Time | Speaker | Title | Resources | |
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09:30 to 10:30 | Wilhelmus van der Hoorn (Eindhoven University of Technology, Eindhoven, Netherlands) |
Geometry and complex networks: A powerful partnership Geometry is a powerful tool in many scientific domains, from fundamental physics to social science. It also plays and important role in the study of complex systems, especially from the point of constructing models for networks. Here nodes are assigned positions in some geometric space and connections are created based on the distances in that space. In this talk I will highlight advances for two key aspects of geometry in complex network and touch upon some challenges geometric network models present us with. |
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10:40 to 11:40 | Piyush Srivastava (TIFR Mumbai, India) |
Some problems regarding Bayesian networks Bayesian networks (or directed acyclic graphical models) have been a cornerstone of the modeling of causal inference. They have also led to the study of rich new combinatorial notions such as d-separation and Markov equivalence. Although these structures have been studied extensively since at least the 80s, many natural combinatorial questions about them—including basic ones regarding counting and uniform sampling—are still not fully understood. This talk will be a broad survey of some such problems, and recent progress on them. While a small part of this talk will be based on joint work with collaborators, most of it will be a survey of work by others, and will be based on discussions with—and work of—Vidya Sagar Sharma, a PhD student at TIFR. |
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12:00 to 13:00 | Rajesh Sundaresan (IISc, Bengaluru, India) |
Asymptotics of invariant measures of mean-field Markov models on countably infinite state spaces Consider the empirical measure process associated with a mean-field Markov interacting particle system of N particles. The Freidlin-Wentzell quasipotential is a natural candidate rate function for the sequence of invariant measures indexed by N. We discuss two counterexamples on countably infinite state spaces where the quasipotential is not the rate function. We will then provide some sufficient conditions where the situation is remedied. The talk will be based on joint work with Sarath Yasodharan. https://arxiv.org/abs/2110.12640 |
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15:00 to 16:00 | Serte Donderwinkel (McGill University, Montreal, Canada) |
The random friend tree I discuss some results on a very simple random recursive tree model that gives rise to interesting emergent phenomena, such as a highly skewed degree sequence. Unlike in the preferential attachment tree, the attachment rule is local: given the tree with n vertices, select a vertex uniformly at random and attach vertex n+1 to a uniformly random neighbour (or friend) of the selected vertex. We study various local and global properties of the resulting tree, but many questions remain open. This talk is based on a work in progress with Louigi Addario-Berry, Simon Briend, Luc Devroye, Céline Kerriou and Gabor Lugosi. |
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16:20 to 17:20 | Moumanti Podder (IISER Pune, India) |
Fixed points of a certain probabilistic tree automaton Consider a \emph{probabilistic tree automaton} (PTA) defined on the rooted regular tree $T_{m}$, comprising the alphabet $\{B,R\}$ (where $B$ stands for the colour blue, and $R$ for the colour red), in which the stochastic update rule, referred to as the \emph{majority policy}, is described as follows: let $u$ be a vertex of $T_{m}$, with children $u_{1}, u_{2}, \ldots, u_{m}$. Let $C_{t}(u_{i}) \in \{B,R\}$ denote the \emph{colour} or \emph{state} of $u_{i}$ at time step $t$, for each $i \in \{1,2,\ldots,m\}$. Associated with $u_{i}$ is a random variable $X_{t}(u_{i})$, where $X_{t}(u_{1}), X_{t}(u_{2}), \ldots, X_{t}(u_{m})$ are i.i.d.\ Bernoulli$(p)$. Conditioned on $C_{t}(u_{1}), C_{t}(u_{2}), \ldots, C_{t}(u_{m})$, we set |

Time | Speaker | Title | Resources | |
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09:30 to 10:30 | Vivek Borkar (IIT Bombay, India) |
Algorithms on networks This talk will give an overview of a class of distributed recursive algorithms on networks. |
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10:40 to 11:40 | Richard Kraaij (Delft University of Technology, Delft, Netherlands) |
Well posedness for Hamilton-Jacobi equations for linearly controlled gradient flows on the Wasserstein space Hamilton-Jacobi (HJ) equations are the equations that descibe the infinitesimal evolution of the value function of control problems, and as such play a key role in the description of dynamic large deviatons principles. In infinite dimensional context, like for the Wasserstein-2 space that plays a role in Dawson-Gärtner type large deviations, well-posedness of the HJ equation is a challenging, and not yet fully understood problem that lately is receiving a lot of attention. |
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12:00 to 13:00 | Sandeep Juneja (TIFR Mumbai, India) |
Best arm identification in multi-armed bandits – optimal algorithm based on fluid analysis We are given finitely many unknown probability distributions that can be sampled from and our aim is, through sequential sampling, to identify the one with the largest mean. This is a classical problem in statistics, simulation and learning theory. Lately, methods have been proposed that identify a sample complexity lower bound that any algorithm providing probabilistic correctness guarantees must satisfy, and algorithms have been developed that asymptotically match these lower bounds even for general sampling distributions, as the probabilistic error guarantees converge to zero. We review these ideas and propose a novel algorithm that relies on exploiting the underlying fluid structure in the evolution of the optimal sampling process and improves upon existing asymptotically optimal algorithms. |
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15:00 to 16:00 | Diego Garlaschelli (IMT School of Advanced Studies, Lucca, Italy) |
Multiscale network renormalization: Scale-invariance without geometry Systems with lattice geometry can be renormalized exploiting their coordinates in metric space, which naturally define the coarse-grained nodes. By contrast, complex networks defy the usual techniques, due to their small-world character and lack of explicit geometric embedding. Current network renormalization approaches require strong assumptions (e.g., community structure, hyperbolicity, scale-free topology), thus remaining incompatible with generic graphs and ordinary lattices. Here we introduce a graph renormalization scheme valid for any hierarchy of heterogeneous coarse-grainings, thereby allowing for the definition of “block-nodes” across multiple scales. This approach identifies a class of scale-invariant networks characterized by a necessary and specific dependence on additive hidden variables attached to nodes, plus optional dyadic factors. If the hidden variables are annealed, they lead to realistic scale-free networks with assortativity and finite local clustering, even in the sparse regime and in the absence of geometry. If they are quenched, they can guide the renormalization of real-world networks with node attributes and distance-dependence or communities. As an application, we derive an accurate multiscale model of the International Trade Network applicable across arbitrary geographic partitions. These results highlight a deep conceptual distinction between scale-free and scale-invariant networks, and they provide a geometry-free route to renormalization. |
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16:20 to 17:20 | Soumendu Sundar Mukherjee (ISI Kolkata, India) |
A dynamic mean-field model of academic collaboration There is empirical evidence that collaboration in academia has increased significantly during the past few decades, perhaps due to the breathtaking advancements in communication and technology during this period. Although there have been several studies on the dynamical aspects of collaboration, systematic statistical models have been lacking. In this talk, we will present a dynamic mean-field model of academic collaboration and discuss the associated estimation framework. We will consider several popular indices of collaboration from the scientometrics literature and study their dynamics under the proposed model. Using metadata from arXiv, we will also look at empirical aspects of the mean-field collaboration dynamics in disciplines such as Computer Science, Mathematics and Physics. Based on joint work with S. Chatterjee and T. Sadhukhan. |