Related papers: On Block Sensitivity and Fractional Block Sensitiv…
Context. We study the relation between the known binary fraction and spectral absorption feature index to judge whether (and potentially which) spectral absorption feature indices are suitable for determining the binary fraction. Aims. The…
Knowledge of the Bs decay fraction of the Y(5S) resonance, fs, is important for Bs meson studies at the Y(5S) energy. Using data collected by the CLEO III detector at CESR consisting of 0.423 1/fb on the Y(5S) resonance, 6.34 1/fb on the…
We study the relationship between two measures of Boolean functions; \emph{algebraic thickness} and \emph{normality}. For a function $f$, the algebraic thickness is a variant of the \emph{sparsity}, the number of nonzero coefficients in the…
Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence…
In this note we compare two measures of the complexity of a class $\mathcal F$ of Boolean functions studied in (unconditional) pseudorandomness: $\mathcal F$'s ability to distinguish between biased and uniform coins (the coin problem), and…
Nisan and Szegedy (CC 1994) showed that any Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ that depends on all its input variables, when represented as a real-valued multivariate polynomial $P(x_1,\ldots,x_n)$, has degree at least $\log…
Let $n$ be a positive integer and $f$ a differentiable function from a convex subset $C$ of the Euclidean space $\mathbb{R}^n$ to a smooth manifold. We define an invariant of $f$ via counting certain threshold functions associated to $f$.…
We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In…
This paper provides yet another look at the mixed fractional Brownian motion (fBm), this time, from the spectral perspective. We derive an approximation for the eigenvalues of its covariance operator, asymptotically accurate up to the…
The Sensitivity Conjecture and the Log-rank Conjecture are among the most important and challenging problems in concrete complexity. Incidentally, the Sensitivity Conjecture is known to hold for monotone functions, and so is the Log-rank…
For every $\epsilon>0$, we give an $\exp(\tilde{O}(\sqrt{n}/\epsilon^2))$-time algorithm for the $1$ vs $1-\epsilon$ \emph{Best Separable State (BSS)} problem of distinguishing, given an $n^2\times n^2$ matrix $\mathcal{M}$ corresponding to…
Boolean matching is significant to digital integrated circuits design. An exhaustive method for Boolean matching is computationally expensive even for functions with only a few variables, because the time complexity of such an algorithm for…
We propose a fluctuation-dissipation theorem in open quantum systems from an information-theoretic perspective. We define the fidelity susceptibility that measures the sensitivity of the systems under perturbation and relate it to the…
We give a non-adaptive algorithm that makes $2^{\tilde{O}(\sqrt{k\log(1/\varepsilon_2 - \varepsilon_1)})}$ queries to a Boolean function $f:\{\pm 1\}^n \rightarrow \{\pm 1\}$ and distinguishes between $f$ being $\varepsilon_1$-close to some…
The randomized query complexity $R(f)$ of a boolean function $f\colon\{0,1\}^n\to\{0,1\}$ is famously characterized (via Yao's minimax) by the least number of queries needed to distinguish a distribution $D_0$ over $0$-inputs from a…
We show conflict complexity of every total Boolean function, recently introduced in [Swagato Sanyal. A composition theorem via conict complexity. arXiv preprint arXiv:1801.03285, 2018.] to prove a composition theorem of randomized decision…
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…
We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs…
We prove two main results on how arbitrary linear threshold functions $f(x) = \sign(w\cdot x - \theta)$ over the $n$-dimensional Boolean hypercube can be approximated by simple threshold functions. Our first result shows that every…
The $\epsilon$-approximate degree $deg_\epsilon(f)$ of a Boolean function $f$ is the least degree of a real-valued polynomial that approximates $f$ pointwise to error $\epsilon$. The approximate degree of $f$ is at least $k$ iff there…