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Even though power-law or close-to-power-law degree distributions are ubiquitously observed in a great variety of large real networks, the mathematically satisfactory treatment of random power-law graphs satisfying basic statistical…
The increasing demand for electricity and the aging infrastructure of power distribution systems have raised significant concerns about future system reliability. Failures in distribution systems, closely linked to system usage and…
Temperature scaling is a popular technique for tuning the sharpness of a model distribution. It is used extensively for sampling likely generations and calibrating model uncertainty, and even features as a controllable parameter to many…
Climate downscaling is a crucial technique within climate research, serving to project low-resolution (LR) climate data to higher resolutions (HR). Previous research has demonstrated the effectiveness of deep learning for downscaling tasks.…
In this paper, we propose a robust data-driven process model whose hyperparameters are robustly estimated using the Schweppe-type generalized maximum likelihood estimator. The proposed model is trained on recorded time-series data of…
We review recent results on the appearance of long-term persistence in climatic records and their relevance for the evaluation of global climate models and rare events.The persistence can be characterized, for example, by the correlation…
We study the sparse entropy-regularized reinforcement learning (ERL) problem in which the entropy term is a special form of the Tsallis entropy. The optimal policy of this formulation is sparse, i.e.,~at each state, it has non-zero…
Modeling financial markets based on empirical data poses challenges in selecting the most appropriate models. Despite the abundance of empirical data available, researchers often face difficulties in identifying the best-fitting model.…
The diffusion of ideas and language in society has conventionally been described by S-shaped models, such as the logistic curve. However, the role of sub-exponential growth -- a slower-than-exponential pattern known in epidemiology -- has…
Fast approximations of power flow results are beneficial in power system planning and live operation. In planning, millions of power flow calculations are necessary if multiple years, different control strategies or contingency policies are…
It is of growing concern to ensure the resilience in electricity infrastructure systems to extreme weather events with the help of appropriate hardening measures and new operational procedures. An effective mitigation strategy requires a…
Extreme weather can substantially change electricity consumption behavior, causing load curves to exhibit sharp spikes and pronounced volatility. If forecasts are inaccurate during those periods, power systems are more likely to face supply…
Modelling of precipitation, including extremes, is important for hydrological and agricultural applications. Traditionally, because of large sample properties for data over a large threshold value, generalised Pareto (GP) distributions are…
The z-transform technique is used to investigate the model for distribution of high-tax payers, which is proposed by two of the authors (K. Y and S. M) and others. Our analysis shows an asymptotic power-law of this model with the exponent…
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and the…
Training large models is both resource-intensive and time-consuming, making it crucial to understand the quantitative relationship between model performance and hyperparameters. In this paper, we present an empirical law that describes how…
We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary…
In this paper, we investigate the scaling limit of heavy-tailed nearly unstable cumulative INAR($\infty$) processes. These processes exhibit a power-law tail of the form $n^{-(1+\alpha)}$ for $\alpha \in (\frac{1}{2}, 1)$, and the $\ell^1$…
We presents results of joint modeling of the probability distribution function (PDF) and the one-dimensional power spectrum (PS) of the Lya forest flux decrement. The sensitivity of these statistical measures to the shape and amplitude of…
In this letter we propose a method for sparse allocation of resources to control spreading processes -- such as epidemics and wildfires -- using convex optimization, in particular exponential cone programming. Sparsity of allocation has…