IBS BIMAG 2024 Summer Internship workshop
2024-07-31 10:30 - 12:00 (Asia/Seoul)
Presentor(s)
Mentor
Talk title

Jaehun Jeong
Gyuyoung Hwang
Analyzing coupled SCN cell frequencies of mammals for multi-step transcriptional model

Hyunsuk Choo, Yonghee Lee
Seok Joo Chae
Development of a data-driven causality detection method using Taken’s Theorem

Juhyeon Kim
Dongju Lim
Accurate initial condition for circadian pacemaker model estimating the circadian phase

Kyeongtae Ko
Dongju Lim
Accurate initial condition estimation of exposed individuals in SEIR model

Ashley L Lawas
Olive R Cawiding
Advancing causal inference in complex systems through ODE-based methods

Sieun Lee
Olive R Cawiding
Improving efficiency of sleep disorder diagnosis via SymScore

Daniel Shin, Anar Rzayev
Olive R Cawiding
Improving Sleep Disorder Diagnosis Questionnaire (SLEEPS) by integrating Lifestyle Factors into Machine-learning algorithms

Shubhangi Kumar
Pan Li
Modelling cardiac pacemaking dysfunction in heart failure progression

Yejin Lee
Pan Li
Modelling beta-adrenergic regulation of calcium dynamics in human ventricular myocytes

Hyungu Lee
Yun Min Song
PSG sleep pattern prediction from actigraphy data

Yujin Park
Yun Min Song
Validating the usefulness of anchor sleep from sleep-wake patterns using ESS

Yoon Kim
Yun Min Song
Predicting sleep onset latency

Hyukpyo Hong, Koopman representation: Linear representation – not an approximation – of nonlinear dynamics
2024-07-31 16:00 - 17:00
Abstract: A system of ordinary differential equations (ODEs) is one of the most widely used tools to describe a deterministic dynamical system. In general, such ODEs involve nonlinear equations, which make analysis of dynamical systems difficult. In this talk, we introduce Koopman theory, which offers a linear representation – not an approximation – of nonlinear dynamics. In particular, we present a data-driven algorithm to find such a linear representation

Yun Min Song, RNA velocity of single cells
2024-08-02 14:00 - 16:00 | B232 Seminar Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Daejeon, 34126, Korea, Republic of
In this talk, we discuss the paper “RNA velocity of single sells” by Gioele La Manno et.al., Nature, 2018.
Abstract
RNA abundance is a powerful indicator of the state of individual cells. Single-cell RNA sequencing can reveal RNA abundance with high quantitative accuracy, sensitivity and throughput. However, this approach captures only a static snapshot at a point in time, posing a challenge for the analysis of time-resolved phenomena such as embryogenesis or tissue regeneration. Here we show that RNA velocity—the time derivative of the gene expression state—can be directly estimated by distinguishing between unspliced and spliced mRNAs in common single-cell RNA sequencing protocols. RNA velocity is a high-dimensional vector that predicts the future state of individual cells on a timescale of hours. We validate its accuracy in the neural crest lineage, demonstrate its use on multiple published datasets and technical platforms, reveal the branching lineage tree of the developing mouse hippocampus, and examine the kinetics of transcription in human embryonic brain. We expect RNA velocity to greatly aid the analysis of developmental lineages and cellular dynamics, particularly in humans.

Uncovering personalized glucose responses and circadian rhythms from multiple wearable biosensors with Bayesian dynamical modeling
2024-08-07 16:00 - 17:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
Abstract:
Wearable biosensors measure physiological variables with high temporal resolution over multiple days and are increasingly employed in clinical settings, such as continuous glucose monitoring in diabetes care. Such datasets bring new opportunities and challenges, and patients, clinicians, and researchers are today faced with a common challenge: how to best summarize and capture relevant information from multimodal wearable time series? Here, we aim to provide insights into individual glucose dynamics and their relationships with food and drink ingestion, time of day, and coupling with other physiological states such as physical and heart activity. To this end, we generate and analyze multiple wearable device data through the lens of a parsimonious mathematical model with interpretable components and parameters. A key innovation of our method is that the models are learned on a personalized level for each participant within a Bayesian framework, which enables the characterization of interindividual heterogeneity in features such as the glucose response time following meals or underlying circadian baseline rhythm. I will also describe how we are currently applying this framework in the context of gestational diabetes.

Gyuyoung Hwang, A universal description of stochastic oscillators
2024-08-09 14:00 - 16:00
In this talk, we discuss the paper “A universal description of stochastic oscillators”, by Alberto Perez-Cervera et. al., PNAS, 2023.
Abstract
Many systems in physics, chemistry, and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example, linear dynamics of a stable focus with fluctuations, limit-cycle systems perturbed by noise, or excitable systems in which random inputs lead to a train of pulses. Despite their diverse origins, the phenomenology of random oscillations can be strikingly similar. Here, we introduce a nonlinear transformation of stochastic oscillators to a complex-valued function Q1*(x) that greatly simplifies and unifies the mathematical description of the oscillator’s spontaneous activity, its response to an external time-dependent perturbation, and the correlation statistics of different oscillators that are weakly coupled. The function Q1* (x) is the eigenfunction of the Kolmogorov backward operator with the least negative (but nonvanishing) eigenvalue λ1 = μ1 + iω1. The resulting power spectrum of the complex-valued function is exactly given by a Lorentz spectrum with peak frequency ω1 and half-width μ1; its susceptibility with respect to a weak external forcing is given by a simple one-pole filter, centered around ω1; and the cross-spectrum between two coupled oscillators can be easily expressed by a combination of the spontaneous power spectra of the uncoupled systems and their susceptibilities. Our approach makes qualitatively different stochastic oscillators comparable, provides simple characteristics for the coherence of the random oscillation, and gives a framework for the description of weakly coupled oscillators.

Kevin Spinicci, SMSSVD : Submatrix selection singular value decomposition
2024-08-16 14:00 - 16:00
In this talk, we discuss the paper, “SMSSVD : Submatrix selection singular value decomposition”, by Rasmus Henningsson and Magnus Fontes, Bioinformatics, 2019.
Abstract

Motivation
High throughput biomedical measurements normally capture multiple overlaid biologically relevant signals and often also signals representing different types of technical artefacts like e.g. batch effects. Signal identification and decomposition are accordingly main objectives in statistical biomedical modeling and data analysis. Existing methods, aimed at signal reconstruction and deconvolution, in general, are either supervised, contain parameters that need to be estimated or present other types of ad hoc features. We here introduce SubMatrix Selection Singular Value Decomposition (SMSSVD), a parameter-free unsupervised signal decomposition and dimension reduction method, designed to reduce noise, adaptively for each low-rank-signal in a given data matrix, and represent the signals in the data in a way that enable unbiased exploratory analysis and reconstruction of multiple overlaid signals, including identifying groups of variables that drive different signals.

Results
The SMSSVD method produces a denoised signal decomposition from a given data matrix. It also guarantees orthogonality between signal components in a straightforward manner and it is designed to make automation possible. We illustrate SMSSVD by applying it to several real and synthetic datasets and compare its performance to golden standard methods like PCA (Principal Component Analysis) and SPC (Sparse Principal Components, using Lasso constraints). The SMSSVD is computationally efficient and despite being a parameter-free method, in general, outperforms existing statistical learning methods.

Quantitative Ecology of Host-associated Microbiomes - Lei Dai
2024-09-04 16:00 - 17:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
Abstract: The realization that microbiomes, associated with virtually all multicellular organisms, have tremendous impact on their host health is considered as one of the most important scientific discoveries in the last decade. The host associated microbiomes, composed of tens to hundreds of co-existing microbial species, are highly heterogenous at multiple scales (e.g. between different hosts and within a host). In this talk, I will share our recent works on understanding the heterogeneity of complex microbial communities, and how these conceptual and technological advances in microbial ecology pave the way for precision microbiome engineering to prevent and treat diseases.

Make Your Science Friendly: A Guide to Engaging Visuals - Sunghwan Bae
2024-09-05 10:00 - 11:00 | B232 Seminar Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Daejeon, 34126, Korea, Republic of
The talk will be hybrid, participants may join via Zoom with the following link: https://us06web.zoom.us/j/99567630778?pwd=[REDACTED]

Olive Cawiding, Predicting multiple observations in complex systems through low-dimensional embeddings
2024-09-06 14:00 - 16:00 | B232 Seminar Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Daejeon, 34126, Korea, Republic of
In this talk, we discuss the paper, “Predicting multiple observations in complex systems through low-dimensional embeddings”, by Tao Wu et. al., Nature Communications, 2024.
Zoom : https://us06web.zoom.us/j/99567630778?pwd=[REDACTED]
Abstract
Forecasting all components in complex systems is an open and challenging task, possibly due to high dimensionality and undesirable predictors. We bridge this gap by proposing a data-driven and model-free framework, namely, feature-and-reconstructed manifold mapping (FRMM), which is a combination of feature embedding and delay embedding. For a high-dimensional dynamical system, FRMM finds its topologically equivalent manifolds with low dimensions from feature embedding and delay embedding and then sets the low-dimensional feature manifold as a generalized predictor to achieve predictions of all components. The substantial potential of FRMM is shown for both representative models and real-world data involving Indian monsoon, electroencephalogram (EEG) signals, foreign exchange market, and traffic speed in Los Angeles Country. FRMM overcomes the curse of dimensionality and finds a generalized predictor, and thus has potential for applications in many other real-world systems.

Hyun Kim, Deep learning linking mechanistic models to single-cell transcriptomics data reveals transcriptional bursting in response to DNA damage
2024-09-13 14:00 - 16:00 | B232 Seminar Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Daejeon, 34126, Korea, Republic of
In this talk, we discuss the paper “Deep learning linking mechanistic models to single-cell transcriptomics data reveals transcriptional bursting in response to DNA damage” by Zhiwei Huang, et. al., bioRxiv, 2024.
Zoom : https://us06web.zoom.us/j/99567630778?pwd=[REDACTED]
Abstract
Cells must adopt flexible regulatory strategies to make decisions regarding their fate, including differentiation, apoptosis, or survival in the face of various external stimuli. One key cellular strategy that enables these functions is stochastic gene expression programs. However, understanding how transcriptional bursting, and consequently, cell fate, responds to DNA damage on a genome-wide scale poses a challenge. In this study, we propose an interpretable and scalable inference framework, DeepTX, that leverages deep learning methods to connect mechanistic models and scRNA-seq data, thereby revealing genome-wide transcriptional burst kinetics. This framework enables rapid and accurate solutions to transcription models and the inference of transcriptional burst kinetics from scRNA-seq data. Applying this framework to several scRNA-seq datasets of DNA-damaging drug treatments, we observed that fluctuations in transcriptional bursting induced by different drugs could lead to distinct fate decisions: IdU treatment induces differentiation in mouse embryonic stem cells by increasing the burst size of gene expression, while 5FU treatment with low and high dose increases the burst frequency of gene expression to induce cell apoptosis and survival in human colon cancer cells. Together, these results show that DeepTX can be used to analyze single-cell transcriptomics data and can provide mechanistic insights into cell fate decisions.

Brenda Gavina, Achieving Occam’s razor: Deep learning for optimal model reduction
2024-09-20 14:00 - 16:00
In this talk, we discuss the paper “Achieving Occam’s razor: Deep learning for optimal model reduction” by Botond B. Antal et.al., PLOS Computational Biology, 2024.
Abstract
All fields of science depend on mathematical models. Occam’s razor refers to the principle that good models should exclude parameters beyond those minimally required to describe the systems they represent. This is because redundancy can lead to incorrect estimates of model parameters from data, and thus inaccurate or ambiguous conclusions. Here, we show how deep learning can be powerfully leveraged to apply Occam’s razor to model parameters. Our method, FixFit, uses a feedforward deep neural network with a bottleneck layer to characterize and predict the behavior of a given model from its input parameters. FixFit has three major benefits. First, it provides a metric to quantify the original model’s degree of complexity. Second, it allows for the unique fitting of data. Third, it provides an unbiased way to discriminate between experimental hypotheses that add value versus those that do not. In three use cases, we demonstrate the broad applicability of this method across scientific domains. To validate the method using a known system, we apply FixFit to recover known composite parameters for the Kepler orbit model and a dynamic model of blood glucose regulation. In the latter, we demonstrate the ability to fit the latent parameters to real data. To illustrate how the method can be applied to less well-established fields, we use it to identify parameters for a multi-scale brain model and reduce the search space for viable candidate mechanisms.

Novel approaches and technologies for the study of sleep and circadian rhythms in health and disease - Derk-Jan Dijk
2024-10-02 16:00 - 17:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
Abstract: The study of sleep and circadian rhythms at scale requires novel technologies and approaches that are valid, cost effective and do not pose much of a burden to the participant. Here we will present our recent studies in which we have evaluated several classes of technologies and approaches including wearables, nearables, blood based biomarkers and combinations of data with mathematical models.

Dongju Lim, Mathematical model for the distribution of DNA replication origins
2024-10-04 14:00 - 16:00 | B232 Seminar Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Daejeon, 34126, Korea, Republic of
In this talk we discuss the paper “Mathematical model for the distribution of DNA replication origins” by Alessandro de Moura and Jens Karschau, Physical Review E, 2024.
Abstract
DNAreplication in yeast and in many other organisms starts from well-defined locations on the DNA known as replication origins. The spatial distribution of these origins in the genome is particularly important in ensuring that replication is completed quickly. Cells are more vulnerable to DNA damage and other forms of stress while they are replicating their genome. This raises the possibility that the spatial distribution of origins is under selection pressure. In this paper we investigate the hypothesis that natural selection favors origin distributions leading to shorter replication times. Using a simple mathematical model, we show that this hypothesis leads to two main predictions about the origin distributions: that neighboring origins that are inefficient (less likely to fire) are more likely to be close to each other than efficient origins; and that neighboring origins with larger differences in firing times are more likely to be close to each other than origins with similar firing times. We test these predictions using next-generation sequencing data, and show that they are both supported by the data.

Eui Min Jeong, A frequency-amplitude coordinator and its optimal energy consumption for biological oscillators
2024-10-11 14:00 - 16:00
In this talk, we discuss the paper, “A frequency-amplitude coordinator and its optimal energy consumption for biological oscillators”, by Bo-Wei Qin et. al., Nature Communications, 2021.
Zoom : https://us06web.zoom.us/j/99567630778?pwd=[REDACTED]
Abstract
Biorhythm including neuron firing and protein-mRNA interaction are fundamental activities with diffusive effect. Their well-balanced spatiotemporal dynamics are beneficial for healthy sustainability. Therefore, calibrating both anomalous frequency and amplitude of biorhythm prevents physiological dysfunctions or diseases. However, many works were devoted to modulate frequency exclusively whereas amplitude is usually ignored, although both quantities are equally significant for coordinating biological functions and outputs. Especially, a feasible method coordinating the two quantities concurrently and precisely is still lacking. Here, for the first time, we propose a universal approach to design a frequency-amplitude coordinator rigorously via dynamical systems tools. We consider both spatial and temporal information. With a single well-designed coordinator, they can be calibrated to desired levels simultaneously and precisely. The practical usefulness and efficacy of our method are demonstrated in representative neuronal and gene regulatory models. We further reveal its fundamental mechanism and optimal energy consumption providing inspiration for biorhythm regulation in future.

Interpretable Machine Learning-Based Scoring System for Clinical Decision Making - Nan Liu
2024-10-18 11:00 - 12:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
Abstract: There has been an increased use of scoring systems in clinical settings for the purpose of assessing risks in a convenient manner that provides important evidence for decision making. Machine learning-based methods may be useful for identifying important predictors and building models; however, their ‘black box’ nature limits their interpretability as well as clinical acceptability. This talk aims to introduce and demonstrate how interpretable machine learning can be used to create scoring systems for clinical decision making.

Yun Min Song - Noise robustness and metabolic load determine the principles of central dogma regulation
2024-10-25 14:00 - 15:00
In this talk, we discuss the paper : “Noise robustness and metabolic load determine the principles of central dogma regulation” by Teresa W. Lo et al, Sci. Adv, https://doi.org/10.1126/sciadv.ado3095.
Zoom: https://us06web.zoom.us/j/99567630778?pwd=[REDACTED]
Abstract
The processes of gene expression are inherently stochastic, even for essential genes required for growth. How does the cell maximize fitness in light of noise? To answer this question, we build a mathematical model to explore the trade-off between metabolic load and growth robustness. The model provides insights for principles of central dogma regulation: Optimal protein expression levels for many genes are in vast overabundance. Essential genes are transcribed above a lower limit of one message per cell cycle. Gene expression is achieved by load balancing between transcription and translation. We present evidence that each of these regulatory principles is observed. These results reveal that robustness and metabolic load determine the global regulatory principles that govern gene expression processes, and these principles have broad implications for cellular function.

Latent space dynamics identification - Youngsoo Choi
2024-10-30 15:00 - 16:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
Abstravt: Latent space dynamics identification (LaSDI) is an interpretable data-driven framework that follows three distinct steps, i.e., compression, dynamics identification, and prediction. Compression allows high-dimensional data to be reduced so that they can be easily fit into an interpretable model. Dynamics identification lets you derive the interpretable model, usually some form of parameterized differential equations that fit the reduced latent space data. Then, in the prediction phase, the identified differential equations are solved in the reduced space for a new parameter point and its solution is projected back to the full space. The efficiency of the LaSDI framework comes from the fact that the solution process in the prediction phase does not involve any full order model size. For the identification, various approaches are possible, e.g., a fixed form as in dynamic mode decomposition and thermodynamics-based LaSDI, a regression form as in sparse identification of nonlinear dynamics (SINDy) and weak SINDy, and a physics-driven form as projection-based reduced order model. Various physics prob- lems were accurately accelerated by the family of LaSDIs, achieving a speed-up of 1000x, e.g., kinetic plasma simulations, pore collapse, and computational fluid problems.

Derivation and simulation of a computational model of active cell populations: How overlap avoidance, deformability, cell-cell junctions and cytoskeletal forces affect alignment - Kevin SPINICCI
2024-11-01 14:00 - 15:00
In this talk, we discuss the paper : “Derivation and simulation of a computational model of active cell populations: How overlap avoidance, deformability, cell-cell junctions and cytoskeletal forces affect alignment” by Leech et al, nature biotechnology, https://doi.org/10.1371/journal.pcbi.1011879.
Zoom: https://us06web.zoom.us/j/99567630778?pwd=[REDACTED]
Abstract
Collective alignment of cell populations is a commonly observed phenomena in biology. An important example are aligning fibroblasts in healthy or scar tissue. In this work we derive and simulate a mechanistic agent-based model of the collective behaviour of actively moving and interacting cells, with a focus on understanding collective alignment. The derivation strategy is based on energy minimisation. The model ingredients are motivated by data on the behaviour of different populations of aligning fibroblasts and include: Self-propulsion, overlap avoidance, deformability, cell-cell junctions and cytoskeletal forces. We find that there is an optimal ratio of self-propulsion speed and overlap avoidance that maximises collective alignment. Further we find that deformability aids alignment, and that cell-cell junctions by themselves hinder alignment. However, if cytoskeletal forces are transmitted via cell-cell junctions we observe strong collective alignment over large spatial scales.

Cluster-based network modeling—From snapshots to complex dynamical systems - Olive R. Cawiding
2024-11-08 14:00 - 16:00 | B232 Seminar Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Daejeon, 34126, Korea, Republic of
Abstract: We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic modeling often assumes a low-dimensional subspace or manifold for the state. We liberate ourselves from this assumption by proposing cluster-based network modeling (CNM) bridging machine learning, network science, and statistical physics. CNM describes short- and long-term behavior and is fully automatable, as it does not rely on application-specific knowledge. CNM is demonstrated for the Lorenz attractor, ECG heartbeat signals, Kolmogorov flow, and a high-dimensional actuated turbulent boundary layer. Even the notoriously difficult modeling benchmark of rare events in the Kolmogorov flow is solved. This automatable universal data-driven representation of complex nonlinear dynamics complements and expands network connectivity science and promises new fast-track avenues to understand, estimate, predict, and control complex systems in all scientific fields.

Mathematical models for malaria - Jennifer Flegg
2024-11-13 16:00 - 17:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
Abstract: The effect of malaria on the developing world is devastating. Each year there are more than 200 million cases and over 400,000 deaths, with children under the age of five the most vulnerable. Ambitious malaria elimination targets have been set by the World Health Organization for 2030. These involve the elimination of the disease in at least 35 countries. However, these malaria elimination targets rest precariously on being able to treat the disease appropriately; a difficult feat with the emergence and spread of antimalarial drug resistance, along with many other challenges. In this talk, I will introduce several statistical and mathematical models that can be used to monitor malaria transmission and to support malaria elimination. For example, I’ll present mechanistic models of disease transmission, statistical models that allow the emergence and spread of antimalarial drug resistance to be monitored, mechanistic models that capture the role of bioclimatic factors on the risk of malaria and optimal geospatial sampling schemes for future malaria surveillance. I will discuss how the results of these models have been used to inform public health policy and support ongoing malaria elimination efforts.

Next generation reservoir computing - Kang Min Lee
2024-11-15 09:00 - 11:00 | B232 Seminar Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Daejeon, 34126, Korea, Republic of
In this talk, we discuss the paper “Next generation reservoir computing”, by Gauthier, et.al, Nat. Comm., 2021.
Abstract : Reservoir computing is a best-in-class machine learning algorithm for processing information generated by dynamical systems using observed time-series data. Importantly, it requires very small training data sets, uses linear optimization, and thus requires minimal computing resources. However, the algorithm uses randomly sampled matrices to define the underlying recurrent neural network and has a multitude of metaparameters that must be optimized. Recent results demonstrate the equivalence of reservoir computing to nonlinear vector autoregression, which requires no random matrices, fewer metaparameters, and provides interpretable results. Here, we demonstrate that nonlinear vector autoregression excels at reservoir computing benchmark tasks and requires even shorter training data sets and training time, heralding the next generation of reservoir computing.

SVD-AE: An asymmetric autoencoder with SVD regularization for multivariate time series anomaly detection - Myna Lim
2024-11-22 10:00 - 11:30 | B232 Seminar Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Daejeon, 34126, Korea, Republic of
In this talk, we discuss the paper “SVD-AE: An asymmetric autoencoder with SVD regularization for multivariate time series anomaly detection” by Yueyue Yao, et.al., Neural Networks, 2024.
Abstract

Anomaly detection in multivariate time series is of critical importance in many real-world applications, such as system maintenance and Internet monitoring. In this article, we propose a novel unsupervised framework called SVD-AE to conduct anomaly detection in multivariate time series. The core idea is to fuse the strengths of both SVD and autoencoder to fully capture complex normal patterns in multivariate time series. An asymmetric autoencoder architecture is proposed, where two encoders are used to capture features in time and variable dimensions and a shared decoder is used to generate reconstructions based on latent representations from both dimensions. A new regularization based on singular value decomposition theory is designed to force each encoder to learn features in the corresponding axis with mathematical supports delivered. A specific loss component is further proposed to align Fourier coefficients of inputs and reconstructions. It can preserve details of original inputs, leading to enhanced feature learning capability of the model. Extensive experiments on three real world datasets demonstrate the proposed algorithm can achieve better performance on multivariate time series anomaly detection tasks under highly unbalanced scenarios compared with baseline algorithms.

Mathematical Modelling of Microtube Driven Invasion of Glioma - Thomas Hillen
2024-11-29 11:00 - 12:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
Abstract: Malignant gliomas are highly invasive brain tumors. Recent attention has focused on their capacity for network-driven invasion, whereby mitotic events can be followed by the migration of nuclei along long thin cellular protrusions, termed tumour microtubes (TM). Here I develop a mathematical model that describes this microtube-driven invasion of gliomas. I show that scaling limits lead to well known glioma models as special cases such as go-or-grow models, the PI model of Swanson, and the anisotropic model of Swan. I compute the invasion speed and I use the model to fit experiments of cancer resection and regrowth in the mouse brain.
(Joint work with N. Loy, K.J. Painter, R. Thiessen, A. Shyntar).

Theoretical studies on biological oscillations by using waveform data and mathematical models - Shingo Gibo
2024-12-09 16:00 - 17:00
Title: Theoretical studies on biological oscillations by using waveform data and mathematical models
Abstract: Temporal waveforms of biological oscillations are of various shapes. In our research, we have explored the functional implications of these waveform shapes. In particular, we theoretically showed that the period of circadian clocks is proportional to the waveform distortion from sinusoidal wave. It suggests that the circadian period can be stable against temperature changes only if the waveform becomes more distorted at higher temperatures. In this talk, I will explain my past research and discuss my future plans.

Reference:
[1] Shingo Gibo, Gen Kurosawa, Non-sinusoidal Waveform in Temperature Compensated Circadian Oscillations, Biophysical Journal 116 (4) 741-751 (2019). doi: 10.1016/j.bpj.2018.12.022
[2] Shingo Gibo, Gen Kurosawa, Theoretical study on the regulation of circadian rhythms by RNA methylation, Journal of Theoretical Biology 490, 110140 (2020). doi; 10.1016/j.jtbi.2019.110140
[3] Shingo Gibo, Teiji Kunihiro, Tetsuo Hatsuda, Gen Kurosawa, Waveform distortion for temperature compensation and synchronization in circadian rhythms: An approach based on the renormalization group method, arXiv (2024). arXiv:2409.02526

Circadian phase in cells and humans - Achim Kramer
2024-12-11 16:00 - 17:00 | ZOOM ID: 997 8258 4700 (Biomedical Mathematics Online Colloquium), (pw: [REDACTED]
Abstract:
Circadian clocks in cells and humans are heterogeneous in period and phase. This heterogeneity can be exploited not only to gain insight into the molecular basis of circadian rhythms, but also to explore plasticity and robustness. In this talk, I will report on two ongoing projects in the lab: (i) We are exploiting the heterogeneity of cells in both circadian period and a metabolic parameter – protein stability – to study their interdependence without the need for genetic manipulation. We have generated cells expressing key circadian proteins (CRYPTOCHROME1/2 (CRY1/2) and PERIOD1/2 (PER1/2)) as endogenous fusions with fluorescent proteins and are simultaneously monitoring circadian rhythm and degradation in thousands of single cells. (ii) We are developing molecular biomarkers of human circadian characteristics that will allow an objective description of the epidemiology of the human circadian clock and an assessment of its robustness and plasticity.

Kolmogorov-Arnold Networks - U Jin Choi
2024-12-13 13:00 - 15:00 | B232 Seminar Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Daejeon, 34126, Korea, Republic of
In this talk, we discuss the paper : “KAN: Kolmogorov-Arnold Networks,” by Z Liu et al. Abstract: Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes (“neurons”), KANs have learnable activation functions on edges (“weights”). KANs have no linear weights at all — every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. For accuracy, much smaller KANs can achieve comparable or better accuracy than much larger MLPs in data fitting and PDE solving. Theoretically and empirically, KANs possess faster neural scaling laws than MLPs. For interpretability, KANs can be intuitively visualized and can easily interact with human users. Through two examples in mathematics and physics, KANs are shown to be useful collaborators helping scientists (re)discover mathematical and physical laws. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving today’s deep learning models which rely heavily on MLPs.

Laplacian renormalization group for heterogeneous networks - Gyuyoung Hwang
2024-12-13 14:00 - 16:00 | B232 Seminar Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Daejeon, 34126, Korea, Republic of
In this talk, we study and discuss the paper “Laplacian renormalization group for heterogeneous networks” by Pablo Villegas et.al, Nature Physics, 2023.
Abstract
The renormalization group is the cornerstone of the modern theory of universality and phase transitions and it is a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its application to complex networks has proven particularly challenging, owing to correlations between intertwined scales. To date, existing approaches have been based on hidden geometries hypotheses, which rely on the embedding of complex networks into underlying hidden metric spaces. Here we propose a Laplacian renormalization group diffusion-based picture for complex networks, which is able to identify proper spatiotemporal scales in heterogeneous networks. In analogy with real-space renormalization group procedures, we first introduce the concept of Kadanoff supernodes as block nodes across multiple scales, which helps to overcome detrimental small-world effects that are responsible for cross-scale correlations. We then rigorously define the momentum space procedure to progressively integrate out fast diffusion modes and generate coarse-grained graphs. We validate the method through application to several real-world networks, demonstrating its ability to perform network reduction keeping crucial properties of the systems intact.

Solving Inverse Problems in Medical Imaging with Score-Based Generative Models - U Jin Choi
2024-12-16 15:00 - 17:00 | B232 Seminar Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Daejeon, 34126, Korea, Republic of
In this talk, we discuss the paper : “Solving Inverse Problems in Medical Imaging with Score-Based Generative Models” by Y Song et al.
Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map measurements to medical images, leveraging a training dataset of paired images and measurements. These measurements are typically synthesized from images using a fixed physical model of the measurement process, which hinders the generalization capability of models to unknown measurement processes. To address this issue, we propose a fully unsupervised technique for inverse problem solving, leveraging the recently introduced score-based generative models. Specifically, we first train a score-based generative model on medical images to capture their prior distribution. Given measurements and a physical model of the measurement process at test time, we introduce a sampling method to reconstruct an image consistent with both the prior and the observed measurements. Our method does not assume a fixed measurement process during training, and can thus be flexibly adapted to different measurement processes at test time. Empirically, we observe comparable or better performance to supervised learning techniques in several medical imaging tasks in CT and MRI, while demonstrating significantly better generalization to unknown measurement processes.

cellFlow: a generative flow-based model for single-cell count data - Hyun Kim
2024-12-20 14:00 - 16:00 | B232 Seminar Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Daejeon, 34126, Korea, Republic of
In this talk, we discuss the paper “cellFlow: a generative flow-based model for single-cell count data” by A. Palma et.al, ICLR, 2024.
Abstract
Generative modeling for single-cell RNA-seq has proven transformative in crucial fields such as learning single-cell representations and perturbation responses. However, despite their appeal in relevant applications involving data augmentation and unseen cell state prediction, use cases like generating artificial biological samples are still in their pioneering phase. While common approaches producing single-cell samples from noise operate in continuous space by assuming normalized gene expression, we argue for the necessity of sample generation in a raw transcription count space to favor processing-agnostic data generation and flexible downstream applications. To this end, we propose cellFlow, a Flow-Matching-based model that generates single-cell count data. In our empirical study, cellFlow performs on par with existing methods operating on normalized data when evaluated on three biological datasets. By carefully considering raw single-cell distributional properties, cellFlow is a promising avenue for future developments in single-cell generative models.

Diffusion Posterior Sampling for Linear Inverse Problem Solving- A Filtering Perspective - U Jin Choi
2024-12-27 10:00 - 12:00 | B232 Seminar Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Daejeon, 34126, Korea, Republic of
In this talk, we discuss the paper : “Diffusion Posterior Sampling for Linear Inverse Problem Solving- A Filtering Perspective” by Z. Dou& Y. Song

Diffusion models have achieved tremendous success in generating high-dimensional data like images, videos and audio. These models provide powerful data priors that can solve linear inverse problems in zero shot through Bayesian posterior sampling. However, exact posterior sampling for diffusion models is intractable. Current solutions often hinge on approximations that are either computationally expensive or lack strong theoretical guarantees. In this work, we introduce an efficient diffusion sampling algorithm for linear inverse problems that is guaranteed to be asymptotically accurate. We reveal a link between Bayesian posterior sampling and Bayesian filtering in diffusion models, proving the former as a specific instance of the latter. Our method, termed filtering posterior sampling, leverages sequential Monte Carlo methods to solve the corresponding filtering problem. It seamlessly integrates with all Markovian diffusion samplers, requires no model re-training, and guarantees accurate samples from the Bayesian posterior as particle counts rise. Empirical tests demonstrate that our method generates better or comparable results than leading zero-shot diffusion posterior samplers on tasks like image inpainting, super-resolution, and deblurring.
