Abstract Intermediate dimensions were recently introduced by Falconer et al. (Math Z 296:813–830, 2020) to interpolate between the Hausdorff and box-counting dimensions. In this paper, we show that for every subset E of symbolic space, intermediate projections under typical self-affine coding maps are constant given formulas in terms capacities. Moreover, extend results generalized Banaji (Monatsh Math 202: 465–506, 2023) several settings, including orthogonal Euclidean spaces images...

Social networks represent complex ecosystems where the interactions between users or groups play a pivotal role in information dissemination, opinion formation, and social interactions. Effectively harnessing event sequence data within to unearth among has persistently posed challenging frontier realm of point processes. Current deep process models face inherent limitations context networks, constraining both their interpretability expressive power. These encounter challenges capturing often...

Abstract We present a bee foraging behavior-driven mutational salp swarm algorithm (BMSSA) based on an improved strategy and unscented mutation strategy. The is leveraged in the follower location update phase to break fixed range search of algorithm, while optimal solution employed enhance quality solution. Extensive experimental results public CEC 2014 benchmark functions validate that proposed BMSSA performs better than nine well-known metaheuristic methods seven state-of-the-art...

In classical Hawkes process, the baseline intensity and triggering kernel are assumed to be a constant parametric function respectively, which limits model flexibility. To generalize it, we present fully Bayesian nonparametric model, namely Gaussian process modulated propose an EM-variational inference scheme. this transformation of is used as prior on kernel. By introducing latent branching structure, decoupled variational scheme embedded into EM framework naturally. We also provide series...

In this paper, we provide an algorithm to estimate from below the dimension of self-similar measures with overlaps. As application, show that for any β ∈ ( 1 , 2 ) $ \beta \in (1,2)$ Bernoulli convolution μ \mu _{\beta }$ satisfies dim ⩾ 0.98040856 \begin{equation*}\hskip7pc \dim (\mu })\geqslant 0.98040856,\hskip-7pc\vspace*{-6pt} \end{equation*} which improves a previous uniform lower bound 0.82 obtained by Hare and Sidorov (Exp. Math. 27 (2018), no. 4, 414–418). This new is very close...

Let $ \mu be the self-similar measure associated with a homogeneous iterated function system \Phi = \{ \lambda x + t_j \}_{j=1}^m on ${\Bbb R}$ and probability vector (p_{j})_{j=1}^m$, where $0\neq \lambda\in (-1,1)$ $t_j\in {\Bbb R}$. Recently by modifying arguments of Varj\'u (2019), Rapaport (2024) showed that if $t_1,\ldots, t_m$ are rational numbers $0<\lambda<1$, then $$ \dim =\min\Big 1, \; \frac{\sum_{j=1}^m p_{j}\log p_{j}}{ \log |\lambda| }\Big\}$$ unless has exact overlaps. In...

Imaging logging is an important technical means in evaluation of complex reservoirs. Through imaging logging, a two-dimensional image the resistivity distribution around well can be obtained, which used to evaluate development wall fractures and caves formation sedimentary structure. However, due characteristics instruments, blank strips will appear on image, increases difficulty computer processing electrical data. The current repair method existing neural network are not effective enough...

Existing permanental processes often impose constraints on kernel types or stationarity, limiting the model's expressiveness. To overcome these limitations, we propose a novel approach utilizing sparse spectral representation of nonstationary kernels. This technique relaxes and allowing for more flexible modeling while reducing computational complexity to linear level. Additionally, introduce deep variant by hierarchically stacking multiple feature mappings, further enhancing expressiveness...

In this paper, we provide an algorithm to estimate from below the dimension of self-similar measures with overlaps. As application, show that for any $ β\in(1,2) $, Bernoulli convolution μ_β$ satisfies \[ \dim (μ_β) \geq 0.9804085,\] which improves a previous uniform lower bound $0.82$ obtained by Hare and Sidorov \cite{HareSidorov2018}. This new is very close known numerical approximation 0.98040931953\pm 10^{-11}$ $\dim μ_{β_3}$, where β_{3} \approx 1.839286755214161$ largest root...

In this paper, we consider the sigmoid Gaussian Hawkes process model: baseline intensity and triggering kernel of are both modeled as transformation random trajectories drawn from processes (GP). By introducing auxiliary latent variables (branching structure, Pólya-Gamma marked Poisson processes), likelihood is converted to two decoupled components with a form which allows for an efficient conjugate analytical inference. Using augmented likelihood, derive expectation-maximization (EM)...

Hawkes process provides an effective statistical framework for analyzing the time-dependent interaction of neuronal spiking activities. Although utilized in many real applications, classic is incapable modelling inhibitory interactions among neurons. Instead, nonlinear allows a more flexible influence pattern with excitatory or interactions. In this paper, three sets auxiliary latent variables (P\'{o}lya-Gamma variables, marked Poisson processes and sparsity variables) are augmented to make...