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This paper reveals a novel linear characteristic exclusive to transformer decoders, including models such as GPT, LLaMA, OPT, BLOOM and others. We analyze embedding transformations between sequential layers, uncovering a near-perfect linear…
In many engineering systems operating with a working fluid, the best efficiency is reached close to a condition of flow separation, which makes its prediction very crucial in industry. Providing that wall-based quantities can be measured,…
Statistical image reconstruction in X-Ray computed tomography yields large-scale regularized linear least-squares problems with nonnegativity bounds, where the memory footprint of the operator is a concern. Discretizing images in…
This paper is devoted to the asymptotic analysis of strongly rotating and stratified fluids, under a $\beta$-plane approximation, and within a three-dimensional spatial domain with strong topography. Our purpose is to propose a linear…
Optimal transitional mechanisms are analysed for an incompressible shear layer developing over a short, pressure gradient-induced laminar separation bubble (LSB) with peak reversed flow of 2%. Although the bubble remains globally stable,…
Analyzing the similarity of internal representations has been an important technique for understanding the behavior of deep neural networks. Most existing methods for analyzing the similarity between representations of high dimensions, such…
Augmented reality applications are beginning to change the way sports are broadcast, providing richer experiences and valuable insights to fans. The first step of augmented reality systems is camera calibration, possibly based on detecting…
To address the challenges of low detection accuracy and high false positive rates of transmission lines in UAV (Unmanned Aerial Vehicle) images, we explore the linear features and spatial distribution. We introduce an enhanced stochastic…
Liquid composites moulding is an important manufacturing technology for fibre reinforced composites, due to its cost-effectiveness. Challenges lie in the optimisation of the process due to the lack of understanding of key characteristic of…
We present a novel multiscale framework for analyzing sequences of probability measures in Wasserstein spaces over Euclidean domains. Exploiting the intrinsic geometry of optimal transport, we construct a multiscale transform applicable to…
The dropwise condensation underneath a horizontal super-hydrophobic surface having unidirectional wettability gradient is modeled with implication to enhance the rate of condensation. The mathematical model includes nucleation, growth by…
We propose a new approach to unambiguous determination of parameters of positive and negative electric streamer discharges. From hydrodynamic equations, in the assumption of a solution in the shape of a streamer, it is possible to derive…
Pretrained molecular encoders have become indispensable in computational chemistry for tasks such as property prediction and molecular generation. However, the standard practice of relying solely on final-layer embeddings for downstream…
Aligned superhydrophobic surfaces with the same texture orientation reduce drag in the channel and generate secondary flows transverse to the direction of the applied pressure gradient. Here we show that a transverse shear can be easily…
The transport properties on the two-dimensional surface of coupled multilayer heterostructures are studied in the integer quantum Hall states. We emphasize the criticality of the surface state and the phase coherent transport properties in…
Swimming cells often have to self-propel through fluids displaying non-Newtonian rheology. While past theoretical work seems to indicate that stresses arising from complex fluids should systematically hinder low-Reynolds number locomotion,…
We study the effect of an inhomogeneous gas density on positive streamer discharges in air using a 3D fluid model with stochastic photoionization, generalizing earlier work with a 2D axisymmetric model by Starikovskiy and Aleksandrov (2019…
We develop numerical methods to simulate the fluid-mechanical erosion of many bodies in two-dimensional Stokes flow. The broad aim is to simulate the erosion of a porous medium (e.g. groundwater flow) with grain-scale resolution. Our fluid…
This work deals with the closed-loop control of streaky structures induced by free-stream turbulence in a zero-pressure gradient, transitional boundary layer, by means of localized sensors and actuators. A linear quadratic gaussian…
Streamer discharges are thin plasma channels that precede lightning and sparks. They usually evolve in bundles as stochastic tree-like structures and are inherently difficult to model due to their multiscale nature. In this paper, we…