Tootfinder

The threshold and quasi-stationary distribution for the SIS model on networks
George Cantwell, Cristopher Moore
https://arxiv.org/abs/2509.11706 https://ar…

The threshold and quasi-stationary distribution for the SIS model on networks
We study the Susceptible-Infectious-Susceptible (SIS) model on arbitrary networks. The well-established pair approximation treats neighboring pairs of nodes exactly while making a mean field approximation for the rest of the network. We improve the method by expanding the state space dynamically, giving nodes a memory of when they last became susceptible. The resulting approximation is simple to implement and appears to be highly accurate, both in locating the epidemic threshold and in computin…

Raiders’ Brock Bowers Gets Blunt Words From Rob Gronkowski https://heavy.com/sports/nfl/las-vegas-raiders/brock-bowers-blunt-words-rob-gronkowski/?adt_ei=[email]

Initial traces and solvability of porous medium equation with power nonlinearity
Kazuhiro Ishige, Nobuhito Miyake, Ryuichi Sato
https://arxiv.org/abs/2507.11826

Initial traces and solvability of porous medium equation with power nonlinearity
In this paper we study qualitative properties of initial traces of solutions to the porous medium equation with power nonlinearity, and obtain necessary conditions for the existence of solutions to the corresponding Cauchy problem. Furthermore, we establish sharp sufficient conditions for the existence of solutions to the Cauchy problem using uniformly local Morrey spaces and their variations, and identify the optimal singularities of the initial data for the solvability of the Cauchy problem.

Near-Infrared Spectroscopy and Detection of Carbon Monoxide in the Type II Supernova SN 2023ixf
Seong Hyun Park, Jeonghee Rho, Sung-Chul Yoon, Jeniveve Pearson, Manisha Shrestha, Samaporn Tinyanont, T. R. Geballe, Ryan J. Foley, Aravind P. Ravi, Jennifer Andrews, David J. Sand, K. Azalee Bostroem, Chris Ashall, Peter Hoeflich, Stefano Valenti, Yize Dong, Nicolas Meza Retamal, Emily Hoang, Darshana Mehta, D. Andrew Howell, Joseph R. Farah, Giacomo Terreran, Estefania Padilla Gonzalez, M…

Near-Infrared Spectroscopy and Detection of Carbon Monoxide in the Type II Supernova SN 2023ixf
Core-collapse supernovae (CCSNe) may contribute a significant amount of dust in the early universe. Freshly formed coolant molecules (e.g., CO) and warm dust can be found in CCSNe as early as ~100 d after the explosion, allowing the study of their evolution with time series observations. In the Type II SN 2023ixf, we aim to investigate the temporal evolution of the temperature, velocity, and mass of CO and compare them with other CCSNe, exploring their implications for the dust formation in CCS…

Rip D'Angelo
Genius brings and bears a price
Torn down to early
Always
#dangelo #goat

In the Time of D’Angelo
With just three studio albums, the R&B icon changed the entire gravity of music. We reflect on the art, soul, and power of the multi-hyphenate star.

Limit Theorems for Verbose Persistence Diagrams
Jeong-hwi Joe, Woojin Kim, Cheolwoo Park
https://arxiv.org/abs/2509.11256 https://arxiv.org/pdf/2509.11256

Limit Theorems for Verbose Persistence Diagrams
The persistence diagram is a central object in the study of persistent homology and has also been investigated in the context of random topology. The more recent notion of the verbose diagram (a.k.a. verbose barcode) is a refinement of the persistence diagram that is obtained by incorporating ephemeral persistence features as extra points along the diagonal. In this work, we initiate the study of random verbose diagrams. We establish a strong law of large numbers for verbose diagrams as a rando…

Brownian motion on the Fubini extension space and applications
Hamed Amini, Nina H. Amini, Sofiane Chalal, Gaoyue Guo
https://arxiv.org/abs/2509.12096 https://

Brownian motion on the Fubini extension space and applications
The aim of this paper is to establish a certain equivalence between a Brownian motion on a Fubini extension space and a collection of essentially pairwise independent Brownian motions on the marginal sample spaces. This equivalence allows us to state a Girsanov theorem that preserves pairwise independence and to formulate graphon stochastic differential equations as a single McKean-Vlasov type equation driven by a standard Brownian motion.

Structural and Electrocatalytic Properties of La-Co-Ni Oxide Thin Films
Patrick Marx, Shivam Shukla, Alejandro Esteban Perez Mendoza, Florian Lourens, Corina Andronescu, Alfred Ludwig
https://arxiv.org/abs/2509.12946

Structural and Electrocatalytic Properties of La-Co-Ni Oxide Thin Films
La-Co-Ni oxides were fabricated in the form of thin-film materials libraries by combinatorial reactive co-sputtering and analyzed for structural and functional properties over large compositional ranges: normalized to the metals of the film they span about 0 - 70 at.-% for Co, 18 - 81 at.-% for La and 11 - 25 at.-% for Ni. Composition-dependent phase analysis shows formation of three areas with different phase constitutions in dependance of Co-content: In the La-rich region with low Co content,…

Localized Floquet modes in arrays of out-of-phase curved waveguides with a quasiperiodic modulation
Yaroslav V. Kartashov, Dmitry A. Zezyulin
https://arxiv.org/abs/2509.10877 ht…

Localized Floquet modes in arrays of out-of-phase curved waveguides with a quasiperiodic modulation
We study light propagation in an array of periodically curved waveguides consisting of pairs of waveguides with out-of-phase oscillations of waveguide centers. We compute the corresponding Floquet propagation constants and find pseudocollapses where the Floquet bands shrink and, respectively, light diffraction is significantly inhibited. When, in addition, the refractive index of the waveguides in the array have quasiperiodic modulation in the transverse direction, we establish the existence of…

On a class of thin obstacle-type problems for the bi-Laplacian operator
Donatella Danielli, Giovanni Gravina
https://arxiv.org/abs/2509.11372 https://arxiv…

On a class of thin obstacle-type problems for the bi-Laplacian operator
This paper investigates the regularity of solutions and structural properties of the free boundary for a class of fourth-order elliptic problems with Neumann-type boundary conditions. The singular and degenerate elliptic operators studied naturally emerge from the extension procedure for higher-order fractional powers of the Laplacian, while the choice of non-linearity considered encompasses two-phase boundary obstacle problems as a special case. After establishing local regularity properties o…