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We survey results on compact Clifford-Klein forms of homogeneous spaces, with a focus on recent contributions and organized around approaches via topology, geometry and dynamics. In addition, we survey results on moduli spaces of compact…
Multimode fibers (MMFs) can transmit multiple guided modes simultaneously, making them a promising platform for high-resolution biomedical imaging, endoscopy and high-bandwidth optical communication. However, their complex modal behavior,…
We investigate discrete fractional Laplacians defined on the half-lattice in several dimensions, allowing possibly different fractional orders along each coordinate direction. By expressing the half-lattice operator as a boundary…
Force distance curves (FCs) are among the most direct measurements performed in atomic force microscopy (AFM), yet their information content is often reduced by filtering and quasi-static interpretation. Here, enabled by a new…
We describe a time-resolved monitoring technique for heterogeneous media. Our approach is based on the spatial variations of the cross-coherence of coda waveforms acquired at fixed positions but at different dates. To locate and…
Several topics in QCD are reviewed, including: the light-cone Fock state representation, which encodes the flavor, spin and other quark and gluon correlations of hadrons in the form of universal process-independent amplitudes; the…
We study waves in a chain of dispersively coupled phase oscillators. Two approaches -- a quasi-continuous approximation and an iterative numerical solution of the lattice equation -- allow us to characterize different types of traveling…
Beta oscillations observed in motor cortical local field potentials (LFPs) recorded on separate electrodes of a multi-electrode array have been shown to exhibit non-zero phase shifts that organize into a planar wave propagation. Here, we…
Identifying and quantifying spatial correlation are important aspects of studying the collective behaviour of multi-agent systems. Pair correlation functions (PCFs) are powerful statistical tools which can provide qualitative and…
We consider the conductance distributions in chaotic mesoscopic cavities for all three invariant classes of random matrices for the arbitrary number of channels N1, N2 in the connecting leads. We show that the Laplace transforms of the…
This study presents a numerical procedure, which we call the macroscopic forcing method (MFM), which reveals the differential operators acting on the mean fields of quantities transported by underlying fluctuating flows. Specifically, MFM…
In this paper we propose Discretely Indexed flows (DIF) as a new tool for solving variational estimation problems. Roughly speaking, DIF are built as an extension of Normalizing Flows (NF), in which the deterministic transport becomes…
We study M and F theory compactifications on Calabi-Yau four-folds in the presence of non-trivial background flux. The geometry is warped and belongs to the class of p-brane metrics. We solve for the explicit warp factor in the orbifold…
We define a notion of stable and measurable map between cones endowed with measurability tests and show that it forms a cpo-enriched cartesian closed category. This category gives a denotational model of an extension of PCF supporting the…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
A compactification over $\overline{M}_g$ of $M_{g,n}$ is obtained by considering the relative Fulton-MacPherson configuration space of the universal curve. The resulting compactification differs from the Deligne-Mumford space…
Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or…
We develop foundations for oriented category theory, an extension of $(\infty,\infty)$-category theory obtained by systematic usage of the Gray tensor product, in order to study lax phenomena in higher category theory. As categorical…
The light-front quantization of gauge theories such as QCD in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a…
Microfluidic channels have emerged as useful tools to control dynamic forcing on transported microscale objects, as encountered in emulsions, biological flows, and other soft matter systems. Tailored channel designs enable precise…