Related papers: Sensitivity, Affine Transforms and Quantum Communi…
We consider the Stochastic Boolean Function Evaluation (SBFE) problem where the task is to efficiently evaluate a known Boolean function $f$ on an unknown bit string $x$ of length $n$. We determine $f(x)$ by sequentially testing the…
The nonlinear Fourier transform has the potential to overcome limits on performance and achievable data rates which arise in modern optical fiber communication systems when nonlinear interference is treated as noise. The periodic nonlinear…
Given an $n$-bit Boolean function with a complexity measure (such as block sensitivity, query complexity, etc.) $M(f) = k$, the hardness condensation question asks whether $f$ can be restricted to $O(k)$ variables such that the complexity…
The main conceptual contribution of this paper is investigating quantum multiparty communication complexity in the setting where communication is \emph{oblivious}. This requirement, which to our knowledge is satisfied by all quantum…
One of the key challenges in machine learning is to find interpretable representations of learned functions. The M\"obius transform is essential for this purpose, as its coefficients correspond to unique importance scores for sets of input…
We revisit the problem of model-based object recognition for intensity images and attempt to address some of the shortcomings of existing Bayesian methods, such as unsuitable priors and the treatment of residuals with a non-robust error…
We derive lower bounds for tradeoffs between the communication C and space S for communicating circuits. The first such bound applies to quantum circuits. If for any function f with image Z the multicolor discrepancy of the communication…
The Transformer is the foundational building block of modern AI, yet offers no principled handling of \emph{uncertainty}, which is prevalent in real applications: cold-start tokens with sparse histories in sequential recommendation,…
We study parity decision trees for Boolean functions. The motivation of our study is the log-rank conjecture for XOR functions and its connection to Fourier analysis and parity decision tree complexity. Let f be a Boolean function with…
We show examples of total Boolean functions that depend on $n$ variables and have spectral sensitivity $\Theta(\sqrt{\log n})$, which is asymptotically minimal. Our main new function combines the Hamming code with the Boolean address…
The next generation of wireless communication technology is anticipated to address the communication reliability challenges encountered in high-speed mobile communication scenarios. An Orthogonal Time Frequency Space (OTFS) system has been…
We study the contact terms that appear in the correlation functions of exactly marginal operators using the AdS/CFT correspondence. It is known that CFT with an exactly marginal deformation requires the existence of the contact terms with…
We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…
In this paper, we study the convolution structure in the special affine Fourier transform domain to combine the advantages of the well known special affine Fourier and Stockwell transforms into a novel integral transform coined as special…
A robust variational approach is used to investigate the sensitivity of the rotation-vibration spectrum of phosphine (PH$_3$) to a possible cosmological variation of the proton-to-electron mass ratio, $\mu$. Whilst the majority of computed…
In this thesis we apply techniques from quantum information theory to study quantum gravity within the framework of the anti-de Sitter / conformal field theory correspondence (AdS/CFT). Through AdS/CFT, progress has been made in…
We establish new upper and lower bounds on the number of queries required to test convexity of functions over various discrete domains. 1. We provide a simplified version of the non-adaptive convexity tester on the line. We re-prove the…
The correlation-immune functions serve as an important metric for measuring resistance of a cryptosystem against correlation attacks. Existing literature emphasize on matrices, orthogonal arrays and Walsh-Hadamard spectra to characterize…
We present Affine Frequency Division Multiplexing (AFDM), a new chirp-based multicarrier transceiver scheme for high mobility communications in next-generation wireless systems. AFDM is based on discrete affine Fourier transform (DAFT), a…
In a recent result, Knop, Lovett, McGuire and Yuan (STOC 2021) proved the log-rank conjecture for communication complexity, up to log n factor, for any Boolean function composed with AND function as the inner gadget. One of the main tools…