Blind Demixing for Low-Latency Communication

In the next generation wireless networks, lowlatency communication is critical to support emerging diversified applications, e.g., Tactile Internet and Virtual Reality. In this paper, a novel blind demixing approach is developed to reduce the channel signaling overhead, thereby supporting low-latency communication. Specifically, we develop a low-rank approach to recover the original information only based on a single observed vector without any channel estimation. Unfortunately, this problem turns out to be a highly intractable non-convex optimization problem due to the multiple non-convex rankone constraints. To address the unique challenges, the quotient manifold geometry of product of complex asymmetric rankone matrices is exploited by equivalently reformulating original complex asymmetric matrices to the Hermitian positive semidefinite matrices. We further generalize the geometric concepts of the complex product manifolds via element-wise extension of the geometric concepts of the individual manifolds. A scalable Riemannian trust-region algorithm is then developed to solve the blind demixing problem efficiently with fast convergence rates and low iteration cost. Numerical results will demonstrate the algorithmic advantages and admirable performance of the proposed algorithm compared with the state-of-art methods.Comment: 14 pages, accepted by IEEE Transaction on Wireless Communicatio

Pair density wave, unconventional superconductivity, and non-Fermi liquid quantum critical phase in frustrated Kondo lattice

Motivated by the recent discovery of an intermediate quantum critical phase between the antiferromagnetic order and the Fermi liquid in the frustrated Kondo lattice CePdAl, we study here a Kondo-Heisenberg chain with frustrated $J_1$-$J_2$ XXZ interactions among local spins using the density matrix renormalization group method. Our simulations reveal a global phase diagram with rich ground states including the antiferromagnetic order, the valence-bond-solid and bond-order-wave orders, the pair density wave state, the uniform superconducting state, and the Luttinger liquid state. We show that both the pair density wave and uniform superconductivity belong to the family of Luther-Emery liquids and may arise from pair instability of an intermediate quantum critical phase with medium Fermi volume in the presence of strong quantum fluctuations, while the Luttinger liquid has a large Fermi volume. This suggests a deep connection between the pair density wave, the unconventional superconductivity, and the non-Fermi liquid quantum critical phase.Comment: 10 pages, 9 figure

Dual-Branch Temperature Scaling Calibration for Long-Tailed Recognition

The calibration for deep neural networks is currently receiving widespread attention and research. Miscalibration usually leads to overconfidence of the model. While, under the condition of long-tailed distribution of data, the problem of miscalibration is more prominent due to the different confidence levels of samples in minority and majority categories, and it will result in more serious overconfidence. To address this problem, some current research have designed diverse temperature coefficients for different categories based on temperature scaling (TS) method. However, in the case of rare samples in minority classes, the temperature coefficient is not generalizable, and there is a large difference between the temperature coefficients of the training set and the validation set. To solve this challenge, this paper proposes a dual-branch temperature scaling calibration model (Dual-TS), which considers the diversities in temperature parameters of different categories and the non-generalizability of temperature parameters for rare samples in minority classes simultaneously. Moreover, we noticed that the traditional calibration evaluation metric, Excepted Calibration Error (ECE), gives a higher weight to low-confidence samples in the minority classes, which leads to inaccurate evaluation of model calibration. Therefore, we also propose Equal Sample Bin Excepted Calibration Error (Esbin-ECE) as a new calibration evaluation metric. Through experiments, we demonstrate that our model yields state-of-the-art in both traditional ECE and Esbin-ECE metrics

Querying a Matrix Through Matrix-Vector Products

We consider algorithms with access to an unknown matrix M in F^{n x d} via matrix-vector products, namely, the algorithm chooses vectors v^1, ..., v^q, and observes Mv^1, ..., Mv^q. Here the v^i can be randomized as well as chosen adaptively as a function of Mv^1, ..., Mv^{i-1}. Motivated by applications of sketching in distributed computation, linear algebra, and streaming models, as well as connections to areas such as communication complexity and property testing, we initiate the study of the number q of queries needed to solve various fundamental problems. We study problems in three broad categories, including linear algebra, statistics problems, and graph problems. For example, we consider the number of queries required to approximate the rank, trace, maximum eigenvalue, and norms of a matrix M; to compute the AND/OR/Parity of each column or row of M, to decide whether there are identical columns or rows in M or whether M is symmetric, diagonal, or unitary; or to compute whether a graph defined by M is connected or triangle-free. We also show separations for algorithms that are allowed to obtain matrix-vector products only by querying vectors on the right, versus algorithms that can query vectors on both the left and the right. We also show separations depending on the underlying field the matrix-vector product occurs in. For graph problems, we show separations depending on the form of the matrix (bipartite adjacency versus signed edge-vertex incidence matrix) to represent the graph. Surprisingly, this fundamental model does not appear to have been studied on its own, and we believe a thorough investigation of problems in this model would be beneficial to a number of different application areas

COMPARISON OF MARKER AND MARKERLESS MOTION CAPTURE SYSTEM FOR GAIT KINEMATICS

The purpose of this study was to compare gait kinematics measured with a markerless motion capture system against data measured with a marker-based motion capture system. A sample of 14 over-ground walking trials were captured simultaneously with two camcorders (60Hz) and an 8-camera marker system. The markerless data was further processed to landmarks using markerless human movement automatic capture system (FastMove). Body landmarks data of X and Z coordinates were highly consistent between the two systems, while data of Y coordinate showed low consistency. The Bland-Altman plots’ results showed low agreement between individual measurements of the maximum and minimum of knee and ankle flexion angles from both systems against the average of the measurement