相关论文: Using the No-Search Easy-Hard Technique for Downwa…

In unitary property testing a quantum algorithm, also known as a tester, is given query access to a black-box unitary and has to decide whether it satisfies some property. We propose a new technique for proving lower bounds on the quantum…

Let $d\geq 2$ and $k\geq 1$ be fixed. We prove that, for every $\epsilon>0$ and every real $\beta$, there exist integers $1\leq b_1,\ldots,b_k\leq N$ such that \[ \left\|\sum_{j=1}^k b_j^{1/d}-\beta\right\| \ll_{d,k,\epsilon}…

For every integer $n \geq 3$, we prove that the n-sublinear generalization of the Bi-Carleson operator of Muscalu, Tao, and Thiele given by nC^{\vec{\alpha}} :(f_1,..., f_n) \mapsto \sup_{M} \left| \int_{\vec{\xi} \cdot \vec{\alpha} >0,…

A nondecreasing sequence of positive integers is $(\alpha,\beta)$-Conolly, or Conolly-like for short, if for every positive integer $m$ the number of times that $m$ occurs in the sequence is $\alpha + \beta r_m$, where $r_m$ is $1$ plus the…

In quantum information, lifting is a systematic procedure that can be used to derive---when provided with a seed Bell inequality---other Bell inequalities applicable in more complicated Bell scenarios. It is known that the procedure of…

We prove that the problem of deciding the consequence relation of the full Lambek calculus with weakening is complete for the class HAck of hyper-Ackermannian problems (i.e., level F_{\omega}^{\omega} of the ordinal-indexed hierarchy of…

Higher-order beta-matching is the following decision problem: given two simply typed lambda-terms, can the first term be instantiated to be beta-equivalent to the second term? This problem was formulated by Huet in the 1970s and shown…

We prove that if $(M,\mathcal{X})$ and $(M,\mathcal{Y})$ are countable models of the theory $\mathrm{WKL}^*_0$ such that $\mathrm{I}\Sigma_1(A)$ fails for some $A \in \mathcal{X} \cap \mathcal{Y}$, then $(M,\mathcal{X})$ and…

The Coleman-Mandula theorem, which states that space-time and internal symmetries cannot be combined in any but a trivial way, is generalized to an arbitrarily higher spacelike dimension. Prospects for further generalizations of the theorem…

The Hardy--Littlewood inequality for $m$-linear forms on $\ell _{p}$ spaces and $m<p\leq 2m$ asserts that \begin{equation*} \left( \sum_{j_{1},...,j_{m}=1}^{\infty }\left\vert T\left( e_{j_{1}},\ldots ,e_{j_{m}}\right) \right\vert…

A typical theme for many well-known decomposition problems is to show that some obvious necessary conditions for decomposing a graph $G$ into copies $H_1, \ldots, H_m$ are also sufficient. One such problem was posed in 1987, by Alavi,…

We prove that the join of two sets may actually fall into a lower level of the extended low hierarchy than either of the sets. In particular, there exist sets that are not in the second level of the extended low hierarchy, EL_2, yet their…

For $\alpha, \beta, \delta \in [0,1], \alpha +\beta = 1 $ we consider sets $$ {\rm BAD}^* (\alpha, \beta ;\delta) = \left\{\xi = (\xi_1,\xi_2) \in [0,1]^2: ,\inf_{p\in \mathbb{N}} \max \{(p\log(p+1))^\alpha ||p\xi_1||, (p\log (p+1))^\beta…

Central limit theorems (CLTs) for high-dimensional random vectors with dimension possibly growing with the sample size have received a lot of attention in the recent times. Chernozhukov et al. (2017) proved a Berry--Esseen type result for…

The theoretical basis of the phenomenon of effective and exact dimensional reduction, or holographic correspondence, is investigated in a wide variety of physical systems. We first derive general inequalities linking quantum systems of…

The Bohnenblust-Hille inequality for $m$-linear forms was proven in 1931 as a generalization of the famous 4/3-Littlewood inequality. The optimal constants (or at least their asymptotic behavior as $m$ grows) is unknown, but significant for…

It is known that $Q$-conditional symmetries of the classical Burgers' equation express in terms of three functions satisfying a coupled system of Burgers-like equations. The search of conditional symmetries of this system leads to a system…

The goal of universal machine translation is to learn to translate between any pair of languages, given a corpus of paired translated documents for \emph{a small subset} of all pairs of languages. Despite impressive empirical results and an…

Hierarchical block diagrams (HBDs) are at the heart of embedded system design tools, including Simulink. Numerous translations exist from HBDs into languages with formal semantics, amenable to formal verification. However, none of these…

In this paper, we provide both a preservation and breaking of symmetry theorem for $2\pi$-periodic problems of the form \begin{align*} \begin{cases} -u''(t) + g(u(t)) = f(t)\cr u(0) - u(2\pi) = u'(0) - u'(2\pi) = 0 \end{cases} \end{align*}…