**rather-interesting**2112

[math/0408099] Tropical Mathematics

22 hours ago by Vaguery

These are the notes for the Clay Mathematics Institute Senior Scholar Lecture which was delivered by Bernd Sturmfels in Park City, Utah, on July 22, 2004. The topic of this lecture is the ``tropical approach'' in mathematics, which has gotten a lot of attention recently in combinatorics, algebraic geometry and related fields. It offers an an elementary introduction to this subject, touching upon Arithmetic, Polynomials, Curves, Phylogenetics and Linear Spaces. Each section ends with a suggestion for further research. The bibliography contains numerousreferences for further reading in this field.

group-theory
mathematics
representation
combinatorics
rather-interesting
to-write-about
22 hours ago by Vaguery

[1804.03032] k-NN Graph Construction: a Generic Online Approach

2 days ago by Vaguery

Nearest neighbor search and k-nearest neighbor graph construction are two fundamental issues arise from many disciplines such as information retrieval, data-mining, machine learning and computer vision. Despite continuous efforts have been taken in the last several decades, these two issues remain challenging. They become more and more imminent given the big data emerges in various fields and has been expanded significantly over the years. In this paper, a simple but effective solution both for k-nearest neighbor search and k-nearest neighbor graph construction is presented. Namely, these two issues are addressed jointly. On one hand, the k-nearest neighbor graph construction is treated as a nearest neighbor search task. Each data sample along with its k-nearest neighbors are joined into the k-nearest neighbor graph by sequentially performing the nearest neighbor search on the graph under construction. On the other hand, the built k-nearest neighbor graph is used to support k-nearest neighbor search. Since the graph is built online, dynamic updating of the graph, which is not desirable from most of the existing solutions, is supported. Moreover, this solution is feasible for various distance measures. Its effectiveness both as a k-nearest neighbor construction and k-nearest neighbor search approach is verified across various datasets in different scales, various dimensions and under different metrics.

graph-theory
algorithms
to-understand
rather-interesting
computational-complexity
data-structures
2 days ago by Vaguery

[1804.10962] Stress anisotropy in shear-jammed packings of frictionless disks

2 days ago by Vaguery

We perform computational studies of repulsive, frictionless disks to investigate the development of stress anisotropy in mechanically stable (MS) packings. We focus on two protocols for generating MS packings: 1) isotropic compression and 2) applied simple or pure shear strain γ at fixed packing fraction ϕ. MS packings of frictionless disks occur as geometric families (i.e. parabolic segments with positive curvature) in the ϕ-γ plane. MS packings from protocol 1 populate parabolic segments with both signs of the slope, dϕ/dγ>0 and dϕ/dγ<0. In contrast, MS packings from protocol 2 populate segments with dϕ/dγ<0 only. For both simple and pure shear, we derive a relationship between the stress anisotropy and dilatancy dϕ/dγ obeyed by MS packings along geometrical families. We show that for MS packings prepared using isotropic compression, the stress anisotropy distribution is Gaussian centered at zero with a standard deviation that decreases with increasing system size. For shear jammed MS packings, the stress anisotropy distribution is a convolution of Weibull distributions that depend on strain, which has a nonzero average and standard deviation in the large-system limit. We also develop a framework to calculate the stress anisotropy distribution for packings generated via protocol 2 in terms of the stress anisotropy distribution for packings generated via protocol 1. These results emphasize that for repulsive frictionless disks, different packing-generation protocols give rise to different MS packing probabilities, which lead to differences in macroscopic properties of MS packings.

physics!
sandpiles
materials-science
simulation
rather-interesting
condensed-matter
phase-transitions
looking-to-see
2 days ago by Vaguery

Coder-Physicists Are Simulating the Universe to Unlock Its Secrets | Quanta Magazine

3 days ago by Vaguery

These small, faint galaxies have always presented problems. The “missing satellite problem,” for instance, is the expectation, based on standard cold dark matter models, that hundreds of satellite galaxies should orbit every spiral galaxy. But the Milky Way has just dozens. This has caused some physicists to contemplate more complicated models of dark matter. However, when Hopkins and colleagues incorporated realistic superbubbles into their simulations, they saw many of those excess satellite galaxies go away. Hopkins has also found potential resolutions to two other problems, called “cusp-core” and “too-big-to-fail,” that have troubled the cold dark matter paradigm.

simulation
looking-to-see
astronomy
rather-interesting
to-write-about
the-mangle-in-practice
(totally)
3 days ago by Vaguery

Tiling with TriCurves

8 days ago by Vaguery

There are a number of ways one can define a tricurve, the one used here is to start with an arc of some angle, replicate two identical curves ard rotate each about some angle about the ends of the arc. The Tricurve is the enclosed area.

plane-geometry
tiling
rather-interesting
define-your-terms
representation
to-write-about
mathematical-recreations
8 days ago by Vaguery

Tiling with One Arc-Sided Shape | Math ∞ Blog

8 days ago by Vaguery

A flat puzzle (tiling) with dozens or hundreds of identical pieces may sound a little dull and predictable. But what is the most interesting shape we can use, to get the most unusual designs and the most variety? To make it more visually interesting, let’s say we want a shape with no straight edges—only curves. The following guidelines should help us get started.

plane-geometry
representation
tiling
rather-interesting
mathematical-recreations
to-write-about
8 days ago by Vaguery

The propagation of error in classical geometry constructions | Joel David Hamkins

9 days ago by Vaguery

I’d like to discuss the issue of error and error propagation in the constructions of classical geometry. How does error propagate in these constructions? How sensitive are the familiar classical constructions to small errors in the use of the straightedge or compass?

plane-geometry
con
structions
robustness
rather-interesting
to-write-about
nudge-targets
consider:multiobjective-selection
9 days ago by Vaguery

[1801.08003] Threadable Curves

9 days ago by Vaguery

We define a plane curve to be threadable if it can rigidly pass through a point-hole in a line L without otherwise touching L. Threadable curves are in a sense generalizations of monotone curves. We have two main results. The first is a linear-time algorithm for deciding whether a polygonal curve is threadable---O(n) for a curve of n vertices---and if threadable, finding a sequence of rigid motions to thread it through a hole. We also sketch an argument that shows that the threadability of algebraic curves can be decided in time polynomial in the degree of the curve. The second main result is an O(n polylog n)-time algorithm for deciding whether a 3D polygonal curve can thread through hole in a plane in R^3, and if so, providing a description of the rigid motions that achieve the threading.

computational-geometry
geometry
rather-interesting
definition
nudge-targets
consider:feature-discovery
to-write-about
consider:algorithms
9 days ago by Vaguery

Computational and Inferential Thinking - Data 8 Textbook

9 days ago by Vaguery

Computational and Inferential Thinking

online-learning
Jupyter
textbook
computer-science
book
rather-interesting
to-read
open-source
9 days ago by Vaguery

Patterns That Eventually Fail | Azimuth

9 days ago by Vaguery

Sometimes patterns can lead you astray.

mathematical-recreations
mathematics
patterns
rather-interesting
to-write-about
9 days ago by Vaguery

[1808.02841] On divergent Series

9 days ago by Vaguery

This is the translation of Leonhard Euler's paper "De Seriebus divergentibus" written in Latin into English. Leonhard Euler defines and discusses divergent series. He is especially interested in the example 1!−2!+3!−etc. and uses different methods to sum it. He finds a value of about 0.59....

mathematics
history
translation
series
to-write-about
rather-interesting
9 days ago by Vaguery

[1808.07006] Observations on continued fractions

9 days ago by Vaguery

This is a translation of Euler's Latin paper "De fractionibus continuis observationes" into English. In this paper Euler describes his theory of continued fractions. He teaches, how to transform series into continued fractions, solves the Riccati-Differential equation by means of continued fractions and finds many other interesting formulas and results (e.g, the continued fraction for the quotient of two hypergeometric series usually attributed to Gau{\ss})

continued-fractions
translation
mathematics
history
rather-interesting
to-write-about
9 days ago by Vaguery

[1810.00173] On solids whose (entire) surface can be unfolded onto a plane

9 days ago by Vaguery

This is the English translation of Leonhard Euler's Latin paper "De solidis quorum superficiem in planum explicare licet". Euler explains several methods to obtain equations for developable surfaces. Therefore, this paper might be interesting for anyone studying the history of Differential Geometry.

geometry
history
mathematics
translation
rather-interesting
9 days ago by Vaguery

DRM-free Bookshops

12 days ago by Vaguery

A regularly updated list of online shops that sell e-books without DRM.

books
shopping
DRM
copyright
rather-interesting
publishing
12 days ago by Vaguery

THE EXTENDED EVOLUTIONARY SYNTHESIS | Proceedings of the Royal Society of London B: Biological Sciences

15 days ago by Vaguery

Scientific activities take place within the structured sets of ideas and assumptions that define a field and its practices. The conceptual framework of evolutionary biology emerged with the Modern Synthesis in the early twentieth century and has since expanded into a highly successful research program to explore the processes of diversification and adaptation. Nonetheless, the ability of that framework satisfactorily to accommodate the rapid advances in developmental biology, genomics and ecology has been questioned. We review some of these arguments, focusing on literatures (evo-devo, developmental plasticity, inclusive inheritance and niche construction) whose implications for evolution can be interpreted in two ways—one that preserves the internal structure of contemporary evolutionary theory and one that points towards an alternative conceptual framework. The latter, which we label the ‘extended evolutionary synthesis' (EES), retains the fundaments of evolutionary theory, but differs in its emphasis on the role of constructive processes in development and evolution, and reciprocal portrayals of causation. In the EES, developmental processes, operating through developmental bias, inclusive inheritance and niche construction, share responsibility for the direction and rate of evolution, the origin of character variation and organism–environment complementarity. We spell out the structure, core assumptions and novel predictions of the EES, and show how it can be deployed to stimulate and advance research in those fields that study or use evolutionary biology.

evolutionary-biology
academic-culture
models-and-modes
theoretical-biology
define-your-terms
rather-interesting
to-write-about
15 days ago by Vaguery

Same-different problems strain convolutional neural networks | the morning paper

17 days ago by Vaguery

Digging deeper, when learning did occur in SD, increasing item size never strained performance. But increasing the overall image size, or increasing the number of items did. (Gray bars in the above figures indicate the number of trials in which learning failed). The results suggest that straining is not simply a direct outcome of an increase in image variability. Using CNNs with more than twice the number of kernels (wide), or twice as many layers (deep) did not change the observed trend.

neural-networks
representation
problem-solving
rather-interesting
ontology
generalization
to-write-about
nudge-targets
consider:feature-discovery
17 days ago by Vaguery

Treating The Prodrome | Slate Star Codex

17 days ago by Vaguery

I think what they are saying is that, as the world becomes even more random and confusing, the brain very slowly adjusts its highest level parameters. It concludes, on a level much deeper than consciousness, that the world does not make sense, that it’s not really useful to act because it’s impossible to predict the consequences of actions, and that it’s not worth drawing on prior knowledge because anything could happen at any time. It gets a sort of learned helplessness about cognition, where since it never works it’s not even worth trying. The onslaught of random evidence slowly twists the highest-level beliefs into whatever form best explains random evidence (usually: that there’s a conspiracy to do random things), and twists the fundamental parameters into a form where they expect evidence to be mostly random and aren’t going to really care about it one way or the other.

psychology
rather-interesting
consider:what-are-we-doing-to-our-machines?
emergence
to-write-about
17 days ago by Vaguery

Phil Stepanian on Twitter: "So, fun fact: birds and insects show up on radar. Often. As in, pretty much every day. Can we visually delineate between migrating birds and insects on radar? Usually. Here is a bumbling threaded attempt to show some telltale s

biology migration data-analysis rather-interesting to-write-about ecology technology

22 days ago by Vaguery

biology migration data-analysis rather-interesting to-write-about ecology technology

22 days ago by Vaguery

[1712.08175] Conversion of Love waves in a forest of trees

26 days ago by Vaguery

We inspect the propagation of shear polarized surface waves akin to Love waves through a forest of trees of same height atop a guiding layer on a soil substrate. We discover that the foliage of trees { brings a radical change in} the nature of the dispersion relation of these surface waves, which behave like spoof plasmons in the limit of a vanishing guiding layer, and like Love waves in the limit of trees with a vanishing height. When we consider a forest with trees of increasing or decreasing height, this hybrid "Spoof Love" wave is either reflected backwards or converted into a downward propagating bulk wave. An asymptotic analysis shows the forest behaves like an anisotropic wedge with effective boundary conditions.

materials-science
simulation
nonlinear-dynamics
rather-interesting
side-effects
consider:pragmatics-of-a-tree
to-write-about
26 days ago by Vaguery

A non-spatial account of place and grid cells based on clustering models of concept learning | bioRxiv

26 days ago by Vaguery

One view is that conceptual knowledge is organized as a "cognitive map" in the brain, using the circuitry in the medial temporal lobe (MTL) that supports spatial navigation. In contrast, we find that a domain-general learning algorithm explains key findings in both spatial and conceptual domains. When the clustering model is applied to spatial navigation tasks, so called place and grid cells emerge because of the relatively uniform sampling of possible inputs in these tasks. The same mechanism applied to conceptual tasks, where the overall space can be higher-dimensional and sampling sparser, leads to representations more aligned with human conceptual knowledge. Although the types of memory supported by the MTL are superficially dissimilar, the information processing steps appear shared.

models-and-modes
emergence
data-analysis
rather-interesting
to-write-about
consider:the-mangle
26 days ago by Vaguery

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