pwc-archive/papers-with-abstracts huggingface dataset:
PatternBoost: Constructions in Mathematics with a Little Help from AI
Authors: François Charton, Jordan S. Ellenberg, Adam Zsolt Wagner, Geordie Williamson
Date: 2024-11-01 00:00:00

We introduce PatternBoost, a flexible method for finding interesting constructions in mathematics. Our algorithm alternates between two phases. In the first ``local'' phase, a classical search algorithm is used to produce many desirable constructions. In the second ``global'' phase, a transformer neural network is trained on the best such constructions. Samples from the trained transformer are then used as seeds for the first phase, and the process is repeated. We give a detailed introduction to this technique, and discuss the results of its application to several problems in extremal combinatorics. The performance of PatternBoost varies across different problems, but there are many situations where its performance is quite impressive. Using our technique, we find the best known solutions to several long-standing problems, including the construction of a counterexample to a conjecture that had remained open for 30 years.
Qualitative analysis of HAART effects on HIV and SARS-CoV-2 coinfection
Authors: João P. S. Maurício de Carvalho
Date: 2024-11-02 00:00:00

HIV is known for causing the destruction of the immune system by affecting different types of cells, while SARS-CoV-2 is an extremely contagious virus that leads to the development of COVID-19. In this study, we propose a mathematical model to investigate the interaction between HIV and SARS-CoV-2 under highly active antiretroviral therapy (HAART). We determine the conditions for the endemic equilibria of both viruses, showing that transcritical bifurcations occur when the basic reproduction numbers of HIV and SARS-CoV-2 pass through 1. We set the condition for the stability of the disease-free equilibrium point of the model with coinfection as a function of the basic reproduction number $\mathcal{R}_0$. Through numerical simulations, we conclude that HAART, used to control HIV, also reduces the proliferation of SARS-CoV-2-infected cells in coinfected hosts. These findings provide important insights into the epidemiological dynamics of HIV and SARS-CoV-2 coinfection.
Global bifurcation in a virus, defective genomes, satellite RNAs tripartite system: breakdown of a coexistence quasi-neutral curve
Authors: Oriol Llopis-Almela, J. Tomas Lazaro, Santiago F. Elena, Josep Sardanyes
Date: 2024-10-31 00:00:00

The dynamics of wild-type (wt) RNA viruses and their defective viral genomes (DVGs) have been extensively studied both experimentally and theoretically. This research has paid special attention to the interference effects of DVGs on wt accumulation, transmission, disease severity, and induction of immunological responses. This subject is currently a highly active. However, viral infections involving wt, DVGs and other subviral genetic elements, like viral RNA satellites (satRNAs) have received scarce attention. Satellites are molecular parasites genetically different from the wt virus, which exploit the products of the latter for their own replication in as much as DVGs do, and thus they need to coinfect host cells along with the wt virus to complete their replication cycle. Here, we analyze a mathematical model describing the initial replication phase of a wt virus producing DVGs and coinfecting with a satRNA. The model has three different dynamical regimes depending upon the wt replication rate ($\alpha$), the fraction of DVGs produced during replication ($\omega$), and the replication rate of the satRNA ($\beta$): ($i$) full extinction when $\beta > \alpha (1 - \omega)$; ($ii$) a bistable regime with full coexistence governed by a quasi-neutral curve of equilibria and full extinction when $\beta = \alpha (1 - \omega)$; and ($iii$) a scenario of bistability separating full extinction from wt-DVGs coexistence with no satRNA when $\beta < \alpha (1 - \omega)$. The transition from scenarios ($i$) to ($iii$) occurs through the creation and destruction of a quasi-neutral curve of equilibria in a global bifurcation that we name as \textit{quasi-neutral nullcline confluence} (QNC) bifurcation: at the bifurcation value, two nullcline hypersurfaces coincide, giving rise to the curve of equilibria.
Quantifying calibration error in modern neural networks through evidence based theory
Authors: Koffi Ismael Ouattara
Date: 2024-10-31 00:00:00
Tasks: Decision Making

Trustworthiness in neural networks is crucial for their deployment in critical applications, where reliability, confidence, and uncertainty play pivotal roles in decision-making. Traditional performance metrics such as accuracy and precision fail to capture these aspects, particularly in cases where models exhibit overconfidence. To address these limitations, this paper introduces a novel framework for quantifying the trustworthiness of neural networks by incorporating subjective logic into the evaluation of Expected Calibration Error (ECE). This method provides a comprehensive measure of trust, disbelief, and uncertainty by clustering predicted probabilities and fusing opinions using appropriate fusion operators. We demonstrate the effectiveness of this approach through experiments on MNIST and CIFAR-10 datasets, where post-calibration results indicate improved trustworthiness. The proposed framework offers a more interpretable and nuanced assessment of AI models, with potential applications in sensitive domains such as healthcare and autonomous systems.
Comparison of two mean-field approaches to modeling an epidemic spread
Authors: Viktoriya Petrakova, Olga Krivorotko
Date: 2024-11-05 00:00:00

The paper describes and compares three approaches to modeling an epidemic spread. The first approach is a well-known system of SIR ordinary differential equations. The second is a mean-field model, in which an isolation strategy for each epidemiological group (Susceptible, Infected, and Removed) is chosen as an optimal control. The third is another meanfield model, in which isolation strategy is common for the entire population. The considered models have been compared analytically, their sensitivity analysis has been carried out and their predictive capabilities have been estimated using sets of synthetic and real data. For one of the meanfield models, its finite-difference analogue has been devised. The models have also been assessed in terms of their applicability for predicting a viral epidemic spread.
A Bregman firmly nonexpansive proximal operator for baryconvex optimization
Authors: Mastane Achab
Date: 2024-11-01 00:00:00

We present a generalization of the proximal operator defined through a convex combination of convex objectives, where the coefficients are updated in a minimax fashion. We prove that this new operator is Bregman firmly nonexpansive with respect to a Bregman divergence that combines Euclidean and information geometries; and that its fixed points are given by the critical points of a certain nonconvex function. Finally, we derive the associated continuous flows.
EARL-BO: Reinforcement Learning for Multi-Step Lookahead, High-Dimensional Bayesian Optimization
Authors: Mujin Cheon, Jay H. Lee, Dong-Yeun Koh, Calvin Tsay
Date: 2024-10-31 00:00:00
Tasks: Bayesian Optimization, Decision Making, Hyperparameter Optimization, Reinforcement Learning (RL), Sequential Decision Making

Conventional methods for Bayesian optimization (BO) primarily involve one-step optimal decisions (e.g., maximizing expected improvement of the next step). To avoid myopic behavior, multi-step lookahead BO algorithms such as rollout strategies consider the sequential decision-making nature of BO, i.e., as a stochastic dynamic programming (SDP) problem, demonstrating promising results in recent years. However, owing to the curse of dimensionality, most of these methods make significant approximations or suffer scalability issues, e.g., being limited to two-step lookahead. This paper presents a novel reinforcement learning (RL)-based framework for multi-step lookahead BO in high-dimensional black-box optimization problems. The proposed method enhances the scalability and decision-making quality of multi-step lookahead BO by efficiently solving the SDP of the BO process in a near-optimal manner using RL. We first introduce an Attention-DeepSets encoder to represent the state of knowledge to the RL agent and employ off-policy learning to accelerate its initial training. We then propose a multi-task, fine-tuning procedure based on end-to-end (encoder-RL) on-policy learning. We evaluate the proposed method, EARL-BO (Encoder Augmented RL for Bayesian Optimization), on both synthetic benchmark functions and real-world hyperparameter optimization problems, demonstrating significantly improved performance compared to existing multi-step lookahead and high-dimensional BO methods.
Derivative-Free Optimization via Finite Difference Approximation: An Experimental Study
Authors: Wang Du-Yi, Liang Guo, Liu Guangwu, Zhang Kun
Date: 2024-10-31 00:00:00

Derivative-free optimization (DFO) is vital in solving complex optimization problems where only noisy function evaluations are available through an oracle. Within this domain, DFO via finite difference (FD) approximation has emerged as a powerful method. Two classical approaches are the Kiefer-Wolfowitz (KW) and simultaneous perturbation stochastic approximation (SPSA) algorithms, which estimate gradients using just two samples in each iteration to conserve samples. However, this approach yields imprecise gradient estimators, necessitating diminishing step sizes to ensure convergence, often resulting in slow optimization progress. In contrast, FD estimators constructed from batch samples approximate gradients more accurately. While gradient descent algorithms using batch-based FD estimators achieve more precise results in each iteration, they require more samples and permit fewer iterations. This raises a fundamental question: which approach is more effective -- KW-style methods or DFO with batch-based FD estimators? This paper conducts a comprehensive experimental comparison among these approaches, examining the fundamental trade-off between gradient estimation accuracy and iteration steps. Through extensive experiments in both low-dimensional and high-dimensional settings, we demonstrate a surprising finding: when an efficient batch-based FD estimator is applied, its corresponding gradient descent algorithm generally shows better performance compared to classical KW and SPSA algorithms in our tested scenarios.
Zero-Coupon Treasury Rates and Returns using the Volatility Index
Authors: Jihyun Park, Andrey Sarantsev
Date: 2024-11-06 00:00:00

We study a multivariate autoregressive stochastic volatility model for the first 3 principal components (level, slope, curvature) of 10 series of zero-coupon Treasury bond rates with maturities from 1 to 10 years. We fit this model using monthly data from 1990. Unlike classic models with hidden stochastic volatility, here it is observed as VIX: the volatility index for the S&P 500 stock market index. Surprisingly, this stock index volatility works for Treasury bonds, too. Next, we prove long-term stability and the Law of Large Numbers. We express total returns of zero-coupon bonds using these principal components. We prove the Law of Large Numbers for these returns. All results are done for discrete and continuous time.
Real-world models for multiple term structures: a unifying HJM semimartingale framework
Authors: Claudio Fontana, Eckhard Platen, Stefan Tappe
Date: 2024-11-04 00:00:00

We develop a unified framework for modeling multiple term structures arising in financial, insurance, and energy markets, adopting an extended Heath-Jarrow-Morton (HJM) approach under the real-world probability. We study market viability and characterize the set of local martingale deflators. We conduct an analysis of the associated stochastic partial differential equation (SPDE), addressing existence and uniqueness of solutions, invariance properties and existence of affine realizations.
Two timescales in stochastic evolutionary games
Authors: Sabin Lessard
Date: 2024-11-01 00:00:00

Convergence of discrete-time Markov chains with two timescales is a powerful tool to study stochastic evolutionary games in subdivided populations. Focusing on linear games within demes, convergence to a diffusion process for the strategy frequencies as the population size increases yields a strong-migration limit. The same limit is obtained for a linear game in a well-mixed population with effective payoffs that depend on reproductive values and identity measures between individuals. The first-order effect of selection on the fixation probability of a strategy introduced as a single mutant can be calculated by using the diffusion approximation, or alternatively by summing the successive expected changes in the mutant strategy frequency that involve expected coalescence times of ancestral lines under neutrality. These can be approached by resorting to the existence of two timescales in the genealogical process. Keeping the population size fixed but letting the intensity of migration go to zero, convergence to a continuous-time Markov chain after instantaneous initial transitions yields a low-migration limit that depends on fixation probabilities within demes in the absence of migration. In the limit of small uniform dispersal, the fixation probability of a mutant strategy in the whole population exceeds its initial frequency if it is risk-dominant over the other strategy with respect to the overall average payoffs in pairwise interactions. Finally, in the low-mutation limit in the presence of recurrent mutation, the average abundance of a strategy in the long run is determined by the fixation probabilities of both strategies when introduced as single mutants in a deme chosen at random.
Discrete approximation of risk-based prices under volatility uncertainty
Authors: Jonas Blessing, Michael Kupper, Alessandro Sgarabottolo
Date: 2024-11-01 00:00:00

We discuss the asymptotic behaviour of risk-based indifference prices of European contingent claims in discrete-time financial markets under volatility uncertainty as the number of intermediate trading periods tends to infinity. The asymptotic risk-based prices form a strongly continuous convex monotone semigroup which is uniquely determined by its infinitesimal generator and therefore only depends on the covariance of the random factors but not on the particular choice of the model. We further compare the risk-based prices with the worst-case prices given by the $G$-expectation and investigate their asymptotic behaviour as the risk aversion of the agent tends to infinity. The theoretical results are illustrated with several examples and numerical simulations showing, in particular, that the risk-based prices lead to a significant reduction of the bid-ask spread compared to the worst-case prices.
Multiscale differential geometry learning for protein flexibility analysis
Authors: Hongsong Feng, Jeffrey Y. Zhao, Guo-Wei Wei
Date: 2024-11-05 00:00:00
Tasks: Prediction

Protein flexibility is crucial for understanding protein structures, functions, and dynamics, and it can be measured through experimental methods such as X-ray crystallography. Theoretical approaches have also been developed to predict B-factor values, which reflect protein flexibility. Previous models have made significant strides in analyzing B-factors by fitting experimental data. In this study, we propose a novel approach for B-factor prediction using differential geometry theory, based on the assumption that the intrinsic properties of proteins reside on a family of low-dimensional manifolds embedded within the high-dimensional space of protein structures. By analyzing the mean and Gaussian curvatures of a set of kernel-function-defined low-dimensional manifolds, we develop effective and robust multiscale differential geometry (mDG) models. Our mDG model demonstrates a 27\% increase in accuracy compared to the classical Gaussian network model (GNM) in predicting B-factors for a dataset of 364 proteins. Additionally, by incorporating both global and local protein features, we construct a highly effective machine learning model for the blind prediction of B-factors. Extensive least-squares approximations and machine learning-based blind predictions validate the effectiveness of the mDG modeling approach for B-factor prediction.
Persistent Directed Flag Laplacian (PDFL)-Based Machine Learning for Protein-Ligand Binding Affinity Prediction
Authors: Mushal Zia, Benjamin Jones, Hongsong Feng, Guo-Wei Wei
Date: 2024-11-04 00:00:00
Tasks: Drug Discovery, Topological Data Analysis

Directionality in molecular and biomolecular networks plays a significant role in the accurate represention of the complex, dynamic, and asymmetrical nature of interactions present in protein-ligand binding, signal transduction, and biological pathways. Most traditional techniques of topological data analysis (TDA), such as persistent homology (PH) and persistent Laplacian (PL), overlook this aspect in their standard form. To address this, we present the persistent directed flag Laplacian (PDFL), which incorporates directed flag complexes to account for edges with directionality originated from polarization, gene regulation, heterogeneous interactions, etc. This study marks the first application of the PDFL, providing an in-depth analysis of spectral graph theory combined with machine learning. Besides its superior accuracy and reliability, the PDFL model offers simplicity by requiring only raw inputs without complex data processing. We validated our multi-kernel PDFL model for its scoring power against other state-of-art methods on three popular benchmarks, namely PDBbind v2007, v2013, and v2016. Computational results indicate that the proposed PDFL model outperforms competitors in protein-ligand binding affinity predictions, indicating that PDFL is a promising tool for protein engineering, drug discovery, and general applications in science and engineering.
On Novel Approach for Computing Distance based Indices of Anti-tuberculosis Drugs
Authors: D. C. Gunawardhana, G. H. J. Lanel, K. K. K. R. Perera, A. G. M. J. Gunaratna
Date: 2024-10-21 00:00:00

This work aims to assess the molecular architectures of anti-tuberculosis drugs using both degree-based topological indices and novel distance based indices. We can represent the chemical arrangement as a graph, with atoms serving as the vertices and connections as the edges. Here, the multi bonds were considered as multi edges and included all the hydrogen atoms. Also, we consider three dimensional molecular graph. As a result, the actual bond lengths have been used for computation of new distance based indices. Compared to numerous studies, this is a significant improvement. Furthermore, the investigation of these indices includes a study on the quantitative structure-property relationship (QSPR). The research demonstrates a notable correlation between these indicators and the physical attributes of anti-tuberculosis drugs. Here, Since we reduced the some of existing critical assumptions in the literature, chemists and pharmaceutical professionals might potentially eliminate the need for clinical trials by employing this theoretical model. These models would enable them to predict the characteristics of anti-tuberculosis medications.
log-RRIM: Yield Prediction via Local-to-global Reaction Representation Learning and Interaction Modeling
Authors: Xiao Hu, Ziqi Chen, Bo Peng, Daniel Adu-Ampratwum, Xia Ning
Date: 2024-10-20 00:00:00
Tasks: Representation Learning

Accurate prediction of chemical reaction yields is crucial for optimizing organic synthesis, potentially reducing time and resources spent on experimentation. With the rise of artificial intelligence (AI), there is growing interest in leveraging AI-based methods to accelerate yield predictions without conducting in vitro experiments. We present log-RRIM, an innovative graph transformer-based framework designed for predicting chemical reaction yields. A key feature of log-RRIM is its integration of a cross-attention mechanism that focuses on the interplay between reagents and reaction centers. This design reflects a fundamental principle in chemical reactions: the crucial role of reagents in influencing bond-breaking and formation processes, which ultimately affect reaction yields. log-RRIM also implements a local-to-global reaction representation learning strategy. This approach initially captures detailed molecule-level information and then models and aggregates intermolecular interactions. Through this hierarchical process, log-RRIM effectively captures how different molecular fragments contribute to and influence the overall reaction yield, regardless of their size variations. log-RRIM shows superior performance in our experiments, especially for medium to high-yielding reactions, proving its reliability as a predictor. The framework's sophisticated modeling of reactant-reagent interactions and precise capture of molecular fragment contributions make it a valuable tool for reaction planning and optimization in chemical synthesis. The data and codes of log-RRIM are accessible through https://github.com/ninglab/Yield_log_RRIM.
A Heterogeneous Network-based Contrastive Learning Approach for Predicting Drug-Target Interaction
Authors: Junwei Hu, Michael Bewong, Selasi Kwashie, Wen Zhang, Vincent M. Nofong, Guangsheng Wu, Zaiwen Feng
Date: 2024-10-20 00:00:00
Tasks: Contrastive Learning, Graph Attention

Drug-target interaction (DTI) prediction is crucial for drug development and repositioning. Methods using heterogeneous graph neural networks (HGNNs) for DTI prediction have become a promising approach, with attention-based models often achieving excellent performance. However, these methods typically overlook edge features when dealing with heterogeneous biomedical networks. We propose a heterogeneous network-based contrastive learning method called HNCL-DTI, which designs a heterogeneous graph attention network to predict potential/novel DTIs. Specifically, our HNCL-DTI utilizes contrastive learning to collaboratively learn node representations from the perspective of both node-based and edge-based attention within the heterogeneous structure of biomedical networks. Experimental results show that HNCL-DTI outperforms existing advanced baseline methods on benchmark datasets, demonstrating strong predictive ability and practical effectiveness. The data and source code are available at https://github.com/Zaiwen/HNCL-DTI.
RapidDock: Unlocking Proteome-scale Molecular Docking
Authors: Rafał Powalski, Bazyli Klockiewicz, Maciej Jaśkowski, Bartosz Topolski, Paweł Dąbrowski-Tumański, Maciej Wiśniewski, Łukasz Kuciński, Piotr Miłoś, Dariusz Plewczynski
Date: 2024-10-16 00:00:00
Tasks: Drug Discovery, GPU, Molecular Docking, Protein Folding

Accelerating molecular docking -- the process of predicting how molecules bind to protein targets -- could boost small-molecule drug discovery and revolutionize medicine. Unfortunately, current molecular docking tools are too slow to screen potential drugs against all relevant proteins, which often results in missed drug candidates or unexpected side effects occurring in clinical trials. To address this gap, we introduce RapidDock, an efficient transformer-based model for blind molecular docking. RapidDock achieves at least a $100 \times$ speed advantage over existing methods without compromising accuracy. On the Posebusters and DockGen benchmarks, our method achieves $52.1\%$ and $44.0\%$ success rates ($\text{RMSD}<2$\r{A}), respectively. The average inference time is $0.04$ seconds on a single GPU, highlighting RapidDock's potential for large-scale docking studies. We examine the key features of RapidDock that enable leveraging the transformer architecture for molecular docking, including the use of relative distance embeddings of $3$D structures in attention matrices, pre-training on protein folding, and a custom loss function invariant to molecular symmetries.