In the standard (LCDM) model of cosmology the universe has emerged out of an early homogeneous and isotropic phase. Structure formation is associated with the growth of density irregularities and pecu...

arXiv abstract link

Density evaluation, random generation, and maximum likelihood estimation for the Mobius-von Mises-Fisher and isotropic scaled von Mises-Fisher distributions on the hypersphere, introduced in Garcia-Portugues and Kato (2026) &lt;<a href="https://doi.org/10.48550%2FarXiv.2607.29280" target="_top">doi:10.48550/arXiv.2607.29280</a>&gt;. Both distributions arise from Mobius transport of a von Mises-Fisher distribution.

Wave propagation in irregular cavities made from conventional isotropic media is typically chaotic. Now odd-shaped cavities made from hyperbolic metamaterials are shown to suppress chaotic wave dynami...

Density evaluation, random generation, and maximum likelihood estimation for the Mobius-von Mises-Fisher and isotropic scaled von Mises-Fisher distributions on the hypersphere, introduced in Garcia-Portugues and Kato (2026) &lt;<a href="https://doi.org/10.48550%2FarXiv.2607.29280" target="_top">doi:10.48550/arXiv.2607.29280</a>&gt;. Both distributions arise from Mobius transport of a von Mises-Fisher distribution.

In networks that grow by isotropic redirection (IR), a new node selects an initial target node uniformly at random and attaches to a randomly chosen neighbor of the target. The emerging networks exhib...

**Authors:** Yuxuan Liu, Youming Qiao, Gang Tang, Chuanqi Zhang Inspired by the planted clique problem for random graphs, we introduce the planted totally-isotropic space problem for random tensors as follows. Let $U\cong \mathbb{F}_q^n$ and $W\cong \mathbb{F}_q^m$ be finite-dimensional vector spaces over a finite field $\mathbb{F}_q$. Given $d\in \mathbb{N}$, choose a random \\(d\\)-dimensional subspace \\(V\leq U\\), and construct a random alternating bilinear map $φ:U\times U\to W$ subject to the constraint \\(φ(V,V)=0\\). Such a $V$ is known as a totally-isotropic space of $φ$, and the goal is to recover $V$. Building on the recent probabilistic analysis of random tensors (Pham--Qiao--Wigderson--Wigderson, \emph{in progress}), we initiate the study of the algorithmic hardness of this problem. Setting $m=\lceil n/\log n\rceil$, we show that this problem admits an average-case polynomial-time algorithm for $d\geq n/2$, by leveraging recent advances on the non-commutative rank problem. We also show that this problem admits a $q^{O(n\log n)}$-time algorithm. We carry out algorithmic experiments using polynomial-system solving. From these results, we conjecture that the planted totally-isotropic space problem for $d=\lceil n/C\rceil$ with some constant $C\geq 3$ is exponentially hard. Based on this evidence of computational hardness, we explore cryptographic applications of the planted totally-isotropic space problem and related planted tensor problems. We present private simultaneous messages and secret sharing protocols based on planted tensor problems, following the protocols based on planted subgraphs in (Abram--Beimel--Ishai--Kushilevitz--Narayanan, \emph{TCC}'23). At the same security level, the public information size of protocols based on planted subgraphs is (moderately) exponential in that of protocols based on planted tensors, while the communication costs of these protocols are polynomially related.

arXiv abstract link

**Authors:** Aleksandr Storozhenko For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant. This removes the dependence on the Poincaré constant in the theorem of Kothari and Steinhardt (arXiv:1711.07465), recovering the optimal moment bounds for log-concave distributions. As an immediate corollary, we obtain computationally efficient algorithms with dimension-free error guarantees for a wide range of high-dimensional statistical estimation problems. Our proof uses stochastic localization to decompose $P$ as an average of random strongly log-concave measures, whose centered moments admit the subgaussian certificates of Diakonikolas, Hopkins, Pensia, and Tiegel (STOC 2025; arXiv:2410.21194). With a covariance-adapted choice of localization, we show that a fourth-moment certificate derived from Letwin's variance inequality for quadratic forms (arXiv:2607.24164) suffices to control this averaging at every even degree.

Objective The anatomy of carotid arteries is evaluated with magnetic resonance angiography (MRA), while its stiffness-related parameters are evaluated using ultrasound. An isotropic three-dimensional…

Objective The anatomy of carotid arteries is evaluated with magnetic resonance angiography (MRA), while its stiffness-related parameters are evaluated using ultrasound. An isotropic three-dimensional…