## Aversion to ambiguity and model misspecification in dynamic stochastic environments

Proceedings of the National Academy of Sciences, Vol. 115, No. 37. (11 September 2018), pp. 9163-9168, https://doi.org/10.1073/pnas.1811243115

### Abstract

[Significance] In many dynamic economic settings, a decision maker finds it challenging to quantify the uncertainty or assess the potential for mistakes in models. We explore alternative ways of acknowledging these challenges by drawing on insights from decision theory as conceptualized in statistics, engineering, and economics. We suggest tractable and revealing ways to incorporate behavioral responses to uncertainty, broadly conceived. Our analysis adopts recursive intertemporal preferences for decision makers that allow them to be ambiguity averse and concerned about the potential misspecification ...

## Parametric transitions between bare and vegetated states in water-driven patterns

Proceedings of the National Academy of Sciences, Vol. 115, No. 32. (07 August 2018), pp. 8125-8130, https://doi.org/10.1073/pnas.1721765115
Keywords:

### Abstract

[Significance] Since the appearance of land plants in Devonian time, vegetation has played a key role in the coevolution of life and landscapes as a result of mutual orchestrated processes between vegetation characteristics, environmental disturbances, and soil allometry. We mathematically frame the interactions between these three processes into a single parameter that discriminates between vegetated and bare states. In agreement with theories linking ecosystem development to hydrosphere and lithosphere connectivity, this theory suggests that the vegetation biodiversity of river sediment deposits occurs ...

## Resilience of networks with community structure behaves as if under an external field

Proceedings of the National Academy of Sciences, Vol. 115, No. 27. (03 July 2018), pp. 6911-6915, https://doi.org/10.1073/pnas.1801588115
Keywords:

### Abstract

[Significance] Much work has focused on phase transitions in complex networks in which the system transitions from a resilient to a failed state. Furthermore, many of these networks have a community structure, whose effects on resilience have not yet been fully understood. Here, we show that the community structure can significantly affect the resilience of the system in that it removes the phase transition present in a single module, and the network remains resilient at this transition. In particular, we show that ...

## Has artificial intelligence become alchemy?

Science, Vol. 360, No. 6388. (04 May 2018), pp. 478-478, https://doi.org/10.1126/science.360.6388.478

### Abstract

Ali Rahimi, a researcher in artificial intelligence (AI) at Google in San Francisco, California, has charged that machine learning algorithms, in which computers learn through trial and error, have become a form of "alchemy." Researchers, he says, do not know why some algorithms work and others don't, nor do they have rigorous criteria for choosing one AI architecture over another. Now, in a paper presented on 30 April at the International Conference on Learning Representations in Vancouver, Canada, Rahimi and his ...

## Generalized 3D fragmentation index derived from lidar point clouds

Open Geospatial Data, Software and Standards, Vol. 2, No. 1. (20 April 2017), https://doi.org/10.1186/s40965-017-0021-8
Keywords:

### Abstract

[Background] Point clouds with increased point densities create new opportunities for analyzing landscape structure in 3D space. Taking advantage of these dense point clouds we have extended a 2D forest fragmentation index developed for regional scale analyses into a 3D index for analyzing vegetation structure at a much finer scale. [Methods] Based on the presence or absence of points in a 3D raster (voxel model) the 3D fragmentation index is used to evaluate the configuration of a cell’s 3D neighborhood resulting in fragmentation classes ...

## The lack of a priori distinctions between learning algorithms

Neural Computation, Vol. 8, No. 7. (1 October 1996), pp. 1341-1390, https://doi.org/10.1162/neco.1996.8.7.1341

### Abstract

This is the first of two papers that use off-training set (OTS) error to investigate the assumption-free relationship between learning algorithms. This first paper discusses the senses in which there are no a priori distinctions between learning algorithms. (The second paper discusses the senses in which there are such distinctions.) In this first paper it is shown, loosely speaking, that for any two algorithms A and B, there are “as many” targets (or priors over targets) for which A has lower ...

## K-groups: a generalization of K-means clustering

(12 Nov 2017)
Keywords:

### Abstract

We propose a new class of distribution-based clustering algorithms, called k-groups, based on energy distance between samples. The energy distance clustering criterion assigns observations to clusters according to a multi-sample energy statistic that measures the distance between distributions. The energy distance determines a consistent test for equality of distributions, and it is based on a population distance that characterizes equality of distributions. The k-groups procedure therefore generalizes the k-means method, which separates clusters that have different means. We propose two k-groups algorithms: k-groups by first variation; and k-groups by ...

## Fluctuations of animal populations and a measure of community stability

Ecology, Vol. 36, No. 3. (1 July 1955), pp. 533-536, https://doi.org/10.2307/1929601
Keywords:

### Abstract

[Excerpt] Three assumptions will be made and a conclusion will be deduced from these. Since the conclusion is not always correct, it mill be justifiable to conclude that one or more of the assumptions is responsible. First, temporarily assume that the amount of energy entering the community (at the lowest trophic level, of course) does not vary with time. Second, assume that the length of time that energy is retained by a species before being passed on to the next doesn't change ...

## Percentiles

In NIST/SEMATECH e-Handbook of Statistical Methods (2012), 7.2.6.2
Keywords:

### Abstract

[Excerpt: Definitions of order statistics and ranks] For a series of measurements Y1, …, YN, denote the data ordered in increasing order of magnitude by Y〈1〉, …, Y〈N〉. These ordered data are called order statistics. If Y〈j〉 is the order statistic that corresponds to the measurement Yᵢ, then the rank for Yᵢ is j; i.e., [::] Y〈j〉 ∼ Yᵢ, rᵢ=j. [Definition of percentiles] Order statistics provide a way of estimating proportions of the data that should fall above and below a ...

## Sample quantiles in statistical packages

The American Statistician, Vol. 50, No. 4. (1 November 1996), pp. 361-365, https://doi.org/10.1080/00031305.1996.10473566
Keywords:

### Abstract

There are a large number of different definitions used for sample quantiles in statistical computer packages. Often within the same package one definition will be used to compute a quantile explicitly, while other definitions may be used when producing a boxplot, a probability plot, or a QQ plot. We compare the most commonly implemented sample quantile definitions by writing them in a common notation and investigating their motivation and some of their properties. We argue that there is a need to ...

## The challenge of knowledge soup

In Research Trends in Science, Technology and Mathematics Education (May 2006), pp. 55-90

### Abstract

People have a natural desire to organize, classify, label, and define the things, events, and patterns of their daily lives. But their best-laid plans are overwhelmed by the inevitable change, growth, innovation, progress, evolution, diversity, and entropy. These rapid changes, which create difficulties for people, are far more disruptive for the fragile databases and knowledge bases in computer systems. The term knowledge soup better characterizes the fluid, dynamically changing nature of the information that people learn, reason about, act upon, and ...

## Fuzziness vs. probability

International Journal of General Systems, Vol. 17, No. 2-3. (June 1990), pp. 211-240, https://doi.org/10.1080/03081079008935108

### Abstract

Fuzziness is explored as an alternative to randomness for describing uncertainty. The new sets-as-points geometric view of fuzzy sets is developed. This view identifies a fuzzy set with a point in a unit hypercube and a nonfuzzy set with a vertex of the cube. Paradoxes of two-valued logic and set theory, such as Russell's paradox, correspond to the midpoint of the fuzzy cube. The fundamental questions of fuzzy theory—How fuzzy is a fuzzy set? How much is one fuzzy set a ...

## The world's simplest impossible problem

MathWorks Technical Articles and Newsletters, Vol. 1 (1990), 92036v00

### Abstract

If the average of two numbers is three, what are the numbers? The solution to this problem is not unique, and the problem is ill-defined, but that does not mean that MATLAB® cannot solve it. [\n] In this article from 1990, Cleve Moler explores this simple yet impossible problem and others like it using MATLAB to find answers with the fewest nonzero components and other “nice” solutions. ...

## Can one take the logarithm or the sine of a dimensioned quantity or a unit? Dimensional analysis involving transcendental functions

Journal of Chemical Education, Vol. 88, No. 1. (1 January 2011), pp. 67-70, https://doi.org/10.1021/ed1000476

### Abstract

The fate of dimensions of dimensioned quantities that are inserted into the argument of transcendental functions such as logarithms, exponentiation, trigonometric, and hyperbolic functions is discussed. Emphasis is placed on common misconceptions that are not often systematically examined in undergraduate courses of physical sciences. The argument of dimensional inhomogeneity of the terms of a Taylor expansion of a transcendental function presented in some nonpeer-reviewed popular Internet sites is shown to be false. ...

## Two-Person Cooperative Games

Econometrica, Vol. 21, No. 1. (1953), pp. 128-140, https://doi.org/10.2307/1906951

### Abstract

In this paper, the author extends his previous treatment of 'The Bargaining Problem" to a wider class of situations in which threats can play a role. A new approach is introduced involving the elaboration of the threat concept. [Introduction] The theory presented here was developed to treat economic (or other) situations involving two individuals whose interests are neither completely opposed nor completely coincident. The word cooperative is used because the two individuals are supposed to be able to discuss the situation ...

## Rejoinder: brownian distance covariance

The Annals of Applied Statistics, Vol. 3, No. 4. (5 Oct 2010), pp. 1303-1308, https://doi.org/10.1214/09-aoas312rej
Keywords:

### Abstract

Rejoinder to "Brownian distance covariance" by Gábor J. Székely and Maria L. Rizzo [arXiv:1010.0297] ...

## Sparse Algorithms Are Not Stable: A No-Free-Lunch Theorem

Pattern Analysis and Machine Intelligence, IEEE Transactions on, Vol. 34, No. 1. (January 2012), pp. 187-193, https://doi.org/10.1109/tpami.2011.177

### Abstract

We consider two desired properties of learning algorithms: *sparsity* and *algorithmic stability*. Both properties are believed to lead to good generalization ability. We show that these two properties are fundamentally at odds with each other: a sparse algorithm cannot be stable and vice versa. Thus, one has to trade off sparsity and stability in designing a learning algorithm. In particular, our general result implies that $\ell_1$-regularized regression (Lasso) cannot be stable, while $\ell_2$-regularized regression is known to have strong stability properties ...

## Clustering by fast search and find of density peaks

Science, Vol. 344, No. 6191. (26 June 2014), pp. 1492-1496, https://doi.org/10.1126/science.1242072

### Abstract

[Abstract] Cluster analysis is aimed at classifying elements into categories on the basis of their similarity. Its applications range from astronomy to bioinformatics, bibliometrics, and pattern recognition. We propose an approach based on the idea that cluster centers are characterized by a higher density than their neighbors and by a relatively large distance from points with higher densities. This idea forms the basis of a clustering procedure in which the number of clusters arises intuitively, outliers are automatically spotted and excluded ...

## The documentary structure of source code

Information and Software Technology, Vol. 44, No. 13. (October 2002), pp. 767-782, https://doi.org/10.1016/s0950-5849(02)00103-9

### Abstract

Many tools designed to help programmers view and manipulate source code exploit the formal structure of the programming language. Language-based tools use information derived via linguistic analysis to offer services that are impractical for purely text-based tools. In order to be effective, however, language-based tools must be designed to account properly for the documentary structure of source code: a structure that is largely orthogonal to the linguistic but no less important. Documentary structure includes, in addition to the language text, all ...

## Extreme terseness: some languages are more agile than others

Lecture Notes in Computer Science In Extreme Programming and Agile Processes in Software Engineering, Vol. 2675 (24 June 2003), pp. 334-336, https://doi.org/10.1007/3-540-44870-5_44

### Abstract

While XP principles are independent of the languages in which software is developed, we can distinguish properties of programming languages that affect the agility of development. Some languages are inherently more agile than others, and the experience of developing software in these languages reflects this. A family of languages descended from the mathematics notation developed at Harvard in the 1950s by Iverson [1] shares properties of extreme terseness and abstractive power with weak data typing. The history of software development in ...

## How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems

Proceedings of the National Academy of Sciences, Vol. 111, No. 19. (13 May 2014), pp. 6905-6910, https://doi.org/10.1073/pnas.1406071111
Keywords:

### Abstract

[Significance] The maximum entropy principle (MEP) states that for many statistical systems the entropy that is associated with an observed distribution function is a maximum, given that prior information is taken into account appropriately. Usually systems where the MEP applies are simple systems, such as gases and independent processes. The MEP has found thousands of practical applications. Whether a MEP holds for complex systems, where elements interact strongly and have memory and path dependence, remained unclear over the past half century. ...

## A bottom-up control on fresh-bedrock topography under landscapes

Proceedings of the National Academy of Sciences, Vol. 111, No. 18. (06 May 2014), pp. 6576-6581, https://doi.org/10.1073/pnas.1404763111
Keywords:

### Abstract

[Significance] Hilly landscapes are typically mantled with soil and underlain by a weathered bedrock zone that may extend tens of meters beneath the surface before reaching fresh bedrock. The weathered bedrock zone influences water runoff to channels, the chemistry of that water, the rates and processes of erosion, and atmospheric processes due to plant uptake of moisture and return to the atmosphere. However, the spatial pattern of the underlying fresh-bedrock surface is essentially unknown. We present a testable model that predicts ...

## Inefficient epidemic spreading in scale-free networks

Physical Review E, Vol. 77, No. 2. (Feb 2008), 026113, https://doi.org/10.1103/physreve.77.026113
Keywords:

### Abstract

Highly heterogeneous degree distributions yield efficient spreading of simple epidemics through networks, but can be inefficient with more complex epidemiological processes. We study diseases with nonlinear force of infection whose prevalences can abruptly collapse to zero while decreasing the transmission parameters. We find that scale-free networks can be unable to support diseases that, on the contrary, are able to persist at high endemic levels in homogeneous networks with the same average degree. ...

## Proof of Pareto’s 80/20 Law and Precise Limits for ABC-Analysis

No. 2002/c. (2002)
Keywords:

### Abstract

In many projects 20% of the total effort yields 80% of the total outcome. This phenomenon is usually termed Pareto’s 80/20 law. In this paper we propose a theory to explain this empirical observation. The yield gained by the subdivision of a project into several tasks is measured. The requirements for such a yield lead to the axioms of Shannon Information. With the right adjustment of units for cost and yield this gives the definition of Entropic Yield. Pareto’s 80/20 law thus results from an economic optimization of Entropic ...

## Pareto 80/20 law: derivation via random partitioning

International Journal of Mathematical Education in Science and Technology, Vol. 40, No. 2. (19 February 2009), pp. 271-277, https://doi.org/10.1080/00207390802213609
Keywords:

### Abstract

The Pareto 80/20 Rule, also known as the Pareto principle or law, states that a small number of causes (20%) is responsible for a large percentage (80%) of the effect. Although widely recognized as a heuristic rule, this proportion has not been theoretically based. The article considers derivation of this 80/20 rule and some other standard quotients from the mean and its interval estimation for the total value defined by the product of two variables in the random partitioning model. ...

## Democratic decisions establish stable authorities that overcome the paradox of second-order punishment

Proceedings of the National Academy of Sciences, Vol. 111, No. 2. (23 January 2013), pp. 201315273-756, https://doi.org/10.1073/pnas.1315273111

### Abstract

[Significance] Humans usually punish free riders but refuse to sanction those who cooperate but do not punish. However, such second-order punishment is essential to maintain cooperation. The central authorities established in modern societies punish both free riders and tax evaders. This is a paradox: would individuals who do not engage in second-order punishment strive for an authority that does? We address this puzzle with a mathematical model and an economic experiment. When individuals can choose between authorities by migrating between different ...

## Social processes and proofs of theorems and programs

Commun. ACM, Vol. 22, No. 5. (May 1979), pp. 271-280, https://doi.org/10.1145/359104.359106

### Abstract

It is argued that formal verifications of programs, no matter how obtained, will not play the same key role in the development of computer science and software engineering as proofs do in mathematics. Furthermore the absence of continuity, the inevitability of change, and the complexity of specification of significantly many real programs make the formal verification process difficult to justify and manage. It is felt that ease of formal verification should not dominate program language design. ...

## Fidelity in mathematical discourse: is one and one really two?

The American Mathematical Monthly, Vol. 79, No. 3. (March 1972), pp. 252-263, https://doi.org/10.2307/2316620

### Abstract

[Excerpt] "I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, ...

## Extending Prolog with Constraint Arithmetic on Real Intervals

In Canadian Conference on Computer & Electrical Engineering (1990)
Keywords:

### Abstract

Prolog can be extended by a system of constraints on closed intervals to perform declarative relational arithmetic. Imposing constraints on an interval can narrow its range and propagate the narrowing to other intervals related to it by constraint equations or inequalities. Relational interval arithmetic can be used to contain floating point errors and, when combined with Prolog backtracking, to obtain numeric solutions to linear and non-linear rational constraint satisfaction problems over the reals (e.g. n-degree polynomial equations). This technique differs from ...

## Management science: science of managing and managing of science

Interfaces, Vol. 24, No. 4. (01 July 1994), pp. 99-110, https://doi.org/10.1287/inte.24.4.99
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### Abstract

As the first editor-in-chief of Management Science, I expressed my ambition for the society (TIMS) and its journal. My notion was that a society and journal in the subject of a science of management would investigate how humans can manage their affairs well. For me, “well” means “ethically,” or in the best interest of humanity in a world of filthy oppression and murder (I'm a philosopher and therefore have a philosophical bias, the same bias Plato had when he wrote the ...

## The literacies of science

In Crossing borders in literacy and science instruction: perspectives on theory and practice (2004), pp. 33-47, https://doi.org/10.1598/0872075192.2
edited by E. Wendy Saul
Keywords:

### Abstract

One starting point for a dialogue between literacy education and science education is the way in which science uses multiple literacies. Literacy education usually begins with an emphasis on language and on texts: how they're made, what they mean. Science education begins with questions about how things happen in the world. We might imagine a scientist studying literacy to be a bit like an ethnographer. An ethnographer of science and its literacies will come across other scientists making and using texts, ...

## Notation as a tool of thought

Communications of the ACM, Vol. 23, No. 8. (August 1980), pp. 444-465, https://doi.org/10.1145/358896.358899
Keywords:

### Abstract

The 1979 ACM 7bring Award was presented to Kenneth E. Iverson by Walter Carlson, Chairman of the Awards Committee, at the ACM Annual Conference in Detroit, Michigan, October 29, 1979. in making its selection, the General Technical Achievement Award Committee cited Iverson for his pioneering effort in programming languages and mathematical notation resulting in what the computing field now knows as APL. Iverson's contributions to the implementation of interactive systems, to the educational uses of APL, and to programming language theory and ...