Galerkin finite element approximation for semilinear stochastic
**time**-tempered fractional wave equations with multiplicative white noise and
fractional Gaussian noise

**space**-

**time**multiplicative white noise and fractional Gaussian noise are discretized, which results in a regularized stochastic fractional wave equation while introducing a modeling error in the mean-square sense. Expand abstract.

**space**and the Caputo tempered fractional derivative in

**time**. The model studied in this paper is semilinear stochastic

**space**-

**time**fractional wave equations driven by infinite dimensional multiplicative white noise and fractional Gaussian noise, because of the potential fluctuations of the external sources. The purpose of this work is to discuss the Galerkin finite element approximation for the semilinear stochastic fractional wave equation. We first provide a complete solution theory, e.g., existence, uniqueness, and regularity. Then the

**space**-

**time**multiplicative white noise and fractional Gaussian noise are discretized, which results in a regularized stochastic fractional wave equation while introducing a modeling error in the mean-square sense. We further present a complete regularity theory for the regularized equation. A standard finite element approximation is used for the spatial operator, and the mean-square priori estimates for the modeling error and for the approximation error to the solution of the regularized problem are established.

7/10 relevant

arXiv

Cosmology in non-local Bopp-Podolski electrodynamics

**times**. Expand abstract.

**space**time, reduces to the Proca theory. However, it will be shown that in curved

**space**

**time**the resulting theory will differ from the coupled Einstein-Proca system. This theory admits de sitter solution. The cosmological perturbations on top of the de Sitter

**space**-

**time**shows that the tensor and vector modes are healthy. However there is a scalar mode in this model which behaves like the Pais-Uhlenbeck oscillator. This shows that this theory contains an Ostrogradski ghost in the scalar sector. Anisotropic cosmology of the model is also investigated and we will show that the behavior of the universe at late

**time**depends strongly on the initial conditions. However, independent of the parameters of the theory, the model predicts an isotropic universe at late

**times**.

7/10 relevant

arXiv

Space-**time** multilevel Monte Carlo methods and their application to
cardiac electrophysiology

**space**-

**time**adaptivity, time-changing domains, and to take advantage of past samples to initialize the space-time solution. Expand abstract.

**time**-dependent problems governed by partial differential equations. In particular, we consider input uncertainties described by a Karhunen-Loeve expansion and compute statistics of high-dimensional quantities-of-interest, such as the cardiac activation potential. Our methodology relies on a close integration of multilevel Monte Carlo methods, parallel iterative solvers, and a

**space**-

**time**finite element discretization. This combination allows for

**space**-

**time**adaptivity,

**time**-changing domains, and to take advantage of past samples to initialize the

**space**-

**time**solution. The resulting sequence of problems is distributed using a multilevel parallelization strategy, allocating batches of samples having different sizes to a different number of processors. We assess the performance of the proposed framework by showing in detail its application to the nonlinear equations of cardiac electrophysiology. Specifically, we study the effect of spatially-correlated perturbations of the heart fibers on the mean and variance of the resulting activation map. As shown by the experiments, the theoretical rates of convergence of multilevel Monte Carlo are achieved. Moreover, the total computational work for a prescribed accuracy is reduced by an order of magnitude with respect to standard Monte Carlo methods.

10/10 relevant

arXiv

Raychaudhuri Equation in Kaluza Klein **space** **time**

**space**-time. Expand abstract.

**space**-time. We derived an additional term that is solely due to Kaluza-Klein's unification. This term affects the defocus of world lines near the singularity of charged higher-dimensional black holes. We illustrated it with a static higher-dimensional black hole generated by Einstein-Maxwell equations. It has been found that the term derived modifies the repulsive effect of kaluza Klein scalar on world lines. We proved some mathematical theorems which give an insight into the interior of the black holes.

10/10 relevant

arXiv

Tuberculosis resistance acquisition in **space** and **time**: an analysis of globally diverse M. tuberculosis whole genome sequences

4/10 relevant

bioRxiv

ELGAR -- a European Laboratory for Gravitation and Atom-interferometric Research

**time**in 2015, one century after Einstein predicted their existence. There is now growing interest to extend the detection bandwidth to low frequency. The scientific potential of multi-frequency GW astronomy is enormous as it would enable to obtain a more complete picture of cosmic events and mechanisms. This is a unique and entirely new opportunity for the future of astronomy, the success of which depends upon the decisions being made on existing and new infrastructures. The prospect of combining observations from the future

**space**-based instrument LISA together with third generation ground based detectors will open the way towards multi-band GW astronomy, but will leave the infrasound (0.1 Hz to 10 Hz) band uncovered. GW detectors based on matter wave interferometry promise to fill such a sensitivity gap. We propose the European Laboratory for Gravitation and Atom-interferometric Research (ELGAR), an underground infrastructure based on the latest progress in atomic physics, to study

**space**-

**time**and gravitation with the primary goal of detecting GWs in the infrasound band. ELGAR will directly inherit from large research facilities now being built in Europe for the study of large scale atom interferometry and will drive new pan-European synergies from top research centers developing quantum sensors. ELGAR will measure GW radiation in the infrasound band with a peak strain sensitivity of $4.1 \times 10^{-22}/\sqrt{\text{Hz}}$ at 1.7 Hz. The antenna will have an impact on diverse fundamental and applied research fields beyond GW astronomy, including gravitation, general relativity, and geology.

4/10 relevant

arXiv

**Space** Efficient Construction of Lyndon Arrays in Linear **Time**

**time**algorithm to construct the $2n$-bit version of the Lyndon array for a string of length $n$ using only $o(n)$ bits of working

**space**. A simpler variant of this algorithm computes the plain ($n\lg n$-bit) version of the Lyndon array using only $\mathcal{O}(1)$ words of additional working

**space**. All previous algorithms are either not linear, or use at least $n\lg n$ bits of additional working

**space**. Also in practice, our new algorithms outperform the previous best ones by an order of magnitude, both in terms of

**time**and

**space**.

4/10 relevant

arXiv

Dark energy as a large scale quantum gravitational phenomenon

**space**-time-matter (STM). Planck scale foam is composed of STM atoms with Planck length as their associated Compton wave-length. The quantum dispersion and accompanying spontaneous localisation of these STM atoms amounts to a cancellation of the enormous curvature on the Planck length scale. However, an effective dark energy term arises in Einstein equations, of the order required by current observations on cosmological scales. This happens if we propose an extremely light particle having a mass of about $10^{-33} \ {\rm eV/c^2}$, forty-two orders of magnitude lighter than the proton. The holographic principle suggests there are about $10^{122}$ such particles in the observed universe. Their net effect on

**space**-

**time**geometry is equivalent to dark energy, this being a low energy quantum gravitational phenomenon. In this sense, the observed dark energy constitutes evidence for quantum gravity. We then invoke Dirac's large number hypothesis to also propose a dark matter candidate having a mass halfway (on the logarithmic scale) between the proton and the dark energy particle, i.e. about $10^{-12}\ {\rm eV/c^2}$.

5/10 relevant

arXiv

Theoretical description and experimental simulation of quantum
entanglement near open **time**-like curves via pseudo-density operators

**space**-

**time**correlations violating entanglement monogamy, such as those arising in black holes. Expand abstract.

**time**-travel. They are afflicted by notorious causality issues (e.g. grandfather's paradox). Quantum models where a qubit travels back in

**time**solve these problems, at the cost of violating quantum theory's linearity - leading e.g. to universal quantum cloning. Interestingly, linearity is violated even by open timelike curves (OTCs), where the qubit does not interact with its past copy, but is initially entangled with another qubit. Non-linear dynamics is needed to avoid violating entanglement monogamy. Here we propose an alternative approach to OTCs, allowing for monogamy violations. Specifically, we describe the qubit in the OTC via a pseudo-density operator - a unified descriptor of both temporal and spatial correlations. We also simulate the monogamy violation with polarization-entangled photons, providing a pseudo-density operator quantum tomography. Remarkably, our proposal applies to any

**space**-

**time**correlations violating entanglement monogamy, such as those arising in black holes.

4/10 relevant

arXiv

ESA Voyage 2050 white paper -- GrailQuest: hunting for Atoms of Space
and **Time** hidden in the wrinkle of **Space**-Time

**space**-time granularity with a new concept of modular observatory of huge overall collecting area consisting in a fleet of small satellites in low orbits, with sub-microsecond

**time**... Expand abstract.

**Space**-Time) is an ambitious astrophysical mission concept that uses a fleet of small satellites, whose scientific objectives are discussed below. Within Quantum Gravity theories, different models for

**space**-

**time**quantisation predict an energy dependent speed for photons. Although the predicted discrepancies are minuscule, Gamma-Ray Bursts, occurring at cosmological distances, could be used to detect this signature of

**space**-

**time**granularity with a new concept of modular observatory of huge overall collecting area consisting in a fleet of small satellites in low orbits, with sub-microsecond

**time**resolution and wide energy band (keV-MeV). The enormous number of collected photons will allow to effectively search these energy dependent delays. Moreover, GrailQuest will allow to perform temporal triangulation of high signal-to-noise impulsive events with arc-second positional accuracies: an extraordinary sensitive X-ray/Gamma all-sky monitor crucial for hunting the elusive electromagnetic counterparts of Gravitational Waves. A pathfinder of GrailQuest is already under development through the HERMES (High Energy Rapid Modular Ensemble of Satellites) project: a fleet of six 3U cube-sats to be launched by the end of 2021.

10/10 relevant

arXiv