The Kato Square Root Problem for Mixed Boundary Conditions

We consider the negative Laplacian subject to mixed boundary conditions on a bounded domain. We prove under very general geometric assumptions that slightly above the critical exponent $\frac{1}{2}$ its fractional power domains still coincide with suitable Sobolev spaces of optimal regularity. In combination with a reduction theorem recently obtained by the authors, this solves the Kato Square Root Problem for elliptic second order operators and systems in divergence form under the same geometric assumptions.Comment: Inconsistencies in Section 6 remove

Green Agendas and White Markets: The Coloniality of Agroecology in Senegal

Development actors in West Africa have been promoting agroecological farming as a solution to combat climate change and to create more sovereign food systems that enhance the autonomy of local smallholders. However, there is a lack of empirical evidence regarding the actual implementation of such programs and their potential to empower smallholders, especially in the West African region. Drawing on co-produced knowledge from anthropological fieldwork in Western Senegal, the case study of an alternative food network explores the interlinkages between the promotion of agroecology, anti-migration policies, and unequal power and market relations. Informed by decolonial political ecologies, the analysis reveals different layers of coloniality which complicate embodied effects on horticultural smallholders. The authors conclude that instead of fostering the emancipation of smallholders, development actors promote a labor-intensive and unprofitable way of farming that exploits local resources for the sake of green agendas and white markets. This article highlights the need for a critical reflection on the potential limitations of agroecology and calls for a more nuanced approach that considers the complex realities of smallholders in West Africa

The Kato Square Root Problem follows from an extrapolation property of the Laplacian

On a domain Ω ⊆ _ Rd we consider second-order elliptic systems in divergence-form with bounded complex coefficients, realized via a sesquilinear form with domain H1/0 (Ω) ⊆ V ⊆ H1 (Ω). Under very mild assumptions on Ω and V we show that the solution to the Kato Square Root Problem for such systems can be deduced from a regularity result for the fractional powers of the negative Laplacian in the same geometric setting. This extends earlier results of McIntosh [25] and Axelsson-Keith-McIntosh [6] to non-smooth coefficients and domains

Revisiting the Uniform Information Density Hypothesis

The uniform information density (UID) hypothesis posits a preference among language users for utterances structured such that information is distributed uniformly across a signal. While its implications on language production have been well explored, the hypothesis potentially makes predictions about language comprehension and linguistic acceptability as well. Further, it is unclear how uniformity in a linguistic signal -- or lack thereof -- should be measured, and over which linguistic unit, e.g., the sentence or language level, this uniformity should hold. Here we investigate these facets of the UID hypothesis using reading time and acceptability data. While our reading time results are generally consistent with previous work, they are also consistent with a weakly super-linear effect of surprisal, which would be compatible with UID's predictions. For acceptability judgments, we find clearer evidence that non-uniformity in information density is predictive of lower acceptability. We then explore multiple operationalizations of UID, motivated by different interpretations of the original hypothesis, and analyze the scope over which the pressure towards uniformity is exerted. The explanatory power of a subset of the proposed operationalizations suggests that the strongest trend may be a regression towards a mean surprisal across the language, rather than the phrase, sentence, or document -- a finding that supports a typical interpretation of UID, namely that it is the byproduct of language users maximizing the use of a (hypothetical) communication channel

Eyettention: An Attention-based Dual-Sequence Model for Predicting Human Scanpaths during Reading

Eye movements during reading offer insights into both the reader's cognitive processes and the characteristics of the text that is being read. Hence, the analysis of scanpaths in reading have attracted increasing attention across fields, ranging from cognitive science over linguistics to computer science. In particular, eye-tracking-while-reading data has been argued to bear the potential to make machine-learning-based language models exhibit a more human-like linguistic behavior. However, one of the main challenges in modeling human scanpaths in reading is their dual-sequence nature: the words are ordered following the grammatical rules of the language, whereas the fixations are chronologically ordered. As humans do not strictly read from left-to-right, but rather skip or refixate words and regress to previous words, the alignment of the linguistic and the temporal sequence is non-trivial. In this paper, we develop Eyettention, the first dual-sequence model that simultaneously processes the sequence of words and the chronological sequence of fixations. The alignment of the two sequences is achieved by a cross-sequence attention mechanism. We show that Eyettention outperforms state-of-the-art models in predicting scanpaths. We provide an extensive within- and across-data set evaluation on different languages. An ablation study and qualitative analysis support an in-depth understanding of the model's behavior

Eye-tracking based classification of Mandarin Chinese readers with and without dyslexia using neural sequence models

Eye movements are known to reflect cognitive processes in reading, and psychological reading research has shown that eye gaze patterns differ between readers with and without dyslexia. In recent years, researchers have attempted to classify readers with dyslexia based on their eye movements using Support Vector Machines (SVMs). However, these approaches (i) are based on highly aggregated features averaged over all words read by a participant, thus disregarding the sequential nature of the eye movements, and (ii) do not consider the linguistic stimulus and its interaction with the reader’s eye movements. In the present work, we propose two simple sequence models that process eye movements on the entire stimulus without the need of aggregating features across the sentence. Additionally, we incorporate the linguistic stimulus into the model in two ways---contextualized word embeddings and manually extracted linguistic features. The models are evaluated on a Mandarin Chinese dataset containing eye movements from children with and without dyslexia. Our results show that (i) even for a logographic script such as Chinese, sequence models are able to classify dyslexia on eye gaze sequences, reaching state-of-the-art performance, and (ii) incorporating the linguistic stimulus does not help to improve classification performance

Extensive geothermal heat use in cities energetic and economic comparison of options for thermal regeneration of the ground

Geothermal energy as a heat source for heat pumps is increasingly unused in the city of Zürich. However, as indicated by other authors, the renewable potential for shallow geothermal heat use is limited due to the fact that natural regeneration in the absence of ground water flow is slow. Constant heat extractions from dense geothermal heat pump installations continuously cool down the affected ground layer.. In this case boreholes have to be drilled deeper or regenerated in order to avoid freezing around the borehole. The aim of this simulation study is to find the most economic geothermal heat pump concept, which does not lead to borehole freezing after 50 years of operation in areas with dense installations (an exemplary mean geothermal heat extraction of 35kWh/m2/a was supposed for this this study). Therefor a multi-family house with a standard ground source heat pump was simulated for a period of 50 years in Polysun. Various solar concepts, an air heat exchanger concept, a geo cooling concept and also a system without regeneration were added to the system. These concepts were compared under the assumption that all neighboring installations are using an equivalent regeneration strategy as the simulated system For the different system concepts, highly variable total borehole length were needed to avoid freezing, reaching from 1020m for a system with a large glazed collector field to 2160m for the un-regenerated case. The heat cost of the analyzed system concepts was in the range of 21- 27 Rp/kWh. The most cost-effective system concepts according to this analysis are the air heat exchanger or unglazed collectors. Increasing the total borehole meters was not only one of the most expensive options, but also the least sustainable, since the continuation of ground tem-perature decrease after 50 years was more pronounced with this option than for any other option

ScanDL: A Diffusion Model for Generating Synthetic Scanpaths on Texts

Eye movements in reading play a crucial role in psycholinguistic research studying the cognitive mechanisms underlying human language processing. More recently, the tight coupling between eye movements and cognition has also been leveraged for language-related machine learning tasks such as the interpretability, enhancement, and pre-training of language models, as well as the inference of reader- and text-specific properties. However, scarcity of eye movement data and its unavailability at application time poses a major challenge for this line of research. Initially, this problem was tackled by resorting to cognitive models for synthesizing eye movement data. However, for the sole purpose of generating human-like scanpaths, purely data-driven machine-learning-based methods have proven to be more suitable. Following recent advances in adapting diffusion processes to discrete data, we propose ScanDL, a novel discrete sequence-to-sequence diffusion model that generates synthetic scanpaths on texts. By leveraging pre-trained word representations and jointly embedding both the stimulus text and the fixation sequence, our model captures multi-modal interactions between the two inputs. We evaluate ScanDL within- and across-dataset and demonstrate that it significantly outperforms state-of-the-art scanpath generation methods. Finally, we provide an extensive psycholinguistic analysis that underlines the model's ability to exhibit human-like reading behavior. Our implementation is made available at https://github.com/DiLi-Lab/ScanDL.Comment: EMNLP 202