Related papers: Sensitivity, Affine Transforms and Quantum Communi…

We consider the $\alpha$-sine transform of the form $T_\alpha f(y)=\int_0^\infty\vert\sin(xy)\vert^\alpha f(x)dx$ for $\alpha>-1$, where $f$ is an integrable function on $\mathbb{R}_+$. First, the inversion of this transform for $\alpha>1$…

The advancement to 6G calls for waveforms that transcend static robustness to achieve intelligent adaptability. Affine Frequency Division Multiplexing (AFDM), despite its strength in doubly-dispersive channels, has been confined by chirp…

For any Boolean function $f:\{0,1\}^n \to \{0,1\}$ with a complexity measure having value $k \ll n$, is it possible to restrict the function $f$ to $\Theta(k)$ variables while keeping the complexity preserved at $\Theta(k)$? This question,…

We estimate sensitivity coefficients to variation of the fine-structure constant alpha and electron-to-proton mass ratio mu for microwave Lambda-type transitions in CH molecule and for inversion-rotational transitions in partly deuterated…

This paper provides a fundamental characterization of the discrete ambiguity functions (AFs) of random communication waveforms under arbitrary orthonormal modulation with random constellation symbols, which serve as a key metric for…

In 2003 we have measured the absolute frequency of the $(1S, F=1, m_F=\pm 1) \leftrightarrow (2S, F'=1, m_F'=\pm 1)$ two-photon transition in atomic hydrogen. We observed a variation of $(-29\pm 57)$ Hz over a 44 months interval separating…

We present an analytic calculation of the layer (parallel) susceptibility at the extraordinary transition in a semi-infinite system with a flat boundary. Using the method of integral transforms put forward by McAvity and Osborn [Nucl. Phys.…

We consider a variant of the Boolean satisfiability problem where a subset E of the propositional variables appearing in formula Fsat encode a symmetric, transitive, binary relation over N elements. Each of these relational variables,…

We study the communication complexity of computing functions $F:\{0,1\}^n\times \{0,1\}^n \rightarrow \{0,1\}$ in the memoryless communication model. Here, Alice is given $x\in \{0,1\}^n$, Bob is given $y\in \{0,1\}^n$ and their goal is to…

We obtain strict upper bounds on the bit transmission rate for communication of Classical bit codewords over Quantum channels. Albeit previous arguments in arXiv: 1804.01797 which have demonstrated that lower bounds can be shown to hold for…

The quasiparticle finite amplitude method (QFAM) is extended to describe charge-exchange transitions based on the relativistic Hartree-Bogoliubov model, adopting the point-coupling energy density functional DD-PC1 and a finite-range…

It is known that the continuous wavelet transform of a function $f$ decays very rapidly near the points where $f$ is smooth, while it decays slowly near the irregular points. This property allows one to precisely identify the singular…

We study nondeterministic communication complexity and related concepts (fooling sets, fractional covering number) of random functions $f\colon X\times Y \to \{0,1\}$ where each value is chosen to be 1 independently with probability…

We study the problem of \emph{architecture selection} for deep learning models trained to solve partial differential equations (PDEs), asking when transformer-based architectures with learned attention outperform Fourier-domain neural…

The wave-function-matching (WFM) technique for first-principles transport-property calculations was modified by S\o{}rensen {\it et al.} so as to exclude rapidly decreasing evanescent waves [S\o{}rensen {\it et al.}, Phys. Rev. B {\bf 77},…

Quantum entanglement cannot be used to achieve direct communication between remote parties, but it can reduce the communication needed for some problems. Let each of k parties hold some partial input data to some fixed k-variable function…

For $S \subseteq \{0,1\}^n$ a Boolean function $f \colon S \to \{-1,1\}$ is a polynomial threshold function (PTF) of degree $d$ and weight $W$ if there is a polynomial $p$ with integer coefficients of degree $d$ and with sum of absolute…

In the development of atomic clocks, some atomic transition frequencies are measured with remarkable precision. These measured spectra may include effects of a new force mediated by a weakly interacting boson. Such effects might be…

The past several years have witnessed a surge of research investigating various aspects of sparse representations and compressed sensing. Most of this work has focused on the finite-dimensional setting in which the goal is to decompose a…

The ^{207}Pb^{19}F molecule possesses a pair of closely spaced levels of opposite parity due to near cancelation of the omega-type doubling and magnetic hyperfine interaction energy shifts [Alphei et al., Phys. Rev. A, 83, 040501 (2011)].…