arXiv subjects

Yi Fu

Publications and source records attributed to Yi Fu.

18 recordsLinked to original sources

arXiv2026

Mutant Fixation for a Stochastic Evolutionary Model in Fragmented Populations

Population fragmentation is a common feature of many biological systems. Understanding mutant fixation in such systems is challenging because the underlying stochastic dynamics are high-dimensional. In this work, we develop a general mathematical framework for analyzing stochastic evolution in fragmented populations connected by rare migration. The framework is sufficiently general to accommodate heterogeneous deme sizes, deme-dependent birth and death processes, and migration on arbitrary strongly connected directed networks with asymmetric migration rates. We show that, in the limit where migration occurs on a much slower timescale than within-deme dynamics, the full stochastic process can be reduced to a lower-dimensional Markov chain whose states correspond to configurations of fully mutant and fully wild-type demes. The reduction theorem establishes that fixation probabilities and absorption times of the original process are asymptotically determined by the corresponding quantities of a reduced chain. As an application, we derive explicit formulas for mutant fixation probabilities and fixation times in fragmented populations initiated by the introduction of a single mutant. The results provide a general and tractable approach for studying evolutionary dynamics in complex fragmented populations.

q-bio.PE↗

arXiv2026

Geometric construction of k-optimal locally repairable codes

A linear code is referred to as a locally repairable code (LRC) with locality r if any erased code symbol can be recovered by accessing at most r other code symbols. LRCs are highly desirable for distributed storage systems to enhance repair efficiency. In this paper, we investigate LRCs with disjoint repair sets via the parity-check matrix method. Firstly, we propose a novel concept of the s-Pasch configuration and present a geometric characterization for the existence of LRCs with minimum distance 5 and locality 3. Subsequently, we construct k-optimal LRCs by exploiting the point-line relationship in PG(2,q). Finally, a family of q-ary k-optimal LRCs with minimum distance 6 and general locality r is constructed using partial r-spreads.

cs.IT↗

arXiv2026

Bernini: Latent Semantic Planning for Video Diffusion

Multimodal large language models (MLLMs) and diffusion models have each reached remarkable maturity: MLLMs excel at reasoning over heterogeneous multimodal inputs with strong semantic grounding, while diffusion models synthesize images and videos with photorealistic fidelity. We argue that these two families can be unified through a simple division of labor: MLLMs perform semantic planning, while diffusion models render pixels from high-level semantic guidance and low-level visual features. Building on this idea, we propose Bernini, a unified framework for video generation and editing. An MLLM-based planner predicts the target semantic representation directly in the ViT embedding space, and a DiT-based renderer synthesizes pixels conditioned on this plan, augmented by text features and, for editing, source VAE features for detail preservation. Because semantics serve as the interface, the planner and renderer can be trained separately and only lightly co-trained, preserving the pretrained strengths of both components while keeping training efficient. To better handle multiple visual inputs, we introduce Segment-Aware 3D Rotary Positional Embedding (SA-3D RoPE), and further incorporate chain-of-thought reasoning in the planner to better transfer understanding into generation. Bernini achieves state-of-the-art performance across a wide range of video generation and editing benchmarks, with the MLLM's pretrained understanding translating into strong generalization on challenging editing tasks.

cs.CV↗

arXiv2026

FinToolBench: Evaluating LLM Agents for Real-World Financial Tool Use

The integration of Large Language Models (LLMs) into the financial domain is driving a paradigm shift from passive information retrieval to dynamic, agentic interaction. While general-purpose tool learning has witnessed a surge in benchmarks, the financial sector, characterized by high stakes, strict compliance, and rapid data volatility, remains critically underserved. Existing financial evaluations predominantly focus on static textual analysis or document-based QA, ignoring the complex reality of tool execution. Conversely, general tool benchmarks lack the domain-specific rigor required for finance, often relying on toy environments or a negligible number of financial APIs. To bridge this gap, we introduce FinToolBench, the first real-world, runnable benchmark dedicated to evaluating financial tool learning agents. Unlike prior works limited to a handful of mock tools, FinToolBench establishes a realistic ecosystem coupling 760 executable financial tools with 295 rigorous, tool-required queries. We propose a novel evaluation framework that goes beyond binary execution success, assessing agents on finance-critical dimensions: timeliness, intent type, and regulatory domain alignment. Furthermore, we present FATR, a finance-aware tool retrieval and reasoning baseline that enhances stability and compliance. By providing the first testbed for auditable, agentic financial execution, FinToolBench sets a new standard for trustworthy AI in finance. The tool manifest, execution environment, and evaluation code will be open-sourced to facilitate future research.

cs.AI↗

arXiv2025

Coclique level structure for stochastic chemical reaction networks

Continuous time Markov chains are commonly used as models for the stochastic behavior of chemical reaction networks. More precisely, these Stochastic Chemical Reaction Networks (SCRNs) are frequently used to gain a mechanistic understanding of how chemical reaction rate parameters impact the stochastic behavior of these systems. One property of interest is mean first passage times (MFPTs) between states. However, deriving explicit formulas for MFPTs can be highly complex. In order to address this problem, we first introduce the concept of coclique level structure and develop theorems to determine whether certain SCRNs have this feature by studying associated graphs. Additionally, we develop an algorithm to identify, under specific assumptions, all possible coclique level structures associated with a given SCRN. Finally, we demonstrate how the presence of such a structure in a SCRN allows us to derive closed form formulas for both upper and lower bounds for the MFPTs. Our methods can be applied to SCRNs taking values in a generic finite state space and can also be applied to models with non-mass-action kinetics. We illustrate our results with examples from the biological areas of epigenetics, neurobiology and ecology.

math.PR↗

arXiv2025

EvoMakeup: High-Fidelity and Controllable Makeup Editing with MakeupQuad

Facial makeup editing aims to realistically transfer makeup from a reference to a target face. Existing methods often produce low-quality results with coarse makeup details and struggle to preserve both identity and makeup fidelity, mainly due to the lack of structured paired data -- where source and result share identity, and reference and result share identical makeup. To address this, we introduce MakeupQuad, a large-scale, high-quality dataset with non-makeup faces, references, edited results, and textual makeup descriptions. Building on this, we propose EvoMakeup, a unified training framework that mitigates image degradation during multi-stage distillation, enabling iterative improvement of both data and model quality. Although trained solely on synthetic data, EvoMakeup generalizes well and outperforms prior methods on real-world benchmarks. It supports high-fidelity, controllable, multi-task makeup editing -- including full-face and partial reference-based editing, as well as text-driven makeup editing -- within a single model. Experimental results demonstrate that our method achieves superior makeup fidelity and identity preservation, effectively balancing both aspects. Code and dataset will be released upon acceptance.

cs.CV↗

arXiv2025

Structure based SAT dataset for analysing GNN generalisation

Satisfiability (SAT) solvers based on techniques such as conflict driven clause learning (CDCL) have produced excellent performance on both synthetic and real world industrial problems. While these CDCL solvers only operate on a per-problem basis, graph neural network (GNN) based solvers bring new benefits to the field by allowing practitioners to exploit knowledge gained from solved problems to expedite solving of new SAT problems. However, one specific area that is often studied in the context of CDCL solvers, but largely overlooked in GNN solvers, is the relationship between graph theoretic measure of structure in SAT problems and the generalisation ability of GNN solvers. To bridge the gap between structural graph properties (e.g., modularity, self-similarity) and the generalisability (or lack thereof) of GNN based SAT solvers, we present StructureSAT: a curated dataset, along with code to further generate novel examples, containing a diverse set of SAT problems from well known problem domains. Furthermore, we utilise a novel splitting method that focuses on deconstructing the families into more detailed hierarchies based on their structural properties. With the new dataset, we aim to help explain problematic generalisation in existing GNN SAT solvers by exploiting knowledge of structural graph properties. We conclude with multiple future directions that can help researchers in GNN based SAT solving develop more effective and generalisable SAT solvers.

cs.LG↗

arXiv2024

Analysis of singularly perturbed stochastic chemical reaction networks motivated by applications to epigenetic cell memory

Epigenetic cell memory, the inheritance of gene expression patterns across subsequent cell divisions, is a critical property of multi-cellular organisms. In recent work [10], a subset of the authors observed in a simulation study how the stochastic dynamics and time-scale differences between establishment and erasure processes in chromatin modifications (such as histone modifications and DNA methylation) can have a critical effect on epigenetic cell memory. In this paper, we provide a mathematical framework to rigorously validate and extend beyond these computational findings. Viewing our stochastic model of a chromatin modification circuit as a singularly perturbed, finite state, continuous time Markov chain, we extend beyond existing theory in order to characterize the leading coefficients in the series expansions of stationary distributions and mean first passage times. In particular, we characterize the limiting stationary distribution in terms of a reduced Markov chain, provide an algorithm to determine the orders of the poles of mean first passage times, and determine how changing erasure rates affects system behavior. The theoretical tools developed in this paper not only allow us to set a rigorous mathematical basis for the computational findings of our prior work, highlighting the effect of chromatin modification dynamics on epigenetic cell memory, but they can also be applied to other singularly perturbed Markov chains beyond the applications in this paper, especially those associated with chemical reaction networks.

math.PR↗

arXiv2023

Collaborative Tracking Learning for Frame-Rate-Insensitive Multi-Object Tracking

Multi-object tracking (MOT) at low frame rates can reduce computational, storage and power overhead to better meet the constraints of edge devices. Many existing MOT methods suffer from significant performance degradation in low-frame-rate videos due to significant location and appearance changes between adjacent frames. To this end, we propose to explore collaborative tracking learning (ColTrack) for frame-rate-insensitive MOT in a query-based end-to-end manner. Multiple historical queries of the same target jointly track it with richer temporal descriptions. Meanwhile, we insert an information refinement module between every two temporal blocking decoders to better fuse temporal clues and refine features. Moreover, a tracking object consistency loss is proposed to guide the interaction between historical queries. Extensive experimental results demonstrate that in high-frame-rate videos, ColTrack obtains higher performance than state-of-the-art methods on large-scale datasets Dancetrack and BDD100K, and outperforms the existing end-to-end methods on MOT17. More importantly, ColTrack has a significant advantage over state-of-the-art methods in low-frame-rate videos, which allows it to obtain faster processing speeds by reducing frame-rate requirements while maintaining higher performance. Code will be released at https://github.com/yolomax/ColTrack

cs.CV↗

arXiv2023

Comparison Theorems for Stochastic Chemical Reaction Networks

Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. When propensity functions are bounded, our method of proof gives an explicit method for coupling two comparable SCRNs, which can be used to simultaneously simulate their sample paths in a comparable manner. We illustrate our results with applications to models of enzymatic kinetics and epigenetic regulation by chromatin modifications.

math.PR↗

arXiv2023

Deep learning numerical methods for high-dimensional fully nonlinear PIDEs and coupled FBSDEs with jumps

We propose a deep learning algorithm for solving high-dimensional parabolic integro-differential equations (PIDEs) and high-dimensional forward-backward stochastic differential equations with jumps (FBSDEJs), where the jump-diffusion process are derived by a Brownian motion and an independent compensated Poisson random measure. In this novel algorithm, a pair of deep neural networks for the approximations of the gradient and the integral kernel is introduced in a crucial way based on deep FBSDE method. To derive the error estimates for this deep learning algorithm, the convergence of Markovian iteration, the error bound of Euler time discretization, and the simulation error of deep learning algorithm are investigated. Two numerical examples are provided to show the efficiency of this proposed algorithm.

math.NA↗

arXiv2021

Observation of superluminal signaling of terahertz pulses

Superluminal tunneling of light through a barrier has attracted broad interest in the last several decades. Despite the observation of such phenomena in various systems, it has been under intensive debate whether the transmitted light truly carry the information of the original pulse. Here we report observation of anomalous time response for terahertz electromagnetic pulses passing through thin metal films, with the pulse shape of the transmitted beam faithfully resembling that of the incident beam. A causal theoretical analysis is developed to explain the experiments, though the theory of Special Relativity may confront a challenge in this exceptional circumstance. These findings may facilitate future applications in high-speed optical communication or signal transmission, and may reshape our fundamental understanding about the tunneling of light.

physics.optics↗

arXiv2020

Coherent Loss: A Generic Framework for Stable Video Segmentation

Video segmentation approaches are of great importance for numerous vision tasks especially in video manipulation for entertainment. Due to the challenges associated with acquiring high-quality per-frame segmentation annotations and large video datasets with different environments at scale, learning approaches shows overall higher accuracy on test dataset but lack strict temporal constraints to self-correct jittering artifacts in most practical applications. We investigate how this jittering artifact degrades the visual quality of video segmentation results and proposed a metric of temporal stability to numerically evaluate it. In particular, we propose a Coherent Loss with a generic framework to enhance the performance of a neural network against jittering artifacts, which combines with high accuracy and high consistency. Equipped with our method, existing video object/semantic segmentation approaches achieve a significant improvement in term of more satisfactory visual quality on video human dataset, which we provide for further research in this field, and also on DAVIS and Cityscape.

cs.CV↗

arXiv2020

Empirical properties of optima in free semidefinite programs

Semidefinite programming is based on optimization of linear functionals over convex sets defined by linear matrix inequalities, namely, inequalities of the form $$L_A(X)=I-A_1X_1-\dots-A_g X_g\succeq0.$$ Here the $X_j$ are real numbers and the set of solutions is called a spectrahedron. These inequalities make sense when the $X_i$ are symmetric matrices of any size, $n\times n$, and enter the formula though tensor product $A_i\otimes X_i$: The solution set of $L_A(X)\succeq0$ is called a free spectrahedron since it contains matrices of all sizes and the defining ``linear pencil" is ``free" of the sizes of the matrices. In this article, we report on empirically observed properties of optimizers obtained from optimizing linear functionals over free spectrahedra restricted to matrices $X_i$ of fixed size $n\times n$. The optimizers we find are always classical extreme points. Surprisingly, in many reasonable parameter ranges, over 99.9\% are also free extreme points. Moreover, the dimension of the active constraint, $\ker(L_A(X^\ell))$, is about twice what we expected. Another distinctive pattern regards reducibility of optimizing tuples $(X_1^\ell,\dots,X_g^\ell)$. We give an algorithm for representing elements of a free spectrahedron as matrix convex combinations of free extreme points; these representations satisfy a very low bound on the number of free extreme points neede

math.FA↗

arXiv2018

Exploiting Spatial-Temporal Modelling and Multi-Modal Fusion for Human Action Recognition

In this report, our approach to tackling the task of ActivityNet 2018 Kinetics-600 challenge is described in detail. Though spatial-temporal modelling methods, which adopt either such end-to-end framework as I3D \cite{i3d} or two-stage frameworks (i.e., CNN+RNN), have been proposed in existing state-of-the-arts for this task, video modelling is far from being well solved. In this challenge, we propose spatial-temporal network (StNet) for better joint spatial-temporal modelling and comprehensively video understanding. Besides, given that multi-modal information is contained in video source, we manage to integrate both early-fusion and later-fusion strategy of multi-modal information via our proposed improved temporal Xception network (iTXN) for video understanding. Our StNet RGB single model achieves 78.99\% top-1 precision in the Kinetics-600 validation set and that of our improved temporal Xception network which integrates RGB, flow and audio modalities is up to 82.35\%. After model ensemble, we achieve top-1 precision as high as 85.0\% on the validation set and rank No.1 among all submissions.

cs.CV↗

arXiv2015

BACOM2: a Java tool for detecting normal cell contamination of copy number in heterogeneous tumor

We develop a cross-platform open-source Java application (BACOM2) with graphic user interface (GUI), and users also can use a XML file to set the parameters of algorithm model, file paths and the dataset of paired samples. BACOM2 implements the new entire pipeline of copy number change analysis for heterogeneous cancer tissues, including extraction of raw copy number signals from CEL files of paired samples, attenuation correction, identification of balanced AB-genotype loci, copy number detection and segmentation, global baseline calculation and absolute normalization, differentiation of deletion types, estimation of the normal tissue fraction and correction of normal tissue contamination. BACOM2 focuses on the common tools for data preparation and absolute normalization for copy number analysis of heterogeneous cancer tissues. The software provides an additional choice for scientists who require a user-friendly, high-speed processing, cross-platform computing environment for large copy number data analysis.

q-bio.GN↗

arXiv2014

A Statistical Approach to Identifying Significant Transgenerational Methylation Changes

Epigenetic aberrations have profound effects on phenotypic output. Genome wide methylation alterations are inheritable to pass down the aberrations through multiple generations. We developed a statistical method, Genome-wide Identification of Significant Methylation Alteration, GISAIM, to study the significant transgenerational methylation changes. GISAIM finds the significant methylation aberrations that are inherited through multiple generations. In a concrete biological study, we investigated whether exposing pregnant rats (F0) to a high fat (HF) diet throughout pregnancy or ethinyl estradiol (EE2)-supplemented diet during gestation days 14 20 affects carcinogen-induced mammary cancer risk in daughters (F1), granddaughters (F2) and great-granddaughters (F3). Mammary tumorigenesis was higher in daughters and granddaughters of HF rat dams, and in daughters, granddaughters and great-granddaughters of EE2 rat dams. Outcross experiments showed that increased mammary cancer risk was transmitted to HF granddaughters equally through the female or male germlines, but is only transmitted to EE2 granddaughters through the female germline. Transgenerational effect on mammary cancer risk was associated with increased expression of DNA methyltransferases, and across all three EE2 generations hypo or hyper methylation of the same 375 gene promoter regions in their mammary glands. Our study shows that maternal dietary estrogenic exposures during pregnancy can increase breast cancer risk in multiple generations of offspring, and the increase in risk may be inherited through non-genetic means, possibly involving DNA methylation.

q-bio.QM↗

arXiv2013

BACOM 2.0 facilitates absolute normalization and quantification of somatic copy number alterations in heterogeneous tumor

BACOM is a statistically principled and unsupervised method that detects copy number deletion types (homozygous versus heterozygous), estimates normal cell fraction, and recovers cancer specific copy number profiles, using allele specific copy number signals. In a subsequent analysis of TCGA ovarian cancer dataset, the average normal cell fraction estimated by BACOM was found higher than expected. In this letter, we first discuss the advantages of the BACOM in relation to alternative approaches. Then, we show that this elevated estimate of normal cell fraction is the combined result of inaccurate signal modeling and normalization. Lastly, we describe an allele specific signal modeling and normalization scheme that can enhance BACOM applications in many biological contexts. An open source MATLAB program was developed to implement our extended method and it is publically available.

q-bio.GN↗