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For a real number $0<\lambda<2$, we introduce a transformation $T_\lambda$ naturally associated to expansion in $\lambda$-continued fraction, for which we also give a geometrical interpretation. The symbolic coding of the orbits of…
Density functional theory (DFT) is used to study vibrations, electrical dipole moments, and polarizabilities of NaF clusters. Because of prior experimental and theoretical studies, this is a good model system for tracking the evolution of…
Topological qubits based on Majorana fermions have the potential to revolutionize the emerging field of quantum computing by making information processing significantly more robust to decoherence. Nanowires (NWs) are a promising medium for…
First-order nonadiabatic coupling matrix elements (fo-NACMEs) are the basic quantities in theoretical descriptions of electronically nonadiabatic processes that are ubiquitous in molecular physics and chemistry. Given the large size of…
In this work, we extend the non-orthogonal amplify-and-forward (NAF) cooperative diversity scheme to the MIMO channel. A family of space-time block codes for a half-duplex MIMO NAF fading cooperative channel with N relays is constructed.…
Full Waveform Inversion (FWI) stands as a nonlinear, high-resolution technology for subsurface imaging via surface-recorded data. This paper introduces an augmented Lagrangian dual formulation for FWI, rooted in the viewpoint that Lagrange…
Open quantum-system dynamics can follow exponential decay, non-exponential relaxation, or oscillatory dynamics, depending on the system-environment coupling. We study a lattice with a boundary defect that transitions between these regimes,…
Epitaxially-grown semiconductor heterostructures give the possibility to tailor the potential landscape for the carriers in a very controlled way. In planar lattice-matched heterostructures, the potential has indeed a very simple and easily…
A Theorem of Wang in [Wa] implies that any holomorphic parallelism on a compact complex manifold M is flat with respect to some complex Lie algebra structure whose dimension coincides with that of M. We study here rational parallelisms on…
We investigate the distribution of the largest digit for a wide class of infinite parabolic Iterated Function Systems (IFSs) of the unit interval. Due to the recurrence to parabolic (neutral) fixed points, the dimension analysis of these…
In this paper, we study inhomogeneous Diophantine approximation with rational numbers of reduced form. The central object to study is the set $W(f,\theta)$ as follows, \begin{eqnarray*} \left\{x\in [0,1]:\left…
The study of constant-weight codes in $\ell_1$-metric was motivated by the duplication-correcting problem for data storage in live DNA. It is interesting to determine the maximum size of a code given the length $n$, weight $w$, minimum…
Every $n$-tuple in $\mathbb{F}^{n}$ has a first non-zero entry and a last non-zero entry. What do the positions of such entries in the elements of a subspace W of $\mathbb{F}^{n}$ reveal about W? It turns out, a great deal! This insight…
The ability to perform mathematical computations using metastructures is an emergent paradigm that carries the potential of wave-based analog computing to the realm of near-speed-of-light, low-loss, compact devices. We theoretically…
We study some aspects of noncommutative differential geometry on a finite Weyl group in the sense of S. Woronowicz, K. Bresser {\it et al.}, and S. Majid. For any finite Weyl group $W$ we consider the subalgebra generated by flat…
This article continues the investigation of the tracial geometry of classifiable $\mathrm{C}^*$-algebras that have real rank zero and stable rank one. Using the language of optimal transport, we describe several situations in which the…
A graph with vertex set V and edge set E is called a (d,c)-expander if the maximum degree of a vertex is d and, for every subset W of V that has cardinality at most |V|/2, the number of edges between vertices in W and vertices outside of W…
We present a computational scheme for orbital-free density functional theory (OFDFT) that simultaneously provides access to all-electron values and preserves the OFDFT linear scaling as a function of the system size. Using the projector…
The maximum size of a binary code is studied as a function of its length N, minimum distance D, and minimum codeword weight W. This function B(N,D,W) is first characterized in terms of its exponential growth rate in the limit as N tends to…
This work introduces NetDiff, an expressive graph denoising diffusion probabilistic architecture that generates wireless ad hoc network link topologies. Such networks, with directional antennas, can achieve unmatched performance when the…