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# Newtons Gravitational constant?

1. Mar 24, 2005

### rbj

many people have offered an explanation for why $$G$$ is what it is. it is what it is because of the units of time, length, and mass we humans have anthropocentrically decided to use. it is a fundamental quantity and if we adjust our definition of units appropriately, we can set it to whatever value we want it to be. you might want to check out the Planck units page at wikipedia: http://en.wikipedia.org/wiki/Planck_units . to ask why $$G$$ is what it is, is to ask why we are as tall (relative to the Planck length $$l_P$$) as we are, why we are as massive (relative to the Planck mass $$m_P$$) as we are and why our sense of time (relative to the Planck time $$t_P$$) is what it is. once you answer those questions, you have an answer to why $$G$$ is what it is or why $$c$$ is what it is or why $$\hbar$$ is what it is.

Frank Wilczek said it best (June 2001 Physics Today)*(http://www.physicstoday.org/pt/vol-54/iss-6/p12.html [Broken]):

...We see that the question [posed] is not, "Why is gravity so feeble?" but rather, "Why is the proton's mass so small?" For in Natural (Planck) Units, the strength of gravity simply is what it is, a primary quantity, while the proton's mass is the tiny number [1/(13 quintillion)]...

The strength of gravity is simply what it is and the strength of the electromagnetic force simply is what it is. The electromagnetic force operates on a different physical quantity (electric charge) than gravity (mass) so it cannot be compared directly to gravity. To note that gravity is an extremely weak force is, from the point-of-view of natural units, like comparing apples to oranges. It is true that the electrostatic repulsive force between two protons (alone in free space) greatly exceeds the gravitational attractive force between the same two protons, and that is because the charge on the protons are approximately a natural unit of charge but the mass of the protons are far, far less than the natural unit of mass.

r b-j

Last edited by a moderator: May 1, 2017
2. Mar 24, 2005

### Andrew Mason

G is just a number used to convert gravity to metric - m. kg. - units. If Planck units were used, Newton's law would be just: F = Mm/r^2

AM

3. Mar 25, 2005

### Andrew Mason

Or one could ask, why is the Planck mass so huge?! Or why is the proton/electron so gigantic? (10^28 Planck lengths). If we all lived in a world where the atom was 10^-28 times its size, we would think that gravity was a pretty big force because every proton would be a black hole. There is no right/wrong way to ask this question.

AM

Last edited by a moderator: May 2, 2017
4. Mar 25, 2005

### rbj

it becomes a sorta philosopical navel gazing, but there are concptually or pedagogically earlier questions to ask. the Planck units are derived from $$c, G, \hbar, 1/(4 \pi \epsilon_0)$$, which are properties of space without any consideration of any particles or objects or "things" to base the definitions of units on. (that's why i think this "gravitational fine-structure constant" is sorta bogus. also, if it were up to me, i would normalize $$4 \pi G$$ instead of $$G$$ and i would normalize $$\epsilon_0$$ instead of the Coulomb Force Constant as they did with the cgs system.) then you introduce these electrons and protons and positrons and neutrinos and whatever quark and other particles into the picture and ask why they have the size or the mass or the charge that they do. and, in terms of Planck units, you will get dimensionless numbers and those numbers are worth pondering. the dimensionful value of $$G$$ is not.

r b-j

5. Mar 26, 2005

### Ian

rbj,
I think the thread was closed because of the forum rules which say,
OK, rules are rules and this forum has its owners, but personally I feel this is a kind of jack-boot mentality. There is no 'expert' in the field of gravitation, neither has anyone been able to produce anything other than mathematical descriptions of gravitation and apply these to the cosmos. Math is not proof; reproduction of gravitational phenomena is proof and we have never seen anything of the sort.

The model I conceived predicts G perfectly and its simplicity makes it extremely difficult to argue against. However, if my name was Hawking, Penrose, Kaiku etc., everyone would listen to me. Its kind of a pharisaical doctrine that applies here.
This is such a great pity because with all the scientific jargon spoken everyone has missed something so simple (with respect to gravity) it defies belief.
AM commented on the Planck mass, but if you apply my thought to this quantity by a change of G at the proton density the Planck mass becomes equivalent to the proton mass, the Planck Length becomes the gravitational length of the proton mass and the planck time becomes the time for light to traverse the gravitational length of the proton mass.
Oh what the heck!

6. Mar 26, 2005

### Integral

Staff Emeritus
Ian,
When your "theory" has been accepted for publication in a peer reviewed journal we can have a discussion about it. Meanwhile it is our experience that the authors of theories such as yours are generally not open to criticism. They argue endlessly about the validity of their "theory", with their strongest suit simply being that they are ignorant of the theory they are attempting to revise. Thus we have terminated this practice as it is a waste of time.

The fact that you seem to be basing your theory on the rubber sheet analogy is an indication that you do not have in depth knowledge of Einstein' General Theory of Relativity.

Proceed with caution.

7. Mar 26, 2005

### rbj

no?

good math is mathematical proof. it is not confirmation of physical experiment, however, both SR and GR have had a few physical confirmations which moved it from the status that string theory has today to real physics.

i couldn't make any sense of it. and your premise of predicting a value for this dimensionful quantity is meaningless. G = 1 or whatever value you want it to be (by judicious choice of units).

i wouldn't attach the label "simplicity" to gobbledegook, but even so, there is a good quote from Einstein about simplicity.

when something is too good or incredible or wild to be true (that everybody just missed this beautiful and elegant idea that you caught), it usually isn't (true).

BTW, not being a physicist (i'm and electrical engineer that works with audio signal processing), i don't have any physics jargon. also there is a lot of modern physics i do not understand sufficiently. but i do understand the concepts of physical units and of dimensionless vs. dimensionful physical quantities and the meaning therein.

i think the terms "Planck mass", "Planck length" and "Planck time" have already been taken (and defined). unless your definitions are equivalent (they're not) you might call your units something else such as "Ian mass", "Ian length" and "Ian time". the proton mass does not ever equal the Planck mass, given the normal definition of the term.

r b-j

8. Mar 26, 2005

### rbj

gee, i would hope that we could talk here about ideas or theories without having to get them published in a real hard-core journal. after all, crappy ideas here only waste time and not trees.

i fully agree if someone is posting about a personal pet theory (i have mine about what are the most natural physical units and i think that Planck was off by a factor of $$\sqrt{4 \pi }$$, but it's picking nits), they need to be open to real discussion where they can potentially learn something from someone else. if Ian (or any of us) can't do that, then it's a waste of time.

i have to confess that, although i'm pretty good at a lot of UG and graduate level applied math, i have great trouble conceptually with tensors and barely understood in classical mechanics what good the Hamiltonian was over the elementary expression of Newtonian mechanics. i understand classical physics pretty good and SR and elementary QM (and a little bit of semiconductor physics), but don't have any idea where all these particles (leptons, etc.) come from and can't do anything serious with GR. i do understand the fundamental concepts (e.g. Equivalence Principle) of GR and am gratified that a limiting (in reasonably flat space-time) expression of GR can be made with something that looks like Maxwell's Eqs. (that seems natural to me since both E&M and gravitation are inverse-square law with speed of propagation equal to $c$.)

as always.

r b-j

9. Mar 26, 2005

### Integral

Staff Emeritus
Rbj
Note that my comments were directed at Ian, the one who posted the original opinion.

It was a common consensus among the mentors to disallow the discussions of personal theories. Simply because they tended to suck up huge amounts of time, reading the posts, attempting to understand them, and explaining the errors. Then, nearly universally, all of this work was rendered wasted simply because the originators of the "theories" had such a poor understanding of Physics in general that they could not understand what was wrong with their ideas. No amount of explaining can change this situation.

We would rather spend our time working with students who wish to learn, or discussing legitimate physical concepts with others, who do understand physics, or are making an honest effort to learn.

Most who bring a personal theory here have spend months or even years believing that they are thinking outside the box, when in reality they are wondering lost in a dark dusty corner of the box with no idea of where the box is. Having but this much effort into faulty thinking they are not eager or willing to change their views. There are many other forums on the web where such topics are discussed and argued endlessly, Personal theories should be taken to one of those sites.


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# All Seminars

Title: A limit theorem in Optimal transportation theory
Seminar: Analysis and Differential Geometry
Speaker: Professor Gershon Wolansky of Israel Institute of Technology - Technion
Contact: Vladimir Oliker, oliker@emory.edu
Date: 2020-02-11 at 4:00PM
Venue: MSC W301
Abstract:
I’ll review the fundamental theory of optimal transportation and define the notion of conditional Wasserstein metric on the set of probability measures. If time permits I’ll discuss various applications to control, regularity of flows, dynamics, and design of optimal networks.
Title: Moduli spaces in computer vision
Colloquium: Algebra and Number Theory
Speaker: Max Lieblich of University of Washington
Contact: David Zureick-Brown, david.zureick-brown@emory.edu
Date: 2020-02-10 at 2:30PM
Venue: Mathematics and Science Center: MSC E208
Abstract:
Moduli theory is one of the cornerstones of algebraic geometry. The underlying idea of the theory is that, given a class of mathematical objects, one can often find a universal space parametrizing those objects, and the geometry of this space gives us insight into the objects being parametrized. After introducing moduli theory with some basic classical examples, I will discuss recent applications to computer vision. As it turns out, the roots of computer vision are tightly intertwined with classical projective geometry. I will present the early history and basic geometric problems of computer vision, and then I will talk about how modern methods give us deeper insight into these problems, including new understandings of core algorithms that are used billions of times a day all over the planet.
Title: The foundation of a matroid
Colloquium: Algebra and Number Theory
Speaker: Matt Baker of Georgia Institute of Technology
Contact: David Zureick-Brown, david.zureick.brown@gmail.com
Date: 2020-02-05 at 4:00PM
Venue: MSC W303
Abstract:
Originally introduced independently by Hassler Whitney and Takeo Nakasawa, matroids are a combinatorial way of axiomatizing the notion of linear independence in vector spaces. If $K$ is a field and $n$ is a positive integer, any linear subspace of $K^n$ gives rise to a matroid; such matroid are called \textbf{representable} over $K$. Given a matroid $M$, one can ask over which fields $M$ is representable. More generally, one can ask about representability over partial fields in the sense of Semple and Whittle. Pendavingh and van Zwam introduced the \textbf{universal partial field} of a matroid $M$, which governs the representations of $M$ over all partial fields. Unfortunately, most matroids (asymptotically 100\%, in fact) are not representable over any partial field, and in this case, the universal partial field gives no information.

Oliver Lorscheid and I have introduced a generalization of the universal partial field which we call the \textbf{foundation} of a matroid. The foundation of $M$ is a type of algebraic object which we call a \textbf{pasture}; pastures include both hyperfields and partial fields. Pastures form a natural class of field-like objects within Lorscheid's theory of ordered blueprints, and they have desirable categorical properties (e.g., existence of products and coproducts) that make them a natural context in which to study algebraic invariants of matroids. The foundation of a matroid $M$ represents the functor taking a pasture $F$ to the set of rescaling equivalence classes of $F$-representations of $M$; in particular, $M$ is representable over a pasture $F$ if and only if there is a homomorphism from the foundation of $M$ to $F$. (In layman's terms, what we're trying to do is recast as much as possible of the theory of matroids and their representations in functorial Grothendieck-style'' algebraic geometry, with the goal of gaining new conceptual insights into various phenomena which were previously understood only through lengthy case-by-case analyses and ad hoc computations.)

As a particular application of this point of view, I will explain the classification which Lorscheid and I have recently obtained of all possible foundations for ternary matroids (matroids representable over the field of three elements). The proof of this classification theorem relies crucially on Tutte's celebrated Homotopy Theorem.
Title: An introduction to counting curves arithmetically
Colloquium: Algebra and Number Theory
Speaker: Jesse Kass of University of South Carolina
Contact: David Zureick-Brown, david.zureick-brown@emory.edu
Date: 2020-02-03 at 2:30PM
Venue: Mathematics and Science Center: MSC E208
Abstract:
A long-standing program in algebraic geometry focuses on counting the number of curves in special configuration such as the lines on a cubic surface (27) or the number of conic curves tangent to 5 given conics (3264). While many important counting results have been proven purely in the language of algebraic geometry, a major modern discovery is that curve counts can often be interpreted in terms of algebraic topology and this topological perspective reveals unexpected properties.

One problem in modern curve counting is that classical algebraic topology is only available when working over the real or complex numbers. A successful solution to this problem should produce curve counts over fields like the rational numbers in such a way as to record interesting arithmetic information. My talk will explain how to derive such counts using ideas from A1-homotopy theory. The talk will focus on joint work with Marc Levine, Jake Solomon, and Kirsten Wickelgren including a new result about lines on the cubic surface.
Title: Deep Learning meets Modeling: Taking the Best out of Both Worlds
Seminar: Computational Mathematics
Speaker: Gitta Kutyniok, Einstein Chair for Mathematic of TU Berlin
Contact: James Nagy, jngay@emory.edu
Date: 2020-02-03 at 4:00PM
Venue: MSC N306
Abstract:
Pure model-based approaches are today often insufficient for solving complex inverse problems in imaging. At the same time, we witness the tremendous success of data-based methodologies, in particular, deep neural networks for such problems. However, pure deep learning approaches often neglect known and valuable information from the modeling world.

In this talk, we will provide an introduction to this problem complex and then focus on the inverse problem of (limited-angle) computed tomography. We will develop a conceptual approach by combining the model-based method of sparse regularization by shearlets with the data-driven method of deep learning. Our solvers are guided by a microlocal analysis viewpoint to pay particular attention to the singularity structures of the data. Finally, we will show that our algorithm significantly outperforms previous methodologies, including methods entirely based on deep learning.
Title: Polynomials vanishing on points in projective space
Colloquium: Algebra and Number Theory
Speaker: Brooke Ullery of Harvard University
Contact: David Zureick-Brown, david.zureick-brown@emory.edu
Date: 2020-01-30 at 4:00PM
Venue: MSC W301
Abstract:
We all know that any two points in the plane lie on a unique line. However, three points will lie on a line only if those points are in a very special position: collinear. More generally if Z is a set of k points in n-space, we can ask what the set of polynomials of degree d in n variables that vanish on all the points of Z looks like. The answer depends not only on the values of k, d, and n but also (as we see in the case of three collinear points) on the geometry of Z. This question, in some form, dates back to at least the 4th century. We will talk about several attempts to answer it throughout history and some surprising connections to modern algebraic geometry.
Title: PDE-Principled Trustworthy Deep Learning Meets Computational Biology
Colloquium: Computational Mathematics
Speaker: Bao Wang of University of California, Los Angeles
Contact: James Nagy, jnagy@emory.edu
Date: 2020-01-23 at 3:00PM
Venue: MSC W303
Abstract:
Deep learning achieves tremendous success in image and speech recognition and machine translation. However, deep learning is not trustworthy. 1. How to improve the robustness of deep neural networks? Deep neural networks are well known to be vulnerable to adversarial attacks. For instance, malicious attacks can fool the Tesla self-driving system by making a tiny change on the scene acquired by the intelligence system. 2. How to compress high-capacity deep neural networks efficiently without loss of accuracy? It is notorious that the computational cost of inference by deep neural networks is one of the major bottlenecks for applying them to mobile devices. 3. How to protect the private information that is used to train a deep neural network? Deep learning-based artificial intelligence systems may leak the private training data. Fredrikson et al. recently showed that a simple model-inversion attack can recover the portraits of the victims whose face images are used to train the face recognition system.

In this talk, I will present some recent work on developing PDE-principled robust neural architecture and optimization algorithms for robust, accurate, private, and efficient deep learning. I will also present some potential applications of the data-driven approach for bio-molecule simulation and computer-aided drug design.
Title: Gradient Flows: From PDE to Data Analysis
Colloquium: Computational Mathematics
Speaker: Franca Hoffmann of California Institute of Technology
Contact: James Nagy, jnagy@emory.edu
Date: 2020-01-21 at 3:00PM
Venue: MSC W303
Abstract:
Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.

In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.

In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.
Title: Comparison principles for stochastic heat equations
Seminar: PDE Seminar
Speaker: Le Chen of Emory University
Date: 2020-01-17 at 1:00PM
Venue: MSC E408
Abstract:
The stochastic heat equation is a canonical model that is related to many models in mathematical physics, mathematical biology, particle systems, etc. It usually takes the following form: $\left(\frac{\partial }{\partial t} -\frac{1}{2}\Delta \right) u(t,x) = \rho(u(t,x)) \:\dot{M}(t,x), \qquad u(0,\cdot) =\mu, \qquad t>0, \: x\in R^d,$ where $\mu$ is the initial data, $\dot{M}$ is a spatially homogeneous Gaussian noise that is white in time and $\rho$ is a Lipschitz continuous function. In this talk, we will study a particular set of properties of this equation --- the comparison principles, which include both {\it sample-path comparison} and {\it stochastic comparison principles}. These results are obtained for general initial data and under the weakest possible requirement on the correlation function --- Dalang's condition, namely, $\int_{ R^d}(1+|\xi|^2)^{-1}\hat{f}(d \xi)<\infty$, where $\hat{f}$ is the spectral measure of the noise. For the sample-path comparison, one can compare solutions pathwisely with respect to different initial conditions $\mu$, while for the stochastic comparison, one can compare certain functionals of the solutions either with respect to different diffusion coefficients $\rho$ or different correlation functions of the noise $f$. This talk is based on some joint works with Jingyu Huang and Kunwoo Kim.
Title: Geometry + Optimization: towards computational anatomy
Colloquium: Computational Mathematics
Speaker: Shahar Kovalsky of Duke University
Contact: James Nagy, jnagy@emory.edu
Date: 2020-01-16 at 3:00PM
Venue: MSC W303
Abstract:
Geometric shape-processing lies at the heart of various branches of science: from finite element simulation in engineering, through animation of virtual avatars, to applications such as the analysis of anatomical variations, or detection of structural anomalies in medicine and biology. The demand for such computational approaches in geometry is constantly growing, as 3-dimensional data becomes readily available and is integrated into various everyday uses.

I will begin my talk with a brief overview of optimization-based approaches for geometric problems, such as identifying pointwise correspondences between exemplars in a collection of shapes, or deforming shapes to satisfy prescribed constraints in a least-distorting manner. After discussing some of the theoretical and computational challenges arising in these optimization problems, I will focus on large-scale geometric problems and efficient first- and second-order algorithms for their optimization. Then, motivated by anatomical shape analysis, I will show applications of these computational approaches for shape characterization and comparison in evolutionary anthropology.

I will finish with briefly presenting two related but tangential works: a theoretical work on the characterization of planar harmonic maps into non-convex domains, and a clinical work on the prediction of thyroid cancer from biopsy images.

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# Mansion point and incenter

In acute triangle $$ABC$$, $$AB>AC$$. Let $$I$$ the incenter, $$\Omega$$ the circumcircle of triangle $$ABC$$, and $$D$$ the foot of perpendicular from $$A$$ to $$BC$$. $$AI$$ intersects $$\Omega$$ at point $$M(\neq A)$$, and the line which passes $$M$$ and perpendicular to $$AM$$ intersects $$AD$$ at point $$E$$. Now let $$F$$ the foot of perpendicular from $$I$$ to $$AD$$. Prove that $$ID\cdot AM=IE\cdot AF$$

What I thought: Notice that $$\triangle IDE$$ and $$\triangle AFM$$ are similar after some angle chasing.

• If $IDE$ and $AFM$ are similar, then $ID/IE=AF/AM$, which is the relation you want to prove. Nov 16 '19 at 22:20
• What is the meaning of "Mansion" in your title ? Nov 17 '19 at 0:45
• This is question 2 from the 2019 Korean National Olympiad. Nov 17 '19 at 10:27

COMMENT:

You correctly found that $$\triangle IDE≈\triangle AFM$$.We rewrite the required relation as:

$$\frac{AF}{AM}=\frac{ID}{IE}$$

That is triangles IAE and DIE must be similar. These two triangles have common angle $$\angle IED$$, therefore we must have:

$$\angle IDE=\angle EIA$$

This is not possible because:

$$\angle IDE=\angle BDE (=90^o)+\angle BDI$$

$$\angle EIA=\angle EIF (≠90^o)+\angle FIA(=BDI)$$

• Great observation! How can I contact you? Nov 23 '19 at 15:34
• through this site or this address (sirous_f20@yahoo.com) Nov 23 '19 at 15:49


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# Strategy dynamics

The word ‘dynamics’ appears frequently in discussions and writing about strategy, and is used in two distinct, though equally important senses.

The dynamics of strategy and performance concerns the ‘content’ of strategy – initiatives, choices, policies and decisions adopted in an attempt to improve performance, and the results that arise from these managerial behaviors.

The dynamic model of the strategy process is a way of understanding how strategic actions occur. It recognizes that strategic planning is dynamic, that is, strategy-making involves a complex pattern of actions and reactions. It is partially planned and partially unplanned.

A literature search shows the first of these senses to be both the earliest and most widely used meaning of ‘strategy dynamics’, though that is not to diminish the importance of the dynamic view of the strategy process.

## Static models of strategy and performance

The static assessment of strategy and performance, and its tools and frameworks dominate research, textbooks and practice in the field. They stem from a presumption dating back to before the 1980s that market and industry conditions determine how firms in a sector perform on average, and the scope for any firm to do better or worse than that average. E.g. the airline industry is notoriously unprofitable, but some firms are spectacularly profitable exceptions.

The ‘industry forces’ paradigm was established most firmly by Michael Porter, (1980) in his seminal book ‘Competitive Strategy’, the ideas of which still form the basis of strategy analysis in many consulting firms and investment companies. Richard Rumelt (1991) was amongst the first to challenge this presumption of the power of ‘industry forces’, and it has since become well-understood that business factors are more important drivers of performance than are industry factors – in essence, this means you can do well in difficult industries, and struggle in industries where others do well. Although the relative importance of industry factors and firm-specific factors continues to be researched, the debate is now essentially over – management of strategy matters.

The increasing interest in how some businesses in an industry perform better than others led to the emergence of the ‘resource based view’ (RBV) of strategy (Wernerfelt, 1984; Barney, 1991; Grant, 1991), which seeks to discover the firm-specific sources of superior performance – an interest that has increasingly come to dominate research.

## The need for a dynamic model of strategy and performance

The debate about the relative influence of industry and business factors on performance, and the RBV-based explanations for superior performance both, however, pass over a more serious problem. This concerns exactly what the ‘performance’ is that management seeks to improve. Would you prefer, for example, (A) to make \$15m per year indefinitely, or (B) \$12m this year, increasing by 20% a year, starting with the same resources?

Nearly half a century ago, Edith Penrose (1959) pointed out that superior profitability (e.g. return on sales or return on assets) was neither interesting to investors – who value the prospect of increasing future cash flows – nor sustainable over time. Profitability is not entirely unimportant – it does after all provide the investment in new resources to enable growth to occur. More recently, Rugman and Verbeke (2002) have reviewed the implications of this observation for research in strategy. Richard Rumelt (2007) has again raised the importance of making progress with the issue of strategy dynamics, describing it as still ‘the next frontier … underresearched, underwritten about, and underunderstood’.

The essential problem is that tools explaining why firm A performs better than firm B at a point in time are unlikely to explain why firm B is growing its performance more rapidly than firm A.

This is not just of theoretical concern, but matters to executives too – efforts by the management of firm B to match A’s profitability could well destroy its ability to grow profits, for example. A further practical problem is that many of the static frameworks do not provide sufficiently fine-grained guidance on strategy to help raise performance. For example, an investigation that identifies an attractive opportunity to serve a specific market segment with specific products or services, delivered in a particular way is unlikely to yield fundamentally different answers from one year to the next. Yet strategic management has much to do from month to month to ensure the business system develops strongly so as to take that opportunity quickly and safely. What is needed, is a set of tools that explain how performance changes over time, and how to improve its future trajectory – i.e. a dynamic model of strategy and performance.

## A possible dynamic model of strategy and performance

To develop a dynamic model of strategy and performance requires components that explain how factors change over time. Most of the relationships on which business analysis are based describe relationships that are static and stable over time. For example, “profits = revenue minus costs”, or “market share = our sales divided by total market size” are relationships that are true. Static strategy tools seek to solve the strategy problem by extending this set of stable relationships, e.g. “profitability = some complex function of product development capability”. Since a company’s sales clearly change over time, there must be something further back up the causal chain that makes this happen. One such item is ‘customers’ – if the firm has more customers now than last month, then (everything else being equal), it will have more sales and profits.

The number of ‘Customers’ at any time, however, cannot be calculated from anything else. It is one example of a factor with a unique characteristic, known as an ‘asset-stock’. This critical feature is that it accumulates over time, so “customers today = customers yesterday +/- customers won and lost”. This is not a theory or statistical observation, but is axiomatic of the way the world works. Other examples include cash (changed by cash-in and cash-out-flows), staff (changed by hiring and attrition), capacity, product range and dealers. Many intangible factors behave in the same way, e.g. reputation and staff skills. Dierickx and Cool (1989) point out that this causes serious problems for explaining performance over time:

• Time compression diseconomies i.e. it takes time to accumulate resources.
• Asset Mass Efficiencies ‘the more you have, the faster you can get more’..
• Interconnectedness of Asset Stocks .. building one resource depends on other resources already in place.
• Asset erosion .. tangible and intangible assets alike deteriorate unless effort and expenditure are committed to maintaining them
• Causal ambiguity .. it can be hard to work out, even for the firm who owns a resource, why exactly it accumulates and depletes at the rate it does.

The consequences of these features is that relationships in a business system are highly non-linear. Statistical analysis will not, then, be able meaningfully to confirm any causal explanation for the number of customers at any moment in time. If that is true then statistical analysis also cannot say anything useful about any performance that depends on customers or on other accumulating asset-stocks – which is always the case.

Fortunately, a method known as system dynamics captures both the math of asset-stock accumulation (i.e. resource- and capability-building), and the interdependence between these components (Forrester, 1961; Sterman, 2000). The asset-stocks relevant to strategy performance are resources [things we have] and capabilities [things we are good at doing]. This makes it possible to connect back to the resource-based view, though with one modification. RBV asserts that any resource which is clearly identifiable, and can easily be acquired or built, cannot be a source of competitive advantage, so only resources or capabilities that are valuable, rare, hard to imitate or buy, and embedded in the organization [the ‘VRIO’ criteria] can be relevant to explaining performance, for example reputation or product development capability. Yet day-to-day performance must reflect the simple, tangible resources such as customers, capacity and cash. VRIO resources may be important also, but it is not possible to trace a causal path from reputation or product development capability to performance outcomes without going via the tangible resources of customers and cash.

Warren (2002, 2007) brought together the specification of resources [tangible and intangible] and capabilities with the math of system dynamics to assemble a framework for strategy dynamics and performance with the following elements:

• Performance, P, at time t is a function of the quantity of resources R1 to Rn, discretionary management choices, M, and exogenous factors, E, at that time (Equation 1).
(1) P(t) = f{R1(t), .. Rn(t), M(t), E(t)}
• The current quantity of each resource Ri at time t is its level at time t-1 plus or minus any resource-flows that have occurred between t-1 and t (Equation 2).
(2) Ri(t) = Ri (t-1) +/- ${\displaystyle \bigtriangleup }$ Ri(t-1 .. t)
• The change in quantity of Ri between time t-1 and time t is a function of the quantity of resources R1 to Rn at time t-1, including that of resource Ri itself, on management choices, M, and on exogenous factors E at that time (Equation 3).
(3) ${\displaystyle \bigtriangleup }$ Ri(t-1 .. t) = f{R1(t-1), .. Rn(t-1), M(t-1), E(t-1)}

This set of relationships gives rise to an ‘architecture’ that depicts, both graphically and mathematically, the core of how a business or other organization develops and performs over time. To this can be added other important extensions, including :

• the consequence of resources varying in one or more qualities or ‘attributes’ [e.g. customer size, staff experience]
• the development of resources through stages [disloyal and loyal customers, junior and senior staff]
• rivalry for any resource that may be contested [customers clearly, but also possibly staff and other factors]
• intangible factors [e.g. reputation, staff skills]
• capabilities [e.g. product development, selling]

## The Static Model of the Strategy Process

According to many introductory strategy textbooks, strategic thinking can be divided into two segments : strategy formulation and strategy implementation. Strategy formulation is done first, followed by implementation.

Strategy formulation involves:

1. Doing a situation analysis: both internal and external; both micro-environmental and macro-environmental.
2. Concurrent with this assessment, objectives are set. This involves crafting vision statements (long term), mission statements (medium term), overall corporate objectives (both financial and strategic), strategic business unit objectives (both financial and strategic), and tactical objectives.
3. These objectives should, in the light of the situation analysis, suggest a strategic plan. The plan provides the details of how to obtain these goals.

This three-step strategy formation process is sometimes referred to as determining where you are now, determining where you want to go, and then determining how to get there.

The next phase, according to this linear model is the implementation of the strategy. This involves:

• Allocation of sufficient resources (financial, personnel, time, computer system support)
• Establishing a chain of command or some alternative structure (such as cross-functional teams)
• Assigning responsibility of specific tasks or processes to specific individuals or groups
• Managing the process. This includes monitoring results, comparing to benchmarks and best practices, evaluating the efficacy and efficiency of the process, controlling for variances, and making adjustments to the process as necessary.
• When implementing specific programs, this involves acquiring the requisite resources, developing the process, training, process testing, documentation, and integration with (and/or conversion from) legacy processes

## The Dynamic Model of the Strategy Process

Several theorists have recognized a problem with this static model of the strategy process: it is not how strategy is developed in real life. Strategy is actually a dynamic and interactive process. Some of the earliest challenges to the planned strategy approach came from Linblom in the 1960s and Quinn in the 1980s.

Charles Lindblom (1959) claimed that strategy is a fragmented process of serial and incremental decisions. He viewed strategy as an informal process of mutual adjustment with little apparent coordination.

James Brian Quinn (1978) developed an approach that he called "logical incrementalism". He claimed that strategic management involves guiding actions and events towards a conscious strategy in a step-by-step process. Managers nurture and promote strategies that are themselves changing. In regard to the nature of strategic management he says: "Constantly integrating the simultaneous incremental process of strategy formulation and implementation is the central art of effective strategic management." (?page 145). Whereas Lindblom saw strategy as a disjointed process without conscious direction, Quinn saw the process as fluid but controllable.

Joseph Bower (1970) and Robert Burgelman (1980) took this one step further. Not only are strategic decisions made incrementally rather than as part of a grand unified vision, but according to them, this multitude of small decisions are made by numerous people in all sections and levels of the organization.

Henry Mintzberg (1978) made a distinction between deliberate strategy and emergent strategy. Emergent strategy originates not in the mind of the strategist, but in the interaction of the organization with its environment. He claims that emergent strategies tend to exhibit a type of convergence in which ideas and actions from multiple sources integrate into a pattern. This is a form of organizational learning, in fact, on this view, organizational learning is one of the core functions of any business enterprise (See Peter Senge's The Fifth Discipline (1990).)

Constantinos Markides (1999) describes strategy formation and implementation as an ongoing, never-ending, integrated process requiring continuous reassessment and reformation.

A particularly insightful model of strategy process dynamics comes from J. Moncrieff (1999). He recognized that strategy is partially deliberate and partially unplanned, though whether the resulting performance is better for being planned or not is unclear. The unplanned element comes from two sources : “emergent strategies” result from the emergence of opportunities and threats in the environment and “Strategies in action” are ad hoc actions by many people from all parts of the organization. These multitudes of small actions are typically not intentional, not teleological, not formal, and not even recognized as strategic. They are emergent from within the organization, in much the same way as “emergent strategies” are emergent from the environment. However, it is again not clear whether, or under what circumstances, strategies would be better if more planned.

In this model, strategy is both planned and emergent, dynamic, and interactive. Five general processes interact. They are strategic intention, the organization's response to emergent environmental issues, the dynamics of the actions of individuals within the organization, the alignment of action with strategic intent, and strategic learning.

The alignment of action with strategic intent (the top line in the diagram), is the blending of strategic intent, emergent strategies, and strategies in action, to produce strategic outcomes. The continuous monitoring of these strategic outcomes produces strategic learning (the bottom line in the diagram). This learning comprises feedback into internal processes, the environment, and strategic intentions. Thus the complete system amounts to a triad of continuously self-regulating feedback loops. Actually, quasi self-regulating is a more appropriate term since the feedback loops can be ignored by the organization. The system is self-adjusting only to the extent that the organization is prepared to learn from the strategic outcomes it creates. This requires effective leadership and an agile, questioning, corporate culture. In this model, the distinction between strategy formation and strategy implementation disappears.

## Criticisms of Dynamic Strategy Process Models

Some detractors claim that these models are too complex to teach. No one will understand the model until they see it in action. Accordingly, the two part linear categorization scheme is probably more valuable in textbooks and lectures.

Also, there are some implementation decisions that do not fit a dynamic model. They include specific project implementations. In these cases implementation is exclusively tactical and often routinized. Strategic intent and dynamic interactions influence the decision only indirectly.

## References

• Barney, J. (1991). Firm resources and sustained competitive advantage. Journal of Management, Vol. 17, No. 1, pp. 99–120.
• Bower, J. (1970). Managing the resource allocation process : A study of planning and investment, Graduate school of business (papers), Harvard University, Boston, 1970.
• Burgelman, R. (1980). Managing Innovating systems: A study in the process of internal corporate venturing, Graduate school of business (PhD dissertation), Columbia University, 1980.
• Dierickx, I. and Cool, K. (1989). Asset stock accumulation and sustainability of competitive advantage. Management Science, Vol. 35, pp. 1504–1511.
• Forrester, J. (1961). Industrial Dynamics. MIT Press, Cambridge MA.
• Grant, R. (1991). The resource-based theory of competitive advantage: implications for strategy formulation. California Management Review (Spring), pp. 119–135.
• Lindblom, C. (1959). The science of muddling through, Public Administration Review, Vol. 19, No. 2, 1959, pp 79–81.
• Lovallo, D. and Mendonca, L. (2007). Strategy’s Strategist: An interview with Richard Rumelt. The McKinsey Quarterly, 2007 No. 4, pp. 56–67.
• Markides, C. (1999). A dynamic view of strategy. Sloan Management Review, vol 40, spring 1999, pp 55–63.
• Markides, C. (1997). Strategic innovation. Sloan Management Review, vol 38, spring 1997, pp 31–42.
• Moncrieff, J. (1999). Is strategy making a difference? Long Range Planning Review, vol 32, no 2, pp 273–276.
• Mintzberg, H. (1978). Patterns in Strategy Formation, Management Science, Vol 24, No 9, 1978, pp 934–948.
• Penrose, E. (1959). The Theory of the Growth of the Firm, Oxford University Press: Oxford.
• Porter, M. (1980). Competitive Strategy, Free Press, New York.
• Quinn, B. (1980). Strategies for Change: Logical Incrementalism, Irwin, Homewood Ill, 1980.
• Rugman, A. and Verbeke, A. (2002). The contribution of Edith Penrose to the resource-based view of strategic management. Strategic Management Journal, 2002, Vol. 23, No. 8, pp. 769–780.
• Rumelt, R. (1991). How Much Does Industry Matter?, Strategic Management Journal, Vol 12, pp 167–185.
• Sterman, J. (2000). Business Dynamics: Systems thinking and modeling for a complex world. McGraw-Hill, New York.
• Warren, K. (2002). Competitive Strategy Dynamics. Wiley, Chichester.
• Warren, K. (2007). Strategic Management Dynamics. Wiley, Chichester.
• Wernerfelt, B. (1984). A Resource-Based View of the Firm. Strategic Management Journal, Vol. 5, pp. 171–180.


text:
Show equation has at most two solutions on (0,2*Pi)

$\sin (\text{ha})\text{ = } \text{dec}'(\text{ha}) (\tan (\text{lat})-\cos (\text{ha}) \tan (\text{dec}(\text{ha})))$

I want to show this equation has at most two solutions for 0 < ha < 2*Pi under these conditions, for ANY function dec[ha] and ANY value of lat satisfying the conditions below:

• lat is fixed and between -Pi/2 and Pi/2, noninclusive

• Abs[dec[ha]] is bounded by Pi/6

• Abs[dec'[ha]] is bounded by 1/36, and dec[ha] is everywhere differentiable.

If this can be shown, what is the weakest bound I can put on dec'[ha] so that this equation still has at most 2 solutions in (0,2*Pi)?

Purpose: resolve http://astronomy.stackexchange.com/questions/962/

-
it might be in your link, but I think you owe it to us to define what "dec" means in your question. This is a math forum, and I don't think that's a standard math term. –  Stefan Smith Nov 30 '13 at 18:29
Thanks, edited. I want this for ANY function dec[ha] (that satisfies the given conditions). –  barrycarter Nov 30 '13 at 18:30


text:
### 3490

The tuned trinity of b-tensors
Samo Lasič1, Henrik Lundell2, and Daniel Topgaard3

1Random Walk Imaging, Lund, Sweden, 2Danish Research Centre for Magnetic Resonance, Centre for Functional and Diagnostic Imaging and Research, Copenhagen University Hospital Hvidovre, Copenhagen, Denmark, 3Division of Physical Chemistry, Department of Chemistry, Lund University, Lund, Sweden, Lund, Sweden

### Synopsis

Unprecedented microstructural details of heterogeneous materials such as tissue are non-invasively accessible by multidimensional diffusion encoding (MDE) MRI using varying shapes of b-tensors. MDE can probe multidimensional distributions of diffusion tensors in terms of their size, shape and orientation. For robust conclusions, time-dependent diffusion effects need to be considered in MDE. A convenient recipe for generating b-tensors of varying shape was implemented including a single adjustable tuning parameter. The resulting b-tensors can thus be tuned for sensitivity to time-dependent diffusion.

### Introduction

Microstructural features of heterogeneous materials, such as average cell eccentricity or variance of cell density, which are inferred from optical microscopy images, can be quantified non-invasively by multidimensional diffusion encoding (MDE) MRI using varying shapes of b-tensors1-5. With MDE, distributions of diffusion tensors can be characterized in terms of size, shape and orientation3,4. This information is directly encoded in the measured signal by MDE, which is not possible by conventional diffusion MRI. In contrast, due to the inability of providing more specific data, conventional approaches heavily rely on data modeling assumptions, rendering conclusions unreliable6,7. If not accounted for, time-dependent diffusion effects may still skew MDE results. This can happen if different b-tensors are probing diffusion at different time scales. As we have demonstrated previously using spherical and linear b-tenors, spectral analysis of encoding and diffusion allows designing tuned MDE waveforms, which yield equal first-order signal attenuation. The tuning dimension also provides an additional orthogonal measurement suited to probe correlations between anisotropy and size of restrictions8. A convenient recipe can be used to yield b-tensors with arbitrary anisotropy and asymmetry3,4. Here we have implemented spectral tuning by modifying the previous recipe with a single adjustable tuning parameter.

### Frequency analysis of encoding

To the first order, signal attenuation is given by9 $$\beta = \frac{1}{2\pi}\int_{-\infty}^{\infty} F_{i}(\omega) D_{ij}(\omega) F^*_{j}(\omega) d\omega,$$ where we adopt the Einstein summation convention, $\mathbf{D}(\omega)$ is the velocity correlation spectrum, $\mathbf{F}(\omega)$ is the spectrum of dephasing $$\mathbf{F}(\omega) = \int_{0}^{\tau} \mathbf{q} (t) \exp^{-i\omega t}dt$$ and dephasing is given by the effective gradient as $\mathbf{q} (t) = \gamma \int_{0}^{t} \mathbf{G} (s) ds$. Directional average of the power spectrum, $F_{i}(\omega) F^*_{j}(\omega)$, is given by the sum of power spectra along any three orthogonal axes, i.e. by the trace at each frequency. Integration of the power spectrum over the entire frequency range yields the b-tensor, $$b_{ij} = \frac{1}{2\pi}\int_{-\infty}^{\infty} F_{i}(\omega) F^*_{j}(\omega) d\omega$$.

### Designing tuned b-tensors of varying shape

Various b-tensor shapes and the associated q-trajectories can be constructed using two key parameters: $\zeta$ and $\Delta\Psi$, yielding anisotropy and asymmetry of b-tensors, $\it{b}_{\mathrm{\Delta}}$ and $\it{b}_{\mathrm{\eta}}$, respectively. Varying anisotropy and asymmetry of b-tensors allows detecting anisotropy and asymmetry of diffusion tensors. Gradient waveforms are generated following the steps outlined in refs. 3,4 and illustrated in Fig. 1A. First, the azimuth angle $\Psi(t)$ is calculated from gradient $G_{\mathrm{a}}(t)$ and $\Delta\Psi$. Then, the polar angle $\zeta$ is used to yield $\mathbf{G}(t)$ and the corresponding dephasing $\mathbf{q}(t)$ (Fig 1B). Introducing the tuning parameter (TP) as an amplitude of oscillation inserted between the bipolar lobes of the $G_{\mathrm{a}}(t)$ (red patch in Fig. 1A) allows tuning the average dephasing power spectrum shown in Fig. 1C. The TP was adjusted for each b-tensor shape to yield approximately equal apparent isotropic diffusivities for diffusion restricted in a sphere of arbitrary size. The colors for b-tensor shapes and average power spectra shown in Figs. 2 and 3 correspond to the average encoding frequency mapped to the range of colors red-green-blue.

### Results and discussion

The original recipe3,4 to generate b-tensors of varying shapes (Fig. 2A) can be easily modified to achieve spectral tuning (Fig. 2B) using a single adjustable tuning parameter (TP). An optimal TP can be found considering restricted diffusion. For a spherical restriction, tuning yields approximately equal apparent isotropic diffusivities in the entire range of relative encoding times $\sqrt{D_0 \tau}/R$ (not shown). Fig. 2 demonstrates how a wide range of average encoding frequencies (color-coded in b-tensor shapes) is homogenized by tuning. The average color-coded power spectra can be seen in Fig. 3. A few caveats need be address with our simplistic tuning implementation. First, our tuning was performed for the case of restricted diffusion with its characteristic diffusion spectrum $D(\omega)$9. Considering a radically different case of e.g. incoherent flow would present a different tuning problem. Achieving perfect tuning for arbitrary $D(\omega)$ remains a difficult if not impossible task. Second, in our tuning implementation, we ignored the effects caused by spectral anisotropy10. This effect has been first described by de Swiet and Mitra11 for the case of spherical b-tensors. We have suggested the potential of using spectral anisotropy as yet another encoding dimension exclusively sensitive to anisotropic restrictions10. Third, additional tuning parameters would be necessary to further improve the tuning, which is particularly important when probing anisotropic restricted diffusion. This task is a subject future work. Forth, the suggested waveform design is conceptually neat but not optimal in terms of hardware demands. Although our waveforms can be applied on high performance gradient systems1-5, optimizations considering gradient amplitude, slew and coil heating limitations12 will be needed for efficient clinical applications.

### Acknowledgements

HL is kindly supported by the European Research Council under the European Union's Horizon 2020 research and innovation program (grant agreement No. 804647 – C-MORPH)

DT is supported by the Swedish Research Council (VR) 2018-03697 and by the Swedish Foundation for Strategic Research (SSF) ITM17-0267

### References

1. Lasič S, Szczepankiewicz F, Eriksson S, Nilsson M, Topgaard D, Microanisotropy imaging: quantification of microscopic diffusion anisotropy and orientational order parameter by diffusion MRI with magic-angle spinning of the q-vector, Front. Phys., 2014, 2, (11), 1–14.

2. Eriksson S, Lasič S, Nilsson M, Westin C-F, Topgaard D, NMR diffusion-encoding with axial symmetry and variable anisotropy: Distinguishing between prolate and oblate microscopic diffusion tensors with unknown orientation distribution, J. Chem. Phys., 2015, 142, 104201.

3. Topgaard D, Director orientations in lyotropic liquid crystals : diffusion MRI mapping of the Saupe order tensor, Phys. Chem. Chem. Phys., 2016, 18, 8545–8553.

4. Topgaard D, Multidimensional diffusion MRI, J. Magn. Reson., 2017, 275, 98–113.

5. Topgaard D, NMR methods for studying microscopic diffusion anisotropy, in Diffusion NMR of confined systems: fluid transport in porous solids and heterogeneous materials, New Developments in NMR no. 9, R. Valiullin, Ed. Cambridge, UK: Royal Society of Chemistry, 2017.

6. Jones DK, Knösche TR, Turner R, White matter integrity, fiber count, and other fallacies: the do’s and don’ts of diffusion MRI, Neuroimage, 2013, 73, 239–254.

7. Novikov DS, Kiselev VG, Jespersen SN, On modeling, Magn. Reson. Med., 2018, 79, 3172–3193.

8. Lundell H, Nilsson M, Dyrby T, Parker G, Cristinacce P, Zhou F, Topgaard D, Lasič S, Microscopic anisotropy with spectrally modulated q-space trajectory encoding., in Proc. Intl. Soc. Mag. Reson. Med. 25, 2017, 1086.

9. Stepišnik J, Time-dependent self-diffusion by NMR spin-echo, Phys. B, 1993, 183, 343–350.

10. Lundell H, Nilsson M, Westin C-F, Topgaard D, Lasič S, Spectral anisotropy in multidimensional diffusion encoding, in Proc. Intl. Soc. Mag. Reson. Med. 26, 2018, 0887.

11. De Swiet TM, Mitra PP, Possible Systematic Errors in Single-Shot Measurements of the Trace of the Diffusion Tensor, J. Magn. Reson. Ser. B, 1996, 111, 15–22.

12. Sjölund J, Szczepankiewicz F, Nilsson M, Topgaard D, Westin C-F, Knutsson H, Constrained optimization of gradient waveforms for generalized diffusion encoding, J. Magn. Reson., 2015, 261, 157–168.

### Figures

Figure 1: Recipe for generating tuned b-tensors of varying shapes. A. The tuning parameter (red patch under the curve) is introduced in the 1D gradient waveform $G_{\mathrm{a}}(t)$. The azimuth angle $\Psi(t)$ is calculated based on a given maximum excursion of the q-trajectory $\Delta\Psi$. The $\Delta\Psi$ together with the polar angle $\zeta$ are used to determine the shape of b-tensors and the corresponding 3D waveforms $\mathbf{G}(t)$. The dephasing waveforms $\mathbf{q}(t)$ (B) and their average power spectrum (C) are calculated as described in the analysis section. The X, Y, Z gradient/dephasing waveforms are color-coded in red, green, blue, respectively.

Figure 2: Different b-tensor shapes (non-tuned and tuned) and the corresponding gradient waveforms for the XYZ channels. The tensors are color-coded as an average encoding frequency weighted by the average power spectra and mapped to the range of colors red-green-blue. The X, Y, Z gradient waveforms are color-coded in red, green, blue, respectively.

Figure 3: Mean power spectra (non-tuned and tuned) corresponding to the b-tensors shown in Figure 2. Patches under the curves are color-coded the same as the b-tensors in Figure 2 (based on the average encoding frequency).

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
3490


text:
# Why don't we consider both time dilations in Special Relativity Questions? [duplicate]

If we have a periodic motion happening in frame A and if a moving frame B was to observe the event, B would see the time period reduced to $$\frac{T_A}{1+v/c}$$. This happens because of the finite amount of time light takes to deliver the message to B that change occurred in A

Apart from this, there is time dilation from SR that affects the mechanism of periodic motion itself. That is if the period of motion is $$T_A$$, (time between ticks of any clock), the period as observed by B would be

$$T_B = T_A\sqrt{1-\frac{v^2}{c^2}}$$

So if two frames are in relative motion, shouldn't we consider both effects? I mean in common physics questions like : If I were to look at the clock in a moving spacecraft, And if my clock ticks once every second, then at what rate would his clock tick? I believe it should be :

$$\frac{1}{1+v/c} \times\text{dilated time between ticks}$$ $$=\frac{1}{1+v/c} \times \ \sqrt{1-v^2/c^2}={\sqrt{\frac{1-v/c}{1+v/c}}}$$

but textbooks just mention the dilation factor only.


text:
# Simple XML to LaTeX Transformation Tutorial

Today, I wanted to share this super simple XML to LaTeX tutorial. Using XSLT, you are going to transform XML data to LaTeX output which you can then go on to compile into your desired output PDF. There will be no fancy stuff whatsoever in this post, just the basics and what to keep in mind with these transformations. It is the quick intro to XML to LaTeX I did with my students a while ago which was done one day after they had their first contact with XSLT, so it should really be beginner-friendly. I labeled it “Advanced LaTeX” anyway because I think starting to automate things is always a step in the right direction 😉

Edit March 2022: Sadly, with WordPress changes (and source code support never working all that well to begin with), the code formatting of this post is pretty broken. Since it tends to re-break soon after I fix it, here is a similar / almost the same template described in this post.

## Configuring the transformation scenario in Oxygen

I am going to assume you use Oxygen now because that’s what a lot of people in the DH do and this post is directed towards my friends in the DH. Especially those who think print editions are an obsolete concept in times of the Digital Edition. Maybe having a nice little intro to XML to LaTeX transformations available will change their minds 😉

To set up the transformation scenario, choose XML transformation using XSLT, then choose your XML document and your XSL stylesheet (set up and open those document in the editor before you configure the scenario). Then choose a Saxon 9 version (whichever you like). Then ignore the FO tab and get right to the output tab.

Here you configure how to name your output. Best click the green arrow and choose cfn, then append -latex.tex. So the result the current filename with -latex.tex appended to it. This is an important step so you don’t accidentally overwrite the original. Which in this case is not so dramatic since it has a different ending anyway but if you do XML to XML transformations, this is even more crucial. Then tell Oxygen to show it in the editor as XML (even though you know it isn’t). The editor will then, of course, complain about the non-valid XML but don’t worry. Just copy all (CTRL+ACTRL+C) and paste it (CTRL+V) into a completely empty (!) project in Overleaf  or just compile the LaTeX directly if you have it installed on your machine.

There it is, you’re set. Now let’s get to the stylesheet.

## The stylesheet

So, this is the whole thing. You can just grab it and go if you don’t care for the explanation or read on to find out why things were done the way they were done. This tutorial assumes you’re already familiar with how XSLT works, just haven’t done transformations to LaTeX yet, by the way. I am also assuming, your base XML is in the TEI standard.

<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform"     xmlns:xs="http://www.w3.org/2001/XMLSchema"     xmlns:t="http://www.tei-c.org/ns/1.0"     exclude-result-prefixes="xs"     version="2.0">
<xsl:strip-space elements="*"/>
<xsl:output method="text" encoding="UTF-8" indent="no" omit-xml-declaration="yes"/>

<xsl:template match="/">
<xsl:text>\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\DeclareUnicodeCharacter{2060}{\nolinebreak} % might not be necessary for you

\title{</xsl:text><xsl:apply-templates select="//t:title"/>
<xsl:text>}
\author{</xsl:text><xsl:apply-templates select="//t:author"/>
<xsl:text>}\date{\today}
\begin{document}
\maketitle
\tableofcontents\newpage</xsl:text>
<xsl:text>\begin{itemize}</xsl:text>
<xsl:text>\item </xsl:text>
<xsl:value-of select="." />
<xsl:text>

</xsl:text>
</xsl:for-each>
<xsl:text>\end{itemize}
\newpage</xsl:text>

<!--  <xsl:apply-templates/> OR -->
<xsl:apply-templates select="//t:text"/>
<!-- just use the pull paradigm on the TEI body so you don't get a meaningless TEI header dump in your document -->

<xsl:text>\end{document}</xsl:text>
</xsl:template>

<xsl:text>\section{</xsl:text><xsl:apply-templates/><xsl:text>} </xsl:text>
</xsl:template>

<xsl:template match="t:p">
<xsl:apply-templates/>
<xsl:text>

</xsl:text>
</xsl:template>

<xsl:template match="t:hi">
<xsl:text>\emph{</xsl:text><xsl:apply-templates/><xsl:text>} </xsl:text>
</xsl:template>

<xsl:template match="text()">
<xsl:analyze-string select="." regex="([&])|([_])|([$])"> <xsl:matching-substring> <xsl:choose> <xsl:when test="regex-group(1)"> <xsl:text>\&</xsl:text> </xsl:when> <xsl:when test="regex-group(2)"> <xsl:text>\_</xsl:text> </xsl:when> <xsl:when test="regex-group(3)"> <xsl:text>\ lt;/xsl:text> </xsl:when> <xsl:otherwise/> </xsl:choose> </xsl:matching-substring> <xsl:non-matching-substring> <xsl:value-of select=”.” /> </xsl:non-matching-substring> </xsl:analyze-string> </xsl:template> </xsl:stylesheet> ### The XSLT declaration and the LaTeX preamble Put the following after your XML declaration. This will ensure output is LaTeX-friendly. <xsl:strip-space elements="*"/> <!-- for LaTeX --> <xsl:output method="text" encoding="UTF-8" indent="no" omit-xml-declaration="yes"/>  \DeclareUnicodeCharacter{2060}{\nolinebreak} was added because LaTeX complained about an undefined character in some of my students XML data. Personally, I had never gotten this error before, so you might as well leave it out. ### Creating environments As we had just learnt some XSLT basics, I wanted the students to use at least one push and one pull paradigm type template. So the task was to process any element from the TEI header using the push paradigm and then a pull paradigm template for the body. To make this little template more efficient teaching-wise, I decided to introduce how to create a LaTeX environment using XSLT for the TEI Header / push paradigm and do at least one other command using the pull paradigm on the TEI body. Also this demonstrates as opposed to for the body. So this next piece of code sets up an itemize environment for persons present in the header. In a “real” stylesheet, it would probably be more wise to check, using whether there is one potential element like that present and only paste the \begin and \end on that condition. Also, as you might have noticed, all the LaTeX commands are inside . This looks a bit confusing at first but really isn’t. Just make sure you don’t create invalid XSLT by shuffling them around. <xsl:text>\begin{itemize}</xsl:text> <xsl:for-each select="//persName[ancestor::t:teiHeader]"> <xsl:text>\item </xsl:text> <xsl:value-of select="." /> <xsl:text> </xsl:text> </xsl:for-each> <xsl:text>\end{itemize}</xsl:text>  ### Pull paradigming emphasis When creating simple commands using the pull paradigm, be sure that you don’t end up with too many “overlaps” since “simple” commands in LaTeX don’t take multiple paragraphs as arguments. If in doubt, always use environment and the global switches (like \bfseries). Since you are automating things, you always have to take into account that data might not always be marked-up in a way which makes sense to you. There can easily be linebreaks inside a single italic highlight. If this is the case in you data, better create an environment. For simple purposes, however, this is good enough: <xsl:template match="t:hi"><xsl:text> \emph{</xsl:text><xsl:apply-templates/><xsl:text>} <xsl:text></xsl:template>  With these commands (and genereally when transforming to LaTeX), you sometimes need to make sure you don’t involuntarily add spaces or lack space which will make the output hard to read and debug. In this example, I made sure not to add any whitespace inside the template rule and also did not have Oxygen format or indent the XML to avoid these unwanted spaces. ### And finally: Escaping entities As you might remember, markup languages tend to use entities to escape certain characters. Bad thing is, LaTeX and XML use different entities. So we need to escape them. I know that the OxGarage standard stylesheet does this using the translate() function but I prefer to use since it’s less “messy” than a nested translate() construct. Ah, and side info by the way: There is this standard stylesheet from the TEI consortium which might be of help if you are looking for inspiration. Since it is very generic, however, it might not be helpful if you are a newbie at both XSLT and LaTeX. The XSLT is pretty advanced and also the LaTeX probably uses some commands you might not be aware of. <xsl:template match="text()"> <xsl:analyze-string select="." regex="([&])|([_])|([$])">
<xsl:matching-substring>
<xsl:choose>
<xsl:when test="regex-group(1)">
<xsl:text>\&</xsl:text>
</xsl:when>
<xsl:when test="regex-group(2)">
<xsl:text>\_</xsl:text>
</xsl:when>
<xsl:when test="regex-group(3)">
<xsl:text>\

lt;/xsl:text>
</xsl:when>
<xsl:otherwise/>
</xsl:choose>
</xsl:matching-substring>
<xsl:non-matching-substring>
<xsl:value-of select=”.” />
</xsl:non-matching-substring>
</xsl:analyze-string>
</xsl:template>
I say some more about escaping the entities and the whole <xsl:analyze-string> process in this post: Automating XML annotation: Get more done using RegEx Search&Replace and xsl:analyze-string.

And that’s it. I hope this was useful to you.

Cheers,

the Ninja

If my content has helped you, donate 3€ to buy me coffee. Thanks a lot, I appreciate it!

€3.00

#### Tags

I like LaTeX, the Humanities and the Digital Humanities. Here I post tutorials and other adventures.

## 12 thoughts on “Simple XML to LaTeX Transformation Tutorial”

1. Sounds interesting! Do you think, this could work in RMarkdown ? I want to use an xml-file to import abbreviations into a tex-template for RMarkdown (pdf-output). I am meanwhile quite familiar with RMarkdown. I am familiar with the way to integrate tables of content as well as lists of tables and of figures. What I am looking for is a way of integrating lists of abbreviations.

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• Overall I think it must be possible but I think I didn’t fully understand the question 😉
Do you mean transforming XML to RMarkdown directly? If yes – XSLT can transform into any text-based format, so you’re in luck. If not, please explain again what the question was 😉

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• Thanks für your answer! My issue is as follows: My RMarkdown file is – for pdf-output – based on a Latex template (*.tex-file), which has been supplied at University Hannover. This template provides for a table of contents as well als lists of figures and tables. These directories are generated automatically. What I don´t have (but need), is a list of abbreviations. RMarkdown does not support – as far as I have figured out – the respective Latex-packages (e.g. acronym). On the other hand I dont´t want to write my list of abbreviations into my Latex template. I would prefer to maintain a separate abbreviations-file in a simple format (xml, json). On rendering the pdf-output my abbreviations should be integrated into the pdf. I thought this would be a common requirement – perhaps in other contexts. Nonetheless I haven´t found a solution for this via google. I am grateful for any hints how to proceed. Sincerely, H.-C. Schneider

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• Yeah I think an XSLT template might be what you need – just let it create .Tex code in a specific file, like “abbrev.tex” (= output file of the XSLT transformation) and /include or /input{abbrev} into your doc. Does this help?

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• Hans-Christian Schneider says:

Thanks a lot! This helps!!

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text:
# OPTICS

OPTICS ( English Ordering Points To Identify the Clustering Structure , arrange [about] points to identify the cluster structure ' ) is a dense-based algorithm for cluster analysis . It was developed by Mihael Ankerst, Markus M. Breunig, Hans-Peter Kriegel and Jörg Sander. The basic principle of the algorithm comes from DBSCAN , but the algorithm solves an important weakness of the DBSCAN algorithm: in contrast to it, it can recognize clusters of different densities. At the same time, it (largely) eliminates the parameter of the DBSCAN algorithm. For this purpose, OPTICS arranges the points of the data set linearly in such a way that spatially adjacent points follow one another in this order. At the same time, the so-called "reachability distance" is noted. If you draw these accessibility distances in a diagram, clusters form “valleys” and can thus be identified. ${\ displaystyle \ varepsilon}$

## Core idea

Like DBSCAN, OPTICS uses two parameters, and . However, here it plays the role of a maximum distance and serves primarily to limit the complexity of the algorithm. Substituting , then the complexity of the algorithm , otherwise they can with the help of appropriate spatial indexing structures such as R * tree to be reduced. Without this optimization, however, the complexity remains at finite . ${\ displaystyle minPts}$${\ displaystyle \ varepsilon}$${\ displaystyle \ varepsilon}$${\ displaystyle \ varepsilon = \ infty}$${\ displaystyle O (n ^ {2})}$${\ displaystyle O (n \ cdot \ log n)}$${\ displaystyle O (n ^ {2})}$${\ displaystyle \ varepsilon}$

In DBSCAN a point is a “core point” if its surroundings contain at least points. In OPTICS, on the other hand, it is checked when a point would be a key point. This is implemented with the "core distance", ie the value from which a point in DBSCAN would be a "core point". If there is no point with which a point would be a core point, its core distance is infinite or “undefined”. ${\ displaystyle \ varepsilon}$${\ displaystyle minPts}$${\ displaystyle \ varepsilon}$${\ displaystyle \ varepsilon}$

The “reachability distance ” of a point from a second point is defined as , i.e. as the maximum of the real distance and the core distance of the referring point. ${\ displaystyle p}$${\ displaystyle o}$${\ displaystyle \ max (core distance (o), dist (o, p))}$

OPTICS now arranges the objects in the database by starting at any unprocessed point, determining the neighbors in the area and memorizing them in a priority queue according to their best reachable distance so far . The point that has the smallest reachable distance is now always included next in the order. By processing a new point, the reachability distances of the unprocessed points can be improved. By sorting this priority queue, OPTICS processes a detected cluster completely before continuing with the next cluster. ${\ displaystyle \ varepsilon}$

## Visualization

OPTICS can be visualized as an accessibility diagram (below). The reachability distance is plotted on the y-axis, the points along the x-axis are sorted according to the order calculated by OPTICS. "Valleys" in this diagram correspond to recognized clusters in the data set; the depth of the valley indicates the density of the cluster. As an additional visualization, here (top right) each point is linked to its predecessor accessibility. The resulting spanning tree visualizes the density connection of the points in the data set determined by OPTICS. Here and were used as parameters . This visualization was created with the OPTICS implementation in ELKI . ${\ displaystyle \ varepsilon \ leq 0.5}$${\ displaystyle minPts = 10}$

## Pseudocode

The basic approach of OPTICS is similar to that of DBSCAN , but instead of maintaining a set of "known but not yet processed" objects, these are managed in a priority queue (for example an indexed heap ).

  OPTICS(DB, eps, MinPts)
for each point p of DB
p.reachability-distance = UNDEFINED
for each unprocessed point p of DB
N = getNeighbors(p, eps)
mark p as processed
output p to the ordered list
Seeds = empty priority queue
if (core-distance(p, eps, Minpts) != UNDEFINED)
update(N, p, Seeds, eps, Minpts)
for each next q in Seeds
N' = getNeighbors(q, eps)
mark q as processed
output q to the ordered list
if (core-distance(q, eps, Minpts) != UNDEFINED)
update(N', q, Seeds, eps, Minpts)

In update () the priority queue is updated with the environment of or : ${\ displaystyle \ varepsilon}$${\ displaystyle p}$${\ displaystyle q}$

  update(N, p, Seeds, eps, Minpts)
coredist = core-distance(p, eps, MinPts)
for each o in N
if (o is not processed)
new-reach-dist = max(coredist, dist(p,o))
if (o.reachability-distance == UNDEFINED) // o is not in Seeds
o.reachability-distance = new-reach-dist
Seeds.insert(o, new-reach-dist)
else               // o in Seeds, check for improvement
if (new-reach-dist < o.reachability-distance)
o.reachability-distance = new-reach-dist
Seeds.move-up(o, new-reach-dist)

OPTICS outputs the points in a certain order, annotated with their smallest reachable distance (the published algorithm also saves the core distance, but it is no longer required).

## Extensions

OPTICS-OF is an OPTICS-based procedure for outlier detection . An important advantage here is that clusters can be determined in the course of a normal OPTICS run without having to carry out a separate outlier detection.

DeLiClu, Density-Link-Clustering combines ideas of single-linkage clustering and OPTICS, thus eliminating the parameter and achieving improved performance compared to OPTICS by using an R-tree as an index. ${\ displaystyle \ varepsilon}$

HiSC is a hierarchical (axis-parallel) subspace clustering method.

HiCO is a hierarchical clustering procedure for any oriented sub-spaces.

DiSH is an improvement of HiSC for more complex hierarchies (with cuts from sub-spaces).

## Availability

A reference implementation is available in the chair's software package ELKI , including implementations of DBSCAN and other comparison methods.

The " scikit-learn " module contains an implementation of OPTICS in Python since version scikit-learn v0.21.2.

## Individual evidence

1. Mihael Ankerst, Markus M. Breunig, Hans-Peter Kriegel , Jörg Sander: OPTICS: Ordering Points To Identify the Clustering Structure . In: ACM SIGMOD international conference on Management of data . ACM Press, 1999, pp. 49-60 ( CiteSeerX ).
2. Martin Ester, Hans-Peter Kriegel , Jörg Sander, Xiaowei Xu: A density-based algorithm for discovering clusters in large spatial databases with noise . In: Evangelos Simoudis, Jiawei Han, Usama M. Fayyad (Eds.): Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD-96) . AAAI Press, 1996, ISBN 1-57735-004-9 , pp. 226-231 ( CiteSeerX ).
3. ^ Markus M. Breunig, Hans-Peter Kriegel , Raymond T. Ng and Jörg Sander: Principles of Data Mining and Knowledge Discovery . Springer, 1999, ISBN 978-3-540-66490-1 , OPTICS-OF: Identifying Local Outliers, p. 262-270 , doi : 10.1007 / b72280 ( metapress.com ).
4. E. Achtert, C. Böhm, P. Kröger: DeLi-Clu: Boosting Robustness, Completeness, Usability, and Efficiency of Hierarchical Clustering by a Closest Pair Ranking . 2006, p. 119 , doi : 10.1007 / 11731139_16 .
5. E. Achtert, C. Böhm, Hans-Peter Kriegel , P. Kröger, I. Müller-Gorman, A. Zimek: Finding Hierarchies of Subspace Clusters . 2006, p. 446 , doi : 10.1007 / 11871637_42 .
6. E. Achtert, C. Böhm, P. Kröger, A. Zimek: Mining Hierarchies of Correlation Clusters . 2006, p. 119 , doi : 10.1109 / SSDBM.2006.35 .
7. E. Achtert, C. Böhm, Hans-Peter Kriegel , P. Kröger, I. Müller-Gorman, A. Zimek: Detection and Visualization of Subspace Cluster Hierarchies . 2007, p. 152 , doi : 10.1007 / 978-3-540-71703-4_15 .
8. sklearn.cluster.OPTICS - scikit-learn 0.21.2 documentation. Retrieved July 3, 2019 .


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text:
# Difficult Ratios & Proportion Solved QuestionAptitude Discussion

 Q. The ratio of marks obtained by Vinod and Basu is $6:5$. If the combined average of their percentage is 68.75 and their sum of the marks is 275, find the total marks for which exam was conducted.
 ✖ A. 150 ✔ B. 200 ✖ C. 400 ✖ D. None

Solution:
Option(B) is correct

Let Vinod marks be $6x$ and Basu's is $5x$. Therefore, the sum of the marks=$6x+5x=11x$

But the sum of the marks is given as $275=11x$. We get $x=25$ therefore, Vinod’s marks is $6x=150$ and Basu’s marks = $5x=125$.

Therefore, the combined average of their marks $\%$ = $\dfrac{150+125}{2}=137.5$

If the total mark of the exam is 100 then their combined average of their percentage is 68.75

Therefore, if their combined average of their percentage is 137.5 then the total marks would be $\dfrac{137.5}{68.75}\times 100=200$


text:
# PCA, relation between the error and variance

As is known, the rank-1 PCA aims to solve the following optimization problem $$\min_{x\in\mathbb{R}^d}\quad -x^T \Sigma x\quad\quad\quad \text{s.t.}\quad \Vert x\Vert_{2}=1,$$ where $$\Sigma\in\mathbb{S}^{d}$$ is the covariance matrix. Thus the optimum $$x^*$$ of the PCA problem is the top unit eigenvector of $$\Sigma$$. Given an approximation $$\tilde{x}$$ (normalized), the error between the $$\tilde{x}$$ and $$x^*$$ is measured by the sine function $$\sin^{2}(\tilde{x}, x^*) = 1-(\tilde{x}^T x^*)^2.$$ I was wondering does there exist any analytical relationship between the objective function $$\tilde{x}^\top\Sigma \tilde{x}$$ and the error $$\sin^2(\tilde{x}, x^*)$$? Any help appreciated.

• Thx! This answer really helps! Can this result be extended to rank-k PCA? In this case, the sine of the angle might be written as $\Vert sin(X, X^*)\Vert_{F}^2 = k-\Vert X^T X^*\Vert_{F}^2$. May 14 at 16:04
• I have post the rank-$k$ case as another new question: link thx for help! May 15 at 8:02