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We obtain new estimates - both upper and lower bounds - on the mean values of the Weyl sums over a small box inside of the unit torus. In particular, we refine recent conjectures of C. Demeter and B. Langowski (2022), and improve some of their results., 36 pages,3 figures

Inertial sensors are widely utilized in smartphones, drones, robots, and IoT devices, playing a crucial role in enabling ubiquitous and reliable localization. Inertial sensor-based positioning is essential in various applications, including personal navigation, location-based security, and human-device interaction. However, low-cost MEMS inertial sensors' measurements are inevitably corrupted by various error sources, leading to unbounded drifts when integrated doubly in traditional inertial navigation algorithms, subjecting inertial positioning to the problem of error drifts. In recent years, with the rapid increase in sensor data and computational power, deep learning techniques have been developed, sparking significant research into addressing the problem of inertial positioning. Relevant literature in this field spans across mobile computing, robotics, and machine learning. In this article, we provide a comprehensive review of deep learning-based inertial positioning and its applications in tracking pedestrians, drones, vehicles, and robots. We connect efforts from different fields and discuss how deep learning can be applied to address issues such as sensor calibration, positioning error drift reduction, and multi-sensor fusion. This article aims to attract readers from various backgrounds, including researchers and practitioners interested in the potential of deep learning-based techniques to solve inertial positioning problems. Our review demonstrates the exciting possibilities that deep learning brings to the table and provides a roadmap for future research in this field.

Self-supervised learning of egomotion and depth has recently attracted great attentions. These learning models can provide pose and depth maps to support navigation and perception task for autonomous driving and robots, while they do not require high-precision ground-truth labels to train the networks. However, monocular vision based methods suffer from pose scale-ambiguity problem, so that can not generate physical meaningful trajectory, and thus their applications are limited in real-world. We propose a novel self-learning deep neural network framework that can learn to estimate egomotion and depths with absolute metric scale from monocular images. Coarse depth scale is recovered via comparing point cloud data against a pretrained model that ensures the consistency of photometric loss. The scale-ambiguity problem is solved by introducing a novel two-stages coarse-to-fine scale recovery strategy that jointly refines coarse poses and depths. Our model successfully produces pose and depth estimates in global scale-metric, even in low-light condition, i.e. driving at night. The evaluation on the public datasets demonstrates that our model outperforms both representative traditional and learning based VOs and VIOs, e.g. VINS-mono, ORB-SLAM, SC-Learner, and UnVIO.

Self-supervised depth learning from monocular images normally relies on the 2D pixel-wise photometric relation between temporally adjacent image frames. However, they neither fully exploit the 3D point-wise geometric correspondences, nor effectively tackle the ambiguities in the photometric warping caused by occlusions or illumination inconsistency. To address these problems, this work proposes Density Volume Construction Network (DevNet), a novel self-supervised monocular depth learning framework, that can consider 3D spatial information, and exploit stronger geometric constraints among adjacent camera frustums. Instead of directly regressing the pixel value from a single image, our DevNet divides the camera frustum into multiple parallel planes and predicts the pointwise occlusion probability density on each plane. The final depth map is generated by integrating the density along corresponding rays. During the training process, novel regularization strategies and loss functions are introduced to mitigate photometric ambiguities and overfitting. Without obviously enlarging model parameters size or running time, DevNet outperforms several representative baselines on both the KITTI-2015 outdoor dataset and NYU-V2 indoor dataset. In particular, the root-mean-square-deviation is reduced by around 4% with DevNet on both KITTI-2015 and NYU-V2 in the task of depth estimation. Code is available at https://github.com/gitkaichenzhou/DevNet., Accepted by European Conference on Computer Vision 2022 (ECCV2022)

Anti-icing superhydrophobic surfaces have been a key research topic due to their potential application value in aviation, telecommunication, energy, etc. However, superhydrophobicity is easily lost during icing & melting cycles, where the water-repellent Cassie-Baxter state turns to the sticky Wenzel state. The reversible transition during icing & melting cycle without external assistance is challenging but vital for reliable anti-icing superhydrophobic performance, such a topic has rarely been reported. Here we demonstrate a spontaneous Wenzel to Cassie-Baxter dewetting transition during icing & melting cycle on well-designed superhydrophobic surfaces. Bubbles in ice droplets rapidly impact the micro-nano valleys under Marangoni force, prompting the continuous recovery of air pockets during melting processes. We establish models to confirm the bubbles movement broadens the dewetting conditions greatly and present three criteria for the dewetting transitions. This research deepens the understanding of wettability theory and extends the design of anti-icing superhydrophobic surfaces., Despite promising for anti-icing applications, structured superhydrophobic surfaces usually lose their hydrophobicity after a few icing/melting cycles. Here, authors investigate specific structured surfaces and air bubbles on frozen ice droplets to propose three criteria to enable dewetting transitions.

Additional file 15: Table S4. The possible TFO and TTS predicted for PLACT1 and IκBα promoter.

Additional file 7: Figure S5. hnRNPA1 is required for PLACT1-induced PDAC progression.

Additional file 10: Figure S8. PLACT1 forms a positive feedback loop with E2F1.

Additional file 9: Figure S7. PLACT1 forms triplexes with promoter sequences of IκBα and regulates its expression.

Given $00$. For any $t/2\le s, Comment: 18 pages

Additional file 1: Supplementary material and methods.

Additional file 2: Figure S1. The identification of PLACT1 in PDAC.

Additional file 3: Table S1. Univariate and multivariate analysis of disease-free survival in PDAC patients.

Accurate and robust localization is a fundamental need for mobile agents. Visual-inertial odometry (VIO) algorithms exploit the information from camera and inertial sensors to estimate position and translation. Recent deep learning based VIO models attract attentions as they provide pose information in a data-driven way, without the need of designing hand-crafted algorithms. Existing learning based VIO models rely on recurrent models to fuse multimodal data and process sensor signal, which are hard to train and not efficient enough. We propose a novel learning based VIO framework with external memory attention that effectively and efficiently combines visual and inertial features for states estimation. Our proposed model is able to estimate pose accurately and robustly, even in challenging scenarios, e.g., on overcast days and water-filled ground , which are difficult for traditional VIO algorithms to extract visual features. Experiments validate that it outperforms both traditional and learning based VIO baselines in different scenes., Comment: Accepted by IEEE Sensors Journal

Additional file 13: Table S3. Antibodies of experiments.

Additional file 5: Figure S3. PLACT1 enhances proliferation, migration, and invasion of PDAC cells.

Additional file 1: Fig. S1. Attributable fraction (AF) and numbers (AN) of extreme precipitation on outpatient visits for depression. Fig. S2. Sensitivity analysis when altering the degrees of freedom (df = 5–8) for controlling for the long-term trend and seasonality. Fig. S3. Sensitivity analysis when altering the degrees of freedom (df = 3–6) for controlling for mean temperature. Fig. S4. Sensitivity analysis when altering the degrees of freedom (df = 3–6) for controlling for relative humidity. Fig. S5. Sensitivity analysis when altering the degrees of freedom (df = 3–6) for controlling for the sunshine duration. Fig. S6. Relative risk and 95%CI of extreme precipitation on depression outpatient visits by adding other air pollutants in the sensitivity analysis. Fig. S7. Sensitivity analysis by changing the cut-off value of extreme precipitation in the model. Table S1. The AIC values of models for various lag period from lag1 to lag20. Table S2. The single-day effects of extreme precipitation on depression outpatient visits in different subgroups in Suzhou, China, with 95th percentile (13.13 mm) of precipitation relative to no precipitation. Table S3. Single-day and cumulative lag effects of extreme precipitation on depression outpatient visits at various lag days in Suzhou, China, with 95th percentile (13.13 mm) of precipitation relative to no precipitation.

We obtain new estimates on the maximal operator applied to the Weyl sums. We also consider the quadratic case (that is, Gauss sums) in more details. In wide ranges of parameters our estimates are optimal and match lower bounds. Our approach is based on a combination of ideas of Baker (2021) and Chen and Shparlinski (2020).

Deoxynivalenol (DON) is a cytotoxic mycotoxin that can cause cell damages. The main effect is to inhibit protein synthesis. Oxidative stress is one of the effects of DON. Selenium (Se) can ameliorate the cell damage caused by DON-induced oxidative stress, but it is unclear whether through selenoprotein glutathione peroxidase 1 (GPX1). We established GPX1-knockdown porcine spleen lymphocytes, and treated them with DON and Se. Untransfected porcine splenic lymphocytes (group P) and transfected cells (group M, GPX1 knockdown) were treated with or without DON (0.824, 0.412, 0.206, or 0.103 μg/mL, group D1-4), Se (Na2SeO3, 2 μM, group Se), or both (group SD1–4) for 6, 12, or 24 h. The cells were collected and the activities of SOD and CAT, levels of GSH, H2O2, malonaldehyde (MDA), total antioxidant capacity (T-AOC), and the inhibition of free hydroxyl radicals were determined. Levels of ROS were measured at 24 h. Compared with group P, the antioxidant capacity of group M was reduced. DON caused greater oxidative damage to the GPX1-knockdown porcine splenic lymphocytes than to the normal control cells. When Na2SeO3 was combined with DON, it reduced the damage in the GPX1-knockdown porcine splenic lymphocytes, but less effectively than in the normal porcine splenic lymphocytes.

We prove that the Hausdorff dimension of the set $\mathbf{x}\in [0,1)^d$, such that $$ \left|\sum_{n=1}^N \exp\left(2 \pi i\left(x_1n+\ldots+x_d n^d\right)\right) \right|\ge c N^{1/2} $$ holds for infinitely many natural numbers $N$, is at least $d-1/2d$ for $d \ge 3$ and at least $3/2$ for $d=2$, where $c$ is a constant depending only on $d$. This improves the previous lower bound of the first and third authors for $d\ge 3$. We also obtain similar bounds for the Hausdorff dimension of the set of large sums with monomials $xn^d$., Comment: All results of this preprint are now included, together with several other results, in 2011.09306 - "Metric theory of Weyl sums", by C. Chen, B. Kerr, J.Maynard, I. Shparlinski

Modern inertial measurements units (IMUs) are small, cheap, energy efficient, and widely employed in smart devices and mobile robots. Exploiting inertial data for accurate and reliable pedestrian navigation supports is a key component for emerging Internet-of-Things applications and services. Recently, there has been a growing interest in applying deep neural networks (DNNs) to motion sensing and location estimation. However, the lack of sufficient labelled data for training and evaluating architecture benchmarks has limited the adoption of DNNs in IMU-based tasks. In this paper, we present and release the Oxford Inertial Odometry Dataset (OxIOD), a first-of-its-kind public dataset for deep learning based inertial navigation research, with fine-grained ground-truth on all sequences. Furthermore, to enable more efficient inference at the edge, we propose a novel lightweight framework to learn and reconstruct pedestrian trajectories from raw IMU data. Extensive experiments show the effectiveness of our dataset and methods in achieving accurate data-driven pedestrian inertial navigation on resource-constrained devices., Comment: Accepted to IEEE Internet of Things Journal

Additional file 12: Table S2. Primer and probes of experiments.

Recent learning-based approaches have achieved impressive results in the field of single-shot camera localization. However, how best to fuse multiple modalities (e.g., image and depth) and to deal with degraded or missing input are less well studied. In particular, we note that previous approaches towards deep fusion do not perform significantly better than models employing a single modality. We conjecture that this is because of the naive approaches to feature space fusion through summation or concatenation which do not take into account the different strengths of each modality. To address this, we propose an end-to-end framework, termed VMLoc, to fuse different sensor inputs into a common latent space through a variational Product-of-Experts (PoE) followed by attention-based fusion. Unlike previous multimodal variational works directly adapting the objective function of vanilla variational auto-encoder, we show how camera localization can be accurately estimated through an unbiased objective function based on importance weighting. Our model is extensively evaluated on RGB-D datasets and the results prove the efficacy of our model. The source code is available at https://github.com/Zalex97/VMLoc.

Additional file 6: Figure S4. PLACT1 promotes proliferation, migration, and invasion of PDAC cells independent of KRAS/p53.

Additional file 14: Figure S9. Full uncut original pictures.

Modern inertial measurements units (IMUs) are small, cheap, energy efficient, and widely employed in smart devices and mobile robots. Exploiting inertial data for accurate and reliable pedestrian navigation supports is a key component for emerging Internet-of-Things applications and services. Recently, there has been a growing interest in applying deep neural networks (DNNs) to motion sensing and location estimation. However, the lack of sufficient labelled data for training and evaluating architecture benchmarks has limited the adoption of DNNs in IMU-based tasks. In this paper, we present and release the Oxford Inertial Odometry Dataset (OxIOD), a first-of-its-kind public dataset for deep learning based inertial navigation research, with fine-grained ground-truth on all sequences. Furthermore, to enable more efficient inference at the edge, we propose a novel lightweight framework to learn and reconstruct pedestrian trajectories from raw IMU data. Extensive experiments show the effectiveness of our dataset and methods in achieving accurate data-driven pedestrian inertial navigation on resource-constrained devices., Accepted to IEEE Internet of Things Journal

Additional file 8: Figure S6. PLACT1 induces activation of the NF-κB signaling pathway in an IκBα-dependent manner.

We study an apparently new question about the behaviour of Weyl sums on a subset $\mathcal{X}\subseteq [0,1)^d$ with a natural measure $\mu$ on $\mathcal{X}$. For certain measure spaces $(\mathcal{X}, \mu)$ we obtain non-trivial bounds for the mean values of the Weyl sums, and for $\mu$-almost all points of $\mathcal{X}$ the Weyl sums satisfy the square root cancellation law. Moreover we characterise the size of the exceptional sets in terms of Hausdorff dimension. Finally, we derive variants of the Vinogradov mean value theorem averaging over measure spaces $(\mathcal{X}, \mu)$. We obtain general results, which we refine for some special spaces $\mathcal{X}$ such as spheres, moment curves and line segments., Comment: 37 pages

Deoxynivalenol (DON) is a mycotoxin that causes immunosuppression, especially in swine. Selenium (Se) is essential for proper functioning of the immune system in animals. However, little is known about the effects of DON and Se on cytokine or immunoglobulin production in piglets. Here, we addressed this gap by examining piglet splenic lymphocyte responses in vitro. Cells were stimulated with concanavalin A, a T cell stimulatory lectin, in the absence or presence of DON (0.1, 0.2, 0.4, and 0.8 μg/mL), Se (Na2SeO3, 2 μM), or combinations of Se 2 μM and DON 0.1–0.8 μg/mL for 12, 24, or 48 h. At each time point, supernatants and cells were collected and the expression of cytokine and immunoglobulin protein and mRNA was examined. Compared with control and Se-alone treatments, DON exposure significantly and dose dependently decreased the expression levels of IL-2, IL-4, IL-6, IL-10, IFN-γ, IgG, and IgM mRNA and protein. By contrast, co-treatment with DON + Se significantly increased the mRNA and protein levels of all factors examined, except IL-4 and IL-6, compared with DON treatment alone. The results of this investigation demonstrate that Se has the potential to counteract DON-induced immunosuppression in piglets and is a promising treatment for DON-mediated toxicity.

Let $\alpha, \beta \in (0,1)$ such that at least one of them is irrational. We take a random walk on the real line such that the choice of $\alpha$ and $\beta$ has equal probability $1/2$. We prove that almost surely the $\alpha\beta$-orbit is uniformly distributed module one, and the exponential sums along its orbit has the square root cancellation. We also show that the exceptional set in the probability space, which does not have the property of uniform distribution modulo one, is large in the terms of topology and Hausdorff dimension., Comment: 17 pages

Deoxynivalenol (DON) is a common contaminant of grain worldwide and is often detected in the human diet and animal feed. Selenium is an essential trace element in animals. It has many biological functions. The role of selenium in the body is mainly orchestrated by selenoprotein. Glutathione peroxidase (GPx) also exists widely in the body and has attracted much attention due to its high antioxidant capacity. In order to explore the effect of the GPx1 gene on toxicity of DON, in this study, we overexpressed or knockdown GPx1 in porcine splenic lymphocytes, then added different concentrations of DON (0.1025, 0.205, 0.41, and 0.82 μg/mL) and sodium selenite (2 μmol/L) to the culture system. Using various techniques, we detected antioxidant function, free radical content, cell apoptosis, and methylation-related gene expression to explore the effect of GPx1 expression on DON-induced cell damage. We also explored whether selenium can antagonize the toxicity of DON in these two cell models and revealed the protective effect of sodium selenite on DON-induced cell damage in GPx1-overexpressing or knockdown splenic lymphocytes. Finally, our findings revealed the following: (1) GPx1 can regulate the antioxidant capacity, apoptosis rate, and expression of DNA methylation-related genes in pig splenic lymphocytes. (2) Na2SeO3 (2 μmol/L) can regulate the antioxidant capacity, apoptosis rate, and expression of DNA methylation-related genes in pig splenic lymphocytes, and this effect is more significant in GPx1-overexpressing cells than in GPx1-knockdown cells. (3) DON can cause oxidative damage, apoptosis, and methylation injury in GPx1-overexpressing or knockdown pig splenic lymphocytes in a concentration-dependent manner. (4) Na2SeO3 (2 μmol/L) can antagonize the toxic effect of DON on GPx1-overexpressing or knockdown pig splenic lymphocytes. Our findings may have important implications for food/feed safety, human health, and environmental protection.

Let $��, ��\in (0,1)$ such that at least one of them is irrational. We take a random walk on the real line such that the choice of $��$ and $��$ has equal probability $1/2$. We prove that almost surely the $����$-orbit is uniformly distributed module one, and the exponential sums along its orbit has the square root cancellation. We also show that the exceptional set in the probability space, which does not have the property of uniform distribution modulo one, is large in the terms of topology and Hausdorff dimension., 17 pages

Advances in micro-electro-mechanical (MEMS) techniques enable inertial measurements units (IMUs) to be small, cheap, energy efficient, and widely used in smartphones, robots, and drones. Exploiting inertial data for accurate and reliable navigation and localization has attracted significant research and industrial interest, as IMU measurements are completely ego-centric and generally environment agnostic. Recent studies have shown that the notorious issue of drift can be significantly alleviated by using deep neural networks (DNNs), e.g. IONet. However, the lack of sufficient labelled data for training and testing various architectures limits the proliferation of adopting DNNs in IMU-based tasks. In this paper, we propose and release the Oxford Inertial Odometry Dataset (OxIOD), a first-of-its-kind data collection for inertial-odometry research, with all sequences having ground-truth labels. Our dataset contains 158 sequences totalling more than 42 km in total distance, much larger than previous inertial datasets. Another notable feature of this dataset lies in its diversity, which can reflect the complex motions of phone-based IMUs in various everyday usage. The measurements were collected with four different attachments (handheld, in the pocket, in the handbag and on the trolley), four motion modes (halting, walking slowly, walking normally, and running), five different users, four types of off-the-shelf consumer phones, and large-scale localization from office buildings. Deep inertial tracking experiments were conducted to show the effectiveness of our dataset in training deep neural network models and evaluate learning-based and model-based algorithms. The OxIOD Dataset is available at: http://deepio.cs.ox.ac.uk

In this paper we obtain a new sum-product estimate in prime fields. In particular, we show that if $A\subseteq \mathbb{F}_p$ satisfies $|A|\le p^{64/117}$ then $$ \max\{|A\pm A|, |AA|\} \gtrsim |A|^{39/32}. $$ Our argument builds on and improves some recent results of Shakan and Shkredov which use the eigenvalue method to reduce to estimating a fourth moment energy and the additive energy $E^+(P)$ of some subset $P\subseteq A+A$. Our main novelty comes from reducing the estimation of $E^+(P)$ to a point-plane incidence bound of Rudnev rather than a point line incidence bound of Stevens and de Zeeuw as done by Shakan and Shkredov., Comment: 16 pages

Inertial information processing plays a pivotal role in ego-motion awareness for mobile agents, as inertial measurements are entirely egocentric and not environment dependent. However, they are affected greatly by changes in sensor placement/orientation or motion dynamics, and it is infeasible to collect labelled data from every domain. To overcome the challenges of domain adaptation on long sensory sequences, we propose a novel framework that extracts domain-invariant features of raw sequences from arbitrary domains, and transforms to new domains without any paired data. Through the experiments, we demonstrate that it is able to efficiently and effectively convert the raw sequence from a new unlabelled target domain into an accurate inertial trajectory, benefiting from the physical motion knowledge transferred from the labelled source domain. We also conduct real-world experiments to show our framework can reconstruct physically meaningful trajectories from raw IMU measurements obtained with a standard mobile phone in various attachments., Comment: NIPS 2018 workshop on Modeling the Physical World: Perception, Learning, and Control. A complete version will be released soon

Due to the sparse rewards and high degree of environment variation, reinforcement learning approaches such as Deep Deterministic Policy Gradient (DDPG) are plagued by issues of high variance when applied in complex real world environments. We present a new framework for overcoming these issues by incorporating a stochastic switch, allowing an agent to choose between high and low variance policies. The stochastic switch can be jointly trained with the original DDPG in the same framework. In this paper, we demonstrate the power of the framework in a navigation task, where the robot can dynamically choose to learn through exploration, or to use the output of a heuristic controller as guidance. Instead of starting from completely random moves, the navigation capability of a robot can be quickly bootstrapped by several simple independent controllers. The experimental results show that with the aid of stochastic guidance we are able to effectively and efficiently train DDPG navigation policies and achieve significantly better performance than state-of-the-art baselines models., Comment: A short version is accepted by the NIPS 2018 workshop: Infer2Control

We study the restricted families of projections in vector spaces over finite fields. We show that there are families of random subspaces which admit a Marstrand-Mattila type projection theorem., Comment: 8 pages. arXiv admin note: substantial text overlap with arXiv:1706.03456

Let $E$ be a subset of a doubling metric space $(X,d)$. We prove that for any $s\in [0, \dim_{A}E]$, where $\dim_{A}$ denotes the Assouad dimension, there exists a subset $F$ of $E$ such that $\dim_{A}F=s$. We also show that the same statement holds for the lower dimension $\dim_L$., Comment: 13 pages

Supplemental Digital Content is available in the text, Several reports suggest that gemcitabine (GEM) plus S-1 combination (GS) is associated to prolong the survival in patients with unresectable pancreatic cancer (PC). We conducted a systemic review and meta-analysis of studies comparing the safety and efficacy of GS versus GEM. Summary data from randomized trials and retrospective studies were searched in PubMed, EMBASE, Web of Science, and the Cochrane Library. Statistical analyses were conducted to calculate the hazard ratios (HRs) and relative risk (RR) with 95% confidence intervals (CIs) using random-effects models. Subgroup analyses based on the chemotherapy cycles were performed to explore the efficacy and toxicity for therapy. Sensitivity analyses were conducted by removing specific studies to assess the effects of study quality. Between January 2004 and August 2012, 4 RCTs and 2 retrospective studies including a total of 1025 cases were identified. The overall survival (OS) (HR: 0.82; 95% CI, 0.70–0.96; P = 0.01) and progression-free survival (PFS) (HR: 0.65; 95% CI, 0.55–0.77; P