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The creation of photorealistic dynamic hair remains a major challenge in digital human modeling because of the complex motions, occlusions, and light scattering.

Persistence diagrams are common representations in topological data analysis, but they do not naturally live in a vector space, and the statistical tools developed for comparing them have largely evolved separately from those used for downstream prediction. We introduce STRAND (Survival Topological Representation ANalysis of Diagrams), which treats (collections of) PDs as survival data: each topological feature with persistence value $p = d - b$ is a fully observed time-to-event, and the persistence survival function $S(t) = \mathbb{P}(p > t)$ is the central object for comparing diagrams. From this single representation we derive (i) a non-parametric two-sample test with calibrated Type I error and high power from a small number of diagrams; (ii) interpretable effect sizes; and (iii) a 1-Wasserstein-stable feature vector for downstream machine learning. We validate calibration and power on synthetic manifolds with controlled topology, demonstrate competitive vectorisation across 14 graph and 3D point cloud benchmarks, and apply the method to study functional brain connectivity in fMRI/neuroscience data. To our knowledge, STRAND is the first method to provide hypothesis testing and vectorisation for persistence diagrams from a single coherent and interpretable representation.

From specialized motors to the use of machine-learning algorithms, Turkey's billion-dollar hair-transplant industry is the result of a constant process of innovation. The astounding growth of the hair-transplant industry in Turkey is not just a medical tourism success story; it's also a tale of "hacked" medical equipment and algorithmic craftsmanship. From a biological and evolutionary perspective, human hair is often viewed as an unremarkable mass of keratin that still plays some important functions--protecting our scalps from the sun's harmful ultraviolet rays and regulating our body temperatures--but, for the most part, is no longer essential to our survival. Yet, since ancient times, our subconscious perceptions of whether another person is healthy, young, or fertile have been based on visual cues such as skin radiance, the integrity of teeth, and hair density. Deep within our perceptions, hair has become one of the most powerful representations of our identity and self-confidence. Today, the global hair-transplant and restoration industry, which has evolved around this deep psychological and evolutionary need, has grown into a massive, multibillion-dollar industry. Various research firms have estimated the total size of the global hair-transplant market as sitting somewhere between $7.33 billion and $11.61 billion in 2024. And those figures don't include the underground economy.

We introduce a doubly hierarchical generative representation for strand-based 3D hairstyle geometry that progresses from coarse, low-pass filtered guide hair to densely populated hair strands rich in high-frequency details. We employ the Discrete Cosine Transform (DCT) to separate low-frequency structural curves from high-frequency curliness and noise, avoiding the Gibbs' oscillation issues associated with the standard Fourier transform in open curves. Unlike the guide hair sampled from the scalp UV map grids which may lose capturing details of the hairstyle in existing methods, our method samples optimal sparse guide strands by utilising $k$-medoids clustering centres from low-pass filtered dense strands, which more accurately retain the hairstyle's inherent characteristics. The proposed variational autoencoder-based generation network, with an architecture inspired by geometric deep learning and implicit neural representations, facilitates flexible, off-the-grid guide strand modelling and enables the completion of dense strands in any quantity and density, drawing on principles from implicit neural representations. Empirical evaluations confirm the capacity of the model to generate convincing guide hair and dense strands, complete with nuanced high-frequency details.

We further give "active local" versions of these heuristics: given atest pointx?,we show how the labelT(x?) With this information, we may decide thathwould not have been of much utility anyway, thereby saving ourselves the resources and effort to label the entire datasetS (and to runA).