pwc-archive/papers-with-abstracts huggingface dataset:
Dynamical behavior of Predator-Prey with Allee Effect on Both Populations and Disease in Predator
Authors: Khushbu Singh, K. Kaladhar
Date: 2024-05-24 00:00:00

In the current study, we took into account a model of nonlinear ``predator-prey'' interactions including the ``Allee effect'' on both populations and disease in the predator population. The population as a whole is split into three: the prey population, susceptible predator, and diseased predator. The ``Takagi-Sugeno (T-S) impulsive control model'' and the Fuzzy impulsive control model have been used to test the stability of the three-dimensional ``Lotka-Volterra predator-prey system'' model. Following the model's formulation, the global-stability and the fuzzy solution are examined using numerical simulations and graphical displays, together with the necessary consultation, to help comprehend the effectiveness of our suggested model.
Modeling the dynamics of the Hepatitis B virus via a variable-order discrete system
Authors: Meriem Boukhobza, Amar Debbouche, Lingeshwaran Shangerganesh, Delfim F. M. Torres
Date: 2024-05-15 00:00:00

We investigate the dynamics of the hepatitis B virus by integrating variable-order calculus and discrete analysis. Specifically, we utilize the Caputo variable-order difference operator in this study. To establish the existence and uniqueness results of the model, we employ a fixed-point technique. Furthermore, we prove that the model exhibits bounded and positive solutions. Additionally, we explore the local stability of the proposed model by determining the basic reproduction number. Finally, we present several numerical simulations to illustrate the richness of our results.
Brain tumour classification using BoF-SURF with filter-based feature selection methods
Authors: Zhana Fidakar Mohammed, Diyari Jalal Mussa
Date: 2024-01-19 00:00:00
Proceeding: Multimedia Tools and Applications 2024 1
Tasks: Cell Detection, Diagnostic, feature selection, Tumour Classification

Currently, cancer is a global concern with a focus on reducing its incidence and advancing diagnostic techniques. Faster and more precise cancer cell detection improves treatment and survival prospects. The objective of this study is to effectively categorize brain tumors with a specific focus on three types: meningioma, glioma, and pituitary tumors. The research adopts a thorough methodology encompassing pre-processing, feature extraction, feature selection, and classification using various techniques such as k-nearest neighbor (kNN), support vector machine (SVM), and Ensemble methods. Features were extracted using the bag of features- speeded-up robust features (BoF-SURF) algorithm for different cluster sizes (500, 250, 375, 750, and 825). Diverse feature selection algorithms, including ReliefF, analysis of variance (ANOVA), Kruskal Wallis, maximum relevance minimum redundancy (MRMR), and chi-square (CHI2), were employed to enhance detection accuracy. The proposed method, assessed on a public dataset comprising 3064 MRI scans of malignant brain tumours. The results of our experiments strongly support the effectiveness of our proposed method, achieving an impressive accuracy rate of 98.7%. Additionally, remarkable values of 98.4%, 98.5%, and 98.6% have been obtained for sensitivity, precision, and F1-score, respectively, when using the kNN classifier with 512 features selected from a cluster size of 750 using the ReliefF method. These outcomes clearly outperform existing approaches.
Generalized Inverse Optimal Control and its Application in Biology
Authors: Julio R. Banga, Sebastian Sager
Date: 2024-05-31 00:00:00

Living organisms exhibit remarkable adaptations across all scales, from molecules to ecosystems. We believe that many of these adaptations correspond to optimal solutions driven by evolution, training, and underlying physical and chemical laws and constraints. While some argue against such optimality principles due to their potential ambiguity, we propose generalized inverse optimal control to infer them directly from data. This novel approach incorporates multi-criteria optimality, nestedness of objective functions on different scales, the presence of active constraints, the possibility of switches of optimality principles during the observed time horizon, maximization of robustness, and minimization of time as important special cases, as well as uncertainties involved with the mathematical modeling of biological systems. This data-driven approach ensures that optimality principles are not merely theoretical constructs but are firmly rooted in experimental observations. Furthermore, the inferred principles can be used in forward optimal control to predict and manipulate biological systems, with possible applications in bio-medicine, biotechnology, and agriculture. As discussed and illustrated, the well-posed problem formulation and the inference are challenging and require a substantial interdisciplinary effort in the development of theory and robust numerical methods.
Constrained monotone mean--variance investment-reinsurance under the Cramér--Lundberg model with random coefficients
Authors: Xiaomin Shi, Zuo Quan Xu
Date: 2024-05-28 00:00:00

This paper studies an optimal investment-reinsurance problem for an insurer (she) under the Cram\'er--Lundberg model with monotone mean--variance (MMV) criterion. At any time, the insurer can purchase reinsurance (or acquire new business) and invest in a security market consisting of a risk-free asset and multiple risky assets whose excess return rate and volatility rate are allowed to be random. The trading strategy is subject to a general convex cone constraint, encompassing no-shorting constraint as a special case. The optimal investment-reinsurance strategy and optimal value for the MMV problem are deduced by solving certain backward stochastic differential equations with jumps. In the literature, it is known that models with MMV criterion and mean--variance criterion lead to the same optimal strategy and optimal value when the wealth process is continuous. Our result shows that the conclusion remains true even if the wealth process has compensated Poisson jumps and the market coefficients are random.
Geometry of Critical Sets and Existence of Saddle Branches for Two-layer Neural Networks
Authors: Leyang Zhang, Yaoyu Zhang, Tao Luo
Date: 2024-05-26 00:00:00

This paper presents a comprehensive analysis of critical point sets in two-layer neural networks. To study such complex entities, we introduce the critical embedding operator and critical reduction operator as our tools. Given a critical point, we use these operators to uncover the whole underlying critical set representing the same output function, which exhibits a hierarchical structure. Furthermore, we prove existence of saddle branches for any critical set whose output function can be represented by a narrower network. Our results provide a solid foundation to the further study of optimization and training behavior of neural networks.
Near-Optimal Distributed Minimax Optimization under the Second-Order Similarity
Authors: Qihao Zhou, Haishan Ye, Luo Luo
Date: 2024-05-25 00:00:00

This paper considers the distributed convex-concave minimax optimization under the second-order similarity. We propose stochastic variance-reduced optimistic gradient sliding (SVOGS) method, which takes the advantage of the finite-sum structure in the objective by involving the mini-batch client sampling and variance reduction. We prove SVOGS can achieve the $\varepsilon$-duality gap within communication rounds of ${\mathcal O}(\delta D^2/\varepsilon)$, communication complexity of ${\mathcal O}(n+\sqrt{n}\delta D^2/\varepsilon)$, and local gradient calls of $\tilde{\mathcal O}(n+(\sqrt{n}\delta+L)D^2/\varepsilon\log(1/\varepsilon))$, where $n$ is the number of nodes, $\delta$ is the degree of the second-order similarity, $L$ is the smoothness parameter and $D$ is the diameter of the constraint set. We can verify that all of above complexity (nearly) matches the corresponding lower bounds. For the specific $\mu$-strongly-convex-$\mu$-strongly-convex case, our algorithm has the upper bounds on communication rounds, communication complexity, and local gradient calls of $\mathcal O(\delta/\mu\log(1/\varepsilon))$, ${\mathcal O}((n+\sqrt{n}\delta/\mu)\log(1/\varepsilon))$, and $\tilde{\mathcal O}(n+(\sqrt{n}\delta+L)/\mu)\log(1/\varepsilon))$ respectively, which are also nearly tight. Furthermore, we conduct the numerical experiments to show the empirical advantages of proposed method.
Inference of Utilities and Time Preference in Sequential Decision-Making
Authors: Haoyang Cao, Zhengqi Wu, Renyuan Xu
Date: 2024-05-24 00:00:00
Tasks: Decision Making, Sequential Decision Making

This paper introduces a novel stochastic control framework to enhance the capabilities of automated investment managers, or robo-advisors, by accurately inferring clients' investment preferences from past activities. Our approach leverages a continuous-time model that incorporates utility functions and a generic discounting scheme of a time-varying rate, tailored to each client's risk tolerance, valuation of daily consumption, and significant life goals. We address the resulting time inconsistency issue through state augmentation and the establishment of the dynamic programming principle and the verification theorem. Additionally, we provide sufficient conditions for the identifiability of client investment preferences. To complement our theoretical developments, we propose a learning algorithm based on maximum likelihood estimation within a discrete-time Markov Decision Process framework, augmented with entropy regularization. We prove that the log-likelihood function is locally concave, facilitating the fast convergence of our proposed algorithm. Practical effectiveness and efficiency are showcased through two numerical examples, including Merton's problem and an investment problem with unhedgeable risks. Our proposed framework not only advances financial technology by improving personalized investment advice but also contributes broadly to other fields such as healthcare, economics, and artificial intelligence, where understanding individual preferences is crucial.
A Unified Theory of Stochastic Proximal Point Methods without Smoothness
Authors: Peter Richtárik, Abdurakhmon Sadiev, Yury Demidovich
Date: 2024-05-24 00:00:00

This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness against imperfect tuning, a trait not shared by the dominant stochastic gradient descent (SGD) algorithm. A framework of assumptions that we introduce encompasses methods employing techniques such as variance reduction and arbitrary sampling. A cornerstone of our general theoretical approach is a parametric assumption on the iterates, correction and control vectors. We establish a single theorem that ensures linear convergence under this assumption and the $\mu$-strong convexity of the loss function, and without the need to invoke smoothness. This integral theorem reinstates best known complexity and convergence guarantees for several existing methods which demonstrates the robustness of our approach. We expand our study by developing three new variants of SPPM, and through numerical experiments we elucidate various properties inherent to them.
Derivatives of Stochastic Gradient Descent in parametric optimization
Authors: Franck Iutzeler, Edouard Pauwels, Samuel Vaiter
Date: 2024-05-24 00:00:00
Tasks: Hyperparameter Optimization, Stochastic Optimization

We consider stochastic optimization problems where the objective depends on some parameter, as commonly found in hyperparameter optimization for instance. We investigate the behavior of the derivatives of the iterates of Stochastic Gradient Descent (SGD) with respect to that parameter and show that they are driven by an inexact SGD recursion on a different objective function, perturbed by the convergence of the original SGD. This enables us to establish that the derivatives of SGD converge to the derivative of the solution mapping in terms of mean squared error whenever the objective is strongly convex. Specifically, we demonstrate that with constant step-sizes, these derivatives stabilize within a noise ball centered at the solution derivative, and that with vanishing step-sizes they exhibit $O(\log(k)^2 / k)$ convergence rates. Additionally, we prove exponential convergence in the interpolation regime. Our theoretical findings are illustrated by numerical experiments on synthetic tasks.
A Fisher-Rao gradient flow for entropic mean-field min-max games
Authors: Razvan-Andrei Lascu, Mateusz B. Majka, Łukasz Szpruch
Date: 2024-05-24 00:00:00

Gradient flows play a substantial role in addressing many machine learning problems. We examine the convergence in continuous-time of a \textit{Fisher-Rao} (Mean-Field Birth-Death) gradient flow in the context of solving convex-concave min-max games with entropy regularization. We propose appropriate Lyapunov functions to demonstrate convergence with explicit rates to the unique mixed Nash equilibrium.
Riemannian Bilevel Optimization
Authors: Sanchayan Dutta, Xiang Cheng, Suvrit Sra
Date: 2024-05-22 00:00:00
Tasks: Bilevel Optimization, Navigate, Stochastic Optimization

We develop new algorithms for Riemannian bilevel optimization. We focus in particular on batch and stochastic gradient-based methods, with the explicit goal of avoiding second-order information such as Riemannian hyper-gradients. We propose and analyze $\mathrm{RF^2SA}$, a method that leverages first-order gradient information to navigate the complex geometry of Riemannian manifolds efficiently. Notably, $\mathrm{RF^2SA}$ is a single-loop algorithm, and thus easier to implement and use. Under various setups, including stochastic optimization, we provide explicit convergence rates for reaching $\epsilon$-stationary points. We also address the challenge of optimizing over Riemannian manifolds with constraints by adjusting the multiplier in the Lagrangian, ensuring convergence to the desired solution without requiring access to second-order derivatives.
Exact phylodynamic likelihood via structured Markov genealogy processes
Authors: Aaron A. King, Qianying Lin, Edward L. Ionides
Date: 2024-05-27 00:00:00

We consider genealogies arising from a Markov population process in which individuals are categorized into a discrete collection of compartments, with the requirement that individuals within the same compartment are statistically exchangeable. When equipped with a sampling process, each such population process induces a time-evolving tree-valued process defined as the genealogy of all sampled individuals. We provide a construction of this genealogy process and derive exact expressions for the likelihood of an observed genealogy in terms of filter equations. These filter equations can be numerically solved using standard Monte Carlo integration methods. Thus, we obtain statistically efficient likelihood-based inference for essentially arbitrary compartment models based on an observed genealogy of individuals sampled from the population.
Intertemporal Cost-efficient Consumption
Authors: Mauricio Elizalde, Stephan Sturm
Date: 2024-05-25 00:00:00
Tasks: Portfolio Optimization

We aim to provide an intertemporal, cost-efficient consumption model that extends the consumption optimization inspired by the Distribution Builder, a tool developed by Sharpe, Johnson, and Goldstein. The Distribution Builder enables the recovery of investors' risk preferences by allowing them to select a desired distribution of terminal wealth within their budget constraints. This approach differs from the classical portfolio optimization, which considers the agent's risk aversion modeled by utility functions that are challenging to measure in practice. Our intertemporal model captures the dependent structure between consumption periods using copulas. This strategy is demonstrated using both the Black-Scholes and CEV models.
Bayesian Uncertainty Quantification for Anaerobic Digestion models
Authors: Antoine Picard-Weibel, Gabriel Capson-Tojo, Benjamin Guedj, Roman Moscoviz
Date: 2024-05-30 00:00:00
Tasks: Inductive Bias, Uncertainty Quantification

Uncertainty quantification is critical for ensuring adequate predictive power of computational models used in biology. Focusing on two anaerobic digestion models, this article introduces a novel generalized Bayesian procedure, called VarBUQ, ensuring a correct tradeoff between flexibility and computational cost. A benchmark against three existing methods (Fisher's information, bootstrapping and Beale's criteria) was conducted using synthetic data. This Bayesian procedure offered a good compromise between fitting ability and confidence estimation, while the other methods proved to be repeatedly overconfident. The method's performances notably benefitted from inductive bias brought by the prior distribution, although it requires careful construction. This article advocates for more systematic consideration of uncertainty for anaerobic digestion models and showcases a new, computationally efficient Bayesian method. To facilitate future implementations, a Python package called 'aduq' is made available.
The development of drug resistance in metastatic tumours under chemotherapy: an evolutionary perspective
Authors: Federica Padovano, Chiara Villa
Date: 2024-05-30 00:00:00

We present a mathematical model of the evolutionary dynamics of a metastatic tumour under chemotherapy, comprising non-local partial differential equations for the phenotype-structured cell populations in the primary tumour and its metastasis. These equations are coupled with a physiologically-based pharmacokinetic model of drug delivery, implementing a realistic delivery schedule. The model is carefully calibrated from the literature, focusing on BRAF-mutated melanoma treated with Dabrafenib as a case study. By means of long-time asymptotic analysis, global sensitivity analysis and numerical simulations, we explore the impact of cell migration from the primary to the metastatic site, physiological aspects of the tumour sites and drug dose on the development of drug resistance and treatment efficacy. Our findings provide a possible explanation for empirical evidence indicating that chemotherapy may foster metastatic spread and that metastatic sites may be less impacted by chemotherapy.
Metadata-guided Feature Disentanglement for Functional Genomics
Authors: Alexander Rakowski, Remo Monti, Viktoriia Huryn, Marta Lemanczyk, Uwe Ohler, Christoph Lippert
Date: 2024-05-29 00:00:00
Tasks: Disentanglement

With the development of high-throughput technologies, genomics datasets rapidly grow in size, including functional genomics data. This has allowed the training of large Deep Learning (DL) models to predict epigenetic readouts, such as protein binding or histone modifications, from genome sequences. However, large dataset sizes come at a price of data consistency, often aggregating results from a large number of studies, conducted under varying experimental conditions. While data from large-scale consortia are useful as they allow studying the effects of different biological conditions, they can also contain unwanted biases from confounding experimental factors. Here, we introduce Metadata-guided Feature Disentanglement (MFD) - an approach that allows disentangling biologically relevant features from potential technical biases. MFD incorporates target metadata into model training, by conditioning weights of the model output layer on different experimental factors. It then separates the factors into disjoint groups and enforces independence of the corresponding feature subspaces with an adversarially learned penalty. We show that the metadata-driven disentanglement approach allows for better model introspection, by connecting latent features to experimental factors, without compromising, or even improving performance in downstream tasks, such as enhancer prediction, or genetic variant discovery. The code for our implemementation is available at https://github.com/HealthML/MFD
ScAtt: an Attention based architecture to analyze Alzheimer's disease at cell type level from single-cell RNA-sequencing data
Authors: Xiaoxia Liu, Robert R Butler III, Prashnna K Gyawali, Frank M Longo, Zihuai He
Date: 2024-03-12 00:00:00
Tasks: Hippocampus

Alzheimer's disease (AD) is a pervasive neurodegenerative disorder that leads to memory and behavior impairment severe enough to interfere with daily life activities. Understanding this disease pathogenesis can drive the development of new targets and strategies to prevent and treat AD. Recent advances in high-throughput single-cell RNA sequencing technology (scRNA-seq) have enabled the generation of massive amounts of transcriptomic data at the single-cell level provided remarkable insights into understanding the molecular pathogenesis of Alzheimer's disease. In this study, we introduce ScAtt, an innovative Attention-based architecture, devised specifically for the concurrent identification of cell-type specific AD-related genes and their associated gene regulatory network. ScAtt incorporates a flexible model capable of capturing nonlinear effects, leading to the detection of AD-associated genes that might be overlooked by traditional differentially expressed gene (DEG) analyses. Moreover, ScAtt effectively infers a gene regulatory network depicting the combined influences of genes on the targeted disease, as opposed to examining correlations among genes in conventional gene co-expression networks. In an application to 95,186 single-nucleus transcriptomes from 17 hippocampus samples, ScAtt shows substantially better performance in modeling quantitative changes in expression levels between AD and healthy controls. Consequently, ScAtt performs better than existing methods in the identification of AD-related genes, with more unique discoveries and less overlap between cell types. Functional enrichments of the corresponding gene modules detected from gene regulatory network show significant enrichment of biologically meaningful AD-related pathways across different cell types.
Spatial modeling algorithms for reactions and transport (SMART) in biological cells
Authors: Emmet A. Francis, Justin G. Laughlin, Jørgen S. Dokken, Henrik N. T. Finsberg, Christopher T. Lee, Marie E. Rognes, Padmini Rangamani
Date: 2024-05-24 00:00:00

Biological cells rely on precise spatiotemporal coordination of biochemical reactions to control their many functions. Such cell signaling networks have been a common focus for mathematical models, but they remain challenging to simulate, particularly in realistic cell geometries. Herein, we present our software, Spatial Modeling Algorithms for Reactions and Transport (SMART), a package that takes in high-level user specifications about cell signaling networks and molecular transport, and then assembles and solves the associated mathematical and computational systems. SMART uses state-of-the-art finite element analysis, via the FEniCS Project software, to efficiently and accurately resolve cell signaling events over discretized cellular and subcellular geometries. We demonstrate its application to several different biological systems, including YAP/TAZ mechanotransduction, calcium signaling in neurons and cardiomyocytes, and ATP generation in mitochondria. Throughout, we utilize experimentally-derived realistic cellular geometries represented by well-conditioned tetrahedral meshes. These scenarios demonstrate the applicability, flexibility, accuracy and efficiency of SMART across a range of temporal and spatial scales.