Seminars

2 - week Workshop on Mathematical Modeling in Development Biology

2 - week Workshop on Mathematical Modeling in Development Biology

The conventional approach to LHC analysis involves comparing the measured data to Monte Carlo simulations. These simulations start at the hard-scattering level, where the potential for new physics is maximal, and proceed through various stages, including showering, hadronization, and detector response. Unfortunately, each stage introduces complexities, resulting in a convoluted representation of the true underlying physics at the simulated detector level. Events measured at the LHC detector are also a somewhat convoluted version of the true underlying physics, due to various latent effects. Eliminating these convolutions is essential for a direct comparison between theoretical predictions and measured data, which can be achieved through the process of 'Unfolding', where reconstructed or measured events are directly mapped to the hard-scattering level. In this seminar, I will discuss the development and application of multi-dimensional unfolding models that utilize machine-learning-based generative techniques, specifically Generative Adversarial Networks and Normalizing Flows. A key focus will be on how multi-dimensional unfolding with NFs allows the reconstruction of observables in their proper rest frame and in a probabilistically faithful way. I will highlight its practical impact through a case study on the measurement of CP-phase in the top Yukawa coupling.

2 - week Workshop on Mathematical Modeling in Development Biology

In this talk, I will present our work on relating atomic-level protein dynamics to its functions, e.g., biological signaling. Cells and organisms react to external and internal signals by proteins that consist of sensor and effector modules. Sensors detect environmental changes, such as light, pH, hormones, etc., while corresponding effectors trigger a response. First, I will discuss the initial step for signaling, i.e., drug molecules binding to proteins. I will exemplify this with our recent simulation and theoretical modeling efforts in collaboration with experimentalists to understand polyelectrolyte–protein interactions and help design polymers for SARS-CoV-2 virus inhibition. Later, I will introduce basic statistical-mechanics concepts to derive transmit functions that describe how a local time-dependent perturbation, which can be a deformation or a force, propagates in a viscoelastic medium such as a protein. Transmit functions are defined by equilibrium fluctuations fromsimulations or experimental observations. We apply this framework to our molecular dynamics simulation data of a bacterial signaling protein, for quantifying signal transfer efficiency of its principal deformation modes, namely shift, splay, and twist. Finally, I will conclude the talk with a few future research directions.

In this talk, I will present our work on relating atomic-level protein dynamics to its functions, e.g., biological signaling. Cells and organisms react to external and internal signals by proteins that consist of sensor and effector modules. Sensors detect environmental changes, such as light, pH, hormones, etc., while corresponding effectors trigger a response. First, I will discuss the initial step for signaling, i.e., drug molecules binding to proteins. I will exemplify this with our recent simulation and theoretical modeling efforts in collaboration with experimentalists to understand polyelectrolyte–protein interactions and help design polymers for SARS-CoV-2 virus inhibition. Later, I will introduce basic statistical-mechanics concepts to derive transmit functions that describe how a local time-dependent perturbation, which can be a deformation or a force, propagates in a viscoelastic medium such as a protein. Transmit functions are defined by equilibrium fluctuations fromsimulations or experimental observations. We apply this framework to our molecular dynamics simulation data of a bacterial signaling protein, for quantifying signal transfer efficiency of its principal deformation modes, namely shift, splay, and twist. Finally, I will conclude the talk with a few future research directions.

2 - week Workshop on Mathematical Modeling in Development Biology

Cluster cluster aggregation (CCA) is a nonequilibrium, irreversible phenomenon where particles, or clusters coalesce on contact to form larger clusters. The most common approach to study CCA is the mean-field Smoluchowski coagulation equation. However, this equation can be exactly solved only when the rate of collision is independent of the colliding masses (constant kernel), is the sum of the masses (sum kernel), or the product of the masses (product kernel). Moreover, the solution of the Smoluchowski equation describes only the typical or average trajectories and moments of the mass distribution, and does not provide any information about atypical or rare trajectories. In this talk, I will describe a biased Monte Carlo algorithm, and the analytical formalism developed to study probabilities of rare events in CCA for arbitrary collision kernels, and the results obtained therein. The algorithm can sample probabilities as low as 10^{-40}, and obtains atypical and typical trajectories. We establish the efficacy of the algorithm by benchmarking the numerically obtained large deviation function of interest, and the trajectories, with the exact answer for constant kernel. We establish an analytical path wise large deviation principle for arbitrary collision kernels, and obtain the explicit large deviation functions, for constant, sum and product kernels, as well as the optimal evolution trajectories for constant and sum kernels, all of which show excellent agreement with Monte Carlo simulations. We use this analytical formalism to obtain the large deviation function of interest and atypical trajectories for $k-$nary coalescence, $kA —> lA$.

Nucleation phenomena are ubiquitous in nature and the impurities are present in almost every real and experimental system showing nucleation. Impurities play a diverse role influencing the nucleation properties of the system. It could boost up or slow down the nucleation rate acting as nucleant, surfactant or blocking particles from getting attached to the growing nucleus. Simple models like Ising and Potts lattice-gas model can be used to get insights about the nucleation properties of such complicated systems. In this talk I am going to explore the role of randomly positioned static and dynamic impurities on nucleation in the 2D Ising lattice-gas model of solute precipitation. Impurity-solute and impurity-solvent interaction energies are varied whilst keeping other interaction energies fixed. We have shown that both the free energy barrier height and critical nucleus size monotonically decreases with increasing the impurity density for the static case when interaction energies are neutral. In the case of dynamic impurities we explore a broad range of both symmetric and anti-symmetric interactions with impurities and map the regime for which the impurities act as a surfactant, decreasing the surface free energy of the nucleating phase. We also characterise different nucleation regimes observed at different values of the interaction energy, which include regimes where impurities play the role of surfactant, inactive-spectator, nucleant or heterogeneous nucleation sites with clustering impurities. References: [1] D. Mandal and D. Quigley, Soft Matter, 2021, 17, 8642-8650. [2] D. Mandal and D. Quigley, arXiv:2312.08342.

NCM-sponsored teacher enrichment workshop https://www.atmschools.org/school/2024/TEW/latds

NCM-sponsored teacher enrichment workshop https://www.atmschools.org/school/2024/TEW/latds

NCM-sponsored teacher enrichment workshop https://www.atmschools.org/school/2024/TEW/latds

NCM-sponsored teacher enrichment workshop https://www.atmschools.org/school/2024/TEW/latds

Let $k$ be an algebraically closed field of characteristic zero. We prove that the Brauer group of the moduli stack of stable parabolic $\textnormal{PGL}(r,k)$-bundles with full flag quasi-parabolic structures at an arbitrary parabolic divisor on a curve $X$ coincides with the Brauer group of the smooth locus of the corresponding coarse moduli space of parabolic $\textnormal{PGL}(r,k)$-bundles. We also compute the Brauer group of the smooth locus of this coarse moduli for more general quasi-parabolic types and weights satisfying certain conditions. If time permits we will discuss the case when $G= Sp(2r,\mathbb C)$. This is joint work with Indranil Biswas and Sujoy Chakraborty.

NCM-sponsored teacher enrichment workshop https://www.atmschools.org/school/2024/TEW/latds

NCM-sponsored teacher enrichment workshop https://www.atmschools.org/school/2024/TEW/latds

Particle diffusion in heterogeneous systems poses the following question: Can a single available model describe the entire dynamics of a particle in complex biological, soft matter systems? Indeed, often several different physical mechanisms are at work and it is more insightful to rank them based on the likelihood of them explaining the dynamics. The first part of this talk will discuss — within the Bayesian framework—(i) how maximum-likelihood model selection can be done by assigning probabilities to each feasible model and (ii) how to estimate the parameters of each model. In particular, the implementation of this powerful statistical tool using the Nested Sampling algorithm to compare—at the single trajectory level—models of Brownian motion, viscoelastic anomalous diffusion and normal yet non-Gaussian diffusion will be discussed. Finally, the application of this method to experimental data of tracer diffusion in polymer-based hydrogels (mucin) will be presented. Viscoelastic anomalous diffusion is often found to be most probable, followed by Brownian motion, while the model with a diffusing diffusion coefficient is only realised rarely. The second part of this talk will discuss how the results of Bayesian analysis can lead to meaningful model building. Fractional Brownian motion (FBM), a Gaussian, non-Markovian, self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion behavior in a great variety of physical systems. The correlation and diffusion properties of this random motion are fully characterized by its index of self-similarity or the Hurst exponent. Inspired by the results discussed in the first part, generalizations of FBM will be presented to include (a) Hurst index that randomly changes from trajectory to trajectory but remains constant along a given trajectory, and (b) Hurst index that varies stochastically in time along a trajectory. A general mathematical framework for analytical, numerical, and statistical analysis for both (a) and (b) will be discussed. An algorithm to distinguish between the three classes of random motions, namely the canonical FBM and its generalizations (a) and (b) will be presented, and the applicability of this algorithm will be demonstrated by analyzing real-world examples for all the three classes