that incorporate the SD measure. We exemplarily show the results for two data sets: the Cape region of South Africa and a Caribbean coral reef community. Finally, we provide user-friendly software at http://www.cibiv.at/software/pda. PMID:25893087
Accurate construction of consensus genetic maps via integer linear programming.
Wu, Yonghui; Close, Timothy J; Lonardi, Stefano
2011-01-01
We study the problem of merging genetic maps, when the individual genetic maps are given as directed acyclic graphs. The computational problem is to build a consensus map, which is a directed graph that includes and is consistent with all (or, the vast majority of) the markers in the input maps. However, when markers in the individual maps have ordering conflicts, the resulting consensus map will contain cycles. Here, we formulate the problem of resolving cycles in the context of a parsimonious paradigm that takes into account two types of errors that may be present in the input maps, namely, local reshuffles and global displacements. The resulting combinatorial optimization problem is, in turn, expressed as an integer linear program. A fast approximation algorithm is proposed, and an additional speedup heuristic is developed. Our algorithms were implemented in a software tool named MERGEMAP which is freely available for academic use. An extensive set of experiments shows that MERGEMAP consistently outperforms JOINMAP, which is the most popular tool currently available for this task, both in terms of accuracy and running time. MERGEMAP is available for download at http://www.cs.ucr.edu/~yonghui/mgmap.html. PMID:20479505
A Mixed Integer Linear Program for Airport Departure Scheduling
NASA Technical Reports Server (NTRS)
Gupta, Gautam; Jung, Yoon Chul
2009-01-01
Aircraft departing from an airport are subject to numerous constraints while scheduling departure times. These constraints include wake-separation constraints for successive departures, miles-in-trail separation for aircraft bound for the same departure fixes, and time-window or prioritization constraints for individual flights. Besides these, emissions as well as increased fuel consumption due to inefficient scheduling need to be included. Addressing all the above constraints in a single framework while allowing for resequencing of the aircraft using runway queues is critical to the implementation of the Next Generation Air Transport System (NextGen) concepts. Prior work on airport departure scheduling has addressed some of the above. However, existing methods use pre-determined runway queues, and schedule aircraft from these departure queues. The source of such pre-determined queues is not explicit, and could potentially be a subjective controller input. Determining runway queues and scheduling within the same framework would potentially result in better scheduling. This paper presents a mixed integer linear program (MILP) for the departure-scheduling problem. The program takes as input the incoming sequence of aircraft for departure from a runway, along with their earliest departure times and an optional prioritization scheme based on time-window of departure for each aircraft. The program then assigns these aircraft to the available departure queues and schedules departure times, explicitly considering wake separation and departure fix restrictions to minimize total delay for all aircraft. The approach is generalized and can be used in a variety of situations, and allows for aircraft prioritization based on operational as well as environmental considerations. We present the MILP in the paper, along with benefits over the first-come-first-serve (FCFS) scheme for numerous randomized problems based on real-world settings. The MILP results in substantially reduced
IESIP - AN IMPROVED EXPLORATORY SEARCH TECHNIQUE FOR PURE INTEGER LINEAR PROGRAMMING PROBLEMS
NASA Technical Reports Server (NTRS)
Fogle, F. R.
1994-01-01
IESIP, an Improved Exploratory Search Technique for Pure Integer Linear Programming Problems, addresses the problem of optimizing an objective function of one or more variables subject to a set of confining functions or constraints by a method called discrete optimization or integer programming. Integer programming is based on a specific form of the general linear programming problem in which all variables in the objective function and all variables in the constraints are integers. While more difficult, integer programming is required for accuracy when modeling systems with small numbers of components such as the distribution of goods, machine scheduling, and production scheduling. IESIP establishes a new methodology for solving pure integer programming problems by utilizing a modified version of the univariate exploratory move developed by Robert Hooke and T.A. Jeeves. IESIP also takes some of its technique from the greedy procedure and the idea of unit neighborhoods. A rounding scheme uses the continuous solution found by traditional methods (simplex or other suitable technique) and creates a feasible integer starting point. The Hook and Jeeves exploratory search is modified to accommodate integers and constraints and is then employed to determine an optimal integer solution from the feasible starting solution. The user-friendly IESIP allows for rapid solution of problems up to 10 variables in size (limited by DOS allocation). Sample problems compare IESIP solutions with the traditional branch-and-bound approach. IESIP is written in Borland's TURBO Pascal for IBM PC series computers and compatibles running DOS. Source code and an executable are provided. The main memory requirement for execution is 25K. This program is available on a 5.25 inch 360K MS DOS format diskette. IESIP was developed in 1990. IBM is a trademark of International Business Machines. TURBO Pascal is registered by Borland International.
Parametric integer linear programming: a synthesis of branch and bound with cutting planes
Rountree, S.L.K.; Gillett, B.E.
1980-01-01
A branch and bound algorithm is designed to solve the general integer linear programing problem with parametric right-hand sides. The right-hand sides have the form b + THETA d, where b and d are conformable vectors, d consists of nonegative constants, and THETA varies from zero to one. The method consists of first determining all possible right-hand side ineger constants and appending this set of integer constants to the initial tableau to form an expanded problem with a finite number of family members. The implicit enumeration method gives a lower bound on the integer solutions. The branch and bound method is used with fathoming tests that allow one family member possibly to fathom other family members. A cutting plane option applies a finite number of cuts to each node before branching. In addition, the cutting plane method is invoked whenever some members are feasible at a node and others are infeasible. The branching and cutting process is repeated until the entire family of problems has been solved. 3 tables.
Li, Zukui; Ding, Ran; Floudas, Christodoulos A.
2011-01-01
Robust counterpart optimization techniques for linear optimization and mixed integer linear optimization problems are studied in this paper. Different uncertainty sets, including those studied in literature (i.e., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geometric relationship is discussed. For uncertainty in the left hand side, right hand side, and objective function of the optimization problems, robust counterpart optimization formulations induced by those different uncertainty sets are derived. Numerical studies are performed to compare the solutions of the robust counterpart optimization models and applications in refinery production planning and batch process scheduling problem are presented. PMID:21935263
An improved exploratory search technique for pure integer linear programming problems
NASA Technical Reports Server (NTRS)
Fogle, F. R.
1990-01-01
The development is documented of a heuristic method for the solution of pure integer linear programming problems. The procedure draws its methodology from the ideas of Hooke and Jeeves type 1 and 2 exploratory searches, greedy procedures, and neighborhood searches. It uses an efficient rounding method to obtain its first feasible integer point from the optimal continuous solution obtained via the simplex method. Since this method is based entirely on simple addition or subtraction of one to each variable of a point in n-space and the subsequent comparison of candidate solutions to a given set of constraints, it facilitates significant complexity improvements over existing techniques. It also obtains the same optimal solution found by the branch-and-bound technique in 44 of 45 small to moderate size test problems. Two example problems are worked in detail to show the inner workings of the method. Furthermore, using an established weighted scheme for comparing computational effort involved in an algorithm, a comparison of this algorithm is made to the more established and rigorous branch-and-bound method. A computer implementation of the procedure, in PC compatible Pascal, is also presented and discussed.
Power Minimization for Dual- and Triple-Supply Digital Circuits via Integer Linear Programming
NASA Astrophysics Data System (ADS)
Ahn, Ki-Yong; Kyung, Chong-Min
This paper proposes an Integer Linear Programming (ILP)-based power minimization method by partitioning into regions, first, with three different VDD's(PM3V), and, secondly, with two different VDD's(PM2V). To reduce the solving time of triple-VDD case (PM3V), we also proposed a partitioned ILP method(p-PM3V). The proposed method provides 29% power saving on the average in the case of triple-VDD compared to the case of single VDD. Power reduction of PM3V compared to Clustered Voltage Scaling (CVS) was about 18%. Compared to the unpartitioned ILP formulation(PM3V), the partitioned ILP method(p-PM3V) reduced the total solution time by 46% at the cost of additional power consumption within 1.3%.
An Application of Parametric Mixed-Integer Linear Programming to Hydropower Development
NASA Astrophysics Data System (ADS)
Turgeon, André
1987-03-01
The problem consists in selecting the sites on the river where reservoirs and hydroelectric power plants are to be built and then determining the type and size of the projected installations. The solution obviously depends on the amount of money the utility is willing to invest, which itself is a function of what the new installations will produce. It is therefore necessary to solve the problem for all possible amounts of firm energy produced, since it is not known at the outset which production level the utility will select. This is done in the paper by a parametric mixed-integer linear programming (MILP) method whose efficiency derives from the fact that the branch-and-bound algorithm for selecting the sites to be developed (and consuming most of the computer time) is solved a minimum number of times. Between the points where the MILP problem is solved, LP parametric analysis is applied.
First, Eric L; Gounaris, Chrysanthos E; Floudas, Christodoulos A
2012-01-23
Reaction mappings are of fundamental importance to researchers studying the mechanisms of chemical reactions and analyzing biochemical pathways. We have developed an automated method based on integer linear optimization, ILP, to identify optimal reaction mappings that minimize the number of bond changes. An alternate objective function is also proposed that minimizes the number of bond order changes. In contrast to previous approaches, our method produces mappings that respect stereochemistry. We also show how to locate multiple reaction mappings efficiently and determine which of those mappings correspond to distinct reaction mechanisms by automatically detecting molecular symmetries. We demonstrate our techniques through a number of computational studies on the GRI-Mech, KEGG LIGAND, and BioPath databases. The computational studies indicate that 99% of the 8078 reactions tested can be addressed within 1 CPU hour. The proposed framework has been incorporated into the Web tool DREAM ( http://selene.princeton.edu/dream/ ), which is freely available to the scientific community. PMID:22098204
NASA Astrophysics Data System (ADS)
Bahri, Susila
2016-04-01
In this research, the minimization of the fire station model is constructed. The maximum time data required by the firefighter is used to construct the minimization model of the fire station in Padang. The model is used to determine the minimum number of the available fire station in Padang town. By using Matlab 2013a, the solution of the model can be found based on the Branch and Bound method. It denotes that the fire station must be built in Lubuk Begalung and Kuranji sub-districts.
A Mixed Integer Linear Program for Solving a Multiple Route Taxi Scheduling Problem
NASA Technical Reports Server (NTRS)
Montoya, Justin Vincent; Wood, Zachary Paul; Rathinam, Sivakumar; Malik, Waqar Ahmad
2010-01-01
Aircraft movements on taxiways at busy airports often create bottlenecks. This paper introduces a mixed integer linear program to solve a Multiple Route Aircraft Taxi Scheduling Problem. The outputs of the model are in the form of optimal taxi schedules, which include routing decisions for taxiing aircraft. The model extends an existing single route formulation to include routing decisions. An efficient comparison framework compares the multi-route formulation and the single route formulation. The multi-route model is exercised for east side airport surface traffic at Dallas/Fort Worth International Airport to determine if any arrival taxi time savings can be achieved by allowing arrivals to have two taxi routes: a route that crosses an active departure runway and a perimeter route that avoids the crossing. Results indicate that the multi-route formulation yields reduced arrival taxi times over the single route formulation only when a perimeter taxiway is used. In conditions where the departure aircraft are given an optimal and fixed takeoff sequence, accumulative arrival taxi time savings in the multi-route formulation can be as high as 3.6 hours more than the single route formulation. If the departure sequence is not optimal, the multi-route formulation results in less taxi time savings made over the single route formulation, but the average arrival taxi time is significantly decreased.
Poos, Alexandra M; Maicher, André; Dieckmann, Anna K; Oswald, Marcus; Eils, Roland; Kupiec, Martin; Luke, Brian; König, Rainer
2016-06-01
Understanding telomere length maintenance mechanisms is central in cancer biology as their dysregulation is one of the hallmarks for immortalization of cancer cells. Important for this well-balanced control is the transcriptional regulation of the telomerase genes. We integrated Mixed Integer Linear Programming models into a comparative machine learning based approach to identify regulatory interactions that best explain the discrepancy of telomerase transcript levels in yeast mutants with deleted regulators showing aberrant telomere length, when compared to mutants with normal telomere length. We uncover novel regulators of telomerase expression, several of which affect histone levels or modifications. In particular, our results point to the transcription factors Sum1, Hst1 and Srb2 as being important for the regulation of EST1 transcription, and we validated the effect of Sum1 experimentally. We compiled our machine learning method leading to a user friendly package for R which can straightforwardly be applied to similar problems integrating gene regulator binding information and expression profiles of samples of e.g. different phenotypes, diseases or treatments. PMID:26908654
Poos, Alexandra M.; Maicher, André; Dieckmann, Anna K.; Oswald, Marcus; Eils, Roland; Kupiec, Martin; Luke, Brian; König, Rainer
2016-01-01
Understanding telomere length maintenance mechanisms is central in cancer biology as their dysregulation is one of the hallmarks for immortalization of cancer cells. Important for this well-balanced control is the transcriptional regulation of the telomerase genes. We integrated Mixed Integer Linear Programming models into a comparative machine learning based approach to identify regulatory interactions that best explain the discrepancy of telomerase transcript levels in yeast mutants with deleted regulators showing aberrant telomere length, when compared to mutants with normal telomere length. We uncover novel regulators of telomerase expression, several of which affect histone levels or modifications. In particular, our results point to the transcription factors Sum1, Hst1 and Srb2 as being important for the regulation of EST1 transcription, and we validated the effect of Sum1 experimentally. We compiled our machine learning method leading to a user friendly package for R which can straightforwardly be applied to similar problems integrating gene regulator binding information and expression profiles of samples of e.g. different phenotypes, diseases or treatments. PMID:26908654
Automatic design of synthetic gene circuits through mixed integer non-linear programming.
Huynh, Linh; Kececioglu, John; Köppe, Matthias; Tagkopoulos, Ilias
2012-01-01
Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver sub-optimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer non-linear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and user-defined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective function given by the user. We evaluated the proposed method in the design of three synthetic circuits (a toggle switch, a transcriptional cascade, and a band detector), with both experimentally constructed and synthetic promoter libraries. Scalability and robustness analysis shows that the proposed framework scales well with the library size and the solution space. The work described here is a step towards a unifying, realistic framework for the automated design of biological circuits. PMID:22536398
Integer Linear Programming for Constrained Multi-Aspect Committee Review Assignment
Karimzadehgan, Maryam; Zhai, ChengXiang
2011-01-01
Automatic review assignment can significantly improve the productivity of many people such as conference organizers, journal editors and grant administrators. A general setup of the review assignment problem involves assigning a set of reviewers on a committee to a set of documents to be reviewed under the constraint of review quota so that the reviewers assigned to a document can collectively cover multiple topic aspects of the document. No previous work has addressed such a setup of committee review assignments while also considering matching multiple aspects of topics and expertise. In this paper, we tackle the problem of committee review assignment with multi-aspect expertise matching by casting it as an integer linear programming problem. The proposed algorithm can naturally accommodate any probabilistic or deterministic method for modeling multiple aspects to automate committee review assignments. Evaluation using a multi-aspect review assignment test set constructed using ACM SIGIR publications shows that the proposed algorithm is effective and efficient for committee review assignments based on multi-aspect expertise matching. PMID:22711970
Li, Y P; Huang, G H
2006-11-01
In this study, an interval-parameter two-stage mixed integer linear programming (ITMILP) model is developed for supporting long-term planning of waste management activities in the City of Regina. In the ITMILP, both two-stage stochastic programming and interval linear programming are introduced into a general mixed integer linear programming framework. Uncertainties expressed as not only probability density functions but also discrete intervals can be reflected. The model can help tackle the dynamic, interactive and uncertain characteristics of the solid waste management system in the City, and can address issues concerning plans for cost-effective waste diversion and landfill prolongation. Three scenarios are considered based on different waste management policies. The results indicate that reasonable solutions have been generated. They are valuable for supporting the adjustment or justification of the existing waste flow allocation patterns, the long-term capacity planning of the City's waste management system, and the formulation of local policies and regulations regarding waste generation and management. PMID:16678336
NASA Astrophysics Data System (ADS)
Noor-E-Alam, Md.; Doucette, John
2015-08-01
Grid-based location problems (GBLPs) can be used to solve location problems in business, engineering, resource exploitation, and even in the field of medical sciences. To solve these decision problems, an integer linear programming (ILP) model is designed and developed to provide the optimal solution for GBLPs considering fixed cost criteria. Preliminary results show that the ILP model is efficient in solving small to moderate-sized problems. However, this ILP model becomes intractable in solving large-scale instances. Therefore, a decomposition heuristic is proposed to solve these large-scale GBLPs, which demonstrates significant reduction of solution runtimes. To benchmark the proposed heuristic, results are compared with the exact solution via ILP. The experimental results show that the proposed method significantly outperforms the exact method in runtime with minimal (and in most cases, no) loss of optimality.
DRIESSEN,BRIAN; SADEGH,NADER
2000-04-25
This work presents a method of finding near global optima to minimum-time trajectory generation problem for systems that would be linear if it were not for the presence of Coloumb friction. The required final state of the system is assumed to be maintainable by the system, and the input bounds are assumed to be large enough so that they can overcome the maximum static Coloumb friction force. Other than the previous work for generating minimum-time trajectories for non redundant robotic manipulators for which the path in joint space is already specified, this work represents, to the best of the authors' knowledge, the first approach for generating near global optima for minimum-time problems involving a nonlinear class of dynamic systems. The reason the optima generated are near global optima instead of exactly global optima is due to a discrete-time approximation of the system (which is usually used anyway to simulate such a system numerically). The method closely resembles previous methods for generating minimum-time trajectories for linear systems, where the core operation is the solution of a Phase I linear programming problem. For the nonlinear systems considered herein, the core operation is instead the solution of a mixed integer linear programming problem.
Baliban, Richard C.; DiMaggio, Peter A.; Plazas-Mayorca, Mariana D.; Young, Nicolas L.; Garcia, Benjamin A.; Floudas, Christodoulos A.
2010-01-01
A novel algorithm, PILOT_PTM, has been developed for the untargeted identification of post-translational modifications (PTMs) on a template sequence. The algorithm consists of an analysis of an MS/MS spectrum via an integer linear optimization model to output a rank-ordered list of PTMs that best match the experimental data. Each MS/MS spectrum is analyzed by a preprocessing algorithm to reduce spectral noise and label potential complimentary, offset, isotope, and multiply charged peaks. Postprocessing of the rank-ordered list from the integer linear optimization model will resolve fragment mass errors and will reorder the list of PTMs based on the cross-correlation between the experimental and theoretical MS/MS spectrum. PILOT_PTM is instrument-independent, capable of handling multiple fragmentation technologies, and can address the universe of PTMs for every amino acid on the template sequence. The various features of PILOT_PTM are presented, and it is tested on several modified and unmodified data sets including chemically synthesized phosphopeptides, histone H3-(1–50) polypeptides, histone H3-(1–50) tryptic fragments, and peptides generated from proteins extracted from chromatin-enriched fractions. The data sets consist of spectra derived from fragmentation via collision-induced dissociation, electron transfer dissociation, and electron capture dissociation. The capability of PILOT_PTM is then benchmarked using five state-of-the-art methods, InsPecT, Virtual Expert Mass Spectrometrist (VEMS), Modi, Mascot, and X!Tandem. PILOT_PTM demonstrates superior accuracy on both the small and large scale proteome experiments. A protocol is finally developed for the analysis of a complete LC-MS/MS scan using template sequences generated from SEQUEST and is demonstrated on over 270,000 MS/MS spectra collected from a total chromatin digest. PMID:20103568
Lee, Dongyul; Lee, Chaewoo
2014-01-01
The advancement in wideband wireless network supports real time services such as IPTV and live video streaming. However, because of the sharing nature of the wireless medium, efficient resource allocation has been studied to achieve a high level of acceptability and proliferation of wireless multimedia. Scalable video coding (SVC) with adaptive modulation and coding (AMC) provides an excellent solution for wireless video streaming. By assigning different modulation and coding schemes (MCSs) to video layers, SVC can provide good video quality to users in good channel conditions and also basic video quality to users in bad channel conditions. For optimal resource allocation, a key issue in applying SVC in the wireless multicast service is how to assign MCSs and the time resources to each SVC layer in the heterogeneous channel condition. We formulate this problem with integer linear programming (ILP) and provide numerical results to show the performance under 802.16 m environment. The result shows that our methodology enhances the overall system throughput compared to an existing algorithm. PMID:25276862
Lee, Chaewoo
2014-01-01
The advancement in wideband wireless network supports real time services such as IPTV and live video streaming. However, because of the sharing nature of the wireless medium, efficient resource allocation has been studied to achieve a high level of acceptability and proliferation of wireless multimedia. Scalable video coding (SVC) with adaptive modulation and coding (AMC) provides an excellent solution for wireless video streaming. By assigning different modulation and coding schemes (MCSs) to video layers, SVC can provide good video quality to users in good channel conditions and also basic video quality to users in bad channel conditions. For optimal resource allocation, a key issue in applying SVC in the wireless multicast service is how to assign MCSs and the time resources to each SVC layer in the heterogeneous channel condition. We formulate this problem with integer linear programming (ILP) and provide numerical results to show the performance under 802.16 m environment. The result shows that our methodology enhances the overall system throughput compared to an existing algorithm. PMID:25276862
Ryan, Jason C; Banerjee, Ashis Gopal; Cummings, Mary L; Roy, Nicholas
2014-06-01
Planning operations across a number of domains can be considered as resource allocation problems with timing constraints. An unexplored instance of such a problem domain is the aircraft carrier flight deck, where, in current operations, replanning is done without the aid of any computerized decision support. Rather, veteran operators employ a set of experience-based heuristics to quickly generate new operating schedules. These expert user heuristics are neither codified nor evaluated by the United States Navy; they have grown solely from the convergent experiences of supervisory staff. As unmanned aerial vehicles (UAVs) are introduced in the aircraft carrier domain, these heuristics may require alterations due to differing capabilities. The inclusion of UAVs also allows for new opportunities for on-line planning and control, providing an alternative to the current heuristic-based replanning methodology. To investigate these issues formally, we have developed a decision support system for flight deck operations that utilizes a conventional integer linear program-based planning algorithm. In this system, a human operator sets both the goals and constraints for the algorithm, which then returns a proposed schedule for operator approval. As a part of validating this system, the performance of this collaborative human-automation planner was compared with that of the expert user heuristics over a set of test scenarios. The resulting analysis shows that human heuristics often outperform the plans produced by an optimization algorithm, but are also often more conservative. PMID:23934675
Li, Jing; Jiang, Tao
2005-01-01
We study the problem of reconstructing haplotype configurations from genotypes on pedigree data with missing alleles under the Mendelian law of inheritance and the minimum-recombination principle, which is important for the construction of haplotype maps and genetic linkage/association analyses. Our previous results show that the problem of finding a minimum-recombinant haplotype configuration (MRHC) is in general NP-hard. This paper presents an effective integer linear programming (ILP) formulation of the MRHC problem with missing data and a branch-and-bound strategy that utilizes a partial order relationship and some other special relationships among variables to decide the branching order. Nontrivial lower and upper bounds on the optimal number of recombinants are introduced at each branching node to effectively prune the search tree. When multiple solutions exist, a best haplotype configuration is selected based on a maximum likelihood approach. The paper also shows for the first time how to incorporate marker interval distance into a rule-based haplotyping algorithm. Our results on simulated data show that the algorithm could recover haplotypes with 50 loci from a pedigree of size 29 in seconds on a Pentium IV computer. Its accuracy is more than 99.8% for data with no missing alleles and 98.3% for data with 20% missing alleles in terms of correctly recovered phase information at each marker locus. A comparison with a statistical approach SimWalk2 on simulated data shows that the ILP algorithm runs much faster than SimWalk2 and reports better or comparable haplotypes on average than the first and second runs of SimWalk2. As an application of the algorithm to real data, we present some test results on reconstructing haplotypes from a genome-scale SNP dataset consisting of 12 pedigrees that have 0.8% to 14.5% missing alleles. PMID:16108713
Zhang, Huiling; Huang, Qingsheng; Bei, Zhendong; Wei, Yanjie; Floudas, Christodoulos A
2016-03-01
In this article, we present COMSAT, a hybrid framework for residue contact prediction of transmembrane (TM) proteins, integrating a support vector machine (SVM) method and a mixed integer linear programming (MILP) method. COMSAT consists of two modules: COMSAT_SVM which is trained mainly on position-specific scoring matrix features, and COMSAT_MILP which is an ab initio method based on optimization models. Contacts predicted by the SVM model are ranked by SVM confidence scores, and a threshold is trained to improve the reliability of the predicted contacts. For TM proteins with no contacts above the threshold, COMSAT_MILP is used. The proposed hybrid contact prediction scheme was tested on two independent TM protein sets based on the contact definition of 14 Å between Cα-Cα atoms. First, using a rigorous leave-one-protein-out cross validation on the training set of 90 TM proteins, an accuracy of 66.8%, a coverage of 12.3%, a specificity of 99.3% and a Matthews' correlation coefficient (MCC) of 0.184 were obtained for residue pairs that are at least six amino acids apart. Second, when tested on a test set of 87 TM proteins, the proposed method showed a prediction accuracy of 64.5%, a coverage of 5.3%, a specificity of 99.4% and a MCC of 0.106. COMSAT shows satisfactory results when compared with 12 other state-of-the-art predictors, and is more robust in terms of prediction accuracy as the length and complexity of TM protein increase. COMSAT is freely accessible at http://hpcc.siat.ac.cn/COMSAT/. PMID:26756402
Alexopoulos, Leonidas G.; Klamt, Steffen
2013-01-01
Cross-referencing experimental data with our current knowledge of signaling network topologies is one central goal of mathematical modeling of cellular signal transduction networks. We present a new methodology for data-driven interrogation and training of signaling networks. While most published methods for signaling network inference operate on Bayesian, Boolean, or ODE models, our approach uses integer linear programming (ILP) on interaction graphs to encode constraints on the qualitative behavior of the nodes. These constraints are posed by the network topology and their formulation as ILP allows us to predict the possible qualitative changes (up, down, no effect) of the activation levels of the nodes for a given stimulus. We provide four basic operations to detect and remove inconsistencies between measurements and predicted behavior: (i) find a topology-consistent explanation for responses of signaling nodes measured in a stimulus-response experiment (if none exists, find the closest explanation); (ii) determine a minimal set of nodes that need to be corrected to make an inconsistent scenario consistent; (iii) determine the optimal subgraph of the given network topology which can best reflect measurements from a set of experimental scenarios; (iv) find possibly missing edges that would improve the consistency of the graph with respect to a set of experimental scenarios the most. We demonstrate the applicability of the proposed approach by interrogating a manually curated interaction graph model of EGFR/ErbB signaling against a library of high-throughput phosphoproteomic data measured in primary hepatocytes. Our methods detect interactions that are likely to be inactive in hepatocytes and provide suggestions for new interactions that, if included, would significantly improve the goodness of fit. Our framework is highly flexible and the underlying model requires only easily accessible biological knowledge. All related algorithms were implemented in a freely
Doolittle, R.
1994-11-15
The title integer anatomy is intended to convey the idea of a systematic method for displaying the prime decomposition of the integers. Just as the biological study of anatomy does not teach us all things about behavior of species neither would we expect to learn everything about the number theory from a study of its anatomy. But, some number-theoretic theorems are illustrated by inspection of integer anatomy, which tend to validate the underlying structure and the form as developed and displayed in this treatise. The first statement to be made in this development is: the way structure of the natural numbers is displayed depends upon the allowed operations.
Linear arrays of InGaAs/InP avalanche photodiodes for 1.0-1.7 micron
NASA Technical Reports Server (NTRS)
Ackley, D. E.; Hladky, J.; Lange, M. J.; Mason, S.; Erickson, G.; Olsen, G. H.; Ban, V. S.; Forrest, S. R.; Staller, C.
1990-01-01
Separate absorption and multiplication InGaAs/InP avalanche photodiodes (SAM-APDs) with a floating guard ring structure that is well-suited to array applications have been successfully demonstrated. Individual APDs have breakdown voltages greater than 80 V, multiplications over 40 at 100 nA dark current, and uniform spatial gain profiles. Uniform I-V characteristics and gains have been measured over linear dimensions as large as 1.2 cm. Gains over 10 at low multiplied dark currents were measured on 21 consecutive devices at the wafer level.
NASA Astrophysics Data System (ADS)
Huang, Shiu-Ming; Yu, Shih-Hsun; Chou, Mitch
2016-08-01
A non-saturating linear magnetoresistance (MR) is observed in Cu0.1Bi2Se3 in a wide range of temperatures. The crossover magnetic field, B*, deviating from the linear MR, increases as the temperature increases. The experimental results show that the normalized B*, inverse MR slope and mobility follow the same temperature dependence that is consistent with the model constructed by Parich and Littlewood (PL model). The mechanism of the T 2 dependent B* is systematically and comprehensively discussed through existing theories, and might be due to the electron‑electron scattering in a highly uniform system with a few low mobility defects.
NASA Astrophysics Data System (ADS)
Guo, P.; Huang, G. H.; Li, Y. P.
2010-01-01
In this study, an inexact fuzzy-chance-constrained two-stage mixed-integer linear programming (IFCTIP) approach is developed for flood diversion planning under multiple uncertainties. A concept of the distribution with fuzzy boundary interval probability is defined to address multiple uncertainties expressed as integration of intervals, fuzzy sets and probability distributions. IFCTIP integrates the inexact programming, two-stage stochastic programming, integer programming and fuzzy-stochastic programming within a general optimization framework. IFCTIP incorporates the pre-regulated water-diversion policies directly into its optimization process to analyze various policy scenarios; each scenario has different economic penalty when the promised targets are violated. More importantly, it can facilitate dynamic programming for decisions of capacity-expansion planning under fuzzy-stochastic conditions. IFCTIP is applied to a flood management system. Solutions from IFCTIP provide desired flood diversion plans with a minimized system cost and a maximized safety level. The results indicate that reasonable solutions are generated for objective function values and decision variables, thus a number of decision alternatives can be generated under different levels of flood flows.
Armutlu, Pelin; Ozdemir, Muhittin E; Uney-Yuksektepe, Fadime; Kavakli, I Halil; Turkay, Metin
2008-01-01
Background A priori analysis of the activity of drugs on the target protein by computational approaches can be useful in narrowing down drug candidates for further experimental tests. Currently, there are a large number of computational methods that predict the activity of drugs on proteins. In this study, we approach the activity prediction problem as a classification problem and, we aim to improve the classification accuracy by introducing an algorithm that combines partial least squares regression with mixed-integer programming based hyper-boxes classification method, where drug molecules are classified as low active or high active regarding their binding activity (IC50 values) on target proteins. We also aim to determine the most significant molecular descriptors for the drug molecules. Results We first apply our approach by analyzing the activities of widely known inhibitor datasets including Acetylcholinesterase (ACHE), Benzodiazepine Receptor (BZR), Dihydrofolate Reductase (DHFR), Cyclooxygenase-2 (COX-2) with known IC50 values. The results at this stage proved that our approach consistently gives better classification accuracies compared to 63 other reported classification methods such as SVM, Naïve Bayes, where we were able to predict the experimentally determined IC50 values with a worst case accuracy of 96%. To further test applicability of this approach we first created dataset for Cytochrome P450 C17 inhibitors and then predicted their activities with 100% accuracy. Conclusion Our results indicate that this approach can be utilized to predict the inhibitory effects of inhibitors based on their molecular descriptors. This approach will not only enhance drug discovery process, but also save time and resources committed. PMID:18834515
Rajgaria, R.; Wei, Y.; Floudas, C. A.
2010-01-01
An integer linear optimization model is presented to predict residue contacts in β, α + β, and α/β proteins. The total energy of a protein is expressed as sum of a Cα – Cα distance dependent contact energy contribution and a hydrophobic contribution. The model selects contacts that assign lowest energy to the protein structure while satisfying a set of constraints that are included to enforce certain physically observed topological information. A new method based on hydrophobicity is proposed to find the β-sheet alignments. These β-sheet alignments are used as constraints for contacts between residues of β-sheets. This model was tested on three independent protein test sets and CASP8 test proteins consisting of β, α + β, α/β proteins and was found to perform very well. The average accuracy of the predictions (separated by at least six residues) was approximately 61%. The average true positive and false positive distances were also calculated for each of the test sets and they are 7.58 Å and 15.88 Å, respectively. Residue contact prediction can be directly used to facilitate the protein tertiary structure prediction. This proposed residue contact prediction model is incorporated into the first principles protein tertiary structure prediction approach, ASTRO-FOLD. The effectiveness of the contact prediction model was further demonstrated by the improvement in the quality of the protein structure ensemble generated using the predicted residue contacts for a test set of 10 proteins. PMID:20225257
2013-01-01
that these constraints can often lead to significant reductions in the gap between the optimal solution and its non-integral linear programming bound relative to the prior art as well as often substantially faster processing of moderately hard problem instances. Conclusion We provide an indication of the conditions under which such an optimal enumeration approach is likely to be feasible, suggesting that these strategies are usable for relatively large numbers of taxa, although with stricter limits on numbers of variable sites. The work thus provides methodology suitable for provably optimal solution of some harder instances that resist all prior approaches. PMID:23343437
ERIC Educational Resources Information Center
Dirks, Michael K.
1984-01-01
The abacus method for instruction on addition, subtraction, and multiplication with integers is explained. How to represent the integers for each operation is detailed with words and illustrations. (MNS)
ERIC Educational Resources Information Center
Pong, Wai Yan
2007-01-01
We begin by answering the question, "Which natural numbers are sums of consecutive integers?" We then go on to explore the set of lengths (numbers of summands) in the decompositions of an integer as such sums.
ERIC Educational Resources Information Center
Siegel, Jonathan W.; Siegel, P. B.
2011-01-01
Integers are sometimes used in physics problems to simplify the mathematics so the arithmetic does not distract students from the physics concepts. This is particularly important in exams where students should not have to spend a lot of time using their calculators. Common uses of integers in physics problems include integer solutions to…
ERIC Educational Resources Information Center
Griffiths, Martin
2011-01-01
One of the author's undergraduate students recently asked him whether it was possible to generate a random positive integer. After some thought, the author realised that there were plenty of interesting mathematical ideas inherent in her question. So much so in fact, that the author decided to organise a workshop, open both to undergraduates and…
Meyers, C A; Schulz, A S
2009-01-07
The integer equal flow problem is an NP-hard network flow problem, in which all arcs in given sets R{sub 1}, ..., R{sub {ell}} must carry equal flow. We show this problem is effectively inapproximable, even if the cardinality of each set R{sub k} is two. When {ell} is fixed, it is solvable in polynomial time.
Aerospace Applications of Integer and Combinatorial Optimization
NASA Technical Reports Server (NTRS)
Padula, S. L.; Kincaid, R. K.
1995-01-01
Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem, for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.
Aerospace applications on integer and combinatorial optimization
NASA Technical Reports Server (NTRS)
Padula, S. L.; Kincaid, R. K.
1995-01-01
Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem. for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.
NASA Astrophysics Data System (ADS)
Patel, Jay Prakash; Senyshyn, Anatoliy; Fuess, Hartmut; Pandey, Dhananjai
2013-09-01
Magnetization, dielectric, and calorimetric studies on Bi0.8 Pb0.2 Fe0.9 Nb0.1O3 (BF-0.2PFN) reveal very weak ferromagnetism but strong dielectric anomaly at the antiferromagnetic transition temperature (TN) characteristic of magnetoelectric coupling. We correlate these results with nuclear and magnetic structure studies using x-ray and neutron powder diffraction techniques, respectively. Rietveld refinements using x-ray powder diffraction data in the temperature range 300 to 673 K reveal pronounced anomalies in the unit cell parameters at TN, indicating strong magnetoelastic coupling. The nuclear and magnetic structures of BF-0.2PFN were determined from neutron powder diffraction data using a representation theory approach. They show the occurrence of a first-order isostructural phase transition (IPT) accompanying the magnetic ordering below TN˜566 K, leading to significant discontinuous change in the ionic polarization (ΔPz˜1.6(3) μC/cm2) and octahedral tilt angle (˜0.3°) at TN. The ionic polarization obtained from refined positional coordinates of the nuclear structure and Born effective charges is shown to scale linearly with sublattice magnetization, confirming the presence of linear magnetoelectric coupling in BF-0.2PFN at the atomic level, despite the very low value of remanent magnetization (Mr).
CRAY-1S integer vector utility library
Rogers, J.N.; Tooman, T.P.
1982-06-01
This report describes thirty-five integer or packed vector utility routines, and documents their testing. These routines perform various vector searches, linear algebra functions, memory resets, and vector boolean operations. They are written in CAL, the assembly language on the CRAY-1S computer. By utilizing the vector processing features of that machine, they are optimized in terms of run time. Each routine has been extensively tested.
Aerospace applications of integer and combinatorial optimization
NASA Technical Reports Server (NTRS)
Padula, S. L.; Kincaid, R. K.
1995-01-01
Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in solving combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem, for example, seeks the optimal locations for vibration-damping devices on a large space structure and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.
Partial integer decorrelation: optimum trade-off between variance reduction and bias amplification
NASA Astrophysics Data System (ADS)
Henkel, Patrick; Günther, Christoph
2010-01-01
Different techniques have been developed for determining carrier phase ambiguities, ranging from float approximations to the efficient solution of the integer least square problem by the LAMBDA method. The focus so far was on double-differenced measurements. Practical implementations of the LAMBDA method lead to a residual probability of wrong fixing of the order one percent. For safety critical applications, this probability had to be reduced by eight orders of magnitude, which could be achieved by linear multi-frequency code-carrier combinations. Scenarios with single or no differences include biases due to orbit errors, satellite clock offsets, as well as residual code and phase biases. For this case, a linear combination of Galileo E1 and E5 code and carrier phase measurements with a wavelength of 3.285 m and a noise level of a few centimeters is derived. This ionosphere-free combination preserves the orbit and clock errors, and suppresses the E1 code multipath by 12.6 dB. Since integer decorrelation transformations, as used in the LAMBDA method, inflate biases, the number of such transformations must be limited, and applied in a judicious order. With a Galileo type constellation, this leads to a vertical standard deviation of ca. 20 cm, while keeping the probability of wrong fixing extremely low for code biases of 10 cm, and phase biases of 0.1 cycle, combined in a worst case.
Investigating data envelopment analysis model with potential improvement for integer output values
NASA Astrophysics Data System (ADS)
Hussain, Mushtaq Taleb; Ramli, Razamin; Khalid, Ruzelan
2015-12-01
The decrement of input proportions in DEA model is associated with its input reduction. This reduction is apparently good for economy since it could reduce unnecessary cost resources. However, in some situations the reduction of relevant inputs such as labour could create social problems. Such inputs should thus be maintained or increased. This paper develops an advanced radial DEA model dealing with mixed integer linear programming to improve integer output values through the combination of inputs. The model can deal with real input values and integer output values. This model is valuable for situations dealing with input combination to improve integer output values as faced by most organizations.
Integer Operations Using a Whiteboard
ERIC Educational Resources Information Center
Andrews, Delise R.
2011-01-01
Interactive whiteboards are somewhat unimpressive at first and look like the whiteboards that already hang on the walls of many classrooms. However, integrating interactive whiteboard technology in a unit on adding and subtracting integers enhances student engagement and understanding. In this article, the author describes how she used an…
Philip, Bobby; Pernice, Michael
2006-09-01
SAMRSolvers is a collection of multilevel solvers for systems of linear equations that result from finite volume discretization of an elliptic partial differential equation on a block-structure (or patch-based) locally refined grid. SAMRSolvers provides implementations of the Fast Adaptive Composite grid (FAC) method, and the AFACx method, which is a less expensive version of AFAC that smooths the error instead of solving for it on all but the coarsest level. These methods can be shown to converge at rates that are independent of the number of refinement levels. SAMRSolvers is intended for use with SAMRAIV2.0 and requires the SAMRUtilities package.
Integers Made Easy: Just Walk It Off
ERIC Educational Resources Information Center
Nurnberger-Haag, Julie
2007-01-01
This article describes a multisensory method for teaching students how to multiply and divide as well as add and subtract integers. The author uses sidewalk chalk and the underlying concept of integers to physically and mentally engage students in understanding the concepts of integers, making connections, and developing computational fluency.…
Energy Science and Technology Software Center (ESTSC)
2006-09-01
SAMRSolvers is a collection of multilevel solvers for systems of linear equations that result from finite volume discretization of an elliptic partial differential equation on a block-structure (or patch-based) locally refined grid. SAMRSolvers provides implementations of the Fast Adaptive Composite grid (FAC) method, and the AFACx method, which is a less expensive version of AFAC that smooths the error instead of solving for it on all but the coarsest level. These methods can be shownmore » to converge at rates that are independent of the number of refinement levels. SAMRSolvers is intended for use with SAMRAIV2.0 and requires the SAMRUtilities package.« less
Order and Value: Transitioning to Integers
ERIC Educational Resources Information Center
Bofferding, Laura
2014-01-01
As students progress from working with whole numbers to working with integers, they must wrestle with the big ideas of number values and order. Using objects to show positive quantities is easy, but no physical negative quantities exist. Therefore, when talking about integers, the author refers to number values instead of number quantities. The…
Prospective Elementary Teachers' Conceptual Understanding of Integers
ERIC Educational Resources Information Center
Reeder, Stacy; Bateiha, Summer
2016-01-01
This investigation examined the degree to which prospective elementary teachers had developed a meaningful and conceptual understanding of what integers are and explored their development of models for multiplication with integers that are related to everyday activities. Additionally, this study explored how these understandings informed…
Molecular solutions to the binary integer programming problem based on DNA computation.
Yeh, Chung-Wei; Chu, Chih-Ping; Wu, Kee-Rong
2006-01-01
Binary optimization is a widely investigated topic in integer linear programming. This study proposes a DNA-based computing algorithm for solving the significantly large binary integer programming (BIP) problem. The proposed approach is based upon Adleman and Lipton's DNA operations to solve the BIP problem. The potential of DNA computation for the BIP problem is promising given the operational time complexity of O(nxk). PMID:16229936
Rational approximations to linear forms of exponentials and binomials
Chudnovsky, G. V.
1983-01-01
Mahler proved the following quantitative result supplementing the Lindemann-Weierstrass theorem: ǀΣi=0nCieriǀ > H-n-ε for any distinct rational numbers r0,r1,..., rn and rational integers C0,C1,...,Cn with H = max0≤i≤n ǀCiǀ. We improve Mahler's estimate by replacing exponentials eri by linearly independent linear forms Li = Σ Lijesij with rational Lij,siji = 0,1,...,n. Similar results are obtained for binomials (a/b)ri or Σ Lij(a/b)sij with integers a,b and logǀbǀ/logǀaǀ > 1 - ε. The simplest examples of new numbers with the irrationality exponent “2 + ε” are sinh 1 or sin 1. PMID:16593320
Code of Federal Regulations, 2012 CFR
2012-01-01
... 16 Commercial Practices 1 2012-01-01 2012-01-01 false The Commission. 0.1 Section 0.1 Commercial Practices FEDERAL TRADE COMMISSION ORGANIZATION, PROCEDURES AND RULES OF PRACTICE ORGANIZATION § 0.1 The Commission. The Federal Trade Commission is an independent administrative agency which was organized in...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 3150.0-1 Section 3150.0-1 Public... Interest Lands Conservation Act (See 50 CFR part 37). ... and Gas Geophysical Exploration; General § 3150.0-1 Purpose. The purpose of this part is to...
Code of Federal Regulations, 2014 CFR
2014-10-01
... 43 Public Lands: Interior 2 2014-10-01 2014-10-01 false Purpose. 3150.0-1 Section 3150.0-1 Public... Interest Lands Conservation Act (See 50 CFR part 37). ... and Gas Geophysical Exploration; General § 3150.0-1 Purpose. The purpose of this part is to...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 3150.0-1 Section 3150.0-1 Public... Interest Lands Conservation Act (See 50 CFR part 37). ... and Gas Geophysical Exploration; General § 3150.0-1 Purpose. The purpose of this part is to...
Code of Federal Regulations, 2012 CFR
2012-04-01
... 26 Internal Revenue 14 2012-04-01 2012-04-01 false Introduction. 25.0-1 Section 25.0-1 Internal...; GIFTS MADE AFTER DECEMBER 31, 1954 Gift Tax § 25.0-1 Introduction. (a) In general. (1) The regulations... Revenue Code of 1954 by Treasury Decision 6091, signed August 16, 1954 (19 FR 5167, Aug. 17, 1954)....
Code of Federal Regulations, 2012 CFR
2012-10-01
... 43 Public Lands: Interior 2 2012-10-01 2012-10-01 false Purpose. 3150.0-1 Section 3150.0-1 Public... Interest Lands Conservation Act (See 50 CFR part 37). ... and Gas Geophysical Exploration; General § 3150.0-1 Purpose. The purpose of this part is to...
Code of Federal Regulations, 2014 CFR
2014-04-01
... 26 Internal Revenue 14 2014-04-01 2013-04-01 true Introduction. 20.0-1 Section 20.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) ESTATE AND GIFT TAXES ESTATE TAX; ESTATES OF DECEDENTS DYING AFTER AUGUST 16, 1954 Introduction § 20.0-1 Introduction. (a) In general. (1) The regulations in this part (part...
Code of Federal Regulations, 2013 CFR
2013-04-01
... 26 Internal Revenue 14 2013-04-01 2013-04-01 false Introduction. 20.0-1 Section 20.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) ESTATE AND GIFT TAXES ESTATE TAX; ESTATES OF DECEDENTS DYING AFTER AUGUST 16, 1954 Introduction § 20.0-1 Introduction. (a) In general. (1) The regulations in this part (part...
28 CFR 0.1 - Organizational units.
Code of Federal Regulations, 2012 CFR
2012-07-01
... Structure of the Department of Justice § 0.1 Organizational units. The Department of Justice shall consist... Register citations affecting § 0.1, see the List of CFR Sections Affected, which appears in the Finding... 28 Judicial Administration 1 2012-07-01 2012-07-01 false Organizational units. 0.1 Section...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 16 Commercial Practices 1 2011-01-01 2011-01-01 false The Commission. 0.1 Section 0.1 Commercial Practices FEDERAL TRADE COMMISSION ORGANIZATION, PROCEDURES AND RULES OF PRACTICE ORGANIZATION § 0.1 The Commission. The Federal Trade Commission is an independent administrative agency which was organized in...
Code of Federal Regulations, 2014 CFR
2014-10-01
... 47 Telecommunication 1 2014-10-01 2014-10-01 false The Commission. 0.1 Section 0.1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL COMMISSION ORGANIZATION Organization General § 0.1 The Commission. The Federal Communications Commission is composed of five (5) members who are appointed by...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 16 Commercial Practices 1 2010-01-01 2010-01-01 false The Commission. 0.1 Section 0.1 Commercial Practices FEDERAL TRADE COMMISSION ORGANIZATION, PROCEDURES AND RULES OF PRACTICE ORGANIZATION § 0.1 The Commission. The Federal Trade Commission is an independent administrative agency which was organized in...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 47 Telecommunication 1 2013-10-01 2013-10-01 false The Commission. 0.1 Section 0.1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL COMMISSION ORGANIZATION Organization General § 0.1 The Commission. The Federal Communications Commission is composed of five (5) members who are appointed by...
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 1 2010-10-01 2010-10-01 false The Commission. 0.1 Section 0.1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL COMMISSION ORGANIZATION Organization General § 0.1 The Commission. The Federal Communications Commission is composed of five (5) members who are appointed by...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 1 2011-10-01 2011-10-01 false The Commission. 0.1 Section 0.1 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL COMMISSION ORGANIZATION Organization General § 0.1 The Commission. The Federal Communications Commission is composed of five (5) members who are appointed by...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 8224.0-1 Section 8224.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS PROCEDURES Fossil Forest Research Natural Area § 8224.0-1...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 8224.0-1 Section 8224.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS PROCEDURES Fossil Forest Research Natural Area § 8224.0-1...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 8365.0-1 Section 8365.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS VISITOR SERVICES Rules of Conduct § 8365.0-1 Purpose. The...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 8200.0-1 Section 8200.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS PROCEDURES General § 8200.0-1 Purpose. This part 8200...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 8351.0-1 Section 8351.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS MANAGEMENT AREAS Designated National Area § 8351.0-1 Purpose....
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 8340.0-1 Section 8340.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS OFF-ROAD VEHICLES General § 8340.0-1 Purpose. The purpose of...
Code of Federal Regulations, 2014 CFR
2014-10-01
... 43 Public Lands: Interior 2 2014-10-01 2014-10-01 false Purpose. 1601.0-1 Section 1601.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR GENERAL MANAGEMENT (1000) PLANNING, PROGRAMMING, BUDGETING Planning § 1601.0-1 Purpose. The purpose of this subpart is to...
Code of Federal Regulations, 2014 CFR
2014-10-01
... 43 Public Lands: Interior 2 2014-10-01 2014-10-01 false Purpose. 2300.0-1 Section 2300.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) LAND WITHDRAWALS Withdrawals, General § 2300.0-1 Purpose. (a) These regulations set...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 8351.0-1 Section 8351.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS MANAGEMENT AREAS Designated National Area § 8351.0-1 Purpose....
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 8365.0-1 Section 8365.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS VISITOR SERVICES Rules of Conduct § 8365.0-1 Purpose. The...
Code of Federal Regulations, 2014 CFR
2014-10-01
... 43 Public Lands: Interior 2 2014-10-01 2014-10-01 false Purpose. 1784.0-1 Section 1784.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR GENERAL MANAGEMENT (1000) COOPERATIVE RELATIONS Advisory Committees § 1784.0-1 Purpose. This subpart contains standards...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 8223.0-1 Section 8223.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS PROCEDURES Research Natural Areas § 8223.0-1 Purpose. The...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 8223.0-1 Section 8223.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS PROCEDURES Research Natural Areas § 8223.0-1 Purpose. The...
Code of Federal Regulations, 2014 CFR
2014-10-01
... 43 Public Lands: Interior 2 2014-10-01 2014-10-01 false Purpose. 2911.0-1 Section 2911.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) LEASES Airport § 2911.0-1 Purpose. This subpart sets forth procedures for issuance of...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 8340.0-1 Section 8340.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS OFF-ROAD VEHICLES General § 8340.0-1 Purpose. The purpose of...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 8200.0-1 Section 8200.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR RECREATION PROGRAMS PROCEDURES General § 8200.0-1 Purpose. This part 8200...
Code of Federal Regulations, 2012 CFR
2012-10-01
... 43 Public Lands: Interior 2 2012-10-01 2012-10-01 false Purpose. 2911.0-1 Section 2911.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) LEASES Airport § 2911.0-1 Purpose. This subpart...
Code of Federal Regulations, 2010 CFR
2010-04-01
... 26 Internal Revenue 15 2010-04-01 2010-04-01 false Introduction. 31.0-1 Section 31.0-1 Internal... OF INCOME TAX AT SOURCE EMPLOYMENT TAXES AND COLLECTION OF INCOME TAX AT SOURCE Introduction § 31.0-1 Introduction. (a) In general. The regulations in this part relate to the employment taxes imposed by subtitle...
Code of Federal Regulations, 2010 CFR
2010-04-01
... 26 Internal Revenue 16 2010-04-01 2010-04-01 true Introduction. 44.0-1 Section 44.0-1 Internal... ON WAGERING; EFFECTIVE JANUARY 1, 1955 Introduction § 44.0-1 Introduction. (a) In general. The... provisions of subtitle F of the Code (Procedure and Administration) which have special application to...
Integer cosine transform for image compression
NASA Technical Reports Server (NTRS)
Cheung, K.-M.; Pollara, F.; Shahshahani, M.
1991-01-01
This article describes a recently introduced transform algorithm called the integer cosine transform (ICT), which is used in transform-based data compression schemes. The ICT algorithm requires only integer operations on small integers and at the same time gives a rate-distortion performance comparable to that offered by the floating-point discrete cosine transform (DCT). The article addresses the issue of implementation complexity, which is of prime concern for source coding applications of interest in deep-space communications. Complexity reduction in the transform stage of the compression scheme is particularly relevant, since this stage accounts for most (typically over 80 percent) of the computational load.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 26 Internal Revenue 14 2011-04-01 2010-04-01 true Introduction. 25.0-1 Section 25.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) ESTATE AND GIFT TAXES GIFT TAX; GIFTS MADE AFTER DECEMBER 31, 1954 Gift Tax § 25.0-1 Introduction. (a) In general. (1) The regulations in this part are designated “Gift...
Code of Federal Regulations, 2013 CFR
2013-04-01
... 26 Internal Revenue 14 2013-04-01 2013-04-01 false Introduction. 25.0-1 Section 25.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) ESTATE AND GIFT TAXES GIFT TAX; GIFTS MADE AFTER DECEMBER 31, 1954 Gift Tax § 25.0-1 Introduction. (a) In general. (1) The regulations in this part are designated “Gift...
Code of Federal Regulations, 2014 CFR
2014-04-01
... 26 Internal Revenue 14 2014-04-01 2013-04-01 true Introduction. 25.0-1 Section 25.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) ESTATE AND GIFT TAXES GIFT TAX; GIFTS MADE AFTER DECEMBER 31, 1954 Gift Tax § 25.0-1 Introduction. (a) In general. (1) The regulations in this part are designated “Gift...
Code of Federal Regulations, 2010 CFR
2010-04-01
... 26 Internal Revenue 14 2010-04-01 2010-04-01 false Introduction. 25.0-1 Section 25.0-1 Internal...; GIFTS MADE AFTER DECEMBER 31, 1954 Gift Tax § 25.0-1 Introduction. (a) In general. (1) The regulations... pursuant to Subchapter C are set forth in §§ 25.2521-1 through 25.2524-1. (4) Procedure and...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 1601.0-1 Section 1601.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR GENERAL MANAGEMENT (1000) PLANNING, PROGRAMMING, BUDGETING Planning §...
Code of Federal Regulations, 2011 CFR
2011-10-01
... transfer of certain public lands under the Recreation and Public Purposes Act as amended (43 U.S.C. 869 et... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Purpose. 2740.0-1 Section 2740.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT,...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 2300.0-1 Section 2300.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) LAND WITHDRAWALS Withdrawals, General §...
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
Code of Federal Regulations, 2012 CFR
2012-10-01
... 43 Public Lands: Interior 2 2012-10-01 2012-10-01 false Purpose. 2300.0-1 Section 2300.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) LAND WITHDRAWALS Withdrawals, General §...
Code of Federal Regulations, 2012 CFR
2012-10-01
... 43 Public Lands: Interior 2 2012-10-01 2012-10-01 false Purpose. 1601.0-1 Section 1601.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT... for public lands administered by the Bureau of Land Management....
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Purpose. 1601.0-1 Section 1601.0-1 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR GENERAL MANAGEMENT (1000) PLANNING, PROGRAMMING, BUDGETING Planning §...
Solution of Mixed-Integer Programming Problems on the XT5
Hartman-Baker, Rebecca J; Busch, Ingrid Karin; Hilliard, Michael R; Middleton, Richard S; Schultze, Michael
2009-01-01
In this paper, we describe our experience with solving difficult mixed-integer linear programming problems (MILPs) on the petaflop Cray XT5 system at the National Center for Computational Sciences at Oak Ridge National Laboratory. We describe the algorithmic, software, and hardware needs for solving MILPs and present the results of using PICO, an open-source, parallel, mixed-integer linear programming solver developed at Sandia National Laboratories, to solve canonical MILPs as well as problems of interest arising from the logistics and supply chain management field.
Code of Federal Regulations, 2012 CFR
2012-10-01
... OF THE INTERIOR TECHNICAL SERVICES (9000) FIRE MANAGEMENT Wildfire Prevention § 9212.0-1 Purpose. The purpose of this subpart is to set forth procedures to prevent wildfires on the public lands....
Code of Federal Regulations, 2011 CFR
2011-10-01
... OF THE INTERIOR TECHNICAL SERVICES (9000) FIRE MANAGEMENT Wildfire Prevention § 9212.0-1 Purpose. The purpose of this subpart is to set forth procedures to prevent wildfires on the public lands....
Code of Federal Regulations, 2014 CFR
2014-10-01
... OF THE INTERIOR TECHNICAL SERVICES (9000) FIRE MANAGEMENT Wildfire Prevention § 9212.0-1 Purpose. The purpose of this subpart is to set forth procedures to prevent wildfires on the public lands....
Code of Federal Regulations, 2013 CFR
2013-10-01
... OF THE INTERIOR TECHNICAL SERVICES (9000) FIRE MANAGEMENT Wildfire Prevention § 9212.0-1 Purpose. The purpose of this subpart is to set forth procedures to prevent wildfires on the public lands....
Code of Federal Regulations, 2011 CFR
2011-10-01
... HORSES AND BURROS General § 4700.0-1 Purpose. The purpose of these regulations is to implement the laws relating to the protection, management, and control of wild horses and burros under the administration...
Code of Federal Regulations, 2013 CFR
2013-10-01
... OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) DESERT-LAND ENTRIES Desert-Land Entries: General § 2520.0-1 Purpose. (a) It is the purpose of the statutes governing desert-land entries to encourage...
Code of Federal Regulations, 2011 CFR
2011-10-01
... OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) DESERT-LAND ENTRIES Desert-Land Entries: General § 2520.0-1 Purpose. (a) It is the purpose of the statutes governing desert-land entries to encourage...
Code of Federal Regulations, 2014 CFR
2014-10-01
... OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) DESERT-LAND ENTRIES Desert-Land Entries: General § 2520.0-1 Purpose. (a) It is the purpose of the statutes governing desert-land entries to encourage...
Code of Federal Regulations, 2012 CFR
2012-10-01
... OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) DESERT-LAND ENTRIES Desert-Land Entries: General § 2520.0-1 Purpose. (a) It is the purpose of the statutes governing desert-land entries to encourage...
Code of Federal Regulations, 2014 CFR
2014-10-01
... HORSES AND BURROS General § 4700.0-1 Purpose. The purpose of these regulations is to implement the laws relating to the protection, management, and control of wild horses and burros under the administration...
Slip and Slide Method of Factoring Trinomials with Integer Coefficients over the Integers
ERIC Educational Resources Information Center
Donnell, William A.
2012-01-01
In intermediate and college algebra courses there are a number of methods for factoring quadratic trinomials with integer coefficients over the integers. Some of these methods have been given names, such as trial and error, reversing FOIL, AC method, middle term splitting method and slip and slide method. The purpose of this article is to discuss…
RSM 1.0 - A RESUPPLY SCHEDULER USING INTEGER OPTIMIZATION
NASA Technical Reports Server (NTRS)
Viterna, L. A.
1994-01-01
RSM, Resupply Scheduling Modeler, is a fully menu-driven program that uses integer programming techniques to determine an optimum schedule for replacing components on or before the end of a fixed replacement period. Although written to analyze the electrical power system on the Space Station Freedom, RSM is quite general and can be used to model the resupply of almost any system subject to user-defined resource constraints. RSM is based on a specific form of the general linear programming problem in which all variables in the objective function and all variables in the constraints are integers. While more computationally intensive, integer programming was required for accuracy when modeling systems with small quantities of components. Input values for component life cane be real numbers, RSM converts them to integers by dividing the lifetime by the period duration, then reducing the result to the next lowest integer. For each component, there is a set of constraints that insure that it is replaced before its lifetime expires. RSM includes user-defined constraints such as transportation mass and volume limits, as well as component life, available repair crew time and assembly sequences. A weighting factor allows the program to minimize factors such as cost. The program then performs an iterative analysis, which is displayed during the processing. A message gives the first period in which resources are being exceeded on each iteration. If the scheduling problem is unfeasible, the final message will also indicate the first period in which resources were exceeded. RSM is written in APL2 for IBM PC series computers and compatibles. A stand-alone executable version of RSM is provided; however, this is a "packed" version of RSM which can only utilize the memory within the 640K DOS limit. This executable requires at least 640K of memory and DOS 3.1 or higher. Source code for an APL2/PC workspace version is also provided. This version of RSM can make full use of any
Integer Solutions of a Special Diophantine Equation
NASA Astrophysics Data System (ADS)
Özkoç, Arzu; Tekcan, Ahmet
2011-09-01
Let t≠1 be an integer. In this work, we determine the integer solutions of Diophantine equation D:x2+(2-t2)y2+(-2t2-2t+2)x+(2t5-6t3+4t)y-t8+4t6-4t4+2t3+t2-2t = 0 over Z and also over finite fields Fp for primes p≥2. Also we derive some recurrence relations on the integer solutions (xn,yn) of D and formulate the the n—th solution (xn,yn) by using the simple continued fraction expansion of xn/yn.
PSLQ: An Algorithm to Discover Integer Relations
Bailey, David H.; Borwein, J. M.
2009-04-03
Let x = (x{sub 1}, x{sub 2} {hor_ellipsis}, x{sub n}) be a vector of real or complex numbers. x is said to possess an integer relation if there exist integers a{sub i}, not all zero, such that a{sub 1}x{sub 1} + a{sub 2}x{sub 2} + {hor_ellipsis} + a{sub n}x{sub n} = 0. By an integer relation algorithm, we mean a practical computational scheme that can recover the vector of integers ai, if it exists, or can produce bounds within which no integer relation exists. As we will see in the examples below, an integer relation algorithm can be used to recognize a computed constant in terms of a formula involving known constants, or to discover an underlying relation between quantities that can be computed to high precision. At the present time, the most effective algorithm for integer relation detection is the 'PSLQ' algorithm of mathematician-sculptor Helaman Ferguson [10, 4]. Some efficient 'multi-level' implementations of PSLQ, as well as a variant of PSLQ that is well-suited for highly parallel computer systems, are given in [4]. PSLQ constructs a sequence of integer-valued matrices B{sub n} that reduces the vector y = xB{sub n}, until either the relation is found (as one of the columns of B{sub n}), or else precision is exhausted. At the same time, PSLQ generates a steadily growing bound on the size of any possible relation. When a relation is found, the size of smallest entry of the vector y abruptly drops to roughly 'epsilon' (i.e. 10{sup -p}, where p is the number of digits of precision). The size of this drop can be viewed as a 'confidence level' that the relation is real and not merely a numerical artifact - a drop of 20 or more orders of magnitude almost always indicates a real relation. Very high precision arithmetic must be used in PSLQ. If one wishes to recover a relation of length n, with coefficients of maximum size d digits, then the input vector x must be specified to at least nd digits, and one must employ nd-digit floating-point arithmetic. Maple and
Reducing Truncation Error In Integer Processing
NASA Technical Reports Server (NTRS)
Thomas, J. Brooks; Berner, Jeffrey B.; Graham, J. Scott
1995-01-01
Improved method of rounding off (truncation of least-significant bits) in integer processing of data devised. Provides for reduction, to extremely low value, of numerical bias otherwise generated by accumulation of truncation errors from many arithmetic operations. Devised for use in integer signal processing, in which rescaling and truncation usually performed to reduce number of bits, which typically builds up in sequence of operations. Essence of method to alternate direction of roundoff (plus, then minus) on alternate occurrences of truncated values contributing to bias.
Theory of the Half-integer Quantum Hall Effect in Graphene
NASA Astrophysics Data System (ADS)
Fujita, Shigeji; Suzuki, Akira
2016-08-01
The unusual quantum Hall effect (QHE) in graphene is described in terms of the composite (c-) bosons, which move with a linear dispersion relation. The "electron" (wave packet) moves easier in the direction [1 1 0 c-axis] ≡ [1 1 0] of the honeycomb lattice than perpendicular to it, while the "hole" moves easier in [0 0 1]. Since "electrons" and "holes" move in different channels, the particle densities can be high especially when the Fermi surface has "necks". The strong QHE arises from the phonon exchange attraction in the neighborhood of the "neck" surfaces. The plateau observed for the Hall conductivity and the accompanied resistivity drop is due to the superconducting energy gap caused by the Bose-Einstein condensation of the c-bosons, each forming from a pair of one-electron-two-fluxons c-fermions by phonon-exchange attraction. The half-integer quantization rule for the Hall conductivity: (1/2)(2P-1)(4e 2/h), P=1,2,..., is derived.
Code of Federal Regulations, 2011 CFR
2011-10-01
... OF THE INTERIOR MINERALS MANAGEMENT (3000) LEASING IN SPECIAL TAR SAND AREAS Leasing in Special Tar Sand Areas § 3141.0-1 Purpose. The purpose of this subpart is to provide for the competitive leasing of lands and issuance of Combined Hydrocarbon Leases, Oil and Gas Leases, or Tar Sand Leases within...
Code of Federal Regulations, 2012 CFR
2012-10-01
... OF THE INTERIOR MINERALS MANAGEMENT (3000) LEASING IN SPECIAL TAR SAND AREAS Leasing in Special Tar Sand Areas § 3141.0-1 Purpose. The purpose of this subpart is to provide for the competitive leasing of lands and issuance of Combined Hydrocarbon Leases, Oil and Gas Leases, or Tar Sand Leases within...
Code of Federal Regulations, 2014 CFR
2014-10-01
... OF THE INTERIOR MINERALS MANAGEMENT (3000) LEASING IN SPECIAL TAR SAND AREAS Leasing in Special Tar Sand Areas § 3141.0-1 Purpose. The purpose of this subpart is to provide for the competitive leasing of lands and issuance of Combined Hydrocarbon Leases, Oil and Gas Leases, or Tar Sand Leases within...
Code of Federal Regulations, 2013 CFR
2013-10-01
... OF THE INTERIOR MINERALS MANAGEMENT (3000) LEASING IN SPECIAL TAR SAND AREAS Leasing in Special Tar Sand Areas § 3141.0-1 Purpose. The purpose of this subpart is to provide for the competitive leasing of lands and issuance of Combined Hydrocarbon Leases, Oil and Gas Leases, or Tar Sand Leases within...
Code of Federal Regulations, 2010 CFR
2010-04-01
...; ESTATES OF DECEDENTS DYING AFTER AUGUST 16, 1954 Introduction § 20.0-1 Introduction. (a) In general. (1... dying after August 16, 1954, and (ii) certain related administrative provisions of subtitle F of the... provided, the Estate Tax Regulations are applicable to the estates of decedents dying after August 16,...
Code of Federal Regulations, 2011 CFR
2011-04-01
...; ESTATES OF DECEDENTS DYING AFTER AUGUST 16, 1954 Introduction § 20.0-1 Introduction. (a) In general. (1... dying after August 16, 1954, and (ii) certain related administrative provisions of subtitle F of the... provided, the Estate Tax Regulations are applicable to the estates of decedents dying after August 16,...
Code of Federal Regulations, 2012 CFR
2012-04-01
...; ESTATES OF DECEDENTS DYING AFTER AUGUST 16, 1954 Introduction § 20.0-1 Introduction. (a) In general. (1... dying after August 16, 1954, and (ii) certain related administrative provisions of subtitle F of the... provided, the Estate Tax Regulations are applicable to the estates of decedents dying after August 16,...
Code of Federal Regulations, 2014 CFR
2014-10-01
... and Mining, Wilderness Review Program § 3802.0-1 Purpose. The purpose of this subpart is to establish procedures to prevent impairment of the suitability of lands under wilderness review for inclusion in the wilderness system and to prevent unnecessary or undue degradation by activities authorized by the U.S....
Code of Federal Regulations, 2012 CFR
2012-10-01
... and Mining, Wilderness Review Program § 3802.0-1 Purpose. The purpose of this subpart is to establish procedures to prevent impairment of the suitability of lands under wilderness review for inclusion in the wilderness system and to prevent unnecessary or undue degradation by activities authorized by the U.S....
Code of Federal Regulations, 2013 CFR
2013-10-01
... and Mining, Wilderness Review Program § 3802.0-1 Purpose. The purpose of this subpart is to establish procedures to prevent impairment of the suitability of lands under wilderness review for inclusion in the wilderness system and to prevent unnecessary or undue degradation by activities authorized by the U.S....
Code of Federal Regulations, 2011 CFR
2011-10-01
... and Mining, Wilderness Review Program § 3802.0-1 Purpose. The purpose of this subpart is to establish procedures to prevent impairment of the suitability of lands under wilderness review for inclusion in the wilderness system and to prevent unnecessary or undue degradation by activities authorized by the U.S....
Semiperfect and Integer-Perfect Numbers.
ERIC Educational Resources Information Center
Costello, Patrick
1991-01-01
The number theory concepts of perfect, deficient, and abundant numbers are subdivided and then utilized to discuss propositions concerning semiperfect, weird, and integer-perfect numbers. Conjectures about relationships among these latter numbers are suggested as avenues for further investigation. (JJK)
Dollars & Sense: Students' Integer Perspectives
ERIC Educational Resources Information Center
Whitacre, Ian; Bishop, Jessica Pierson; Philipp, Randolph A.; Lamb, Lisa L.; Schappelle, Bonnie P.
2014-01-01
A story problem about borrowing money, presented in this article, may be represented with positive or negative numbers and thought about in different ways. The authors describe ideas related to integers (both positive and negative) and how students used them in relation to a story problem, and how they related these ideas to equations.
How to Differentiate an Integer Modulo n
ERIC Educational Resources Information Center
Emmons, Caleb; Krebs, Mike; Shaheen, Anthony
2009-01-01
A number derivative is a numerical mapping that satisfies the product rule. In this paper, we determine all number derivatives on the set of integers modulo n. We also give a list of undergraduate research projects to pursue using these maps as a starting point.
Mixed integer evolution strategies for parameter optimization.
Li, Rui; Emmerich, Michael T M; Eggermont, Jeroen; Bäck, Thomas; Schütz, M; Dijkstra, J; Reiber, J H C
2013-01-01
Evolution strategies (ESs) are powerful probabilistic search and optimization algorithms gleaned from biological evolution theory. They have been successfully applied to a wide range of real world applications. The modern ESs are mainly designed for solving continuous parameter optimization problems. Their ability to adapt the parameters of the multivariate normal distribution used for mutation during the optimization run makes them well suited for this domain. In this article we describe and study mixed integer evolution strategies (MIES), which are natural extensions of ES for mixed integer optimization problems. MIES can deal with parameter vectors consisting not only of continuous variables but also with nominal discrete and integer variables. Following the design principles of the canonical evolution strategies, they use specialized mutation operators tailored for the aforementioned mixed parameter classes. For each type of variable, the choice of mutation operators is governed by a natural metric for this variable type, maximal entropy, and symmetry considerations. All distributions used for mutation can be controlled in their shape by means of scaling parameters, allowing self-adaptation to be implemented. After introducing and motivating the conceptual design of the MIES, we study the optimality of the self-adaptation of step sizes and mutation rates on a generalized (weighted) sphere model. Moreover, we prove global convergence of the MIES on a very general class of problems. The remainder of the article is devoted to performance studies on artificial landscapes (barrier functions and mixed integer NK landscapes), and a case study in the optimization of medical image analysis systems. In addition, we show that with proper constraint handling techniques, MIES can also be applied to classical mixed integer nonlinear programming problems. PMID:22122384
Multi-objective mixed integer strategy for the optimisation of biological networks.
Sendín, J O H; Exler, O; Banga, J R
2010-05-01
In this contribution, the authors consider multi-criteria optimisation problems arising from the field of systems biology when both continuous and integer decision variables are involved. Mathematically, they are formulated as mixed-integer non-linear programming problems. The authors present a novel solution strategy based on a global optimisation approach for dealing with this class of problems. Its usefulness and capabilities are illustrated with two metabolic engineering case studies. For these problems, the authors show how the set of optimal solutions (the so-called Pareto front) is successfully and efficiently obtained, providing further insight into the systems under consideration regarding their optimal manipulation. PMID:20500003
ALPS - A LINEAR PROGRAM SOLVER
NASA Technical Reports Server (NTRS)
Viterna, L. A.
1994-01-01
Linear programming is a widely-used engineering and management tool. Scheduling, resource allocation, and production planning are all well-known applications of linear programs (LP's). Most LP's are too large to be solved by hand, so over the decades many computer codes for solving LP's have been developed. ALPS, A Linear Program Solver, is a full-featured LP analysis program. ALPS can solve plain linear programs as well as more complicated mixed integer and pure integer programs. ALPS also contains an efficient solution technique for pure binary (0-1 integer) programs. One of the many weaknesses of LP solvers is the lack of interaction with the user. ALPS is a menu-driven program with no special commands or keywords to learn. In addition, ALPS contains a full-screen editor to enter and maintain the LP formulation. These formulations can be written to and read from plain ASCII files for portability. For those less experienced in LP formulation, ALPS contains a problem "parser" which checks the formulation for errors. ALPS creates fully formatted, readable reports that can be sent to a printer or output file. ALPS is written entirely in IBM's APL2/PC product, Version 1.01. The APL2 workspace containing all the ALPS code can be run on any APL2/PC system (AT or 386). On a 32-bit system, this configuration can take advantage of all extended memory. The user can also examine and modify the ALPS code. The APL2 workspace has also been "packed" to be run on any DOS system (without APL2) as a stand-alone "EXE" file, but has limited memory capacity on a 640K system. A numeric coprocessor (80X87) is optional but recommended. The standard distribution medium for ALPS is a 5.25 inch 360K MS-DOS format diskette. IBM, IBM PC and IBM APL2 are registered trademarks of International Business Machines Corporation. MS-DOS is a registered trademark of Microsoft Corporation.
Slip and slide method of factoring trinomials with integer coefficients over the integers
NASA Astrophysics Data System (ADS)
Donnell, William A.
2012-06-01
In intermediate and college algebra courses there are a number of methods for factoring quadratic trinomials with integer coefficients over the integers. Some of these methods have been given names, such as trial and error, reversing FOIL, AC method, middle term splitting method and slip and slide method. The purpose of this article is to discuss the Slip and Slide Method and present a theoretical justification of why it works.
On the computation of the best integer equivariant estimator
NASA Astrophysics Data System (ADS)
Teunissen, P. J. G.
Carrier phase integer ambiguity resolution is the key to high precision Global Navigation Satellite System (GNSS) positioning and navigation. In this contribution we study some of the computational aspects of best integer equivariant estimation. The best integer equivariant (BIE) estimator is the optimal estimator of the class of integer equivariant estimators, which is one of the three classes of estimators for carrier phase ambiguity resolution. The two other classes are the class of integer estimators and the class of integer aperture estimators. Since the BIE-estimator can not be computed exactly, it is shown how to approximate this estimator while retaining the property of integer equivariance. It is also shown how the decorrelating Z-transformation and the integer search of the LAMBDA method can be used to speed up the computation of the BIE-estimator.
Currency arbitrage detection using a binary integer programming model
NASA Astrophysics Data System (ADS)
Soon, Wanmei; Ye, Heng-Qing
2011-04-01
In this article, we examine the use of a new binary integer programming (BIP) model to detect arbitrage opportunities in currency exchanges. This model showcases an excellent application of mathematics to the real world. The concepts involved are easily accessible to undergraduate students with basic knowledge in Operations Research. Through this work, students can learn to link several types of basic optimization models, namely linear programming, integer programming and network models, and apply the well-known sensitivity analysis procedure to accommodate realistic changes in the exchange rates. Beginning with a BIP model, we discuss how it can be reduced to an equivalent but considerably simpler model, where an efficient algorithm can be applied to find the arbitrages and incorporate the sensitivity analysis procedure. A simple comparison is then made with a different arbitrage detection model. This exercise helps students learn to apply basic Operations Research concepts to a practical real-life example, and provides insights into the processes involved in Operations Research model formulations.
Unlimited Capacity Parallel Quantity Comparison of Multiple Integers
ERIC Educational Resources Information Center
Blanc-Goldhammer, Daryn R.; Cohen, Dale J.
2014-01-01
Research has shown that integer comparison is quick and efficient. This efficiency may be a function of the structure of the integer comparison system. The present study tests whether integers are compared with an unlimited capacity system or a limited capacity system. We tested these models using a visual search task with time delimitation. The…
Integer sparse distributed memory: analysis and results.
Snaider, Javier; Franklin, Stan; Strain, Steve; George, E Olusegun
2013-10-01
Sparse distributed memory is an auto-associative memory system that stores high dimensional Boolean vectors. Here we present an extension of the original SDM, the Integer SDM that uses modular arithmetic integer vectors rather than binary vectors. This extension preserves many of the desirable properties of the original SDM: auto-associativity, content addressability, distributed storage, and robustness over noisy inputs. In addition, it improves the representation capabilities of the memory and is more robust over normalization. It can also be extended to support forgetting and reliable sequence storage. We performed several simulations that test the noise robustness property and capacity of the memory. Theoretical analyses of the memory's fidelity and capacity are also presented. PMID:23747569
Resupply Scheduler Program Using Integer Optimization
NASA Technical Reports Server (NTRS)
Viterna, L. A.; Reed, D. M.
1994-01-01
Resupply Scheduling Modeler (RSM) fully menu-driven computer program using integer programming techniques to determine optimum schedule for replacing components on or before ends of fixed replacement periods. Written to analyze electrical power system on Space Station Freedom, also used to model resupply of almost any system subject to user-defined constraints on resources. Lifetimes of components, assembly schedules, and other constraints taken into account. Written in APL2(R).
Trimpl, M.; Yarema, R.; Newcomer, M.; Dressnandt, N.; Villani, G.; Weber, M.; Holt, R.; /Rutherford
2011-05-01
This document describes the Serial Powering Interface (SPi) ASIC. SPi is a general purpose ASIC prototype designed for use in serial powering of silicon detector instrumentation. This description is written as a user manual to aid application, not as a design description. SPi is a generic custom ASIC, manufactured in 0.25 {mu}m CMOS by TSMC, to interface between a constant current source and silicon detector read-out chips. There is no SEU (single event upset) protection, but most (not all) components are radiation tolerant design. An operating voltage of 1.2 to 2.5 volts and other design features make the IC suitable for a variety of serial powering architectures and ROICs. It should be noted that the device is likely to be a prototype for demonstration rather than a product for inclusion in a detector. The next design(s), SPin, are likely to be designed for a specific application (eg SLHC). The component includes: (1) Seven bi-directional LVDS-like buffers for high data rate links to/from the read-out chips. These are AC coupled (series capacitor) off-chip for DC level conversion; (2) A programmable internal programmable shunt regulator to provide a defined voltage to readout chips when linked in a serial powering chain; (3) A programmable internal shunt regulator control circuit for external transistor control; (4) Shunt current measurement (for internal shunt regulator); (5) A programmable internal shunt regulator current alarm; and (6) Two programmable linear regulators.
Horizontal visibility graphs from integer sequences
NASA Astrophysics Data System (ADS)
Lacasa, Lucas
2016-09-01
The horizontal visibility graph (HVG) is a graph-theoretical representation of a time series and builds a bridge between dynamical systems and graph theory. In recent years this representation has been used to describe and theoretically compare different types of dynamics and has been applied to characterize empirical signals, by extracting topological features from the associated HVGs which have shown to be informative on the class of dynamics. Among some other measures, it has been shown that the degree distribution of these graphs is a very informative feature that encapsulates nontrivial information of the series's generative dynamics. In particular, the HVG associated to a bi-infinite real-valued series of independent and identically distributed random variables is a universal exponential law P(k)=(1/3){(2/3)}k-2, independent of the series marginal distribution. Most of the current applications have however only addressed real-valued time series, as no exact results are known for the topological properties of HVGs associated to integer-valued series. In this paper we explore this latter situation and address univariate time series where each variable can only take a finite number n of consecutive integer values. We are able to construct an explicit formula for the parametric degree distribution {P}n(k), which we prove to converge to the continuous case for large n and deviates otherwise. A few applications are then considered.
Topologically induced fractional Hall steps in the integer quantum Hall regime of MoS 2.
Islam, S K Firoz; Benjamin, Colin
2016-09-23
The quantum magnetotransport properties of a monolayer of molybdenum disulfide are derived using linear response theory. In particular, the effect of topological terms on longitudinal and Hall conductivity is analyzed. The Hall conductivity exhibits fractional steps in the integer quantum Hall regime. Further complete spin and valley polarization of the longitudinal conductivitity is seen in presence of these topological terms. Finally, the Shubnikov-de Hass oscillations are suppressed or enhanced contingent on the sign of these topological terms. PMID:27533362
Solving Integer Programming Problems by Using Artificial Bee Colony Algorithm
NASA Astrophysics Data System (ADS)
Akay, Bahriye; Karaboga, Dervis
This paper presents a study that applies the Artificial Bee Colony algorithm to integer programming problems and compares its performance with those of Particle Swarm Optimization algorithm variants and Branch and Bound technique presented to the literature. In order to cope with integer programming problems, in neighbour solution production unit, solutions are truncated to the nearest integer values. The experimental results show that Artificial Bee Colony algorithm can handle integer programming problems efficiently and Artificial Bee Colony algorithm can be considered to be very robust by the statistics calculated such as mean, median, standard deviation.
NASA Technical Reports Server (NTRS)
Ferencz, Donald C.; Viterna, Larry A.
1991-01-01
ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.
Menu-Driven Solver Of Linear-Programming Problems
NASA Technical Reports Server (NTRS)
Viterna, L. A.; Ferencz, D.
1992-01-01
Program assists inexperienced user in formulating linear-programming problems. A Linear Program Solver (ALPS) computer program is full-featured LP analysis program. Solves plain linear-programming problems as well as more-complicated mixed-integer and pure-integer programs. Also contains efficient technique for solution of purely binary linear-programming problems. Written entirely in IBM's APL2/PC software, Version 1.01. Packed program contains licensed material, property of IBM (copyright 1988, all rights reserved).
Camera placement in integer lattices (extended abstract)
NASA Astrophysics Data System (ADS)
Pocchiola, Michel; Kranakis, Evangelos
1990-09-01
Techniques for studying an art gallery problem (the camera placement problem) in the infinite lattice (L sup d) of d tuples of integers are considered. A lattice point A is visible from a camera C positioned at a vertex of (L sup d) if A does not equal C and if the line segment joining A and C crosses no other lattice vertex. By using a combination of probabilistic, combinatorial optimization and algorithmic techniques the position they must occupy in the lattice (L sup d) in the order to maximize their visibility can be determined in polynomial time, for any given number s less than or equal to (5 sup d) of cameras. This improves previous results for s less than or equal to (3 sup d).
NASA Astrophysics Data System (ADS)
Pratheep Kumar, Sathasivam; Gopal, Buvaneswari
2015-03-01
In this work, incorporation of hexavalent molybdenum and selected trivalent lanthanides using divalent calcium as charge compensator into the monazite structure were studied. Rare earth substituted phosphomolybdates of the formula REE0.9Ca0.1P0.9Mo0.1O4 (REE = Ce, Nd, Sm, Gd) and the wasteform La0.4Nd0.1Y0.1Gd0.1Sm0.1Ce0.1Ca0.1P0.9Mo0.1O4 were synthesized by simple solution route. The prepared compounds were characterized by powder X-ray diffraction, Fourier transformed infrared spectra, thermogravimetric analysis, energy dispersive X-ray analysis and scanning electron microscopic techniques. Chemical durability of the wasteform was studied by dynamic MCC-5 test for a period of one month. Normalized elemental mass loss and leach rate of molybdenum was found to be in the order of 103 g/m2 and 103-101 g/m2/d respectively. Polymer-monazite composite wasteform was prepared to control the leaching of molybdenum. The composite approach reduced molybdenum leach rate order from 101 to 10-4 g/m2/d.
A Proposed Instructional Theory for Integer Addition and Subtraction
ERIC Educational Resources Information Center
Stephan, Michelle; Akyuz, Didem
2012-01-01
This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional…
Certain integers related to Ankeny-Artin-Chowla conjecture
NASA Astrophysics Data System (ADS)
Hashimoto, RyÅ«ta
2008-01-01
Let d be a non-square integer which is congruent to 1 modulo 4. Let t and u be the fundamental solution of the diophantine equation X2-dY2 = -4. A family of integers d satisfying d
Improving integer ambiguity resolution for GLONASS precise orbit determination
NASA Astrophysics Data System (ADS)
Liu, Yang; Ge, Maorong; Shi, Chuang; Lou, Yidong; Wickert, Jens; Schuh, Harald
2016-05-01
The frequency division multiple access adopted in present GLONASS introduces inter-frequency bias (IFB) at the receiver-end both in code and phase observables, which makes GLONASS ambiguity resolution rather difficult or even not available, especially for long baselines up to several thousand kilometers. This is one of the major reasons that GLONASS could hardly reach the orbit precision of GPS, both in terms of consistency among individual International GNSS Service (IGS) analysis centers and discontinuity at the overlapping day boundaries. Based on the fact that the GLONASS phase IFB is similar on L1 and L2 bands in unit of length and is a linear function of the frequency number, several approaches have been developed to estimate and calibrate the IFB for integer ambiguity resolution. However, they are only for short and medium baselines. In this study, a new ambiguity resolution approach is developed for GLONASS global networks. In the approach, the phase ambiguities in the ionosphere-free linear combination are directly transformed with a wavelength of about 5.3 cm, according to the special frequency relationship of GLONASS L1 and L2 signals. After such transformation, the phase IFB rate can be estimated and corrected precisely and then the corresponding double-differenced ambiguities can be directly fixed to integers even for baselines up to several thousand kilometers. To evaluate this approach, experimental validations using one-month data of a global network with 140 IGS stations was carried out for GLONASS precise orbit determination. The results show that the GLONASS double-difference ambiguity resolution for long baselines could be achieved with an average fixing-rate of 91.4 %. Applying the fixed ambiguities as constraints, the GLONASS orbit overlapping RMS at the day boundaries could be reduced by 37.2 % in ideal cases and with an averaged reduction of about 21.4 %, which is comparable with that by the GPS ambiguity resolution. The orbit improvement is
Improving integer ambiguity resolution for GLONASS precise orbit determination
NASA Astrophysics Data System (ADS)
Liu, Yang; Ge, Maorong; Shi, Chuang; Lou, Yidong; Wickert, Jens; Schuh, Harald
2016-08-01
The frequency division multiple access adopted in present GLONASS introduces inter-frequency bias (IFB) at the receiver-end both in code and phase observables, which makes GLONASS ambiguity resolution rather difficult or even not available, especially for long baselines up to several thousand kilometers. This is one of the major reasons that GLONASS could hardly reach the orbit precision of GPS, both in terms of consistency among individual International GNSS Service (IGS) analysis centers and discontinuity at the overlapping day boundaries. Based on the fact that the GLONASS phase IFB is similar on L1 and L2 bands in unit of length and is a linear function of the frequency number, several approaches have been developed to estimate and calibrate the IFB for integer ambiguity resolution. However, they are only for short and medium baselines. In this study, a new ambiguity resolution approach is developed for GLONASS global networks. In the approach, the phase ambiguities in the ionosphere-free linear combination are directly transformed with a wavelength of about 5.3 cm, according to the special frequency relationship of GLONASS L1 and L2 signals. After such transformation, the phase IFB rate can be estimated and corrected precisely and then the corresponding double-differenced ambiguities can be directly fixed to integers even for baselines up to several thousand kilometers. To evaluate this approach, experimental validations using one-month data of a global network with 140 IGS stations was carried out for GLONASS precise orbit determination. The results show that the GLONASS double-difference ambiguity resolution for long baselines could be achieved with an average fixing-rate of 91.4 %. Applying the fixed ambiguities as constraints, the GLONASS orbit overlapping RMS at the day boundaries could be reduced by 37.2 % in ideal cases and with an averaged reduction of about 21.4 %, which is comparable with that by the GPS ambiguity resolution. The orbit improvement is
Polynomial-time algorithms for the integer minimal principle for centrosymmetric structures.
Vaia, Anastasia; Sahinidis, Nikolaos V
2005-07-01
The minimal principle for structure determination from single-crystal X-ray diffraction measurements has recently been formulated as an integer linear optimization model for the case of centrosymmetric structures. Solution of this model via established combinatorial branch-and-bound algorithms provides the true global minimum of the minimal principle while operating exclusively in reciprocal space. However, integer programming techniques may require an exponential number of iterations to exhaust the search space. In this paper, a new approach is developed to solve the integer minimal principle to global optimality without requiring the solution of an optimization problem. Instead, properties of the solution of the optimization problem, as observed in a large number of computational experiments, are exploited in order to reduce the optimization formulation to a system of linear equations in the number field of two elements (F(2)). Two specialized Gaussian elimination algorithms are then developed to solve this system of equations in polynomial time in the number of atoms. Computational results on a collection of 38 structures demonstrate that the proposed approach provides very fast and accurate solutions to the phase problem for centrosymmetric structures. This approach also provided much better crystallographic R values than SHELXS for all 38 structures tested. PMID:15972998
Harmonic oscillator states with integer and non-integer orbital angular momentum
NASA Astrophysics Data System (ADS)
Land, Martin
2011-12-01
We study the quantum mechanical harmonic oscillator in two and three dimensions, with particular attention to the solutions as basis states for representing their respective symmetry groups — O(2), O(1,1), O(3), and O(2,1). The goal of this study is to establish a correspondence between Hilbert space descriptions found by solving the Schrodinger equation in polar coordinates, and Fock space descriptions constructed by expressing the symmetry operators in terms of creation/annihilation operators. We obtain wavefunctions characterized by a principal quantum number, the group Casimir eigenvalue, and one group generator whose eigenvalue is m + s, for integer m and real constant parameter s. For the three groups that contain O(2), the solutions split into two inequivalent representations, one associated with s = 0, from which we recover the familiar description of the oscillator as a product of one-dimensional solutions, and the other with s > 0 (in three dimensions, solutions are found for s = 0 and s = 1/2) whose solutions are non-separable in Cartesian coordinates, and are hence overlooked by the standard Fock space approach. The O(1,1) solutions are singlet states, restricted to zero eigenvalue of the symmetry operator, which represents the boost, not angular momentum. For O(2), a single set of creation and annihilation operators forms a ladder representation for the allowed oscillator states for any s, and the degeneracy of energy states is always finite. However, in three dimensions, the integer and half-integer eigenstates are qualitatively different: the former can be expressed as finite dimensional irreducible tensors under O(3) or O(2,1) while the latter exhibit infinite degeneracy. Creation operators that produce the allowed integer states by acting on the non-degenerate ground state are constructed as irreducible tensor products of the fundamental vector representation. However, the half-integer eigenstates are infinite-dimensional, as expected for the non
Stacking-sequence optimization for buckling of laminated plates by integer programming
NASA Technical Reports Server (NTRS)
Haftka, Raphael T.; Walsh, Joanne L.
1991-01-01
Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily available software. This is in contrast to the continuous case, where the design variables are the thicknesses of layers with specified ply orientations, and the optimization problem is nonlinear. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm.
Smart-Grid Backbone Network Real-Time Delay Reduction via Integer Programming.
Pagadrai, Sasikanth; Yilmaz, Muhittin; Valluri, Pratyush
2016-08-01
This research investigates an optimal delay-based virtual topology design using integer linear programming (ILP), which is applied to the current backbone networks such as smart-grid real-time communication systems. A network traffic matrix is applied and the corresponding virtual topology problem is solved using the ILP formulations that include a network delay-dependent objective function and lightpath routing, wavelength assignment, wavelength continuity, flow routing, and traffic loss constraints. The proposed optimization approach provides an efficient deterministic integration of intelligent sensing and decision making, and network learning features for superior smart grid operations by adaptively responding the time-varying network traffic data as well as operational constraints to maintain optimal virtual topologies. A representative optical backbone network has been utilized to demonstrate the proposed optimization framework whose simulation results indicate that superior smart-grid network performance can be achieved using commercial networks and integer programming. PMID:25935050
The integer quantum hall effect revisited
Michalakis, Spyridon; Hastings, Matthew
2009-01-01
For T - L x L a finite subset of Z{sup 2}, let H{sub o} denote a Hamiltonian on T with periodic boundary conditions and finite range, finite strength intetactions and a unique ground state with a nonvanishing spectral gap. For S {element_of} T, let q{sub s} denote the charge at site s and assume that the total charge Q = {Sigma}{sub s {element_of} T} q{sub s} is conserved. Using the local charge operators q{sub s}, we introduce a boundary magnetic flux in the horizontal and vertical direction and allow the ground state to evolve quasiadiabatically around a square of size one magnetic flux, in flux space. At the end of the evolution we obtain a trivial Berry phase, which we compare, via a method reminiscent of Stokes Theorem. to the Berry phase obtained from an evolution around an exponentially small loop near the origin. As a result, we show, without any averaging assumption, that the Hall conductance is quantized in integer multiples of e{sup 2}/h up to exponentially small corrections of order e{sup -L/{zeta}}, where {zeta}, is a correlation length that depends only on the gap and the range and strength of the interactions.
Mixed-Integer Formulations for Constellation Scheduling
NASA Astrophysics Data System (ADS)
Valicka, C.; Hart, W.; Rintoul, M.
Remote sensing systems have expanded the set of capabilities available for and critical to national security. Cooperating, high-fidelity sensing systems and growing mission applications have exponentially increased the set of potential schedules. A definitive lack of advanced tools places an increased burden on operators, as planning and scheduling remain largely manual tasks. This is particularly true in time-critical planning activities where operators aim to accomplish a large number of missions through optimal utilization of single or multiple sensor systems. Automated scheduling through identification and comparison of alternative schedules remains a challenging problem applicable across all remote sensing systems. Previous approaches focused on a subset of sensor missions and do not consider ad-hoc tasking. We have begun development of a robust framework that leverages the Pyomo optimization modeling language for the design of a tool to assist sensor operators planning under the constraints of multiple concurrent missions and uncertainty. Our scheduling models have been formulated to address the stochastic nature of ad-hoc tasks inserted under a variety of scenarios. Operator experience is being leveraged to select appropriate model objectives. Successful development of the framework will include iterative development of high-fidelity mission models that consider and expose various schedule performance metrics. Creating this tool will aid time-critical scheduling by increasing planning efficiency, clarifying the value of alternative modalities uniquely provided by multi-sensor systems, and by presenting both sets of organized information to operators. Such a tool will help operators more quickly and fully utilize sensing systems, a high interest objective within the current remote sensing operations community. Preliminary results for mixed-integer programming formulations of a sensor scheduling problem will be presented. Assumptions regarding sensor geometry
A review of «integer PPP» applications
NASA Astrophysics Data System (ADS)
Perosanz, Felix; Mercier, Flavien; Loyer, Sylvain; Petit, Gérard; Marty, Jean-Charles
2016-04-01
The possibility of fixing GNSS phase observations to integer values in PPP mode has been demonstrated by several authors. Various scientific and commercial services have started offering this option. In this presentation we first summarize the mathematical formalism needed to recover integer ambiguities while processing un-differenced GNSS phase observations. The improvements but also the limitations of "integer PPP" (IPPP) solutions are discussed. Then we make a review of several scientific results based on this method to illustrate its wide field of applications like oceanic buoy tracking, glacier deformation, atomic oscillator frequency transfer, LEO satellite orbit determination. Several ideas for future improvement are also discussed including the recommendation to IGS Analysis Centers to adopt a compatible approach to deliver "integer" clock products for a combined solution that would allow for IPPP solutions.
Computer Corner: Spreadsheets, Power Series, Generating Functions, and Integers.
ERIC Educational Resources Information Center
Snow, Donald R.
1989-01-01
Implements a table algorithm on a spreadsheet program and obtains functions for several number sequences such as the Fibonacci and Catalan numbers. Considers other applications of the table algorithm to integers represented in various number bases. (YP)
Integer aperture ambiguity resolution based on difference test
NASA Astrophysics Data System (ADS)
Zhang, Jingyu; Wu, Meiping; Li, Tao; Zhang, Kaidong
2015-07-01
Carrier-phase integer ambiguity resolution (IAR) is the key to highly precise, fast positioning and attitude determination with Global Navigation Satellite System (GNSS). It can be seen as the process of estimating the unknown cycle ambiguities of the carrier-phase observations as integers. Once the ambiguities are fixed, carrier phase data will act as the very precise range data. Integer aperture (IA) ambiguity resolution is the combination of acceptance testing and integer ambiguity resolution, which can realize better quality control of IAR. Difference test (DT) is one of the most popular acceptance tests. This contribution will give a detailed analysis about the following properties of IA ambiguity resolution based on DT: 1.
Fractal electrodynamics via non-integer dimensional space approach
NASA Astrophysics Data System (ADS)
Tarasov, Vasily E.
2015-09-01
Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.
Adaptive Source Coding Schemes for Geometrically Distributed Integer Alphabets
NASA Technical Reports Server (NTRS)
Cheung, K-M.; Smyth, P.
1993-01-01
Revisit the Gallager and van Voorhis optimal source coding scheme for geometrically distributed non-negative integer alphabets and show that the various subcodes in the popular Rice algorithm can be derived from the Gallager and van Voorhis code.
Linear systems of equations solved using mathematical algorithms
NASA Technical Reports Server (NTRS)
Bareiss, E. H.
1968-01-01
New mathematical algorithm solves linear systems of equations, AX equals B, and preserves the integer properties of the coefficients. The algorithms presented can also be used for the efficient evaluation of determinates and their leading minors.
A Class of Integer Order and Fractional Order Hyperchaotic Systems via the Chen System
NASA Astrophysics Data System (ADS)
Xu, Fei
2016-06-01
In this article, we investigate the generation of a class of hyperchaotic systems via the Chen chaotic system using both integer order and fractional order differential equation systems. Based on the Chen chaotic system, we designed a system with four nonlinear ordinary differential equations. For different parameter sets, the trajectory of the system may diverge or display a hyperchaotic attractor with double wings. By linearizing the ordinary differential equation system with divergent trajectory and designing proper switching controls, we obtain a chaotic attractor. Similar phenomenon has also been observed in linearizing the hyperchaotic system. The corresponding fractional order systems are also considered. Our investigation indicates that, switching control can be applied to either linearized chaotic or nonchaotic differential equation systems to create chaotic attractor.
Non-integer expansion embedding techniques for reversible image watermarking
NASA Astrophysics Data System (ADS)
Xiang, Shijun; Wang, Yi
2015-12-01
This work aims at reducing the embedding distortion of prediction-error expansion (PE)-based reversible watermarking. In the classical PE embedding method proposed by Thodi and Rodriguez, the predicted value is rounded to integer number for integer prediction-error expansion (IPE) embedding. The rounding operation makes a constraint on a predictor's performance. In this paper, we propose a non-integer PE (NIPE) embedding approach, which can proceed non-integer prediction errors for embedding data into an audio or image file by only expanding integer element of a prediction error while keeping its fractional element unchanged. The advantage of the NIPE embedding technique is that the NIPE technique can really bring a predictor into full play by estimating a sample/pixel in a noncausal way in a single pass since there is no rounding operation. A new noncausal image prediction method to estimate a pixel with four immediate pixels in a single pass is included in the proposed scheme. The proposed noncausal image predictor can provide better performance than Sachnev et al.'s noncausal double-set prediction method (where data prediction in two passes brings a distortion problem due to the fact that half of the pixels were predicted with the watermarked pixels). In comparison with existing several state-of-the-art works, experimental results have shown that the NIPE technique with the new noncausal prediction strategy can reduce the embedding distortion for the same embedding payload.
A Polynomial Time, Numerically Stable Integer Relation Algorithm
NASA Technical Reports Server (NTRS)
Ferguson, Helaman R. P.; Bailey, Daivd H.; Kutler, Paul (Technical Monitor)
1998-01-01
Let x = (x1, x2...,xn be a vector of real numbers. X is said to possess an integer relation if there exist integers a(sub i) not all zero such that a1x1 + a2x2 + ... a(sub n)Xn = 0. Beginning in 1977 several algorithms (with proofs) have been discovered to recover the a(sub i) given x. The most efficient of these existing integer relation algorithms (in terms of run time and the precision required of the input) has the drawback of being very unstable numerically. It often requires a numeric precision level in the thousands of digits to reliably recover relations in modest-sized test problems. We present here a new algorithm for finding integer relations, which we have named the "PSLQ" algorithm. It is proved in this paper that the PSLQ algorithm terminates with a relation in a number of iterations that is bounded by a polynomial in it. Because this algorithm employs a numerically stable matrix reduction procedure, it is free from the numerical difficulties, that plague other integer relation algorithms. Furthermore, its stability admits an efficient implementation with lower run times oil average than other algorithms currently in Use. Finally, this stability can be used to prove that relation bounds obtained from computer runs using this algorithm are numerically accurate.
Estimating Tree-Structured Covariance Matrices via Mixed-Integer Programming
Bravo, Héctor Corrada; Wright, Stephen; Eng, Kevin H.; Keles, Sündüz; Wahba, Grace
2011-01-01
We present a novel method for estimating tree-structured covariance matrices directly from observed continuous data. Specifically, we estimate a covariance matrix from observations of p continuous random variables encoding a stochastic process over a tree with p leaves. A representation of these classes of matrices as linear combinations of rank-one matrices indicating object partitions is used to formulate estimation as instances of well-studied numerical optimization problems. In particular, our estimates are based on projection, where the covariance estimate is the nearest tree-structured covariance matrix to an observed sample covariance matrix. The problem is posed as a linear or quadratic mixed-integer program (MIP) where a setting of the integer variables in the MIP specifies a set of tree topologies of the structured covariance matrix. We solve these problems to optimality using efficient and robust existing MIP solvers. We present a case study in phylogenetic analysis of gene expression and a simulation study comparing our method to distance-based tree estimating procedures. PMID:22081761
Bosonic Integer Quantum Hall Effect in Optical Flux Lattices
NASA Astrophysics Data System (ADS)
Sterdyniak, A.; Cooper, Nigel R.; Regnault, N.
2015-09-01
In two dimensions strongly interacting bosons in a magnetic field can realize a bosonic integer quantum Hall state, the simplest two-dimensional example of a symmetry-protected topological phase. We propose a realistic implementation of this phase using an optical flux lattice. Through exact diagonalization calculations, we show that the system exhibits a clear bulk gap and the topological signature of the bosonic integer quantum Hall state. In particular, the calculation of the many-body Chern number leads to a quantized Hall conductance in agreement with the analytical predictions. We also study the stability of the phase with respect to some of the experimentally relevant parameters.
FPGA Implementation of Optimal 3D-Integer DCT Structure for Video Compression
Jacob, J. Augustin; Kumar, N. Senthil
2015-01-01
A novel optimal structure for implementing 3D-integer discrete cosine transform (DCT) is presented by analyzing various integer approximation methods. The integer set with reduced mean squared error (MSE) and high coding efficiency are considered for implementation in FPGA. The proposed method proves that the least resources are utilized for the integer set that has shorter bit values. Optimal 3D-integer DCT structure is determined by analyzing the MSE, power dissipation, coding efficiency, and hardware complexity of different integer sets. The experimental results reveal that direct method of computing the 3D-integer DCT using the integer set [10, 9, 6, 2, 3, 1, 1] performs better when compared to other integer sets in terms of resource utilization and power dissipation. PMID:26601120
FPGA Implementation of Optimal 3D-Integer DCT Structure for Video Compression.
Jacob, J Augustin; Kumar, N Senthil
2015-01-01
A novel optimal structure for implementing 3D-integer discrete cosine transform (DCT) is presented by analyzing various integer approximation methods. The integer set with reduced mean squared error (MSE) and high coding efficiency are considered for implementation in FPGA. The proposed method proves that the least resources are utilized for the integer set that has shorter bit values. Optimal 3D-integer DCT structure is determined by analyzing the MSE, power dissipation, coding efficiency, and hardware complexity of different integer sets. The experimental results reveal that direct method of computing the 3D-integer DCT using the integer set [10, 9, 6, 2, 3, 1, 1] performs better when compared to other integer sets in terms of resource utilization and power dissipation. PMID:26601120
A fast DFT algorithm using complex integer transforms
NASA Technical Reports Server (NTRS)
Reed, I. S.; Truong, T. K.
1978-01-01
Winograd's algorithm for computing the discrete Fourier transform is extended considerably for certain large transform lengths. This is accomplished by performing the cyclic convolution, required by Winograd's method, by a fast transform over certain complex integer fields. This algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithms.
INTEGER ELEVATION MODEL GRIDS FOR US EPA REGION 9
Integer Digital Elevation Models in GRID format for the mainland US administrative boundary of the US EPA Region 9 developed from the United States Geological Survey (USGS) National Elevation Dataset (NED). The administrative boundary is represented by the state boundaries of Ca...
Using Set Model for Learning Addition of Integers
ERIC Educational Resources Information Center
Lestari, Umi Puji; Putri, Ratu Ilma Indra; Hartono, Yusuf
2015-01-01
This study aims to investigate how set model can help students' understanding of addition of integers in fourth grade. The study has been carried out to 23 students and a teacher of IVC SD Iba Palembang in January 2015. This study is a design research that also promotes PMRI as the underlying design context and activity. Results showed that the…
Negative Integer Understanding: Characterizing First Graders' Mental Models
ERIC Educational Resources Information Center
Bofferding, Laura
2014-01-01
This article presents results of a research study. Sixty-one first graders' responses to interview questions about negative integer values and order and directed magnitudes were examined to characterize the students' mental models. The models reveal that initially, students overrelied on various combinations of whole-number principles as…
Optimizing a Library's Loan Policy: An Integer Programming Approach.
ERIC Educational Resources Information Center
Al-Fares, Hesham K.
1998-01-01
Discusses the length of library loan periods and the number of books allowed to be borrowed. An integer programming model is formulated whose solution yields the optimum user satisfaction, and a case study conducted at King Fahd University of Petroleum and Minerals (Saudi Arabia) is presented. (Author/LRW)
Unique Factorization in Cyclotomic Integers of Degree Seven
ERIC Educational Resources Information Center
Duckworth, W. Ethan
2008-01-01
This article provides a survey of some basic results in algebraic number theory and applies this material to prove that the cyclotomic integers generated by a seventh root of unity are a unique factorization domain. Part of the proof uses the computer algebra system Maple to find and verify factorizations. The proofs use a combination of historic…
Informing Practice: Making Sense of Integers through Storytelling
ERIC Educational Resources Information Center
Wessman-Enzinger, Nicole M.; Mooney, Edward S.
2014-01-01
The authors asked fifth-grade and eighth-grade students to pose stories for number sentences involving the addition and subtraction of integers. In this article, the authors look at eight stories from students. Which of these stories works for the given number sentence? What do they reveal about student thinking? When the authors examined these…
Using the Finite Difference Calculus to Sum Powers of Integers.
ERIC Educational Resources Information Center
Zia, Lee
1991-01-01
Summing powers of integers is presented as an example of finite differences and antidifferences in discrete mathematics. The interrelation between these concepts and their analogues in differential calculus, the derivative and integral, is illustrated and can form the groundwork for students' understanding of differential and integral calculus.…
Happy and Sad Thoughts: An Exploration of Children's Integer Reasoning
ERIC Educational Resources Information Center
Whitacre, Ian; Bishop, Jessica Pierson; Lamb, Lisa L. C.; Philipp, Randolph A.; Schappelle, Bonnie P.; Lewis, Melinda L.
2012-01-01
The purpose of this study was to investigate elementary children's conceptions that might serve as foundations for integer reasoning. Working from an abstract algebraic perspective and using an opposite-magnitudes context that is relevant to children, we analyzed the reasoning of 33 children in grades K-5. We focus our report on three prominent…
Orbital rendezvous mission planning using mixed integer nonlinear programming
NASA Astrophysics Data System (ADS)
Zhang, Jin; Tang, Guo-jin; Luo, Ya-Zhong; Li, Hai-yang
2011-04-01
The rendezvous and docking mission is usually divided into several phases, and the mission planning is performed phase by phase. A new planning method using mixed integer nonlinear programming, which investigates single phase parameters and phase connecting parameters simultaneously, is proposed to improve the rendezvous mission's overall performance. The design variables are composed of integers and continuous-valued numbers. The integer part consists of the parameters for station-keeping and sensor-switching, the number of maneuvers in each rendezvous phase and the number of repeating periods to start the rendezvous mission. The continuous part consists of the orbital transfer time and the station-keeping duration. The objective function is a combination of the propellant consumed, the sun angle which represents the power available, and the terminal precision of each rendezvous phase. The operational requirements for the spacecraft-ground communication, sun illumination and the sensor transition are considered. The simple genetic algorithm, which is a combination of the integer-coded and real-coded genetic algorithm, is chosen to obtain the optimal solution. A practical rendezvous mission planning problem is solved by the proposed method. The results show that the method proposed can solve the integral rendezvous mission planning problem effectively, and the solution obtained can satisfy the operational constraints and has a good overall performance.
Triangular Numbers, Gaussian Integers, and KenKen
ERIC Educational Resources Information Center
Watkins, John J.
2012-01-01
Latin squares form the basis for the recreational puzzles sudoku and KenKen. In this article we show how useful several ideas from number theory are in solving a KenKen puzzle. For example, the simple notion of triangular number is surprisingly effective. We also introduce a variation of KenKen that uses the Gaussian integers in order to…
Leveraging Structure: Logical Necessity in the Context of Integer Arithmetic
ERIC Educational Resources Information Center
Bishop, Jessica Pierson; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P.
2016-01-01
Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…
Currency Arbitrage Detection Using a Binary Integer Programming Model
ERIC Educational Resources Information Center
Soon, Wanmei; Ye, Heng-Qing
2011-01-01
In this article, we examine the use of a new binary integer programming (BIP) model to detect arbitrage opportunities in currency exchanges. This model showcases an excellent application of mathematics to the real world. The concepts involved are easily accessible to undergraduate students with basic knowledge in Operations Research. Through this…
Exploring the Sums of Powers of Consecutive q-Integers
ERIC Educational Resources Information Center
Kim, T.; Ryoo, C. S.; Jang, L. C.; Rim, S. H.
2005-01-01
The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They first appeared in the posthumous work "Ars Conjectandi" (1713) by Jacob Bernoulli (1654-1705) in connection with sums of powers of consecutive integers (Bernoulli, 1713; or Smith, 1959). Bernoulli numbers are particularly important in number…
Automorphisms of semigroups of invertible matrices with nonnegative integer elements
Semenov, Pavel P
2012-09-30
Let G{sub n}(Z) be the subsemigroup of GL{sub n}(Z) consisting of the matrices with nonnegative integer coefficients. In the paper, the automorphisms of this semigroup are described for n{>=}2. Bibliography: 5 titles.
Solving the Water Jugs Problem by an Integer Sequence Approach
ERIC Educational Resources Information Center
Man, Yiu-Kwong
2012-01-01
In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and…
NASA Astrophysics Data System (ADS)
Yang, Shuyu; Zamora, Gilberto; Wilson, Mark; Mitra, Sunanda
2000-06-01
Existing lossless coding models yield only up to 3:1 compression. However, a much higher lossless compression can be achieved for certain medical images when the images are segmented prior to applying integer to integer wavelet transform and lossless coding. The methodology used in this research work is to apply a contour detection scheme to segment the image first. The segmented image is then wavelet transformed with integer to integer mapping to obtain a lower weighted entropy than the original. An adaptive arithmetic model is then applied to code the transformed image losslessly. For the male visible human color image set, the overall average lossless compression using the above scheme is around 10:1 whereas the compression ratio of an individual slice can be as high as 16:1. The achievable compression ratio depends on the actual bit rate of the segmented images attained by lossless coding as well as the compression obtainable from segmentation alone. The computational time required by the entire process is fast enough for application on large medical images.
Kaur, Imanpreet Verma, N. K.
2015-05-15
Multiferroic nanocomposite of (Bi{sub 0.1}Fe{sub 0.1}O{sub 3}) - (Ni{sub 0.1}Fe{sub 2(0.1)}O{sub 4}) was prepared by sol gel technique and characterized by X-ray diffraction, transmission electron microscopy, superconducting quantum interference device. X-ray diffraction confirmed the formation of desired crystallographic phase of the composite. The average particle size found to be 13.97nm. The transmission electron microscopy depicts the presence of the polycrystalline nanoparticles. In order to investigate the magnetic behavior superconducting quantum interference device was used. The sample was analyzed by increasing the magnetic field up to 25kOe and magnetization was found to be 16.8emu/g, which is optimum for the technological applications. The magnetic properties in such composite result as determined both by the ferrite concentration and properties and by the degree of connectivity of the two phases. The appropriate combination of two phases gives rise to higher magnetization.
Spin analysis of 0+1-->0+1 and its application to π+d-->π+d data
NASA Astrophysics Data System (ADS)
Arash, Firooz; Moravcsik, Michael J.; Goldstein, Gary R.
1985-11-01
The polarization structure of the reaction 0+1-->0+1 is discussed in the optimal transversity frame. First, the relationship between the observables and the bilinear products of amplitudes (``bicoms'') is given when only Lorentz invariance is imposed. Then parity conservation and time-reversal invariance are also imposed, resulting in modified relationships. The measurements of spin correlations between initial- and final-state spins needed to determine the amplitudes completely are enumerated. The results are applied to the existing π-d data, and the consequences of any possible dibaryon resonances are examined.
ERIC Educational Resources Information Center
Bolyard, Johnna; Moyer-Packenham, Patricia
2012-01-01
This study investigated how the use of virtual manipulatives in integer instruction impacts student achievement for integer addition and subtraction. Of particular interest was the influence of using virtual manipulatives on students' ability to create and translate among representations for integer computation. The research employed a…
A Note on the Visibility in the [1, N ] x [1, N ] Integer Domain
ERIC Educational Resources Information Center
Kim, G. D.; Engelhardt, J.
2007-01-01
A k-dimensional integer point is called visible if the line segment joining the point and the origin contains no proper integer points. This note proposes an explicit formula that represents the number of visible points on the two-dimensional [1,N]x[1,N] integer domain. Simulations and theoretical work are presented. (Contains 5 figures and 2…
A first digit theorem for powerful integer powers.
Hürlimann, Werner
2015-01-01
For any fixed power exponent, it is shown that the first digits of powerful integer powers follow a generalized Benford law (GBL) with size-dependent exponent that converges asymptotically to a GBL with the inverse double power exponent. In particular, asymptotically as the power goes to infinity these sequences obey Benford's law. Moreover, the existence of a one-parametric size-dependent exponent function that converges to these GBL's is established, and an optimal value that minimizes its deviation to two minimum estimators of the size-dependent exponent is determined. The latter is undertaken over the finite range of powerful integer powers less than [Formula: see text], where [Formula: see text] is a fixed power exponent. PMID:26543711
Two dimensional convolute integers for machine vision and image recognition
NASA Technical Reports Server (NTRS)
Edwards, Thomas R.
1988-01-01
Machine vision and image recognition require sophisticated image processing prior to the application of Artificial Intelligence. Two Dimensional Convolute Integer Technology is an innovative mathematical approach for addressing machine vision and image recognition. This new technology generates a family of digital operators for addressing optical images and related two dimensional data sets. The operators are regression generated, integer valued, zero phase shifting, convoluting, frequency sensitive, two dimensional low pass, high pass and band pass filters that are mathematically equivalent to surface fitted partial derivatives. These operators are applied non-recursively either as classical convolutions (replacement point values), interstitial point generators (bandwidth broadening or resolution enhancement), or as missing value calculators (compensation for dead array element values). These operators show frequency sensitive feature selection scale invariant properties. Such tasks as boundary/edge enhancement and noise or small size pixel disturbance removal can readily be accomplished. For feature selection tight band pass operators are essential. Results from test cases are given.
Integer-ambiguity resolution in astronomy and geodesy
NASA Astrophysics Data System (ADS)
Lannes, A.; Prieur, J.-L.
2014-02-01
Recent theoretical developments in astronomical aperture synthesis have revealed the existence of integer-ambiguity problems. Those problems, which appear in the self-calibration procedures of radio imaging, have been shown to be similar to the nearest-lattice point (NLP) problems encountered in high-precision geodetic positioning and in global navigation satellite systems. In this paper we analyse the theoretical aspects of the matter and propose new methods for solving those NLP~problems. The related optimization aspects concern both the preconditioning stage, and the discrete-search stage in which the integer ambiguities are finally fixed. Our algorithms, which are described in an explicit manner, can easily be implemented. They lead to substantial gains in the processing time of both stages. Their efficiency was shown via intensive numerical tests.
Factorization of large integers on a massively parallel computer
Davis, J.A.; Holdridge, D.B.
1988-01-01
Our interest in integer factorization at Sandia National Laboratories is motivated by cryptographic applications and in particular the security of the RSA encryption-decryption algorithm. We have implemented our version of the quadratic sieve procedure on the NCUBE computer with 1024 processors (nodes). The new code is significantly different in all important aspects from the program used to factor number of order 10/sup 70/ on a single processor CRAY computer. Capabilities of parallel processing and limitation of small local memory necessitated this entirely new implementation. This effort involved several restarts as realizations of program structures that seemed appealing bogged down due to inter-processor communications. We are presently working with integers of magnitude about 10/sup 70/ in tuning this code to the novel hardware. 6 refs., 3 figs.
Two-dimensional convolute integers for analytical instrumentation
NASA Technical Reports Server (NTRS)
Edwards, T. R.
1982-01-01
As new analytical instruments and techniques emerge with increased dimensionality, a corresponding need is seen for data processing logic which can appropriately address the data. Two-dimensional measurements reveal enhanced unknown mixture analysis capability as a result of the greater spectral information content over two one-dimensional methods taken separately. It is noted that two-dimensional convolute integers are merely an extension of the work by Savitzky and Golay (1964). It is shown that these low-pass, high-pass and band-pass digital filters are truly two-dimensional and that they can be applied in a manner identical with their one-dimensional counterpart, that is, a weighted nearest-neighbor, moving average with zero phase shifting, convoluted integer (universal number) weighting coefficients.
SCIAMACHY: The new Level 0-1 Processor
NASA Astrophysics Data System (ADS)
Lichtenberg, Günter; Slijkhuis, Sander; Aberle, Bernd; Sherbakov, Denis; Meringer, Markus; Noel, Stefan; Bramstedt, Klaus; Liebing, Patricia; Bovensmann, Heinrich; Snel, Ralph; Krijger, Mathijs; van Hees, Richard; van der Meer, Pieter; Lerot, Christophe; Dehn, Angelika; Fehr, Thorsten
2016-04-01
SCIAMACHY (SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY) is a scanning nadir and limb spectrometer covering the wavelength range from 212 nm to 2386 nm in 8 channels. It is a joint project of Germany, the Netherlands and Belgium and was launched in February 2002 on the ENVISAT platform. After the platform failure in April 2012, SCIAMACHY is now in the postprocessing phase F. SCIAMACHYs originally specified in-orbit lifetime was double the planned lifetime. SCIAMACHY was designed to measure column densities and vertical profiles of trace gas species in the mesosphere, in the stratosphere and in the troposphere (Bovensmann et al., 1999). It can detect O3 , H2CO, SO2 , BrO, OClO, NO2 , H2 O, CO, CO2 , CH4 , N2 O , O2 , (O2)2 and can provide information about aerosols and clouds. The operational processing of SCIAMACHY is split into Level 0-1 processing (essentially providing calibrated radiances) and Level 1-2 processing providing geophysical products. The operational Level 0-1 processor has been completely re-coded and embedded in a newly developed framework that speeds up processing considerably. Currently Version 9 of the Level 0-1 processor is implemented. It will include - An updated degradation correction - Several improvements in the SWIR spectral range like a better dark correction, an improved dead & bad pixel characterisation and an improved spectral calibration - Improvements to the polarisation correction algorithm - Improvements to the geolocation by a better pointing characterisation Additionally a new format for the Level 1b and Level 1c will be implemented. The version 9 products will be available in netCDF version 4 that is aligned with the formats of the GOME-1 and Sentinel missions. We will present the first results of the new Level 0-1 processing in this paper.
Solving the water jugs problem by an integer sequence approach
NASA Astrophysics Data System (ADS)
Man, Yiu-Kwong
2012-01-01
In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and lecturers involved in teaching mathematical problem solving, recreational mathematics, or elementary number theory.
Contrasting energy scales of reentrant integer quantum Hall states
NASA Astrophysics Data System (ADS)
Deng, Nianpei; Watson, J. D.; Rokhinson, L. P.; Manfra, M. J.; Csáthy, G. A.
2012-11-01
We report drastically different onset temperatures of the reentrant integer quantum Hall states in the second and third Landau level. This finding is in quantitative disagreement with the Hartree-Fock theory of the bubble phases which is thought to describe these reentrant states. Our results indicate that the number of electrons per bubble in either the second or the third Landau level is likely different than predicted.
Electron interferometry in integer quantum Hall edge channels
NASA Astrophysics Data System (ADS)
Rech, J.; Wahl, C.; Jonckheere, T.; Martin, T.
2016-05-01
We consider the electronic analog of the Hong-Ou-Mandel interferometer from quantum optics. In this realistic condensed matter device, single electrons are injected and travel along opposite chiral edge states of the integer quantum Hall effect, colliding at a quantum point contact (QPC). We monitor the fate of the colliding excitations by calculating zero-frequency current correlations at the output of the QPC. In the simpler case of filling factor $\
Optimal source codes for geometrically distributed integer alphabets
NASA Technical Reports Server (NTRS)
Gallager, R. G.; Van Voorhis, D. C.
1975-01-01
An approach is shown for using the Huffman algorithm indirectly to prove the optimality of a code for an infinite alphabet if an estimate concerning the nature of the code can be made. Attention is given to nonnegative integers with a geometric probability assignment. The particular distribution considered arises in run-length coding and in encoding protocol information in data networks. Questions of redundancy of the optimal code are also investigated.
Population transfer HMQC for half-integer quadrupolar nuclei
Wang, Qiang; Xu, Jun; Feng, Ningdong; Deng, Feng E-mail: jean-paul.amoureux@univ-lille1.fr; Li, Yixuan; Trébosc, Julien; Lafon, Olivier; Hu, Bingwen; Chen, Qun; Amoureux, Jean-Paul E-mail: jean-paul.amoureux@univ-lille1.fr
2015-03-07
This work presents a detailed analysis of a recently proposed nuclear magnetic resonance method [Wang et al., Chem. Commun. 49(59), 6653-6655 (2013)] for accelerating heteronuclear coherence transfers involving half-integer spin quadrupolar nuclei by manipulating their satellite transitions. This method, called Population Transfer Heteronuclear Multiple Quantum Correlation (PT-HMQC), is investigated in details by combining theoretical analyses, numerical simulations, and experimental investigations. We find that compared to instant inversion or instant saturation, continuous saturation is the most practical strategy to accelerate coherence transfers on half-integer quadrupolar nuclei. We further demonstrate that this strategy is efficient to enhance the sensitivity of J-mediated heteronuclear correlation experiments between two half-integer quadrupolar isotopes (e.g., {sup 27}Al-{sup 17}O). In this case, the build-up is strongly affected by relaxation for small T{sub 2}′ and J coupling values, and shortening the mixing time makes a huge signal enhancement. Moreover, this concept of population transfer can also be applied to dipolar-mediated HMQC experiments. Indeed, on the AlPO{sub 4}-14 sample, one still observes experimentally a 2-fold shortening of the optimum mixing time albeit with no significant signal gain in the {sup 31}P-({sup 27}Al) experiments.
Population transfer HMQC for half-integer quadrupolar nuclei.
Wang, Qiang; Li, Yixuan; Trébosc, Julien; Lafon, Olivier; Xu, Jun; Hu, Bingwen; Feng, Ningdong; Chen, Qun; Amoureux, Jean-Paul; Deng, Feng
2015-03-01
This work presents a detailed analysis of a recently proposed nuclear magnetic resonance method [Wang et al., Chem. Commun. 49(59), 6653-6655 (2013)] for accelerating heteronuclear coherence transfers involving half-integer spin quadrupolar nuclei by manipulating their satellite transitions. This method, called Population Transfer Heteronuclear Multiple Quantum Correlation (PT-HMQC), is investigated in details by combining theoretical analyses, numerical simulations, and experimental investigations. We find that compared to instant inversion or instant saturation, continuous saturation is the most practical strategy to accelerate coherence transfers on half-integer quadrupolar nuclei. We further demonstrate that this strategy is efficient to enhance the sensitivity of J-mediated heteronuclear correlation experiments between two half-integer quadrupolar isotopes (e.g., (27)Al-(17)O). In this case, the build-up is strongly affected by relaxation for small T2' and J coupling values, and shortening the mixing time makes a huge signal enhancement. Moreover, this concept of population transfer can also be applied to dipolar-mediated HMQC experiments. Indeed, on the AlPO4-14 sample, one still observes experimentally a 2-fold shortening of the optimum mixing time albeit with no significant signal gain in the (31)P-{(27)Al} experiments. PMID:25747074
An integer programming model for gate assignment problem at airline terminals
NASA Astrophysics Data System (ADS)
Chun, Chong Kok; Nordin, Syarifah Zyurina
2015-05-01
In this paper, we concentrate on a gate assignment problem (GAP) at the airlines terminal. Our problem is to assign an arrival plane to a suitable gate. There are two considerations needed to take. One of its is passenger walking distance from arrival gate to departure gate while another consideration is the transport baggage distance from one gate to another. Our objective is to minimize the total distance between the gates that related to assign the arrival plane to the suitable gates. An integer linear programming (ILP) model is proposed to solve this gate assignment problem. We also conduct a computational experiment using CPLEX 12.1 solver in AIMMS 3.10 software to analyze the performance of the model. Results of the computational experiments are presented. The efficiency of flights assignment is depends on the ratio of the weight for both total passenger traveling distances and total baggage transport distances.
Fast integer least squares estimation methods: applications-oriented review and improvement
NASA Astrophysics Data System (ADS)
Xu, Peiliang
2013-04-01
The integer least squares (ILS) problem, also known as the weighted closest point problem, is highly interdisciplinary, but no algorithms can find its global optimal integer solution in polynomial time. In this talk, we will review fast algorithms for estimation of integer parameters. First, we will outline two suboptimal integer solutions, which can be important either in real time communication systems or to solve high dimensional GPS integer ambiguity unknowns. We then focus on the most efficient algorithms to search for the exact integer solution, which is shown to be much faster than LAMBDA in the sense that the ratio of integer candidates to be checked by efficient algorithms to those by LAMBDA can be theoretically expressed by rm, where r < 1 and m is the number of integer unknowns. Finally, we further improve the searching efficiency of the most powerful combined algorithms by implementing two sorting strategies, which can either be used for finding the exact integer solution or for constructing a suboptimal integer solution. A test example clearly demonstrates that the improved methods can perform significantly better than the most powerful combined algorithm to simultaneously find the optimal and second optimal integer solutions. More mathematical and algorithmic details of this talk can be found in Xu (2001, J Geod, 75, 408-423); Xu (2006, IEEE Trans Information Theory, 52, 3122-3138); Xu (2012, J Geod, 86, 35-52) and Xu et al. (2012, Survey Review, 44, 59-71).
On linear structure and phase rotation invariant properties of block M-PSK modulation codes
NASA Technical Reports Server (NTRS)
Kasami, Tadao; Takata, Toyoo; Fujiwara, Toru; Lin, Shu
1991-01-01
Two important structural properties of block M(=2')-ary PSK modulation codes, linear structure and phase symmetry, are investigated. An M-ary modulation code is first represented as a code with symbols from the integer group S(MPSK) = (0,1,2,...M-1) under modulo-M addition. Then the linear structure of block MPSK modulation codes over S(M-PSK) with respect to modulo-M vector addition is defined, and conditions are derived under which a block MPSK modulation code is linear. Once the linear structure is developed, the phase symmetry of block M-PSK modulation codes is studied. In particular, a necessary and sufficient condition for a block MPSK modulation code that is linear as a binary code to be invariant under 2 h 180 deg/M phase rotation (for h = 1 to l) is derived. Finally, a list of short 8PSK and 16PSK modulation codes is given, together with their linear structure and the smallest phase rotation for which a code is invariant.
He, Li; Huang, Guo-He; Zeng, Guang-Ming; Lu, Hong-Wei
2009-01-01
The previous inexact mixed-integer linear programming (IMILP) method can only tackle problems with coefficients of the objective function and constraints being crisp intervals, while the existing inexact mixed-integer semi-infinite programming (IMISIP) method can only deal with single-objective programming problems as it merely allows the number of constraints to be infinite. This study proposes, an inexact mixed-integer bi-infinite programming (IMIBIP) method by incorporating the concept of functional intervals into the programming framework. Different from the existing methods, the IMIBIP can tackle the inexact programming problems that contain both infinite objectives and constraints. The developed method is applied to capacity planning of waste management systems under a variety of uncertainties. Four scenarios are considered for comparing the solutions of IMIBIP with those of IMILP. The results indicate that reasonable solutions can be generated by the IMIBIP method. Compared with IMILP, the system cost from IMIBIP would be relatively high since the fluctuating market factors are considered; however, the IMILP solutions are associated with a raised system reliability level and a reduced constraint violation risk level. PMID:18406594
Mass spectra of 0+-, 1-+, and 2+- exotic glueballs
NASA Astrophysics Data System (ADS)
Tang, Liang; Qiao, Cong-Feng
2016-03-01
With appropriate interpolating currents the mass spectra of 0+-, 1-+, and 2+- oddballs are studied in the framework of QCD sum rules (QCDSR). We find there exits one stable 0+- oddball with mass of 4.57 ± 0.13GeV, and one stable 2+- oddball with mass of 6.06 ± 0.13GeV, whereas, no stable 1-+ oddball shows up. The possible production and decay modes of these glueballs with unconventional quantum numbers are analyzed, which are hopefully measurable in either BELLEII, PANDA, Super-B or LHCb experiments.
A Radio Transient 0.1 Parsecs from Sagittarius A*
NASA Astrophysics Data System (ADS)
Bower, Geoffrey C.; Roberts, Doug A.; Yusef-Zadeh, Farhad; Backer, Donald C.; Cotton, W. D.; Goss, W. M.; Lang, Cornelia C.; Lithwick, Yoram
2005-11-01
We report the discovery of a transient radio source 2.7" (0.1 pc projected distance) south of the Galactic center massive black hole, Sgr A*. The source flared with a peak of at least 80 mJy in 2004 March. The source was resolved by the Very Large Array into two components with a separation of ~0.7" and characteristic sizes of ~0.2". The two components of the source faded with a power-law index of 1.1+/-0.1. We detect an upper limit to the proper motion of the eastern component of ~3×103 km s-1 relative to Sgr A*. We detect a proper motion of ~104 km s-1 for the western component relative to Sgr A*. The transient was also detected at X-ray wavelengths with the Chandra X-Ray Observatory and XMM-Newton and given the designation CXOGC J174540.0-290031. The X-ray source falls in between the two radio components. The maximum luminosity of the X-ray source is ~1036 ergs s-1, significantly sub-Eddington. The radio jet flux density predicted by the X-ray/radio correlation for X-ray binaries is orders of magnitude less than the measured flux density. We conclude that the radio transient is the result of a bipolar jet originating in a single impulsive event from the X-ray source and interacting with the dense interstellar medium of the Galactic center.
Step fluctuations and step interactions on Mo(0 1 1)
NASA Astrophysics Data System (ADS)
Ondrejcek, M.; Swiech, W.; Durfee, C. S.; Flynn, C. P.
2003-09-01
Step fluctuations have been studied on Mo(0 1 1) thin single crystal films with various orientations of miscut, in order to determine the step stiffnesses. Effects of unseen defect structures were clearly visible in some data. Measurements of fluctuation amplitudes and relaxation times were made in the temperature range 1100-1680 K. The results show an anisotropic stiffness of about 0.36 eV/nm along [0 1¯ 1] and about 0.15 eV/nm along [1 0 0]. No temperature dependence of the stiffness was detected. The step free energies derived from the stiffnesses average about 0.27 eV/nm and are less anisotropic by about a factor 3. From the temperature dependence of the relaxation rates, an activation energy of 0.8 ± 0.2 eV was determined for the mass diffusion of the mobile defects responsible for the fluctuations. An appendix details an investigation of correlations induced in the motions of neighboring steps by diffusion and by energetic interactions.
Crystal growth mechanisms of the (0 1 0) face of α-lactose monohydrate crystals
NASA Astrophysics Data System (ADS)
Dincer, T. D.; Ogden, M. I.; Parkinson, G. M.
2009-04-01
The growth rates of the (0 1 0) face of α-lactose monohydrate crystals were measured at 30, 40 and 50 °C in the relative supersaturation range 0.55-2.33 in aqueous solutions. The mechanisms of growth were investigated. Spiral growth was found to be the mechanism of growth up to a critical relative supersaturation ( s-1) crit=1.9 at 30 °C. Above the critical relative supersaturation, the crystal growth mechanisms were predicted to change. All growth models fit equally well to the growth rates. No two-dimensional nucleation was observed above critical supersaturation by AFM. On the other hand increased step height and roughness on the edges of steps were observed. It was concluded that the growth mechanism of the (0 1 0) face of α-lactose monohydrate crystal is spiral growth. A parabolic relationship was obtained below critical supersaturation followed by a linear relationship with relative supersaturation.
Thermal analysis of Al + 0.1% CNT ribbon
NASA Astrophysics Data System (ADS)
Revo, Sergiy; Hamamda, Smail; Ivanenko, Kateryna; Boshko, Oleh; Djarri, Ahmed; Boubertakh, Abdelhamid
2015-04-01
The objective of this work is a dilatometric study of Al + 0.1% of multiwall carbon nanotubes nanocomposite material (NCM) in three directions: X - parallel to the rolling direction; Y - perpendicular to the rolling direction and (Z) perpendicular to the ribbon plane. NCM specimens were made in the form of a 0.1-mm-thick ribbon. The temperature range used for measurements was 20°C to 600°C. The obtained results show that presence of nanotubes affects the thermal expansion coefficient (TEC) measured in different directions. αx(T) and αy(T) - TEC plots as a function of temperature along X and Y directions, respectively - have substantially the same shape and overlap in the area of 400°C. The expansion along X-axis becomes greater than along Y-axis below this temperature value. It is clear that the coefficient αz(T) is lower than αx(T) and αy(T) over the entire temperature range. The expansion along Z-axis is smaller compared to that along X- and Y-axes. This behaviour suggests that there is a strong interatomic interaction along this direction (Z). αz(T) becomes monotonous and constant and is equal to 8 × 10-6°C-1 at temperatures above 300°C. Such order of magnitude had not been obtained in earlier studies of aluminium alloys. The obtained TEC shows high anisotropy, which grows with the increase of temperature. The heat flow (differential scanning calorimetry, (DSC)) of Al + 0.1% carbon nanotubes (CNT) NCM is more intense compared to that of pure aluminium produced in similar conditions. The two representative curves have similar shape and are almost entirely overlapped. The thermogravimetry results confirm those of DSC. The Raman spectrum of this nanomaterial shows that intensity of G and D bonds is significantly increased compared to that of the pure material. The infrared diagram also confirms that in this case the mentioned bonds are more intensive NCM. The tensile strength measurements (σB) of the studied NCM also demonstrate that its value
Bosonic Integer Quantum Hall Effect in an Interacting Lattice Model
NASA Astrophysics Data System (ADS)
He, Yin-Chen; Bhattacharjee, Subhro; Moessner, R.; Pollmann, Frank
2015-09-01
We study a bosonic model with correlated hopping on a honeycomb lattice, and show that its ground state is a bosonic integer quantum Hall (BIQH) phase, a prominent example of a symmetry-protected topological (SPT) phase. By using the infinite density matrix renormalization group method, we establish the existence of the BIQH phase by providing clear numerical evidence: (i) a quantized Hall conductance with |σx y|=2 , (ii) two counterpropagating gapless edge modes. Our simple model is an example of a novel class of systems that can stabilize SPT phases protected by a continuous symmetry on lattices and opens up new possibilities for the experimental realization of these exotic phases.
An analytical study on the carrier-phase linear combinations for triple-frequency GNSS
NASA Astrophysics Data System (ADS)
Li, Jinlong; Yang, Yuanxi; He, Haibo; Guo, Hairong
2016-08-01
The linear combinations of multi-frequency carrier-phase measurements for Global Navigation Satellite System (GNSS) are greatly beneficial to improving the performance of ambiguity resolution (AR), cycle slip correction as well as precise positioning. In this contribution, the existing definitions of the carrier-phase linear combination are reviewed and the integer property of the resulting ambiguity of the phase linear combinations is examined. The general analytical method for solving the optimal integer linear combinations for all triple-frequency GNSS is presented. Three refined triple-frequency integer combinations solely determined by the frequency values are introduced, which are the ionosphere-free (IF) combination that the Sum of its integer coefficients equal to 0 (IFS0), the geometry-free (GF) combination that the Sum of its integer coefficients equal to 0 (GFS0) and the geometry-free and ionosphere-free (GFIF) combination. Besides, the optimal GF, IF, extra-wide lane and ionosphere-reduced integer combinations for GPS and BDS are solved exhaustively by the presented method. Their potential applications in cycle slip detection, AR as well as precise positioning are discussed. At last, a more straightforward GF and IF AR scheme than the existing method is presented based on the GFIF integer combination.
Operational method of solution of linear non-integer ordinary and partial differential equations.
Zhukovsky, K V
2016-01-01
We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black-Scholes-like equations etc. are demonstrated by the operational technique. PMID:26900541
Generalized integer aperture estimation for partial GNSS ambiguity fixing
NASA Astrophysics Data System (ADS)
Brack, Andreas; Günther, Christoph
2014-05-01
In satellite navigation, the key to high precision is to make use of the carrier-phase measurements. The periodicity of the carrier-phase, however, leads to integer ambiguities. Often, resolving the full set of ambiguities cannot be accomplished for a given reliability constraint. In that case, it can be useful to resolve a subset of ambiguities. The selection of the subset should be based not only on the stochastic system model but also on the actual measurements from the tracking loops. This paper presents a solution to the problem of joint subset selection and ambiguity resolution. The proposed method can be interpreted as a generalized version of the class of integer aperture estimators. Two specific realizations of this new class of estimators are presented, based on different acceptance tests. Their computation requires only a single tree search, and can be efficiently implemented, e.g., in the framework of the well-known LAMBDA method. Numerical simulations with double difference measurements based on Galileo E1 signals are used to evaluate the performance of the introduced estimation schemes under a given reliability constraint. The results show a clear gain of partial fixing in terms of the probability of correct ambiguity resolution, leading to improved baseline estimates.
Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks
NASA Technical Reports Server (NTRS)
Cheung, Kar-Ming; Lee, Charles H.
2012-01-01
We developed framework and the mathematical formulation for optimizing communication network using mixed integer programming. The design yields a system that is much smaller, in search space size, when compared to the earlier approach. Our constrained network optimization takes into account the dynamics of link performance within the network along with mission and operation requirements. A unique penalty function is introduced to transform the mixed integer programming into the more manageable problem of searching in a continuous space. The constrained optimization problem was proposed to solve in two stages: first using the heuristic Particle Swarming Optimization algorithm to get a good initial starting point, and then feeding the result into the Sequential Quadratic Programming algorithm to achieve the final optimal schedule. We demonstrate the above planning and scheduling methodology with a scenario of 20 spacecraft and 3 ground stations of a Deep Space Network site. Our approach and framework have been simple and flexible so that problems with larger number of constraints and network can be easily adapted and solved.
A Secret Image Sharing Method Using Integer Wavelet Transform
NASA Astrophysics Data System (ADS)
Huang, Chin-Pan; Li, Ching-Chung
2007-12-01
A new image sharing method, based on the reversible integer-to-integer (ITI) wavelet transform and Shamir's [InlineEquation not available: see fulltext.] threshold scheme is presented, that provides highly compact shadows for real-time progressive transmission. This method, working in the wavelet domain, processes the transform coefficients in each subband, divides each of the resulting combination coefficients into [InlineEquation not available: see fulltext.] shadows, and allows recovery of the complete secret image by using any [InlineEquation not available: see fulltext.] or more shadows [InlineEquation not available: see fulltext.]. We take advantages of properties of the wavelet transform multiresolution representation, such as coefficient magnitude decay and excellent energy compaction, to design combination procedures for the transform coefficients and processing sequences in wavelet subbands such that small shadows for real-time progressive transmission are obtained. Experimental results demonstrate that the proposed method yields small shadow images and has the capabilities of real-time progressive transmission and perfect reconstruction of secret images.
Graphs on uniform points in [0,1]d
NASA Astrophysics Data System (ADS)
Appel, Martin J. B.; Russo, Ralph P.; Yang, King J.
1995-06-01
Statistical problems in pattern or structure recognition for a random multidimensional point set may be addressed by variations on the random graph model of Erdos and Renyui. The imposition of graph structure with a variable edge criterion on a large random point set allows a search for signature quantities or behavior under the given distributional hypothesis. The work is motivated by the question of how to make statistical inferences from sensed mine field data. This article describes recent results obtained in the following special cases. On independent random points U1,...,Un distributed uniformly on [0,1]d, a random graph Gn(x) is constructed in which two distinct such points are joined by an edge if the l(infinity )-distance between them is at most some prescribed value 0
Ellrott, Kyle; Guo, Jun-tao; Olman, Victor; Xu, Ying
2006-01-01
Integer programming is a combinatorial optimization method that has been successfully applied to the protein threading problem. We seek to expand the model optimized by this technique to allow for a more accurate description of protein threading. We have developed and implemented an expanded model of integer programming that has the capability to model secondary structure element deletion, which was not possible in previous version of integer programming based optimization. PMID:17503397
NASA Astrophysics Data System (ADS)
Skulovich, Olya; Bent, Russell; Judi, David; Perelman, Lina Sela; Ostfeld, Avi
2015-06-01
Despite their potential catastrophic impact, transients are often ignored or presented ad hoc when designing water distribution systems. To address this problem, we introduce a new piece-wise function fitting model that is integrated with mixed integer programming to optimally place and size surge tanks for transient control. The key features of the algorithm are a model-driven discretization of the search space, a linear approximation nonsmooth system response surface to transients, and a mixed integer linear programming optimization. Results indicate that high quality solutions can be obtained within a reasonable number of function evaluations and demonstrate the computational effectiveness of the approach through two case studies. The work investigates one type of surge control devices (closed surge tank) for a specified set of transient events. The performance of the algorithm relies on the assumption that there exists a smooth relationship between the objective function and tank size. Results indicate the potential of the approach for the optimal surge control design in water systems.
High Performance Humidity Sensor Based on Electrospun Zr0.9Mg0.1O2-δ Nanofibers
NASA Astrophysics Data System (ADS)
Su, Mei-Ying; Wang, Jing; Yao, Peng-Jun; Du, Hai-Ying
2012-11-01
Zr0.9Mg0.1O2-δ nanofibers and ZrO2 nanofibers are synthesized using electrospinning and the calcination technique. The nanofibers are characterized using x-ray diffraction (XRD), a field emission scanning electron microscope (FE-SEM), and a Brunauer—Emmett—Teller (BET) surface analyzer. The humidity sensing properties of Zr0.9Mg0.1O2-δ nanofiber sensors are analyzed and compared with those of ZrO2 nanofiber sensors. The Zr0.9Mg0.1O2-δ nanofiber humidity sensors exhibit a broader humidity range of 11-97% relative humidity (RH), good linearity, small humidity hysteresis, and rapid response and recovery times. The complex impedance plots of the Zr0.9Mg0.1O2-δ sensor at different RHs are drawn, and the humidity sensing mechanism is discussed via an equivalent circuit.
BOLD fractional contribution to resting-state functional connectivity above 0.1 Hz.
Chen, Jingyuan E; Glover, Gary H
2015-02-15
Blood oxygen level dependent (BOLD) spontaneous signals from resting-state (RS) brains have typically been characterized by low-pass filtered timeseries at frequencies ≤ 0.1 Hz, and studies of these low-frequency fluctuations have contributed exceptional understanding of the baseline functions of our brain. Very recently, emerging evidence has demonstrated that spontaneous activities may persist in higher frequency bands (even up to 0.8 Hz), while presenting less variable network patterns across the scan duration. However, as an indirect measure of neuronal activity, BOLD signal results from an inherently slow hemodynamic process, which in fact might be too slow to accommodate the observed high-frequency functional connectivity (FC). To examine whether the observed high-frequency spontaneous FC originates from BOLD contrast, we collected RS data as a function of echo time (TE). Here we focus on two specific resting state networks - the default-mode network (DMN) and executive control network (ECN), and the major findings are fourfold: (1) we observed BOLD-like linear TE-dependence in the spontaneous activity at frequency bands up to 0.5 Hz (the maximum frequency that can be resolved with TR=1s), supporting neural relevance of the RSFC at a higher frequency range; (2) conventional models of hemodynamic response functions must be modified to support resting state BOLD contrast, especially at higher frequencies; (3) there are increased fractions of non-BOLD-like contributions to the RSFC above the conventional 0.1 Hz (non-BOLD/BOLD contrast at 0.4-0.5 Hz is ~4 times that at <0.1 Hz); and (4) the spatial patterns of RSFC are frequency-dependent. Possible mechanisms underlying the present findings and technical concerns regarding RSFC above 0.1 Hz are discussed. PMID:25497686
Integer aperture bootstrapping: a new GNSS ambiguity estimator with controllable fail-rate
NASA Astrophysics Data System (ADS)
Teunissen, P. J. G.
2005-08-01
In this contribution, we introduce a new bootstrap-based method for Global Navigation Satellite System (GNSS) carrier-phase ambiguity resolution. Integer bootstrapping is known to be one of the simplest methods for integer ambiguity estimation with close-to-optimal performance. Its outcome is easy to compute due to the absence of an integer search, and its performance is close to optimal if the decorrelating Z-transformation of the LAMBDA method is used. Moreover, the bootstrapped estimator is presently the only integer estimator for which an exact and easy-to-compute expression of its fail-rate can be given. A possible disadvantage is, however, that the user has only a limited control over the fail-rate. Once the underlying mathematical model is given, the user has no freedom left in changing the value of the fail-rate. Here, we present an ambiguity estimator for which the user is given additional freedom. For this purpose, use is made of the class of integer aperture estimators as introduced in Teunissen (2003). This class is larger than the class of integer estimators. Integer aperture estimators are of a hybrid nature and can have integer outcomes as well as non-integer outcomes. The new estimator is referred to as integer aperture bootstrapping. This new estimator has all the advantages known from integer bootstrapping with the additional advantage that its fail-rate can be controlled by the user. This is made possible by giving the user the freedom over the aperture of the pull-in region. We also give an exact and easy-to-compute expression for its controllable fail-rate.
Pure scaling operators at the integer quantum Hall plateau transition.
Bondesan, R; Wieczorek, D; Zirnbauer, M R
2014-05-01
Stationary wave functions at the transition between plateaus of the integer quantum Hall effect are known to exhibit multifractal statistics. Here we explore this critical behavior for the case of scattering states of the Chalker-Coddington network model with point contacts. We argue that moments formed from the wave amplitudes of critical scattering states decay as pure powers of the distance between the points of contact and observation. These moments in the continuum limit are proposed to be correlation functions of primary fields of an underlying conformal field theory. We check this proposal numerically by finite-size scaling. We also verify the conformal field theory prediction for a three-point function involving two primary fields. PMID:24856714
Validation and assessment of integer programming sensor placement models.
Uber, James G.; Hart, William Eugene; Watson, Jean-Paul; Phillips, Cynthia Ann; Berry, Jonathan W.
2005-02-01
We consider the accuracy of predictions made by integer programming (IP) models of sensor placement for water security applications. We have recently shown that IP models can be used to find optimal sensor placements for a variety of different performance criteria (e.g. minimize health impacts and minimize time to detection). However, these models make a variety of simplifying assumptions that might bias the final solution. We show that our IP modeling assumptions are similar to models developed for other sensor placement methodologies, and thus IP models should give similar predictions. However, this discussion highlights that there are significant differences in how temporal effects are modeled for sensor placement. We describe how these modeling assumptions can impact sensor placements.
Reconstructing cerebrovascular networks under local physiological constraints by integer programming
Rempfler, Markus; Schneider, Matthias; Ielacqua, Giovanna D.; Xiao, Xianghui; Stock, Stuart R.; Klohs, Jan; Szekely, Gabor; Andres, Bjoern; Menze, Bjoern H.
2015-04-23
We introduce a probabilistic approach to vessel network extraction that enforces physiological constraints on the vessel structure. The method accounts for both image evidence and geometric relationships between vessels by solving an integer program, which is shown to yield the maximum a posteriori (MAP) estimate to the probabilistic model. Starting from an over-connected network, it is pruning vessel stumps and spurious connections by evaluating the local geometry and the global connectivity of the graph. We utilize a high-resolution micro computed tomography (µCT) dataset of a cerebrovascular corrosion cast to obtain a reference network and learn the prior distributions of our probabilistic model. As a result, we perform experiments on micro magnetic resonance angiography (µMRA) images of mouse brains and discuss properties of the networks obtained under different tracking and pruning approaches.
Reconstructing cerebrovascular networks under local physiological constraints by integer programming
Rempfler, Markus; Schneider, Matthias; Ielacqua, Giovanna D.; Xiao, Xianghui; Stock, Stuart R.; Klohs, Jan; Szekely, Gabor; Andres, Bjoern; Menze, Bjoern H.
2015-04-23
We introduce a probabilistic approach to vessel network extraction that enforces physiological constraints on the vessel structure. The method accounts for both image evidence and geometric relationships between vessels by solving an integer program, which is shown to yield the maximum a posteriori (MAP) estimate to the probabilistic model. Starting from an over-connected network, it is pruning vessel stumps and spurious connections by evaluating the local geometry and the global connectivity of the graph. We utilize a high-resolution micro computed tomography (µCT) dataset of a cerebrovascular corrosion cast to obtain a reference network and learn the prior distributions of ourmore » probabilistic model. As a result, we perform experiments on micro magnetic resonance angiography (µMRA) images of mouse brains and discuss properties of the networks obtained under different tracking and pruning approaches.« less
Parallel integer sorting with medium and fine-scale parallelism
NASA Technical Reports Server (NTRS)
Dagum, Leonardo
1993-01-01
Two new parallel integer sorting algorithms, queue-sort and barrel-sort, are presented and analyzed in detail. These algorithms do not have optimal parallel complexity, yet they show very good performance in practice. Queue-sort designed for fine-scale parallel architectures which allow the queueing of multiple messages to the same destination. Barrel-sort is designed for medium-scale parallel architectures with a high message passing overhead. The performance results from the implementation of queue-sort on a Connection Machine CM-2 and barrel-sort on a 128 processor iPSC/860 are given. The two implementations are found to be comparable in performance but not as good as a fully vectorized bucket sort on the Cray YMP.
Analytical estimation of the correlation dimension of integer lattices
Lacasa, Lucas; Gómez-Gardeñes, Jesús
2014-12-01
Recently [L. Lacasa and J. Gómez-Gardeñes, Phys. Rev. Lett. 110, 168703 (2013)], a fractal dimension has been proposed to characterize the geometric structure of networks. This measure is an extension to graphs of the so called correlation dimension, originally proposed by Grassberger and Procaccia to describe the geometry of strange attractors in dissipative chaotic systems. The calculation of the correlation dimension of a graph is based on the local information retrieved from a random walker navigating the network. In this contribution, we study such quantity for some limiting synthetic spatial networks and obtain analytical results on agreement with the previously reported numerics. In particular, we show that up to first order, the correlation dimension β of integer lattices ℤ{sup d} coincides with the Haussdorf dimension of their coarsely equivalent Euclidean spaces, β = d.
Integer-Valued Characters for Some Sporadic Groups
NASA Astrophysics Data System (ADS)
Gilani, Alireza; Moghani, Ali
2010-11-01
Using the concept of markaracter tables proposed by a Chemist S. Fujita who applied his results in this area of research to enumerate isomers of molecules, we are able to discuss characters and marks concerning a group of a finite order on a common basis. He also introduced tables of integer-valued characters that are obtained for finite groups. According to the main result of W. Feit and G. M. Seitz (see, Illinois J. Math. 33 (1), 103-131, 1988), the sporadic Mathieu groups M11, M12 and Higman-Sims (HS) group are unmatured. In this paper, at first all the dominant classes and Q- conjugacy characters for the above groups are derived.
Integer Representation of Decimal Numbers for Exact Computations.
Bernal, Javier; Witzgall, Christoph
2006-01-01
A scheme is presented and software is documented for representing as integers input decimal numbers that have been stored in a computer as double precision floating point numbers and for carrying out multiplications, additions and subtractions based on these numbers in an exact manner. The input decimal numbers must not have more than nine digits to the left of the decimal point. The decimal fractions of their floating point representations are all first rounded off at a prespecified location, a location no more than nine digits away from the decimal point. The number of digits to the left of the decimal point for each input number besides not being allowed to exceed nine must then be such that the total number of digits from the leftmost digit of the number to the location where round-off is to occur does not exceed fourteen. PMID:27274918
Insulating States in the Integer Quantum Hall Regime
NASA Astrophysics Data System (ADS)
Knighton, Talbot; Serafin, Alessandro; Wu, Zhe; Tarquini, Vinicio; Xia, J. F.; Sullivan, Neil; Pfeiffer, Loren; West, Ken; Huang, Jian
Quantum Hall measurements are performed at temperatures 20-300 mK in high quality p-type GaAs quantum well systems having mobility μ = 4 ×106 cm2/V .s for density 5 ×1010 cm-2. We report a series of insulating phases appearing at or near integer filling factors ν >= 1 . The DC resistance demonstrates a maximum of 25M Ω, much larger than the quantum resistance h /e2 , with threshold transport behavior at low currents around 10 pA at low temperatures. The threshold diminishes upon heating up to 200 mK, consistent with a finite temperature melting of bubble phases or Wigner crystal. Additionally, these peaks have a complex electrical impedance for AC signals, with large phase shifts down to 1Hz. In this regime, the ac impedance of the two chiral edges show distinct correlated characteristics. NSF DMR-1410302.
Mixed Integer Programming and Heuristic Scheduling for Space Communication
NASA Technical Reports Server (NTRS)
Lee, Charles H.; Cheung, Kar-Ming
2013-01-01
Optimal planning and scheduling for a communication network was created where the nodes within the network are communicating at the highest possible rates while meeting the mission requirements and operational constraints. The planning and scheduling problem was formulated in the framework of Mixed Integer Programming (MIP) to introduce a special penalty function to convert the MIP problem into a continuous optimization problem, and to solve the constrained optimization problem using heuristic optimization. The communication network consists of space and ground assets with the link dynamics between any two assets varying with respect to time, distance, and telecom configurations. One asset could be communicating with another at very high data rates at one time, and at other times, communication is impossible, as the asset could be inaccessible from the network due to planetary occultation. Based on the network's geometric dynamics and link capabilities, the start time, end time, and link configuration of each view period are selected to maximize the communication efficiency within the network. Mathematical formulations for the constrained mixed integer optimization problem were derived, and efficient analytical and numerical techniques were developed to find the optimal solution. By setting up the problem using MIP, the search space for the optimization problem is reduced significantly, thereby speeding up the solution process. The ratio of the dimension of the traditional method over the proposed formulation is approximately an order N (single) to 2*N (arraying), where N is the number of receiving antennas of a node. By introducing a special penalty function, the MIP problem with non-differentiable cost function and nonlinear constraints can be converted into a continuous variable problem, whose solution is possible.
Integer-spin electron paramagnetic resonance of iron proteins.
Hendrich, M P; Debrunner, P G
1989-01-01
A quantitative interpretation is presented for EPR spectra from integer-spin metal centers having large zero-field splittings. Integer-spin, or non-Kramers, centers are common in metalloproteins and many give EPR signals, but a quantitative understanding has been lacking until now. Heterogeneity of the metal's local environment will result in a significant spread in zero-field splittings and in broadened EPR signals. Using the spin Hamiltonian Hs = S.D.S + beta S.g.B and some simple assumptions about the nature of the zero-field parameter distributions, a lineshape model was devised which allows accurate simulation of single crystal and frozen solution spectra. The model was tested on single crystals of magnetically dilute ferrous fluosilicate. Data and analyses from proteins and active-site models are presented with the microwave field B1 either parallel or perpendicular to B. Quantitative agreement of observed and predicted signal intensities is found for the two B1 orientations. Methods of spin quantitation are given and are shown to predict an unknown concentration relative to a standard with known concentration. The fact that the standard may be either a non-Kramers or a Kramers center is further proof of the model's validity. The magnitude of the splitting in zero magnetic field is of critical importance; it affects not only the chance of signal observation, but also the quantitation accuracy. Experiments taken at microwave frequencies of 9 and 35 GHz demonstrate the need for high-frequency data as only a fraction of the molecules give signals at 9 GHz. PMID:2551404
Hyper-Sums of Powers of Integers and the Akiyama-Tanigawa Matrix
NASA Astrophysics Data System (ADS)
Inaba, Yoshinari
2005-05-01
In this short essay, we consider hyper-sums of powers of integers, namely sums of power sums. We can obtain easily their formulae as polynomials by using formulae for ordinary sums of powers of integers. The coefficient of the first-degree term in each polynomial coincides with the matrix element of the Akiyama-Tanigawa matrix.
Integral-valued polynomials over sets of algebraic integers of bounded degree☆
Peruginelli, Giulio
2014-01-01
Let K be a number field of degree n with ring of integers OK. By means of a criterion of Gilmer for polynomially dense subsets of the ring of integers of a number field, we show that, if h∈K[X] maps every element of OK of degree n to an algebraic integer, then h(X) is integral-valued over OK, that is, h(OK)⊂OK. A similar property holds if we consider the set of all algebraic integers of degree n and a polynomial f∈Q[X]: if f(α) is integral over Z for every algebraic integer α of degree n, then f(β) is integral over Z for every algebraic integer β of degree smaller than n. This second result is established by proving that the integral closure of the ring of polynomials in Q[X] which are integer-valued over the set of matrices Mn(Z) is equal to the ring of integral-valued polynomials over the set of algebraic integers of degree equal to n. PMID:26949270
ERIC Educational Resources Information Center
Han, Kyung T.; Rudner, Lawrence M.
2014-01-01
This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal information…
NASA Astrophysics Data System (ADS)
Tian, Yumiao; Ge, Maorong; Neitzel, Frank
2015-11-01
GLONASS could hardly reach the positioning performance of GPS, especially for fast and real-time precise positioning. One of the reasons is the phase inter-frequency bias (IFB) at the receiver end prevents its integer ambiguity resolution. A number of studies were carried out to achieve the integer ambiguity resolution for GLONASS. Based on some of the revealed IFB characteristics, for instance IFB is a linear function of the received carrier frequency and L1 and L2 have the same IFB in unit of length, most of recent methods recommend estimating the IFB rate together with ambiguities. However, since the two sets of parameters are highly correlated, as demonstrated in previous studies, observations over several hours up to 1 day are needed even with simultaneous GPS observations to obtain a reasonable solution. Obviously, these approaches cannot be applied for real-time positioning. Actually, it can be demonstrated that GLONASS ambiguity resolution should also be available even for a single epoch if the IFB rate is precisely known. In addition, the closer the IFB rate value is to its true value, the larger the fixing RATIO will be. Based on this fact, in this paper, a new approach is developed to estimate the IFB rate by means of particle filtering with the likelihood function derived from RATIO. This approach is evaluated with several sets of experimental data. For both static and kinematic cases, the results show that IFB rates could be estimated precisely just with GLONASS data of a few epochs depending on the baseline length. The time cost with a normal PC can be controlled around 1 s and can be further reduced. With the estimated IFB rate, integer ambiguity resolution is available immediately and as a consequence, the positioning accuracy is improved significantly to the level of GPS fixed solution. Thus the new approach enables real-time precise applications of GLONASS.
Thermodynamic functions of hydration of hydrocarbons at 298.15 K and 0.1 MPa
NASA Astrophysics Data System (ADS)
Plyasunov, Andrey V.; Shock, Everett L.
2000-02-01
An extensive compilation of experimental data yielding the infinite dilution partial molar Gibbs energy of hydration Δ hGO, enthalpy of hydration Δ hHO, heat capacity of hydration Δ hCpO, and volume V2O, at the reference temperature and pressure, 298.15 K and 0.1 MPa, is presented for hydrocarbons (excluding polyaromatic compounds) and monohydric alcohols. These results are used in a least-squares procedure to determine the numerical values of the corresponding properties of the selected functional groups. The simple first order group contribution method, which in general ignores nearest-neighbors and steric hindrance effects, was chosen to represent the compiled data. Following the precedent established by Cabani et al. (1981), the following groups are considered: CH 3, CH 2, CH, C for saturated hydrocarbons; c-CH 2, c-CH, c-C for cyclic saturated hydrocarbons; CH ar, C ar for aromatic hydrocarbons (containing the benzene ring); C=C, C≡C for double and triple bonds in linear hydrocarbons, respectively; c-C=C for the double bond in cyclic hydrocarbons; H for a hydrogen atom attached to the double bond (both in linear and cyclic hydrocarbons) or triple bond; and OH for the hydroxyl functional group. In addition it was found necessary to include the "pseudo"-group I(C-C) to account for the specific interactions of the neighboring hydrocarbon groups attached to the benzene or cyclic ring (in the latter case only for cis-isomers). Results of this study, the numerical values of the group contributions, will allow in most cases reasonably accurate estimations of Δ hGO, Δ hHO, Δ hCpO, and V2O at 298.15 K, 0.1 MPa for many hydrocarbons involved in geochemical and environmental processes.
Caprara, Alberto; Carr, Robert; Istrail, Sorin; Lancia, Giuseppe; Walenz, Brian
2004-01-01
Protein structure comparison is a fundamental problem for structural genomics, with applications to drug design, fold prediction, protein clustering, and evolutionary studies. Despite its importance, there are very few rigorous methods and widely accepted similarity measures known for this problem. In this paper we describe the last few years of developments on the study of an emerging measure, the contact map overlap (CMO), for protein structure comparison. A contact map is a list of pairs of residues which lie in three-dimensional proximity in the protein's native fold. Although this measure is in principle computationally hard to optimize, we show how it can in fact be computed with great accuracy for related proteins by integer linear programming techniques. These methods have the advantage of providing certificates of near-optimality by means of upper bounds to the optimal alignment value. We also illustrate effective heuristics, such as local search and genetic algorithms. We were able to obtain for the first time optimal alignments for large similar proteins (about 1,000 residues and 2,000 contacts) and used the CMO measure to cluster proteins in families. The clusters obtained were compared to SCOP classification in order to validate the measure. Extensive computational experiments showed that alignments which are off by at most 10% from the optimal value can be computed in a short time. Further experiments showed how this measure reacts to the choice of the threshold defining a contact and how to choose this threshold in a sensible way. PMID:15072687
Tracking Simulation of Third-Integer Resonant Extraction for Fermilab's Mu2e Experiment
Park, Chong Shik; Amundson, James; Michelotti, Leo
2015-02-13
The Mu2e experiment at Fermilab requires acceleration and transport of intense proton beams in order to deliver stable, uniform particle spills to the production target. To meet the experimental requirement, particles will be extracted slowly from the Delivery Ring to the external beamline. Using Synergia2, we have performed multi-particle tracking simulations of third-integer resonant extraction in the Delivery Ring, including space charge effects, physical beamline elements, and apertures. A piecewise linear ramp profile of tune quadrupoles was used to maintain a constant averaged spill rate throughout extraction. To study and minimize beam losses, we implemented and introduced a number of features, beamline element apertures, and septum plane alignments. Additionally, the RF Knockout (RFKO) technique, which excites particles transversely, is employed for spill regulation. Combined with a feedback system, it assists in fine-tuning spill uniformity. Simulation studies were carried out to optimize the RFKO feedback scheme, which will be helpful in designing the final spill regulation system.
Uncluttered Single-Image Visualization of Vascular Structures using GPU and Integer Programming
Won, Joong-Ho; Jeon, Yongkweon; Rosenberg, Jarrett; Yoon, Sungroh; Rubin, Geoffrey D.; Napel, Sandy
2013-01-01
Direct projection of three-dimensional branching structures, such as networks of cables, blood vessels, or neurons onto a 2D image creates the illusion of intersecting structural parts and creates challenges for understanding and communication. We present a method for visualizing such structures, and demonstrate its utility in visualizing the abdominal aorta and its branches, whose tomographic images might be obtained by computed tomography or magnetic resonance angiography, in a single two-dimensional stylistic image, without overlaps among branches. The visualization method, termed uncluttered single-image visualization (USIV), involves optimization of geometry. This paper proposes a novel optimization technique that utilizes an interesting connection of the optimization problem regarding USIV to the protein structure prediction problem. Adopting the integer linear programming-based formulation for the protein structure prediction problem, we tested the proposed technique using 30 visualizations produced from five patient scans with representative anatomical variants in the abdominal aortic vessel tree. The novel technique can exploit commodity-level parallelism, enabling use of general-purpose graphics processing unit (GPGPU) technology that yields a significant speedup. Comparison of the results with the other optimization technique previously reported elsewhere suggests that, in most aspects, the quality of the visualization is comparable to that of the previous one, with a significant gain in the computation time of the algorithm. PMID:22291148
Anisotropic fractal media by vector calculus in non-integer dimensional space
Tarasov, Vasily E.
2014-08-15
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.
Anisotropic fractal media by vector calculus in non-integer dimensional space
NASA Astrophysics Data System (ADS)
Tarasov, Vasily E.
2014-08-01
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.
Preconditioning 2D Integer Data for Fast Convex Hull Computations.
Cadenas, José Oswaldo; Megson, Graham M; Luengo Hendriks, Cris L
2016-01-01
In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved. PMID:26938221