pwc-archive/papers-with-abstracts huggingface dataset:
On Selecting Distance Metrics in $n$-Dimensional Normed Vector Spaces of Cells: A Novel Criterion and Similarity Measure Towards Efficient and Accurate Omics Analysis
Authors: Okezue Bell, Arthur Lee, Elizabeth Engle
Date: 2023-06-13 00:00:00
Tasks: Computational Efficiency, Dimensionality Reduction

Single-cell omics enable the profiles of cells, which contain large numbers of biological features, to be quantified. Cluster analysis, a dimensionality reduction process, is used to reduce the dimensions of the data to make it computationally tractable. In these analyses, cells are represented as vectors in $n$-Dimensional space, where each dimension corresponds to a certain cell feature. The distance between cells is used as a surrogate measure of similarity, providing insight into the cell's state, function, and genetic mechanisms. However, as cell profiles are clustered in 3D or higher-dimensional space, it remains unknown which distance metric provides the most accurate spatiotemporal representation of similarity, limiting the interpretability of the data. I propose and prove a generalized proposition and set of corollaries that serve as a criterion to determine which of the standard distance measures is most accurate for conveying cell profile heterogeneity. Each distance method is evaluated via statistical, geometric, and topological proofs, which are formalized into a set of criteria. In this paper, I present the putative, first-ever method to elect the most accurate and precise distance metrics with any profiling modality, which are determined to be the Wasserstein distance and cosine similarity metrics, respectively, in general cases. I also identify special cases in which the criterion may select non-standard metrics. Combining the metric properties selected by the criterion, I develop a novel, custom, optimal distance metric that demonstrates superior computational efficiency, peak annotation, motif identification, and footprinting for transcription factor binding sites when compared with leading methods.
Population growth in discrete time: a renewal equation oriented survey
Authors: B. Boldin, O. Diekmann, J. A. J. Metz
Date: 2023-06-15 00:00:00
Tasks: Survey

Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the population distribution at the next time point. The renewal equation alternative concentrates on newborn individuals and the model specifies the production of offspring as a function of age. This has two advantages: (i) as a rule, there are far fewer birth states than individual states in general, so the dimension is often low; (ii) it relates seamlessly to the next-generation matrix and the basic reproduction number. Here we start from the renewal equation for the births and use results of Feller and Thieme to characterise the asymptotic large time behaviour. Next we explicitly elaborate the relationship between the two bookkeeping schemes. This allows us to transfer the characterisation of the large time behaviour to traditional structured-population models.
Dynamics of infectious diseases in predator-prey populations: a stochastic model, sustainability, and invariant measure
Authors: Yujie Gao, Malay Banerjee, Ton Viet Ta
Date: 2023-06-14 00:00:00

This paper introduces an innovative model for infectious diseases in predator-prey populations. We not only prove the existence of global non-negative solutions but also establish essential criteria for the system's decline and sustainability. Furthermore, we demonstrate the presence of a Borel invariant measure, adding a new dimension to our understanding of the system. To illustrate the practical implications of our findings, we present numerical results. With our model's comprehensive approach, we aim to provide valuable insights into the dynamics of infectious diseases and their impact on predator-prey populations.
Survival of the flattest in the quasispecies model
Authors: Maxime Berger, Raphaël Cerf
Date: 2023-06-15 00:00:00
Tasks: model

Viruses present an amazing genetic variability. An ensemble of infecting viruses, also called a viral quasispecies, is a cloud of mutants centered around a specific genotype. The simplest model of evolution, whose equilibrium state is described by the quasispecies equation, is the Moran--Kingman model. For the sharp peak landscape, we perform several exact computations and we derive several exact formulas. We obtain also an exact formula for the quasispecies distribution, involving a series and the mean fitness. A very simple formula for the mean Hamming distance is derived, which is exact and which do not require a specific asymptotic expansion (like sending the length of the macromolecules to $\infty$ or the mutation probability to $0$). We try also to extend these formulas to a general fitness landscape. We obtain an equation involving the covariance of the fitness and the Hamming class number in the quasispecies distribution. With the help of these formulas, we discuss the phenomenon of the error threshold and the notion of quasispecies. We recover the limiting quasipecies distribution in the long chain regime. We go beyond the sharp peak landscape and we consider fitness landscapes having finitely many peaks and a plateau--type landscape. We finally prove rigorously within this framework the possible occurrence of the survival of the flattest, a phenomenon which has been previously discovered by Wilke, Wang, Ofria, Lenski and Adami and which has been investigated in several works.
Asymptotics for the Laplace transform of the time integral of the geometric Brownian motion
Authors: Dan Pirjol, Lingjiong Zhu
Date: 2023-06-15 00:00:00

We present an asymptotic result for the Laplace transform of the time integral of the geometric Brownian motion $F(\theta,T) = \mathbb{E}[e^{-\theta X_T}]$ with $X_T = \int_0^T e^{\sigma W_s + ( a - \frac12 \sigma^2)s} ds$, which is exact in the limit $\sigma^2 T \to 0$ at fixed $\sigma^2 \theta T^2$ and $aT$. This asymptotic result is applied to pricing zero coupon bonds in the Dothan model of stochastic interest rates. The asymptotic result provides an approximation for bond prices which is in good agreement with numerical evaluations in a wide range of model parameters. As a side result we obtain the asymptotics for Asian option prices in the Black-Scholes model, taking into account interest rates and dividend yield contributions in the $\sigma^{2}T\to 0$ limit.
A Novel Approach to Encode Two-Way Epistatic Interactions Between Single Nucleotide Polymorphisms
Authors: Nathaniel Gunter, Prashanthi Vemuri, Vijay Ramanan, Robel K Gebre
Date: 2023-06-15 00:00:00

Modelling gene-gene epistatic interactions when computing genetic risk scores is not a well-explored subfield of genetics and could have potential to improve risk stratification in practice. Though applications of machine learning (ML) show promise as an avenue of improvement for current genetic risk assesments, they frequently suffer from the problem of two many features and to little data. We propose a method that when combined with ML allows information from individual genetic contributors to be preserved while incorporating information on their interactions in a single feature. This allows second-order analysis, while simultaneously increasing the number of input features to ML models as little as possible. We presented three methods that can be utilized to account for genetic interactions. We found that interaction methods that preserved information from the constituent SNPs performed significantly better than the simplest interaction method. Since the currently available ML methods are able to account for complex interactions, utilizing raw SNP genotypes alone is sufficient because the simplest model outperforms all the interaction methods Given that understanding and accounting for epistatic interactions is one of the most promising avenues for increasing explained variability in heritable disease, this work represents a first step toward an algorithmic interaction method that preserves the information in each component. This is relevant not only because of potential improvements in model quality, but also because explicit interaction terms allow a human readable interpretation of potential interaction pathways within the disease.
Collection of prokaryotic genome contents expectation rules from scientific literature
Authors: Serena Lam, Giorgio Gonnella
Date: 2023-06-14 00:00:00

Shaped by natural selection and other evolutionary forces, an organism's evolutionary history is reflected through its genome sequence, content of functional elements and organization. Consequently, organisms connected through phylogeny, metabolic or morphological traits, geographical proximity, or habitat features are likely to exhibit similarities in their genomes. These similarities give rise to expectations about the content of genomes within these organism groups. Such expectations are often informally expressed in scientific literature, focusing on the analysis of individual genomes or comparisons among related groups of organisms. Our objective is to develop a system for formalized expectations as rules, facilitating automated verification, and evaluation of newly sequenced genomes. In this study, we present a database comprising rules manually extracted from scientific literature. Furthermore, we explore the feasibility of automatizing the extraction and analysis process using large language models, such as GPT3.5 and GPT4. We have developed a web application, EGCWebApp, which enables users to visualize and edit the rules. Additionally, we provided a Python library and command-line tools collection, egctools, to further extend the functionality for processing and managing these rules.
A local polynomial moment approximation for compartmentalised biochemical systems
Authors: Tommaso Bianucci, Christoph Zechner
Date: 2023-06-15 00:00:00

Compartmentalised biochemical reactions are a ubiquitous building block of biological systems. The interplay between chemical and compartmental dynamics can drive rich and complex dynamical behaviors that are difficult to analyse mathematically -- especially in the presence of stochasticity. We have recently proposed an effective moment equation approach to study the statistical properties of compartmentalised biochemical systems. So far, however, this approach is limited to polynomial rate laws and moreover, it relies on suitable moment closure approximations, which can be difficult to find in practice. In this work we propose a systematic method to derive closed moment dynamics for compartmentalised biochemical systems. We show that for the considered class of systems, the moment equations involve expectations over functions that factorize into two parts, one depending on the molecular content of the compartments and one depending on the compartment number distribution. Our method exploits this structure and approximates each function with suitable polynomial expansions, leading to a closed system of moment equations. We demonstrate the method using three systems inspired by cell populations and organelle networks and study its accuracy across different dynamical regimes.
A sub-Riemannian model of the functional architecture of M1 for arm movement direction
Authors: Caterina Mazzetti, Alessandro Sarti, Giovanna Citti
Date: 2023-06-13 00:00:00

In this paper we propose a neurogeometrical model of the behaviour of cells of the arm area of the primary motor cortex (M1). We mathematically express the hypercolumnar organization of M1 discovered by Georgopoulos, as a fiber bundle, as in classical sub-riemannian models of the visual cortex (Hoffmann, Petitot, Citti-Sarti). On this structure, we consider the selective tuning of M1 neurons of kinematic variables of positions and directions of movement. We then extend this model to encode the notion of fragments of movements introduced by Hatsopoulos. In our approach fragments are modelled as integral curves of vector fields in a suitable sub-Riemannian space. These fragments are in good agreements with movement decomposition from neural activity data. Here, we recover these patterns through a spectral clustering algorithm in the subriemannian structure we introduced, and compare our results with the neurophysiological ones of Kadmon-Harpaz et al.
Statistical inference of the rates of cell proliferation and phenotypic switching in cancer
Authors: Einar Bjarki Gunnarsson, Jasmine Foo, Kevin Leder
Date: 2023-06-13 00:00:00

Recent evidence suggests that nongenetic (epigenetic) mechanisms play an important role at all stages of cancer evolution. In many cancers, these mechanisms have been observed to induce dynamic switching between two or more cell states, which commonly show differential responses to drug treatments. To understand how these cancers evolve over time, and how they respond to treatment, we need to understand the state-dependent rates of cell proliferation and phenotypic switching. In this work, we propose a rigorous statistical framework for estimating these parameters, using data from commonly performed cell line experiments, where phenotypes are sorted and expanded in culture. The framework explicitly models the stochastic dynamics of cell division, cell death and phenotypic switching, and it provides likelihood-based confidence intervals for the model parameters. The input data can be either the fraction of cells or the number of cells in each state at one or more time points. Through a combination of theoretical analysis and numerical simulations, we show that when cell fraction data is used, the rates of switching may be the only parameters that can be estimated accurately. On the other hand, using cell number data enables accurate estimation of the net division rate for each phenotype, and it can even enable estimation of the state-dependent rates of cell division and cell death. We conclude by applying our framework to a publicly available dataset.
Failure of Fourier pricing techniques to approximate the Greeks
Authors: Tobias Behrens, Gero Junike, Wim Schoutens
Date: 2023-06-14 00:00:00
Tasks: Management

The Greeks Delta and Gamma of plain vanilla options play a fundamental role in finance, e.g., in hedging or risk management. These Greeks are approximated in many models such as the widely used Variance Gamma model by Fourier techniques such as the Carr-Madan formula, the COS method or the Lewis formula. However, for some realistic market parameters, we show empirically that these three Fourier methods completely fail to approximate the Greeks. As an application we show that the Delta-Gamma VaR is severely underestimated in realistic market environments. As a solution, we propose to use finite differences instead to obtain the Greeks.
Leveraging Machine Learning for Multichain DeFi Fraud Detection
Authors: Georgios Palaiokrassas, Sandro Scherrers, Iason Ofeidis, Leandros Tassiulas
Date: 2023-05-17 00:00:00
Tasks: Fraud Detection

Since the inception of permissionless blockchains with Bitcoin in 2008, it became apparent that their most well-suited use case is related to making the financial system and its advantages available to everyone seamlessly without depending on any trusted intermediaries. Smart contracts across chains provide an ecosystem of decentralized finance (DeFi), where users can interact with lending pools, Automated Market Maker (AMM) exchanges, stablecoins, derivatives, etc. with a cumulative locked value which had exceeded 160B USD. While DeFi comes with high rewards, it also carries plenty of risks. Many financial crimes have occurred over the years making the early detection of malicious activity an issue of high priority. The proposed framework introduces an effective method for extracting a set of features from different chains, including the largest one, Ethereum and it is evaluated over an extensive dataset we gathered with the transactions of the most widely used DeFi protocols (23 in total, including Aave, Compound, Curve, Lido, and Yearn) based on a novel dataset in collaboration with Covalent. Different Machine Learning methods were employed, such as XGBoost and a Neural Network for identifying fraud accounts detection interacting with DeFi and we demonstrate that the introduction of novel DeFi-related features, significantly improves the evaluation results, where Accuracy, Precision, Recall, F1-score and F2-score where utilized.
A multi-agent targeted trading equilibrium with transaction costs
Authors: Jin Hyuk Choi, Jetlir Duraj, Kim Weston
Date: 2023-06-14 00:00:00

We prove the existence of a continuous-time Radner equilibrium with multiple agents and transaction costs. The agents are incentivized to trade towards a targeted number of shares throughout the trading period and seek to maximize their expected wealth minus a penalty for deviating from their targets. Their wealth is further reduced by transaction costs that are proportional to the number of stock shares traded. The agents' targeted number of shares is publicly known, making the resulting equilibrium fully revealing. In equilibrium, each agent optimally chooses to trade for an initial time interval before stopping trade. Our equilibrium construction and analysis involves identifying the order in which the agents stop trade. The transaction cost level impacts the equilibrium stock price drift. We analyze the equilibrium outcomes and provide numerical examples.
Optimal Portfolio Execution in a Regime-switching Market with Non-linear Impact Costs: Combining Dynamic Program and Neural Network
Authors: Xiaoyue Li, John M. Mulvey
Date: 2023-06-15 00:00:00

Optimal execution of a portfolio have been a challenging problem for institutional investors. Traders face the trade-off between average trading price and uncertainty, and traditional methods suffer from the curse of dimensionality. Here, we propose a four-step numerical framework for the optimal portfolio execution problem where multiple market regimes exist, with the underlying regime switching based on a Markov process. The market impact costs are modelled with a temporary part and a permanent part, where the former affects only the current trade while the latter persists. Our approach accepts impact cost functions in generic forms. First, we calculate the approximated orthogonal portfolios based on estimated impact cost functions; second, we employ dynamic program to learn the optimal selling schedule of each approximated orthogonal portfolio; third, weights of a neural network are pre-trained with the strategy suggested by previous step; last, we train the neural network to optimize on the original trading model. In our experiment of a 10-asset liquidation example with quadratic impact costs, the proposed combined method provides promising selling strategy for both CRRA (constant relative risk aversion) and mean-variance objectives. The running time is linear in the number of risky assets in the portfolio as well as in the number of trading periods. Possible improvements in running time are discussed for potential large-scale usages.
Efficient 3D Semantic Segmentation with Superpoint Transformer
Authors: Damien Robert, Hugo Raguet, Loic Landrieu
Date: 2023-06-13 00:00:00
Proceeding: ICCV 2023 1
Tasks: 3D Semantic Segmentation, GPU, Semantic Segmentation

We introduce a novel superpoint-based transformer architecture for efficient semantic segmentation of large-scale 3D scenes. Our method incorporates a fast algorithm to partition point clouds into a hierarchical superpoint structure, which makes our preprocessing 7 times faster than existing superpoint-based approaches. Additionally, we leverage a self-attention mechanism to capture the relationships between superpoints at multiple scales, leading to state-of-the-art performance on three challenging benchmark datasets: S3DIS (76.0% mIoU 6-fold validation), KITTI-360 (63.5% on Val), and DALES (79.6%). With only 212k parameters, our approach is up to 200 times more compact than other state-of-the-art models while maintaining similar performance. Furthermore, our model can be trained on a single GPU in 3 hours for a fold of the S3DIS dataset, which is 7x to 70x fewer GPU-hours than the best-performing methods. Our code and models are accessible at github.com/drprojects/superpoint_transformer.
Dynamic Clustering Transformer Network for Point Cloud Segmentation
Authors: Dening Lu, Jun Zhou, Kyle Yilin Gao, Dilong Li, Jing Du, Linlin Xu, Jonathan Li
Date: 2023-05-30 00:00:00
Tasks: Clustering, Decoder, Point Cloud Segmentation, Scene Understanding

Point cloud segmentation is one of the most important tasks in computer vision with widespread scientific, industrial, and commercial applications. The research thereof has resulted in many breakthroughs in 3D object and scene understanding. Previous methods typically utilized hierarchical architectures for feature representation. However, the commonly used sampling and grouping methods in hierarchical networks are only based on point-wise three-dimensional coordinates, ignoring local semantic homogeneity of point clusters. Additionally, the prevalent Farthest Point Sampling (FPS) method is often a computational bottleneck. To address these issues, we propose a novel 3D point cloud representation network, called Dynamic Clustering Transformer Network (DCTNet). It has an encoder-decoder architecture, allowing for both local and global feature learning. Specifically, we propose novel semantic feature-based dynamic sampling and clustering methods in the encoder, which enables the model to be aware of local semantic homogeneity for local feature aggregation. Furthermore, in the decoder, we propose an efficient semantic feature-guided upsampling method. Our method was evaluated on an object-based dataset (ShapeNet), an urban navigation dataset (Toronto-3D), and a multispectral LiDAR dataset, verifying the performance of DCTNet across a wide variety of practical engineering applications. The inference speed of DCTNet is 3.8-16.8$\times$ faster than existing State-of-the-Art (SOTA) models on the ShapeNet dataset, while achieving an instance-wise mIoU of $86.6\%$, the current top score. Our method similarly outperforms previous methods on the other datasets, verifying it as the new State-of-the-Art in point cloud segmentation.
BPKD: Boundary Privileged Knowledge Distillation For Semantic Segmentation
Authors: Liyang Liu, Zihan Wang, Minh Hieu Phan, BoWen Zhang, Jinchao Ge, Yifan Liu
Date: 2023-06-13 00:00:00
Tasks: Knowledge Distillation, Segmentation, Semantic Segmentation

Current knowledge distillation approaches in semantic segmentation tend to adopt a holistic approach that treats all spatial locations equally. However, for dense prediction, students' predictions on edge regions are highly uncertain due to contextual information leakage, requiring higher spatial sensitivity knowledge than the body regions. To address this challenge, this paper proposes a novel approach called boundary-privileged knowledge distillation (BPKD). BPKD distills the knowledge of the teacher model's body and edges separately to the compact student model. Specifically, we employ two distinct loss functions: (i) edge loss, which aims to distinguish between ambiguous classes at the pixel level in edge regions; (ii) body loss, which utilizes shape constraints and selectively attends to the inner-semantic regions. Our experiments demonstrate that the proposed BPKD method provides extensive refinements and aggregation for edge and body regions. Additionally, the method achieves state-of-the-art distillation performance for semantic segmentation on three popular benchmark datasets, highlighting its effectiveness and generalization ability. BPKD shows consistent improvements across a diverse array of lightweight segmentation structures, including both CNNs and transformers, underscoring its architecture-agnostic adaptability. The code is available at \url{https://github.com/AkideLiu/BPKD}.