Markets are efficient if and only if P = NP
Abstract:
I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can “program” the market to solve NP-complete problems. Since P probably does not equal NP, markets are probably not efficient. Specifically, markets become increasingly inefficient as the time series lengthens or becomes more frequent. An illustration by way of partitioning the excess returns to momentum strategies based on data
availability confirms this prediction.
https://arxiv.org/pdf/1002.2284.pdf
#abstract
Abstract:
I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can “program” the market to solve NP-complete problems. Since P probably does not equal NP, markets are probably not efficient. Specifically, markets become increasingly inefficient as the time series lengthens or becomes more frequent. An illustration by way of partitioning the excess returns to momentum strategies based on data
availability confirms this prediction.
https://arxiv.org/pdf/1002.2284.pdf
#abstract
https://www.youtube.com/watch?v=IkrCax_Upa8
"inside a neural network"
"inside a neural network"
YouTube
Text-to-Image recursive zoom movie
See here for more info https://softologyblog.wordpress.com/2021/06/10/text-to-image-summary/
Created with Visions of Chaos https://softology.pro/voc.htm
Soundtrack available here https://softology.pro/music/music.htm
Created with Visions of Chaos https://softology.pro/voc.htm
Soundtrack available here https://softology.pro/music/music.htm
Assessing Generalization of SGD via Disagreement
Abstract:
We empirically show that the test error of deep networks can be estimated by simply training the same architecture on the same training set but with a different run of Stochastic Gradient Descent (SGD), and measuring the disagreement rate between the two networks on unlabeled test data. This builds on -- and is a stronger version of -- the observation in Nakkiran & Bansal '20, which requires the second run to be on an altogether fresh training set. We further theoretically show that this peculiar phenomenon arises from the \emph{well-calibrated} nature of \emph{ensembles} of SGD-trained models. This finding not only provides a simple empirical measure to directly predict the test error using unlabeled test data, but also establishes a new conceptual connection between generalization and calibration.
https://arxiv.org/abs/2106.13799
#abstract
Abstract:
We empirically show that the test error of deep networks can be estimated by simply training the same architecture on the same training set but with a different run of Stochastic Gradient Descent (SGD), and measuring the disagreement rate between the two networks on unlabeled test data. This builds on -- and is a stronger version of -- the observation in Nakkiran & Bansal '20, which requires the second run to be on an altogether fresh training set. We further theoretically show that this peculiar phenomenon arises from the \emph{well-calibrated} nature of \emph{ensembles} of SGD-trained models. This finding not only provides a simple empirical measure to directly predict the test error using unlabeled test data, but also establishes a new conceptual connection between generalization and calibration.
https://arxiv.org/abs/2106.13799
#abstract
Walrasian equilibrium behavior in nature
Abstract:
The interaction between land plants and mycorrhizal fungi (MF) forms perhaps the world’s most prevalent biological market. Most plants participate in such markets, in which MF collect nutrients from the soil and trade them with host plants in exchange for carbon. In a recent study, M. D. Whiteside et al. [Curr. Biol. 29, 2043–2050.e8 (2019)] conducted experiments that allowed them to quantify the behavior of arbuscular MF when trading phosphorus with their host roots. Their experimental techniques enabled the researchers to infer the quantities traded under multiple scenarios involving different amounts of phosphorus resources initially held by different MF patches. We use these observations to confirm a revealed preference hypothesis, which characterizes behavior in Walrasian equilibrium, a centerpiece of general economic equilibrium theory.
https://www.pnas.org/content/118/27/e2020961118
tl;dr - fungi embrace fundamental economic theory as they engage in trading
#abstract
Abstract:
The interaction between land plants and mycorrhizal fungi (MF) forms perhaps the world’s most prevalent biological market. Most plants participate in such markets, in which MF collect nutrients from the soil and trade them with host plants in exchange for carbon. In a recent study, M. D. Whiteside et al. [Curr. Biol. 29, 2043–2050.e8 (2019)] conducted experiments that allowed them to quantify the behavior of arbuscular MF when trading phosphorus with their host roots. Their experimental techniques enabled the researchers to infer the quantities traded under multiple scenarios involving different amounts of phosphorus resources initially held by different MF patches. We use these observations to confirm a revealed preference hypothesis, which characterizes behavior in Walrasian equilibrium, a centerpiece of general economic equilibrium theory.
https://www.pnas.org/content/118/27/e2020961118
tl;dr - fungi embrace fundamental economic theory as they engage in trading
#abstract
PNAS
Walrasian equilibrium behavior in nature
Mutualisms are commonly observed ecological interactions, often involving the exchange of resources across species. Such exchanges can be thought of as biological markets. Biologists modeling these markets often employ an informal mix of economics and game…
A topological solution to object segmentation and tracking
Abstract:
The world is composed of objects, the ground, and the sky. Visual perception of objects requires solving two fundamental challenges: segmenting visual input into discrete units, and tracking identities of these units despite appearance changes due to object deformation, changing perspective, and dynamic occlusion. Current computer vision approaches to segmentation and tracking that approach human performance all require learning, raising the question: can objects be segmented and tracked without learning? Here, we show that the mathematical structure of light rays reflected from environment surfaces yields a natural representation of persistent surfaces, and this surface representation provides a solution to both the segmentation and tracking problems. We describe how to generate this surface representation from continuous visual input, and demonstrate that our approach can segment and invariantly track objects in cluttered synthetic video despite severe appearance changes, without requiring learning.
https://arxiv.org/abs/2107.02036
Abstract:
The world is composed of objects, the ground, and the sky. Visual perception of objects requires solving two fundamental challenges: segmenting visual input into discrete units, and tracking identities of these units despite appearance changes due to object deformation, changing perspective, and dynamic occlusion. Current computer vision approaches to segmentation and tracking that approach human performance all require learning, raising the question: can objects be segmented and tracked without learning? Here, we show that the mathematical structure of light rays reflected from environment surfaces yields a natural representation of persistent surfaces, and this surface representation provides a solution to both the segmentation and tracking problems. We describe how to generate this surface representation from continuous visual input, and demonstrate that our approach can segment and invariantly track objects in cluttered synthetic video despite severe appearance changes, without requiring learning.
https://arxiv.org/abs/2107.02036
>Once in the brain, the nanosensors are highly sensitive to local changes in the electric field. In laboratory tests, in vitro prototypes of the NeuroSWARM3 were able to generate a signal-to-noise ratio of over 1,000, a sensitivity level that is suitable for detecting the electrical signal generated when a single neuron fires.
https://phys.org/news/2021-07-tiny-sensors-brain-surgery-implants.html
https://phys.org/news/2021-07-tiny-sensors-brain-surgery-implants.html
phys.org
Tiny, injectable sensors could monitor brain activity without surgery or implants
Researchers have developed nanoscale sensors that could be injected into the body to noninvasively track brain activity using light. The approach could one day offer a new way to study the brain or assess ...
https://www.youtube.com/watch?v=60z_hpEAtD8
Old, but gold
Old, but gold
YouTube
A Swift Introduction to Geometric Algebra
This video is an introduction to geometric algebra, a severely underrated mathematical language that can be used to describe almost all of physics. This video was made as a presentation for my lab that I work in. While I had the people there foremost in…