scholarly journals Towards a Theory of Quantum Gravity from Neural Networks

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 7
Author(s):  
Vitaly Vanchurin
Keyword(s):  
Neural Network ◽  
Degrees Of Freedom ◽  
Space Time ◽  
Learning System ◽  
Einstein Equations ◽  
Localized States ◽  
Batch Size ◽  
Step Size ◽  
Equilibrium Dynamics ◽  
Non Equilibrium

Neural network is a dynamical system described by two different types of degrees of freedom: fast-changing non-trainable variables (e.g., state of neurons) and slow-changing trainable variables (e.g., weights and biases). We show that the non-equilibrium dynamics of trainable variables can be described by the Madelung equations, if the number of neurons is fixed, and by the Schrodinger equation, if the learning system is capable of adjusting its own parameters such as the number of neurons, step size and mini-batch size. We argue that the Lorentz symmetries and curved space-time can emerge from the interplay between stochastic entropy production and entropy destruction due to learning. We show that the non-equilibrium dynamics of non-trainable variables can be described by the geodesic equation (in the emergent space-time) for localized states of neurons, and by the Einstein equations (with cosmological constant) for the entire network. We conclude that the quantum description of trainable variables and the gravitational description of non-trainable variables are dual in the sense that they provide alternative macroscopic descriptions of the same learning system, defined microscopically as a neural network.

scholarly journals Learning the non-equilibrium dynamics of Brownian movies

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Federico S. Gnesotto ◽  
Grzegorz Gradziuk ◽  
Pierre Ronceray ◽  
Chase P. Broedersz
Keyword(s):  
Degrees Of Freedom ◽  
Time Lapse ◽  
Direct Access ◽  
Dynamical Analysis ◽  
Entropy Production Rate ◽  
Microscopy Imaging ◽  
Time Resolved ◽  
Equilibrium Dynamics ◽  
Many Body Systems ◽  
Non Equilibrium

Abstract Time-lapse microscopy imaging provides direct access to the dynamics of soft and living systems. At mesoscopic scales, such microscopy experiments reveal intrinsic thermal and non-equilibrium fluctuations. These fluctuations, together with measurement noise, pose a challenge for the dynamical analysis of these Brownian movies. Traditionally, methods to analyze such experimental data rely on tracking embedded or endogenous probes. However, it is in general unclear, especially in complex many-body systems, which degrees of freedom are the most informative about their non-equilibrium nature. Here, we introduce an alternative, tracking-free approach that overcomes these difficulties via an unsupervised analysis of the Brownian movie. We develop a dimensional reduction scheme selecting a basis of modes based on dissipation. Subsequently, we learn the non-equilibrium dynamics, thereby estimating the entropy production rate and time-resolved force maps. After benchmarking our method against a minimal model, we illustrate its broader applicability with an example inspired by active biopolymer gels.

scholarly journals Temperature chaos is present in off-equilibrium spin-glass dynamics

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Marco Baity-Jesi ◽  
Enrico Calore ◽  
Andrés Cruz ◽  
Luis Antonio Fernandez ◽  
José Miguel Gil-Narvion ◽  
...  
Keyword(s):  
Spin Glass ◽  
Dynamic Effect ◽  
Large Degree ◽  
Equilibrium Temperature ◽  
Experimental Conditions ◽  
Temperature Changes ◽  
Equilibrium Dynamics ◽  
Glass Dynamics ◽  
Extreme Sensitivity ◽  
Non Equilibrium

AbstractExperiments featuring non-equilibrium glassy dynamics under temperature changes still await interpretation. There is a widespread feeling that temperature chaos (an extreme sensitivity of the glass to temperature changes) should play a major role but, up to now, this phenomenon has been investigated solely under equilibrium conditions. In fact, the very existence of a chaotic effect in the non-equilibrium dynamics is yet to be established. In this article, we tackle this problem through a large simulation of the 3D Edwards-Anderson model, carried out on the Janus II supercomputer. We find a dynamic effect that closely parallels equilibrium temperature chaos. This dynamic temperature-chaos effect is spatially heterogeneous to a large degree and turns out to be controlled by the spin-glass coherence length ξ. Indeed, an emerging length-scale ξ* rules the crossover from weak (at ξ ≪ ξ*) to strong chaos (ξ ≫ ξ*). Extrapolations of ξ* to relevant experimental conditions are provided.

scholarly journals Epidemic growth and Griffiths effects on an emergent network of excited atoms

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
T. M. Wintermantel ◽  
M. Buchhold ◽  
S. Shevate ◽  
M. Morgado ◽  
Y. Wang ◽  
...  
Keyword(s):  
Complex Systems ◽  
Power Laws ◽  
Excitation Density ◽  
Griffiths Phase ◽  
Many Body ◽  
Excited Atoms ◽  
Equilibrium Dynamics ◽  
Many Body Systems ◽  
Excitation Number ◽  
Non Equilibrium

AbstractWhether it be physical, biological or social processes, complex systems exhibit dynamics that are exceedingly difficult to understand or predict from underlying principles. Here we report a striking correspondence between the excitation dynamics of a laser driven gas of Rydberg atoms and the spreading of diseases, which in turn opens up a controllable platform for studying non-equilibrium dynamics on complex networks. The competition between facilitated excitation and spontaneous decay results in sub-exponential growth of the excitation number, which is empirically observed in real epidemics. Based on this we develop a quantitative microscopic susceptible-infected-susceptible model which links the growth and final excitation density to the dynamics of an emergent heterogeneous network and rare active region effects associated to an extended Griffiths phase. This provides physical insights into the nature of non-equilibrium criticality in driven many-body systems and the mechanisms leading to non-universal power-laws in the dynamics of complex systems.

scholarly journals AFibNet: an implementation of atrial fibrillation detection with convolutional neural network

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Bambang Tutuko ◽  
Siti Nurmaini ◽  
Alexander Edo Tondas ◽  
Muhammad Naufal Rachmatullah ◽  
Annisa Darmawahyuni ◽  
...  
Keyword(s):  
Neural Network ◽  
Atrial Fibrillation ◽  
Convolutional Neural Network ◽  
Learning System ◽  
Single Frequency ◽  
Feature Maps ◽  
Normal Sinus ◽  
Unseen Data ◽  
Specific Device ◽  
Model Formation

Abstract Background Generalization model capacity of deep learning (DL) approach for atrial fibrillation (AF) detection remains lacking. It can be seen from previous researches, the DL model formation used only a single frequency sampling of the specific device. Besides, each electrocardiogram (ECG) acquisition dataset produces a different length and sampling frequency to ensure sufficient precision of the R–R intervals to determine the heart rate variability (HRV). An accurate HRV is the gold standard for predicting the AF condition; therefore, a current challenge is to determine whether a DL approach can be used to analyze raw ECG data in a broad range of devices. This paper demonstrates powerful results for end-to-end implementation of AF detection based on a convolutional neural network (AFibNet). The method used a single learning system without considering the variety of signal lengths and frequency samplings. For implementation, the AFibNet is processed with a computational cloud-based DL approach. This study utilized a one-dimension convolutional neural networks (1D-CNNs) model for 11,842 subjects. It was trained and validated with 8232 records based on three datasets and tested with 3610 records based on eight datasets. The predicted results, when compared with the diagnosis results indicated by human practitioners, showed a 99.80% accuracy, sensitivity, and specificity. Result Meanwhile, when tested using unseen data, the AF detection reaches 98.94% accuracy, 98.97% sensitivity, and 98.97% specificity at a sample period of 0.02 seconds using the DL Cloud System. To improve the confidence of the AFibNet model, it also validated with 18 arrhythmias condition defined as Non-AF-class. Thus, the data is increased from 11,842 to 26,349 instances for three-class, i.e., Normal sinus (N), AF and Non-AF. The result found 96.36% accuracy, 93.65% sensitivity, and 96.92% specificity. Conclusion These findings demonstrate that the proposed approach can use unknown data to derive feature maps and reliably detect the AF periods. We have found that our cloud-DL system is suitable for practical deployment

scholarly journals Using Wearable Sensors and a Convolutional Neural Network for Catch Detection in American Football

Sensors ◽  
2020 ◽  
Vol 20 (23) ◽  
pp. 6722
Author(s):  
Bernhard Hollaus ◽  
Sebastian Stabinger ◽  
Andreas Mehrle ◽  
Christian Raschner
Keyword(s):  
Neural Network ◽  
Degrees Of Freedom ◽  
Wearable Sensors ◽  
Professional Sports ◽  
American Football ◽  
Data Logging ◽  
Sensor Platform ◽  
Magnetometer Data ◽  
Audio Data ◽  
New Type

Highly efficient training is a must in professional sports. Presently, this means doing exercises in high number and quality with some sort of data logging. In American football many things are logged, but there is no wearable sensor that logs a catch or a drop. Therefore, the goal of this paper was to develop and verify a sensor that is able to do exactly that. In a first step a sensor platform was used to gather nine degrees of freedom motion and audio data of both hands in 759 attempts to catch a pass. After preprocessing, the gathered data was used to train a neural network to classify all attempts, resulting in a classification accuracy of 93%. Additionally, the significance of each sensor signal was analysed. It turned out that the network relies most on acceleration and magnetometer data, neglecting most of the audio and gyroscope data. Besides the results, the paper introduces a new type of dataset and the possibility of autonomous training in American football to the research community.

CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

Dynamic Characteristics of Double Helical Planetary Gear Train With Tooth Friction

2015 ◽  
Author(s):  
Fengxia Lu ◽  
Rupeng Zhu ◽  
Haofei Wang ◽  
Heyun Bao ◽  
Miaomiao Li
Keyword(s):  
Degrees Of Freedom ◽  
Sliding Friction ◽  
Planetary Gear ◽  
Gear Train ◽  
Variable Step Size ◽  
Step Size ◽  
Planetary Gear Train ◽  
Gear Mesh ◽  
Meshing Stiffness ◽  
Nonlinear Dynamics Model

A new nonlinear dynamics model of the double helical planetary gear train with 44 degrees of freedom is developed, and the coupling effects of the sliding friction, time-varying meshing stiffness, gear backlashes, axial stagger as well as gear mesh errors, are taken into consideration. The solution of the differential governing equation of motion is solved by variable step-size Runge-Kutta numerical integration method. The influence of tooth friction on the periodic vibration and nonlinear vibration are investigated. The results show that tooth friction makes the system motion become stable by the effects of the periodic attractor under the specific meshing frequency and leads to the frequency delay for the bifurcation behavior and jump phenomenon in the system.

COMPUTING AN ADAPTIVE MESH IN FLUID PROBLEMS USING NEURAL NETWORK AND GENETIC ALGORITHM WITH ADAPTIVE RELAXATION

2008 ◽  
Vol 17 (06) ◽  
pp. 1089-1108 ◽  
Author(s):  
NAMEER N. EL. EMAM ◽  
RASHEED ABDUL SHAHEED
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Numerical Experiments ◽  
Back Propagation ◽  
Adaptive Mesh ◽  
Learning System ◽  
Back Propagation Algorithm ◽  
Adaptive Smoothing ◽  
Different Types ◽  
Optimal Values

A method based on neural network with Back-Propagation Algorithm (BPA) and Adaptive Smoothing Errors (ASE), and a Genetic Algorithm (GA) employing a new concept named Adaptive Relaxation (GAAR) is presented in this paper to construct learning system that can find an Adaptive Mesh points (AM) in fluid problems. AM based on reallocation scheme is implemented on different types of two steps channels by using a three layer neural network with GA. Results of numerical experiments using Finite Element Method (FEM) are discussed. Such discussion is intended to validate the process and to demonstrate the performance of the proposed learning system on three types of two steps channels. It appears that training is fast enough and accurate due to the optimal values of weights by using a few numbers of patterns. Results confirm that the presented neural network with the proposed GA consistently finds better solutions than the conventional neural network.

Non-equilibrium dynamics of colloids on disordered substrates

2003 ◽  
Vol 318 (1-2) ◽  
pp. 146-151 ◽  
Author(s):  
Jiangxing Chen ◽  
Yigang Cao ◽  
Zhengkuan Jiao
Keyword(s):  
Equilibrium Dynamics ◽  
Non Equilibrium
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