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Reverse salients | West Hunter
Edison thought in terms of reverse salients and critical problems.

“Reverse salients are areas of research and development that are lagging in some obvious way behind the general line of advance. Critical problems are the research questions, cast in terms of the concrete particulars of currently available knowledge and technique and of specific exemplars or models that are solvable and whose solutions would eliminate the reverse salients. ”

What strikes you as as important current example of a reverse salient, and the associated critical problem or problems?
west-hunter  scitariat  discussion  science  technology  innovation  low-hanging  list  top-n  research  open-problems  the-world-is-just-atoms  marginal  definite-planning  frontier  🔬  speedometer  ideas  the-trenches  hi-order-bits 
9 weeks ago by nhaliday
[PDF] Unsolved problems in Combinatorial Games
We have sorted the problems into sections:
They have been given new numbers. The numbers in parentheses are the old numbers used in each of the lists of unsolved problems given on pp. 183–189 of AMS Proc. Sympos. Appl. Math. 43 (1991), called PSAM 43 below; on pp. 475–491 of Games of No Chance, hereafter referred to as GONC; and on pp. 457–473 of More Games of No Chance (MGONC). Missing numbers are of problems which have been solved, or for which we have nothing new to add. References [year] may be found in Fraenkel’s Bibliography at the end of this volume. References [#] are at the end of this article. A useful reference for the rules and an introduction to many of the specific games mentioned below is M. Albert, R. J. Nowakowski and D. Wolfe, Lessons in Play: An Introduction to the Combinatorial Theory of Games, A K Peters, 2007 (LIP).
open-problems  game-theory  combinatorial-game-theory  rather-interesting  nudge-targets 
february 2019 by Vaguery
Home | Open Problem Garden
Welcome to the Open Problem Garden, a collection of unsolved problems in mathematics. Here you may:

Read descriptions of open problems.
Post comments on them.
Create and edit open problems pages (please contact us and we will set you up an account. Unfortunately, the automatic process is too prone to spammers at this moment.)
open-problems  mathematical-recreations  mathematics  computer-science  to-write-about  nudge-targets 
march 2018 by Vaguery
[1206.0303] A History of Flips in Combinatorial Triangulations
Given two combinatorial triangulations, how many edge flips are necessary and sufficient to convert one into the other? This question has occupied researchers for over 75 years. We provide a comprehensive survey, including full proofs, of the various attempts to answer it.
computational-geometry  plane-geometry  rather-interesting  algorithms  open-problems  nudge-targets  to-write-about  to-simulate 
november 2017 by Vaguery
[1606.03881] Length of the continued logarithm algorithm on rational inputs
The continued logarithm algorithm was introduced by Gosper around 1978, and recently studied by Borwein, Calkin, Lindstrom, and Mattingly. In this note I show that the continued logarithm algorithm terminates in at most 2 log_2 p + O(1) steps on input a rational number p/q >= 1. Furthermore, this bound is tight, up to an additive constant.
number-theory  algorithms  rather-interesting  representation  open-problems  nudge-targets  to-write-about 
november 2017 by Vaguery
[1702.01027] Random Triangles and Polygons in the Plane
We consider the problem of finding the probability that a random triangle is obtuse, which was first raised by Lewis Caroll. Our investigation leads us to a natural correspondence between plane polygons and the Grassmann manifold of 2-planes in real n-space proposed by Allen Knutson and Jean-Claude Hausmann. This correspondence defines a natural probability measure on plane polygons. In these terms, we answer Caroll's question. We then explore the Grassmannian geometry of planar quadrilaterals, providing an answer to Sylvester's four-point problem, and describing explicitly the moduli space of unordered quadrilaterals. All of this provides a concrete introduction to a family of metrics used in shape classification and computer vision.
probability-theory  open-problems  mathematical-recreations  geometry  rather-interesting  to-write-about 
october 2017 by Vaguery
[1709.08071] Autonomous Agents Modelling Other Agents: A Comprehensive Survey and Open Problems
Much research in artificial intelligence is concerned with the development of autonomous agents that can interact effectively with other agents. An important aspect of such agents is the ability to reason about the behaviours of other agents, by constructing models which make predictions about various properties of interest (such as actions, goals, beliefs) of the modelled agents. A variety of modelling approaches now exist which vary widely in their methodology and underlying assumptions, catering to the needs of the different sub-communities within which they were developed and reflecting the different practical uses for which they are intended. The purpose of the present article is to provide a comprehensive survey of the salient modelling methods which can be found in the literature. The article concludes with a discussion of open problems which may form the basis for fruitful future research.
agent-based  collective-behavior  machine-learning  artificial-intelligence  open-problems  nudge-targets  to-write-about 
october 2017 by Vaguery
[1709.01670] Parameterized complexity of machine scheduling: 15 open problems
Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 interesting open questions in this area.
open-problems  operations-research  scheduling  benchmarking  to-write-about  nudge-targets  consider:looking-to-see  consider:performance-measures 
september 2017 by Vaguery
[0909.1666] On Sets of Integers where Each Pair Sums to a Square
We discuss the problem of finding distinct integer sets {x1,x2,...,xn} where each sum xi+xj,i≠j is a square, and n≤7. We confirm minimal results of Lagrange and Nicolas for n=5 and for the related problem with triples. We provide new solution sets for n=6 to add to the single known set. This provides new information for problem D15 in Guy's {\it Unsolved Problems in Number Theory}
number-theory  algebra  constraint-satisfaction  open-problems  nudge-targets  consider:looking-to-see 
april 2017 by Vaguery
Information Processing: Big, complicated data sets
This Times article profiles Nick Patterson, a mathematician whose career wandered from cryptography, to finance (7 years at Renaissance) and finally to bioinformatics. “I’m a data guy,” Dr. Patterson said. “What I know about is how to analyze big, complicated data sets.”

If you're a smart guy looking for something to do, there are 3 huge computational problems staring you in the face, for which the data is readily accessible.

1) human genome: 3 GB of data in a single genome; most data freely available on the Web (e.g., Hapmap stores patterns of sequence variation). Got a hypothesis about deep human history (evolution)? Test it yourself...

2) market prediction: every market tick available at zero or minimal subscription-service cost. Can you model short term movements? It's never been cheaper to build and test your model!

3) internet search: about 10^3 Terabytes of data (admittedly, a barrier to entry for an individual, but not for a startup). Can you come up with a better way to index or search it? What about peripheral problems like language translation or picture or video search?

The biggest barrier to entry is, of course, brainpower and a few years (a decade?) of concentrated learning. But the necessary books are all in the library :-)

Patterson has worked in 2 of the 3 areas listed above! Substituting crypto for internet search is understandable given his age, our cold war history, etc.
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february 2017 by nhaliday

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