A
bstract
The emergence of the bulk Hilbert space is a mysterious concept in holography. In
1
, the SYK model was solved in the double scaling limit by summing chord diagrams. Here, we explicitly ...construct the bulk Hilbert space of double scaled SYK by slicing open these chord diagrams; this Hilbert space resembles that of a lattice field theory where the length of the lattice is dynamical and determined by the chord number. Under a calculable bulk-to-boundary map, states of fixed chord number map to particular entangled 2-sided states with a corresponding size. This bulk reconstruction is well-defined even when quantum gravity effects are important. Acting on the double scaled Hilbert space is a Type II
1
algebra of observables, which includes the Hamiltonian and matter operators. In the appropriate quantum Schwarzian limit, we also identify the JT gravitational algebra including the physical SL(2
,
ℝ) symmetry generators, and obtain explicit representations of the algebra using chord diagram techniques.
Abstract A new approach to solving random matrix models directly in the large N limit is developed. First, a set of numerical values for some low-pt correlation functions is guessed. The large N loop ...equations are then used to generate values of higher-pt correlation functions based on this guess. Then one tests whether these higher-pt functions are consistent with positivity requirements, e.g., (tr M 2k ) ≥ 0. If not, the guessed values are systematically ruled out. In this way, one can constrain the correlation functions of random matrices to a tiny subregion which contains (and perhaps converges to) the true solution. This approach is tested on single and multi-matrix models and handily reproduces known solutions. It also produces strong results for multi-matrix models which are not believed to be solvable. A tantalizing possibility is that this method could be used to search for new critical points, or string worldsheet theories.
We show how the success of deep learning could depend not only on mathematics but also on physics: although well-known mathematical theorems guarantee that neural networks can approximate arbitrary ...functions well, the class of functions of practical interest can frequently be approximated through “cheap learning” with exponentially fewer parameters than generic ones. We explore how properties frequently encountered in physics such as symmetry, locality, compositionality, and polynomial log-probability translate into exceptionally simple neural networks. We further argue that when the statistical process generating the data is of a certain hierarchical form prevalent in physics and machine learning, a deep neural network can be more efficient than a shallow one. We formalize these claims using information theory and discuss the relation to the renormalization group. We prove various “no-flattening theorems” showing when efficient linear deep networks cannot be accurately approximated by shallow ones without efficiency loss; for example, we show that
n
variables cannot be multiplied using fewer than
2
n
neurons in a single hidden layer.
ABSTRACT
Gaia measures the five astrometric parameters for stars in the Milky Way, but only four of them (positions and proper motion, but not distance) are well measured beyond a few kpc from the ...Sun. Modern spectroscopic surveys such as APOGEE cover a large area of the Milky Way disc and we can use the relation between spectra and luminosity to determine distances to stars beyond Gaia’s parallax reach. Here, we design a deep neural network trained on stars in common between Gaia and APOGEE that determines spectro-photometric distances to APOGEE stars, while including a flexible model to calibrate parallax zero-point biases in Gaia DR2. We determine the zero-point offset to be $-52.3 \pm 2.0\, \mu \mathrm{as}$ when modelling it as a global constant, but also train a multivariate zero-point offset model that depends on G, GBP − GRP colour, and Teff and that can be applied to all ≈58 million stars in Gaia DR2 within APOGEE’s colour–magnitude range and within APOGEE’s sky footprint. Our spectro-photometric distances are more precise than Gaia at distances ${\gtrsim} 2\, \mathrm{kpc}$ from the Sun. We release a catalogue of spectro-photometric distances for the entire APOGEE DR14 data set which covers Galactocentric radii $2\, \mathrm{kpc} \lesssim R \lesssim 19\, \mathrm{kpc}$; ${\approx} 150\, 000$ stars have ${\lt} 10{{\ \rm per\ cent}}$ uncertainty, making this a powerful sample to study the chemo-dynamical structure of the disc. We use this sample to map the mean Fe/H and 15 abundance ratios X/Fe from the Galactic Centre to the edge of the disc. Among many interesting trends, we find that the bulge and bar region at $R \lesssim 5\, \mathrm{kpc}$ clearly stands out in Fe/H and most abundance ratios.
The COVID-19 pandemic led to the implementation of worldwide restrictive measures to reduce social contact and viral spread. These measures have been reported to have a negative effect on physical ...activity (PA). Studies of PA during the pandemic have primarily used self-reported data. The single academic study that used tracked data did not report on demographics.
This study aimed to explore patterns of smartphone-tracked activity before, during, and immediately after lockdown in the United Kingdom, and examine differences by sociodemographic characteristics and prior levels of PA.
Tracked longitudinal weekly minutes of PA were captured using the BetterPoints smartphone app between January and June 2020. Data were plotted by week, demographics, and activity levels at baseline. Nonparametric tests of difference were used to assess mean and median weekly minutes of activity at significant points before and during the lockdown, and as the lockdown was eased. Changes over time by demographics (age, gender, Index of Multiple Deprivation, baseline activity levels) were examined using generalized estimating equations (GEEs).
There were 5395 users with a mean age of 41 years (SD 12) and 61% (n=3274) were female. At baseline, 26% (n=1422) of users were inactive, 23% (n=1240) were fairly active, and 51% (n=2733) were active. There was a relatively even spread across deprivation deciles (31% n=1693 in the least deprived deciles and 23% in the most n=1261). We found significant changes in PA from the week before the first case of COVID-19 was announced (baseline) to the week that social distancing restrictions were relaxed (Friedman test: χ
=2331, P<.001). By the first full week of lockdown, the median change in PA was 57 minutes less than baseline. This represents a 37% reduction in weekly minutes of PA. Overall, 63% of people decreased their level of activity between baseline and the first week of COVID-19 restrictions. Younger people showed more PA before lockdown but the least PA after lockdown. In contrast, those aged >65 years appeared to remain more active throughout and increased their activity levels as soon as lockdown was eased. Levels of PA among those classed as active at baseline showed a larger drop compared with those considered to be fairly active or inactive. Socioeconomic group and gender did not appear to be associated with changes in PA.
Our tracked PA data suggests a significant drop in PA during the United Kingdom's COVID-19 lockdown. Significant differences by age group and prior PA levels suggests that the government's response to COVID-19 needs to be sensitive to these individual differences and the government should react accordingly. Specifically, it should consider the impact on younger age groups, encourage everyone to increase their PA, and not assume that people will recover prior levels of PA on their own.
A
bstract
It is widely believed that exact global symmetries do not exist in theories that admit quantum black holes. Here we propose a way to quantify the degree of global symmetry violation in the ...Hawking radiation of a black hole by using certain relative entropies. While the violations of global symmetry that we consider are non-perturbative effects, they nevertheless give
O
(1) contributions to the relative entropy after the Page time. Furthermore, using “island” formulas, these relative entropies can be computed within semi-classical gravity, which we demonstrate with explicit examples. These formulas give a rather precise operational sense to the statement that a global charge thrown into an old black hole will be lost after a scrambling time.
The relative entropies considered here may also be computed using a replica trick. At integer replica index, the global symmetry violating effects manifest themselves as charge flowing through the replica wormhole.
A
bstract
We derive simple bootstrap bounds on correlation functions of the BFSS matrix theory/D0-brane quantum mechanics. The result strengthens and extends Polchinski’s virial theorem bound to ...finite energies and gives the first non-trivial bound on ⟨Tr
X
2
⟩. Despite their simplicity, the bounds hint at some features of the dual black hole geometry. Our best lower bounds are already a factor of ∼ 2 from existing Monte Carlo results.
Symmetries near the horizon Lin, Henry W.; Maldacena, Juan; Zhao, Ying
The journal of high energy physics,
08/2019, Volume:
2019, Issue:
8
Journal Article
Peer reviewed
Open access
A
bstract
We consider a nearly-AdS
2
gravity theory on the two-sided wormhole geometry. We construct three gauge-invariant operators in NAdS
2
which move bulk matter relative to the dynamical ...boundaries. In a two-sided system, these operators satisfy an SL(2) algebra (up to non perturbative corrections). In a semiclassical limit, these generators act like SL(2) transformations of the boundary time, or conformal symmetries of the two sided boundary theory. These can be used to define an operator-state mapping. A particular large N and low temperature limit of the SYK model has precisely the same structure, and this construction of the exact generators also applies. We also discuss approximate, but simpler, constructions of the generators in the SYK model. These are closely related to the “size” operator and are connected to the maximal chaos behavior captured by out of time order correlators.
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