30 NOV 2023
10:00 - 12:30

One of the major challenges in modern day statistics is to formulate models and develop inferential procedures to understand the complex multivariate relationships present in high-dimensional datasets. We address the issue of model determination for DAGs, with respect to a given ordering of the variables, together with the corresponding parameter estimation. For this, we use a hierarchical mixture prior and develop a Gibbs sampling algorithm to carry out the posterior computations. We focus on the Gaussian DAG models and calculate the posterior probability of being the edge between two nodes. We then extend our idea to construct a DAG for discrete data under the assumption that the data generated by discretization of the marginal distributions of a latent multivariate Gaussian distribution via a set of predetermined threshold values. Results show that the proposed method has high accuracy.


This Seminar is free and open to the public

30 NOV 2023
11:00 - 12:00

Abstract:

After a short review of possible impact of vector neutral current NSI on the neutrino
oscillation patterns, I present a class of models based on a $U(1)$ gauge symmetry with a gauge
boson of mass $\sim 10$ MeV that lead to vector neutral current NSI with sizable couplings. I
will then discuss how Coherent Elastic neutrino Nucleus Scattering (CEnuNS) experiments can
test these models. In the end, I will focus on the axial neutral current NSI and show how the
DUNE experiment will be able to constrain its couplings.

Meeting Place:
Seminar Room, School of Particles and Accelerators, IPM

Link to Join Virtually:
https://meet.google.com/fnv-dfkk-ghb

Link: https://meet.google.com/fnv-dfkk-ghb

30 NOV 2023
11:00 - 12:30

The Ehrenfeucht-Fraïssé games and their variants are a natural game-theoretic tool for investigating the similarity and dissimilarity between two mathematical structures. Although the study of these games is quite different in finite and infinite model theory, one might ask: if not all natural numbers are equal, why should all infinities be equal? In fact, it is within the framework of countably infinite model theory, not infinite model theory, that these games are often successful! Even at the level of the first uncountable cardinal, the picture is very mixed, but this is not surprising: The Sikorski extension theorem vs. non-trivial forcing axioms, countability and uncountability in Shelah's classification theory, descriptive set theory vs. generalised descriptive set theory. In this series of lectures (for some n> 1) I will talk about an area of research that started in the early 1990s and is an intersection of several independent topics. The lectures will start with a brief introduction to infinite games, then continue with an introduction to the classical Ehrenfeucht-Fraïssé games, and then look at these games for uncountable structures. We will see how they lead to large Aronszajn trees and the notion of weak embeddability between them. The notion of weak embeddability between ordered structures goes back to the early post-Cantor era (e.g. in a 1915 paper by Hartogs), possibly in a different terminology. The notion has attracted attention in various mathematical contexts after being explored and popularised by Todorcevic, Mekler and Väänänen. Part of the talk will be devoted to this topic. I will discuss the concept of weak embeddability between ordered structures, emphasising its historical significance and mathematical importance. I will mention recent progress on the famous problem of a universal tree in the class of (wide) Aronszajn trees. If time permits, I will also present a proof sketch showing that the universality number of (wide) Aronszajn trees is never the first uncountable cardinal number.
Venue: Niavaran, Lecture Hall 2

4 DEC 2023
11:00 - 12:00

Abstract:

The theory of the strong force, quantum chromodynamics, describes the proton in terms of quarks and gluons. The proton is a state of two up quarks and one down quark bound by gluons, but quantum theory predicts that in addition there is an infinite number of quark-antiquark pairs. Both light and heavy quarks, whose mass is respectively smaller or bigger than the mass of the proton, are revealed inside the proton in high-energy collisions. However, it is unclear whether heavy quarks also exist as a part of the proton wavefunction, which is determined by non-perturbative dynamics and accordingly unknown: so-called intrinsic heavy quarks. It has been argued for a long time that the proton could have a sizable intrinsic component of the lightest heavy quark, the charm quark. Innumerable efforts to establish intrinsic charm in the proton have remained inconclusive. Here we provide evidence for intrinsic charm by exploiting a high-precision determination of the quark-gluon content of the nucleon based on machine learning and a large experimental dataset. We disentangle the intrinsic charm component from charm-anticharm pairs arising from high-energy radiation. We establish the existence of intrinsic charm at the 3-standard-deviation level, with a momentum distribution in remarkable agreement with model predictions. We confirm these findings by comparing to very recent data on Z-boson production with charm jets from the LHCb experiment.

Based on:
https://arxiv.org/abs/2208.08372

Meeting Place:
Seminar Room, School of Particles and Accelerators, IPM

Link to Join Virtually:
https://meet.google.com/fnv-dfkk-ghb

Link: https://meet.google.com/fnv-dfkk-ghb

7 DEC 2023
11:00 - 12:30

The Ehrenfeucht-Fraïssé games and their variants are a natural game-theoretic tool for investigating the similarity and dissimilarity between two mathematical structures. Although the study of these games is quite different in finite and infinite model theory, one might ask: if not all natural numbers are equal, why should all infinities be equal? In fact, it is within the framework of countably infinite model theory, not infinite model theory, that these games are often successful!
Even at the level of the first uncountable cardinal, the picture is very mixed, but this is not surprising: The Sikorski extension theorem vs. non-trivial forcing axioms, countability and uncountability in Shelah's classification theory, descriptive set theory vs. generalised descriptive set theory.

In this series of lectures (for some n> 1) I will talk about an area of research that started in the early 1990s and is an intersection of several independent topics.
The lectures will start with a brief introduction to infinite games, then continue with an introduction to the classical Ehrenfeucht-Fraïssé games, and then look at these games for uncountable structures. We will see how they lead to large Aronszajn trees and the notion of weak embeddability between them. The notion of weak embeddability between ordered structures goes back to the early post-Cantor era (e.g. in a 1915 paper by Hartogs), possibly in a different terminology. The notion has attracted attention in various mathematical contexts after being explored and popularised by Todorcevic, Mekler and Väänänen. Part of the talk will be devoted to this topic. I will discuss the concept of weak embeddability between ordered structures, emphasising its historical significance and mathematical importance. I will mention recent progress on the famous problem of a universal tree in the class of (wide) Aronszajn trees. If time permits, I will also present a proof sketch showing that the universality number of (wide) Aronszajn trees is never the first uncountable cardinal number.


Venue: Niavaran, Lecture Hall 2