On admissibility criteria for weak solutions of the Euler equations

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique in more than one space dimension.Comment: 33 pages, 1 figure; v2: 35 pages, corrected typos, clarified proof

Oculomotoric Biometric Identification under the Influence of Alcohol and Fatigue

Patterns of micro- and macro-movements of the eyes are highly individual and can serve as a biometric characteristic. It is also known that both alcohol inebriation and fatigue can reduce saccadic velocity and accuracy. This prompts the question of whether changes of gaze patterns caused by alcohol consumption and fatigue impact the accuracy of oculomotoric biometric identification. We collect an eye tracking data set from 66 participants in sober, fatigued and alcohol-intoxicated states. We find that after enrollment in a rested and sober state, identity verification based on a deep neural embedding of gaze sequences is significantly less accurate when probe sequences are taken in either an inebriated or a fatigued state. Moreover, we find that fatigue and intoxication appear to randomize gaze patterns: when the model is fine-tuned for invariance with respect to inebriation and fatigue, and even when it is trained exclusively on inebriated training person, the model still performs significantly better for sober than for sleep-deprived or intoxicated subjects

Características fenotípicas de 44 progênies de Maytenus ilicifolia Mart. ex Reiss. cultivadas no município de Ponta Grossa, PR.

Resumo

Catastrophic Phase Transitions and Early Warnings in a Spatial Ecological Model

Gradual changes in exploitation, nutrient loading, etc. produce shifts between alternative stable states (ASS) in ecosystems which, quite often, are not smooth but abrupt or catastrophic. Early warnings of such catastrophic regime shifts are fundamental for designing management protocols for ecosystems. Here we study the spatial version of a popular ecological model, involving a logistically growing single species subject to exploitation, which is known to exhibit ASS. Spatial heterogeneity is introduced by a carrying capacity parameter varying from cell to cell in a regular lattice. Transport of biomass among cells is included in the form of diffusion. We investigate whether different quantities from statistical mechanics -like the variance, the two-point correlation function and the patchiness- may serve as early warnings of catastrophic phase transitions between the ASS. In particular, we find that the patch-size distribution follows a power law when the system is close to the catastrophic transition. We also provide links between spatial and temporal indicators and analyze how the interplay between diffusion and spatial heterogeneity may affect the earliness of each of the observables. We find that possible remedial procedures, which can be followed after these early signals, are more effective as the diffusion becomes lower. Finally, we comment on similarities and differences between these catastrophic shifts and paradigmatic thermodynamic phase transitions like the liquid-vapour change of state for a fluid like water

Singular and regular solutions of a non-linear parabolic system

We study a dissipative nonlinear equation modelling certain features of the Navier-Stokes equations. We prove that the evolution of radially symmetric compactly supported initial data does not lead to singularities in dimensions $n\leq 4$. For dimensions $n>4$ we present strong numerical evidence supporting existence of blow-up solutions. Moreover, using the same techniques we numerically confirm a conjecture of Lepin regarding existence of self-similar singular solutions to a semi-linear heat equation.Comment: 16 page

Pre-Trained Language Models Augmented with Synthetic Scanpaths for Natural Language Understanding

Human gaze data offer cognitive information that reflects natural language comprehension. Indeed, augmenting language models with human scanpaths has proven beneficial for a range of NLP tasks, including language understanding. However, the applicability of this approach is hampered because the abundance of text corpora is contrasted by a scarcity of gaze data. Although models for the generation of human-like scanpaths during reading have been developed, the potential of synthetic gaze data across NLP tasks remains largely unexplored. We develop a model that integrates synthetic scanpath generation with a scanpath-augmented language model, eliminating the need for human gaze data. Since the model's error gradient can be propagated throughout all parts of the model, the scanpath generator can be fine-tuned to downstream tasks. We find that the proposed model not only outperforms the underlying language model, but achieves a performance that is comparable to a language model augmented with real human gaze data. Our code is publicly available.Comment: Pre-print for EMNLP 202