Current methods for predicting gene expression from histone modifications rely on arbitrary binary classification thresholds such as the median to distinguish between high and low expression for genes. This approach lacks biological justification, creates dataset-dependent classifications, and ignores the relative regulatory relationships between genes that are often more biologically meaningful than absolute cutoffs. We developed a deep learning method using pairwise ranking to determine the relative gene expression levels between gene pairs based on their histone modification signals. The approach adopted the DirectRanker architecture, which enforces antisymmetry by construction through a twin-subnet design with asymmetric subtraction, and was evaluated against three baseline classifiers (Random Forest, Logistic Regression, and SVM Linear) on identical features and data splits. Ablation testing across all 31 non-empty subsets of five histone marks (H3K4me3, H3K9ac, H3K9me3, H3K27ac, H3K27me3) was conducted to identify their individual contributions. Datasets were strictly partitioned (80

A bstract RNA structure sampling is central to modelling RNA ensembles, yet stochastic sampling methods are non-exhaustive, scale poorly, and are biased towards low-free-energy structures, while current suboptimal folding approaches generate an unpredictable exponential number of structures. These limitations are particularly problematic for modelling cotranscriptional folding, where vectorial synthesis continuously reshapes the energy landscape during transcription, stabilising transient out-of-equilibrium structures. Here we introduce iterative sampling , a deterministic framework that enumerates unique RNA secondary structures in strict order of increasing free energy, enabling progressive and exhaustive exploration of the structure space up to an arbitrary stopping criterion. To implement this approach, we developed two scalable algorithms, iterative deepening and a persistent data structure approach, that incrementally traverse the expansion tree by evolving partial structures in place, avoiding redundant recomputation and fixed energy windows. Implemented in memerna , this approach achieves orders-of-magnitude speedups over existing tools (10x over ViennaRNA ; 100x over RNAstructure ). Integration within the sample-and-select framework ( R2D2 ) improves structural diversity and identifies conformations with greater agreement with experimental data. Comprehensive sampling further enables direct comparison of equilibrium and cotranscriptionally restrained ensembles. Analysis of the resulting structural probability distributions uncovers kinetic traps and putative transcriptional pause sites, supporting an intuitive cotranscriptional folding mechanism in which local 3′-hairpin formation transiently stabilises upstream structure to delay large-scale rearrangement. Together, these results establish iterative sampling as a scalable and general framework for resolving out-of-equilibrium RNA cotranscriptional folding. Graphical abstract

mRNA medicines hold great promise, but designing sequences with high translation efficiency, robust in-solution stability, and manufacturability remains a major challenge due to the vast combinatorial space of synonymous coding sequences. Computational approaches such as mRNA folding algorithms have emerged as powerful tools by co-optimizing for in-solution stability and translation efficiency, yet current methods face important limitations. Here, we present "mRNAfold", an improved mRNA folding algorithm and software package that addresses these gaps by enabling efficient exploration of diverse near-optimal solutions, incorporating untranslated regions (UTRs), parallel execution, and supporting tunable control over local structural features across the mRNA. Thermodynamically optimized mRNAs from mRNAfold were more stable (≈2-fold) in-solution than those generated by simple GC maximization for the same encoded protein. In addition, mRNAs designed to vary local structure near the start codon while maintaining consistent structure and codon optimality elsewhere showed a complex relationship between local structure near the start codon and protein production in cells. We observed no impact of structure in the start codon region for a set of mRNAs with high codon optimality, but it did impact protein production for a set of mRNAs with lower codon optimality. Together, these results underscore the potential of structure-aware, multi-objective design to improve mRNA medicines and offer a framework for exploring how sequence, structure, and expression are interrelated. ### Competing Interest Statement The authors have declared no competing interest.

The diverse regulatory functions, protein production capacity, and stability of natural and synthetic RNAs are closely tied to their ability to fold into intricate structures. Determining RNA structure is thus fundamental to RNA biology and bioengineering. Among existing approaches to structure determination, computational secondary structure prediction offers a rapid and low-cost strategy and is thus widely used, especially when seeking to identify functional RNA elements in large transcriptomes or screen massive libraries of novel designs. While traditional approaches rely on detailed measurements of folding energetics and/or probabilistic modeling of structural data, recent years have witnessed a surge in deep learning methods, inspired by their tremendous success in protein structure prediction. However, the limited diversity and volume of known RNA structures can impede their ability to accurately predict structures markedly different from the ones they have seen. This is known as the generalization gap and currently poses a major barrier to progress in the field. In this Perspective article, we gauge method generalizability using a new benchmark dataset of structured RNAs we curated from the Protein Data Bank. We also discuss the emergence of deep learning methods for predicting structure probing data and use a new dataset to underscore generalization challenges unique to this domain along with directions for future improvement. Expanding beyond improving predictive accuracy, we review how advances in deep learning have recently enabled scalable and accessible optimization of traditional structure prediction methods and their seamless integration with modern neural networks.

mRNA technology has revolutionized vaccine development, protein replacement therapies, and cancer immunotherapies, offering rapid production and precise control over sequence and efficacy. However, the inherent instability of mRNA poses significant challenges for drug storage and distribution, particularly in resource-limited regions. Co-optimizing RNA structure and codon choice has emerged as a promising strategy to enhance mRNA stability while preserving efficacy. Given the vast sequence and structure design space, specialized algorithms are essential to achieve these qualities. Recently, several effective algorithms have been developed to tackle this challenge that all use similar underlying principles. We call these specialized methods mRNA folding algorithms as they generalize classical RNA folding algorithms. Initial laboratory testing of mRNA folding optimized mRNA vaccines, such as those encoding SARS-CoV-2 spike and VZV gE, has shown promising improvements in both in-solution stability and immunogenicity. While these biological properties are beginning to be evaluated experimentally, a comprehensive in silico analysis of the underlying principles, performance, and limitations of these design algorithms is equally essential. Thus, this review aims to provide an in-depth understanding of these algorithms, identify opportunities for improvement, and benchmark existing software implementations in terms of scalability, correctness, and feature support.

In this paper, we propose a novel choke point metric for the elimination of attack paths. Our study is motivated by its applications in the widely used Active Directory (AD) attack graphs. Choke points are typically defined as critical locations where the largest number of attack paths converge. Identifying these choke points is crucial. Enumeration of all attack paths is implied in this definition, but the immensity of paths in AD attack graphs makes the task extremely challenging. Consequently, industry solutions and research often rely on mapping only the shortest paths or prioritizing their elimination as a method for hardening AD attack graphs. We theoretically describe and empirically measure major limitations with the shortest path approach. To address the limitations, we introduce a new choke point metric that quantifies the intersection of connections rather than attack paths, which improves upon shortest path mapping. Additionally, we present human experiments to observe how white-hat hackers use shortest path mapping, provide simple graph examples that visually demonstrate failure cases where shortest path-based methods do not yield optimal results, and conduct experiments with a diverse set of real-world and synthetic AD datasets. From the results, we conclude that uninformed attack path mapping cannot capture the complexity of the attack path composition in a real-world attack, and reliance on shortest path mapping leads to significant volatility in security-hardening outcomes. In contrast, the connection-based choke point metric we propose offers greater optimality and utility in mitigating the attack surface.

Active Directory (AD) is the default security management system for Windows domain networks. An AD environment can be described as a cyber-attack graph, with nodes representing computers, accounts, etc., and edges indicating existing accesses or known exploits that enable attackers to move from one node to another. This paper explores a Stackelberg game model between one attacker and one defender on an AD attack graph. The attacker’s goal is to maximize their chances of successfully reaching the destination before getting detected. The defender’s aim is to block a constant number of edges to minimize the attacker’s chance of success. The paper shows that the problem is #P-hard and, therefore, intractable to solve exactly. To defend the AD graph from cyber attackers, this paper proposes two defensive approaches. In the first approach, we convert the attacker’s problem to an exponential sized Dynamic Program that is approximated by a Neural Network (NN). Once trained, the NN serves as an efficient fitness function for defender’s Evolutionary Diversity Optimization based defensive policy. The diversity emphasis on the defender’s solution provides a diverse set of training samples, improving the training accuracy of our NN for modeling the attacker. In the second approach, we propose a RL based policy to solve the attacker’s problem and Critic network assisted Evolutionary Diversity Optimization based defensive policy to solve defender’s problem. Experimental results on synthetic AD graphs show that the proposed defensive policies are scalable, highly effective, approximate attacker’s problem accurately, and generate good defensive plans.

Improving the efficiency of data compression remains essential for feature selection and data modelling. Current approaches for compressing epigenomic/genomic data highly rely on autoencoder that requires substantial computing resources, parameter fine-tuning, training, and time. Here, we developed a training-free, Fast Fourier Transform (FFT)-based method, for data compression with high efficiency and full interpretability. Our FFT method compresses epigenomic data of histone modification up to 1,000-fold while still maintaining high reconstruction fidelity (cosine similarity, 99.7

SUMMARY:Differentiable folding is an emerging paradigm for RNA design in which a probabilistic sequence representation is optimized via gradient descent. However, given the significant memory overhead of differentiating the expected partition function over all RNA sequences, the existing proof-of-concept algorithm only scales to ≤50 nucleotides. We present JAX-RNAfold, an open-source software package for our drastically improved differentiable folding algorithm that scales to 1,250 nucleotides on a single GPU. Our software permits the natural inclusion of differentiable folding as a module in larger deep learning pipelines, as well as complex RNA design procedures such as mRNA design with flexible objective functions. AVAILABILITY AND IMPLEMENTATION:JAX-RNAfold is hosted on GitHub (https://github.com/rkruegs123/jax-rnafold) and can be installed locally as a Python package. All source code is also archived on Zenodo (https://doi.org/10.5281/zenodo.15003072).

Glioblastoma and osteosarcoma originate from the same lineage, yet patients with these two tumour types show significant differences in survival outcomes. Transcriptomic analysis comparing these tumors reveals that over 65 % genes show similar expression patterns. Principal component analysis further demonstrates substantial similarities between these two tumour types, albeit with discernible differences. Deep learning analysis employing an autoencoder unveils nuanced distinctions and similarities of these two tumors at a high resolution. A classification model, leveraging gradient boosting with eXtreme Gradient Boosting (XGBoost), achieves high accuracy in distinguishing between these two tumour types. Identification of key contributors to the model's performance is facilitated by SHapley Additive exPlanations (SHAP), yielding two lists of top target genes with and without considering gender. Notably, these SHAP targets tend to cluster within one or two networks of signalling pathways. Remarkably, gene expression levels of many of these SHAP targets alone can recapitulate survival differences solely based on clinical data between glioblastoma and osteosarcoma patients. Of particular interest, C2ORF72 emerges as a common target from both lists, representing an uncharacterized protein with promising potential as a novel target for the diagnosis, prognosis, and therapy of both glioblastoma and osteosarcoma.

Current methods for predicting gene expression from histone modifications rely on arbitrary binary classification thresholds such as the median to distinguish between high and low expression for genes. This approach lacks biological justification, creates dataset-dependent classifications, and ignores the relative regulatory relationships between genes that are often more biologically meaningful than absolute cutoffs. We introduce a novel pairwise ranking approach that compares relative expression levels between gene pairs based on their histone modification patterns, eliminating arbitrary threshold selection. Evaluation using the REMC E066 and GSE76344 datasets showed that our pairwise classification framework demonstrated consistent ranking performance in both datasets. The ablation study found that only a subset of histone modification types is necessary, giving evidence of redundancy in the biological code. ### Competing Interest Statement The authors have declared no competing interest. Jack Tiddy Fellowship

The Nearest Neighbor model is the $\textit{de facto}$ thermodynamic model of RNA secondary structure formation and is a cornerstone of RNA structure prediction and sequence design. The current functional form (Turner 2004) contains $\approx13,000$ underlying thermodynamic parameters, and fitting these to both experimental and structural data is computationally challenging. Here, we leverage recent advances in $\textit{differentiable folding}$, a method for directly computing gradients of the RNA folding algorithms, to devise an efficient, scalable, and flexible means of parameter optimization that uses known RNA structures and thermodynamic experiments. Our method yields a significantly improved parameter set that outperforms existing baselines on all metrics, including an increase in the average predicted probability of ground-truth sequence-structure pairs for a single RNA family by over 23 orders of magnitude. Our framework provides a path towards drastically improved RNA models, enabling the flexible incorporation of new experimental data, definition of novel loss terms, large training sets, and even treatment as a module in larger deep learning pipelines. We make available a new database, RNAometer, with experimentally-determined stabilities for small RNA model systems.

Breast cancer is a leading cause of cancer-related deaths among women. The identification of survival-related target genes is critical for improving the prognosis and outcomes of breast cancer patients. Many methods have been applied to this investigation, such as bioinformatics and machine learning approaches, yet few targets identified from these approaches have been applied in clinics. Here, we present a novel approach by using classical statistical methods of Kolmogorov-Smirnov (KS) test and Jensen-Shannon (JS) divergence to analyse the survival time and gene expression data of breast cancer patients (BRCA) from The Cancer Genome Atlas (TCGA). These methods help compare the survival time distributions and differentiate patients into high and low-risk groups based on gene expression profiles. 1,124 survival-related genes were identified based on the KS test and 18 from JS divergence values. We also identified the optimal thresholds of the expression level of these target genes, which enabled the best separation of survival groups for all breast cancer patients and each subtype of breast cancer patients. These targets were further validated through bootstrapping to ensure that significant results are not due to chance. By comparing those survival targets from previous studies, we found two were novel targets, and two were consistent with previous reports. Overall, our study provides a novel approach for identifying survival targets for breast cancer patients by integrating a series of classical statistical methods, such as the KS test, JS divergence, and bootstrapping. Our approach could also be applied to identifying the survival targets for other cancer types and provide valuable insights into cancer research and clinical applications. ### Competing Interest Statement The authors have declared no competing interest.

Ribonucleic acid (RNA) is an essential molecule in a wide range of biological functions. In 1990, McCaskill introduced a dynamic programming algorithm for computing the partition function of an RNA sequence. McCaskill's algorithm is widely used today for understanding the thermodynamic properties of RNA. In this work, we introduce a generalization of McCaskill's algorithm that is well-defined over continuous inputs. Crucially, this enables us to implement an end-to-end differentiable partition function calculation. The derivative can be computed with respect to the input, or to any other fixed values, such as the parameters of the energy model. This builds a bridge between RNA thermodynamics and the tools of differentiable programming including deep learning as it enables the partition function to be incorporated directly into any end-to-end differentiable pipeline. To demonstrate the effectiveness of our new approach, we tackle the inverse folding problem directly using gradient optimization. We find that using the gradient to optimize the sequence directly is sufficient to arrive at sequences with a high probability of folding into the desired structure. This indicates that the gradients we compute are meaningful.

Security engineering has shifted from the paradigm of securing a list of assets to defending interconnected graphs. In this new paradigm, security researchers have employed higher-order graphs such as directed hypergraphs, where nodes represent sets of elements, and directed edges connect these sets. Higher-order graphs are unmatched in their flexibility to naturally model a broad range of network systems where higherorder relationships exist among their interacting parts. Despite their powerful expressiveness, higher-order graphs have been underexplored in the security modeling literature because of their inherent complexity and the lack of appropriate tools and algorithms. In this paper, we give an introduction to various types of higher-order graphs, including metagraphs, directed hypergraphs, and explore their relationships with similar concepts such as Petri nets. We also present the applications of higherorder graphs in a couple of network security modeling problems with recently developed algorithms for analyzing these types of graphs.

Given a directed graph, a set of source nodes, a target node and a budget, we study the problem of maximizing the number of source nodes disconnected from the target node by removing edges not exceeding the budget. Our model is mainly motivated by a cyber security use case where we need to minimize the attack surface of a Windows Active Directory system. In these high-profile attacks, the attackers first compromise a source (i.e., a compromised user node) and then laterally move to a destination (i.e., a high-privileged admin node). Our aim is to minimize the number of users with a path to the admin. We first prove that the problem is NP-hard. Algorithms for exact optimality usually struggle to converge on graphs that approach real-world network scales and therefore are not practical for usage. In light of this, we study anytime algorithms that return an acceptable result whenever the algorithm is terminated, and can improve optimality by allowing longer computational time. We observe the source connectivity of directed graphs, based on which we propose a novel anytime algorithm---the spiral algorithm. We also develop two Monte Carlo Tree Search (MCTS) algorithms as a baseline to study the performance of typical anytime algorithms for our problem, and show that the spiral algorithm improves the optimality at a significantly faster speed and therefore exhibits better anytime behavior compared with MCTS.

mRNA is an emerging therapeutic platform with applications ranging from vaccines to genome editing. However, there are an exponential number of mRNA sequences to deliver a given payload and the choice in nucleotide sequence largely determines stability and translation efficiency. There exist several computational approaches for optimizing mRNA sequences but these algorithms are limited in performance or the choice of optimization metric. In this work we describe a new mRNA design algorithm that overcomes both of these limitations and is based on differentiable folding, a recently developed paradigm for RNA design in which a probabilistic sequence representation is optimized via gradient-based methods. First, we present major improvements to the original differentiable folding algorithm that drastically reduce the memory overhead of the gradient calculation. Second, we formulate the mRNA design problem in the context of continuous sequences, requiring the generalization of existing metrics and careful treatment of constraints. Given this scaled algorithm and our mRNA design formalism, we then developed a generative deep learning approach that treats our differentiable folding algorithm as a module in a larger optimization pipeline to learn a network that samples optimized sequences. As a demonstration of our method, we optimize mRNA sequences via complex, therapeutically relevant objective functions. ### Competing Interest Statement The authors have declared no competing interest.

A bstract Determining RNA secondary structure is a core problem in computational biology. Fast algorithms for predicting secondary structure are fundamental to this task. We describe a modified formulation of the Zuker-Stiegler algorithm with coaxial stacking, a stabilizing interaction in which the ends of multi-loops are stacked. In particular, optimal coaxial stacking is computed as part of the dynamic programming state, rather than inline. We introduce a new notion of sparsity, which we call replaceability . The modified formulation along with replaceability allows sparsification to be applied to coaxial stacking as well, which increases the speed of the algorithm. We implemented this algorithm in software we call memerna , which we show to have the fastest exact RNA folding implementation out of several popular RNA folding packages supporting coaxial stacking. We also introduce a new notation for secondary structure which includes coaxial stacking, terminal mismatches, and dangles (CTDs) information.

We consider the problem of computing an $(s,d)$-hypernetwork in an acyclic F-hypergraph. This is a fundamental computational problem arising in directed hypergraphs, and is a foundational step in tackling problems of reachability and redundancy. This problem was previously explored in the context of general directed hypergraphs (containing cycles), where it is NP-hard, and acyclic B-hypergraphs, where a linear time algorithm can be achieved. In a surprising contrast, we find that for acyclic F-hypergraphs the problem is NP-hard, which also implies the problem is hard in BF-hypergraphs. This is a striking complexity boundary given that F-hypergraphs and B-hypergraphs would at first seem to be symmetrical to one another. We provide the proof of complexity and explain why there is a fundamental asymmetry between the two classes of directed hypergraphs.

Active Directory (AD) is a popular information security management system for Windows domain networks and is an ongoing common target for cyber attacks. Most real-world Active Directory systems consist of millions of entities and links, and there are currently no efficient and effective solutions for hardening Active Directory systems of such scale. In this paper, we propose a novel and scalable double oracle-based algorithm for hardening large AD systems. We formulate the problem as a Stackelberg game between the defender and the attacker on a weighted AD attack graph, where the defender acts as the leader with a budget, and the objective is to find an optimal defender's pure strategy. We show that our double oracle-based solution has significantly improved speed and scalability compared with previous solutions for hardening AD systems. Lastly, we compare with GoodHound weakest links and show that our solution provides better recommendations for targeting the elimination of optimal attack paths.