Fundamental Cycle of a Periodic Box-Ball System

We investigate a soliton cellular automaton (Box-Ball system) with periodic boundary conditions. Since the cellular automaton is a deterministic dynamical system that takes only a finite number of states, it will exhibit periodic motion. We determine its fundamental cycle for a given initial state.Comment: 28 pages, 6 figure

Entanglement Cost of Three-Level Antisymmetric States

We show that the entanglement cost of the three-dimensional antisymmetric states is one ebit.Comment: 8page

Tropical Krichever construction for the non-periodic box and ball system

A solution for an initial value problem of the box and ball system is constructed from a solution of the periodic box and ball system. The construction is done through a specific limiting process based on the theory of tropical geometry. This method gives a tropical analogue of the Krichever construction, which is an algebro-geometric method to construct exact solutions to integrable systems, for the non-periodic system.Comment: 13 pages, 1 figur

Region-of-Interest Based Neural Video Compression

Humans do not perceive all parts of a scene with the same resolution, but rather focus on few regions of interest (ROIs). Traditional Object-Based codecs take advantage of this biological intuition, and are capable of non-uniform allocation of bits in favor of salient regions, at the expense of increased distortion the remaining areas: such a strategy allows a boost in perceptual quality under low rate constraints. Recently, several neural codecs have been introduced for video compression, yet they operate uniformly over all spatial locations, lacking the capability of ROI-based processing. In this paper, we introduce two models for ROI-based neural video coding. First, we propose an implicit model that is fed with a binary ROI mask and it is trained by de-emphasizing the distortion of the background. Secondly, we design an explicit latent scaling method, that allows control over the quantization binwidth for different spatial regions of latent variables, conditioned on the ROI mask. By extensive experiments, we show that our methods outperform all our baselines in terms of Rate-Distortion (R-D) performance in the ROI. Moreover, they can generalize to different datasets and to any arbitrary ROI at inference time. Finally, they do not require expensive pixel-level annotations during training, as synthetic ROI masks can be used with little to no degradation in performance. To the best of our knowledge, our proposals are the first solutions that integrate ROI-based capabilities into neural video compression models.Comment: Updated arxiv version to the camera-ready version after acceptance at British Machine Vision Conference (BMVC) 202

Environmental Conditions and COVID-19 Incident

COVID-19 is a new infectious disease caused by the SARS-CoV-2 virus and was designated as a pandemic since March 12, 2020, because there are a lot of case in several countries. On February 1, 2021, the total number of COVID-19 cases reached 103 million in the world, and in Indonesia it reached 1.09 million. Many factors influence the transmission and death of COVID-19, for example environmental conditions. This study aims to provide an overview of environmental conditions that can be a factor for transmission and death due to COVID-19. The method in this research is literature review, which is a literature review with secondary data obtained through research journals which are then synthesized and obtained 23 articles as a reference for preparing literature reviews. COVID-19 and environmental degradation have decreased air, water, noise and marine pollution due to the lockdown, but there has been an increase in the volume of hazardous and toxic waste from COVID-19 patients. Then from air pollution, the results of decreases in CO, NO2, and PM10 during lockdown. Meanwhile, for climatology and meteorology, the result is that every 1oC increase in temperature from the average temperature can reduce daily cases of COVID-19 by 36% and 57% when the average humidity is at 67% and 85.5%. Likewis,e humidity each 1oC increase relatively reduces daily cases of COVID-19 by 11% to 22% with a temperature range of 5.04oC to 8.2oC. The conclusion of this research is that the environmental conditions during a pandemic had their own polemic. However, several pollutants such as CO, NO2, O3, PM2,5, and PM10  is closely related to the spread of COVID-19. This literature review can provide recommendations for an overall global government demonstration policy in the prevention and control of environmental pollution and recycling of medical waste

Bethe ansatz at q=0 and periodic box-ball systems

A class of periodic soliton cellular automata is introduced associated with crystals of non-exceptional quantum affine algebras. Based on the Bethe ansatz at q=0, we propose explicit formulas for the dynamical period and the size of certain orbits under the time evolution in A^{(1)}_n case.Comment: 12 pages, Introduction expanded, Summary added and minor modifications mad

"Squashed Entanglement" - An Additive Entanglement Measure

In this paper, we present a new entanglement monotone for bipartite quantum states. Its definition is inspired by the so-called intrinsic information of classical cryptography and is given by the halved minimum quantum conditional mutual information over all tripartite state extensions. We derive certain properties of the new measure which we call "squashed entanglement": it is a lower bound on entanglement of formation and an upper bound on distillable entanglement. Furthermore, it is convex, additive on tensor products, and superadditive in general. Continuity in the state is the only property of our entanglement measure which we cannot provide a proof for. We present some evidence, however, that our quantity has this property, the strongest indication being a conjectured Fannes type inequality for the conditional von Neumann entropy. This inequality is proved in the classical case.Comment: 8 pages, revtex4. v2 has some more references and a bit more discussion, v3 continuity discussion extended, typos correcte

Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry

The box-ball system is an integrable cellular automaton on one dimensional lattice. It arises from either quantum or classical integrable systems by the procedures called crystallization and ultradiscretization, respectively. The double origin of the integrability has endowed the box-ball system with a variety of aspects related to Yang-Baxter integrable models in statistical mechanics, crystal base theory in quantum groups, combinatorial Bethe ansatz, geometric crystals, classical theory of solitons, tau functions, inverse scattering method, action-angle variables and invariant tori in completely integrable systems, spectral curves, tropical geometry and so forth. In this review article, we demonstrate these integrable structures of the box-ball system and its generalizations based on the developments in the last two decades.Comment: 73 page