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[1806.03346] Some Continued Fractions for $pi$ AND $G$
We present here two classes of infinite series and the associated continued fractions involving π and Catalan's constant G based on the work of Euler and Ramanujan. A few sundry continued fractions are also given.
continued-fractions  representation  nudge-targets  to-write-about 
2 days ago by Vaguery
[1712.08175] Conversion of Love waves in a forest of trees
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 
2 days ago by Vaguery
A non-spatial account of place and grid cells based on clustering models of concept learning | bioRxiv
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 
2 days ago by Vaguery
The Pinball Problem – Daniel Reynolds – Refractory: a Journal of Entertainment Media
In the forms that play and games have taken over time, from games of “imagination” to formalized sports to more materially mediated forms of gameplay such as boardgames, pinball, and video games, there has been an historical fluctuation in cultural consideration and engagement. Bagatelle, the predecessor to pinball, enjoyed massive popularity among the French aristocracy and subsequently the general populace of that country in the late 18th century. Video games are currently ascendant as a medium for gameplay, and their cultural acceptability as an adult activity has steadily increased in recent decades. Sports were of immense philosophical importance to the ancient Greeks; they have never since enjoyed the same high-cultural esteem, though they have rarely been regarded as wholly trivial, and they enjoy a special cultural status among games in many modern societis. There have been some notable exceptions, however. In 1457, golf was banned in Scotland, ostensibly because it was interfering with the more useful pursuit of archery. In 1491, according to the eleventh edition of the Encyclopedia Britannica, the ban was extended to encompass “fute-ball, golfe, or uther sik unprofitibill sportis.” Profitability, it seems, has always come into consideration in the assessment of games; their less visible benefits tend to be ignored when legislation is involved.
social-norms  games  nanohistory  rather-interesting  the-ludic-in-law  to-write-about 
3 days ago by Vaguery
Roto-Tiler – The Inner Frame
Today we look at a puzzle invented by Alan Schoen that he calls Roto-Tiler. He explained this to me a few years ago, and when I showed him notes I made for a class, he denied that this is the puzzle he described. I insist it is, and it is quite certainly not mine.
mathematical-recreations  puzzles  tiling  representation  rather-interesting  to-write-about  nudge-targets 
7 days ago by Vaguery
[1808.05845] Popular Products and Continued Fractions
We prove bounds for the popularity of products of sets with weak additive structure, and use these bounds to prove results about continued fractions. Namely, we obtain a nearly sharp upper bound for the cardinality of Zaremba's set modulo p.
continued-fractions  number-theory  to-write-about  nudge-targets  consider:looking-to-see 
7 days ago by Vaguery
[1808.05587] Deep Convolutional Networks as shallow Gaussian Processes
We show that the output of a (residual) convolutional neural network (CNN) with an appropriate prior over the weights and biases is a Gaussian process (GP) in the limit of infinitely many convolutional filters, extending similar results for dense networks. For a CNN, the equivalent kernel can be computed exactly and, unlike "deep kernels", has very few parameters: only the hyperparameters of the original CNN. Further, we show that this kernel has two properties that allow it to be computed efficiently; the cost of evaluating the kernel for a pair of images is similar to a single forward pass through the original CNN with only one filter per layer. The kernel equivalent to a 32-layer ResNet obtains 0.84% classification error on MNIST, a new record for GPs with a comparable number of parameters.
via:cshalizi  neural-networks  approximation  rather-interesting  representation  deep-learning  algorithms  to-write-about  equivalences-of-motion-over-different-paths 
26 days ago by Vaguery
Should Climate Scientists Fly? - Scientific American Blog Network
This is why climate action is about moral courage. Yes, we must have the courage to align our personal actions with our understanding of the science, through decreasing and stopping our flying. But, more importantly, we must have to courage to speak truth to power, despite how this might change our public or professional standing. Climate action is one of the most fundamental social justice movements of our time. No more and no less, our choices now to act as brave stewards of planetary life, despite political realities and institutional denialism, will change the trajectory of the planet forever. It is worth it.
climate-change  politics  activism  neoliberalism  to-write-about  social-justice 
26 days ago by Vaguery
The Mathematical Beauty of the Game SET | The Aperiodical
It is my hope that this post has given you some insight into the deep and elegant complexities of the game of SET besides just trying to be the fastest SET-finder in a game. It is miraculous that such a simple game can have such beautiful and joyful connections to some advanced domains of mathematics, even with some open research questions. If interested, the reader is encouraged to explore some of these considerations or generalizations, either playing with finite geometry or doing some combinatorics. The SET community has also developed some other very interesting variations on SET and their connections to other geometries, such as projective geometry, known as ProSet.
mathematical-recreations  games  set-theory  representation  have-explored  nudge-targets  to-write-about 
26 days ago by Vaguery
Botanical parasitism of an insect by a parasitic plant: Current Biology
We report evidence of a new trophic interaction in nature whereby a parasitic plant attacks multiple species of insects that manipulate plant tissue when the two co-occur on a shared primary host plant. Most plant species are attacked by a great diversity of external and internal herbivores [1]. One common herbivore guild, gall-forming insects, induce tumor-like structures of nutrient-rich plant tissue within which immature insects feed and develop [2, 3]. While the gall is made of plant tissue, its growth and development are controlled by the insect and it therefore represents an extended phenotype of the gall former [4]. Typically, parasitic plants attack other plants to gain nutritional requirements by connecting directly to the vascular system of their hosts using modified root structures called haustoria [5]. Here, we document the first observation of a parasitic plant attacking the insect-induced galls of multiple gall-forming species and provide evidence that this interaction negatively affects gall former fitness.
biology  parasitism  rather-interesting  evolutionary-biology  Occam-ain't-evolved  to-write-about  what-gets-possible-gets-done 
28 days ago by Vaguery
Julia 1.0
The much anticipated 1.0 release of Julia is the culmination of nearly a decade of work to build a language for greedy programmers. JuliaCon2018 celebrated the event with a reception where the community officially set the version to 1.0.0 together.
programming-language  Julia-language  to-do  to-write-about 
4 weeks ago by Vaguery
[1808.01862] Yes, Aboriginal Australians Can and Did Discover the Variability of Betelgeuse
Recently, a widely publicized claim has been made that the Aboriginal Australians discovered the variability of the red star Betelgeuse in the modern Orion, plus the variability of two other prominent red stars: Aldebaran and Antares. This result has excited the usual healthy skepticism, with questions about whether any untrained peoples can discover the variability and whether such a discovery is likely to be placed into lore and transmitted for long periods of time. Here, I am offering an independent evaluation, based on broad experience with naked-eye sky viewing and astro-history. I find that it is easy for inexperienced observers to detect the variability of Betelgeuse over its range in brightness from V = 0.0 to V = 1.3, for example in noticing from season-to-season that the star varies from significantly brighter than Procyon to being greatly fainter than Procyon. Further, indigenous peoples in the Southern Hemisphere inevitably kept watch on the prominent red star, so it is inevitable that the variability of Betelgeuse was discovered many times over during the last 65 millennia. The processes of placing this discovery into a cultural context (in this case, put into morality stories) and the faithful transmission for many millennia is confidently known for the Aboriginal Australians in particular. So this shows that the whole claim for a changing Betelgeuse in the Aboriginal Australian lore is both plausible and likely. Given that the discovery and transmission is easily possible, the real proof is that the Aboriginal lore gives an unambiguous statement that these stars do indeed vary in brightness, as collected by many ethnographers over a century ago from many Aboriginal groups. So I strongly conclude that the Aboriginal Australians could and did discover the variability of Betelgeuse, Aldebaran, and Antares.
cultural-assumptions  astronomy  history-of-science  colonialism  science-studies  to-write-about 
4 weeks ago by Vaguery
[1808.05563] Learning Invariances using the Marginal Likelihood
Generalising well in supervised learning tasks relies on correctly extrapolating the training data to a large region of the input space. One way to achieve this is to constrain the predictions to be invariant to transformations on the input that are known to be irrelevant (e.g. translation). Commonly, this is done through data augmentation, where the training set is enlarged by applying hand-crafted transformations to the inputs. We argue that invariances should instead be incorporated in the model structure, and learned using the marginal likelihood, which correctly rewards the reduced complexity of invariant models. We demonstrate this for Gaussian process models, due to the ease with which their marginal likelihood can be estimated. Our main contribution is a variational inference scheme for Gaussian processes containing invariances described by a sampling procedure. We learn the sampling procedure by back-propagating through it to maximise the marginal likelihood.
machine-learning  generalization  representation  rather-interesting  HOWEVER  consider:genetic-programming  consider:evolution-of-code  to-write-about 
4 weeks ago by Vaguery
SMT solutions | The Math Less Traveled
In my last post I described the general approach I used to draw orthogons using an SMT solver, but left some of the details as exercises. In this post I’ll explain the solutions I came up with.
geometry  programming  rather-interesting  representation  testing  to-write-about  mathematical-recreations  nudge-targets  consider:looking-to-see 
4 weeks ago by Vaguery
Literate Programming in Rust -
I’ll add a disclaimer that this article is meant to briefly showcase how everyday programming can be influenced by the idea of literate programming. For a technical overview of that topic, visit Knuth’s page, and for a more direct port of WEB/noweb (the canonical literate programming language) to Rust, you’ll want to take a look at the tango project by pnkfelix.
software-development  communication  code-is-not-for-computers-to-read  rather-interesting  literate-programming  to-write-about  documentation  rust-language 
4 weeks ago by Vaguery
Repeat yourself, do more than one thing, and... — programming is terrible
As Sandi Metz put it, “duplication is far cheaper than the wrong abstraction”.

You can’t really write a re-usable abstraction up front. Most successful libraries or frameworks are extracted from a larger working system, rather than being created from scratch. If you haven’t built something useful with your library yet, it is unlikely anyone else will. Code reuse isn’t a good excuse to avoid duplicating code, and writing reusable code inside your project is often a form of preemptive optimization.

When it comes to repeating yourself inside your own project, the point isn’t to be able to reuse code, but rather to make coordinated changes. Use abstractions when you’re sure about coupling things together, rather than for opportunistic or accidental code reuse—it’s ok to repeat yourself to find out when.
software-development  cultural-norms  refactoring  advice  to-write-about 
4 weeks ago by Vaguery
[1808.05875] Co-evolution of nodes and links: diversity driven coexistence in cyclic competition of three species
When three species compete cyclically in a well-mixed, stochastic system of N individuals, extinction is known to typically occur at times scaling as the system size N. This happens, for example, in rock-paper-scissors games or conserved Lotka-Volterra models in which every pair of individuals can interact on a complete graph. Here we show that if the competing individuals also have a "social temperament" to be either introverted or extroverted, leading them to cut or add links respectively, then long-living state in which all species coexist can occur when both introverts and extroverts are present. These states are non-equilibrium quasi-steady states, maintained by a subtle balance between species competition and network dynamcis. Remarkably, much of the phenomena is embodied in a mean-field description. However, an intuitive understanding of why diversity stabilizes the co-evolving node and link dynamics remains an open issue.
coevolution  theoretical-biology  rather-interesting  population-biology  social-norms  to-write-about  to-simulate  artificial-life  it's-more-complicated-than-you-think  complexology  agent-based 
4 weeks ago by Vaguery
[1808.04730] Analyzing Inverse Problems with Invertible Neural Networks
In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse problem is ambiguous: one measurement may map to multiple different sets of parameters. In this setting, the posterior parameter distribution, conditioned on an input measurement, has to be determined. We argue that a particular class of neural networks is well suited for this task -- so-called Invertible Neural Networks (INNs). Although INNs are not new, they have, so far, received little attention in literature. While classical neural networks attempt to solve the ambiguous inverse problem directly, INNs are able to learn it jointly with the well-defined forward process, using additional latent output variables to capture the information otherwise lost. Given a specific measurement and sampled latent variables, the inverse pass of the INN provides a full distribution over parameter space. We verify experimentally, on artificial data and real-world problems from astrophysics and medicine, that INNs are a powerful analysis tool to find multi-modalities in parameter space, to uncover parameter correlations, and to identify unrecoverable parameters.
machine-learning  neural-networks  inverse-problems  rather-interesting  representation  to-write-about 
4 weeks ago by Vaguery

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