Related papers: Tutorial: Classifying Photonic Topology Using the …
Entanglement, as studied in quantum information science, and non-local quantum correlations, as studied in condensed matter physics, are fundamentally akin to each other. However, their relationship is often hard to quantify due to the lack…
In this paper we report that notions of topological protection can be applied to stationary configurations that are driven far from equilibrium by active, dissipative processes. We show this for physically two disparate cases : stochastic…
Spatial labeling assigns labels to specific spatial locations to characterize their spatial properties and relationships, with broad applications in scientific research and practice. Measuring the similarity between two spatial labelings is…
We present a rigorous spectral analysis of plasmonic resonances in the nonlocal regime of spatially dispersive media. We adopt the quasi-static approximation of the hydrodynamic Drude model, which provides an analytically tractable setting…
In this paper we focus on the challenging problem of place categorization and semantic mapping on a robot without environment-specific training. Motivated by their ongoing success in various visual recognition tasks, we build our system…
The study of topological phases of light suggests novel opportunities for creating robust optical structures and on-chip photonic devices which are immune against scattering losses and structural disorder. However, many recent…
It is increasingly common for data to possess intricate structure, necessitating new models and analytical tools. Graphs, a prominent type of structure, can encode the relationships between any two entities (nodes). However, graphs neither…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
Surface plasmon resonances (SPRs) are crucial for confining light beyond the diffraction limit, yet heavy metal losses often limit their spectral localization. Here, we propose a practical strategy for enabling the spectral localization of…
The machine learning technique of persistent homology classifies complex systems or datasets by computing their topological features over a range of characteristic scales. There is growing interest in applying persistent homology to…
Wireless Technology Recognition (WTR) and localization are essential in modern communication systems, enabling efficient spectrum management, seamless coexistence of diverse technologies, and accurate positioning in dynamic environments. In…
The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it…
We introduce a new topological invariant of a rigidly-compactly generated tensor-triangulated category and two new notions of support. The first is based on smashing subcategories: it is unknown whether the frame of smashing subcategories…
In recent studies in hyperspectral imaging, biometrics and energy analytics, the framework of deep dictionary learning has shown promise. Deep dictionary learning outperforms other traditional deep learning tools when training data is…
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
We describe a framework for defining high-order image models that can be used in a variety of applications. The approach involves modeling local patterns in a multiscale representation of an image. Local properties of a coarsened image…
Diffractive nonlocal metasurfaces have recently opened a broad range of exciting developments in nanophotonics research and applications, leveraging spatially extended (yet locally patterned) resonant modes to control light with new degrees…
In the study of high-dimensional data, it is often assumed that the data set possesses an underlying lower-dimensional structure. A practical model for this structure is an embedded compact manifold with boundary. Since the underlying…
Localization of Floer homology is first introduced by Floer \cite{floer:fixed} in the context of Hamiltonian Floer homology. The author employed the notion in the Lagrangian context for the pair $(\phi_H^1(L),L)$ of compact Lagrangian…
Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…