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If we interpret the Bekenstein-Hawking entropy of the Hubble horizon as thermodynamic entropy, then the entanglement entropy of the superhorizon modes of curvature perturbation entangled with the subhorizon modes will exceed the Bekenstein-Hawking bound at some point; we call this the unitary paradox of cosmological perturbations by analogy with black hole. In order to avoid a fine-tuned problem, the paradox must occur during the inflationary era at the critical time $t_c=\ln(3\sqrt{\pi}/\sqrt{2}\epsilon_HH_{inf})/2H_{inf}$ (in Planck units), where $\epsilon_H= -\dot{H}/H^2$ is the first Hubble slow-roll parameter and $H_{inf}$ is the Hubble rate during inflation. If we instead accept the fine-tuned problem, then the paradox will occur during the dark energy era at the critical time $t_c'=\ln(3\sqrt{\pi}H_{inf}/\sqrt{2}fe^{2N}H_\Lambda^2)/2H_\Lambda$, where $H_\Lambda$ is the Hubble rate dominated by dark energy, $N$ is the total number of e-folds of inflation, and $f$ is a purification factor that takes the range $0, Comment: 13 pages, 3 figures; close to published version

We know that space and time are treated almost equally in classical physics, but we also know that this is not the case for quantum mechanics. A quantum description of both space and time is important to really understand the quantum nature of reality. The Page-Wootters mechanism of quantum time is a promising starting point, according to which the evolution of the quantum system is described by the entanglement between it and quantum temporal degrees of freedom. In this paper, we consider a qubit clock that is entangled with a quantum system due to the Wigner rotation induced by Lorentz transformation. We study how this time-system entanglement depends on the rapidity of the Lorentz boost. We consider the case of a spin-1/2 particle with Gaussian momentum distribution as a concrete example. We also compare the time-system entanglement entropy with the spin-momentum entanglement entropy and find that the former is smaller than the latter., 6 pages, 4 figures; a new paragraph comparing Time-System entanglement entropy with Spin-Momentum entanglement entropy is provided

Board localization within logs using image analysis approaches for traceability and quality assessment in sawmills EffiQuAss project ANR‐21‐CE10‐0002‐01

In the first scenario, we revise the upper bound of the cutoff scale of the dimension-six potential Higgs operator required for a successful electroweak baryogenesis in the case of a modified expansion history caused by the existence of a non-interacting scalar field at the time phase transition happens. The upper bound 860 GeV of the cutoff scale in the conventional case can be improved to 1 TeV in the modified expansion case under certain conditions. In the second scenario, we consider the Randall-Sundrum type II model. We show that the lower bound of the five-dimensional Planck scale in this model, which is determined from the validity of Newtonian gravitational potential at small distance, turns out to be crucial in eliminating this model as a viable candidate to satisfy the sphaleron bound; however, again modifying the expansion history by including a non-interacting scalar field at the electroweak scale can then make this model satisfy the sphaleron bound with a certain parameter space., 16 pages, 6 figures, 1 table

Shaft inflation is a model in which the inflaton potential approaches a plateau far from the origin, while it resembles chaotic inflation near the origin. Meanwhile, the Randall-Sundrum type II model (RSII) is an interesting extra-dimensional model to study cosmological phenomenology. In this paper, we study shaft inflation in the RSII model. We find that the predictions are in excellent agreement with observation. The fundamental five-dimensional Planck scale is found to be $M_5\simeq 10^{16}$ GeV, which is consistent with the lower bound $M_5\gtrsim 10^{9}$ GeV obtained from experimental Newtonian gravitational bound. This is an important result that can be used to explore further the implications of extra dimension in other contexts., 14 pages, 5 figures, 2 tables; published version in JCAP

Within the $SP(2,R)$ symmetry, the Two-time model (2T model) has six dimensions with two dimensions of time and the dilaton field that can be identified as inflaton in a warm inflation scenario with potential of the form $\sim\phi^4$. From that consideration, we derive the range of parameters for the Higgs-Dilaton potential, the coupling constant between Higgs and Dialton ($\alpha$) is larger than $0.0053$ and the mass of Dilaton is smaller than $10^{-7}$ GeV. Therefore, the 2T-model indirectly suggests that extra-dimension can also be a source of inflation., Comment: 15 pages and 2 figures

International audience; The SolHoM(a) project aims at determining the degree of landscape anthropisation in the Fossard massif (Remiremont, Vosges, France) by estimating the impact of past human occupations on current soils. Nowadays, a forest covers this relatively inhospitable mountain (hard climate, steep slopes, acid soils ...), but some remains suggest human presence for at least 1400 years.The Saint-Mont is a variscan orogenic granitic summit (height 672m) with valuable preserved archaeological relics, located south of the Fossard. At the top was founded the monasterium Habendum (from the 7th century to the French Revolution), which potentially comes after a late-antic castrum.Furthermore, monumental enclosure dry-stones walls, not yet clearly linked with the monastery, crosses the massif.Our methodology is first experienced on the Saint-Mont, well documented by recent archaeological research. It features:- sampling soil transects presenting a clear gradient from highly to poorly human impacted areas. According to those transects, soils are sampled and characterised (physico-chemistry, soil micromorphology, analysis of organic matter, dating); this should highlight traces of past human activity;- a development of algorithms to detect geometric structures in the raw LiDAR data provided by the PCR AGER(b) (Ch. Kraemer, dir). This research might help archaeologists to determine areas influenced or not by men.Once tested on the Saint-Mont, this approach will be applied to another archaeologically less investigated area of the Fossard.First field works highlight two soil sequences:- the first one, near a probable merovingian wall close to the monastery, reveals a very black 80cm deep unit,- the second one, far-off the monastery and beside the enclosure dry-stone wall, is less thick but have a thin black unit buried under 20 cm of pedogenised sediment.Physico-chemical and soil micromorphological analyses are in progress. The coming study of profiles/sequences more distant from archaeological sites will contribute to estimate the degree of soils anthropisation in the Saint-Mont.(a) Interactions Sol-Hommes-Milieux(b) ArchéoGEographie du premier Remiremont et de ses abords

International audience

Determining the solvability of equations has been an extended and fundamental study in Mathematics. The local-global principle states two objects are equivalent globally if and only if they are equivalent locally at all places. By applying this principle, the Hasse - Minkowski theorem is able to identify the existence of rational solutions of an equation. This paper explores the applications of the Hasse-Minkowski theorem to homogeneous quadratic forms in two and three variables. After providing some of the necessary proofs and definitions, we have been able to introduce some complete computer programs implementing the Hasse-Minkowski theorems and Legendre theorem with some supporting functions like the Eratosthenes sieve.This article was retracted on January 03, 2022.

Our paper was hugely inspired by Dr. Hohner’s master thesis, “The Hasse-Minkowski Theorem in Two and Three Variables.” More than half the length of our paper is our original programming implementation of various theorems, like the Hasse-­Minkowski theorem and Legendre’s theorem, and many supporting concepts, along with the algorithm analysis. We also shorten many proofs from Dr. Hohner’s paper by either providing an alternative shorter version or summarizing them. We credit him in section 1 on the binary and ternary quadratic form and the bibliography. However, the location of the credit section 1 was supposed to be before section 1, and this is a formatting mistake. Even though we made an effort to credit Dr. Hohner’s work, it could still be insufficient. We think it would be best to retract the paper for those listed reasons.

By adding the dimension-six operator for the Higgs potential (denoted $\mathcal{O}_6$) in Standard Model, we have a first-order electroweak phase transition (EWPT) whose strength is larger than unity. The cutoff parameter of the dimension-six Higgs operator ($\Lambda$) is found to be in the range 593-860 GeV with the Wilson parameter equals to unity; it is also shown that the greater the $\Lambda$, the lower the phase transition strength and the larger the Wilson parameter, the wider the domain of $\Lambda$. At zero temperature, the sphaleron energy is calculated with a smooth ansatz and an ansatz with scale-free parameters, thereby we find that smooth profiles are not more accurate than profiles with scale-free parameters. Then, using the one-loop effective Higgs potential with the inclusion of $\mathcal{O}_6$ instead of all possible dimension-six operators, we directly calculate the electroweak sphaleron energy at finite temperature with the scale-free parameters ansatz and show that the decoupling condition is satisfied during the phase transition. Moreover, we can reevaluate the upper bound of the cutoff scale inferred from the first-order phase transition. In addition, with the upper bound of the cutoff parameter (about 800-860 GeV), EWPT is a solution to the energy scale of the dimension-six operators. There is an extended conclusion that EWPT can only be solved at a large energy scale than that of SM., Comment: 34 pages, 7 figures. We would like to thank all comments (of Amine Ahriche, Jorinde van de Vis, Carlos Tamarit, Michael Spannowsky, Mikael Chala, Graham White, Jordy de Vries) for arxiv:2003.09625v1 and the comments of the reviewer for DQ12720-Phong; matches journal version (PRD)

This document presents complementary experiments on the published algorithm of Thick Line Segment Detection with Fast Directional Tracking. The main paper is actually published at ICIAP 2019. First tests compare the performance of the detector with and without adaptive directional scans (ADS) and assigned thickness control (ATC). On the detector without ADS, the fine tracking step must be performed twice to get less risk of growing blurred segment escape from the scan strip.

International audience; Reliable hand gesture recognition is an important problem for automatic sign language recognition for the people with hearing and speech disabilities. In this paper, we create a new benchmark database of multi-oriented, isolated ASL numeric images using recently launched Kinect V2. Further, we design an effective statistical-topological feature combinations for recognition of the hand gestures using the available V1 sensor dataset and also over the new V2 dataset. For V1, our best accuracy is 98.4% which is comparable with the best one reported so far and for V2 we achieve an accuracy of 92.2% which is first of its kind.

Foreign direct investment (FDI) enterprises are playing a key role in Vietnam’s economy. By the end of 2016, there are more than 21,398 FDI projects in force, with the total registered capital of nearly 293 billion USD. One hundred six countries and territories have invested in 19 industries in 68 provinces and cities of Vietnam. These investments have added a large amount of capital to the economy, which has basically been used effectively, contributing to the economic growth of Vietnam. In this context, the study focuses on the analysis of statistical data from 1988 to 2016 on the sources of funds, the number of projects, the invested sectors, and countries invested in Vietnam; research also includes three main factors that affect the quality of FDI attraction in Vietnam, namely resources, infrastructure, and other support policies. In this study, the support policy factor is thought to have the greatest impact. In addition to the use of statistical techniques, quantitative research is also applied to three data analysis techniques, including descriptive statistics, scale reliability analysis, and regression analysis, to verify the hypothesis. Policy implications are also proposed in this study to improve the quality of FDI attraction in Vietnam in the coming years.

This paper discusses the relationship between quadratic irrational numbers and periodic continued fractions. By using some basic properties of this relationship, we will show how to compare exactly two quadratic irrationals. Instead of using their numerical values which are approximations of the real values, we use their corresponding continued fractions each of which contains only a finite set of integers.

International audience