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Consider a Gaussian relay network where a number of sources communicate to a destination with the help of several layers of relays. Recent work has shown that a compress-and-forward based strategy at the relays can achieve the capacity of…
This article investigates correlational properties of two-dimensional chaotic maps on the unit circle. We give analytical forms of higher-order covariances. We derive the characteristic function of their simultaneous and lagged ergodic…
Four dimensional geometric shell shaping (4D-GSS) is introduced as an approach for closing the nonlinearity-caused shaping gap. This format is designed at the spectral efficiency of 8 b/4D-sym and is compared against…
Gaussian Splatting has recently emerged as the go-to representation for reconstructing and rendering 3D scenes. The transition from 3D to 2D Gaussian primitives has further improved multi-view consistency and surface reconstruction…
We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…
In this paper an approach to generate multi-dimensionally consistent $N$-component systems is proposed. The approach starts from scalar multi-dimensionally consistent quadrilateral systems and makes use of the cyclic group. The obtained…
Large apertures in space are critical for high-power and high-bandwidth applications spanning wireless power transfer (WPT) and communication, however progress on this front is stunted by the geometric limitations of rocket flight. Here, we…
Shaping modulation formats in multi-dimensional (MD) space is an effective approach to harvest spectral efficiency gains in both the additive white Gaussian noise (AWGN) channel and the optical fiber channel. In the first part of this…
Maximal Common Subsequences (MCSs) between two strings X and Y are subsequences of both X and Y that are maximal under inclusion. MCSs relax and generalize the well known and widely used concept of Longest Common Subsequences (LCSs), which…
Linear complementary dual (LCD) codes is a class of linear codes introduced by Massey in 1964. LCD codes have been extensively studied in literature recently. In addition to their applications in data storage, communications systems, and…
Adjacent dyadic systems are pivotal in analysis and related fields to study continuous objects via collections of dyadic ones. In our prior work (joint with Jiang, Olson and Wei) we describe precise necessary and sufficient conditions for…
We use a way to extend partial combinatory algebras (pcas) by forcing them to represent certain functions. In the case of Scott's Graph model, equality is computable relative to the complement function. However, the converse is not true.…
Multidimensional scaling (MDS) is the act of embedding proximity information about a set of $n$ objects in $d$-dimensional Euclidean space. As originally conceived by the psychometric community, MDS was concerned with embedding a fixed set…
In this paper, we present a new construction of simplicial complexes of subpolynomial degree with arbitrarily good local spectral expansion. Previously, the only known high-dimensional expanders (HDXs) with arbitrarily good expansion and…
Extremely large-scale array (XL-array) has emerged as a promising technology to enable near-field communications for achieving enhanced spectrum efficiency and spatial resolution, by drastically increasing the number of antennas. However,…
A new design and novel architecture suitable for FPGA/ASIC implementation of a 2D Gaussian surround function for image processing application is presented in this paper. The proposed scheme results in enormous savings of memory normally…
The Galileons are a set of terms within four-dimensional effective field theories, obeying symmetries that can be derived from the dynamics of a 3+1-dimensional flat brane embedded in a 5-dimensional Minkowski Bulk. These theories have some…
Theoretically, the three-dimensional (3D) array architecture provides a higher communication degree of freedom (DoF) compared to the planar arrays, allowing for greater capacity potential in multiple-input multiple-output (MIMO) systems.…
Since some years, non-overlapping sets of strings (also called cross-bifix-free sets) have had an increasing interest in the frame of the researches about Theory of Codes. Recently some non-overlapping sets of strings with variable length…
Dimension-varying linear systems are investigated. First, a dimension-free state space is proposed. A cross dimensional distance is constructed to glue vectors of different dimensions together to form a cross-dimensional topological space.…