Abstract Physicians use clinical guidelines to inform judgment about therapy. Clinical guidelines do not address three important uncertainties: (1) uncertain relevance of tested populations to the individual patient, (2) the patient's uncertain preferences among possible outcomes, and (3) uncertain subjective and financial costs of intervention. Unreliable probabilistic information is available for some of these uncertainties; no probabilities are available for others. The uncertainties are in the values of parameters and in the shapes of functions. We explore the usefulness of info-gap decision theory in patient-physician decision making in managing cholesterol level using clinical guidelines. Info-gap models of uncertainty provide versatile tools for quantifying diverse uncertainties. Info-gap theory provides two decision functions for evaluating alternative therapies. The robustness function assesses the confidence—in light of uncertainties—in attaining acceptable outcomes. The opportuneness function assesses the potential for better-than-anticipated outcomes. Both functions assist in forming preferences among alternatives. Hypothetical case studies demonstrate that decisions using the guidelines and based on best estimates of the expected utility are sometimes, but not always, consistent with robustness and opportuneness analyses. The info-gap analysis provides guidance when judgment suggests that a deviation from the guidelines would be productive. Finally, analysis of uncertainty can help resolve ambiguous situations.
Acknowledgement The authors gratefully acknowledge the support of the Abramson Center for the Future of Health. The authors are indebted to comments by Scott Ferson, Malka Gorfine, Matthias Troffaes and Miriam Zacksenhouse.
This is a typical Info-Gap paper: it is full of the usual errors, misconceptions, and obfuscations that by now have become part and parcel of the Info-Gap enterprise.
Fact 1: Info-Gap's robustness model is a simple instance of Wald's famous Maximin model (circa 1940).
Fact 2: Info-Gap decision theory is a classic example of a voodoo decision theory.
The reason that the truth about Fact 1 is embarrassing is simple. Since its introduction in the late 1990s, Info-Gap decision theory has been acclaimed as distinct, novel, revolutionary, and radically different from all current theories for decision under severe uncertainty.
Yet, my Maximin Theorem shows this claim for what it is: a pure myth!
The reason that the truth here is embarrassing is not merely that Info-Gap's robustness model is a reinvention of the wheel. Indeed, the truth here is hugely embarrassing because Info-Gap's robustness model is in fact a simple instance of none other than the most famous model in classical decision theory for the treatment of severe uncertainty: Wald's Maximin model. In other words, Info-Gap's robustness model is a simple instance of a model that, since the 1950s, has become the bread and butter approach to the management of severe uncertainty in classical decision theory and robust optimization.
Yet, my Invariance Theorem shows this claim for what it is: a pure myth!
It shows that Info-Gap decision theory in fact constitutes the precise antithesis of what a theory for the treatment of severe uncertainty ought to be. In other words, it shows that Info-Gap decision theory "deals" with severe uncertainty by simply ... ignoring the severity of the uncertainty altogether. This fact renders Info-Gap decision theory a voodoo decision theory par excellence.
Details concerning these and other myths about Info-Gap decision theory can be found in my discussion on Myths and Facts about Info-Gap and in FAQs about Info-Gap.
So, you may well wonder: given that Info-Gap decision theory is so gravely flawed, and that its flaws are so detrimental to it, how is it that the paper under review here was accepted for publication in a refereed journal?
The answer is very simple: whatever Info-Gap decision theory lacks in substance and rigor, is made up for, and covered up, by heavy fog, spin, and rhetoric.
Indeed, to be able to pin down the truth about this theory, I had to cut through some mighty fog, spin, and rhetoric.
where û denotes the estimate of the parameter of interest, the black area represents the complete region of uncertainty under consideration, the red area around û represents the region of uncertainty that actually affects the results generated by Info-Gap's robustness analysis, and the vast No Man's Land represents that part of the complete region of uncertainty that has no impact whatsoever on the results generated by Info-Gap's robustness model.
Recalling that under conditions of severe uncertainty the estimate û is a wild guess, a poor indication of the true value of the parameter of interest and is likely to be substantially wrong, it is immediately clear that Info-Gap decision theory violates the universally accepted Garbage In Garbage Out (GIGO) Axiom. This crucial fact renders this theory a voodoo decision theory par excellence.
Example 1: On q' and q''.
where q' and q'' are two decisions, Rc=6 is the critical reward level associated with the performance constraint R(q,u) ≤ Rc, and u denotes the parameter of interest whose true value is subject to severe uncertainty. Note that the estimate of the true value of u is û = 0, and that the complete region of uncertainty is U=(-∞,∞).
The performance requirement R(q,u) ≤ Rc means that we prefer decisions whose R(q,u) values are small — ideally below the critical level Rc = 6 — over U.
It is assumed that R(q'',u) continues its (linear) ascent in both directions and that R(q',u) continues its (quadratic) descent in both directions. The colored (red and blue) areas at the bottom of the picture show the regions of U where the performance requirement is satisfied by these two decisions.
It is clear that q' dominates q'' over most of the uncertainty space U=(-∞,∞). In fact, q'' violates the performance requirement on most of U, whereas q' satisfices the performance requirement on most of U.
But this does not prevent Info-Gap decision theory to deem q'' to be more robust than q'.
So, there are no too ways about it: q' is far more robust than q'' with respect to the given performance requirement R(q,u) ≤ Rc relative to the complete uncertainty space U. Yet, Info-Gap's peculiar (local) definition of robustness deems q'' to be more robust.
You are cordially invited to a guided tour of Info-Gap robustness analysis including an interactive animation and an explanation of the reasons why Info-Gap decision theory regards q'' to be more robust than q'.
In so doing, Info-Gap decision theory puts itself at loggerheads with the universally accepted Garbage In — Garbage Out (GIGO) Axiom and the well known dictum that the results of an analysis can be only as good as the estimate on which they are based. So, the point is that in the case of Info-Gap decision theory the results yielded by its analysis can be no better than ... wild guesses.
To suggest otherwise would amount to suggesting that Info-Gap decision theory possesses mysterious (magical) powers that enable it to translate an analysis around a wild guess into a reliable methodology for the treatment of severe uncertainty.
If this is not a classic example of a voodoo decision theory what is? And isn't it also modern alchemy?
The trouble of course is that this simple fact is, as a rule, enveloped in the Info-Gap publications by fog, spin, and rhetoric. The article under review here is no exception. If anything, the fog, spin, and rhetoric have reached here unprecedented heights. Therefore, to give a full account of this phenomenon will take volumes.
But, to give you an idea, I shall illustrate it in action in connection with the Maximin issue. That is, I shall show how the simple fact that Info-Gap's robustness model is actually a simple instance of Wald's famous Maximin model is covered up by vintage Info-Gap fog, spin, and rhetoric.
In 2007 I advised users/promoters of Info-Gap decision theory that — contrary to repeated claims in the Info-Gap literature — not only is Info-Gap's robustness model neither new nor radically "different" from classical decision theory models, it is in fact a simple instance of Wald's famous Maximin model (circa 1940).
To substantiate this claim, I provided a detailed proof.
where f(d,α,u) = α if r(d,u) ≤ r*; and f(d,α,u) = -∞, otherwise.
More on this model can be found in the discussion on the Maximin model.
This simple instance of Wald's famous Maximin model always yields the same results as those yielded by Info-Gap's robustness model. No amount of empty rhetoric and spin can change this fact.
Note that the Maximin Theorem is constructive: it sets out a simple recipe for constructing that instance of the generic Maximin model that represents Info-Gap's robustness model.
No amount of fancy rhetoric or spin or fog can change this bottom line.
Given this proof, the question of course is: how can anyone possibly argue that Info-Gap's robustness model is not a Maximin model?
In other words, the proof of the Maximin Theorem is so simple, indeed straightforward, so how can one possibly prove the opposite?
Answer: faulty reasoning supported by plenty of fog, spin and rhetoric.
For the benefit of readers who are not familiar with Info-Gap decision theory, let me begin the illustration with a simple example that requires no knowledge of Info-Gap.
How would you prove formally that a perfectly healthy, seven year old kangaroo from Western Australia, call her Jill, is not a marsupial?
Of course, if your reasoning is sound and you are using conventional scientific methods of biological identification/classification it is impossible to do this.
Because, as it is a well-established fact that kangaroos are marsupials, and Jill being a healthy kangaroo, it follows that Jill is a marsupial.
But employing the type of faulty reasoning that underlies Info-Gap decision theory, showing that Jill is not a marsupial is a trifle.
Because, all one needs to do to this end is to find a certified ... koala. Yes, trust me, a ... certified koala, not a kangaroo.
So, to simplify the discussion assume that we found a certified koala, call him Jack.
We now have a certified koala called Jack, and a kangaroo called Jill.
Clearly, Jack is a marsupial.
Clearly, Jill is different from Jack.
Therefore, clearly Jill is not a marsupial.
Example 3: On p and q.
Clearly, p(x):= x4 is a polynomial.
Clearly, q is different from p.
Therefore, clearly q(x)=1 + x + x2 is not a polynomial.
In line with the reasoning illustrated above, the first thing to do is to come up with a Maximin/Minimax model that is not equivalent to Info-Gap's robustness model.
where α'>0 is some given real number.
Note that this is a Minimax, rather than a Maximin, model!
Obviously, there is a value of α' such that the optimal decision generated by Ben-Haim's model for this value of α' is optimal with respect to the Info-Gap model. The difficulty is that this specific value of α is not known in advance.
Thus, it is very easy to show that, in general, this specific Minimax model is not equivalent to Info-Gap's robustness model.
Ben-Haim uses this trivial argument as "proof" that Info-Gap's robustness model is not a Minimax/Maximin model.
This, however, is not approximate reasoning: this is faulty reasoning.
All that Ben-Haim's "proof" shows is that the ad hoc, inappropriate, Minimax model that he created for this exercise is not equivalent to Info-Gap's robustness model. But, this does not show that Info-Gap's robustness model is not an instance of Wald's Maximin model. Indeed, as shown by the Maximin Theorem, there is definitely an instance of Wald's Maximin model that is equivalent to Info-Gap's robustness model.
Note: α' is a pre-specified positive number. Note: a◊b =1 iff a≤b; a◊b =0 otherwise.
Note that in contrast to Ben-Haim's incorrect Minimax model, the correct Maximin model generates, as an integral part of the maximization operation, the specific value of α that is required by Ben-Haim's incorrect Minimax model, namely α'=α(û).
Of course, had Ben-Haim's "proof" been shown for what it is, namely had it been formulated as shown above, then even the referees of journals specializing in approximate reasoning would no doubt have identified the flaw in the reasoning underlying the "proof".
But the trouble is that Ben-Haim — the Founder of Info-Gap decision theory — and his co-authors, set out to "make the case" for the indefensible claim that Info-Gap's robustness model is not a Maximin and/or Minimax model with the aid of an avalanche of empty rhetoric and spin that are unprecedented even by Info-Gap standards.
Min–max decisions. The min–max approach identifies a set of possible contingencies or models or relevant functions and seeks the decision which minimizes the worst (maximal) loss on this set. (The max-min approach maximizes the lowest (minimal) gain when considering benefits rather than losses.) This concept is implicit in many robust Bayesian realizations, and many of our comments there apply here as well. Epistemically, the info-gap and min–max approaches are similar in representing uncertainty without measure functions, though the min-max approach requires the choice of a specific set. The hybridization of a min-max with an info-gap approach is often attractive, as discussed in connection with Bayesian methods. Indeed, Wald's work in the early 1940s on min-max considers sets of uncertain probability distributions .
Behavior. We will discuss two concepts: the observational equivalence of min-max with info-gap robust-satisficing, and the behavioral difference of these methods .
Observational equivalence: Suppose a robust-satisficing decision maker must choose between two options, D1 and D2, and requires an outcome no worse than Lc in Fig. 14. This leads the robust-satisficer to choose decision D1, which is more robust than D2 at this requirement. An observer can describe this behavior by supposing the decision maker to be an min-maxer who believes that the horizon of uncertainty is α1, because at this level of uncertainty the maximum potential loss from D1 is less than from D2. Conversely, a min-maxing decision maker who believes that α1 is the true horizon of uncertainty would likewise choose D1 over D2. An observer could describe this by supposing the decision maker is a robust-satisficer whose requirement is Lc. In short, either strategy can be used to describe observed behavior by ascribing particular beliefs to the decision maker. In other words, the modelling of decision-behavior under uncertainty is under-determined in choosing between robust-satisficing and min-maxing.
Fig. 14. Crossing robustness curves, illustrating the observational equivalence and behavioral difference between min-maxing and robust-satisficing.
Behavioral difference: Suppose a min-maxing decision maker believes that the horizon of uncertainty can be as large as α2 in Fig. 14, but no larger. The min-maxer will prefer D2, whose loss can be as large as Lm, but less than the maximum potential loss of D1. Suppose a robust-satisficing decision maker can accept a loss as large as Lc, but no larger. This robust-satisficing decision maker will prefer D1 over D2 since D1 can tolerate greater uncertainty for achieving this requirement. The robust-satisficer will choose D1 over D2 even if the min-maxer has convinced the robust-satisficer that α2 is the true horizon of uncertainty. In short, when the robustness curves for two decisions cross one another, a min-maxer and robust-satisficer may disagree about the decision, depending on their beliefs and requirements.
In conclusion, the observational equivalence between min-maxing and robust-satisficing means that modellers can use either strategy to describe observed behavior of decision makers. In contrast, the behavioral difference means that actual decision makers will not necessarily be indifferent between these strategies, and will choose a strategy according to their beliefs and aspirations.
Every [Dempster-Shafer] belief function can be represented as a lower envelope of a set of probability measures. This is merely a mathematical representation, however; it is misleading and unnecessary to regard a belief function as a lower bound for some unknown probability measure. In the same way, every coherent lower prevision can be represented as a lower envelope of a set of linear previsions, but this is no reason to regard the lower prevision as a model for partial information about an unknown linear prevision.
The observational equivalence of min-maxing and robust-satisficing asserts that either can be used as a mathematical representation of the other. The behavioral difference between these methods asserts that real decision makers with specific beliefs and requirements need not be indifferent between these methods.
Note: Fig. 14 is mine. It is very similar to the original.
As clearly indicated by the Maximin Theorem, the authors' conclusion regarding the relationship between Info-Gap's robustness model and Wald's Maximin model is out and out false!
This ill-conceived min-max model is discussed in detail in the article Anatomy of a Misguided Maximin formulation of Info-Gap's Robustness Model and in FAQ # 20.
Indeed, the Maximin Theorem assures us that Info-Gap's robustness model is a simple instance of this model.
To so much as attempt a comparison between Info-Gap's robustness model and Wald's Maximin model, in a manner suggesting that the two models are equals, is already grossly misleading, because such a comparison puts a general prototype model on the same footing with one of its countless instances.
Wald's Maximin model, as anyone in the business of decision theory would no doubt know, is an all-embracing, extremely flexible, hence powerful paradigm. This means of course that it has the inherent ability to subsume infinitely many instances. And as indicated by the Maximin Theorem, Info-Gap's robustness model is one of these instances. So, as one of the countless instances of Wald's generic Maximin model, Info-Gap's robustness model will (surprise, surprise!) be different from other instances. Hence, as one of the instances of Wald's generic Maximin model, Info-Gap's robustness model is different from the ad hoc model formulated by Ben-Haim, which is equally an instance of Wald's generic Maximin model.
This fact merely indicates the obvious, namely that Wald's generic Maximin model is incomparably more general and powerful than Info-Gap's robustness model.
All one needs to do to prove formally that Info-Gap's robustness model is an instance of Wald's Maximin model is to show that at least one of the infinitely many instances of Wald's generic Maximin model is equivalent to Info-Gap's robustness model.
Instead, Ben-Haim, prefers to engage in empty rhetoric. That is, rather than go for the legitimate, perfectly suitable instance that is staring at him from the Maximin Theorem, Ben-Haim always picks his ill-considered instance of Wald's Maximin that is not equivalent to Info-Gap's robustness model, to "make a case" for an alleged difference" between Info-Gap's robustness model and Maximin.
All this means then is that the authors' conclusion applies only to the ill-considered Minimax model that they formulate in this paper. It does not apply to the simple instance of Wald's generic Maximin model that is specified by the Maximin Theorem. Indeed, this instance of Wald's Maximin model always yields the same results as those yielded by Info-Gap's robustness model. Therefore, the difference between these two models, namely Info-Gap's robustness model and the Maximin model specified by the Maximin Theorem, has to do with style not with substance. And as a consequence, the decision makers' choice between the two models has absolutely nothing to do with their beliefs and aspirations. Both are Maximin models and both yield the same results.
And so, the authors erroneous thesis does not prove that Info-Gap's robustness model is not a Maximin model. All it proves is the authors' obvious misconceptions about the modeling aspects of the Maximin/Minimax paradigm, their misapprehension as to how the Maximin/Minimax paradigm handles constraints, and so on. All this bars them from grasping the full extent of the affinity between Info-Gap's robustness model and Wald's Maximin model.
Note that the Maximin Theorem is constructive: it sets out a simple recipe for constructing the instance of the generic Maximin model that represents Info-Gap's robustness model.
No amount of fog/rhetoric/spin can change this bottom line.
As indicated above, the conceptual and technical mistakes that led Ben-Haim astray on this matter are discussed in detail in the article Anatomy of a Misguided Maximin formulation of Info-Gap's Robustness Model and in FAQ # 20.
The trouble of course is that the avalanche of empty rhetoric and spin hides all this from view. What is more, it hides from view some fundamental technical errors.
Unfortunately, even in this department the authors are on extremely shaky grounds.
Epistemically, the info-gap and min–max approaches are similar in representing uncertainty without measure functions, though the min-max approach requires the choice of a specific set.
How did the authors come up with this manifestly erroneous idea? Where did they get it from?
Here the uncertainty space is associated with the inner (min) player and is denoted by S(x), where x denotes the decision selected by the outer (max) player. So, as it is there for all to see, the uncertainty space of the inner (min) player is not fixed at all: it is allowed to depend on the choice made by the outer (max) player. But what is more, nothing here "requires the choice of a specific set".
As a matter of fact, the uncertainty sets (S(x): x∈ X) are extremely flexible, certainly far more so than the uncertainty sets (U(α,û): α>0) deployed by Info-Gap decision theory. In particular, the sets (S(x): x∈ X) are not required to have any specific structure at all thus giving the modeller great freedom in their formulation. In contrast, the sets (U(α,û): α>0) deployed by Info-Gap decision theory are required to be nested (increasing with α).
Of course, this is precisely what makes Info-Gap's robustness and opportunessness models local, hence utterly unsuitable for decision-making under severe uncertainty. The nesting property of the uncertainty regions (U(α,û): α>0) prevents Info-Gap's robustness and opportunessess models from exploring globally the complete uncertainty space.
More importantly, perhaps, Info-Gap decision theory assumes that the uncertainty regions [U(α,û): α>0] are not dependent on the decisions made by the decision-maker. In contrast, the Maximin model allows the sets [S(x): x∈ X] to depend on the decisions made by the decision maker.
recalling that the sets [U(α,û): α≥0] are nested (increasing with α).
The point to note here is that in this setting, the flexibility allowed by the Maximin model cannot be (indeed, is not) fully utilized in that S(d,α) does not depend on d, and furthermore, the sets (S(d,α): α≥0) are nested (increasing with α).
observing that g(d,α,u) is equal to either α or 0.
In sum, the Maximin paradigm provides a modeling medium that is incomparably more general and powerful than the one offered by Info-Gap's robustness model. Is it surprising then that Info-Gap's robustness model is a simple instance of Wald's generic Maximin model?
For the benefit of readers who are not familiar with Info-Gap decision theory I need to point out that the dissertation in this paper, on the alleged differences and similarities between Info-Gap's robustness model and the Maximin model, must be placed in its proper context. Observe then that the discussion in this paper comes in the wake of a long list of grossly misleading and unsubstantiated assertions on Info-Gap's role and place in decision theory and its capabilities to deal with severe uncertainty.
Info-gap decision theory is radically different from all current theories of decision under uncertainty. The difference originates in the modeling of uncertainty as an information gap rather than as a probability. The need for info-gap modeling and management of uncertainty arises in dealing with severe lack of information and highly unstructured uncertainty.
In this book we concentrate on the fairly new concept of information-gap uncertainty, whose differences from more classical approaches to uncertainty are real and deep. Despite the power of classical decision theories, in many areas such as engineering, economics, management, medicine and public policy, a need has arisen for a different format for decisions based on severely uncertain evidence.
Optimization of the robustness in eq. (3.172) is emphatically not a worst-case analysis. In classical worst-case min-max analysis the decision maker minimizes the impact of the maximally damaging case. But an info-gap model of uncertainty is an unbounded family of nested sets: U(α,û), for all α≥0. Consequently, there usually is no worst case: any adverse occurrence is less damaging than some other more extreme event occurring at a larger value of α. What eqs. (3.169) and (3.172) express is the greatest level of uncertainty consistent with satisficing to level rc. When the decision maker chooses the action q to maximize α(q,rc), what is maximized is the immunity to an unbounded ambient uncertainty. The closest this comes to "min-maxing" is that the action is chosen so that "bad" events (causing reward R* less than rc) occur as "far away" as possible (beyond a maximized value of α).
What happens when the uncertainties facing a decision maker are so severe that the assumptions in conventional methods based on probabilistic decision analysis are untenable? Jim Hall and Yakov Ben-Haim describe how the challenges of really severe uncertainties in domains as diverse as climate change, protection against terrorism and financial markets are stimulating the development of quantified theories of robust decision making.
These assertions can easily give the impression that Jim Hall and Yakov Ben-Haim have made a colossal breakthrough in decision theory. Indeed that they have managed to devise a methodology for responsible decision-making in the face of severe uncertainty that is capable of the most incredible feats.
The paper under review here is further testimony to the fact that Ben-Haim and his followers have no qualms to continue promulgating the same old myths about Info-Gap decision theory. Their method for dealing with the challenges exposing these myths for what they are is to ... intensify the fog, spin, and rhetoric.
For the record, I should point out that Ben-Haim is fully aware of the existence of the Maximin Theorem, what is more, that he does not dispute its validity. The same is true about the Invariance Theorem.
Regrettably, Ben-Haim has chosen to waltz around these theorems by means of spurious explanations whose only effect is to extend already existing errors.
It will be interesting to see how long will Ben-Haim and his followers pursue this deliberate strategy of avoiding to deal with theorems that invalidate Ben-Haim's repeated pronouncements on Info-Gap's unique role and place in decision theory.
Ben-Haim is also fully aware of the very rich literature on Robust Optimization and the kinship between Info-Gap's robustness model and run-of-the-mill robust optimization models. Yet, in the list of 56 references cited in the paper under review not one reference is made to this body of knowledge.
The good news is that there are signs that, in response to my criticism of Info-Gap decision theory, some of Info-Gap's adherents begin to question the validity of Ben-Haim's judgments on Info-Gap decision theory. For instance, as indicated in Review 11, Bryan Beresford-Smith and Colin J. Thompson (2009) now concede that Info-Gap's robustness model is a Maximin model.
Ranger et al. (2011) : Adaptation in the UK: a decision-making process.
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Sniedovich, M. (2011) A classic decision theoretic perspective on worst-case analysis, Applications of Mathematics, 56(5), 499-509.
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Sniedovich, M. (2011) Dynamic Programming: Foundations and Principles, Second Edition, Taylor & Francis.
Sniedovich, M. (2010) A bird's view of Info-Gap decision theory, Journal of Risk Finance, 11(3), 268-283.
Sniedovich M. (2009) Modeling of robustness against severe uncertainty, pp. 33- 42, Proceedings of the 10th International Symposium on Operational Research, SOR'09, Nova Gorica, Slovenia, September 23-25, 2009.
Sniedovich M. (2009) A Critique of Info-Gap Robustness Model. In: Martorell et al. (eds), Safety, Reliability and Risk Analysis: Theory, Methods and Applications, pp. 2071-2079, Taylor and Francis Group, London.
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Sniedovich, M. (2008) A call for the reassessment of Info-Gap decision theory, Decision Point, 24, 10.
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Sniedovich, M. (2008) Wald's Maximin model: a treasure in disguise!, Journal of Risk Finance, 9(3), 287-291.
In this paper I explain, again, the misconceptions that Info-Gap proponents seem to have regarding the relationship between Info-Gap's robustness model and Wald's Maximin model.
This paper is dedicated to the modeling aspects of Maximin and robust optimization.
Sniedovich, M. (2007) The art and science of modeling decision-making under severe uncertainty, Decision Making in Manufacturing and Services, 1-2, 111-136. (PDF File) .
In this paper I examine the two fundamental flaws in Info-Gap decision theory, and the flawed attempts to shrug off my criticism of Info-Gap decision theory.
Ben-Haim's response confirms my assessment of Info-Gap. It is clear that Info-Gap is fundamentally flawed and therefore unsuitable for decision-making under severe uncertainty.
Ben-Haim is not familiar with the fundamental concept point estimate. He does not realize that a function can be a point estimate of another function.
So when you read my papers make sure that you do not misinterpret the notion point estimate. The phrase "A is a point estimate of B" simply means that A is an element of the same topological space that B belongs to. Thus, if B is say a probability density function and A is a point estimate of B, then A is a probability density function belonging to the same (assumed) set (family) of probability density functions.
Ben-Haim mistakenly assumes that a point estimate is a point in a Euclidean space and therefore a point estimate cannot be say a function. This is incredible!
It shows that Info-Gap is not a new theory but rather a simple instance of Wald's famous Maximin Principle dating back to 1945, which in turn goes back to von Neumann's work on Maximin problems in the context of Game Theory (1928).
This is a very short article entitled The Fundamental Flaw in Info-Gap's Uncertainty Model (PDF File) .
It shows that because Info-Gap deploys a single point estimate under severe uncertainty, there is no reason to believe that the solutions it generates are likely to be robust.
This is a very short article entitled The GAP in Info-Gap (PDF File) .
It is a math-free version of the paper above. Read it if you are allergic to math.
A long essay entitled What's Wrong with Info-Gap? An Operations Research Perspective (PDF File) (December 31, 2006).
This is a paper that I presented at the ASOR Recent Advances in Operations Research (PDF File) mini-conference (December 1, 2006, Melbourne, Australia).
If your organization is promoting Info-Gap, I suggest that you invite me for a seminar at your place. I promise to deliver a lively, informative, entertaining and convincing presentation explaining why it is not a good idea to use — let alone promote — Info-Gap as a decision-making tool.
Here is a list of relevant lectures/seminars on this topic that I gave in the last two years.
ASOR Recent Advances, 2011, Melbourne, Australia, November 16 2011. Presentation: The Power of the (peer-reviewed) Word. (PDF file).
Alex Rubinov Memorial Lecture The Art, Science, and Joy of (mathematical) Decision-Making, November 7, 2011, The University of Ballarat. (PDF file).
Black Swans, Modern Nostradamuses, Voodoo Decision Theories, and the Science of Decision-Making in the Face of Severe Uncertainty (PDF File) .
(Invited tutorial, ALIO/INFORMS Conference, Buenos Aires, Argentina, July 6-9, 2010).
A Critique of Info-Gap Decision theory: From Voodoo Decision-Making to Voodoo Economics(PDF File) .
Robust decision-making in the face of severe uncertainty(PDF File) .
Decision-making in the face of severe uncertainty(PDF File) .
Modeling robustness against severe uncertainty (PDF File) .
How do you recognize a Voodoo decision theory?(PDF File) .
(School of Mathematical and Geospatial Sciences, RMIT, June 26, 2009).
Black Swans, Modern Nostradamuses, Voodoo Decision Theories, Info-Gaps, and the Science of Decision-Making in the Face of Severe Uncertainty (PDF File) .
(Department of Econometrics and Business Statistics, Monash University, May 8, 2009).
The Rise and Rise of Voodoo Decision Theory.
ASOR Recent Advances, Deakin University, November 26, 2008. This presentation was based on the pages on my website (voodoo.moshe-online.com).
Responsible Decision-Making in the face of Severe Uncertainty (PDF File) .
A Critique of Info-Gap's Robustness Model (PDF File) .
Robust Decision-Making in the Face of Severe Uncertainty (PDF File) .
The Art and Science of Robust Decision-Making (PDF File) .
The Fundamental Flaws in Info-Gap Decision Theory (PDF File) .
Decision-Making Under Severe Uncertainty: An Australian, Operational Research Perspective (PDF File) .
A Critique of Info-Gap (PDF File) .
What exactly is wrong with Info-Gap? A Decision Theoretic Perspective (PDF File) .
A Formal Look at Info-Gap Theory (PDF File) .
The Art and Science of Decision-Making Under Severe Uncertainty (PDF File) .
ASOR Recent Advances in Operations Research mini-conference (December 1, 2006, Melbourne, Australia).


Gunnar Optiks are the performance-enhancing eyewear of the digital generation. Digerati, gamers, and those spending long hours behind a computer screen appreciate the lenses' subtle magnification and glare filtering. In six weeks the Pensar team created a women's line that embodied Gunnar's high-tech aesthetic and gave shape to healthy computing. Pensar took it from concept to digital databases of the glasses, ensuring accurate reproduction of the designs by offshore suppliers.
Pensar is dedicated to helping Gunnar strengthen their brand and expand their product lines. We focus on creating fashion forward designs that speak to Gunnar's customers whether they're creative artists, gamers or business visionaries.


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Justice Ruth Bader Ginsburg Will Retire from the US Supreme Court in January, 2019
by	BZ ⒾAM Riger	/ Monday, 12 November 2018	/ Published in Absolute Data
Speaking privately, a law clerk says the Justice's Cancer has come out of remission
By Stan Greene, published on The Santa Monica Observer, published on November 11, 2018
While the Nation is preoccupied with the appointment of Judge Brett Kavanaugh to replace Justice Anthony Kennedy, it appears there will soon be another vacancy on the US Supreme Court
U.S. Supreme Court Justice Ruth Bader Ginsburg has had a re-occurrence of malignant melanoma, she has told her law clerks. Ginsburg was treated in 1999 for colon cancer and had surgery in 2009 for pancreatic cancer.
She has told key Democratic members of the Senate about her medical condition, including ranking Democratic member of the Judiciary Committee Dianne Feinstein. This explains in part the "take no prisoners" attitude of the Democrats during the Kavanaugh nomination, carefully orchestrating weak 37 year old allegations against Kavanaugh by Women he barely remembers knowing in High School and College.
Kavanaugh is a player in this drama. He's in the wrong place at the wrong time . President Donald J Trump will be replacing Notorious RBG, the lovechild of the left, and so will remake the Supreme Court for a generation. The Democrats simply must win back the Senate in November 2018, progressives feel.
Ginsburg, 85 was appointed by President Bill Clinton and took the oath of office on August 10, 1993. She is the second female justice (after Sandra Day O'Connor) of four to be confirmed to the court (along with Sonia Sotomayor and Elena Kagan, who are still serving). Following O'Connor's retirement, and until Sotomayor joined the court, Ginsburg was the only female justice on the Supreme Court. During that time, Ginsburg became more forceful with her dissents, which were noted by legal observers and in popular culture. She is generally viewed as belonging to the liberal wing of the court. Ginsburg has authored notable majority opinions, including United States v. Virginia, Olmstead v. L.C., and Friends of the Earth, Inc. v. Laidlaw Environmental Services, Inc.
Ginsburg was born in Brooklyn, New York, to Russian Jewish immigrants. Her older sister died when she was a baby, and her mother, one of her biggest sources of encouragement, died shortly before Ginsburg graduated from high school. She then earned her bachelor's degree at Cornell University, and was a wife and mother before starting law school at Harvard, where she was one of the few women in her class. Ginsburg transferred to Columbia Law School, where she graduated tied for first in her class.
Following law school, Ginsburg turned to academia. She was a professor at Rutgers School of Law and Columbia Law School, teaching civil procedure as one of the few women in her field. Ginsburg spent a considerable part of her legal career as an advocate for the advancement of gender equality and women's rights, winning multiple victories arguing before the Supreme Court. She advocated as a volunteer lawyer for the American Civil Liberties Union and was a member of its board of directors and one of its general counsels in the 1970s. In 1980, President Jimmy Carter appointed her to the U.S. Court of Appeals for the District of Columbia Circuit, where she served until her appointment to the Supreme Court.
1 Comment to " Justice Ruth Bader Ginsburg Will Retire from the US Supreme Court in January, 2019"
Richard says :Reply
As much as I detest Ginsburg's beliefs, attitude, and politics in general, I could cure her cancer with less than 1 cent's worth of electricity, and I would do it if they would let me because I will not let hate rule or run my life (I prefer Love). But alas, she will die from their own ignorance of the design of the human body and their lack of knowledge about our Electric Universe (which they still teach children isn't real). Yes, it's sad. But, I do see it changing, and I also see a future where we will finally teach our children the truth about who and what we are, and what happened to our planet (or I should say the entire Sol system) so long ago. The controllers are in serious panic mode right now, even though some will never believe that, but it doesn't mean we are "out of the woods" just yet. Keep your wits about you, and don't let fear run your life. Our primary weapon is Love & Light and the total reduction of all fear, for it is that fear that feeds and sustains them, and as cruel as it sounds to starve another being, it is what must be done to win the war that continues to this day. Educate, show kindness to all (even to your enemy), and we shall prevail. The grid they built now looks like Swiss Cheese, and we can only hope it comes down entirely in the very near future. In fact, I set that as my true intention – I see the Grid Ended, Removed, Dismantled, GONE FOREVER. Join me? Please.

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Home/TECHNOLOGY
Playing Jeopardy! While You Drive Is the Best Way to Deal With Your Boring Commute
Ben Hider, Getty Images / Ben Hider, Getty Images
More than 55 years after making its television debut, Jeopardy! continues to hold a prominent place in popular culture. Last spring, James Holzhauer went on a 32-game winning streak, coming just $58,484 short of beating all-time champion (and Mental Floss contributor) Ken Jennings' $2.52 million winnings.
If only Holzhauer had an app to practice with during the drive to the studio. Now, thanks to Drivetime, future contestants and general trivia enthusiasts have that opportunity. The service just launched a Jeopardy! add-on that allows players to answer questions from the first 35 seasons of the show using Drivetime's voice-based, hands-free interface. A new show will be available to Drivetime users daily. If they subscribe for $9.99 monthly, they can choose any show from past seasons. Questions are read by host Alex Trebek in both archival and recently taped audio.
The game offers one tweak for civilians: As each clue is read, the app offers three possible responses, turning it into a multiple-choice quiz. Money is still accrued and you can still wager on Final Jeopardy to walk away with a victory.
[h/t Engadget]


text:
Tokenized VC Fund SPiCE and Polymath Launch Industry Initiative To Advance Tokenized Securities Market
Fighting Fraud in the 2020's
Managing Cross Channel Communications in a Regulatory Swell
Glenn Mcgrath partners with Thinkmarkets to promote cricket and female empowerment
Twenty-four percent of 18 to 24 year olds don't know what an ISA is
Onguard continues to invest in UK growth strategy with latest appointment
Partnership will focus on the framework for security token protocols, working with regulators across jurisdictions and with exchanges.
Polymath, the first-ever securities token launch pad, and SPiCE VC, a liquid security tokenized VC fund are launching an industry initiative. Together, the companies will work on implementing governance mechanisms for security tokens, work with regulators on improved frameworks for security tokens in major jurisdictions, improve on protocols and standards for securities tokens, and work with exchanges to support their regulatory needs. The collaboration between Polymath and SPiCE VC is a significant step in the construction of an industry consortium designed to progress the high potential of the tokenized securities market.
Carlos Domingo, Co-Founder and Managing Partner of SPiCE VC, said "SPiCE VC is one of the first security tokens to be issued in the market, disrupting the traditional VC model by making it liquid on the blockchain. We believe that this will be the predominant way for people to digitize all their assets in the future, and we will make significant investments in companies supporting and developing this space. However, a lot of the infrastructure is missing so we are very happy to join hands with a company like Polymath and with others who share our vision about the future of this industry in building the ecosystem that will drive the industry forward."
Both Polymath and SPiCE VC believe that regulation-compliant security tokens are the future of the token world, with a potential that is orders of magnitude larger than the previous wave of utility tokens.
Domingo added, "Unlike utility tokens, which are suitable for relatively few use cases, security tokens can eventually be relevant for almost any company, fund, or asset."
Trevor Koverko, CEO of Polymath said, "The main restriction of utility tokens, which are typically borne from an Ethereum powered Initial Coin Offering, is they are not applicable for all companies because they do not offer dividends or other similar economic rights of ownership. Security tokens, on the other hand, can offer ownership in all types and forms of assets with an existing regulatory framework in place. The potential market of assets subject to being tokenized as securities dwarves today's cryptocurrency market. Polymath and SPiCE VC aim to bridge this gap. Polymath's pipeline of issuers interested in launching a tokenized product will benefit greatly from SPiCE's resources, evidenced by their success in navigating their own security token offering. We are excited to partner with a like-minded pioneer and work together to help scale this early-stage market, which is currently a small fraction of the size of the much-larger utility and app token markets."
The partnership between Polymath and SPiCE VC aims to see collaboration with exchanges on establishing a healthy secondary market for security tokens, as well as two way dialogue with local regulatory bodies to support issuing frameworks and guidelines and organizing industry conferences to bring the ecosystem together.
Sonm Releases Minimum Viable Product To Developer Community
Capgemini and Startupbootcamp join forces in Innovation and Technology Program


Google Smartwatch is coming soon with Google Now integration. Tech giant is reportedly in close talks with its Asian suppliers to start mass production of its Android smartwatch within months.
Google is almost ready to enter into the smartwatch market. Google smartwatch is in final stages of its development. Tech giant is going to launch its intelligent digital assistant with Google Now integration and Android operating system.
The wearable device market is rapidly growing. It is expected to reach 485 million devices by 2018. But there are still questions about their limited functionality and short battery life. Samsung has recently released its Galaxy Gear smartwatch, but it did not overcome these problems. However, Google is working on such a smartwatch that will cover these issues.
The smartwatch will be able to communicate with other devices. Like Google Now integration will help user to reach its email and get all info like his travel schedules and more. With the launch of its own smartwatch device, Google wants to take the leading position against its rivals Apple and Microsoft. Both tech giants are also expected to launch their smartwatches in near future.


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Home Features Power Sector: Fashola's New Approach
Power Sector: Fashola's New Approach
Barely a week ago, at an event in Lagos which was a public lecture, the Minister of Power, Works and Housing, Babatunde Fashola, SAN gave an account of his stewardship in the last five months. In a paper titled "Nigeria's Electricity Challenge: A Roadmap for Change", Fashola acknowledged the shortfalls in meeting the electricity demands of consumers in the country over the past years . He however ended on an optimistic note that President Muhammadu Buhari's administration has all it takes to overcome the electricity challenges the country currently faces.
One noticeable trait in the minister's paper is the sincerity in his presentation. Fashola neither claims that all is well in the electricity sector, nor claim to hold the magic wand that will transform it. In his characteristic candour, the minister bared his mind thus, "In charting the roadmap for change, I am of the view that we must first tell ourselves what is wrong. The simplest way I can put it is to say that we do not have enough power".
From the above quote, it is clear that the minister is modest in describing the nation's power situation. It can also be deduced that the minister is more concerned about new perspectives that will lead to what he called "A Road Map for Change" and how we as a united people, can resolve the electricity challenge in the country. In charting a way forward, he has refused to be distracted by calls from a section of the public to probe his predecessors over the amount of fund spent on power in the past or to recommend cancellation of the privatization process. His major preoccupation is on how to bring about power that will satisfy the needs of Nigerians. This objective he intends to achieve through a three pronged process: incremental power, stable power and uninterrupted power. The ultimate goal of these processes is to take Nigeria to a point where people can enjoy stable and uninterrupted power supply.
The Buhari administration has demonstrated both in words and actions, its avowed commitment to boosting the power sector. It hopes to achieve this goal through a combination of energy mix and energy preservation policy. For instance, the government just approved about 14 different solar projects to generate a combined capacity of 1,286mw. It is noteworthy here to state that this is the biggest aggregation of solar projects that the country has ever undertaken. These solar projects are expected to be delivered in the next 12 to 18 months. Again, in the 2016 budget, government will spend N99 billion to revamp the nation's power sector.
In an attempt to bridge the power gap created partly by ageing and weak transmission infrastructure, a number of repairs and rehabilitation projects are currently being executed. The government is also looking at technical possibilities that support the decentralization of the grid while keeping them interconnected. At the 5th Monthly Power Sector Operators meeting hosted by Fashola at Shiroro Hydro Power Plant in Niger State, the Transmission Company of Nigeria (TCN) provided progress update on 16 critical projects identified by distribution and generation companies. These projects include the repair of the Owerri /Ahoda/Yenagoa line which now connects the newly commissioned Gbarain plant to grid. TCN also announced completion of repairs to transmission projects in Ajah, Akoka, Afam and Kainji.
The nation's hydro power plants are also being rehabilitated. For instance the first overhaul of Jebba Hydro power plant since it was commissioned in 1985 has just been completed and more of these will be undertaken. The turbines were supposed to be overhauled once every 5-6 years but this never happened. The Egbin power plant in Ikorodu which hitherto had only 2 functional turbines in 2013 now has all of its 6 turbines operational. Government is accelerating repairs of the Forcados pipeline damaged by vandals. Repair works should be completed by the end of this month which will allow gas to be supplied to thermal, power stations and result in an increased quantum of power on the grid.
Attention has been focused on the front runner Azura Independent Power Project in Edo State which is expected to deliver 450mw upon completion in 2018. Government securities and guarantees have already been issued to enable the financing of the project. Government has resolved the Zungeru Power plant dispute in Niger State which was held up in court for several years. Parties are out of court and over 800 workers are back on site. The power plant when completed is to deliver 700mw to the national grid.
There is also plan for the completion of rural electricity projects which have been left uncompleted for up to 10 years in some instances. In addition about 2,000 rural projects, most of them constituency projects, are being pursued to completion in the 2016 budget. There is also a well-coordinated inter- agency collaboration in place aimed at achieving an optimal energy mix that will assist power producers, investors and all stakeholders in siting of solar and hydro projects in the North, coal ones in the North- Central, and South East as well as gas plants in the South-West and South- South.
The Ministry of Petroleum Resources will facilitate the provision of gas and encourage investors to produce and allocate gas for power production while the Ministry of Water Resources is to provide access to dams and river basins for hydropower use and the Ministry of Solid Minerals is providing coal data to assist the revival of some coal-to- power initiatives
The minister deserves commendation for taking the advantage of the Lagos event to give account of his stewardship since he assumed office. It is also encouraging to see a well-articulated Road Map for Change in the power sector to address Nigeria's electricity challenge. It is hoped that these efforts will actually lead to stable and uninterrupted power.
Babatunde Fashola
Minister of Power
Ministry of Petroleum Resources
Transmission Company of Nigeria (TCN)
Works and Housing
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Below is a graph of student enrollment at the University of Virginia beginning with the school's first session in 1825 and continuing into the early postbellum period. The graph was created using data from the University's early catalogues. Students are split into three categories: Virginians, other southerners, and other — students from north of the Mason-Dixon line, the midwest, the west, or other countries.
The most visually striking feature of the graph is also its least surprising. The Civil War decimated enrollment. In 1860, total enrollment was 604; in 1861, just 66 students attended the University. When war broke out, young men abandoned their studies and rushed off to fight, with few exceptions, for the Confederacy.
What's far more surprising about this graph is what happens just before the Civil War. In 1845, 138 students were enrolled in the University. Eleven years later, in 1856, that number had more than quadrupled, as the 1856-57 session saw a record 645 students enrolled. In the 1850s Virginia was larger than even the most prestigious and established private schools like Harvard and Yale (Wall, 2).
This dramatic leap was caused by a mixture of small administrative changes, shifts in the internal culture of the school, and growing national division between the North and the South. In the late 1840s, in part because of the actions of the school's administration, student life at the University changed for the better and became more appealing to many young men. Meanwhile, tension between the North and South grew, and affluent southern families sought to keep their sons in the South rather than send them to the old schools of the North.
Primary documents from this period provide evidence that administrative changes played a role in the school's growth. First, the University began to provide free admission to a set number of qualified Virginian students. In the Board of Visitors meeting on June 25, 1846, the Board resolved "one Student from each Senatorial district, qualified to enter the University according to the enactments shall be received at each session hereafter, without payment of the Professors fees, & without charge for any of the University dues, fines & penalties excepted." The process for selecting state students was at least in part based upon helping students who otherwise would not have access to the University. "In making such selection the Faculty shall regard as well the capacity, as the moral fitness of the Candidate, and shall have satisfactory evidence, that the applicant his parent or guardian is not in a situation to incur the expenses of his education," the Board resolved. The expansion of the state student program indicates that the board did, to some degree, desire to expand the school's enrollment. The way they talk about the expansion suggests a feeling of duty to the state — they felt expansion would, in the words of the meeting minutes, "diffuse as far as practicable through the State the benefits of education at the University and thereby to extend its usefulness." Funding the state student program surely contributed in part to the increase of Virginian students from 103 in 1845 to 337 in 1855.
A series of other seemingly small institutional changes made during this period aggregated to change the culture of the school for the better, making the University safer and more appealing to many prospective students. In the first twenty years of U.Va.'s existence, relations between the students and the faculty were rocky at best, and the faculty minutes abound with reports of rowdy drinking and disrespectful behavior towards the faculty and other school authorities. Two incidents are in particular indicative of the University's struggles during this time. The first is the killing of Professor John Davis (P33195) in 1840. A pair of masked students were wandering the grounds at night firing pistols for fun, a fairly typical activity for students of the time. Professor Davis tackled one of the students in an attempt to identify him and was fatally shot at close range (Wall, 174). The second is the student riot of 1845, in which a group of "50 or more" organized students gathered in the night to make noise, ride horses, deface University buildings, and fire pistols (Faculty minutes, 1845). Class was cancelled for a week and a state militia was called in to control the outbreak. 38 students were dismissed for having participated, which is the cause of the downward tick in the enrollment graph just before the beginning of sustained growth in 1846. For the first twenty years of its existence, the University of Virginia was not an environment conducive to learning (Wall, 209).
A number of administrative changes in the 1840s ameliorated the school's disciplinary issues and no doubt contributed to the University's rapid expansion. In the 1830s, an early-rising rule was strictly enforced. Students were often forced to be out of bed by 5:00 in the morning, and those who lagged were reprimanded (Wall, 165). Faculty also strictly enforced a dress code, much to the annoyance of the students. Charles Ellis (P43085) writes in 1835 that "the Faculty have had a meeting to try the fellows who wore rebellious coats and those who wore shorts" (Head). The Faculty made a big show of enforcing these persnickety regulations and thus created an adversarial relationship between themselves and the students. The abolishment of the early-rising rule in 1842 and the uniform rule in 1844 immediately helped to make the school safer and more appealing. In 1842, newly minted Chairman Henry St. George Tucker (P43676) delivered the session's opening speech, emphasizing discipline based on adherence to the rules under which both the students and faculty lived. The students were so enthused by the speech and the new rules it represented that they asked to have it published (Wall, 254).
In addition, a temperance movement began to take hold at the University in the latter half of the 1840s. The first temperance society was founded at the University in 1842 and began to exert serious influence in 1845, when 70 students signed a pledge to abstain from alcohol. Though drinking was still common, it became less contentious and rowdy (Wall, 79). An incident recorded in Socrates Maupin's (P43731) 1855-56 Chairman's Journal exemplifies the more congenial relationship between faculty and students. A student named Thomas T. Johnston (P27776) was called before Maupin for the second time in the session for being drunk. Maupin was on the verge of dismissing Johnston when he and 14 other students signed a petition promising to join the Sons of Temperance if Johnston was allowed to continue. Maupin consulted with the Faculty and "concluded that the interests of discipline would be subserved, by accepting the offered pledge" (Chairman's Journal, 1855-56). Fifteen years earlier, Johnston surely would have been swiftly dismissed, which in turn would have angered his friends and fellow students. The disciplinary reforms of the 1840s greatly improved student-faculty relations, made the University a much more appealing place, and doubtless contributed to the school's rapid growth.
However, the Board of Visitors' meeting minutes from this period suggest that the administrative changes made were not the sole reason for the school's dramatic expansion. The members of the board discuss the school's swelling enrollment in a tone wavering somewhere between matter-of-fact and worried. This growth surprised them, and the minutes reveal that the school's infrastructure was not ready to take on so many new students.
In 1849, the University was forced to rearrange the way it scheduled its lectures. "The duty of arranging the lectures in the different schools of the University so as to prevent any interference or serious inconvenience to the Students has become from year to year a more difficult task," reported the faculty in the annual Board of Visitors meeting. "This session, however, it has been found utterly impossible to make such an arrangement, owing partly to the considerable increase of the number of Students." During the same meeting, the Faculty stressed the "urgent want of additional lecture rooms — A want heretofore productive of most serious inconvenience and calculated materially to affect the usefulness of their instruction, should the present number of Students continue or increase" (Board of Visitors minutes, 17 October 1849). The next year a "Committee of Inspection" emphasized to the Board "the necessity of providing without delay enlarged space for the accommodation of many classes by increased numbers too large to be accommodated at lecture with such a regard to health or comfort as prudence demands" (Board of Visitors minutes, 28 June 1850). The University's logistical and physical infrastructure was insufficient for the new students. The growth was not intended to be so dramatic.
The Board, for their part, resolved in 1850 to procure "300,000 bricks to be used in the erection of such additional Buildings as may, in the opinion of the Board of Visitors become necessary for the successful operation of the University" (Board of Visitors minutes, 28 June 1850). From 1845 to 1850, enrollment nearly tripled, and the board was playing catch-up. Though the administration took action in the late 1840s to grow the school, it's clear that they were unprepared for the number of new students they soon faced.
If the growth was not entirely the result of internal change, further explanation for the University's transformation must be found by looking externally. In the 1850s sectional tensions between the North and South were rapidly growing. As a result, many southerners who would have sent their children to northern colleges chose instead to keep them in the South. This trend is reflected in the graph — the growth is driven by non-Virginian southerners. In 1848, 30 students from secession states, Maryland, and Washington, D.C. were enrolled, a contingent making up roughly 11% of the school's total enrollment. By 1856, 305 such students were enrolled, and roughly 47% of the University was comprised of southerners from outside Virginia.
The large numbers of new southerners were arriving at U.Va. because they and their families felt they couldn't go north. "Southern life, habits, thoughts, and aims, are so essentially different from those of the North, that here a different character of books . . . and training is required," wrote one magazine in 1851 (McPherson, 431). Northern colleges were perceived as agents of abolitionism and thus mistrusted by wealthy southerners. In 1859, a Mississippi newspaper told its readers that "there is every reason to expect that young men sent for education to Harvard or Yale will come back poisoned with anti-slavery heresy" (Groen, 29).
The enrollment at northern schools during this time period also reflects the effects of growing sectional tension. Many schools saw their population of southern students dramatically decrease in the lead up to the Civil War. One institution which kept particularly comprehensive and well-organized enrollment records is the University of Pennsylvania's Medical School, and closely examining the enrollments at Penn can shed further light on the ways in which sectional tensions manifested themselves on campuses. Below is a graph of the total enrollment numbers for the Penn Medical School during U.Va.'s pre-war growth period, split in to Northern and Southern students.
This graph tells a slightly different story than the graph of U.Va.'s enrollment, but both graphs underscore the strong effect of rising North-South tension on enrollments. The U.Va. graph suggests that sectional tensions rose steadily during this period and that student enrollments changed steadily as a result, with the number of new Southern students continuously rising. The Penn graph suggests that North-South animosity reached a boiling point just a few years before the actual war began, and that students began to respond in the late 1850s. Though the inflection points are different, the effect on display is the same: sectional tension caused southerners to leave northern schools and return home.
The reason the graphs aren't perfectly comparable is a result of the fundamental differences between the two institutions. Penn's Medical School was one of the premier medical schools in the nation at this time, roughly three times the size of Virginia's. Philadelphia was a national center of medical research, home to other important institutions like the Jefferson Medical College, the Philadelphia College of Medicine, and the Pennsylvania Hospital (Poethig). It makes sense that southern students at Penn would have been hard to dislodge from their impressive institution. They likely would not have headed south unless they felt they had absolutely no choice.
Yet leave they did. On December 21, 1859 — a year and a half before actual fighting began — 200 students from Penn and other Philadelphia medical colleges boarded trains for Richmond and never returned, choosing instead to further their education in the south. From 1859 to1861, enrollment of southern students at Penn fell from 222 to 22. "Southern pride, rather than administrative mistakes or severe competition, caused the decline in Penn's enrollment," declares an exhibit on Penn's University Archives and Records Center website. Sectional tensions mattered, even to students entrenched at prestigious places like Penn. The agitation affected U.Va. earlier than it affected Penn, but it certainly played an important role at both institutions.
There is plenty of anecdotal evidence of students and even faculty transferring directly from Northern schools to U.Va. during this period. Rev. Dabney Harrison (P34260) was a member of the Princeton class of 1848, but returned to Virginia for law school. Harrison's brother's roommate at Princeton, Basil Gildersleeve (P43681), was class of 1851, but after graduating returned south and became the classics professor at U.Va. Harrison was later killed and Gildersleeve wounded while fighting for the Confederacy (Maynard). Their stories exemplify the effects of growing sectional tensions. Regional loyalties were emphasized in this period, and the result was a greater number of southerners in attendance at the University of Virginia.
The school's rapid growth in the decade before the Civil War was caused by a combination of internal and external factors. New Virginians were attracted by the inception of scholarships for in-state students. The quality of life at the University increased during this period thanks to common-sense disciplinary reforms implemented by the faculty. Meanwhile, North-South tensions grew in the run up to the war. Students from the South chose to stay in the South, and southern students who had ventured north returned to Virginia to further their education on friendly soil. Thanks to the cultural shifts in and around the school, University enrollment quadrupled from 1845 to 1856. Paradoxically, this tension over abolition soon precipitated an enrollment collapse even more dramatic than the growth, as the 645 students in attendance in 1856 dwindled to just 66 by the beginning to the Civil War five years later.
Head, Ronald B., ed., "The Student Diary of Charles Ellis, Jr., March 10- June 25, 1835," The Magazine of Albemarle County History, 1978.
Maynard, W. Barksdale. "Princeton in the Confederacy's Service." Princeton Alumni Weekly, 23 March 2011.
McPherson, James. "Antebellum Southern Exceptionalism: A New Look at an Old Question." Civil War History, vol. 50, no. 4, 2004, pp. 418-433.
Poethig, Luke. "The Evolution of Penn's Medical School in the Middle and Late Nineteenth Century." Penn University Archives and Records Center. www.archives.upenn.edu. 2011.
Wall, Charles Coleman. "Students and Student Life at the University of Virginia, 1825 to 1861." University of Virginia Ph.D. dissertation, 1978.


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Q: Definition of Disjoint Union Spaces The following is the definition of disjoint union spaces in John Lee's "Introduction to Topological Manifolds":

Let $(X_{\alpha})_{\alpha\in A}$ be an indexed family of nonempty topological spaces. We define the disjoint union topology on $\amalg_{\alpha\in A}X_{\alpha}$ by declaring a subset of the disjoint union to be open if and only if its intersection with each set $X_{\alpha}$ (considered as a subset of the disjoint union) is open in $X_{\alpha}$. With this topology, $\amalg_{\alpha\in A}X_{\alpha}$ is called a disjoint union space.

In this definition, what does it mean for a set to be open in $X_{\alpha}$? Here the disjoint union $\amalg_{\alpha\in A}X_{\alpha}$ is defined by $$\amalg_{\alpha\in A}X_{\alpha}=\{(x,\alpha):\alpha\in A, x\in X_{\alpha}\},$$
and by "considered as a subset of the disjoint union", he means that he is identifying the set $X_{\alpha}$ with the set $$\{(x,\alpha): x\in X_{\alpha}\}.$$

A: For every index $\alpha \in A$ there is a canonical inclusion map $\sigma_\alpha :X_\alpha \to \coprod_{\alpha \in A} X_\alpha$ given by $x \mapsto (x,\alpha)$. A subset $V$ of $\coprod_{\alpha \in A} X_\alpha$ is declared as open if $\sigma_\alpha^{-1}(V)$ is open in $X_\alpha$ for every $\alpha \in A$. More precisely, we define a topology $\mathfrak{T}$ on $\coprod_{\alpha \in A} X_\alpha$ as follows:
$$
\mathfrak{T} = \left\{ V \subseteq \coprod_{\alpha \in A} X_\alpha : \sigma_\alpha^{-1}(V) \text{ is open in $X_\alpha$, for all $\alpha$} \right\}.
$$
As you pointed out, we then identify $X_\alpha$ with the set
$$
Y_\alpha := \{ (x,\alpha) : x \in X_\alpha\}.
$$
Then, $\sigma_\alpha^{-1}(V)$ can be viewed as the "intersection of $V$ with $X_\alpha$". Indeed, after identifying $X_\alpha$ with $Y_\alpha$ above, the pre-image $\sigma_\alpha^{-1}(V)$ asks which points in $V$ live in $X_\alpha$.

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redpajama_set_name: RedPajamaGithub


SDHGPA is now officially registered and listed as a 501 (c) (7) Tax Exempt nonprofit; thank you Mr. Helliwell for all your efforts.
Palomar has lots of Site Rules as requested by our Land Owners. They are clearly described in the site guide, and continued use of the site is dependent on everyone following them. As with Blossom, Palomar is on private property and it is a hard-won privilege to fly there. The owners have asked us to only allow pilots to fly there if they demonstrate that they are smart enough to read. Carry your membership cards, display your placard, lock the gate, call Pala security and John Smiley every time before you go launch. Land only in designated LZs and for sure do not land in areas designated as being close. Pala security and other Land Owners are watching you, and they are calling us.
We have already experienced two injury accidents at Little Black this spring. Recent conditions have been more summer-like than spring-like, and awareness of both conditions and your own capabilities is critical to your survival and continued ability to enjoy this sport.
Contributing factors in both incidences: these pilots were flying in inappropriate locations to prevailing conditions. We are continuing to see this with many pilots at our more complex non simple ridge sites like Little Black and Palomar to name a few.
Again. Remember that paragliding and hang gliding are really dangerous, and your family and friends want you to be safe more than they want you to fly high and go far. Remember no one cares how long you stayed up, if you set XC records, or do cool acro. No one. Really. You are the pilot in command of your glider, or your wheelchair, and of your life.
Spring fly-in will be in May, likely at Palomar May 2nd, or possibly on Memorial Day Weekend. Experiencing some difficulties coordinating with mothers, XC leagues, etc. Any suggestions are welcome!
Doug P and Jody L offered to help with planning and coordination in addition to the social committee.
Keep an eye out for an upcoming Spring Fly-in Flier/ blog post.


text:
DFRLab investigation leads to Facebook takedown of assets affiliated with Georgian March party
Assets linked to Georgian far-right and
Assets linked to Georgian far-right and pro-Kremlin party were camouflaged as entertainment content
(Source: Reuters / Rafael Henrique / SOPA Images/ Sipa USA)
By Sopo Gelava and Eto Buziashvili
Amid a deepening political crisis in Georgia related to the detention of the leader of the main opposition party, Facebook removed a network connected to the violent far-right and pro-Kremlin party Georgian March. The network of 70 assets camouflaged itself as a collection of entertainment and online shopping platforms and included 24 Facebook pages, 12 groups, 23 user accounts, and 11 Instagram profiles.
The takedown comes after a December 2020 DFRLab investigation that identified an inauthentic network promoting Georgian March and pro-government media outlet PosTV on Facebook.
In a statement released by a Facebook spokesperson, the company said:
The people behind this activity used fake and duplicate accounts to post, comment and manage Pages and Groups. This network had multiple strikes for violating our Community Standards related to hate speech. They focused primarily on amplifying the content of Georgian March, a political party on the right in Georgia. This network posted in Georgian about news and current events including elections, claims of voter fraud, covid-19 pandemic, and criticism of the US President Biden. This network was early in its operation when we removed it.
We found this network after reviewing public reporting on this activity by researchers at the Digital Forensic Research Lab at the Atlantic Council. Although the people behind this activity attempted to conceal their identities and coordination, our investigation found links to individuals associated with Georgian March, a political party in Georgia, and its youth wing.
Before transforming itself into a political party prior to the 2020 parliamentary elections, Georgian March was formed in 2017. The group has routinely targeted migrants, the LGBT community, and democracy activists.
An Estonian Intelligence Service report referred to Georgian March as a Russian-backed "umbrella organization for extremist movements" promoting "so-called traditional values." Georgian March has strong ties with local pro-Kremlin actors, including the Y. M. Primakov Georgian-Russian Centre and Levan Vasadze, a millionaire who gained his fortune in Russia and is a supporter of local far-right groups. Vasadze himself has connections with Alexander Dugin, aka "Putin's brain," a geopolitical theorist known for fascist views and close ties to the Kremlin.
Civil society representatives and political analysts have long raised concerns about the connections between Georgian March with the Georgian Dream led-government. Until 2016, the leader of Georgian March, Sandro Bregadze, served as a Deputy Minister of Diaspora Affairs; his relatives donated to Georgian Dream prior to 2016 parliamentary elections. Some researchers have suggested that Georgian Dream neglects the threat posed by Georgian March and other far-right groups, and instrumentalizes them for intimidating liberal groups that are also critical of the government.
Facebook took down 24 pages; according to the company, around 119,000 accounts followed one or more of them. Among these pages were several official pages of Georgian March and the dormant page of Irakli Shikhiashvili, one of the leaders of the political party.
Another removed page, მარში ტვ ("March TV"), was created ahead of the Georgian parliamentary elections and announced the broadcasting of the Georgian March-affiliated TV channel. As investigated by the DFRLab, the page shared content from Georgian March's official page and also managed two public groups, საგიჟეთი, ღამურები, შერეკილები ("Madhouse, Bats, Eccentrics") and ყიდვა გაყიდვა საქართველოში ("Buy and Sell in Georgia"). The content from this page was also promoted by Beka Kvitsiani, an author with the Kremlin-affiliated disinformation outlet News Front Georgia. The page had been inactive since February 2021.
Georgian March, together with other far-right and pro-Kremlin actors, fueled sentiments around Davit-Gareji, the disputed historical monastery complex between Georgia and Azerbaijan, that was followed by detainment of two cartographers of the Delimitation and Demarcation Commission, accusing them of attempting to cede land to Azerbaijan ahead of the 2020 parliamentary elections. The timing of the accusation and other inconsistencies in the case have raised concerns among Georgian civil society groups and the political opposition, who have assessed the investigation as politically motivated and intended to consolidate power around the Georgian Dream party. The official page of Georgian March sponsored several posts on the Davit-Gareji controversy and held several demonstrations at the Gareji complex with the slogan "Davit-Gareji is Georgia." One of the demonstrations at the Azerbaijan border was held amid the 2020 Nagorno-Karabakh conflict between Armenia and Azerbaijan.
Georgian March sponsored two posts on Davit-Gareji and held several demonstrations with the slogan "Davit-Gareji is Georgia." (Source, left/center: Facebook ads library; right: RFE/RL)
Facebook also deleted pages connected to George Toreli, a photographer and video blogger. DFRLab has previously reported on the Facebook network linked to Toreli, which was used by Georgian March and pro-government TV channel PosTV to promote its content. Pages in Toreli's network presented themselves as focused on general interest topics, such as online sales and marketing, travel, photography, movies, and entertainment. In reality, however, they promoted Georgian March and PosTV content on their Facebook timelines and to related groups in a coordinated manner. Giorgi Gabedava, one of the leaders of Georgian March, responded to DFRLab's previous article claiming that George Toreli is his close friend and shared the videos from Georgian March to support the party. Since the DFRLab's investigation, pages in Toreli's network no longer disseminated posts promoting Georgian March and PosTV.
Facebook pages camouflaged as entertaining content promoted far-right Georgian March and pro-government PosTV in a coordinated fashion. (Source: Facebook)
Pages in this network also included two well-known far-right pages, "წინააღმდეგობა • Resistance" and the page "გათბობის სისტემები — "ბეგიო" / Boil Systems — "BeGio," formerly known as "რუხი კარდინალი" ("Grey Cardinal"), as well as the newly established dormant page "CoronaVirus News."
Facebook accounts
The network also included 23 user accounts. Nine of these accounts had stolen profile pictures from elsewhere on the internet, and were likely inauthentic. The DFRLab previously identified that the same fake accounts as sharing content from Georgian March-affiliated pages in a coordinated manner. Two of the removed accounts also indicated that they worked as PR managers for Georgian March.
Accounts promoting Georgian March used stolen profile pictures. (Source: Facebook, left; Google Images, top right; Yandex bottom right)
Fake accounts shared content from Georgian March-affiliated page in a coordinated manner. (Source: Facebook)
Some of the accounts that promoted Georgian March, at the same time shared PosTV's content and a Facebook post from Shalva Ramishvili, a shareholder and an anchor at PosTV. One of the users in this network disseminated a PosTV video published by "Georgian March Ball," a page connected to Georgian March, in anti-liberal groups such as "ქართული მარში — ეროვნული მოძრაობის მხარდამჭერთა" ჯგუფი ("Georgian March — National Movement" supporters group) and "ანტილიბერალური სივრცე" ("Anti-Liberal Space").
Accounts promoted Georgian March and shared content from PosTV on their timelines and in anti-liberal groups. (Source: Facebook)
Other accounts in this network also shared content from another far-right page "წინააღმდეგობა • Resistance ." Three accounts camouflaged themselves under general names such as "employment agent," "Georgian emigrants," and "Tbilisi, Georgia." Remaining deleted accounts were connected to George Toreli.
The 12 Facebook groups in the network, some of which were private, had a combined membership of around 10,500 accounts. Engagement with their posts was low and, in many cases, close to zero. Similar to the pages, the groups used deceptive names that indicated they were focused on apolitical topics, such as entertainment or job vacancies, while hosting political content related to Georgian March for an unsuspecting audience. Only two out of 12 groups identified themselves as for Georgian March supporters.
The users in the group "ქართული მარში — ეროვნული მოძრაობის მხარდამჭერთა ჯგუფი" ("Georgian March — supporters of national movement"), which had 2,500 members, also fueled negative sentiment toward Turkey — a common tactic applied by far-right and pro-Kremlin groups in Georgia in order to provoke ethnic and religious tension and distract attention from threats Georgia faces from Russia; and promoting Georgian far-right group Alt-Info, which has spread anti-Western and anti-LGBT narratives and engaged in coordinated inauthentic behavior that resulted in a previous Facebook takedown.
The users in the group "ქართული მარში — ეროვნული მოძრაობის მხარდამჭერთა ჯგუფი" (Georgian March — supporters of national movement) fueled negative sentiment toward Turkey and promoted far-right group Alt-Info. (Source: Facebook)
Similar to the pages, the groups used deceptive names that indicated they were focused on apolitical topics, while hosting political content related to Georgian March.
Misleading names of some of the Facebook groups, indicating they were devoted to various apolitical topics, such as job vacancies (left) and social media marketing (right). (Source: Facebook)
According to the information given in the about section, one of the groups in the network, "შავი ღრუბელი / Black Cloud," was created specifically for mobilizing people to reporting "liberal Facebook pages" (i.e. attacking Facebook pages that have culturally liberal values) in a coordinated way. The description of the group said, "whenever possible, everyone's suggestions on the targets of coordinated report will be taken into consideration….[T]here will be an announced exact time when everyone should find five minutes to report [the targeted page] in a coordinated way." Apparently, the network employed the group for targeting people and pages they opposed and used the Facebook reporting mechanism as a tool to silence or disrupt pro-Western accounts.
One of the groups in the network was employed to mobilize internet users for reporting pro-Western Facebook pages in a coordinated way. (Source: Facebook)
Multiple groups were managed by common administrators– Facebook pages and accounts titled with variations of George Toreli's name, as well as with names dedicated to shopping and job vacancy pages.
The network also included 11 Instagram accounts, some of which were personal accounts of Georgian March supporters. These were the same users that had accounts on Facebook as well. Images of George Toreli appeared on four accounts, however, under different names. Two accounts also posed as advertising and entertaining platforms that the DFRLab has previously identified as part of Toreli's network.
George Toreli, who operated a network that promoted Georgian March and PosTV had several accounts on Instagram with different names. (Source: Instagram)
Sopo Gelava is a Research Associate, Caucasus, with the Digital Forensic Research Lab.
Eto Buziashvili is a Research Associate, Caucasus, with the Digital Forensic Research Lab.
Sopo Gelava and Eto Buziashvili, "DFRLab investigation leads to Facebook takedown of assets affiliated with Georgian March party," Digital Forensic Research Lab (DFRLab), April 6, 2021, https://medium.com/dfrlab/dfrlab-investigation-leads-to-facebook-takedown-of-assets-affiliated-with-georgian-march-party-c556777795e3.


text:
The First National Bank is a five-story building in Grand Forks, North Dakota, that was built in 1914–15 and listed on the National Register of Historic Places in 1982.    It was built for the Scandinavian-American Bank, but has been identified as the First National Bank building since 1929.

History
When it was founded, the Scandinavian-American Bank had its offices in the Metropolitan Opera House in Grand Forks. The new bank building was constructed in 1914–15 and occupied in 1915. When the bank later obtained a charter as a national bank, it took the name Northwestern National Bank. In 1929, it merged with the First National Bank, and the combined bank located in this building. First National Bank failed in 1933, during the Great Depression, but was replaced by a new First National Bank entity that later became Alerus Financial in 2000.

The building is located on a corner lot, approximately  in size, at the intersection of DeMers Avenue and North Fourth Street. It is considered an "outstanding example" of the use of Classical Revival architecture in the context of a large commercial building. The two sides that face the street have two-part facades in which the lower two stories are fronted by rusticated ashlar piers built on top of polished granite blocks and the three upper stories are faced with red brick. The top of the building is decorated with a stone cornice.

The property was included in a 1981 study of the historical resources of downtown Grand Forks. It was damaged by flooding and fire in the 1997 Red River flood; it is the only building on the block that was not demolished as a result of flooding and fire.

References

Related reading
Ashley Shelby (2008) Red River Rising: The Anatomy of a Flood and the Survival of an American City (Minnesota Historical Society)

Bank buildings on the National Register of Historic Places in North Dakota
Buildings designated early commercial in the National Register of Historic Places in North Dakota
Neoclassical architecture in North Dakota
Vernacular architecture in North Dakota
Commercial buildings completed in 1915
National Register of Historic Places in Grand Forks, North Dakota
Scandinavian-American history
1915 establishments in North Dakota

redpajama_set_name: RedPajamaWikipedia


Writing the script for your video appearance can seem daunting but here are a few quick tips to get you started. Keep in mind that a 60 second script is around 200-300 words.
What's the hook? Can you think of something to draw your viewers in? Often this is you asking the viewer a question, or it can be a startling statistic or fun fact.
You wouldn't risk your business image by having an amateur logo, why would you risk your image by using amateur video?
Did you know that in a recent survey, 60% of respondents said they felt businesses with video content on their site to be more professional and trustworthy than those who just bombarded them with text?
Tell people who you are. Just a single quick sentence to let people know about you.
Hi, I'm Jeff and I'm a video producer specialising in online video for small business.
What is your business? Write a couple of sentences telling people what you do.
I work with my clients from initial idea to finished production in order to create great web videos that get their message out to their clients.
Who are your customers? What is your ideal target audience?
I love to work with forward thinking small businesses who recognise the importance of video in their marketing.
What sets you apart from your competition? Tell us what makes you unique.
I'm really passionate about helping people communicate with their clients and do everything I can to make the experience as stress-free as possible. I work with you to make sure you always put your best foot forward.
Add a call to action. After all, we usually want the people watching a video to actually do something… so what would that be?
I love helping people with their video projects so give me a call to arrange a free, no obligation consultation about your next video project.
Once you've got a sentence or two down under each topic put them together and try reading it out loud. This is important because sometime what looks perfect on the page can be almost impossible to actually say in real life. If you don't feel comfortable saying it, you'll look uncomfortable and unbelievable on the screen. Keep it as natural as you can.
Change things as needed. Try the script out on someone you can trust to give you honest feedback. Most importantly, try to keep the script simple and natural.
Still not sure where to start? Feel free to give Jeff Kirkland a call any time to talk through your options.