We propose a topological framework for the detection of Hopf bifurcations directly from time series, based on persistent homology applied to phase space reconstructions via Takens embedding within the framework of Topological Data Analysis. The central idea is that changes in the dynamical regime are reflected in the emergence or disappearance of a dominant one-dimensional homological features in the reconstructed attractor. To quantify this behavior, we introduce a simple and interpretable scalar topological functional defined as the maximum persistence of homology classes in dimension one. This functional is used to construct a computable criterion for identifying critical parameters in families of dynamical systems without requiring knowledge of the underlying equations. The proposed approach is validated on representative systems of increasing complexity, showing consistent detection of the bifurcation point. The results support the interpretation of dynamical transitions as topological phase transitions and demonstrate the potential of topological data analysis as a model-free tool for the quantitative analysis of nonlinear time series.

This paper presents Generalized Correspondence-LDA (GC-LDA), a generalization of the Correspondence-LDA model that allows for variable spatial representations to be associated with topics, and increased flexibility in terms of the strength of the correspondence between data types induced by the model. We present three variants of GC-LDA, each of which associates topics with a different spatial representation, and apply them to a corpus of neuroimaging data. In the context of this dataset, each topic corresponds to a functional brain region, where the region's spatial extent is captured by a probability distribution over neural activity, and the region's cognitive function is captured by a probability distribution over linguistic terms. We illustrate the qualitative improvements offered by GC-LDA in terms of the types of topics extracted with alternative spatial representations, as well as the model's ability to incorporate a-priori knowledge from the neuroimaging literature. We furthermore demonstrate that the novel features of GC-LDA improve predictions for missing data.

Spatial representation learning (SRL) aims at learning general-purpose neural network representations from various types of spatial data (e.g., points, polylines, polygons, networks, images, etc.) in their native formats. Learning good spatial representations is a fundamental problem for various downstream applications such as species distribution modeling, weather forecasting, trajectory generation, geographic question answering, etc. Even though SRL has become the foundation of almost all geospatial artificial intelligence (GeoAI) research, we have not yet seen significant efforts to develop an extensive deep learning framework and benchmark to support SRL model development and evaluation. To fill this gap, we propose TorchSpatial, a learning framework and benchmark for location (point) encoding,which is one of the most fundamental data types of spatial representation learning. TorchSpatial contains three key components: 1) a unified location encoding framework that consolidates 15 commonly recognized location encoders, ensuring scalability and reproducibility of the implementations; 2) the LocBench benchmark tasks encompassing 7 geo-aware image classification and 10 geo-aware imageregression datasets; 3) a comprehensive suite of evaluation metrics to quantify geo-aware models' overall performance as well as their geographic bias, with a novel Geo-Bias Score metric. Finally, we provide a detailed analysis and insights into the model performance and geographic bias of different location encoders. We believe TorchSpatial will foster future advancement of spatial representationlearning and spatial fairness in GeoAI research.

We propose a normative model for spatial representation in the hippocampal formation that combines optimality principles, such as maximizing coding range and spatial information per neuron, with an algebraic framework for computing in distributed representation. Spatial position is encoded in a residue number system, with individual residues represented by high-dimensional, complex-valued vectors. These are composed into a single vector representing position by a similarity-preserving, conjunctive vector-binding operation. Self-consistency between the vectors representing position and the individual residues is enforced by a modular attractor network whose modules correspond to the grid cell modules in entorhinal cortex. The vector binding operation can also be used to bind different contexts to spatial representations, yielding a model for entorhinal cortex and hippocampus. We provide model analysis of scaling, similarity preservation and convergence behavior as well as experiments demonstrating noise robustness, sub-integer resolution in representing position, and path integration. The model formalizes the computations in the cognitive map and makes testable experimental predictions.

Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Alexander brothers' alleged HIGH SCHOOL gang rape video: Classmates speak out on sick'taking turns' footage... as creepy unseen photos are exposed Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Tucker Carlson erupts at Trump adviser as she hurls'SLANDER' claim linking him to synagogue shooting NFL superstar Xavier Worthy spills all on Travis Kelce, the Chiefs' struggles... and having Taylor Swift as his No 1 fan Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Nancy Mace throws herself into Iran warzone as she goes rogue on Middle East rescue mission: 'I AM that person' Hidden toxins in kids' treats EXPOSED: Health guru Jillian Michaels' sit-down with Casey DeSantis reveals dangers lurking in popular foods READ MORE: I communicated with non-human intelligence... and what they told me proves God's existence New research has suggested that UFOs could be clustering around underwater canyons off the US coastline, raising fresh questions about whether mysterious craft could be operating beneath the ocean. An analysis of more than 80,000 reports found concentrated clusters of sightings near steep submarine canyon systems, particularly along the West Coast. The findings stem from an independent study testing the so-called'cryptoterrestrial hypothesis,' which proposes that unidentified aerial phenomena could originate from hidden non-human intelligence on Earth rather than distant planets. Using publicly available UFO sighting data and detailed ocean depth maps, the report identified correlations between reported sightings and deep underwater terrain features. The analysis also uncovered a striking geographical anomaly, with clustering patterns appearing on the West Coast but not on the East or Gulf coasts.

Vision Language Models (VLMs) have demonstrated remarkable performance in 2D vision and language tasks. However, their ability to reason about spatial arrangements remains limited. In this work, we introduce Spatial Region GPT (SpatialRGPT) to enhance VLMs' spatial perception and reasoning capabilities.

In the visual spatial understanding (VSU) area, spatial image-to-text (SI2T) and spatial text-to-image (ST2I) are two fundamental tasks that appear in dual form. Existing methods for standalone SI2T or ST2I perform imperfectly in spatial understanding, due to the difficulty of 3D-wise spatial feature modeling.

However, such a solution often shows unsatisfactory editability on the source image. To address this, we propose DreamSteerer, a plug-in method for augmenting existing T2I personalization methods. Specifically, we enhance the source image conditioned editability of a personalized diffusion model via a novel Editability Driven Score Distillation (EDSD) objective. Moreover, we identify amodetrapping issuewithEDSD, andpropose amodeshifting regularization with spatial feature guided sampling to avoid such an issue.

Although freely accessible, it is provided in individual files for each year, and is difficult to combine in order to analyze spatial or temporal trends.