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• 1.
University of Skovde, Jonkoping University.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för svetsteknologi (SV). Jonkoping University, Orebro Univ, University University West - Sweden.
An approach towards generating surrogate models by using RBFN with a priori bias2014Inngår i: PROCEEDINGS OF THE ASME INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES AND COMPUTERS AND INFORMATION IN ENGINEERING CONFERENCE, 2014, VOL 2B, AMER SOC MECHANICAL ENGINEERS , 2014, Vol. 2BKonferansepaper (Fagfellevurdert)

In this paper, an approach to generate surrogate models constructed by radial basis function networks (RBFN) with a priori bias is presented. RBFN as a weighted combination of radial basis functions only, might become singular and no interpolation is found. The standard approach to avoid this is to add a polynomial bias, where the bias is defined by imposing orthogonality conditions between the weights of the radial basis functions and the polynomial basis functions. Here, in the proposed a priori approach, the regression coefficients of the polynomial bias are simply calculated by using the normal equation without any need of the extra orthogonality prerequisite. In addition to the simplicity of this approach, the method has also proven to predict the actual functions more accurately compared to the RBFN with a posteriori bias. Several test functions, including Rosenbrock, Branin-Hoo, Goldstein-Price functions and two mathematical functions (one large scale), are used to evaluate the performance of the proposed method by conducting a comparison study and error analysis between the RBFN with a priori and a posteriori known biases. Furthermore, the aforementioned approaches are applied to an engineering design problem, that is modeling of the material properties of a three phase spherical graphite iron (SGI). The corresponding surrogate models are presented and compared.

• 2.
Högskolan Väst, Institutionen för ekonomi och it, Avd för juridik, ekonomi, statistik och politik.
Högskolan Väst, Institutionen för ekonomi och it, Avd för juridik, ekonomi, statistik och politik.
Employment and Economic Activity in Different Swedish Border Regions2015Inngår i: Uddevalla Symposium 2015. Regional Development in an International Context. Regional, National, Cross Border and International Factors for Growth and Development: Revised papers presented at the 18th Uddevalla Symposium, 11-13 June, Sönderborg, Denmark / [ed] Iréne Bernhard, Trollhättan: University West , 2015, s. 45-57Konferansepaper (Fagfellevurdert)

This study investigate how the effect of cross border activities between Sweden and its three Nordic neighbours influence the Swedish local economies along the border using municipal data from 2009. Two measures for the local economies are examined, economic activity (measured by gross pay per inhabitant) and employment rates. The Swedish border regions where divided into four regions: The Swedish border to Finland, The Swedish border to the part of Norway not included in the Oslo labour market, The Swedish border to the Oslo labour market, and the Swedish-Danish border region. The regression models show how the the regions compare to the Swedish average when controlled for market structure and accessibility to population. For Sweden's border regions to Denmark and the Oslo labour market there are significant improvements in both economic activity and employment rates when the border activity is included. The improvement is highest for the Oslo border regions. For the Swedish border to Finland and to the part of Norway not included inte the Olso labour market the border activity has no significant influence on either economic activity or employment rates.

• 3.
Högskolan Väst, Institutionen för ekonomi och it, Avd för juridik, politik och ekonomi. Högskolan Väst, Institutionen för ekonomi och it, Avd för juridik, ekonomi, statistik och politik.
Högskolan Väst, Institutionen för ekonomi och it, Avd för juridik, politik och ekonomi. Högskolan Väst, Institutionen för ekonomi och it, Avd för juridik, ekonomi, statistik och politik.
University Colleges Effect on Municipal Growth in Swedish Middle-sized Municipalities2008Inngår i: Uddevalla Symposium 2008: Spatial Dispersed Production and Network Governance: Revised papers presented at the 11th Uddevalla Symposium, 15-17 May, 2008, Kyoto, Japan / [ed] Iréne Bernhard, Trollhättan: University West , 2008, s. 85-98Konferansepaper (Fagfellevurdert)

The main purpose in this paper is to study to what extent accessibility to R&D is an important factor of explaining municipal economic growth. Of special interests is the question whether, the effect of company (private) R&D efforts on economic growth differ if a university college is present in the municipality or not. Therefore the empirical analysis is conducted on a reduced dataset (92 out of 290 municipalities), containing only middle-sized municipalities without traditional ´old´ universities. The idea of the selection process was to find two sets of comparable municipalities with one containing municipalities with university colleges and one with municipalities without university colleges. In the empirical analysis a knowledge production function is estimated with the difference in Gross Municipal Product, GMP, between 1993 and 2001 as the output. In order to account for the importance of proximity, the explanatory variables are expressed as accessibilities to university and company R&D. The total accessibility is then decomposed into local, intra-regional and inter-regional accessibility to R&D. The main results show that local and intra-regional accessibility to company R&D has positive effects on economic growth. On the other hand, local accessibility to university R&D is of no importance, while there are influential effects of intra-regional university R&D. Moreover, the presence of university college R&D activities decreases the importance of the local accessibilitiy to company R&D or put it differently, local accessibility to company R&D is more important in municipalitites without university college activities.

• 4.
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap.
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap. Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
Generalizations of the normal basis theorem2004Inngår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 94, s. 5s. 185-190Artikkel i tidsskrift (Fagfellevurdert)
• 5.
Högskolan Väst, Institutionen för ingenjörsvetenskap.
University Pierre and Marie Curie, Paris, France.
Non equilibrium ionization in magnetized two-temperature thermal plasma2011Inngår i: Kinetic and Related Models, ISSN 1937-5093, E-ISSN 1937-5077, ISSN 1, Vol. 4, nr 3, s. 669-700Artikkel i tidsskrift (Fagfellevurdert)

A thermal plasma is studied accounting for both impact ionization, and an electromagnetic field. This plasma problem is modeled based on a system of Boltzmann type transport equations. Electron-neutral collisions are assumed to be much more frequently elastic than inelastic, to complete previous investigations of thermal plasma . A viscous hydrodynamic/diffusion limit is derived in two stagesdoing an Hilbert expansion and using the  Chapman-Enskog method. The resultant viscous fluid model is characterized by two temperatures, and non equilibrium ionization. Its diffusion coefficients depend on the magnetic field, and can be computed explicitely.

• 6.
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap, Avd för maskinteknik.
A Comparison between Moving Mesh Implementations for Metal Deposition Simulations2006Inngår i: Proceedings of the Nordic COMSOL Conference: Lyngby, Denmark, 2006, s. 107-110Konferansepaper (Annet vitenskapelig)
• 7.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för industriell produktion.
An Investigation of Mesh Moving Methods for Simulating the Deformation of Incompressible Fluid Bodies2009Inngår i: COMSOL Conference: 14-16 okt. 2009, Milan, 2009Konferansepaper (Annet vitenskapelig)

In this article we apply a finite element method for approximating the geometrical deformation of a two dimensional incompressible fluid body the flow velocity of which is not constrained along its top boundary. As a pressure force is applied on the free boundary, the domain occupied by the fluid deforms. There are several well established methods for treating this type of problem. The purpose of the present work is to investigate the computational efficiency of a number domain-mapping methods, which are akin to many solid mechanical applications involving large deformations, in that they employ a mapping of the initial configuration range onto the current. However, in fluid dynamical applications the deformation of the fluid body may be very large and contain several vortices. When employing domain-mapping methods, the spatial representations of the element domains are attached to the motion, and the Lagrange formulation is therefore inadequate. Instead we wish to find a motion which minimizes the element deformations and the computational complexity of the problem, while satisfying the kinematic constraint along the boundaries.

• 8.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för industriell produktion.
Weld Pool Simulations2008Licentiatavhandling, monografi (Annet vitenskapelig)

This investigation is devoted to the study of welding and its effect on the workpiece, focusing on the thermo and fluid dynamical phenomena occuring during a autogenous or nonautogenous arc fusion welding process. Its aim is to simulate the behaviour of the weld pool and analyze the consequence of the solid-liquid phase change, thus obtaining a methodology for predicting the appearance of weld defects related to solidification and cooling. In order to accomplish this, we solve equations governing a number of continuum mechanical and electromagnetical quantities, as well as consider the motion of the freely moving boundary of the weld pool. Since the state of these quantities is strongly influenced by phenomena such as arc and droplet impingement, non-isothermal phase change, surface tension, Marangoni forces and Lorentz forces, much effort is necessarily devoted to the modelling of the corresponding fluxes and sources, as well as to the implementation of computationally efficient techniques for simulating the geometrical deformation of the workpiece, which in our setting is entirely determined by the motion of the weld pool surface.

Common to all arc fusion welding processes is the employment of a welding arc. Many techniques rely on the arc to clean and shield the workpiece during the process, however in this study we consider it to be its main purpose to cause the local increase of thermal energy that is required for the establishment of the weld pool, and also to exert the mechanical forces that provoke the subsequent fluid flow which enhances heat transfer and facilitates weld penetration. The physics of the welding arc itself is quite intricate, and although the modelling of the arc is not the prime objective of this research project, we conclude that arc forces act on the pool surface, and that the investigation of the arc behaviour is important insofar that it provides input to the pool model and thus enables a more accurate prediction of the quality of the weldment that is created once the pool has solidified

• 9.
Royal Institute of Technology Division of Geodesy .
On the estimation of variance in unstable condition adjustment models2011Inngår i: Acta Geodaetica et Geophysica Hungarica, ISSN 1217-8977, E-ISSN 1587-1037, ISSN 1217-8977, Vol. 46, nr 1, s. 71-83Artikkel i tidsskrift (Fagfellevurdert)

Estimation of variance in an ordinary adjustment model is straightforward, but if the model becomes unstable or ill-conditioned its solution and the variance of the solution will be very sensitive to the errors of observations. This sensitivity can be controlled by stabilizing methods but the results will be distorted due to stabilization. In this paper, stabilizing an unstable condition model using Tikhonov regularization, the estimations of variance of unit weight and variance components are investigated. It will be theoretically proved that the estimator of variance or variance components has not the minimum variance property when the model is stabilized, but unbiased estimation of variance is possible. A simple numerical example is provided to show the performance of the theory.

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• 10.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för data-, elektro- och lantmäteriteknik. Royal Institute of Technology, Division of Geodesy, Stockholm, Sweden .
Royal Institute of Technology, Division of Geodesy, Stockholm, Sweden .
The modified best quadratic unbiased non-negative estimator (MBQUNE) of variance components2008Inngår i: Studia Geophysica et Geodaetica, ISSN 0039-3169, E-ISSN 1573-1626, Vol. 52, nr 3, s. 305-320Artikkel i tidsskrift (Fagfellevurdert)

Estimated variance components may come out as negative numbers without physical meaning. One way out of this problem is to use non-negative methods. Different approaches have been presented for the solution. Sjöberg presented a method of Best Quadratic Unbiased Non-Negative Estimator (BQUNE) in the Gauss-Helmert model. This estimator does not exist in the general case. Here we present the Modified BQUNE (MBQUNE) obtained by a simple transformation from the misclosures used in the BQUE to residuals. In the Gauss-Markov adjustment model the BQUNE and MBQUNE are identical, and they differ in condition and Gauss-Helmert models only by a simple transformation. If the observations are composed of independent/disjunctive groups the MBQUNE exists in any adjustment model and it carries all the properties of the BQUNE (when it exists). The presented variance component models are tested numerically in some simple examples. It is shown that the MBQUNE works well for disjunctive groups of observations.

• 11.
Högskolan Väst, Institutionen för ekonomi och it, Avd för informatik.
Technische Hochschule Nürnberg Georg Simon Ohm / University Nuremberg, Germany.
Das älteste gedruckte schwedische Rechenbuch (Aegidius Aurelius, Arithmetica, Uppsala 1614): (Aegidius Aurelius, Arithmetica, Uppsala 1614)2017Inngår i: Tagungsband zum wissenschaftlichen Kolloquium vom 21.–23. April 2017 in der Berg- und Adam-Ries-Stadt Annaberg-Buchholz / [ed] Gebhardt, Rainer, Annaberg-Buchholz: Adam-Ries-Bund , 2017, s. 313-326Konferansepaper (Annet vitenskapelig)
• 12.
Högskolan Väst, Institutionen för ekonomi och it, Avd för datavetenskap och informatik.
M12: Medicinsk statistik2004 (oppl. 1)Bok (Annet vitenskapelig)
• 13.
Högskolan Väst, Institutionen för arbete, ekonomi och hälsa (HTU).
Statistical issues: significantly important in medical research.2002Inngår i: Allergy. European Journal of Allergy and Clinical Immunology, ISSN 0105-4538, E-ISSN 1398-9995, Vol. 57, nr 2, s. 76-82Artikkel, forskningsoversikt (Annet vitenskapelig)
• 14.
Högskolan Väst, Institutionen för ekonomi och it, Avd för datavetenskap och informatik.
Statistiska metoder för kvalitetsutveckling1997 (oppl. 1)Bok (Annet vitenskapelig)
• 15.
Högskolan Väst, Institutionen för ekonomi och it, Avd för datavetenskap och informatik.
Högskolan Väst, Institutionen för ekonomi och it, Avd för datavetenskap och informatik.
Www means win win win in education: some experiences from online courses in applied statistics2010Inngår i: OZCOTS 2010 Proceedings of the 7th Australian Conferenceon Teaching Statistics / [ed] Helen MacGillivray & Brian Phillips, Statistical society of Australia , 2010, s. 51-56Konferansepaper (Fagfellevurdert)

This paper reports on the experiences from online courses in applied statistics. The courses were designed with the ambition of making studies in statistics, fun, interesting, useful, not that difficult and directly supported the possibility to combine studies and work. When designing the courses we considered three dimensions: "pedagogies","community" and "structure". Experiences after giving a first-year course three times show that the online course succeeds in attracting new studen ts since 90% of the participants would not be able to follow an on-campus course and 62% worked full time.

The pedagogies were highly appreciated because focusing on the interpretation of results and using computer analyses really changed the prejudices about statistics. Structure and prompt feedback was experienced as important factors. It was possible to combine online studies with employment, and the student completion rate was (84%, 55% and 61%), with a potential for further improvements.

• 16.
Högskolan Väst, Institutionen för individ och samhälle.
Högskolan Väst, Institutionen för individ och samhälle, Avd för utbildningsvetenskap och språk.
Gymnasielevers problem med procenträkning.2009Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave

• 17.
McMaster University, Department of Chemistry and Chemical Biology.
Pontificia Universidad Catlica de Chile, Facultad de Qumica, Laboratorio de Qumica Terica Computacional (QTC). Pontificia Universidad Catlica de Chile, Facultad de Qumica, Laboratorio de Qumica Terica Computacional (QTC). Högskolan Väst, Institutionen för ekonomi och it, Avd för datavetenskap och informatik. Högskolan Väst, Institutionen för ekonomi och it, Avd för datavetenskap och informatik. McMaster University, Department of Chemistry and Chemical Biology.
Pointing the way to the products Comparison of the stress tensor and the second-derivative tensor of the electron density2011Inngår i: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 134, nr 23, s. 234106-Artikkel i tidsskrift (Fagfellevurdert)

The eigenvectors of the electronic stress tensor can be used to identify where new bond paths form in a chemical reaction. In cases where the eigenvectors of the stress tensor are not available, the gradient-expansion- approximation suggests using the eigenvalues of the second derivative tensor of the electron density instead; this approximation can be made quantitatively accurate by scaling and shifting the second-derivative tensor, but it has a weaker physical basis and less predictive power for chemical reactivity than the stress tensor. These tools provide an extension of the quantum theory of atoms and molecules from the characterization of molecular electronic structure to the prediction of chemical reactivity. Â© 2011 American Institute of Physics.

• 18.
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap.
A finite element method on composite grids based on Nitsche's method2002Rapport (Annet (populærvitenskap, debatt, mm))
• 19.
Department of Geodesy and Geomatics, Zanjan University, Iran.
Royal Institute of Technology, Stockholm, Sweden.
Estimating variance components of ellipsoidal, orthometric and geoidalheights through the GPS/levelling Network in Iran2008Inngår i: Journal of the Earth and Space Physics, Vol. 34, nr 3, s. 1-13Artikkel i tidsskrift (Fagfellevurdert)

The Best Quadratic Unbiased Estimation (BQUE) of variance components in the Gauss-Helmert model is used to combine adjustment of GPS/levelling and geoid to determinethe individual variance components for each of the three height types. Through theresearch, different reasons for achievement of the negative variance components werediscussed and a new modified version of the Best Quadratic Unbiased Non-negativeEstimator (MBQUNE) was successfully developed and applied. This estimation could beuseful for estimating the absolute accuracy level which can be achieved using theGPS/levelling method. A general MATLAB function is presented for numericalestimation of variance components by using the different parametric models. Themodified BQUNE and developed software was successfully applied for estimating thevariance components through the sample GPS/levelling network in Iran. In the followingresearch, we used the 75 outlier free and well distributed GPS/levelling data. Threecorrective surface models based on the 4, 5 and 7 parameter models were used throughthe combined adjustment of the GPS/levelling and geoidal heights. Using the 7-parametermodel, the standard deviation indexes of the geoidal, geodetic and orthometric heights inIran were estimated to be about 27, 39 and 35 cm, respectively.

• 20.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för maskinteknik. Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Industriell ekonomi, Elektro- och Maskinteknik.
Competence development through Project-based learning in higher education i Sweden and England2012Inngår i: 40th annual congress of the Nordic Educational Research association, NPFP/NERA: 8-10 mars, 2012, Copenhagen, Aarhus: Department of Eduation, Aarhus University , 2012, s. 286-Konferansepaper (Fagfellevurdert)

The focus of higher education curricula has been changing from factual knowledge acquisition to developing students competences in response to a changing professional environment in the context of a knowledge economy and labour market globalisation.

Despite these social changes, existing teaching and learning strategies in Engineering are still mainly lecture-based.

We investigate competence development using a Project- Based Learning (PrBL) environment on a range of Engineering programmes at Lancaster University, UK and Högskolan VÃ¤st, Sweden. We evaluate the PrBL potential to enhance student employability prospects.

PrBL is an example of collaborative student-focussed learning underpinned by constructivist theory which encourages deeper learning via construction of meaning, connection of ideas and creation of meaningful artefacts. PrBL stimulates collaborative knowledge building among participants and develops a range of skills through creating an informal learning environment. First and second-year students on undergraduate programmes in Engineering departments in both universities with projects as part of their course participated in this study. In the UK the students had to design, build and test two types of robots. The Swedish students were given a project to make calculations for a pump with preset parameters. The projects were designed to help the students acquire competences relevant to their future career. All students worked in small groups. After finishing their projects, the students completed an open-ended questionnaire about their experiences.

The students evaluated PrBL positively, stating that they developed problem solving and analytical skills and the ability to apply mathematical tools. They highly rated collaboration with peers and emphasised the necessity of developing time management, communication and organisational skills.

Higher education systems in Europe including Scandinavia are facing new challenges in developing students' employability. We conclude with recommendations for promoting PrBL in university courses as it contributes to competence development and is an efficient tool when administrative resources are limited and when academic staff are faced with large student numbers.

• 21.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för maskinteknik och naturvetenskap.
Evaluation of a Surrogate Based Method for Global Optimization2015Inngår i: International Journal of Computer, Electrical, Automation, Control and Information Engineering, E-ISSN 1307-6892, Vol. 9, nr 7, s. 1636-1642Artikkel i tidsskrift (Fagfellevurdert)

We evaluate the performance of a numerical method for global optimization of expensive functions. The method is using a response surface to guide the search for the global optimum. This metamodel could be based on radial basis functions, kriging, or a combination of different models. We discuss how to set the cyclic parameters of the optimization method to get a balance between local and global search. We also discuss the eventual problem with Runge oscillations in the response surface.

• 22.
Högskolan Väst, Institutionen för ingenjörsvetenskap.
Robustness analysis of airfoil performance: DETC2010-282612010Inngår i: Proceedings of the ASME 2010 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference: August 15-18, 2010, Montreal, Quebec, Canada, ASME, the American Society of Mechanical Engineers , 2010, s. 1-6Konferansepaper (Fagfellevurdert)

We demonstrate a technique to evaluate the aerodynamic robustness of a given blade profile which it is exposed to stochastic geometrical variation. The technique is based on random fields, with geometrical deviations continuously defined over the entire structure, with a prescribed statistical distribution function and a given correlation between these deviations. Control points are defined on the blade surface to model the blade geometry disturbances. At each control point a stochastic deviation is defined, which acts in the normal direction of the blade. By modeling disturbances in the normal direction instead of in the separate Cartesian directions, we automatically reduce the number of stochastic variables by a factor two. The perturbation variables are transformed via Karhunen-Loève eigenvalue decomposition, giving stochastically independent variables. The robustness is finally estimated by a Monte Carlo simulation, where computational fluid dynamic simulations are performed to evaluate the resulting change in blade performance for given geometrical perturbations.

• 23.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för maskinteknik och naturvetenskap.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för maskinteknik och naturvetenskap.
A surrogate model based global optimization method2008Inngår i: 38th International Conference on Computers and Industrial Engineering 2008, 2008, s. 226-232Konferansepaper (Fagfellevurdert)

A new surrogate model based algorithm for global optimization is derived. A metamodel such as a kriging model or a radial basis function model is used to build an interpolant of the objective function. Evaluation points are chosen in such a way that local search and global exploration is balanced. Instead of putting the next point exactly where it is most likely to find the global optimum, the new method also prepares for steps to come by minimizing the total uncertainty of the interpolated function within the most interesting areas of the search space.

• 24.
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap.
Brauer group rings2004Inngår i: JP Journal of Algebra, Number Theory & Applications, Vol. 4, s. 22s. 465-494Artikkel i tidsskrift (Fagfellevurdert)
• 25.
Högskolan Väst, Institutionen för teknik (HTU).
Cohomology and Self-dual Normal Bases for Infinite Galois Field Extensions2002Inngår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 256, s. 531-541Artikkel i tidsskrift (Fagfellevurdert)

We generalize an injectivity result obtained by Bayer-Fluckiger and Lenstra concerning pointed cohomology sets, defined by norm-one groups of finite-dimensional algebras with involution over fields k of characteristic different from 2, to the case of inverse limits of finite-dimensional k-algebras with involution. We use this generalization to obtain a result about self-dual normal bases for infinite Galois field extensions.

• 26.
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap, Avd för matematik och naturvetenskap.
Cohomology and the normal basis theorem2007Inngår i: Indagationes mathematicae, ISSN 0019-3577, E-ISSN 1872-6100, Vol. 18, s. 69-72Artikkel i tidsskrift (Fagfellevurdert)
• 27.
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap.
Crossed product algebras defined by separable extensions2005Inngår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 283, s. 14s. 723-737Artikkel i tidsskrift (Fagfellevurdert)
• 28.
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap.
Fuzzified categories of composition graphs2005Rapport (Annet (populærvitenskap, debatt, mm))

Serving as a generalization of many examples of fuzzy algebraical systems equipped with a binary operation, we introduce fuzzy composition graphs and show that categories formed by such graphs are, in the sense of Wyler [10], top categories. By using this, we investigate projective and injective objects in such categories, and we determine when various limits and colimits, such as terminal and initial objects, products, coproducts, pullbacks, pushouts, equalizers, coequalizers, kernels and cokernels, exist in categories of this type and what they look like. These results are then applied to the categories of fuzzy sets, fuzzy categories, fuzzy groupoids, fuzzy monoids, fuzzy groups and fuzzy abelian groups.

• 29.
Högskolan Väst, Institutionen för teknik (HTU). Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
Generalized Brauer Algebras2002Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 30, nr 5, s. 2229-2270Artikkel i tidsskrift (Fagfellevurdert)

Using some ideas of Brauer, we introduce what we call generalized Brauer algebras and, as a special case, Brauer orders. We show that many well-known classes of so-called crossed product algebras, and in particular, the well-known crossed product orders, can be obtained as special instances of our construction. We prove several results showing when Brauer orders are Azumaya, maximal, hereditary or Gorenstein.

• 30.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för naturvetenskap, lantmäteri- och maskinteknik.
Good Magma Gradings On Rings2014Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 42, nr 12, s. 5357-5373Artikkel i tidsskrift (Fagfellevurdert)

Suppose that G and H are magmas and that R is a strongly G-graded ring. We show that there is a bijection between the set of good (zero) H-gradings of R and the set of (zero) magma homomorphisms from G to H. Thereby we generalize a result by Dascalescu, Ion, Nastasescu and Rios Montes from group gradings of matrix rings to strongly magma graded rings. We also show that there is an isomorphism between the preordered set of good (zero) H-filters on R and the preordered set of (zero) submagmas of G \times H. These results are applied to category graded rings and, in particular, to the case when G and H are groupoids. In the latter case, we use this bijection to determine the cardinality of the set of good H-gradings on R.

• 31.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för lantmäteriteknik och matematik.
Hilbert 90 for Rings with ConjugationManuskript (preprint) (Annet vitenskapelig)

We show a version of Hilbert 90 that is valid for a large class ofalgebras many of which are not commutative, distributive orassociative. This class contains the n:th iteration of theConway-Smith doubling procedure. We use our version of Hilbert 90 toparametrize all solutions in ordered fields to the norm one equation for such algebras.

• 32.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för lantmäteriteknik och matematik.
Hilbert 90 for algebras with conjugation2012Inngår i: Algebras and Representation Theory, ISSN 1386-923X, E-ISSN 1572-9079, Vol. 15, nr 1, s. 119-135Artikkel i tidsskrift (Fagfellevurdert)

We show a version of Hilbert 90 that is valid for a large class ofalgebras many of which are not commutative, distributive orassociative. This class contains the n:th iteration of theConway-Smith doubling procedure. We use our version of Hilbert 90 toparametrize all solutions in ordered fields to the norm one equation for such algebras.

• 33.
Högskolan Väst, Institutionen för teknik (HTU).
Normal Bases for Infinite Galois Ring Extensions1999Inngår i: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 79, s. 235-240Artikkel i tidsskrift (Fagfellevurdert)
• 34.
Högskolan Väst, Institutionen för teknik (HTU). Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.
Normal Integral Bases for Infinite Abelian Extensions2001Inngår i: Acta Arithmetica, ISSN 0065-1036, E-ISSN 1730-6264, Vol. 100, s. 79-83Artikkel i tidsskrift (Fagfellevurdert)
• 35.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för lantmäteriteknik och matematik.
Pythagoreiska tripplar på sex olika sätt2008Inngår i: Normat, ISSN 0801-3500, Vol. 56, nr 3, s. 111-119Artikkel i tidsskrift (Fagfellevurdert)

Six different ways of parametrising Pythagorean triplets are presented, from the elementary arguments supplied by the Greek, via trigonometry to Gaussian integers and applications of Hilbers 90th theorem.

• 36.
Högskolan Väst, Institutionen för teknik (HTU).
Self-dual Normal Bases for Infinite Galois Field Extensions1998Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 26, s. 4331-4341Artikkel i tidsskrift (Fagfellevurdert)
• 37.
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap.
Self-dual normal bases for infinite odd abelian Galois ring extensions2006Inngår i: Acta Arithmetica, ISSN 0065-1036, E-ISSN 1730-6264, Vol. 123, nr 1, s. 1-8Artikkel i tidsskrift (Fagfellevurdert)
• 38.
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap.
Self-dual Normal Integral Bases for Infinite Unramified Extensions2002Inngår i: Journal of Number Theory, ISSN 0022-314X, E-ISSN 1096-1658, Vol. 97, nr 2, s. 350-367Artikkel i tidsskrift (Fagfellevurdert)

We prove a generalization to infinite Galois extensions of local fields, of a classical result by Noether on the existence of normal integral bases for finite tamely ramified Galois extensions. We also prove a self-dual normal integral basis theorem for infinite unramified Galois field extensions of local fields with finite residue fields of characteristic different from 2. This generalizes a result by Fainsilber for the finite case. To do this, we obtain an injectivity result concerning pointed cohomology sets, defined by inverse limits of norm-one groups of free finite-dimensional algebras with involution over complete discrete valuation rings.

• 39.
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap, Avd för matematik och naturvetenskap.
Separable Groupoid Rings2006Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 34, nr 8, s. 3029-3041Artikkel i tidsskrift (Fagfellevurdert)

We show that groupoid rings are separable over their ring of coefficients if and only if the groupoid is finite and the orders of the associated principal groups are invertible in the ring of coefficients. We use this to show that if we are given a finite groupoid, then the associated groupoid ring is semisimple (or hereditary) if and only if the ring of coefficients is semisimple (or hereditary) and the orders of the principal groups are invertible in the ring of coefficients. To this end, we extend parts of the theory of graded rings and modules from the group graded case to the category graded, and, hence, groupoid graded situation. In particular, we show that strongly groupoid graded rings are separable over their principal components if and only if the image of the trace map contains the identity

• 40.
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap.
Separable groupoid rings2006Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 34, s. 13s. 3029-3041Artikkel i tidsskrift (Annet (populærvitenskap, debatt, mm))
• 41.
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap.
The category of groupoid graded modules2004Inngår i: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 100, s. 15s. 195-211Artikkel i tidsskrift (Fagfellevurdert)
• 42.
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap.
The Picard Groupoid and Strongly Groupoid Graded Modules2006Inngår i: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 106, s. 1-13Artikkel i tidsskrift (Fagfellevurdert)
• 43.
Högskolan Väst, Institutionen för ingenjörsvetenskap.
The Picard Groupoid and Strongly Groupoid Graded Modules2006Inngår i: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 106, s. 1-13Artikkel i tidsskrift (Fagfellevurdert)
• 44.
Högskolan Väst, Institutionen för teknik, matematik och datavetenskap.
Von Neumann finite endomorphism rings2003Inngår i: Indagationes mathematicae, ISSN 0019-3577, E-ISSN 1872-6100, Vol. 14, s. 9s. 223-232Artikkel i tidsskrift (Fagfellevurdert)
• 45.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för lantmäteriteknik och matematik.
Weak topological functors2008Inngår i: Journal of Generalized Lie Theory and Applications, ISSN 1736-5279, E-ISSN 1736-4337, Vol. 2, nr 3, s. 211-215Artikkel i tidsskrift (Fagfellevurdert)

We introduce weak topological functors and show that they lift and preserve weak limits and weak colimits. We also show that if then the induced functor of Wyler’s top categories and in particular to functor categories of fuzzy maps, fuzzy relations, fuzzy topological spaces and fuzzy measurable spaces. A ! B is a topological functor and J is a category,AJ ! BJ is topological. These results are applied to a generalization

• 46.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för lantmäteriteknik och matematik.
Commutativity and Ideals in Category Crossed Products2010Inngår i: Proceedings of the Estonian Academy of Sciences: Physics, Mathematics, ISSN 1406-0086, E-ISSN 2228-0685, Vol. 59, nr 4, s. 338-346Artikkel i tidsskrift (Fagfellevurdert)
• 47.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för lantmäteriteknik och matematik.
LTH.
Miyashita Action in Strongly Groupoid Graded RingsManuskript (preprint) (Annet vitenskapelig)

We determine the commutant of homogeneous subringsin strongly groupoid graded rings in terms of an action on the ring induced by the grading. Thereby we generalize a classical result of Miyashita from the groupgraded case to the groupoid graded situation. In the end of the article we exemplify this result. To this end, we show, by an explicit construction,that given a finite groupoid $G$, equipped with a nonidentitymorphism t : d(t) -> c(t), there is a strongly G-graded ring R with the properties that each R_s, for s in G, is nonzero and R_t is a nonfree left R_c(t)-module.

• 48.
Högskolan Väst, Institutionen för ingenjörsvetenskap.
LTH.
Miyashita Action in Strongly Groupoid Graded Rings2012Inngår i: International Electronic Journal of Algebra, ISSN 1306-6048, E-ISSN 1306-6048, Vol. 11, s. 46-63Artikkel i tidsskrift (Fagfellevurdert)

We determine the commutant of homogeneous subrings in strongly groupoid graded rings in terms of an action on the ring induced by the grading. Thereby we generalize a classical result of Miyashita from the groupgraded case to the groupoid graded situation. In the end of the article we exemplify this result. To this end, we show, by an explicit construction,that given a finite groupoid $G$, equipped with a nonidentitymorphism t : d(t) -> c(t), there is a strongly G-graded ring R with the properties that each R_s, for s in G, is nonzero and R_t is a nonfree left R_c(t)-module.

• 49.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för elektro, lantmäteri och naturvetenskap.
Köpenhamns Universitet.
Skew category algebras associated with partially defined dynamical systems2012Inngår i: International Journal of Mathematics, ISSN 0129-167X, Vol. 23, nr 4, s. 16-Artikkel i tidsskrift (Fagfellevurdert)

We introduce partially defined dynamical systems defined on a topological space. To each such system we associate a functor s from a category G to Top^op and show that it defines what we call a skew category algebra AxG. We study the connection between topological freeness of s and, on the one hand, ideal properties of AxG and, on the other hand, maximal commutativity of A in AxG. In particular, we show that if G is a groupoid and for each e in ob(G) the group of all morphisms from e to e is countable and the topological space s(e) is Tychonoff and Baire, then the following assertions are equivalent: (i) s is topologically free; (ii) A has the ideal intersection property, that is if I is a nonzero ideal of AxG, then I \cap A is not equal to zero; (iii) the ring A is a maximal abelian complex subalgebra of AxG. Thereby, we generalize a result by Svensson, Silvestrov and de Jeu from the additive group of integers to a large class of groupoids.

• 50.
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avd för lantmäteriteknik och matematik.
LTH.
The Ideal Intersection Property for Groupoid Graded Rings2012Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 40, nr 5, s. 1860-1871Artikkel i tidsskrift (Fagfellevurdert)

We show that if a groupoid graded ring hasa certain nonzero ideal property, then the commutant of the center of the principal component of the ringhas the ideal intersection property, that is it intersects nontrivially every nonzero ideal of the ring. Furthermore, we show that for skew groupoid algebras withcommutative principal component, the principal componentis maximal commutative if and only if it has the ideal intersection property.

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# Quantifiers and contrapositives in proof of fundamental lemma of variational calc

In Gelfand and Fomin's Calculus of Variations, they present the lemma

If $$\alpha(x)$$ is continuous in $$[a, b]$$, and if $$\int_a^b \alpha (x) h(x) \textrm{d}x = 0$$ for every continuous function $$h(x)$$ such that $$h(a) = h(b) = 0$$, then $$\alpha(x) = 0$$ for all $$x \in [a, b]$$.

The authors claim that the proof that follows is by contradiction, but from what I can tell, it appears to be a proof by contrapositive---yet, I can't quite grasp it. They assume $$\alpha(x) > 0$$ on some interval $$[x_1, x_2] \subset [a, b]$$ and set $$h(x) = (x - x_1)(x - x_2)$$ in $$[x_1,x_2]$$ (but equal to zero elsewhere $$[a, b]$$), then show that the integral is also greater than zero.

In a rough first-order sense, the lemma seems to have the form $$(\forall a)(P(a) \rightarrow Q)$$, with the integral being $$P$$, the quantified variable representing all functions $$h$$ that satisfy the given conditions, and $$Q$$ being the state of $$\alpha = 0$$. But it seems to me that the authors prove $$(\exists a)(\neg Q \rightarrow \neg P(a))$$, when the contrapositive proof should have a $$\forall$$ quantifier instead.

Shouldn't the proof involve $$h$$ being literally all/any possible functions that satisfy the necessary properties? It seems like picking one specific function proves nothing at all, and I can't see why it works to just pick one function. Did I mess my first-order logic up?

• The statement is of the form $(\forall a)P(a)\to Q$, and the authors are proving the contrapositive $\lnot Q\to\lnot(\forall a)P(a)$, i.e. $\lnot Q\to(\exists a)\lnot P(a)$. Jan 30 at 23:43

The lemma is of the form $$(\forall\alpha)\big( \big( (\forall h)P(\alpha,h) \big) \implies Q(\alpha) \big)$$, and thus the contrapositive of the implication would yield $$(\forall\alpha)\big( \lnot Q(\alpha) \implies \big( (\exists h)(\lnot P(\alpha,h)) \big) \big)$$. And indeed this is what the proof demonstrates: given a suitable (but generic) $$\alpha$$, it constructs an $$h$$. [Side note: $$\lnot Q(\alpha)$$ literally says that there's a single point at which $$\alpha(x)\ne0$$, but then WLOG $$\alpha(x)>0$$ and then continuity provides an interval containing $$x$$ on which $$\alpha$$ is positive.]

format: plain


text:
# How To Contribute¶

## Clone and Provision Environment¶

1. Make sure you have a GitHub account

2. Clone the cilium repository into your GOPATH.

mkdir -p $GOPATH/src/github.com/cilium cd$GOPATH/src/github.com/cilium
git clone https://github.com/cilium/cilium.git
cd cilium

3. Set up your Development Setup.

4. Check the GitHub issues for good tasks to get started.

## Submitting a pull request¶

Contributions must be submitted in the form of pull requests against the github repository at: https://github.com/cilium/cilium.

1. Fork the Cilium repository to your own personal GitHub space or request access to a Cilium developer account on Slack
2. Push your changes to the topic branch in your fork of the repository.
3. Submit a pull request on https://github.com/cilium/cilium.

Before hitting the submit button, please make sure that the following requirements have been met:

1. Each commit compiles and is functional on its own to allow for bisecting of commits.

2. All code is covered by unit and/or runtime tests where feasible.

3. All changes have been tested and checked for regressions by running the existing testsuite against your changes. See the End-To-End Testing Framework section for additional details.

4. All commits contain a well written commit description including a title, description and a Fixes: #XXX line if the commit addresses a particular GitHub issue. Note that the GitHub issue will be automatically closed when the commit is merged.

apipanic: Log stack at debug level

Previously, it was difficult to debug issues when the API panicked
because only a single line like the following was printed:

level=warning msg="Cilium API handler panicked" client=@ method=GET
panic_message="write unix /var/run/cilium/cilium.sock->@: write: broken
pipe"

This patch logs the stack at this point at debug level so that it can at
least be determined in developer environments.

Fixes: #4191

Signed-off-by: Joe Stringer <joe@cilium.io>

5. If any of the commits fixes a particular commit already in the tree, that commit is referenced in the commit message of the bugfix. This ensures that whoever performs a backport will pull in all required fixes:

daemon: use endpoint RLock in HandleEndpoint

Fixes: a804c7c7dd9a ("daemon: wait for endpoint to be in ready state if specified via EndpointChangeRequest")

Signed-off-by: André Martins <andre@cilium.io>

6. If you change CLI arguments of any binaries in this repo, the CI will reject your PR if you don’t also update the command reference docs. To do so, make sure to run the postcheck make target.

$make postcheck$ git add Documentation/cmdref

### Triage issues for Triage team¶

Dedicated expectation time for each member of Triage team: 15/30 minutes per day. Works best if done first thing in the working day.

1. Committers belonging to the Triage team should make sure that:

1. Add the label kind/community-report;
2. If feasible, try to reproduce the issue described;
3. Assign a member that is responsible for that code section to that GitHub issue;
4. If it is a relevant bug to the rest of the committers, bring the issue up in the weekly meeting. For example:
• The issue may impact an upcoming release; or
• The resolution is unclear and assistance is needed to make progress; or
• The issue needs additional attention from core contributors to confirm the resolution is the right path.
1. If there is someone already assigned to that GitHub issue and that committer hasn’t provided an answer to that user for a while, ping that committer directly on Slack;
2. If the issue cannot be solved, bring the issue up in the weekly meeting.

### Backporting PR for Backport team¶

Dedicated expectation time for each member of Backport team: 60 minutes per week depending on releases that need to be performed at the moment.

Even if the next release is not imminently planned, it is still important to perform backports to keep the process smooth and to catch potential regressions in stable branches as soon as possible. If backports are delayed, this can also delay releases which is important to avoid especially if there are security-sensitive bug fixes that require an immediate release.

In addition, when a backport PR is open, the person opening it is responsible to drive it to completion, even if it stretches after the assigned week of backporting hat. If this is not feasible (e.g. PTO), you are responsible to initiate handover of the PR to the next week’s backporters.

If you can’t backport a PR due technical constraints feel free to contact the original author of that PR directly so they can backport the PR themselves.

Follow the Backporting process guide to know how to perform this task.

#### Coordination¶

In general, coordinating in the #launchpad Slack channel with the other hat owner for the week is encouraged. It can reduce your workload and it will avoid backporting conflicts such as opening a PR with the same backports. Such discussions will typically revolve around which branches to tackle and which day of the week.

Starting backport round for v1.7 and v1.8 now
cc @other-hat-wearer

The other hat owner can then handle v1.9 and v1.10 backports the next day, for example.

If there are many backports to be done, then splitting up the rounds can be beneficial. Typically, backporters opt to start a round in the beginning of the week and then another near the end of the week.

By the start / end of the week, if there are other backport PRs that haven’t been merged, then please coordinate with the previous / next backporter to check what the status is and establish who will work on getting the backports into the tree (for instance by investigating CI failures and addressing review feedback). There’s leeway to negotiate depending on who has time available.

## Developer’s Certificate of Origin¶

To improve tracking of who did what, we’ve introduced a “sign-off” procedure.

The sign-off is a simple line at the end of the explanation for the commit, which certifies that you wrote it or otherwise have the right to pass it on as open-source work. The rules are pretty simple: if you can certify the below:

Developer Certificate of Origin
Version 1.1

Copyright (C) 2004, 2006 The Linux Foundation and its contributors.
1 Letterman Drive
Suite D4700
San Francisco, CA, 94129

Everyone is permitted to copy and distribute verbatim copies of this
license document, but changing it is not allowed.

Developer's Certificate of Origin 1.1

By making a contribution to this project, I certify that:

(a) The contribution was created in whole or in part by me and I
have the right to submit it under the open source license
indicated in the file; or

(b) The contribution is based upon previous work that, to the best
of my knowledge, is covered under an appropriate open source
license and I have the right under that license to submit that
work with modifications, whether created in whole or in part
by me, under the same open source license (unless I am
permitted to submit under a different license), as indicated
in the file; or

(c) The contribution was provided directly to me by some other
person who certified (a), (b) or (c) and I have not modified
it.

(d) I understand and agree that this project and the contribution
are public and that a record of the contribution (including all
personal information I submit with it, including my sign-off) is
maintained indefinitely and may be redistributed consistent with
this project or the open source license(s) involved.

then you just add a line saying:

Signed-off-by: Random J Developer <random@developer.example.org>

Use your real name (sorry, no pseudonyms or anonymous contributions.)


text:
## CryptoDB

### William P. Marnane

#### Publications

Year
Venue
Title
2010
EPRINT
The second round of the NIST public competition is underway to find a new hash algorithm(s) for inclusion in the NIST Secure Hash Standard (SHA-3). Computational efficiency of the algorithms in hardware is to be addressed during the second round of the contest. For software implementations NIST specifies an application programming interface (API) along with reference implementation for each of the designs, thereby enabling quick and easy comparison and testing on software platforms, however no such specification was given for hardware analysis. In this paper we present a hardware wrapper interface which attempts to encompass all the competition entries (and indeed, hash algorithms in general) across any number of both FPGA and ASIC hardware platforms. This interface comprises communications and padding, and attempts to standardise the hashing algorithms to allow accurate and fair area, timing and power measurement between the different designs.
2009
EPRINT
This paper presents implementation results of a reconfigurable elliptic curve processor defined over prime fields $GF(p)$. We use this processor to compare a new algorithm for point addition and point doubling operations on the twisted Edwards curves, against a current standard algorithm in use, namely the Double-and-Add. Secure power analysis versions of both algorithms are also examined and compared. The algorithms are implemented on an FPGA, and the speed, area and power performance of each are then evaluated for various modes of circuit operation using parallel processing. To the authors' knowledge, this work introduces the first documented FPGA implementation for computations on twisted Edwards curves over fields $GF(p)$.
2005
CHES
2005
EPRINT
In this paper the benefits of implementation of the Tate pairing computation in dedicated hardware are discussed. The main observation lies in the fact that arithmetic architectures in the extension field $GF(3^{6m})$ are good candidates for parallelization, leading to a similar calculation time in hardware as for operations over the base field $GF(3^m)$. Using this approach an architecture for the hardware implementation of the Tate pairing calculation based on a modified Duursma-Lee algorithm is proposed.
2005
EPRINT
The $\eta$ pairing is an efficient computation technique based on a generalization of the Duursma Lee method for calculating the Tate pairing. The pairing can be computed very efficiently on genus 2 hyperelliptic curves. In this paper it is demonstrated that this pairing operation is well suited to a dedicated parallel hardware implementation. An $\eta$ pairing processor is described in detail and the architectures required for such a system are discussed. Prototype implementation results are presented over a base field of $\mathbb{F}_{2^{103}}$ and the advantages of implementing the pairing on the dedicated processor are discussed.

CHES 2009


text:
# math: find an equation from a graph

Discussion in 'Homework Help' started by bug13, Apr 29, 2012.

1. ### bug13 Thread Starter Well-Known Member

Feb 13, 2012
1,214
39
as seen in the pic, how do I find the equation from the graph, I am lost with these two graph.

thanks

Feb 5, 2010
3,887
987
3. ### blah2222 Well-Known Member

May 3, 2010
565
33
(ii)

You have four pieces of information to use:

1) y = 0 at x = 0
2) y = 0 at x = 3
3) dy/dx = 0 at x = 0
4) dy/dx = 0 at around x = 2.5

Since y = 0 at x = 0, 3, they must be factors of y and in the form:

$y = Ax^P(x - 3)^Q$

dy/dx must be in the form of:

$\frac{dy}{dx} = Bx^{P - 1}(x - 2.5)^R$

(iv)

Right off the bat this looks like an exponential graph but flipped in the x-axis, so with that in mind it has the form:

$y = Ae^{-x} + C$

At x = 0, y = 2 so this concludes that A could be 2 and C = 0:

$y = 2e^{-x}$

Testing y(3) we get 0.0996 which is pretty much 0.1 and there you have it.

bug13 likes this.
4. ### bug13 Thread Starter Well-Known Member

Feb 13, 2012
1,214
39
Thanks blah2222, your solution gives me a new way to look at this problem, I now learn I can use information like these:

That's something I have never thought off before

Feb 13, 2012
1,214
39
6. ### WBahn Moderator

Mar 31, 2012
18,261
4,941
My first impression is that it is a cubic expression of the form:

$
y = ax^3+bx^2+cx+d
$

And you know the following:

y goes to +oo as x goes to -oo
y goes to -oo as x goes to +oo
y' = dy/dx = 0 at x = 0
y = 0 at x=0
y = 0 at x=3

Since y(0) = d, we know that d = 0.

Since y'(0) = 0, we know that c = 0.

Hence we are left with

$
y = (ax+b)x^2
$

From y(3) = 0, we know that b = -3a. so now we have

$
y = a(x-3)x^2
$

We also know that a<0 in order to get the tails to go in the right direction.

Is this consistent with the answers offered in the book?

Assuming this is correct, the slope goes to zero at x=0 and x=2 (not x=2.5).

Since there is no scaling information on the y-axis, we have to leave 'a' as an arbitrary scale factor that must be negative.

If I were more up to speed on cubics, I could probably have noted that there is a root at +3 (that much was obvious) but that there was a double root at zero (it was obvious there was one, but I couldn't remember if it required two there). I suspected that there had to be a double root at either 0 or 3 because if there weren't, then it would have meant that the other root had to be complex. But, IIRC, on a real function the complex roots have to come in complex conjugate pairs and since there are only three roots and we know two of them, then this isn't possible. Given that the third root either has to be a double at 0 or 3, I suspected it was at zero.

But hopefully you can see how you can still get the form of the equation by looking at the zero crossings and the asymptotic behavior of both the function and the derivatives to figure things out without having to recall a bunch of specifics about roots and such.

bug13 likes this.
7. ### bug13 Thread Starter Well-Known Member

Feb 13, 2012
1,214
39
That's the answer I get too,
, and then I am stucked, I don't have the answer yet, it's an per exam exercise, I will need to wait until Monday to ask my tutor for the answer.

I assumed I will need to get the value of a too, but I am out of ideas.

Thanks for your answer, I have never come across the idea of double root, that's something learned

8. ### WBahn Moderator

Mar 31, 2012
18,261
4,941
You can't get the value of 'a' beyond noting that it must be negative. The sign of 'a' determines whether the graph you get is the one on the page or one that is mirrored about the x-axis. But the magnitude of 'a' determines the vertical scaling and there is absolutely no vertical scaling information given in the graph. You don't know if the peak at x=2 occurs at a y value of 1 or 1000 or 0.0001. Given that value, you can determine the value of 'a', otherwise it has to remain a negative constant of arbitrary magnitude.

9. ### bug13 Thread Starter Well-Known Member

Feb 13, 2012
1,214
39
The answer I got from my tutor is:

Y=-x^2(x-3)

But I think it's incomplete

10. ### WBahn Moderator

Mar 31, 2012
18,261
4,941
Yes, arguably it is incomplete because this equation peaks at a specific value, namely 4, at x=2 while the graph peaks at an arbitrary and unknown value. In many respects, it is like saying that the (indefinite) integral of 2x is x^2 and not x^2+C. Forgeting the arbitrary scaling factor goes unnoticed for many people, but doing so is wrong and can get you into trouble.

11. ### bug13 Thread Starter Well-Known Member

Feb 13, 2012
1,214
39
My plan is stick to my own answer but not to argue with my tutor

12. ### WBahn Moderator

Mar 31, 2012
18,261
4,941
Good plan! Sure wish I had been smart enough to follow that route when I was at that point in my life.

13. ### steveb Senior Member

Jul 3, 2008
2,433
469
The answer is not incomplete. It is the question that is incomplete. The question needs to be clear about assumptions for the function. However, the assumptions that lead to this answer are very reasonalbe ones to make in the absence of a rigorously clear question.

Last edited: Apr 30, 2012
14. ### WBahn Moderator

Mar 31, 2012
18,261
4,941
I'm gonna disagree with you on this one. The question may be incomplete, but the answer still needs to match the question. If someone asks me how much gasoline they need to drive 1000 miles in their car, I can tell them that they need 1000mi/M where M is their car's gas mileage. It would not be correct for me to arbitrarily set "M equal to 1" (1mpg, that is) and say that the "complete answer" is 1000 gallons. Or, using the example I used earlier, if the question is to take the integral of 2x (perhaps stated something like, "What function of x has a slope that is everywhere equal to 2x?", an answer of x^2 can't be claimed to be a "complete answer" to an incomplete question. If the question is defined only to within an arbitrary constant, then the answer needs to reflect the existance and influence of that constant.

15. ### steveb Senior Member

Jul 3, 2008
2,433
469
I can find many other answers to the question that are not the same as the one you suggested. So, your answer does not match the question any better than the tutor's does. You have made specific assumptions about the question and hence feel your answer is complete. The tutor did the same. The fact that your answer is more general than the tutor's does not mean that someone else does not have an answer that is more general than yours.

The second question with the exponential decay is also wide open to interpretation without some constraints, or more information given.

For the second one, I would suggest the following, but there are alternatives.

$y={{2}\over{20^{x/3}}}$

16. ### WBahn Moderator

Mar 31, 2012
18,261
4,941
I'll grant you that. In any question like that there is virtually always the unstated goal of using the "simplest" solution possible, but as I remarked in another thread, what is the metric by which "simple" is judged? Having said that, the heart of most of these types of questions is whether or not the person can make the "correct" initial assumption about the basic form of the underlying equation.

I'm not sure I'll grant you that, but I definitely understand your point.

That's what I got, though I may have come at it from a different direction. I started with a generic decaying exponential and fit the two points. The result reduces to your solution. That same solution can reasonably be arrived at by inspection.

One thing that I think is reasonable to expect from any proposed answer to most questions like this (and I'm referring to an academic setting such as this) is that the anwers match the information that IS given exactly. Not almost, but exactly. Also, I think it is pretty important not to infer information that is not there as part of the solution. That last statement is almost certainly too broad to capture what I mean, so what I mean by that is doing something like saying that the zero crossing on a graph appears to be about 2/3 of the way from 4 and 7 and so we will impose the constraint that y(6)=0.

17. ### bug13 Thread Starter Well-Known Member

Feb 13, 2012
1,214
39
the answer given by my tutor is:

he starts off with the assumption of it's exponential equation with a base of e, however, I personally like the answer of:

this answer makes more sense to me, can you explain how did you get this answer please? thanks

Wu

PS: my tutor's solution

18. ### WBahn Moderator

Mar 31, 2012
18,261
4,941
If you believe that solutions to these types of questions should provide exact matches to the data values given, then this is wrong. If you are willing to settle for numerical approximations that are close, then this is almost certainly close enough.

An exponential equation is an exponential equation, the choice of base is arbitrary and merely introduces a scaling factor.

Your tutor was just a step away. They have:

$
y=2e^{-kx}

k = \frac{ln \left( \frac{0.1}{2} \right)}{-3}
$

But at this point they grabbed for their calculator instead of working the problem just a bit further.

$
k \ = \ \frac{-ln (0.1/2) }{3} \ = \ \frac{ln (2/0.1) }{3} \ = \ \frac{ln (20) }{3}

y=2e^{\frac{-ln(20)x }{3}}
y=2 {\left( e^{ln20} \right)}^{\frac{-x}{3}}
y=2 {\left(20)}^{\frac{-x}{3}}
y=\frac{2}{20^{x/3}}

$

19. ### steveb Senior Member

Jul 3, 2008
2,433
469
The tutor's method is correct, but the answer is not mathematically exact, hence making it wrong in most math contexts. It might be good enough for engineering or science purposes, but the constant k is not exactly equal to one.

I got my answer by the same method as your tutor, but I did not make any approximations. Let's pick up where he went wrong.

$y=2 {\rm e}^{{{x}\over{3}}{\rm ln}(0.05)}$

Now use a property of exponents.

$y=2 ({\rm e}^{{\rm ln}(0.05)})^{{{x}\over{3}}}$

Now, note that ln and exp are inverse functions.

$y=2 (0.05)^{{{x}\over{3}}}={{2}\over{20^{x/3}}}$

20. ### bug13 Thread Starter Well-Known Member

Feb 13, 2012
1,214
39
To WBahn:

Point taken, thanks for pointing this out, sometime I do a bit too captious

To WBahn and steveb:

Thanks for the solutions, that's something I wasn't aware of before, appreciate it!!


text:
# Gravitational potential energy

Gravitational potential energy is the energy possessed by masses according to their spatial arrangement and the gravitational force (one of the four fundamental forces) that pulls them towards one another. Since Earth is so large compared to the objects on it, it's easy to watch these objects being pulled (falling) towards the center of the planet, not the planet being pulled towards the object. The direction of Earth's gravitational pull is just called "down."

There's a simulation to play with potential energy that shows the interaction of gravitational potential energy, kinetic energy and spring energy. The simulation below shows how energy flows back and forth between kinetic energy and gravitational potential energy (this is called mechanical energy).

Potential energy due to gravity is calculated using the following formula:

$E = mgh$

• E is energy, measured in joules (J)
• m is mass, measured in kilograms (kg)
• g is the acceleration due to gravity measured in m/s2. On the surface of Earth this is 9.81 m/s2.
• h is the height of an object relative to where it would be if it fell, measured in metres (m)
1. The more mass an object has, the more energy it stores. A 20 kg mass stores twice as much gravitational potential energy as a 10 kg mass at the same height.
2. The higher up an object is, the more energy it stores. A mass 10 m above the ground stores twice as much energy as the same mass only 5 m above the ground.
3. A stronger gravitational pull will also result in more gravitational potential energy. A mass 8 m above the surface of Earth stores much more gravitational potential energy than it would if it were 8 m above the moon.

Some forms of hydropower indirectly harness gravitational potential energy. The water behind a hydroelectric dam stores gravitational potential energy since it is at a higher level than the water on the other side of the dam. As the water falls, this potential energy is converted into kinetic energy, which turns turbines to generate electricity.

### PhET: Energy skate park

The University of Colorado has graciously allowed us to use the following Phet simulation. Explore this simulation to see how gravitational potential energy and kinetic energy go back and forth but keep mechanical energy the same. Notice how mechanical energy can be lost and turned into thermal energy, but the total amount of energy still stays the same:

## Authors and Editors

Jordan Hanania, James Jenden, Ellen Lloyd, Kailyn Stenhouse, Jason Donev


text:
## Tuesday Seminar on Topology

Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) KOHNO Toshitake, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya Tea: 16:30 - 17:00 Common Room

### 2011/11/22

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Toshitake Kohno (The University of Tokyo)
Quantum and homological representations of braid groups (JAPANESE)
[ Abstract ]
Homological representations of braid groups are defined as
the action of homeomorphisms of a punctured disk on
the homology of an abelian covering of its configuration space.
These representations were extensively studied by Lawrence,
Krammer and Bigelow. In this talk we show that specializations
of the homological representations of braid groups
are equivalent to the monodromy of the KZ equation with
values in the space of null vectors in the tensor product
of Verma modules when the parameters are generic.
To prove this we use representations of the solutions of the
KZ equation by hypergeometric integrals due to Schechtman,
Varchenko and others.

In the case of special parameters these representations
are extended to quantum representations of mapping
class groups. We describe the images of such representations
and show that the images of any Johnson subgroups
contain non-abelian free groups if the genus and the
level are sufficiently large. The last part is a joint
work with Louis Funar.


text:
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text:
# Solving large Markov Chains¶

This page shows how to compute the stationary distribution pi of a large Markov chain. The example is a tandem of two M/M/1 queues. Generally the transition matrix P of the Markov chain is sparse, so that we can either use scipy.sparse or Pysparse. Here we demonstrate how to use both of these tools.

## Power Method¶

In this section we find pi by means of iterative methods called the Power method. More specifically, given a (stochastic) transition matrix P, and an initial vector pi_0, compute iteratively pi_n = pi_{n-1} P until the distance (in some norm) between pi_n and pi_{n-1} is small enough.

Fist we build the generator matrix Q for the related Markov chain. Then we turn Q into a transition matrix P by the method of uniformization, that is, we define P as I - Q/l, where I is the identity matrix (of the same size as Q) and l is the smallest element on the diagonal of Q. Once we have P, we approximate pi (the left eigenvector of P that satisfies pi = pi P) by the iterates pi_n = pi_0 P\^n, for some initial vector pi_0.

More details of the above approach can be found in (more or less) any book on probability and Markov Chains. A fine example, with many nice examples and attention to the numerical solution of Markov chains, is Queueing networks and Markov Chains' by G. Bolch et al., John Wiley, 2nd edition, 2006.

You can get the source code for this tutorial here: tandemqueue.py

In [ ]:
#!/usr/bin/env python

labda, mu1, mu2 = 1., 1.01, 1.001
N1, N2 = 50, 50
size = N1*N2

from numpy import ones, zeros, empty
import scipy.sparse as sp
import  pysparse
from pylab import matshow, savefig
from scipy.linalg import norm
import time

This simple function converts the state (i,j), which represents that the first queue contains i jobs and the second queue j jobs, to a more suitable form to define a transition matrix.

In [ ]:
def state(i,j):
return j*N1 + i

Build the off-diagonal elements of the generator matrix Q.

In [ ]:
def fillOffDiagonal(Q):
# labda
for i in range(0,N1-1):
for j in range(0,N2):
Q[(state(i,j),state(i+1,j))]= labda
# mu2
for i in range(0,N1):
for j in range(1,N2):
Q[(state(i,j),state(i,j-1))]= mu2
# mu1
for i in range(1,N1):
for j in range(0,N2-1):
Q[(state(i,j),state(i-1,j+1))]= mu1

In this function we use scipy.sparse

In [ ]:
def computePiMethod1():
e0 = time.time()
Q = sp.dok_matrix((size,size))
fillOffDiagonal(Q)
# Set the diagonal of Q such that the row sums are zero
Q.setdiag( -Q*ones(size) )
# Compute a suitable stochastic matrix by means of uniformization
l = min(Q.values())*1.001  # avoid periodicity, see the book of Bolch et al.
P = sp.speye(size, size) - Q/l
# compute Pi
P =  P.tocsr()
pi = zeros(size);  pi1 = zeros(size)
pi[0] = 1;
n = norm(pi - pi1,1); i = 0;
while n > 1e-3 and i < 1e5:
pi1 = pi*P
pi = pi1*P   # avoid copying pi1 to pi
n = norm(pi - pi1,1); i += 1
print "Method 1: ", time.time() - e0, i
return pi

Now use Pysparse.

In [ ]:
def computePiMethod2():
e0 = time.time()
Q = pysparse.spmatrix.ll_mat(size,size)
fillOffDiagonal(Q)
# fill diagonal
x =  empty(size)
Q.matvec(ones(size),x)
Q.put(-x)
# uniformize
l = min(Q.values())*1.001
P = pysparse.spmatrix.ll_mat(size,size)
P.put(ones(size))
P.shift(-1./l, Q)
# Compute pi
P = P.to_csr()
pi = zeros(size);  pi1 = zeros(size)
pi[0] = 1;
n = norm(pi - pi1,1); i = 0;
while n > 1e-3 and i < 1e5:
P.matvec_transp(pi,pi1)
P.matvec_transp(pi1,pi)
n = norm(pi - pi1,1); i += 1
print "Method 2: ", time.time() - e0, i
return pi

Output the results.

In [ ]:
def plotPi(pi):
pi = pi.reshape(N2,N1)
matshow(pi)
savefig("pi.eps")
if __name__ == "__main__":
pi = computePiMethod1()
pi = computePiMethod2()
plotPi(pi)
`

Here is the result:

## Improvements of this Tutorial¶

Include other methods such as Jacobi's method or Gauss Seidel.

Section author: nokfi

Attachments


text:
# Building notification functionality into my notes app

Big thanks to binu.nz, matteas.nz, and pancake.nz for their help on this project.

Earlier this year I moved to a new note taking solution, Trilium Notes. After a lengthy discovery process including learning about the world of networked brain apps and Zettlekasten, I settled on Trilium for several reasons: it’s open source, self-hosted with a browser interface, has extensive markup functionality including the ability to export to Markdown (this article was written in Trilium), and is extensible via a note type called a ‘script note’. This allows you to extend functionality by simply writing JavaScript to run on either the frontend (chromium via electron) or backend (node.js) of the application. There are honestly so few downsides to this application, but if I had to list some it would be a slightly ugly interface (fixable via CSS), and no mobile app.

Previously, with Google Keep, I used to write myself notes, and then add alerts to be reminded of their content when I needed it. This worked as a reminder system for me well. So, I’ve set out to replicate this in Trilium, via the aforementioned script notes, and a self-hosted push notification service called Gotify. Let’s get started.

## Architecture

Trilium features a number of proof-of-concept implementations of script notes. One of these is a task manager, that allows you to group tasks in to categories, provide a to-do date, and a done date. These are stored in attributes called todoDate and doneDate, respectively.

I have been using this task manager for a while now, so I’d like to add notification functionality to it. The target functionality is that when a note’s todoDate is the current date, I should get a push notification on my Android phone, with the title of the note as the notification content.

### Gotify

To achieve this, I need a way of facilitating the notification on a mobile device. As Trilium has no mobile app, we can’t use direct notification integration. Instead, we can use a notification service, such as Gotify. Gotify is an incredibly simple websocket based notification server. It takes notification messages in from ‘apps’, and publishes all notifications received to ‘clients’. Gotfiy has a webclient and an Android app, which provides the Android notification integration I’m looking for.

Gotify was trivial to set-up. I used docker-compose to have a container up and running in about 10 minutes. My config ended up looking like this:

    version: "3"

services:
gotify:
image: gotify/server
restart: "unless-stopped"
ports:
- 8085:80
environment:
- TZ="Pacific/<redacted>"
volumes:
- "./gotify_data:/app/data"
- "./config.yml:/etc/gotify/config.yml"

I’ve added an additional volume where I’ve overridden the default config.yml. I’ll explain why later, but take note it was important for my implementation.

Some additional configuration was required to allow websocket requests through my reverse proxy server, which also applies HTTPS encapsulation. Examples on how to do this can be found on the Gotify website for all major reverse proxies.

So now we have Gotify up and running, let’s test it. An easy first test can be achieved with curl:

    [email protected]:~> curl "https://push.576i.nz/message?token=AHu8O88QRGLNaG0" -F "title=test 123" -F "message=holy guac it works" -F "priority=5"

And the result:

    {"id":2,"appid":1,"message":"holy guac it works","title":"test 123","priority":5,"date":"2021-10-30T05:32:09.401684375Z"}

We can see on the webclient they’ve come through:

Okay. So we have a working notification server. Now how do we implement this in Trilium?

### Websockets and JavaScript

Converting our simple curl one-liner to JavaScript proved more… difficult. By the end of the process, I knew substantially more about the differences between web-browser JS, node.js JS, and how to structure a websocket request than I bargained for.

Trilium, as a modern Electron webapp, is made up of two separate halves, the frontend and backend. The frontend runs in chromium (the embedded browser in Electron), and as such you can expect a typical web-browser based JS setup. The backend, in this case, is based on node.js. node.js doesn’t implement a number of typical browser-based JS libraries.

Naively, I started by writing the script externally in VSCode, testing in browser. Gotify’s example script uses Axios, a library used for HTTP operations. I had difficulty getting it to work successfully, so I consulted the experts, who advised me to use fetch. Fetch is a native browser-based HTTP library, and with some tinkering, we got the following going:

    const url = "https://push.576i.nz/message?token=AHu8O88QRGLNaG0";

let bodyFormData = new FormData();
bodyFormData.append('title', 'hello from trilium');
bodyFormData.append('message', 'omg it actually works from my note app');
bodyFormData.append('priority', '5');

fetch(url, {
method: "POST",

"Content-Type": "Content-Type: multipart/form-data; charset=utf-8; boundary='';"
},
body: bodyFormData
});

To get to this point, we had to wrestle with several speed bumps. You may recall I had overridden the default config for Gotify in my docker-compose.yml.

The reason for this is so that I could add a CORS header to all requests. The scope of this article doesn’t expand to CORS. but essentially the main thing that you need to know is that it’s a security check based on domains. Gotify’s Docker image has a number of environment variables that allow you to configure these headers, but the ‘*’ required for any origin is incompatible with the yaml globbing in docker-compose. I circumvented this by simply storing the default config locally and then importing it into Docker as a volume, which allows me to specify this line in the configuration:

    responseheaders: # response headers are added to every response (default: none)
Access-Control-Allow-Origin: "*"

This resolves the CORS issues.

### Trilium

So, we have a working fetch-based script. I pulled this into Trilium, and loaded it up as a frontend script. Upon testing, it worked! So, how do I populate this push function with data from my todo notes? Turns out the ability to get attributes of notes (what the todoDate label is) can only be done from the backend. Okay, no problem, I can pass from the frontend to the backend to get the data I need, and do the rest of the logic in the frontend.

The next snag is that Trilium’s in-built triggers that will fire my script for me, can only be run from the backend. You can pass from the frontend to the backend, but not the inverse of this. What this means is that if your script starts in the backend, it cannot be passed to the frontend at any point. Okay, no problem. I can just put fetch function into the backend script and run everything entirely in the backend.

Unfortunately, fetch is not implemented natively in node.js. This can be installed with npm, but with Trilium, I can’t add packages to the backend. So I’m stuck.

Luckily, the Trilium backend implements Axios! This is only slightly annoying, because I could’ve theoretically skipped the fetch stage entirely. However, it wasn’t a waste as it gave good opportunity to debug the CORS headers.

I rewrote the fetch request in Axois, based on the supplied example from Gotify:

    const axios = require("axios");

const url = "https://push.576i.nz/message?token=AHu8O88QRGLNaG0";
let bodyFormData = {
title: a,
message: b,
priority: c
};

axios({
method: "post",
"Content-Type": "application/json"
},
url: url,
data: bodyFormData
}

This was then added to a larger script that call’s Trilium’s API, following simple logic:

1. Get today’s date
2. Convert this to ISO format and truncate it to just yyyy-mm-dd
3. Get all notes with this value in the todoDate field as an array
4. Iterate through this array and send a push request for each one

So the final complete Trilium script is:

    // Get current date and format it using the ISO standard
let today = new Date();
let isotoday = today.toISOString();

// Get all notes with the label 'todoDate' and today's date as the value, truncating the time from the ISO date
let todoToday = api.getNotesWithLabel("todoDate", isotoday.substring(0, 10))

// Iterate through the array and send a push with the title as the message body
for (let i = 0; i < todoToday.length; i++) {
sendPush('Trilium Reminder', todoToday[i].title, 5)
}

function sendPush(a, b, c) {
const axios = require("axios");

const url = "https://push.576i.nz/message?token=AHu8O88QRGLNaG0";
let bodyFormData = {
title: a,
message: b,
priority: c
};

axios({
method: "post",
};


text:
Meteor strikes again

Part of a phone call:

-...well why didn't you just say so?

-It wasn't as easy as you thought, Jack. All the power lines here were destro---

-I know...It's not like we're living on a different planet Mark..

-Haha, good one. But you see, a second meteor hit this area. The good news is it was much smaller. The bad news is, there are absolutely zero power stations working.

-So how did you--

-This is what I'm trying to tell you. I went inside this place which seems to have been a really old battery store, which had a ton of charged batteries, I have no idea why it was abandoned. I'm talking from my mobile phone right now. The place also has a generator in case of emergency, which I've managed to get working with gas from my car. Listen, we don't have much time before the spaceship comes back. I've sent you an email, which you need to decrypt in order to see which part of the spaceship we need to---

-Hold on..did you say decrypt?

-They're monitoring everything on this planet, Jack.

-But then they'll know that it is encrypted.

-They're aliens, Jack.

-Oh. Yeah.

-Look, you don't have to decrypt it...just find the hidden message with the two keys I've included and I'll carry the rest otherwise. Just hurry up!

It seems he left a message for me in a part of his code he emailed me. Unfortunately, some of the text has been lost, so part of the message must be gone now. The following is the only thing saved. It's from the comments in his code.

Source code is written in one or more programming languages.
The programming of artificially intelligent robots to suffice...

The two keys:

• Pi $$\rightarrow$$ yes and no
• 413111 $$\rightarrow$$ position $$\rightarrow$$ anagram
• Any hints or places to start? (bumping old unanswered question) – shoover Sep 17 '17 at 1:21