Shock waves and delay of hyperfast growth in de Sitter complexity

We study the holographic complexity in de Sitter spacetime, especially how the hyperfast growth of holographic complexity in de Sitter spacetime is affected under a small and early perturbation. The perturbed geometry is de Sitter spacetime with shock waves. We find that the critical time, at which de Sitter holographic complexity diverges, becomes always greater in the presence of the shock waves, which satisfies the averaged null energy conditions. This means that the hyperfast property of de Sitter complexity is delayed by small perturbations.Comment: 39 pages, 12 figure

The local SYK model and its triple scaling limit

We study a model of fermions with random couplings similar to conventional SYK with $N$ number of flavours of fermions, at large $N$. Unlike the conventional SYK model, which has all-to-all couplings, the model we study, which we call local SYK, has a much less number of random couplings, just $N$ in number and with only local interactions. It is shown that there exists a limit in which the local SYK model can be solved using the chord diagram techniques, analogous to the double-scaled limit of conventional SYK. This limit corresponds to taking the size of the fermion coupling terms, $q$, to scale linearly with $N$. A further triple scaling limit is taken to analyze the low energy limit and it is shown that the OTOCs saturate the chaos bound, paralleling the analysis in the conventional SYK.Comment: 8 pages, 2 figure

Deep Semantic Hashing for Aerial Livestock Detection

The goal of this project is to be able to accurately detect and count livestock in footage captured by a drone in real time. The main problems with this arise from the fact that a drone can only carry limited computing resources, and hashing is conventionally thought of as a great method of doing image classification very quickly and thus even on low-power devices. In this project, we use both a Faster-RCNN, which is a state-of-the art object detection model as a benchmark to develop a hashing model that can perform a similar task much more quickly. These two models provide a trade-off between accuracy and speed, where the Faster-RCNN is more accurate and gives precise locations of the livestock in the image, while the hashing is significantly faster but is less accurate and only provides the number of livestock in the image. Given that the dataset is very limited in quantity, we also build a generative network to create more images for the model to train on so that it has a more diverse set of hash codes to reference

Wormholes and holographic decoherence

We study a class of decoherence process which admits a 3 dimensional holographic bulk. Starting from a thermo-field double dual to a wormhole, we prepare another thermo-field double which plays the role of environment. By allowing the energy flow between the original and environment thermo-field double, the entanglement of the original thermo-field double eventually decoheres. We model this decoherence by four-boundary wormhole geometries, and study the time-evolution of the moduli parameters to see the change of the entanglement pattern among subsystems. A notable feature of this holographic decoherence processes is that at the end point of the processes, the correlations of the original thermo-field double are lost completely both classically and also quantum mechanically. We also discuss distinguishability between thermo-field double state and thermo mixed double state, which contains only classical correlations, and construct a code subspace toy model for that.Comment: 34 pages, 11 figures. v2: numerical plots of section 3.1 corrected. references adde

Late time behavior of nn-point spectral form factors in Airy and JT gravities

We study the late time behavior of $n$-point spectral form factors (SFFs) in two-dimensional Witten-Kontsevich topological gravity, which includes both Airy and JT gravities as special cases. This is conducted in the small $\hbar$ expansion, where $\hbar \sim e^{- {1}/{G_N}}$ is the genus counting parameter and nonperturbative in Newton's constant $G_N$. For one-point SFF, we study its absolute square at two different late times. We show that it decays by power law at $t \sim \hbar^{-2/3}$ while it decays exponentially at $t \sim \hbar^{-1}$ due to the higher order corrections in $\hbar$. We also study general $n (\ge 2)$-point SFFs at $t \sim \hbar^{-1}$ in the leading order of the $\hbar$ expansion. We find that they are characterized by a single function, which is essentially the connected two-point SFF and is determined by the classical eigenvalue density $\rho_0(E)$ of the dual matrix integral. These studies suggest that qualitative behaviors of $n$-point SFFs are similar in both Airy and JT gravities, where our analysis in the former case is based on exact results.Comment: 31 pages, 7 figures. v2: Improved calculation of integrals in section 4.

Is Action Complexity better for de Sitter space in Jackiw-Teitelboim gravity?

Volume complexity in dS$_2$ remains $O(1)$ up to a critical time, after which it suddenly diverges. On the other hand, for the dS$_2$ solution in JT gravity there is a linear dilaton which smoothly grows towards the future infinity. From the dimensional reduction viewpoint, the growth of the dilaton is due to the expansion of the orthogonal sphere in higher-dimensional dS$_d$ ($d \ge 3$). Since in higher dimensions complexity becomes very large even before the critical time, by properly taking into account the dilaton, the same behavior is expected for complexity in dS$_2$ JT gravity. We show that this expectation is met by complexity = action (CA) conjecture. For this purpose, we obtain an appropriate action for dS$_2$ in JT gravity, by dimensional reduction from dS$_3$. In addition, we discuss complexity = "refined volume" where we choose an appropriate Weyl field-redefinition such that refined volume avoids the discontinuous jump in time evolution.Comment: v2, 30 pages, 3 figures, minor typos corrected, references adde

A system for recognizing numeric strings from topographical maps

The paper proposes a system for recognizing numeric strings from topographical maps, which is composed of an automatic recognition stage and an interactive recognition stage. In this method, uncertain numeric strings extracted through the automatic recognition stage based on topographical map features only are confirmed and corrected by the interactive recognition stage. Therefore one can obtain highly precise recognition results. The method was applied to numeric string recognition from a map image which includes 102 strings made up of 249 numerals. As a result, 95.1% of 102 numeric strings were correctly recognized.Third International Conference on Document Analysis and Recognition, August 14-16, 1995, Montreal, Canad