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Sub-Weyl type range for twisted GL(2) short sums
No full textLet (Formula presented.) where (Formula presented.) is a bump function supported on the interval [1,2] and satisfying (Formula presented.) and (Formula presented.) ’s are the normalized Fourier coefficients of Hecke eigenform, and (Formula presented.) is a primitive character of conductor (Formula presented.). In this article, we prove a sub-Weyl type cancellation range (Formula presented.) provided that (Formula presented.). Note that the above bound is nontrivial if (Formula presented.)
Supervised Feature Selection via Collaborative Neurodynamic Optimization
No full textAs a crucial part of machine learning and pattern recognition, feature selection aims at selecting a subset of the most informative features from the set of all available features. In this article, supervised feature selection is at first formulated as a mixed-integer optimization problem with an objective function of weighted feature redundancy and relevancy subject to a cardinality constraint on the number of selected features. It is equivalently reformulated as a bound-constrained mixed-integer optimization problem by augmenting the objective function with a penalty function for realizing the cardinality constraint. With additional bilinear and linear equality constraints for realizing the integrality constraints, it is further reformulated as a bound-constrained biconvex optimization problem with two more penalty terms. Two collaborative neurodynamic optimization (CNO) approaches are proposed for solving the formulated and reformulated feature selection problems. One of the proposed CNO approaches uses a population of discrete-time recurrent neural networks (RNNs), and the other use a pair of continuous-time projection networks operating concurrently on two timescales. Experimental results on 13 benchmark datasets are elaborated to substantiate the superiority of the CNO approaches to several mainstream methods in terms of average classification accuracy with three commonly used classifiers
The commitment of the human cell atlas to humanity
No full textThe Human Cell Atlas (HCA) is a global partnership “to create comprehensive reference maps of all human cells—the fundamental units of life – as a basis for both understanding human health and diagnosing, monitoring, and treating disease.” (https://www.humancellatlas.org/) The atlas shall characterize cells from diverse individuals across the globe to better understand human biology. HCA proactively considers the priorities of, and benefits accrued to, contributing communities. Here, we lay out principles and action items that have been adopted to affirm HCA’s commitment to equity so that the atlas is beneficial to all of humanity
The index of certain Stiefel manifolds
No full textThis paper computes the Fadell–Husseini index of Stiefel manifolds in the case where the group acts via permutations of the orthogonal vectors. The computations are carried out in the case of elementary Abelian p-groups. The results are shown to imply certain generalizations of the Kakutani–Yamabe–Yujobo theorem
Turbulence in a wall-wake flow downstream of two horizontal cylinders
No full textExperimental investigations of flow past two (one above other) horizontal cylinders have been presented in this paper. The experimental data captured over a rough-bed with double cylinders having three different diameters, were used for the analysis. Firstly, general characteristics such as streamwise velocity, Reynolds shear stress and turbulence intensity profiles have been elucidated at different downstream locations from cylinder position; then some advanced analysis such as length scales, turbulent kinetic energy (TKE) fluxes and budget have been investigated to exhibit their variations. Length scale profiles exhibit higher values in near bed; indicating comparatively larger eddies’ downstream of both cylinders. TKE budget profiles indicate highly negative pressure energy diffusion rate together with a sufficient TKE production rate, stabilized by the amplified TKE diffusion and dissipation rates. To determine one of the most prime behaviors of turbulence characteristics, namely TKE dissipation rate more accurately, the concept of structure function has been employed. Primarily velocity gradient method elucidates TKE dissipation rate, then it has been verified by Kolmogorov’s two-thirds law using second order structure function and Kolmogorov’s − 5/3 law using the method of power spectra
Wave scattering by ⊓-shaped breakwaters in finite depth water
No full textThis article illustrates surface gravity wave scattering by ⊓-shaped and inverse ⊓-shaped breakwaters in water of finite depth. The ⊓-shaped breakwater consists of a thick rectangular structure with two thin vertical plates protruding vertically downward when it is floating on the free surface. An inverse ⊓-shaped breakwater is a bottom-standing structure with two thin plates protruding upwards. The breakwater\u27s geometrical symmetry is used to simplify the wave scattering problems. Using Havelock expansion of water wave potentials, integral equations of Fredholm type are developed for the horizontal component of fluid velocity across the gap below or above the thin plates. The analysis presents the reflection and transmission coefficients in terms of integrals involving the unknown function of the integral equations. A Galerkin expansion with a collocation method is used to solve the integral equations approximately. The developed method produces the known numerical results for a rectangular breakwater without thin plates. The ⊓-shaped breakwater shows lower wave transmission than a traditional rectangular breakwater. Furthermore, increasing plate length makes the wave transmission even less. Fluid velocity is high in the vicinity of plate edge. By the present method, it is shown that the ⊓-shaped breakwaters offer higher reflection and lower transmission. Thus, attaching thin plates to a traditional rectangular breakwater enhances its performance in wave scattering
Weighted Fuzzy C-Means: Unsupervised Feature Selection to Realize a Target Partition
No full textWe introduce an unsupervised feature selection method based on regularized weighted Fuzzy C-Means (WRFCM) clustering. When the target task is clustering, our objective should be to select a subset of features that can generate the same/similar partition matrix to the partition matrix obtained from the original high dimensional data by a clustering algorithm. To achieve this we propose a novel objective function keeping in view the Fuzzy-C-Means (FCM) clustering algorithm. This approach realizes feature selection within the WRFCM framework, emphasizing features to maintain the FCM-based target partition. We evaluate our method using Normalized Mutual Information (NMI), Adjusted Rand Index (ARI) and Kuhn-Munkres index (KM-index). NMI, and ARI measure the agreement between clusters, i.e, the partition in the lower dimension and the partition of the original data. On the other hand, KM-index measures the disagreement between the two partitions. Experimental results on synthetic and real datasets showcase our method\u27s efficacy in selecting informative features. This approach fills a crucial gap in unsupervised feature selection, making it valuable for real-world applications. The approach is very general in the sense that the target partition can be generated by any clustering algorithm or even by the actual class labels of the data, when they are available
What determines women\u27s labor supply? the role of home productivity and social norms
No full textWe highlight the role of home productivity and social norms in explaining the gender gap in labor force participation (LFP), and the non-monotonic relationship of women\u27s LFP with their education in India. We construct a model of couples\u27 time allocation decisions allowing for both market and home productivity to improve with own education. Incorporating individual preference to produce a minimum level of the home good due to social norms, we show that our theoretical model can closely replicate the U-shaped relationship between women\u27s education and their labor supply. Our analysis suggests that home productivity, along with social benchmarks on couples\u27 time allocation to home good, can be critical determinants of women\u27s labor supply in developing countries
Autonomous Automotives on the Edge
No full textWith autonomous automotives routinely leveraging computationally intensive tasks to enable robust navigation, a number of design challenges have emerged. Whilst processing tasks is traditionally carried out on the vehicles, the emergence of Multi-Access Edge Computing (MEC) has paved the way to transfer such tasks to be executed not just locally on the vehicles but also offloads such tasks to powerful MEC servers co-located with cellular base-stations. In a vehicular MEC environment, a computation offloading policy determines which tasks are to be executed locally on the vehicles and which tasks are to be transferred to MEC servers for further processing. In recent years, a number of offloading policies in have been delineated considering several optimization objectives. However, the uncertainty associated with observability metrics due to the high stochasticity of the network environment has been less explored. In this paper, we highlight the impact of this uncertainty on timeliness guarantees for safe autonomy and propose a quantitative model checking approach towards offloading tasks to MEC servers. We believe our article can motivate new research directions towards offloading in the vehicular MEC context
Configuring Safe Spiking Neural Controllers for Cyber-Physical Systems through Formal Verification
No full textIn this paper, we address the problem of safety verification for Spiking Neural Networks (SNNs) with Spiking Rectified Linear Activation (SRLA). The SNNs are obtained by first training Artificial Neural Networks (ANNs) and then translating to SNN with subsequent hyperparameter tuning. We propose a solution which tunes the temporal window hyperparameter of the translated SNN to ensure both accuracy and compliance with the safe range specification that requires the SNN outputs to remain within a safe range. We demonstrate our approach with experiments on 5 benchmark neural controllers