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Text entry with word-gesture keyboards (WGK) is emerging as a popular method and becoming a key interaction for Extended Reality (XR). However, the diversity of interaction modes, keyboard sizes, and visual feedback in these environments introduces divergent word-gesture trajectory data patterns, thus leading to complexity in decoding trajectories into text. Template-matching decoding methods, such as SHARK^2, are commonly used for these WGK systems because they are easy to implement and configure. However, these methods are susceptible to decoding inaccuracies for noisy trajectories. While conventional neural-network-based decoders (neural decoders) trained on word-gesture trajectory data have been proposed to improve accuracy, they have their own limitations: they require extensive data for training and deep-learning expertise for implementation. To address these challenges, we propose a novel solution that combines ease of implementation with high decoding accuracy: a generalizable neural decoder enabled by pre-training on large-scale coarsely discretized word-gesture trajectories. This approach produces a ready-to-use WGK decoder that is generalizable across mid-air and on-surface WGK systems in augmented reality (AR) and virtual reality (VR), which is evident by a robust average Top-4 accuracy of 90.4% on four diverse datasets. It significantly outperforms SHARK^2 with a 37.2% enhancement and surpasses the conventional neural decoder by 7.4%. Moreover, the Pre-trained Neural Decoder's size is only 4 MB after quantization, without sacrificing accuracy, and it can operate in real-time, executing in just 97 milliseconds on Quest 3.

Monitoring plankton distribution, particularly harmful phytoplankton, is vital for preserving aquatic ecosystems, regulating the global climate, and ensuring environmental protection. Traditional methods for monitoring are often time-consuming, expensive, error-prone, and unsuitable for large-scale applications, highlighting the need for accurate and efficient automated systems. In this study, we evaluate several state-of-the-art CNN models, including ResNet, ResNeXt, DenseNet, and EfficientNet, using three transfer learning approaches: linear probing, fine-tuning, and a combined approach, to classify eleven harmful phytoplankton genera from microscopic images. The best performance was achieved by ResNet-50 using the fine-tuning approach, with an accuracy of 96.97%. The results also revealed that the models struggled to differentiate between four harmful phytoplankton types with similar morphological features., Comment: 8 pages, 5 figures

Social media images have proven to be a valuable source of information for understanding human interactions with important subjects such as cultural heritage, biodiversity, and nature, among others. The task of grouping such images into a number of semantically meaningful clusters without labels is challenging due to the high diversity and complex nature of the visual content in addition to their large volume. On the other hand, recent advances in Large Visual Models (LVMs), Large Language Models (LLMs), and Large Visual Language Models (LVLMs) provide an important opportunity to explore new productive and scalable solutions. This work proposes, analyzes, and compares various approaches based on one or more state-of-the-art LVM, LLM, and LVLM, for mapping social media images into a number of predefined classes. As a case study, we consider the problem of understanding the interactions between humans and nature, also known as Nature's Contribution to People or Cultural Ecosystem Services (CES). Our experiments show that the highest-performing approaches, with accuracy above 95%, still require the creation of a small labeled dataset. These include the fine-tuned LVM DINOv2 and the LVLM LLaVA-1.5 combined with a fine-tuned LLM. The top fully unsupervised approaches, achieving accuracy above 84%, are the LVLMs, specifically the proprietary GPT-4 model and the public LLaVA-1.5 model. Additionally, the LVM DINOv2, when applied in a 10-shot learning setup, delivered competitive results with an accuracy of 83.99%, closely matching the performance of the LVLM LLaVA-1.5., Comment: 17 pages, 9 figures

Pumpkin is a vital crop cultivated globally, and its productivity is crucial for food security, especially in developing regions. Accurate and timely detection of pumpkin leaf diseases is essential to mitigate significant losses in yield and quality. Traditional methods of disease identification rely heavily on subjective judgment by farmers or experts, which can lead to inefficiencies and missed opportunities for intervention. Recent advancements in machine learning and deep learning offer promising solutions for automating and improving the accuracy of plant disease detection. This paper presents a comprehensive analysis of state-of-the-art Convolutional Neural Network (CNN) models for classifying diseases in pumpkin plant leaves. Using a publicly available dataset of 2000 highresolution images, we evaluate the performance of several CNN architectures, including ResNet, DenseNet, and EfficientNet, in recognizing five classes: healthy leaves and four common diseases downy mildew, powdery mildew, mosaic disease, and bacterial leaf spot. We fine-tuned these pretrained models and conducted hyperparameter optimization experiments. ResNet-34, DenseNet-121, and EfficientNet-B7 were identified as top-performing models, each excelling in different classes of leaf diseases. Our analysis revealed DenseNet-121 as the optimal model when considering both accuracy and computational complexity achieving an overall accuracy of 86%. This study underscores the potential of CNNs in automating disease diagnosis for pumpkin plants, offering valuable insights that can contribute to enhancing agricultural productivity and minimizing economic losses., Comment: 10 pages, 8 figures

We consider the Cauchy problem in $\mathbb{R}^{n}$ for wave and beam equations with frictional, viscoelastic damping, and a new power nonlinearity. In addition to the solution and its total energy, we define the following quantity: $$Q[u](t):=\|u_{t}(t,\cdot)+(-\Delta)^{\sigma}u(t,\cdot)\|_{L^{2}(\mathbb{R}^{n})}.$$ Our aim is to show that the interaction between frictional and viscoelastic damping in a linear model leads to an exponential decay of $Q[u](t)$ as $t\to \infty$. This decay motivates us to define a new power nonlinearity of the form $N[u]:=|u_{t}+(-\Delta)^{\sigma}u|^{p}$. Surprisingly, $N[u]$ can be considered a small perturbation for any $p>1$, in the sense that, the decay estimates of the unique global solution, the total energy and $Q[u](t)$ coincide with those for solutions to the corresponding linear Cauchy problem with vanishing right-hand side., Comment: A new nonlinearity is defined

Our aim in this paper is to discuss the critical exponent in semi-linear structurally damped wave and beam equations with additional dispersion term. The special model we have in mind is $$ u_{tt}(t,x)+(-\Delta)^{\sigma}u(t,x)+(-\Delta)^{2\delta}u(t,x)+2(-\Delta)^{\delta}u_{t}(t,x)=\left|u(t,x)\right| ^{p} $$ where the initial displacement $u(0,x)=u_{0}(x)$, the initial velocity $u_{t}(0,x)=u_{1}(x)$ and the parameters $ t\in [0,\infty)$, $x\in \mathbb{R}^{n}$, $\sigma\geq 1$, $\delta\in(0,\frac{\sigma}{2})$, $p>1$. The solution to the linear equation at low frequency region involves an interplay of diffusion and oscillation phenomena represented by a real-complex Fourier multiplier of the form $$m(t,\xi)=\frac{e^{-|\xi|^{2\delta}t\pm i|\xi|^{\sigma}t}}{2i|\xi|^{\sigma}}, \ \ \xi\in \mathbb{R}^{n}, \ \ i=\sqrt{-1}.$$ The scaling argument shows that the diffusive part leads to faster decay rates compared to the oscillatory one. This interplay creates a new gap in the critical exponent between the blow up (in finite time) result when $11+\frac{\sigma+2\delta}{n-\sigma}$ (super-critical case). We leave an open to show if this gap will be closed at least in low or high space dimensions because, to the best of authors knowledge, the necessary Fourier multiplier that leads to the sub-critical case does not explicitly appear in $m(t,\xi)$., Comment: Wave equation, beam equation, structural damping, dispersion terms, global existence, blow up, critical exponent

Monitoring the distribution and size of long-living large shrubs, such as junipers, is crucial for assessing the long-term impacts of global change on high-mountain ecosystems. While deep learning models have shown remarkable success in object segmentation, adapting these models to detect shrub species with polymorphic nature remains challenging. In this research, we release a large dataset of individual shrub delineations on freely available satellite imagery and use an instance segmentation model to map all junipers over the treeline for an entire biosphere reserve (Sierra Nevada, Spain). To optimize performance, we introduced a novel dual data construction approach: using photo-interpreted (PI) data for model development and fieldwork (FW) data for validation. To account for the polymorphic nature of junipers during model evaluation, we developed a soft version of the Intersection over Union metric. Finally, we assessed the uncertainty of the resulting map in terms of canopy cover and density of shrubs per size class. Our model achieved an F1-score in shrub delineation of 87.87% on the PI data and 76.86% on the FW data. The R2 and RMSE of the observed versus predicted relationship were 0.63 and 6.67% for canopy cover, and 0.90 and 20.62 for shrub density. The greater density of larger shrubs in lower altitudes and smaller shrubs in higher altitudes observed in the model outputs was also present in the PI and FW data, suggesting an altitudinal uplift in the optimal performance of the species. This study demonstrates that deep learning applied on freely available high-resolution satellite imagery is useful to detect medium to large shrubs of high ecological value at the regional scale, which could be expanded to other high-mountains worldwide and to historical and forthcoming imagery., Comment: 24 pages, 11 figures

We introduce a mathematical model in $\mathbb{R}^{n}$ for evolution equations with modified generalized Hartree nonlinearity given by $S_{\alpha,p,q}(u)=I_{\alpha}(|u|^{p+q}).$ One can see that this nonlinearity is not integrable due to the boundedness property of Riesz potential. In other words, we cannot deal with the Cauchy problem of semi-linear evolution equations with $S_{\alpha,p,q}(u)$ and $L^{1}$-initial velocity. We will show that $S_{\alpha,p,q}(u)$ produces the same semi-critical exponent that guarantees the global existence of small data solutions as in the well known generalized Hartree nonlinearity $H_{\alpha,p,q}(u)=|u|^{p}I_{\alpha}(|u|^{q})$ provided that the initial velocity belongs to $L^{m}(\mathbb{R}^{n})$, with $m>1$. We can expect a relation between some physical systems that are modeled and solved using Hartree nonlinearity and those in their modified form due to this coincidence property in the semi-critical exponent.

Remotely sensed data are dominated by mixed Land Use and Land Cover (LULC) types. Spectral unmixing (SU) is a key technique that disentangles mixed pixels into constituent LULC types and their abundance fractions. While existing studies on Deep Learning (DL) for SU typically focus on single time-step hyperspectral (HS) or multispectral (MS) data, our work pioneers SU using MODIS MS time series, addressing missing data with end-to-end DL models. Our approach enhances a Long-Short Term Memory (LSTM)-based model by incorporating geographic, topographic (geo-topographic), and climatic ancillary information. Notably, our method eliminates the need for explicit endmember extraction, instead learning the input-output relationship between mixed spectra and LULC abundances through supervised learning. Experimental results demonstrate that integrating spectral-temporal input data with geo-topographic and climatic information significantly improves the estimation of LULC abundances in mixed pixels. To facilitate this study, we curated a novel labeled dataset for Andalusia (Spain) with monthly MODIS multispectral time series at 460m resolution for 2013. Named Andalusia MultiSpectral MultiTemporal Unmixing (Andalusia-MSMTU), this dataset provides pixel-level annotations of LULC abundances along with ancillary information. The dataset (https://zenodo.org/records/7752348) and code (https://github.com/jrodriguezortega/MSMTU) are available to the public.