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Ptychography is a scanning coherent diffractive imaging technique that enables imaging nanometer-scale features in extended samples. One main challenge is that widely used iterative image reconstruction methods often require significant…
Progress on graph foundation models is hindered by benchmark practices that conflate the contributions of node features and graph structure, making it hard to tell whether a model actually learns from connectivity, or whether it even needs…
Molecular phylogenetic and phylogeographic reconstructions generally assume time-homogeneous substitution processes. Motivated by computational convenience, this assumption sacrifices biological realism and offers little opportunity to…
We propose a new method for performing multiscale analysis of functions defined on the vertices of a finite connected weighted graph. Our approach relies on a random spanning forest to downsample the set of vertices, and on approximate…
Multimodal pathology-genomic analysis has become increasingly prominent in cancer survival prediction. However, existing studies mainly utilize multi-instance learning to aggregate patch-level features, neglecting the information loss of…
The goal of branch length estimation in phylogenetic inference is to estimate the divergence time between a set of sequences based on compositional differences between them. A number of software is currently available facilitating branch…
Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical…
Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit,…
Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees…
The inference of phylogenetic networks, which model complex evolutionary processes including hybridization and gene flow, remains a central challenge in evolutionary biology. Until now, statistically consistent inference methods have been…
We discuss how maximum entropy methods may be applied to the reconstruction of Markov processes underlying empirical time series and compare this approach to usual frequency sampling. It is shown that, at least in low dimension, there…
Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…
This paper studies a Markov chain for phylogenetic reconstruction which uses a popular transition between tree topologies known as subtree pruning-and-regrafting (SPR). We analyze the Markov chain in the simpler setting that the generating…
The topological framework of circuit topology has recently been introduced to complement knot theory and to help in understanding the physics of molecular folding. Naturally evolved linear molecular chains, such as proteins and nucleic…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
Phylogenetic networks are necessary to represent the tree of life expanded by edges to represent events such as horizontal gene transfers, hybridizations or gene flow. Not all species follow the paradigm of vertical inheritance of their…
Previous statistical approaches to hierarchical clustering for social network analysis all construct an "ultrametric" hierarchy. While the assumption of ultrametricity has been discussed and studied in the phylogenetics literature, it has…
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…
Spatio-temporal hidden Markov models are extremely difficult to estimate because their latent joint distributions are available only in trivial cases. In the estimation phase, these latent distributions are usually substituted with…
The phylogenetic tree construction is to infer the evolutionary relationship between species from the experimental data. However, the experimental data are often imperfect and conflicting each others. Therefore, it is important to extract…