Tootfinder

Versatile and reconfigurable integrated silicon nitride photonic microresonator
Tong Lin, Haoran Wang, Xiaoyu Hao, Liu Li, Ziyang Xiong, Hao Deng, Yan Fan, Shihua Chen, Junpeng Lu, Zhenhua Ni
https://arxiv.org/abs/2509.13028

Versatile and reconfigurable integrated silicon nitride photonic microresonator
Unlocking the full potential of integrated photonics requires versatile, multi-functional devices that can adapt to diverse application demands. However, confronting this challenge with conventional single-function resonators often results in tedious and complex systems. We present an elegant solution: a versatile and reconfigurable dual-polarization Si3N4 microresonator that represents a paradigm shift in on-chip photonic designs. Our device, based on a binary-star orbital architecture, can be…

The Henstock-Kurzweil Functional Calculus on Self-Adjoint Operators
Marin Matei-Luca
https://arxiv.org/abs/2510.09622 https://arxiv.org/pdf/2510.09622

The Henstock-Kurzweil Functional Calculus on Self-Adjoint Operators
This dissertation focuses on developing a new construction of a functional calculus using Henstock-Kurzweil integration methods. The assignment of a functional calculus will be applied to self-adjoint operators. We will address both the bounded and unbounded cases, examine the advantage of the underlying function space compared to larger spaces, prove the spectral mapping theorem, and explore one application of this functional calculus in abstract differential equations.

Superfluidity in Fermi systems within the framework of Density Functional Theory
Piotr Magierski
https://arxiv.org/abs/2510.07410 https://arxiv.org/pdf/251…

Superfluidity in Fermi systems within the framework of Density Functional Theory
This review is based on lectures given by the author at the Enrico Fermi Summer School in Varenna. It presents the basics of Density Functional Theory (DFT) for Fermi superfluids, with particular emphasis on nuclear systems. Special attention is given to the foundations of both DFT and time-dependent DFT (TDDFT). The review explores the advantages and challenges involved in the practical application of TDDFT to superfluid systems, as well as the typical approximations employed. Various applicat…

Functional Information Decomposition: A First-Principles Approach to Analyzing Functional Relationships
Clifford Bohm, Vincent R. Ragusa, Arend Hintze, Christoph Adami
https://arxiv.org/abs/2509.18522 …

Discrete Heat Kernels on Simplicial Complexes and Its Application to Functional Brain Networks
Sixtus Dakurah
https://arxiv.org/abs/2509.16908 https://arxi…

Discrete Heat Kernels on Simplicial Complexes and Its Application to Functional Brain Networks
Networks constitute fundamental organizational structures across biological systems, although conventional graph-theoretic analyses capture exclusively pairwise interactions, thereby omitting the intricate higher-order relationships that characterize network complexity. This work proposes a unified framework for heat kernel smoothing on simplicial complexes, extending classical signal processing methodologies from vertices and edges to cycles and higher-dimensional structures. Through Hodge Lap…

Sectional curvature and matrix displacement convexity
Gautam Aishwarya, Liran Rotem, Yair Shenfeld
https://arxiv.org/abs/2509.23399 https://arxiv.org/pdf/2…

Sectional curvature and matrix displacement convexity
We show that the sectional curvature of a Riemannian manifold is nonnegative if, and only if, the entropy functional is matrix displacement convex. As an application we obtain intrinsic dimensional evolution variational inequalities, and the corresponding Wasserstein contraction along heat flows, which improve on their dimensional counterparts.