pwc-archive/papers-with-abstracts huggingface dataset:
PDEs for pricing interest rate derivatives under the new generalized Forward Market Model (FMM)
Authors: J. G. López-Salas, S. Pérez-Rodríguez, C. Vázquez
Date: 2024-08-05 00:00:00

In this article we derive partial differential equations (PDEs) for pricing interest rate derivatives under the generalized Forward Market Model (FMM) recently presented by A. Lyashenko and F. Mercurio in \cite{lyashenkoMercurio:Mar2019} to model the dynamics of the Risk Free Rates (RFRs) that are replacing the traditional IBOR rates in the financial industry. Moreover, for the numerical solution of the proposed PDEs formulation, we develop some adaptations of the finite differences methods developed in \cite{LopezPerezVazquez:sisc} that are very suitable to treat the presence of spatial mixed derivatives. This work is the first article in the literature where PDE methods are used to value RFR derivatives. Additionally, Monte Carlo-based methods will be designed and the results are compared with those obtained by the numerical solution of PDEs.
The $B_2$ index of galled trees
Authors: François Bienvenu, Jean-Jil Duchamps, Michael Fuchs, Tsan-Cheng Yu
Date: 2024-07-28 00:00:00
Tasks: Specificity

In recent years, there has been an effort to extend the classical notion of phylogenetic balance, originally defined in the context of trees, to networks. One of the most natural ways to do this is with the so-called $B_2$ index. In this paper, we study the $B_2$ index for a prominent class of phylogenetic networks: galled trees. We show that the $B_2$ index of a uniform leaf-labeled galled tree converges in distribution as the network becomes large. We characterize the corresponding limiting distribution, and show that its expected value is 2.707911858984... This is the first time that a balance index has been studied to this level of detail for a random phylogenetic network. One specificity of this work is that we use two different and independent approaches, each with its advantages: analytic combinatorics, and local limits. The analytic combinatorics approach is more direct, as it relies on standard tools; but it involves slightly more complex calculations. Because it has not previously been used to study such questions, the local limit approach requires developing an extensive framework beforehand; however, this framework is interesting in itself and can be used to tackle other similar problems.
Interplay between Foraging Choices and Population Growth Dynamics
Authors: Jimmy Calvo-Monge, Baltazar Espinoza, Fabio Sanchez
Date: 2024-08-05 00:00:00

In this study, we couple a population dynamics model with a model for optimal foraging to study the interdependence between individual-level cost-benefits and population-scale dynamics. Specifically, we study the logistic growth model, which provides insights into population dynamics under resource limitations. Unlike exponential growth, the logistic model incorporates the concept of carrying capacity, thus offering a more realistic depiction of biological populations as they near environmental limits. We aim to study the impact of individual-level incentives driving behavioral responses in a dynamic environment. Specifically, explore the coupled dynamics between population density and individuals' foraging times. Our results yield insights into the effects of population size on individuals' optimal foraging efforts, which impacts the population's size.
Numerical approximations of McKean Anticipative Backward Stochastic Differential Equations arising in Initial Margin requirements
Authors: A. Agarwal, S. De Marco, E. Gobet, J. G. Lopez-Salas, F. Noubiagain, A. Zhou
Date: 2024-08-02 00:00:00

We introduce a new class of anticipative backward stochastic differential equations with a dependence of McKean type on the law of the solution, that we name MKABSDE. We provide existence and uniqueness results in a general framework with relatively general regularity assumptions on the coefficients. We show how such stochastic equations arise within the modern paradigm of derivative pricing where a central counterparty (CCP) requires the members to deposit variation and initial margins to cover their exposure. In the case when the initial margin is proportional to the Conditional Value-at-Risk (CVaR) of the contract price, we apply our general result to define the price as a solution of a MKABSDE. We provide several linear and non-linear simpler approximations, which we solve using different numerical (deterministic and Monte-Carlo) methods.
Optimal retirement in presence of stochastic labor income: a free boundary approach in an incomplete market
Authors: Daniele Marazzina
Date: 2024-07-27 00:00:00

In this work, we address the optimal retirement problem in the presence of a stochastic wage, formulated as a free boundary problem. Specifically, we explore an incomplete market setting where the wage cannot be perfectly hedged through investments in the risk-free and risky assets that characterize the financial market.
Bonus-malus Systems vs Delays in Claims Reporting and Settlement: Analysis of Ruin Probabilities
Authors: Dhiti Osatakul, Shuanming Li, Xueyuan Wu
Date: 2024-07-17 00:00:00

Our paper explores a discrete-time risk model with time-varying premiums, investigating two types of correlated claims: main claims and by-claims. Settlement of the by-claims can be delayed for one time period, representing real-world insurance practices. We examine two premium principles based on reported and settled claims, using recursively computable finite-time ruin probabilities to evaluate the performance of time-varying premiums. Our findings suggest that, under specific assumptions, a higher probability of by-claim settlement delays leads to lower ruin probabilities. Moreover, a stronger correlation between main claims and their associated by-claims results in higher ruin probabilities. Lastly, the premium adjustment principles based on settled claims experience contribute to higher ruin probabilities compared to those based on reported claims experience, assuming all other factors remain constant. Notably, this difference becomes more pronounced when there is a high likelihood of by-claim delays.
Approximating particle-based clustering dynamics by stochastic PDEs
Authors: Nathalie Wehlitz, Mohsen Sadeghi, Alberto Montefusco, Christof Schütte, Grigorios A. Pavliotis, Stefanie Winkelmann
Date: 2024-07-12 00:00:00
Tasks: Clustering, Computational Efficiency, parameter estimation

This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we formulate a stochastic particle-based model for diffusion and pairwise interaction of particles, leading to intriguing clustering phenomena. Employing numerical simulation and cluster detection methods, we explore the approximation of the particle-based clustering dynamics through mean-field approaches. We find that SPDEs successfully reproduce spatiotemporal clustering dynamics, not only in the initial cluster formation period, but also on longer time scales where the successive merging of clusters cannot be tracked by deterministic mean-field models. The computational efficiency of the SPDE approach allows us to generate extensive statistical data for parameter estimation in a simpler model that uses a Markov jump process to capture the temporal evolution of the cluster number.
Compact assessment of molecular surface complementarities enhances neural network-aided prediction of key binding residues
Authors: Greta Grassmann, Lorenzo Di Rienzo, Giancarlo Ruocco, Mattia Miotto, Edoardo Milanetti
Date: 2024-07-30 00:00:00

Predicting interactions between biomolecules, such as protein-protein complexes, remains a challenging problem. Despite the many advancements done so far, the performances of docking protocols are deeply dependent on their capability of identify binding regions. In this context, we present a novel approach that builds upon our previous works modeling protein surface patches via sets of orthogonal polynomials to identify regions of high shape/electrostatic complementarity. By incorporating another key binding property, such as the balance between hydrophilic and hydrophobic contributions, we define new binding matrices that serve an effective inputs for training a neural network. Our approach also allows for the quantitative definition of a typical binding site area - approximately 10\AA~in radius - where hydrophobic contribution and shape complementarity, which reflects the Lennard-Jones interaction, are maximized. Using this new architecture, CIRNet (Core Interacting Residues Network), we achieve an accuracy of approximately 0.82 in identifying pairs of core interacting residues on a balanced dataset. In a blind search for core interacting residues, CIRNet distinguishes these from decoys with a ROC AUC of 0.72. This protocol can enahnce docking algorithms by rescaling the proposed poses. When applied to the top ten models from three popular docking server, CIRNet improves docking outcomes, reducing the the average RMSD between the refined poses and the native state by up to 58%.
Dimeric Drug Polymeric Micelles with Acid-Active Tumor Targeting and FRET-indicated Drug Release
Authors: Xing Guo, Lin Wang, Kayla Duval, Jing Fan, Shaobing Zhou, Zi Chen
Date: 2024-07-30 00:00:00

Trans-activating transcriptional activator (TAT), a cell-penetrating peptide, has been extensively used for facilitating cellular uptake and nuclear targeting of drug delivery systems. However, the positively charged TAT peptide usually strongly interacts with serum components and undergoes substantial phagocytosis by the reticuloendothelial system, causing a short blood circulation in vivo. In this work, an acid-active tumor targeting nanoplatform DA-TAT-PECL was developed to effectively inhibit the nonspecific interactions of TAT in the bloodstream. 2,3-dimethylmaleic anhydride (DA) was first used to convert the TAT amines to carboxylic acid, the resulting DA-TAT was further conjugated to get DA-TAT-PECL. After self-assembly into polymeric micelles, they were capable of circulating in the physiological condition for a long time and promoting cell penetration upon accumulation at the tumor site and de-shielding the DA group. Moreover, camptothecin (CPT) was used as the anticancer drug and modified into a dimer (CPT)2-ss-Mal, in which two CPT molecules were connected by a reduction-labile maleimide thioether bond. The FRET signal between CPT and maleimide thioether bond was monitored to visualize the drug release process and effective targeted delivery of antitumor drugs was demonstrated. This pH/reduction dual-responsive micelle system provides a new platform for high fidelity cancer therapy.
ToF-SIMS data analysis of Shewanella oneidensis MR-1 biofilms
Authors: Gabriel D. Parker, Andrew Plymale, Luke Hanley, Xiao-Ying Yu
Date: 2024-07-29 00:00:00

Analysis of bacterial biofilms is particularly challenging and important with diverse applications from systems biology to biotechnology. Among the variety of techniques that have been applied, time-of-flight secondary ion mass spectrometry (ToF-SIMS) has many promising features in studying the surface characteristics of biofilms. ToF-SIMS offers high spatial resolution and high mass accuracy, which permit surface sensitive analysis of biofilm components. Thus, ToF-SIMS provides a powerful solution to addressing the challenge of bacterial biofilm analysis. This dataset covers ToF-SIMS analysis of Shewanella oneidensis MR-1 isolated from freshwater lake sediment in New York state. The MR-1 strain is known to have metal and sulfur reducing properties and it can be used for bioremediation and wastewater treatment. There is a current need to identify small molecules and fragments produced from bacterial biofilms. Static ToF-SIMS spectra of MR-1 were obtained using an IONTOF TOF.SIMS V instrument equipped with a 25 keV Bi3+ metal ion gun. Identified molecules and molecular fragments are compared against known biological databases and the reported peaks have at least 65 ppm mass accuracy. These molecules range from lipids and fatty acids to flavonoids, quinolones, and other naturally occurring organic compounds. It is anticipated that the spectral identification of key peaks will assist detection of metabolites, extracellular polymeric substance molecules like polysaccharides, and biologically relevant small molecules using ToF-SIMS in future surface and interface research.
On Machine Learning Approaches for Protein-Ligand Binding Affinity Prediction
Authors: Nikolai Schapin, Carles Navarro, Albert Bou, Gianni de Fabritiis
Date: 2024-07-15 00:00:00
Tasks: Active Learning, Benchmarking, Computational Efficiency, Drug Discovery, Language Modelling, Large Language Model

Binding affinity optimization is crucial in early-stage drug discovery. While numerous machine learning methods exist for predicting ligand potency, their comparative efficacy remains unclear. This study evaluates the performance of classical tree-based models and advanced neural networks in protein-ligand binding affinity prediction. Our comprehensive benchmarking encompasses 2D models utilizing ligand-only RDKit embeddings and Large Language Model (LLM) ligand representations, as well as 3D neural networks incorporating bound protein-ligand conformations. We assess these models across multiple standard datasets, examining various predictive scenarios including classification, ranking, regression, and active learning. Results indicate that simpler models can surpass more complex ones in specific tasks, while 3D models leveraging structural information become increasingly competitive with larger training datasets containing compounds with labelled affinity data against multiple targets. Pre-trained 3D models, by incorporating protein pocket environments, demonstrate significant advantages in data-scarce scenarios for specific binding pockets. Additionally, LLM pretraining on 2D ligand data enhances complex model performance, providing versatile embeddings that outperform traditional RDKit features in computational efficiency. Finally, we show that combining 2D and 3D model strengths improves active learning outcomes beyond current state-of-the-art approaches. These findings offer valuable insights for optimizing machine learning strategies in drug discovery pipelines.
Stochastic Gene Expression Model of Nuclear-to-Cell Ratio Homeostasis
Authors: Xuesong Bai, Thomas G. Fai
Date: 2024-07-26 00:00:00
Tasks: Translation

Cell size varies between different cell types, and between different growth and osmotic conditions. However, the nuclear-to-cell volume ratio (N/C ratio) remains nearly constant. In this paper, we build on existing deterministic models of N/C ratio homeostasis and develop a simplified gene translation model to study the effect of stochasticity on the N/C ratio homeostasis. We solve the corresponding chemical master equation and obtain the mean and variance of the N/C ratio. We also use a Taylor expansion approximation to study the effects of the system size on the fluctuations of the N/C ratio. We then combine the translation model with a cell division model to study the effects of extrinsic noises from cell division on the N/C ratio. Our model demonstrates that the N/C ratio homeostasis is maintained when the stochasticity in cell growth is taken into account, that the N/C ratio is largely determined by the gene fraction of nuclear proteins, and that the fluctuations in the N/C ratio diminish as the system size increases.
Refinement of genetic variants needs attention
Authors: Omar Abdelwahab, Davoud Torkamaneh
Date: 2024-08-01 00:00:00

Variant calling refinement is crucial for distinguishing true genetic variants from technical artifacts in high-throughput sequencing data. Manual review is time-consuming while heuristic filtering often lacks optimal solutions. Traditional variant calling methods often struggle with accuracy, especially in regions of low read coverage, leading to false-positive or false-negative calls. Here, we introduce VariantTransformer, a Transformer-based deep learning model, designed to automate variant calling refinement directly from VCF files in low-coverage data (10-15X). VariantTransformer, trained on two million variants, including SNPs and short InDels, from low-coverage sequencing data, achieved an accuracy of 89.26% and a ROC AUC of 0.88. When integrated into conventional variant calling pipelines, VariantTransformer outperformed traditional heuristic filters and approached the performance of state-of-the-art AI-based variant callers like DeepVariant. Comparative analysis demonstrated VariantTransformer's superiority in functionality, variant type coverage, training size, and input data type. VariantTransformer represents a significant advancement in variant calling refinement for low-coverage genomic studies.
Are gene-by-environment interactions leveraged in multi-modality neural networks for breast cancer prediction?
Authors: Monica Isgut, Andrew Hornback, Yunan Luo, Asma Khimani, Neha Jain, May D. Wang
Date: 2024-07-30 00:00:00

Polygenic risk scores (PRSs) can significantly enhance breast cancer risk prediction when combined with clinical risk factor data. While many studies have explored the value-add of PRSs, little is known about the potential impact of gene-by-gene or gene-by-environment interactions towards enhancing the risk discrimination capabilities of multi-modal models combining PRSs with clinical data. In this study, we integrated data on 318 individual genotype variants along with clinical data in a neural network to explore whether gene-by-gene (i.e., between individual variants) and/or gene-by-environment (between clinical risk factors and variants) interactions could be leveraged jointly during training to improve breast cancer risk prediction performance. We benchmarked our approach against a baseline model combining traditional univariate PRSs with clinical data in a logistic regression model and ran an interpretability analysis to identify feature interactions. While our model did not demonstrate improved performance over the baseline, we discovered 248 (<1%) statistically significant gene-by-gene and gene-by-environment interactions out of the ~53.6k possible feature pairs, the most contributory of which included rs6001930 (MKL1) and rs889312 (MAP3K1), with age and menopause being the most heavily interacting non-genetic risk factors. We also modeled the significant interactions as a network of highly connected features, suggesting that potential higher-order interactions are captured by the model. Although gene-by-environment (or gene-by-gene) interactions did not enhance breast cancer risk prediction performance in neural networks, our study provides evidence that these interactions can be leveraged by these models to inform their predictions. This study represents the first application of neural networks to screen for interactions impacting breast cancer risk using real-world data.
Selective pruning and neuronal death generate heavy-tail network connectivity
Authors: Rodrigo Siqueira Kazu, Kleber Neves, Bruno Mota
Date: 2024-08-05 00:00:00

From the proliferative mechanisms generating neurons from progenitor cells to neuron migration and synaptic connection formation, several vicissitudes culminate in the mature brain. Both component loss and gain remain ubiquitous during brain development. For example, rodent brains lose over half of their initial neurons and synapses during healthy development. The role of deleterious steps in network ontogeny remains unclear, yet it is unlikely these costly processes are random. Like neurogenesis and synaptogenesis, synaptic pruning and neuron death likely evolved to support complex, efficient computations. In order to incorporate both component loss and gain in describing neuronal networks, we propose an algorithm where a directed network evolves through the selective deletion of less-connected nodes (neurons) and edges (synapses). Resulting in networks that display scale-invariant degree distributions, provided the network is predominantly feed-forward. Scale-invariance offers several advantages in biological networks: scalability, resistance to random deletions, and strong connectivity with parsimonious wiring. Whilst our algorithm is not intended to be a realistic model of neuronal network formation, our results suggest selective deletion is an adaptive mechanism contributing to more stable and efficient networks. This process aligns with observed decreasing pruning rates in animal studies, resulting in higher synapse preservation. Our overall findings have broader implications for network science. Scale-invariance in degree distributions was demonstrated in growing preferential attachment networks and observed empirically. Our preferential detachment algorithm offers an alternative mechanism for generating such networks, suggesting that both mechanisms may be part of a broader class of algorithms resulting in scale-free networks.
State-dependent Filtering of the Ring Model
Authors: Jing Yan, Yunxuan Feng, Wei Dai, Yaoyu Zhang
Date: 2024-08-03 00:00:00
Tasks: model

Robustness is a measure of functional reliability of a system against perturbations. To achieve a good and robust performance, a system must filter out external perturbations by its internal priors. These priors are usually distilled in the structure and the states of the system. Biophysical neural network are known to be robust but the exact mechanisms are still elusive. In this paper, we probe how orientation-selective neurons organized on a 1-D ring network respond to perturbations in the hope of gaining some insights on the robustness of visual system in brain. We analyze the steady-state of the rate-based network and prove that the activation state of neurons, rather than their firing rates, determines how the model respond to perturbations. We then identify specific perturbation patterns that induce the largest responses for different configurations of activation states, and find them to be sinusoidal or sinusoidal-like while other patterns are largely attenuated. Similar results are observed in a spiking ring model. Finally, we remap the perturbations in orientation back into the 2-D image space using Gabor functions. The resulted optimal perturbation patterns mirror adversarial attacks in deep learning that exploit the priors of the system. Our results suggest that based on different state configurations, these priors could underlie some of the illusionary experiences as the cost of visual robustness.