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Power consumption is a critical consideration in high performance computing systems and it is becoming the limiting factor to build and operate Petascale and Exascale systems. When studying the power consumption of existing systems running…
Understanding the properties of response time distributions is a long-standing problem in cognitive science. We provide a tutorial overview of several contemporary models that assume power law scaling is a plausible description of the…
Cumulative prospect theory (CPT) is known to model human decisions well, with substantial empirical evidence supporting this claim. CPT works by distorting probabilities and is more general than the classic expected utility and coherent…
Reinforcement Learning (RL) enhances LLM reasoning, yet a paradox emerges as models scale: strong base models saturate standard benchmarks (e.g., MATH), yielding correct but homogeneous solutions. In such environments, the lack of failure…
Model pruning is a popular approach to enable the deployment of large deep learning models on edge devices with restricted computational or storage capacities. Although sparse models achieve performance comparable to that of their dense…
Power-law probability distributions are widely used to model extreme statistical events in complex systems, with applications to a vast array of natural phenomena ranging from earthquakes to stock market crashes to pandemics. We show that…
A key strategy in societal adaptation to climate change is using alert systems to prompt preventative action and reduce the adverse health impacts of extreme heat events. This paper implements and evaluates reinforcement learning (RL) as a…
Low voltage (LV) distribution transformers face accelerating demand growth while replacement lead times and costs continue to rise, making improved utilisation of existing assets essential. Static and conservative protection devices (PDs)…
Traditional scaling laws in natural language processing suggest that increasing model size and training data enhances performance. However, recent studies reveal deviations, particularly in large language models, where performance…
An exclusion particle model is considered as a highly simplified model of a limit order market. Its price behavior reproduces the well known crossover from over-diffusion (Hurst exponent H>1/2) to diffusion (H=1/2) when the time horizon is…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
This study introduces adaptive robust optimization (ARO) and adaptive robust stochastic optimization (ARSO) approaches to address long- and short-term uncertainties in the optimal sizing and placement of distributed energy resources in…
Power laws have been found to describe a wide variety of natural (physical, biological, astronomic, meteorological, geological) and man-made (social, financial, computational) phenomena over a wide range of magnitudes, although their…
The future power grid may rely on distributed optimization to determine the set-points for huge numbers of distributed energy resources. There has been significant work on applying distributed algorithms to optimal power flow (OPF)…
In this paper we revisit random linear under-determined systems with sparse solutions. We consider $\ell_1$ optimization heuristic known to work very well when used to solve these systems. A collection of fundamental results that relate to…
Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and…
Many natural processes exhibit power-law behavior. The power-law exponent is linked to the underlying physical process and therefore its precise value is of interest. With respect to the energy content of nanoflares, for example, a…
We provide a quantitative analysis of the phenomenon of crowding of near-extreme events by computing exactly the density of states (DOS) near the maximum of a set of independent and identically distributed random variables. We show that the…
Electrical Distribution Systems are extensively penetrated with Distributed Energy Resources (DERs) to cater the energy demands with the general perception that it enhances the system's resilience. However, integration of DERs may adversely…