Tootfinder

Lagrangian-Eulerian Multiscale Data Assimilation in Physical Domain based on Conditional Gaussian Nonlinear System
Hyeonggeun Yun, Quanling Deng
https://arxiv.org/abs/2509.14586

Lagrangian-Eulerian Multiscale Data Assimilation in Physical Domain based on Conditional Gaussian Nonlinear System
This research aims to further investigate the process of Lagrangian-Eulerian Multiscale Data Assimilation (LEMDA) by replacing the Fourier space with the physical domain. Such change in the perspective of domain introduces the advantages of being able to deal in non-periodic system and more intuitive representation of localised phenomena or time-dependent problems. The context of the domain for this paper was set as sea ice floe trajectories to recover the ocean eddies in the Arctic regions, wh…

Eliciting reference measures of law-invariant functionals
Felix-Benedikt Liebrich, Ruodu Wang
https://arxiv.org/abs/2507.13763 https://arxiv.org/pdf/2507.1…

Eliciting reference measures of law-invariant functionals
Law-invariant functionals are central to risk management and assign identical values to random prospects sharing the same distribution under an atomless reference probability measure. This measure is typically assumed fixed. Here, we adopt the reverse perspective: given only observed functional values, we aim to either recover the reference measure or identify a candidate measure to test for law invariance when that property is not {\em a priori} satisfied. Our approach is based on a key observ…

A Compositional Kernel Model for Feature Learning
Feng Ruan, Keli Liu, Michael Jordan
https://arxiv.org/abs/2509.14158 https://arxiv.org/pdf/2509.14158

A Compositional Kernel Model for Feature Learning
We study a compositional variant of kernel ridge regression in which the predictor is applied to a coordinate-wise reweighting of the inputs. Formulated as a variational problem, this model provides a simple testbed for feature learning in compositional architectures. From the perspective of variable selection, we show how relevant variables are recovered while noise variables are eliminated. We establish guarantees showing that both global minimizers and stationary points discard noise coordin…

Consistent causal discovery with equal error variances: a least-squares perspective
Anamitra Chaudhuri, Yang Ni, Anirban Bhattacharya
https://arxiv.org/abs/2509.15197 https://…

Consistent causal discovery with equal error variances: a least-squares perspective
We consider the problem of recovering the true causal structure among a set of variables, generated by a linear acyclic structural equation model (SEM) with the error terms being independent and having equal variances. It is well-known that the true underlying directed acyclic graph (DAG) encoding the causal structure is uniquely identifiable under this assumption. In this work, we establish that the sum of minimum expected squared errors for every variable, while predicted by the best linear c…

Ultrafast Extreme Events: Empirical Analysis of Mechanisms and Recovery in a Historical Perspective
Luca Henrichs, Anton J. Heckens, Thomas Guhr
https://arxiv.org/abs/2509.10376

Ultrafast Extreme Events: Empirical Analysis of Mechanisms and Recovery in a Historical Perspective
To understand the emergence of Ultrafast Extreme Events (UEEs), the influence of algorithmic trading or high-frequency traders is of major interest as they make it extremely difficult to intervene and to stabilize financial markets. In an empirical analysis, we compare various characteristics of UEEs over different years for the US stock market to assess the possible non-stationarity of the effects. We show that liquidity plays a dominant role in the emergence of UEEs and find a general pattern…

PhysicalAgent: Towards General Cognitive Robotics with Foundation World Models
Artem Lykov, Jeffrin Sam, Hung Khang Nguyen, Vladislav Kozlovskiy, Yara Mahmoud, Valerii Serpiva, Miguel Altamirano Cabrera, Mikhail Konenkov, Dzmitry Tsetserukou
https://arxiv.org/abs/2509.13903

PhysicalAgent: Towards General Cognitive Robotics with Foundation World Models
We introduce PhysicalAgent, an agentic framework for robotic manipulation that integrates iterative reasoning, diffusion-based video generation, and closed-loop execution. Given a textual instruction, our method generates short video demonstrations of candidate trajectories, executes them on the robot, and iteratively re-plans in response to failures. This approach enables robust recovery from execution errors. We evaluate PhysicalAgent across multiple perceptual modalities (egocentric, third-p…

Why doesn't the West threaten Putin with open #warfare, possibly involving the use of nuclear weapons? We must be prepared to do so, and if #Putin ignores this, then forces should be mobilized and nuclear weapons deployed.
If war breaks out, Russia will never recover, while the West has good prospects …

A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning
Juan Diego Toscano, Daniel T. Chen, Vivek Oommen, George Em Karniadakis
https://arxiv.org/abs/2509.14198

A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning
Residual-based adaptive strategies are widely used in scientific machine learning but remain largely heuristic. We introduce a unifying variational framework that formalizes these methods by integrating convex transformations of the residual. Different transformations correspond to distinct objective functionals: exponential weights target the minimization of uniform error, while linear weights recover the minimization of quadratic error. Within this perspective, adaptive weighting is equivalen…

Diligently done all the physio exercises prescribed for my recovering fractured wrist for two weeks only to find it's just 4% complete.
And what's the reward for me doing that? They double the work and time it takes!
What bullshit is this? A year of wall pressups and wrist stretches taking ten minutes a day doubling every two weeks? My god.

Topological Data Analysis in Finsler Spaces
Rafael Cavalcanti, Nelson Leal, Serafim Rodrigues, Danilo Barros, Mathieu Desroches
https://arxiv.org/abs/2509.12660 https://

Topological Data Analysis in Finsler Spaces
We introduce a new approach to Topological Data Analysis (TDA) based on Finsler metrics and we also generalize the classical concepts of Vietoris-Rips and Cech complexes within this framework. In particular, we propose a class of directionally dependent Finsler metrics and establish key results demonstrating their relevance to TDA. Moreover, we show that several Information Theoretic perspectives on TDA can often be recovered through the lens of Finsler geometry.