Matrix denoising is central to signal processing and machine learning. Its statistical analysis when the matrix to infer has a factorized structure with a rank growing proportionally to its dimension remains a challenge, except when it is rotationally invariant. In this case, the information-theoretic limits and an efficient Bayes-optimal denoising algorithm, called the rotational invariant estimator, are known. Beyond this setting, few results can be found. The reason is that the model is not a usual spin system because of the growing rank dimension, nor a matrix model (as appearing in high-energy physics) due to the lack of rotation symmetry, but rather a hybrid between the two. In this paper, we make progress toward the understanding of Bayesian matrix denoising when the hidden signal is a factored matrix XX^{⊺} that is not rotationally invariant. Monte Carlo simulations suggest the existence of a denoising-factorization transition separating a phase where denoising using the rotational-invariant estimator remains Bayes-optimal due to universality properties of the same nature as in random matrix theory, from one where universality breaks down and better denoising is possible, though algorithmically hard. We also argue that it is only beyond the transition that factorization, i.e., estimating X itself, becomes possible up to irresolvable ambiguities. On the theoretical side, we combine mean-field techniques in an interpretable multiscale fashion in order to access the minimum mean-square error and mutual information. Interestingly, our alternative method yields equations reproducible by the replica approach of Sakata and Kabashima. Using numerical insights, we delimit the portion of phase diagram where we conjecture the mean-field theory to be exact and correct it using universality when it is not. Our complete Ansatz matches well the numerics in the whole phase diagram when considering finite-size effects.
Along with the shutdown of schools, the coronavirus outbreak caused problems for implementing face-to-face classroom instruction. During this period, digital technologies offered a helpful substitute. This study investigated how students at Nguyen Tat Thanh University used digital technology following the coronavirus outbreak. The Technology Acceptance Model (TAM) and Constructivist Learning Theory were used to explain the findings. Thirty students were interviewed as part of the qualitative research design employed in the study. The results showed that, following the outbreak, students primarily used laptops and mobile phones to support their education. Additionally, it was discovered that these devices had the necessary software loaded, enabling communication between course instructors and students via Moodle, Zoom, WhatsApp, and YouTube. This study found that these tools were beneficial in helping students refine their typing, research, and information-seeking skills. However, drawbacks to using these devices included hardware failures, costly data bundles, and a lack of expertise with software operating protocols. When addressing these issues, the students used a variety of coping techniques. The study highlights several practical implications based on these conclusions.
For wireless networks with multiple sources, an omnidirectional relay scheme is developed, where each node can simultaneously relay different messages in different directions. This is accomplished by the decode-forward relay strategy, with each relay binning the multiple messages to be transmitted, in the same spirit of network coding. Specially for the all-source all-cast problem, where each node is an independent source to be transmitted to all the other nodes, this scheme completely eliminates interference in the whole network, and the signal transmitted by any node can be used by any other node. For networks with some kind of symmetry, assuming no beamforming is to be performed, this omnidirectional relay scheme is capable of achieving the maximum achievable rate.
Визначені необхідні умови, за яких рівняння може мати розв’язок у цілих додатних числах. Параметри рівняння узгоджені з і належать обмеженим замкненим множинам. Показники степенів і змінні розділені на класи. Доведено, що у просторі змішаних змінних, зв’язаних рівнянням, де одна із змінних дійсна, а інші цілі числа, значення дійсної змінної ірраціональне, що є достатньою умовою нерозв’язності рівняння у цілих додатних числах для всіх показників степенів більших трьох. На кривих Ферма існує лише дві раціональні точки. Побудована матрична (лінійна) модель степенів цілих додатних чисел.
Theory and practice of education, Information theory
The increasing use of digital media and technologies in sports pedagogical settings comes along with fundamental changes in basic sports pedagogical categories such as body, movement, and experience (Ruin & Giese, 2023). In health education in particular, digital devices are playing a growingly important role (McCall et al., 2018). Thereby digitalisation offers multi-layered and sometimes paradoxical opportunities and risks for health education. On the one hand, tools can help people to actively look after their own health by providing them with differentiated information about their bodies, for example. On the other hand, the information provided by such tools is always pre-formatted, limited to certain factors, subject to measurement errors and mostly geared towards young, healthy and trained men and therefore not very sensitive to the specific concerns of other groups of people. To date these opportunities and risks have not been sufficiently discussed from a sports pedagogical perspective.
To gain a deeper understanding of these changes, in this theoretical contribution the mechanisms, opportunities and challenges created by digital health education in physical education are examined with a focus on the use of tools such as wearables. Based on a Bildung-oriented perspective (Wibowo et al. 2023) the possibilities and limits for digital health education in physical education are examined in a first step at the surface level, before a deeper investigation of body, movement, and experience in a digitalised world is undertaken. Bildung-theory serves as a critical background for assessing the (in)appropriateness of pedagogical interventions. This enables critical reflection at a structural level.
The investigation reveals that the use of digital technologies run the risk of going hand in hand with reductionist images of humankind and a narrow understanding of education. This tends to reduce people to functional objects that are intended to increase their human capital in the interests of society, which is not pedagogically appropriate. At the same time, however, using digital technologies in digital health education opens up opportunities for experiencing differences between supposedly objective and subjective views of one’s own body and movement behaviour. This has the potential to lead to Bildung processes in which the relationship between oneself and the world is profoundly questioned. An example of the impetus for such a process could be when two children are doing the same activity and feel quite similar, but notice through a device that their bodies react in noticeably different ways. This opens up new horizons for exploring the complexity of the connections between physical activity, physical reactions and one’s own well-being. Exploring such potential of a Bildung oriented digital health education in a differentiated way can be identified as a fundamental future task of sports pedagogy.
References
McCall, M., Spencer, E., Owen, H., Roberts, N., & Heneghan, C. (2018). Characteristics and efficacy of digital health education: An overview of systematic reviews. Health Education Journal, 77(5), 497–514. https://doi.org/10.1177/0017896918762013
Ruin, S., & Giese, M. (2023). What is real? (Re-)Locating body, movement and experience in an increasingly digitized world. Current Issues in Sport Science, 8(3), Article 002. https://doi.org/10.36950/2023.3ciss002
Wibowo, J., Krieger, C., Gaum, C., & Dyson, B. (2023). Bildung: A German student-centered approach to health and physical education. European Physical Education Review, 29(2), 233-250. https://doi.org/10.1177/1356336X221133060
Apoorav Maulik Sharma, Renu Vig, Ayush Dogra
et al.
Abstract This manuscript introduces an innovative multi-stage image fusion framework that adeptly integrates infrared (IR) and visible (VIS) spectrum images to surmount the difficulties posed by low-light settings. The approach commences with an initial preprocessing stage, utilizing an Efficient Guided Image Filter for the infrared (IR) images to amplify edge boundaries and a function for the visible (VIS) images to boost local contrast and brightness. Utilizing a two-scale decomposition technique that incorporates Lipschitz constraints-based smoothing, the images are effectively divided into distinct base and detail layers, thereby guaranteeing the preservation of essential structural information. The process of fusion is carried out in two distinct stages: firstly, a method grounded in Bayesian theory is employed to effectively combine the base layers, so effectively addressing any inherent uncertainty. Secondly, a Surface from Shade (SfS) method is utilized to ensure the preservation of the scene's geometry by enforcing integrability on the detail layers. Ultimately a Choose Max principle is employed to determine the most prominent textural characteristics, resulting in the amalgamation of the base and detail layers to generate an image that exhibits a substantial enhancement in both clarity and detail. The efficacy of our strategy is substantiated by rigorous testing, showcasing notable progressions in edge preservation, detail enhancement, and noise reduction. Consequently, our method presents significant advantages for real-world applications in image analysis.
Using information theory, we propose an estimation method for traits parameters in a Darwinian evolution model for species with on trait or multiple traits. We use the Fisher's information to obtain the errors on the estimation for one species with one or multiple traits. We perform simulations to illustrate the method.