A note on the equivalence of Gromov boundary and metric boundary
In this paper, we introduce the concept of quasihyperbolically visible spaces. As a tool, we study the connection between the Gromov boundary and the metric boundary.
math.MG↗
arXiv subjects
Abhishek Pandey
Publications and source records attributed to Abhishek Pandey.
GlassMol: Interpretable Molecular Property Prediction with Concept Bottleneck Models
Machine learning accelerates molecular property prediction, yet state-of-the-art Large Language Models and Graph Neural Networks operate as black boxes. In drug discovery, where safety is critical, this opacity risks masking false correlations and excluding human expertise. Existing interpretability methods suffer from the effectiveness-trustworthiness trade-off: explanations may fail to reflect a model's true reasoning, degrade performance, or lack domain grounding. Concept Bottleneck Models (CBMs) offer a solution by projecting inputs to human-interpretable concepts before readout, ensuring that explanations are inherently faithful to the decision process. However, adapting CBMs to chemistry faces three challenges: the Relevance Gap (selecting task-relevant concepts from a large descriptor space), the Annotation Gap (obtaining concept supervision for molecular data), and the Capacity Gap (degrading performance due to bottleneck constraints). We introduce GlassMol, a model-agnostic CBM that addresses these gaps through automated concept curation and LLM-guided concept selection. Experiments across thirteen benchmarks demonstrate that \method generally matches or exceeds black-box baselines, suggesting that interpretability does not sacrifice performance and challenging the commonly assumed trade-off. Code is available at https://github.com/walleio/GlassMol.
cs.LG↗
Scalable Batch Correction for Cell Painting via Batch-Dependent Kernels and Adaptive Sampling
Cell Painting is a microscopy-based, high-content imaging assay that produces rich morphological profiles of cells and can support drug discovery by quantifying cellular responses to chemical perturbations. At scale, however, Cell Painting data is strongly affected by batch effects arising from differences in laboratories, instruments, and protocols, which can obscure biological signal. We present BALANS (Batch Alignment via Local Affinities and Subsampling), a scalable batch-correction method that aligns samples across batches by constructing a smoothed affinity matrix from pairwise distances. Given $n$ data points, BALANS builds a sparse affinity matrix $A \in \mathbb{R}^{n \times n}$ using two ideas. (i) For points $i$ and $j$, it sets a local scale using the distance from $i$ to its $k$-th nearest neighbor within the batch of $j$, then computes $A_{ij}$ via a Gaussian kernel calibrated by these batch-aware local scales. (ii) Rather than forming all $n^2$ entries, BALANS uses an adaptive sampling procedure that prioritizes rows with low cumulative neighbor coverage and retains only the strongest affinities per row, yielding a sparse but informative approximation of $A$. We prove that this sampling strategy is order-optimal in sample complexity and provides an approximation guarantee, and we show that BALANS runs in nearly linear time in $n$. Experiments on diverse real-world Cell Painting datasets and controlled large-scale synthetic benchmarks demonstrate that BALANS scales to large collections while improving runtime over native implementations of widely used batch-correction methods, without sacrificing correction quality.
cs.LG↗
Spatially-Coupled Network RNA Velocities: A Control-Theoretic Perspective
RNA velocity is an important model that combines cellular spliced and unspliced RNA counts to infer dynamical properties of various regulatory functions. Despite its wide applicability and many variants used in practice, the model has not been adequately designed to directly account for both intracellular gene regulatory network interactions and spatial intercellular communications. Here, we propose a new RNA velocity approach that jointly and directly captures two new network structures: an intracellular gene regulatory network (GRN) and an intercellular interaction network that captures interactions between (neighboring) cells, with relevance to spatial transcriptomics. We theoretically analyze this two-level network system through the lens of control and consensus theory. In particular, we investigate network equilibria, stability, cellular network consensus, and optimal control approaches for targeted drug intervention.
math.DS↗
DMol: A Highly Efficient and Chemical Motif-Preserving Molecule Generation Platform
We introduce a new graph diffusion model for small molecule generation, DMol, which outperforms the state-of-the-art DiGress model in terms of validity by roughly 1.5% across all benchmarking datasets while reducing the number of diffusion steps by at least 10-fold, and the running time to roughly one half. The performance improvements are a result of a careful change in the objective function and a graph noise scheduling approach which, at each diffusion step, allows one to only change a subset of nodes of varying size in the molecule graph. Another relevant property of the method is that it can be easily combined with junction-tree-like graph representations that arise by compressing a collection of relevant ring structures into supernodes. Unlike classical junction-tree techniques that involve VAEs and require complicated reconstruction steps, compressed DMol directly performs graph diffusion on a graph that compresses only a carefully selected set of frequent carbon rings into supernodes, which results in straightforward sample generation. This compressed DMol method offers additional validity improvements over generic DMol of roughly 2%, increases the novelty of the method, and further improves the running time due to reductions in the graph size.
cs.LG↗
Binding Affinity Prediction: From Conventional to Machine Learning-Based Approaches
Protein-ligand binding is the process by which a small molecule (drug or inhibitor) attaches to a target protein. Binding affinity, which characterizes the strength of biomolecular interactions, is essential for tackling diverse challenges in life sciences, including therapeutic design, protein engineering, enzyme optimization, and elucidating biological mechanisms. Much work has been devoted to predicting binding affinity over the past decades. Here, we review recent significant works, with a focus on methods, evaluation strategies, and benchmark datasets. We note growing use of both traditional machine learning and deep learning models for predicting binding affinity, accompanied by an increasing amount of data on proteins and small drug-like molecules. With improved predictive performance and the FDA's phasing out of animal testing, AI-driven in silico models, such as AI virtual cells (AIVCs), are poised to advance binding affinity prediction; reciprocally, progress in building binding affinity predictors can refine AIVCs. Future efforts in binding affinity prediction and AI-driven in silico models can enhance the simulation of temporal dynamics, cell-type specificity, and multi-omics integration to support more accurate and personalized outcomes.
q-bio.QM↗
POLO: Preference-Guided Multi-Turn Reinforcement Learning for Lead Optimization
Lead optimization in drug discovery requires efficiently navigating vast chemical space through iterative cycles to enhance molecular properties while preserving structural similarity to the original lead compound. Despite recent advances, traditional optimization methods struggle with sample efficiency-achieving good optimization performance with limited oracle evaluations. Large Language Models (LLMs) provide a promising approach through their in-context learning and instruction following capabilities, which align naturally with these iterative processes. However, existing LLM-based methods fail to leverage this strength, treating each optimization step independently. To address this, we present POLO (Preference-guided multi-turn Optimization for Lead Optimization), which enables LLMs to learn from complete optimization trajectories rather than isolated steps. At its core, POLO introduces Preference-Guided Policy Optimization (PGPO), a novel reinforcement learning algorithm that extracts learning signals at two complementary levels: trajectory-level optimization reinforces successful strategies, while turn-level preference learning provides dense comparative feedback by ranking intermediate molecules within each trajectory. Through this dual-level learning from intermediate evaluation, POLO achieves superior sample efficiency by fully exploiting each costly oracle call. Extensive experiments demonstrate that POLO achieves 84% average success rate on single-property tasks (2.3x better than baselines) and 50% on multi-property tasks using only 500 oracle evaluations, significantly advancing the state-of-the-art in sample-efficient molecular optimization.
cs.LG↗
A Survey of Large Language Models for Text-Guided Molecular Discovery: from Molecule Generation to Optimization
Large language models (LLMs) are introducing a paradigm shift in molecular discovery by enabling text-guided interaction with chemical spaces through natural language, symbolic notations, with emerging extensions to incorporate multi-modal inputs. To advance the new field of LLM for molecular discovery, this survey provides an up-to-date and forward-looking review of the emerging use of LLMs for two central tasks: molecule generation and molecule optimization. Based on our proposed taxonomy for both problems, we analyze representative techniques in each category, highlighting how LLM capabilities are leveraged across different learning settings. In addition, we include the commonly used datasets and evaluation protocols. We conclude by discussing key challenges and future directions, positioning this survey as a resource for researchers working at the intersection of LLMs and molecular science. A continuously updated reading list is available at https://github.com/REAL-Lab-NU/Awesome-LLM-Centric-Molecular-Discovery.
cs.LG↗
Federated Discrete Denoising Diffusion Model for Molecular Generation with OpenFL
Generating unique molecules with biochemically desired properties to serve as viable drug candidates is a difficult task that requires specialized domain expertise. In recent years, diffusion models have shown promising results in accelerating the drug design process through AI-driven molecular generation. However, training these models requires massive amounts of data, which are often isolated in proprietary silos. OpenFL is a federated learning framework that enables privacy-preserving collaborative training across these decentralized data sites. In this work, we present a federated discrete denoising diffusion model that was trained using OpenFL. The federated model achieves comparable performance with a model trained on centralized data when evaluating the uniqueness and validity of the generated molecules. This demonstrates the utility of federated learning in the drug design process. OpenFL is available at: https://github.com/securefederatedai/openfl
cs.LG↗
Visible quasihyperbolic geodesics
In this paper, motivated by the work of Bonk, Heinonen, and Koskela (Asterisque, 2001), we consider the problem of the equivalence of the Gromov boundary and Euclidean boundary. Our strategy to study this problem comes from the recent work of Bharali and Zimmer (Adv. Math., 2017) and Bracci, Nikolov, and Thomas (Math. Z., 2021). We present the concept of a quaihyperbolic visibility domain (QH-visibility domain) for domains that meet the visibility property in relation to the quasihyperbolic metric. By utilizing this visibility property, we offer a comprehensive solution to this problem. Indeed, we prove that such domains are precisely the QH-visibility domains that have no geodesic loops in the Euclidean closure. Furthermore, we establish a general criterion for a domain to be the QH-visibility domain. Using this criterion, one can determine that uniform domains, John domains, and domains that satisfy quasihyperbolic boundary conditions are QH-visibility domains. We also compare the visibility of hyperbolic and quasihyperbolic metrics for planar hyperbolic domains. As an application of the visibility property, we study the homeomorphic extension of quasiconformal maps. Moreover, we also study the QH-visibility of unbounded domains in $\mathbb{R}^n$. Finally, we present a few examples of QH-visibility domains that are not John domains or QHBC domains.
math.CV↗
Understanding the transport behaviour of PbSe: A combined experimental and computational study
Lead chalcogenides are the promising thermoelectric (TE) materials having narrow band gap. The present work investigates the TE behaviour of PbSe in the temperature range 300-500 K. The transport properties of the sample have been studied using the Abinit and BoltzTrap code. The experimentally observed value of \textit{S} at 300 and 500 K is found to be $\sim$ 198 and 266 $μ$V K$^{-1}$, respectively. The rate of increase in \emph{S} from 300 to 460 (460 to 500) K is found to be $\sim$ 0.4 (0.09). The temperature dependent electrical conductivity \textit{($σ$)} shows the increasing trend, with values of $\sim $ 0.35 $\times $ 10$^{3}$ and $\sim$ 0.58 $\times$ 10$^{3}$ $Ω$$^{-1}$ m$^{-1}$ at 300 and 500 K, respectively. Further, the value of thermal conductivity \textit{($κ$)} at 300 (500) K is found to be 0.74 (1.07) W m$^{-1}$ K$^{-1}$. The value of \textit{$κ$} is found to be increasing upto 460 K and then starts decreasing. The dispersion plot indicates that PbSe is a direct band gap semiconductor with band gap value of 0.16 (0.27) eV considering spin-orbit coupling (without SOC). The partial density of states (PDOS) plot shows that Pb 6p and Se 4p states have a major contribution in the transport properties. The observed and calculated values of \textit{S} gives a good match for SOC case. The calculated \textit{$σ$} and electronic part of thermal conductivity (\textit{$κ{_e}$}) gives good match with the experimental data. The maximum power factor (PF) value of $\sim$ 4.3 $\times$ 10$^{-5}$ W/mK$^{2}$ is observed at 500 K. This work helps in understanding the TE behaviour of PbSe through a novel and insightful alliance of experimental measurements and DFT approach.
cond-mat.mtrl-sci↗
Neargeodesics in Gromov hyperbolic John domains in Banach spaces
In this paper, we prove that neargeodesics in Gromov hyperbolic John domains in Banach space are cone arcs. This result gives an improvement of a result of Li [Theorem 1, Int. J. Math. 25 (2014)].
math.CV↗
On the generalized Zalcman conjecture
Let $\mathcal{S}$ denote the class of analytic and univalent ({\it i.e.}, one-to-one) functions $ f(z)= z+\sum_{n=2}^{\infty}a_n z^n$ in the unit disk $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$. For $f\in \mathcal{S}$, In 1999, Ma proposed the generalized Zalcman conjecture that $$|a_{n}a_{m}-a_{n+m-1}|\le (n-1)(m-1),\,\,\,\mbox{ for } n\ge2,\, m\ge 2,$$ with equality only for the Koebe function $k(z) = z/(1 - z)^2$ and its rotations. In the same paper, Ma \cite{Ma-1999} asked for what positive real values of $λ$ does the following inequality hold? \begin{equation}\label{conjecture} |λa_na_m-a_{n+m-1}|\le λnm -n-m+1 \,\,\,\,\, (n\ge 2, \,m\ge3). \end{equation} Clearly equality holds for the Koebe function $k(z) = z/(1 - z)^2$ and its rotations. In this paper, we prove the inequality (\ref{conjecture}) for $λ=3, n=2, m=3$. Further, we provide a geometric condition on extremal function maximizing (\ref{conjecture}) for $λ=2,n=2, m=3$.
math.CV↗
BaMn$_2$P$_2$: Highest magnetic ordering temperature 122-pnictide compound
We report the growth of high-quality single crystals of ThCr$_2$Si$_2$-type tetragonal BaMn$_2$P$_2$ and investigation of its structural, electrical transport, thermal and magnetic properties. Our results of basal plane electrical resistivity and heat capacity measurements show that the compound has an insulating ground state with a small band gap. Anisotropic susceptibility $χ_{ab,c}(T)$ data infer a collinear local-moment Néel-type antiferromagnetic (AFM) ground state below the ordering temperature $T_{\rm N} = 795(15)$~K, which is highest among all the ThCr$_2$Si$_2$- and CaAl$_2$Si$_2$-type 122-pnictide compounds reported so far suggesting that the strength of magnetic exchange interactions is strongest in this material. The magnetic transition temperatures of BaMn$_2$$Pn_{2}$ ($Pn$ = P, As, Sb, Bi) compounds exhibit a monotonic decrease with the increase of tetragonal unit cell parameters $a$ and $c$, suggesting a strong dependence of the strength of the decisive magnetic exchange interactions on the separation between the localized spins residing on the Mn-ions. The observed monotonic increase of both $χ_{ab}$ and $χ_{c}$ for $T > T_{\rm N}$ suggests that short-range dynamic quasi-two dimensional AFM correlations persist above the $T_{\rm N}$ up to the highest temperature of the measurements. The large $T_{\rm N}$ of BaMn$_2$P$_2$ demands for systematic hole-doping studies on this material as similar investigations on related BaMn$_2$As$_{2}$ with $T_{\rm N} = 618$~K have led to the discovery of an outstanding ground state where AFM of localized Mn-spins and itinerant half-metallic ferromagnetism with $T_{\rm c} \approx 100$~K originating from the doped holes coexist together.
cond-mat.str-el↗
Exploring the effect of strong electronic correlations in Seebeck Coefficient of the NdCoO3 compound : Using experimental and DFT+U approach
The presence of complexity in the electronic structure of strongly correlated electron system NdCoO$_3$ (NCO) have sparked interest in the investigation of its physical properties. Here, we study the the Seebeck coefficient ($α$) of NCO by using the combined experimental and DFT+$U$ based methods. The experimentally measured $α$ is found to be $\sim$ 444 $μV/K$ at 300 K, which decreases to 109.8 $μV/K$ at 600 K. In order to understand the measured $α$, we have calculated the PDOS and band structure of the NCO. Furthermore, the calculated occupancy of 6.4 for Co $3d$ orbitals and presence of large unoccupied O $2p$ states indicate the covalent nature of the bonding. Apart from this, the maximum effective mass is found to be 36.75 (28.13) for the spin-up (dn) channel in conduction band indicates the n-type behaviour of the compound in contrast to our experimentally observed p-type behaviour. While, the calculated $α$ at the temperature-dependent chemical potential ($μ$) at 300 K shows the p-type behaviour of the compound. Fairly good agreement is seen between the calculated and measured values of $α$ at U$_f$$_f$ = 5.5 eV and U$_d$$_d$ = 2.7 eV. The maximum power factor (PF) is found to be 47.6 (114.4) $\times$ $10^1$$^4 $ $μ$$W$$K^-$$^2$$cm^-$$^1$$s^-$$^1$ at 1100 K, which corresponds to p (n)-type doping of $\sim$ 1.4 (0.7) $\times$ 10$^2$$^1$ cm$^-$$^3$. This study suggests the importance of strong on-site electron correlation in understanding the thermoelectric property of the compound.
cond-mat.mtrl-sci↗
Conformal Warped Product Submersion
In this paper, the concept of Riemannian warped product submersion is generalized to the conformal case. We introduce the notion of conformal warped product submersion. It is a submersion between warped product manifolds that preserves angles between the horizontal vectors. The fundamental tensors of submersion are derived for conformal warped product submersion.
math.DG↗
Proof of The Generalized Zalcman Conjecture for Initial Coefficients of Univalent Functions
Let $\mathcal{S}$ denote the class of analytic and univalent ({\it i.e.}, one-to-one) functions $f(z)= z+\sum_{n=2}^{\infty}a_n z^n$ in the unit disk $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$. For $f\in \mathcal{S}$, Ma proposed the generalized Zalcman conjecture that $$|a_{n}a_{m}-a_{n+m-1}|\le (n-1)(m-1),\,\,\,\mbox{ for } n\ge2,\, m\ge 2,$$ with equality only for the Koebe function $k(z) = z/(1 - z)^2$ and its rotations. In this paper using the properties of holomorphic motion and Krushkal's Surgery Lemma \cite{Krushkal-1995}, we prove the generalized Zalcman conjecture when $n=2$, $m=3$ and $n=2$, $m=4$.
math.CV↗
Support points of some classes of analytic and univalent functions
Let $\mathcal{A}$ denote the class of analytic functions in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$ satisfying $f(0)=0$ and $f'(0)=1$. Let $\mathcal{U}$ be the class of functions $f\in\mathcal{A}$ satisfying $$\left|f'(z)\left(\frac{z}{f(z)}\right)^2-1 \right|< 1 \quad\mbox{ for } z\in\mathbb{D},$$ and $\mathscr{G}$ denote the class of functions $f\in \mathcal{A}$ satisfying $${\rm Re\,}\left(1+\frac{zf''(z)}{f'(z)}\right)>-\frac{1}{2} \quad\mbox{ for } z\in\mathbb{D}.$$
math.CV↗