Zobrazeno 1 - 10
of 311
pro vyhledávání: '"Ben Lee"'
We design a deterministic subexponential time algorithm that takes as input a multivariate polynomial $f$ computed by a constant-depth circuit over rational numbers, and outputs a list $L$ of circuits (of unbounded depth and possibly with division ga
Externí odkaz:
http://arxiv.org/abs/2403.01965
We construct explicit pseudorandom generators that fool $n$-variate polynomials of degree at most $d$ over a finite field $\mathbb{F}_q$. The seed length of our generators is $O(d \log n + \log q)$, over fields of size exponential in $d$ and characte
Externí odkaz:
http://arxiv.org/abs/2402.11915
We show that for every homogeneous polynomial of degree $d$, if it has determinantal complexity at most $s$, then it can be computed by a homogeneous algebraic branching program (ABP) of size at most $O(d^5s)$. Moreover, we show that for $\textit{mos
Externí odkaz:
http://arxiv.org/abs/2308.04599
Autor:
Bhargavee Gnanasambandam, Jacob Prince, Siddharth Limaye, Eric Moran, Ben Lee, Justin Huynh, Joseph Irudayaraj, Michael Tsipursky
Publikováno v:
Therapeutic Advances in Ophthalmology, Vol 16 (2024)
Retinal hypoxia stands as a pivotal yet often underappreciated factor in the etiology and progression of many retinal disorders such as glaucoma, hypertensive retinopathy, diabetic retinopathy, retinal vein occlusions, and retinal artery occlusions.
Externí odkaz:
https://doaj.org/article/588edba65e7c494db84aa5da87e48edc
We construct explicit deterministic extractors for polynomial images of varieties, that is, distributions sampled by applying a low-degree polynomial map $f : \mathbb{F}_q^r \to \mathbb{F}_q^n$ to an element sampled uniformly at random from a $k$-dim
Externí odkaz:
http://arxiv.org/abs/2211.14497
We give reconstruction algorithms for subclasses of depth-3 arithmetic circuits. In particular, we obtain the first efficient algorithm for finding tensor rank, and an optimal tensor decomposition as a sum of rank-one tensors, when given black-box ac
Externí odkaz:
http://arxiv.org/abs/2209.04177
Publikováno v:
Tehnički Vjesnik, Vol 31, Iss 1, Pp 48-55 (2024)
The rapid expansion of the Internet of Things (IoT) has led to increased concerns regarding the security of IoT systems. Attacks targeting IoT devices, such as code injection and code reuse, have become more sophisticated, compromising device control
Externí odkaz:
https://doaj.org/article/99ec5b4824474452bbf84f38e003413a
Publikováno v:
Quantum 6, 652 (2022)
The stabilizer rank of a quantum state $\psi$ is the minimal $r$ such that $\left| \psi \right \rangle = \sum_{j=1}^r c_j \left|\varphi_j \right\rangle$ for $c_j \in \mathbb{C}$ and stabilizer states $\varphi_j$. The running time of several classical
Externí odkaz:
http://arxiv.org/abs/2106.03214
Autor:
Kumar, Mrinal, Volk, Ben Lee
The determinantal complexity of a polynomial $P \in \mathbb{F}[x_1, \ldots, x_n]$ over a field $\mathbb{F}$ is the dimension of the smallest matrix $M$ whose entries are affine functions in $\mathbb{F}[x_1, \ldots, x_n]$ such that $P = Det(M)$. We pr
Externí odkaz:
http://arxiv.org/abs/2009.02452
Autor:
Kumar, Mrinal, Volk, Ben Lee
We show that there is a defining equation of degree at most $\mathsf{poly}(n)$ for the (Zariski closure of the) set of the non-rigid matrices: that is, we show that for every large enough field $\mathbb{F}$, there is a non-zero $n^2$-variate polynomi
Externí odkaz:
http://arxiv.org/abs/2003.12938