Asymptotic nonnegative rank of matrices

The nonnegative rank of nonnegative matrices is an important quantity that appears in many fields, such as combinatorial optimization, communication complexity, and information theory. In this paper, we study the asymptotic growth of the nonnegative rank of a fixed nonnegative matrix under Kronecker product. This quantity is called the asymptotic nonnegative rank, which is already studied in information theory. By applying the theory of asymptotic spectra of V. Strassen (J. Reine Angew. Math. 1988), we introduce the asymptotic spectrum of nonnegative matrices and give a dual characterization of the asymptotic nonnegative rank. As the opposite of nonnegative rank, we introduce the notion of the subrank of a nonnegative matrix and show that it is exactly equal to the size of the maximum induced matching of the bipartite graph defined on the support of the matrix (therefore, independent of the value of entries). Finally, we show that two matrix parameters, namely rank and fractional cover number, belong to the asymptotic spectrum of nonnegative matrices

Sparsity in neural networks can improve their privacy

This article measures how sparsity can make neural networks more robust to membership inference attacks. The obtained empirical results show that sparsity improves the privacy of the network, while preserving comparable performances on the task at hand. This empirical study completes and extends existing literature

BoMb-OT: On Batch of Mini-batches Optimal Transport

Mini-batch optimal transport (m-OT) has been successfully used in practical applications that involve probability measures with intractable density, or probability measures with a very high number of supports. The m-OT solves several sparser optimal transport problems and then returns the average of their costs and transportation plans. Despite its scalability advantage, the m-OT does not consider the relationship between mini-batches which leads to undesirable estimation. Moreover, the m-OT does not approximate a proper metric between probability measures since the identity property is not satisfied. To address these problems, we propose a novel mini-batching scheme for optimal transport, named Batch of Mini-batches Optimal Transport (BoMb-OT), that finds the optimal coupling between mini-batches and it can be seen as an approximation to a well-defined distance on the space of probability measures. Furthermore, we show that the m-OT is a limit of the entropic regularized version of the BoMb-OT when the regularized parameter goes to infinity. Finally, we carry out extensive experiments to show that the BoMb-OT can estimate a better transportation plan between two original measures than the m-OT. It leads to a favorable performance of the BoMb-OT in the matching and color transfer tasks. Furthermore, we observe that the BoMb-OT also provides a better objective loss than the m-OT for doing approximate Bayesian computation, estimating parameters of interest in parametric generative models, and learning non-parametric generative models with gradient flow.Comment: 36 pages, 20 figure

Chronic scrotal heat stress causes testicular interstitial inflammation and fibrosis: An experimental study in mice

Background: Chronic heat stress is a risk factor that adversely affects the reproduction system. Inflammation and fibrosis are 2 important response processes to damaged tissues. Objective: This study investigates the association of chronic scrotal heat stress with testicular interstitial inflammation and fibrosis in mice. Materials and Methods: For all experiments, 8-10 wk old male Swiss mice (Mus musculus) (20-23 gr) were divided into 3 groups (n = 10/each). The heat-stress groups were submerged in a water bath at 37°C and 40°C, while the control group was treated at 25°C. The testicular tissues underwent hematoxylin and eosin staining, picro sirius red staining, and immunohistochemistry for intercellular adhesion molecule-1, fibroblast-specific protein 1, F4/80, collagen I, and Ki-67 staining to determine the testicular interstitial inflammation and fibrosis. Results: Chronic scrotal heat stress impairs spermatogenesis and reverses testicular histological structure. In this study, heat stress significantly induced increased interstitial cell proliferation and upregulation of intercellular adhesion molecule-1 expression in the interstitial testicular tissue. In the interstitial testicular tissue, the number of F4/80-positive macrophages and the number of fibroblast-specific protein 1- positive fibroblasts were significantly increased in the heat-exposed groups compared to those in the control group. The heat exposed groups had substantially increased extracellular matrix collagen accumulation in their testicular interstitial tissues. Conclusion: Heat stress adversely affects the testicular structure and spermatogenesis, causes inflammation, and leads to testicular interstitial fibrosis. Key words: Heat stress, Testicular, Inflammation, Fibrosis

Criblage virtuel sur grille de composés isolés au Vietnam

Criblage virtuel sur grille de composés isolés au Vietna

F2SD: A dataset for end-to-end group detection algorithms

The lack of large-scale datasets has been impeding the advance of deep learning approaches to the problem of F-formation detection. Moreover, most research works on this problem rely on input sensor signals of object location and orientation rather than image signals. To address this, we develop a new, large-scale dataset of simulated images for F-formation detection, called F-formation Simulation Dataset (F2SD). F2SD contains nearly 60,000 images simulated from GTA-5, with bounding boxes and orientation information on images, making it useful for a wide variety of modelling approaches. It is also closer to practical scenarios, where three-dimensional location and orientation information are costly to record. It is challenging to construct such a large-scale simulated dataset while keeping it realistic. Furthermore, the available research utilizes conventional methods to detect groups. They do not detect groups directly from the image. In this work, we propose (1) a large-scale simulation dataset F2SD and a pipeline for F-formation simulation, (2) a first-ever end-to-end baseline model for the task, and experiments on our simulation dataset.Comment: Accepted at ICMV 202

Exploiting Idioms and Proverbs of Vietnamese Regions in Teaching Mathematics in Primary Schools

Mathematics and idioms, as well as proverbs, all reflect the laws of life. At the same time, primary school children may have heard idioms and proverbs before attending school. Therefore, there are many possibilities to exploit and apply idioms and proverbs in teaching mathematics in primary schools. This study aims to identify appropriate situations and apply idioms and proverbs in different regions of Vietnam to teaching mathematics. The researchers selected 1155 expressions related to mathematics from many typical pieces of research on idioms and proverbs in Vietnam. After surveying 1822 teachers three times in many provinces and cities in all 3 regions of Vietnam: the North, the Central and the South, the researchers have classified the data according to the criteria from closed to open-ended questions. The results show a prominent level of interest (level 4/5) of all teachers participating in the survey, and there is no difference in the effectiveness in the three regions, but there is a clear difference in regions in using idioms and proverbs. Particularly, identifying situations to teach geometric and quantitative knowledge, as well as probability and statistics, allows one to apply idioms and proverbs at a high level. It is concluded that if idioms and proverbs from Vietnamese regions are appropriately selected and applied in teaching mathematics in primary schools, they will contribute to improving students' mathematical ability and preserving the national cultural heritage. Doi: 10.28991/ESJ-2022-SIED-015 Full Text: PD

A Novel Wideband Circularly Polarized Antenna for RF Energy Harvesting in Wireless Sensor Nodes

A novel wideband circularly polarized antenna array using sequential rotation feeding network is presented in this paper. The proposed antenna array has a relative bandwidth of 38.7% at frequencies from 5.05 GHz to 7.45 GHz with a highest gain of 12 dBi at 6 GHz. A corresponding left-handed metamaterial is designed in order to increase antenna gain without significantly affecting its polarization characteristics. The wideband circularly polarized antenna with 2.4 GHz of bandwidth is a promising solution for wireless communication system such as tracking or wireless energy harvesting from Wi-Fi signal based on IEEE 802.11ac standard or future 5G cellular. A potential application of this antenna as a receiving antenna for RF-DC device to obtain DC power for a wireless sensor node from Wi-Fi signal is shown