Parabolic equations in Musielak -- Orlicz **spaces** with discontinuous in
**time** $N$-function

**time**and spatial variable. We do not assume continuity in

**time**for the $N$-function. Using an additional regularization effect coming from the equation, we establish the existence of weak solutions and in the particular case of isotropic $N$-function, we also prove their uniqueness. This general result applies to equations studied in the literature like $p(t,x)$-Laplacian and double-phase problems.

4/10 relevant

arXiv

On the rigidity of stationary charged black holes: small perturbations of the non-extremal Kerr-Newman family

**space**-

**time**with bifurcate horizons, if it agrees with a non-extremal Kerr-Newman space-time asymptotically flat at infinity and it is sufficiently close to the Kerr-Newman family, then the space-time... Expand abstract.

**space**-

**time**with bifurcate horizons, if it agrees with a non-extremal Kerr-Newman

**space**-

**time**asymptotically flat at infinity and it is sufficiently close to the Kerr-Newman family, then the

**space**-

**time**must be one of the Kerr-Newman solutions. The closeness to the Kerr-Newman family is measured by the smallness of a pair of Mars-Simon type tensors, which were introduced by Wong in \cite{Wong_09} to detect the Kerr-Newmann family.

7/10 relevant

arXiv

Ofdm-based optical spatial modulation

**space**-

**time**block coding (STBC)-MIMO. Expand abstract.

**time**while the rest of them remain silent. The index of the active transmitter carries information. This spatial information is in addition to the data carried by the constellation symbols in the signal domain. Therefore, SM increases the transmission rate of the communication system compared to single-input-single-output and

**space**-

**time**block coding (STBC)-MIMO. For signal domain data encoding, orthogonal frequency division multiplexing (OFDM) has been widely adopted. The key benefits in multi-carrier intensity-modulation and direct-detection (IM/DD) systems are: i) the capability to achieve high spectral efficiency and ii) the ability to effectively mitigate direct-current (DC) wander effects and the impact of ambient light. However, current off-the shelf light emitting diodes (LEDs) which are used as transmit entities are primarily bandwidth limited. Thus, there are benefits of combining SM and OFDM to enhance transmission speeds while maintaining low complexity. In this paper, the two most common OFDM-based SM types, namely frequency domain SM (FD-SM) and

**time**domain SM (TD-SM), are investigated for optical wireless communications (OWC). Moreover, proof-ofconcept experimental results are presented to showcase practical feasibility of both techniques. The obtained results are also compared with Monte Carlo simulations. The results show that TDSM with an optimal maximum-a-posteriori-probability (MAP) detector significantly outperforms FD-SM. It can be inferred from the results that TD SM is a strong candidate among OFDM-based optical SM systems for future optical IM/DD wireless communication systems.

4/10 relevant

arXiv

Invariant sub**spaces** and exact solutions for some types of scalar and
coupled **time**-**space** fractional diffusion equations

**time**-

**space**(i) fractional diffusion-convection equation, (ii) fractional reaction-diffusion equation, (iii) fractional diffusion equation with source term, (iv) two-coupled system of the fractional diffusion equation, (v) two-coupled system... Expand abstract.

**time**-

**space**fractional partial differential equations. The effectiveness and applicability of the method have been illustrated through

**time**-

**space**(i) fractional diffusion-convection equation, (ii) fractional reaction-diffusion equation, (iii) fractional diffusion equation with source term, (iv) two-coupled system of the fractional diffusion equation, (v) two-coupled system of fractional stationary transonic plane-parallel gas flow equation and (vi) three-coupled system of fractional Hirota-Satsuma KdV equation. Also, we explicitly presented how to derive more than one exact solution of the equations as mentioned above using the invariant subspace method.

4/10 relevant

arXiv

Analysis of amplification mechanisms and cross-frequency interactions in nonlinear flows via the harmonic resolvent

**time**scales. More specifically, we consider a periodically

**time**-varying base flow, and perform a frequency-domain analysis of periodic perturbations about this base flow; the response of these perturbations is governed by the harmonic resolvent, which is a linear operator similar to the harmonic transfer function introduced by Wereley (1991). This approach makes it possible to explicitly capture the triadic interactions that are responsible for the energy transfer between different

**time**scales in the flow. For instance, perturbations at frequency $\alpha$ are coupled with perturbations at frequency $\omega$ through the base flow at frequency $\omega-\alpha$. We draw a connection with resolvent analsyis, which is a special case of the harmonic resolvent when evaluated about a steady base flow. We show that the left and right singular vectors of the harmonic resolvent are the optimal response and forcing modes, which can be understood as full spatio-temporal signals that reveal

**space**-

**time**amplification characteristics of the flow. We illustrate the method on examples, including a three-dimensional system of ordinary differential equations and the flow over an airfoil at near-stall angle of attack.

4/10 relevant

arXiv

LL/SC and Atomic Copy: Constant **Time**, **Space** Efficient Implementations
using only pointer-width CAS

**time**either use unbounded sequence numbers (and thus base objects of unbounded size), or require $\Omega(MP)$

**space**for $M$ LL/SC object (where $P$ is the number of processes). We present a constant

**time**implementation of $M$ LL/SC objects using only $\Theta(M+P^2)$

**space**and requiring only pointer-sized CAS objects. Our implementation can also be used to implement $L$-word $LL/SC$ objects in $\Theta(L)$

**time**(for both $LL$ and $SC$) and $\Theta((M+P^2)L)$

**space**. We focus on the setting where each process can have at most one LL/SC pair at a

**time**. To support $k$ overlapping LL/SC pairs per process, our algorithms incur an extra factor of $k$ in their

**space**usage. To achieve these bounds, we begin by implementing a new primitive called Single-Writer Copy which takes a pointer to a word sized memory location and atomically copies its contents into another memory location. The only restriction is that the destination of the copy must be single-writer, which means that only one process is allowed to write/copy into it. We believe this primitive will be very useful in designing other concurrent algorithms as well.

4/10 relevant

arXiv

New structures to solve aggregated queries for trips over public transportation networks

**times**. Expand abstract.

**time**for each stop. In addition, each vehicle journey follows exactly the sequence of stops corresponding to its line, which makes it unnecessary to represent that sequence for each journey. To solve data management for transportation systems, we designed a conceptual model that gave us a better insight into this data domain and allowed us the definition of relevant terms and the detection of redundancy sources among those data. Then, we designed two compact representations focused on users' trips (TTCTR) and on vehicle trips (AcumM), respectively. Each approach owns some strengths and is able to answer some queries efficiently. We include experimental results over synthetic trips generated from accurate schedules obtained from a real network description (from the bus transportation system of Madrid) to show the space/time trade-off of both approaches. We considered a wide range of different queries about the use of the transportation network such as counting-based or aggregate queries regarding the load of any line of the network at different

**times**.

4/10 relevant

arXiv

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