Related papers: A wave-geometric duality for hyperdimensional comp…
Recently, a codimension two holography called wedge holography is proposed as a generalization of AdS/CFT. It is conjectured that a gravitational theory in $d+1$ dimensional wedge spacetime is dual to a $d-1$ dimensional CFT on the corner…
High-throughput DFT calculations are key to screening existing/novel materials, sampling potential energy surfaces, and generating quantum mechanical data for machine learning. By including a fraction of exact exchange (EXX), hybrid…
Hyperdimensional computing (HDC) is an increasingly popular computing paradigm with immense potential for future intelligent applications. Although the main ideas already took form in the 1990s, HDC recently gained significant attention,…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…
The holographic model for S-wave high T_c superconductors developed by Hartnoll, Herzog and Horowitz is generalized to describe D-wave superconductors. The 3+1 dimensional gravitational theory consists a symmetric, traceless second-rank…
We propose a material platform comprised of transition metal dichalcogenide (TMDC) heterostructures to realize the two-dimensional (2D) helical superconductivity with an intrinsic gap. By van der Waals stacking a 2D superconductor…
Three-dimensional epitaxial heterostructures are based on covalently-bonded interfaces, whereas those from 2-dimensional (2D) materials exhibit van der Waals interactions. Under the right conditions, however, material structures with mixed…
Current and future surveys of large-scale cosmic structure are associated with a massive and complex datastream to study, characterize, and ultimately understand the physics behind the two major components of the 'Dark Universe', dark…
Digital and analog semantic communications (SemCom) face inherent limitations such as data security concerns in analog SemCom, as well as leveling-off and cliff-edge effects in digital SemCom. In order to overcome these challenges, we…
A novel sequence architecture is introduced, Versor, which uses Conformal Geometric Algebra (CGA) in place of traditional linear operations to achieve structural generalization and significant performance improvements on a variety of tasks,…
Hyperdimensional computing (HD) is an emerging paradigm for machine learning based on the evidence that the brain computes on high-dimensional, distributed, representations of data. The main operation of HD is encoding, which transfers the…
We introduce a framework for emulating graphs and, through them, curved spaces of arbitrary dimension, using arrays of superconducting wires. The array consists of two stacked layers of wires, horizontal and vertical, such that wires are…
Metasurfaces represent one of the most vibrant fields of modern science and technology. A metasurface is a complex electromagnetic structure, that is typically deeply subwavelength in thickness, electrically large in transverse size and…
Using symbolic regression to discover physical laws from observed data is an emerging field. In previous work, we combined genetic algorithm (GA) and machine learning to present a data-driven method for discovering a wave equation. Although…
A high-resolution time-to-digital converter (TDC) based on wave union (four-edge WU A), dual-sampling, and sub-TDL methods is proposed and implemented in a 16-nm Xilinx UltraScale+ field-programmable gate array (FPGA). We combine WU and…
An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a natural hierarchical embedding. Such hierarchical structure can be global in the data…
This is a tutorial and survey paper on unification of spectral dimensionality reduction methods, kernel learning by Semidefinite Programming (SDP), Maximum Variance Unfolding (MVU) or Semidefinite Embedding (SDE), and its variants. We first…
Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with…
Multimodal Large Language Models (MLLMs) have demonstrated immense potential in Earth observation. However, the massive visual tokens generated when processing Ultra-High-Resolution (UHR) imagery introduce prohibitive computational…