Hasil untuk "Maps"

Alfonso García-Velo, Alberto Ibort

The theory of symmetry of quantum mechanical systems is applied to study the structure and properties of several classes of relevant maps in quantum information theory: CPTP, PPT and Schwarz maps. First, we develop the general structure that equivariant maps $Φ:\mathcal A \to \mathcal B$ between $C^\ast$-algebras satisfy. Then, we undertake a systematic study of unital, Hermiticity-preserving maps that are equivariant under natural unitary group actions. Schwarz maps satisfy Kadison's inequality $Φ(X^\ast X) \geq Φ(X)^\ast Φ(X)$ and form an intermediate class between positive and completely positive maps. We completely classify $U(n)$-equivariant on $M_n(\mathbb C)$ and determine those that are completely positive and Schwarz. Partial classifications are then obtained for the weaker $DU(n)$-equivariance (diagonal unitary symmetry) and for tensor-product symmetries $U(n_1) \otimes U(n_2)$. In each case, the parameter regions where $Φ$ is Schwarz or completely positive are described by explicit algebraic inequalities, and their geometry is illustrated. Finally, we further show that the $U(n)$-equivariant family satisfies $\mathrm{PPT} \iff \mathrm{EB}$, while the $DU(2)$, symmetric $DU(3)$, $U(2) \otimes U(2)$ and $U(2) \otimes U(3)$, families obey the $\mathrm{PPT}^2$ conjecture through a direct symmetry argument. These results reveal how group symmetry controls the structure of non-completely positive maps and provide new concrete examples where the $\mathrm{PPT}^2$ property holds.

Lorin Achey, Alec Reed, Brendan Crowe et al.

We present a novel approach for enhancing robotic exploration by using generative occupancy mapping. We implement SceneSense, a diffusion model designed and trained for predicting 3D occupancy maps given partial observations. Our proposed approach probabilistically fuses these predictions into a running occupancy map in real-time, resulting in significant improvements in map quality and traversability. We deploy SceneSense on a quadruped robot and validate its performance with real-world experiments to demonstrate the effectiveness of the model. In these experiments we show that occupancy maps enhanced with SceneSense predictions better estimate the distribution of our fully observed ground truth data ($24.44\%$ FID improvement around the robot and $75.59\%$ improvement at range). We additionally show that integrating SceneSense enhanced maps into our robotic exploration stack as a ``drop-in'' map improvement, utilizing an existing off-the-shelf planner, results in improvements in robustness and traversability time. Finally, we show results of full exploration evaluations with our proposed system in two dissimilar environments and find that locally enhanced maps provide more consistent exploration results than maps constructed only from direct sensor measurements.

David Futer

This paper proves that every periodic automorphism of a closed hyperbolic surface S sends some curve to a nearly disjoint curve. In particular, periodic maps cannot have the property that every curve fills with its image, so no such map can give a positive answer to a question of Wright. This paper also answers a question of Schleimer about irreducible periodic surface maps.

Charalampos Evripidou, Pavlos Kassotakis, Anastasios Tongas

We classify rational solutions of a specific type of the set theoretical version of the pentagon equation. That is, we find all quadrirational maps $R:(x,y)\mapsto (u(x,y),v(x,y)),$ where $u, v$ are two rational functions on two arguments, that serve as solutions of the pentagon equation. Furthermore, provided a pentagon map that admits a partial inverse, we obtain genuine entwining pentagon set theoretical solutions. Finally, we show how to obtain Yang-Baxter maps from entwining pentagon maps.

Joel Loo, David Hsu

Humans are remarkable in their ability to navigate without metric information. We can read abstract 2D maps, such as floor-plans or hand-drawn sketches, and use them to navigate in unseen rich 3D environments, without requiring prior traversals to map out these scenes in detail. We posit that this is enabled by the ability to represent the environment abstractly as interconnected navigational behaviours, e.g., "follow the corridor" or "turn right", while avoiding detailed, accurate spatial information at the metric level. We introduce the Scene Action Map (SAM), a behavioural topological graph, and propose a learnable map-reading method, which parses a variety of 2D maps into SAMs. Map-reading extracts salient information about navigational behaviours from the overlooked wealth of pre-existing, abstract and inaccurate maps, ranging from floor-plans to sketches. We evaluate the performance of SAMs for navigation, by building and deploying a behavioural navigation stack on a quadrupedal robot. Videos and more information is available at: https://scene-action-maps.github.io.

C. Gigli, A. Saba, A. B. Ayoub et al.

Deep neural networks trained on physical losses are emerging as promising surrogates for nonlinear numerical solvers. These tools can predict solutions to Maxwell’s equations and compute gradients of output fields with respect to the material and geometrical properties in millisecond times which makes them attractive for inverse design or inverse scattering applications. Here we develop a tunable version of MaxwellNet with respect to incident power, a physics driven neural network able to compute light scattering from inhomogenous media with a size comparable with the incident wavelength in the presence of the optical Kerr effect. MaxwellNet maps the relation between the refractive index and scattered field through a convolutional neural network. We introduce here extra fully connected layers to dynamically adjust the convolutional kernels to take into account the intensity-dependent refractive index of the material. Finally, we provide an example of how this network can be used for the topology optimization of microlenses that is robust to perturbations due to self-focusing.

Yuan Fang, Di Ding, Yujia Gu et al.

Bacterial panicle blight, bacterial leaf streak, and bacterial brown stripe are common bacterial diseases in rice that represent global threats to stable rice yields. In this study, we used the rice variety HZ, Nekken and their 120 RIL population as experimental materials. Phenotypes of the parents and RILs were quantitatively analyzed after inoculation with <i>Burkholderia glumae</i>, <i>Xanthomonas oryzae</i> pv. <i>oryzicola</i>, and <i>Acidovorax avenae</i> subsp. <i>avenae</i>. Genetic SNP maps were also constructed and used for QTL mapping of the quantitative traits. We located 40 QTL loci on 12 chromosomes. The analysis of disease resistance-related candidate genes in the QTL regions with high LOD value on chromosomes 1, 3, 4, and 12 revealed differential expression before and after treatment, suggesting that the identified genes mediated the variable disease resistance profiles of Huazhan and Nekken2. These results provide an important foundation for cloning bacterial-resistant QTLs of panicle blight, leaf streak, and brown stripe in rice.

Yue Wu, Steven Mascaro, Mejbah Bhuiyan et al.

<h4>Background</h4>Pneumonia remains a leading cause of hospitalization and death among young children worldwide, and the diagnostic challenge of differentiating bacterial from non-bacterial pneumonia is the main driver of antibiotic use for treating pneumonia in children. Causal Bayesian networks (BNs) serve as powerful tools for this problem as they provide clear maps of probabilistic relationships between variables and produce results in an explainable way by incorporating both domain expert knowledge and numerical data.<h4>Methods</h4>We used domain expert knowledge and data in combination and iteratively, to construct, parameterise and validate a causal BN to predict causative pathogens for childhood pneumonia. Expert knowledge elicitation occurred through a series of group workshops, surveys and one-on-one meetings involving 6-8 experts from diverse domain areas. The model performance was evaluated based on both quantitative metrics and qualitative expert validation. Sensitivity analyses were conducted to investigate how the target output is influenced by varying key assumptions of a particularly high degree of uncertainty around data or domain expert knowledge.<h4>Results</h4>Designed to apply to a cohort of children with X-ray confirmed pneumonia who presented to a tertiary paediatric hospital in Australia, the resulting BN offers explainable and quantitative predictions on a range of variables of interest, including the diagnosis of bacterial pneumonia, detection of respiratory pathogens in the nasopharynx, and the clinical phenotype of a pneumonia episode. Satisfactory numeric performance has been achieved including an area under the receiver operating characteristic curve of 0.8 in predicting clinically-confirmed bacterial pneumonia with sensitivity 88% and specificity 66% given certain input scenarios (i.e., information that is available and entered into the model) and trade-off preferences (i.e., relative weightings of the consequences of false positive versus false negative predictions). We specifically highlight that a desirable model output threshold for practical use is very dependent upon different input scenarios and trade-off preferences. Three commonly encountered scenarios were presented to demonstrate the potential usefulness of the BN outputs in various clinical pictures.<h4>Conclusions</h4>To our knowledge, this is the first causal model developed to help determine the causative pathogen for paediatric pneumonia. We have shown how the method works and how it would help decision making on the use of antibiotics, providing insight into how computational model predictions may be translated to actionable decisions in practice. We discussed key next steps including external validation, adaptation and implementation. Our model framework and the methodological approach can be adapted beyond our context to broad respiratory infections and geographical and healthcare settings.

Shuxiang Feng, Yingbo Han, Kaige Jiang et al.

In this paper, we motivate and extend the study of harmonic maps or $Φ_{(1)}$-harmonic maps (cf [15], Remark 1.3 (iii)), $Φ$-harmonic maps or $Φ_{(2)}$-harmonic maps (cf. [24], Remark 1.3 (v)), and explore geometric properties of $Φ_{(3)}$-harmonic maps by unified geometric analytic methods. We define the notion of $Φ_{(3)}$-harmonic maps and obtain the first variation formula and the second variation formula of the $Φ_{(3)}$-energy functional $E_{Φ_{(3)}}$. By using a stress-energy tensor, the $Φ_{(3)}$-conservation law, a monotonicity formula, and the asymptotic assumption of maps at infinity, we prove Liouville type results for $Φ_{(3)}$-harmonic maps. We introduce the notion of $Φ_{(3)}$-Superstrongly Unstable ($Φ_{(3)}$-SSU) manifold and provide many interesting examples. By using an extrinsic average variational method in the calculus of variations (cf. [51, 49]), we find $Φ_{(3)}$-SSU manifold and prove that for $i=1,2,3$, every compact $Φ_{(i)}$-$\operatorname{SSU}$ manifold is $Φ_{(i)}$-$\operatorname{SU}$, and hence is $Φ_{(i)}$-$\operatorname{U}$ (cf. Theorem 9.3). As consequences, we obtain topological vanishing theorems and sphere theorems by employing a $Φ_{(3)}$-harmoic map as a catalyst. This is in contrast to the approaches of utilizing a geodesic ([45]), minimal surface, stable rectifiable current ([34, 29, 50]), $p$-harmonic map (cf. [53]), etc., as catalysts. These mysterious phenomena are analogs of harmonic maps or $Φ_{(1)}$-harmonic maps, $p$-harmonic maps, $Φ_{S}$-harmonic maps, $Φ_{S,p}$-harmonic maps, $Φ_{(2)}$-harmonic maps, etc., (cf. [21, 40, 42, 41, 12, 13]).

Ana Anusic, Roberto De Leo

The tent map family is arguably the simplest 1-parametric family of maps with non-trivial dynamics and it is still an active subject of research. In recent works the second author, jointly with J. Yorke, studied the graph and backward limits of S-unimodal maps. In this article we generalize those results to tent-like unimodal maps. By tent-like here we mean maps that share fundamental properties that characterize tent maps, namely unimodal maps without wandering intervals nor attracting cycles and whose graph has a finite number of nodes.

Hugo Lavenant

How can one lift a functional defined on maps from a space X to a space Y into a functional defined on maps from X into P(Y) the space of probability distributions over Y? Looking at measure-valued maps can be interpreted as knowing a classical map with uncertainty, and from an optimization point of view the main gain is the convexification of Y into P(Y). We will explain why trying to single out the largest convex lifting amounts to solve an optimal transport problem with an infinity of marginals which can be interesting by itself. Moreover we will show that, to recover previously proposed liftings for functionals depending on the Jacobian of the map, one needs to add a restriction of additivity to the lifted functional.

Aaron S. Crandall, Steven Mamolo, Mathew Morgan

Monitoring and gathering data on sporting activities holds significant promise for athletes, equipment developers, and physical fitness clinicians. Wireless Body Area Networks are being used in sporting environments as a means of gathering data, providing feedback, and helping to gain understanding of athletic activities. Applying WBANs to skiing situations, which have higher vibration, velocities, and damp environments than many other sports, can open up opportunities to understand the dynamics of skiing equipment behaviors, skiing routes on mountains, and how individuals react when skiing. To support these outcomes, a prototype WBAN-style off the shelf component system called SkiMon was proposed, implemented, and tested. The SkiMon system uses inexpensive ESP8266, Raspberry Pi, and sensor devices to gather high quality motion and location tracking data on skiers in real-world skiing conditions. By using IEEE 802.11b/g/n wireless networks, SkiMon is able to sample data at a minimum of 50 Hz, which is enough to model most ski vibration behaviors. These data results are shown to reflect ground truth 3D maps and the acceleration data comports with earlier works on ski vibration testing. Overall, a WBAN-based commodity components solution shows promise as a high quality sensor platform for tracking and modeling skiing activities.

Mathilde Letard, Antoine Collin, Thomas Corpetti et al.

Coastal areas host highly valuable ecosystems that are increasingly exposed to the threats of global and local changes. Monitoring their evolution at a high temporal and spatial scale is therefore crucial and mostly possible through remote sensing. This article demonstrates the relevance of topobathymetric lidar data for coastal and estuarine habitat mapping by classifying bispectral data to produce 3D maps of 21 land and sea covers at very high resolution. Green lidar full waveforms are processed to retrieve tailored features corresponding to the signature of those habitats. These features, along with infrared intensities and elevations, are used as predictors for random forest classifications, and their respective contribution to the accuracy of the results is assessed. We find that green waveform features, infrared intensities, and elevations are complimentary and yield the best classification results when used in combination. With this configuration, a classification accuracy of 90.5% is achieved for the segmentation of our dual-wavelength lidar dataset. Eventually, we produce an original mapping of a coastal site under the form of a point cloud, paving the way for 3D classification and management of land and sea covers.

Manish K Gupta

This paper introduces an isometry between the modular rings $\Z_{2^s}$ and $\Z_{2^{s-1}}$ with respect to the homogeneous weights. Certain product of these maps gives Carlet's generalised Gray map and also Vega's Gray map. For $s=2$ this reduces to popular Gray map. Several interesting properties of these maps are studied. Towards the end we list several interesting problems to work on.

Lorenzo Amabili, Nicole Sultanum

Given the wealth of scientific publications, perusing papers is becoming a larger and more complex burden, especially for junior researchers. In this work, we suggest a visualization-based method to mitigate this problem via the use of paper maps, i.e., concept maps for the summarization of scientific papers. We provide design principles of paper maps and discuss design considerations based on exploratory design studies. We also conducted an initial evaluation for assessing the effectiveness of paper maps in summarizing scientific papers, suggesting that paper maps can improve the readability of scientific papers.

Christian Ayala, Carlos Aranda, Mikel Galar

Building footprints and road networks are important inputs for a great deal of services. For instance, building maps are useful for urban planning, whereas road maps are essential for disaster response services. Traditionally, building and road maps are manually generated by remote sensing experts or land surveying, occasionally assisted by semi-automatic tools. In the last decade, deep learning-based approaches have demonstrated their capabilities to extract these elements automatically and accurately from remote sensing imagery. The building footprint and road network detection problem can be considered a multi-class semantic segmentation task, that is, a single model performs a pixel-wise classification on multiple classes, optimizing the overall performance. However, depending on the spatial resolution of the imagery used, both classes may coexist within the same pixel, drastically reducing their separability. In this regard, binary decomposition techniques, which have been widely studied in the machine learning literature, are proved useful for addressing multi-class problems. Accordingly, the multi-class problem can be split into multiple binary semantic segmentation sub-problems, specializing different models for each class. Nevertheless, in these cases, an aggregation step is required to obtain the final output labels. Additionally, other novel approaches, such as multi-task learning, may come in handy to further increase the performance of the binary semantic segmentation models. Since there is no certainty as to which strategy should be carried out to accurately tackle a multi-class remote sensing semantic segmentation problem, this paper performs an in-depth study to shed light on the issue. For this purpose, open-access Sentinel-1 and Sentinel-2 imagery (at 10 m) are considered for extracting buildings and roads, making use of the well-known U-Net convolutional neural network. It is worth stressing that building and road classes may coexist within the same pixel when working at such a low spatial resolution, setting a challenging problem scheme. Accordingly, a robust experimental study is developed to assess the benefits of the decomposition strategies and their combination with a multi-task learning scheme. The obtained results demonstrate that decomposing the considered multi-class remote sensing semantic segmentation problem into multiple binary ones using a One-vs.-All binary decomposition technique leads to better results than the standard direct multi-class approach. Additionally, the benefits of using a multi-task learning scheme for pushing the performance of binary segmentation models are also shown.

Marián Halás, Vojtěch Blažek, Pavel Klapka et al.

The paper presents new approaches to the visualisation of origin–destination flows, in which all three basic parameters of flows between pairs of geographic objects are cartographically expressed simply and clearly: the length of flows, their intensity, and the proportional distribution of both directions between pairs of objects (polarisation of flows). The data on population movements based on mobile phone location are used as the input information, which were collected from the whole territory of the Czech Republic. Apart from the visualisation of origin–destination flows, the paper addresses the issue of the transformation of these data through the application of two different interaction measures. The transformed flows are also cartographically visualised and the functional regions based on the respective interaction measures are used as base maps.

A. S. Kents, Y. A. Hamad, K. V. Simonov et al.

In recent years computed tomography of the lungs has been the most common diagnostic procedure aimed at detection of the pathological changes associated with COVID-19. The study is aimed at the use of the developed algorithmic support in combination with texture (geometric) analysis to highlight a number of indicators characterizing the clinical state of the object of interest. Processing is aimed at the solution of a number of diagnostic tasks such as highlighting and contrasting the objects of interest, taking into account the color coding. Further, an assessment is performed according to the appropriate criteria in order to find out the nature of the changes and increase both the visualization of pathological changes and the accuracy of the X-ray diagnostic report. For these purposes, it is proposed to use preprocessing algorithms for a series of images in dynamics. Segmentation of the lungs and areas of possible pathology are performed using wavelet transform and Otsu threshold value. Delta-maps and maps obtained using Shearlet transform with contrasting color coding are used as a means of visualization and selection of features (markers). The analysis of the experimental and clinical material carried out in the work shows the effectiveness of the proposed combination of methods for studying of the variability of the internal geometric features (markers) of the object of interest in the images.

Ricardo Barbosa Jr., Ryan Burns