We propose a novel kernel-based two-sample test that leverages the spectral decomposition of the maximum mean discrepancy (MMD) statistic to identify and utilize well-estimated directional components in reproducing kernel Hilbert space (RKHS). Our approach is motivated by the observation that the estimation quality of these components varies significantly, with leading eigen-directions being more reliably estimated in finite samples. By focusing on these directions and aggregating information across multiple kernels, the proposed test achieves higher power and improved robustness, especially in high-dimensional and unbalanced sample settings. We further develop a computationally efficient multiplier bootstrap procedure for approximating critical values, which is theoretically justified and significantly faster than permutation-based alternatives. Extensive simulations and empirical studies on microarray datasets demonstrate that our method maintains the nominal Type I error rate and delivers superior power compared to other existing MMD-based tests.

Deep neural networks require principled uncertainty quantification, yet existing variational inference methods often employ isotropic Gaussian approximations in weight space that poorly match the network's inherent geometry. We address this mismatch by introducing Concentration-Adapted Perturbations (CAP), a variational framework that models weight uncertainties directly on the unit hypersphere using von Mises-Fisher distributions. Building on recent work in radial-directional posterior decompositions and spherical weight constraints, CAP provides the first complete theoretical framework connecting directional statistics to practical noise regularization in neural networks. Our key contribution is an analytical derivation linking vMF concentration parameters to activation noise variance, enabling each layer to learn its optimal uncertainty level through a novel closed-form KL divergence regularizer. In experiments on CIFAR-10, CAP significantly improves model calibration - reducing Expected Calibration Error by 5.6x - while providing interpretable layer-wise uncertainty profiles. CAP requires minimal computational overhead and integrates seamlessly into standard architectures, offering a theoretically grounded yet practical approach to uncertainty quantification in deep learning.

We describe a new method for estimating the direction of sound in a reverberant environment from basic principles of sound propagation. The method utilizes SNR-adaptive features from time-delay and energy of the directional components after acoustic wave decomposition of the observed sound field to estimate the line-of-sight direction under noisy and reverberant conditions. The effectiveness of the approach is established with measured data of different microphone array configurations under various usage scenarios.

Many real world problems can be effectively modeled as pairwise relationship in networks where nodes represent entities of interest and links mimic the interactions or relationships between them. The study of networks, recently referred to as network science, can provide insight into their structures and properties. One particularly interesting problem in network studies is searching for important sub-networks which are called communities, modules or groups. A community in a network is typically characterized by a group of nodes that have more links connected within the community than connected to other nodes (Fortunato, 2010). In many practical applications, the networks in study are directed in nature, such as the World Wide Web, tweeter's follower-followee network, and citation networks. Compared with in-depth studies of community structures in undirected networks (Danon et al., 2005; Fortunato, 2010; Coscia, Giannotti and Pedreschi, 2011), community detection in directed networks has not been as fruitful.