Related papers: A Simple Constructive Bound on Circuit Size Change…

An error model with asymmetric single magnitude four error is considered. This paper is about constructions of codes correcting single error over $\mathbb{Z}_{2^{a}3^{b}r}$. Firstly, we reduce the construction of a maximal size…

Photonic structures with high-$Q$ resonances are essential for many practical applications, and they can be relatively easily realized by modifying ideal structures with bound states in the continuum (BICs). When an ideal photonic structure…

We study the binomial channel and the structure of its capacity-achieving input and output distributions. It is known that the capacity-achieving input distribution is discrete and supported on finitely many points. The best previously…

We show that every triangulation (maximal planar graph) on $n\ge 6$ vertices can be flipped into a Hamiltonian triangulation using a sequence of less than $n/2$ combinatorial edge flips. The previously best upper bound uses $4$-connectivity…

We show that there is a language in $\mathsf{S}_2\mathsf{E}/_1$ (symmetric exponential time with one bit of advice) with circuit complexity at least $2^n/n$. In particular, the above also implies the same near-maximum circuit lower bounds…

We prove new upper bounds on the tolerable level of noise in a quantum circuit. We consider circuits consisting of unitary k-qubit gates each of whose input wires is subject to depolarizing noise of strength p, as well as arbitrary…

Supersymmetric extensions of the Standard Model generally give a theoretical upper limit on the lightest Higgs boson mass which may be uncomfortably close to the current experimental lower bound of $m_h$ > 114 GeV. Here we show ways in…

Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which has led to a wide variety of applications. Over the past decades, advances in quantum computing provide opportunities for…

For the minimal $\lambda$-supersymmetry, it stays perturbative to the GUT scale for $\lambda \leq 0.7$. This upper bound is relaxed when one either takes the criteria that all couplings close to $\sim 4\pi$ for non-perturbation or allows…

In a general supersymmetric standard model there is an upper bound $m_h$ on the tree level mass of the $CP=+1$ lightest Higgs boson which depends on the electroweak scale, $\tan \beta$ and the gauge and Yukawa couplings of the theory. When…

Let $T$ be an $n$-node tree of maximum degree 4, and let $P$ be a set of $n$ points in the plane with no two points on the same horizontal or vertical line. It is an open question whether $T$ always has a planar drawing on $P$ such that…

A classical result by Erd\H{o}s, and later on by Bondy and Simonivits, states that every $n$-vertex graph with no cycle of length $2k$ has at most $O(n^{1+1 /k})$ edges. This bound is known to be tight when $k \in \{2,3,5\},$ but it is a…

Let $\eta_0$ be the supremum of those $\eta$ for which every poly-size quantum circuit can be simulated by another poly-size quantum circuit with gates of fan-in $\leq 2$ that tolerates random noise independently occurring on all wires at…

Let $A(n,d)$ (respectively $A(n,d,w)$) be the maximum possible number of codewords in a binary code (respectively binary constant-weight $w$ code) of length $n$ and minimum Hamming distance at least $d$. By adding new linear constraints to…

We compute all of the one-loop corrections that are enhanced, $O(\lambda_i \lambda_j / 16 \pi^2)$, in the limit $s \gg |\lambda_i | v^2 \gg M_{W}^2$, $s \gg m_{12}^2$ to all the $2 \to 2$ longitudinal vector boson and Higgs boson scattering…

Let M(n, d) be the maximum size of a permutation array on n symbols with pairwise Hamming distance at least d. We use various combinatorial, algebraic, and computational methods to improve lower bounds for M(n, d). We compute the Hamming…

We show that there is a constant $k$ such that Buss's intuitionistic theory $\mathsf{IS}^1_2$ does not prove that SAT requires co-nondeterministic circuits of size at least $n^k$. To our knowledge, this is the first unconditional…

We prove a lower bound of $\Omega(n^2/\log^2 n)$ on the size of any syntactically multilinear arithmetic circuit computing some explicit multilinear polynomial $f(x_1, \ldots, x_n)$. Our approach expands and improves upon a result of Raz,…

Generating functions for the size of a $r$-sphere, with respect to the Manhattan distance in an $n$-dimensional grid, are used to provide explicit formulas for the minimum and maximum size of an $r$-ball centered at a point of the grid.…

In this paper we show that the largest possible size of a subset of $\mathbb{F}_q^n$ avoiding right angles, that is, distinct vectors $x,y,z$ such that $x-z$ and $y-z$ are perpendicular to each other is at most $O(n^{q-2})$. This improves…