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Multiple Timescale Dynamics of Network Adaptation with Constraints
Erik Andreas Martens, Christian Bick
https://arxiv.org/abs/2507.06359 https://

Multiple Timescale Dynamics of Network Adaptation with Constraints
Adaptive network dynamical systems describe the co-evolution of dynamical quantities on the nodes as well as dynamics of the network connections themselves. For dense networks of many nodes, the resulting dynamics are typically high-dimensional. Here we consider adaptive dynamical systems subject to constraints on network adaptation: Asymptotically, the adaptive dynamics of network connections evolve on a low-dimensional subset of possible connectivity. Such dimension reduction may be intrinsic…

Non-symmetric solutions to an overdetermined problem for the Helmholtz equation in the plane
Miles H. Wheeler
https://arxiv.org/abs/2509.00455 https://arxi…

Non-symmetric solutions to an overdetermined problem for the Helmholtz equation in the plane
In this note we construct smooth bounded domains $Ω\subset \mathbb R^2$, other than disks, for which the overdetermined problem $$ \left\{ \begin{alignedat}{2} Δu + λu &= 0 &\qquad& \text{ in } Ω, \newline u &= b &\qquad& \text{ on } \partial Ω, \newline \frac{\partial u}{\partial n} &= c &\qquad& \text{ on } \partial Ω \end{alignedat} \right. $$ has a solution for some constants $λ,b,c \ne 0$. These appear to be the first counterexamples to a conjecture of Willms and Gladw…

Environmental (in)considerations in the Design of Smartphone Settings
Thomas Thibault, L\'ea Mosesso, Camille Adam, Aur\'elien Tabard, Ana\"elle Beignon, Nolwenn Maudet
https://arxiv.org/abs/2507.19094

Environmental (in)considerations in the Design of Smartphone Settings
Designing for sufficiency is one of many approaches that could foster more moderate and sustainable digital practices. Based on the Sustainable Information and Communication Technologies (ICT) and Human-Computer Interaction (HCI) literature, we identify five environmental settings categories. However, our analysis of three mobile OS and nine representative applications shows an overall lack of environmental concerns in settings design, leading us to identify six pervasive anti-patterns. Environ…

Replaced article(s) found for nlin.SI. https://arxiv.org/list/nlin.SI/new
[1/1]:
- Kuramoto meets Koopman: Constants of motion, symmetries, and network motifs
Vincent Thibeault, Benjamin Claveau, Antoine Allard, Patrick Desrosiers

Be sure to take your vitamins! https://pubmed.ncbi.nlm.nih.gov/40628762/

Replaced article(s) found for nlin.PS. https://arxiv.org/list/nlin.PS/new
[1/1]:
- Geometrically constrained sine-Gordon field: BPS solitons and their collisions
E. da Hora, L. Pereira, C. dos Santos, F. C. Simas

Equality condition for a matrix inequality by partial transpose
Nalan Wang, Lin Chen
https://arxiv.org/abs/2508.18644 https://arxiv.org/pdf/2508.18644

Equality condition for a matrix inequality by partial transpose
The partial transpose map is a linear map widely used quantum information theory. We study the equality condition for a matrix inequality generated by partial transpose, namely $\rank(\sum^K_{j=1} A_j^T \otimes B_j)\le K \cdot \rank(\sum^K_{j=1} A_j \otimes B_j)$, where $A_j$'s and $B_j$'s are respectively the matrices of the same size, and $K$ is the Schmidt rank. We explicitly construct the condition when $A_i$'s are column or row vectors, or $2\times 2$ matrices. For the case where the Schmi…

A High-Order, Pressure-Robust, and Decoupled Finite Difference Method for the Stokes Problem
Qiwei Feng, Bin Han, Michael Neilan
https://arxiv.org/abs/2506.13645

A High-Order, Pressure-Robust, and Decoupled Finite Difference Method for the Stokes Problem
In this paper, we consider the Stokes problem with Dirichlet boundary conditions and the constant kinematic viscosity $ν$ in an axis-aligned domain $Ω$. We decouple the velocity $\bm u$ and pressure $p$ by deriving a novel biharmonic equation in $Ω$ and third-order boundary conditions on $\partialΩ$. In contrast to the fourth-order streamfunction approach, our formulation does not require $Ω$ to be simply connected. For smooth velocity fields $\bm u$ in two dimensions, we explicitly constr…

Three Generalizations of Erd\H{o}s Szekeres: $k$-Modal Subsequences
Charles Gong
https://arxiv.org/abs/2508.20360 https://arxiv.org/pdf/2508.20360

Three Generalizations of Erdős Szekeres: $k$-Modal Subsequences
Erdős and Szekeres showed that given a permutation $p$ of $[n]$, and the sequence defined by \newline $(p(1), p(2), \ldots, p(n))$, there exists either a decreasing or increasing subsequence, not necessarily contiguous, of length at least $\sqrt{n}$. Fan Chung considered subsequences that can have at most one change of direction, i.e. an increasing and then decreasing subsequence, or a decreasing and then increasing subsequence. She called these unimodal subsequences, and showed there exists a…

Replaced article(s) found for nlin.AO. https://arxiv.org/list/nlin.AO/new
[1/1]:
- Kuramoto meets Koopman: Constants of motion, symmetries, and network motifs
Vincent Thibeault, Benjamin Claveau, Antoine Allard, Patrick Desrosiers