arXiv subjects

Shuni Li

Publications and source records attributed to Shuni Li.

3 recordsLinked to original sources

arXiv2026

DeepRHP: A Hybrid Variational Autoencoder for Designing Random Heteropolymers as Protein Mimics

Synthetic random heteropolymers (RHPs), consisting of a predefined set of monomers, offer an approach toward the design of protein-like materials. These RHPs, if designed appropriately, can mimic protein behavior and function. As such, there is a need for computational tools to efficiently guide RHP design. We bridge this gap by developing DeepRHP, a modified variational autoencoder (VAE) model under a semi-supervised framework. By equipping a classical VAE with an additional feature-based VAE, DeepRHP forces the latent space to capture structures of critical chemical features as well as individual RHP sequence patterns. In this sense, our method is versatile by allowing any relevant features to be incorporated in a hybrid manner. We demonstrate the effectiveness of DeepRHP by suggesting potential monomer compositions that stabilize membrane proteins (e.g. Aquaporin Z) in non-native environments and cross-validating our prediction with published results. The concordance between our model and true RHP function suggests strong potential in utilizing hybrid autoencoder architectures to guide RHP design for proteins and other biological compounds.

cs.LG↗

arXiv2019

Scalable $M$-Channel Critically Sampled Filter Banks for Graph Signals

We investigate a scalable $M$-channel critically sampled filter bank for graph signals, where each of the $M$ filters is supported on a different subband of the graph Laplacian spectrum. For analysis, the graph signal is filtered on each subband and downsampled on a corresponding set of vertices. However, the classical synthesis filters are replaced with interpolation operators. For small graphs, we use a full eigendecomposition of the graph Laplacian to partition the graph vertices such that the $m^{th}$ set comprises a uniqueness set for signals supported on the $m^{th}$ subband. The resulting transform is critically sampled, the dictionary atoms are orthogonal to those supported on different bands, and graph signals are perfectly reconstructable from their analysis coefficients. We also investigate fast versions of the proposed transform that scale efficiently for large, sparse graphs. Issues that arise in this context include designing the filter bank to be more amenable to polynomial approximation, estimating the number of samples required for each band, performing non-uniform random sampling for the filtered signals on each band, and using efficient reconstruction methods. We empirically explore the joint vertex-frequency localization of the dictionary atoms, the sparsity of the analysis coefficients for different classes of signals, the reconstruction error resulting from the numerical approximations, and the ability of the proposed transform to compress piecewise-smooth graph signals. The proposed filter bank also yields a fast, approximate graph Fourier transform with a coarse resolution in the spectral domain.

cs.IT↗

arXiv2016

The set splittability problem

The set splittability problem is the following: given a finite collection of finite sets, does there exits a single set that contains exactly half the elements from each set in the collection? (If a set has odd size, we allow the floor or ceiling.) It is natural to study the set splittability problem in the context of combinatorial discrepancy theory and its applications, since a collection is splittable if and only if it has discrepancy $\leq1$. We introduce a natural generalization of splittability problem called the $p$-splittability problem, where we replace the fraction $\frac12$ in the definition with an arbitrary fraction $p\in(0,1)$. We first show that the $p$-splittability problem is NP-complete. We then give several criteria for $p$-splittability, including a complete characterization of $p$-splittability for three or fewer sets ($p$ arbitrary), and for four or fewer sets ($p=\frac12$). Finally we prove the asymptotic prevalence of splittability over unsplittability in an appropriate sense.

math.CO↗