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ETH-Tight Complexity of Optimal Morse Matching on Bounded-Treewidth Complexes
arXiv:2603.05406v2 Announce Type: replace Abstract: The Optimal Morse Matching (OMM) problem asks for a discrete gradient vector field on a simplicial complex that minimizes the number of critical simplices. It is NP-hard and has been studied extensively in heuristic, approximation, and parameterized complexity settings. Parameterized by treewidth $k$, OMM has long been known to be solvable on triangulations of $3$-manifolds in $2^{O(k^2)} n^{O(1)}$ time and in FPT time for triangulations of...
Palindrome complexity versus factor complexity
arXiv:2606.08127v1 Announce Type: cross Abstract: Let ${\bf x} = (a_i)_{i \geq 0}$ be an infinite word over a finite alphabet $\Sigma$. Let $\rho (n)$ be the factor complexity function for $\bf x$ and ${\rm Pal}(n)$ be the palindrome complexity function for $\bf x$. We give a new relationship between these two quantities; namely, if $\bf x$ is not ultimately periodic, then $$ \lim_{n \rightarrow \infty} {{ {\rm Pal} (n) \log ({\rm Pal} (n) + 1)} \over {\rho (n)}} = 0.
Local Clustering on Complex Graphs and Complex Hypergraphs
Announce Type: replace Abstract: Local/seeded clustering aims to find a compact cluster near the given starting instances. While most existing studies on graph clustering assume a discrete graph setting (i.e., unweighted, undirected graphs without self-loops), real-world graphs can be more complex. In this paper, we extend the classic non-approximating Andersen-Chung-Lang (ACL) clustering algorithm beyond discrete graphs and generalize its quadratic optimality to a wider range of complex...
Bit-counting complexity classes
arXiv:2606.04406v1 Announce Type: new Abstract: We define a new family of complexity classes called bit-counting complexity classes, since membership depends not merely on the number of accepting paths, but also on the binary profile of that number. We study the relationship between this new family of complexity classes and the classical complexity classes. We prove that the classical complexity class ${\bf PP}$ is contained in our comparison based bit-counting complexity classes ${\bf...
Video: Israel claims strike on Iranian petrochemical complex
Israel claims strike on Iranian petrochemical complex Video: Israel claims strike on Iranian petrochemical complex Video shows plumes of smoke rising from Mahshahr Petrochemical Complex in Iran’s Khuzestan Province on Monday. Israel says it hit the complex and other military targets; an Iranian official said parts of the plant were damaged. Published On 8 Jun 2026
Structural basis for chaperone-guided assembly of RNA-induced silencing complex
Abstract The RNA-induced silencing complex (RISC), comprising an Argonaute (AGO) protein and a small RNA, is the central effector in RNA silencing. Small RNAs are loaded onto AGO as bulky duplexes in an HSP70- and HSP90-dependent process1,2,3, but the molecular mechanism remains poorly understood. Here we identify the human AGO–HSP90–p23 complex, which captures AGO in an RNA-free state, termed the AGO maturation complex (AMC).
Cohomology of Finite Element Stokes Complexes on Alfeld Splits
arXiv:2605.31348v1 Announce Type: new Abstract: We show that the cohomology of the finite element Stokes complex consisting of piecewise polynomials spaces on an Alfeld split mesh from Fu, Guzm\'{a}n, & Neilan (2020, Math. Comp., 89, 1059--1091) is isomorphic to the cohomologies of the continuous Stokes and de Rham complexes. We also construct novel "minimal" conforming finite element complexes where the $H^1$-conforming space is the lowest-order space from Guzm\'{a}n & Neilan (2018, SIAM J....
The NF-operator and the NF-Numbers of Simplicial Complexes
arXiv:2605.30781v1 Announce Type: cross Abstract: Let $\bigtriangleup$ be a simplicial complex and let $\delta_{\mathcal{NF}}$ denote the NF-operator. The NF-complex $\delta_{\mathcal{NF}}(\bigtriangleup)$ is defined as the Stanley--Reisner complex of the facet ideal of $\bigtriangleup$. Iterating $\delta_{\mathcal{NF}}$ gives a periodic orbit (up to isomorphism), and the smallest positive integer $t$ for which $\delta_{\mathcal{NF}}^{\,t}(\bigtriangleup)\cong \bigtriangleup$ is called the...
Complex Bounded Operators in Isabelle/HOL
Announce Type: replace Abstract: We present a formalization of bounded operators on complex vector spaces in Isabelle/HOL. Our formalization contains material on complex vector spaces (normed spaces, Banach spaces, Hilbert spaces) that complements and goes beyond the developments of real vectors spaces in the Isabelle/HOL standard library. We define the type of bounded operators between complex vector spaces (cblinfun) and develop the theory of unitaries, projectors, extension of bounded...
ComplexityMT: Benchmarking the Interaction Between Text Complexity and Machine Translation
arXiv:2606.05421v1 Announce Type: new Abstract: When a text is translated, does the translation retain the complexity of the original? We introduce ComplexityMT, a new challenge for assessing how text complexity and machine translation interact with and influence each other, using the Common European Framework of Reference for Languages (CEFR) levels as the measure of text complexity. Across six languages, including Arabic, Dutch, English, French, Hindi, and Russian, we evaluate three...