Related papers: Sensitivity, Affine Transforms and Quantum Communi…
The sensitivity of rotational transitions in CH and CD to a possible variation of fundamental constants has been investigated. Largely enhanced sensitivity coefficients are found for specific transitions which are due to accidental…
Buhrman, Cleve and Wigderson (STOC'98) observed that for every Boolean function $f : \{-1, 1\}^n \to \{-1, 1\}$ and $\bullet : \{-1, 1\}^2 \to \{-1, 1\}$ the two-party bounded-error quantum communication complexity of $(f \circ \bullet)$ is…
The noise sensitivity of a Boolean function $f: \{0,1\}^n \rightarrow \{0,1\}$ is one of its fundamental properties. A function of a positive noise parameter $\delta$, it is denoted as $NS_{\delta}[f]$. Here we study the algorithmic problem…
We characterize the pre-softmax attention matrix $\mathbf{QK^\top}$ in transformers as an associative memory matrix encoding pairwise associations between input features. By decomposing this matrix into its symmetric and skew-symmetric…
Affine frequency division multiplexing (AFDM) is a chirp-based multicarrier waveform that was recently proposed for communication over doubly dispersive channels. Given its chirp nature, AFDM is expected to have superior sensing…
We propose a new frequency standard based on a $4f^{14} 6s6p~ ^3\!P_0 - 4f^{13} 6s^2 5d ~(J=2)$ transition in neutral Yb. This transition has a potential for high stability and accuracy and the advantage of the highest sensitivity among…
Invariance with respect to linear or affine transformations of the domain is arguably the most common symmetry exhibited by natural algebraic properties. In this work, we show that any low complexity affine-invariant property of…
Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…
Error correction code is a major part of the communication physical layer, ensuring the reliable transfer of data over noisy channels. Recently, neural decoders were shown to outperform classical decoding techniques. However, the existing…
This paper presents a novel method for the sensitivity analysis of electromagnetic (EM) systems whose transfer function (TF), that is the input-output (I/O) relationship between the input parameters affected by tolerance and the system…
Artificial Neural Networks of varying architectures are generally paired with affine transformation at the core. However, we find dot product neurons with global influence less interpretable as compared to local influence of euclidean…
Let $\mathcal{P}$ be a property of function $\mathbb{F}_p^n \to \{0,1\}$ for a fixed prime $p$. An algorithm is called a tester for $\mathcal{P}$ if, given a query access to the input function $f$, with high probability, it accepts when $f$…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
Certain aspects of the AdS/CFT correspondence are studied in detail. We investigate the one-loop mass shift to certain two-impurity string states in light-cone string field theory on a plane wave background. We find that there exist…
The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission…
We revisit the Fourier transform of a Hankel function, of considerable importance in the theory of knife edge diffraction. Our approach is based directly upon the underlying Bessel equation, which admits manipulation into an alternate…
For any $n$-bit boolean function $f$, we show that the randomized communication complexity of the composed function $f\circ g^n$, where $g$ is an index gadget, is characterized by the randomized decision tree complexity of $f$. In…
Different transformer architectures implement identical linguistic computations via distinct connectivity patterns, yielding model imprinted ``computational fingerprints'' detectable through spectral analysis. Using graph signal processing…
In this note we give a new separation between sensitivity and block sensitivity of Boolean functions: $bs(f)=(2/3)s(f)^2-(1/3)s(f)$.
In this paper, we establish a lemma in algebraic coding theory that frequently appears in the encoding and decoding of, e.g., Reed-Solomon codes, algebraic geometry codes, and affine variety codes. Our lemma corresponds to the…