12,574 research outputs found
Tensor product approach to modelling epidemics on networks
To improve mathematical models of epidemics it is essential to move beyond the traditional assumption of homogeneous well--mixed population and involve more precise information on the network of contacts and transport links by which a stochastic process of the epidemics spreads. In general, the number of states of the network grows exponentially with its size, and a master equation description suffers from the curse of dimensionality. Almost all methods widely used in practice are versions of the stochastic simulation algorithm (SSA), which is notoriously known for its slow convergence. In this paper we numerically solve the chemical master equation for an SIR model on a general network using recently proposed tensor product algorithms. In numerical experiments we show that tensor product algorithms converge much faster than SSA and deliver more accurate results, which becomes particularly important for uncovering the probabilities of rare events, e.g. for number of infected people to exceed a (high) threshold
Techniques for high-multiplicity scattering amplitudes and applications to precision collider physics
In this thesis, we present state-of-the-art techniques for the computation of scattering amplitudes in Quantum Field Theories. Following an introduction to the topic, we describe a robust framework that enables the calculation of multi-scale two-loop amplitudes directly relevant to modern particle physics phenomenology at the Large Hadron Collider and beyond. We discuss in detail the use of finite fields to bypass the algebraic complexity of such computations, as well as the method of integration-by-parts relations and differential equations. We apply our framework to calculate the two-loop amplitudes contributing to three process: Higgs boson production in association with a bottom-quark pair, W boson production with a photon and a jet, as well as lepton-pair scattering with an off-shell and an on-shell photon. Finally, we draw our conclusions and discuss directions for future progress of amplitude computations
New techniques for integrable spin chains and their application to gauge theories
In this thesis we study integrable systems known as spin chains and their applications to the study of the AdS/CFT duality, and in particular to N “ 4 supersymmetric Yang-Mills theory (SYM) in four dimensions.First, we introduce the necessary tools for the study of integrable periodic spin chains, which are based on algebraic and functional relations. From these tools, we derive in detail a technique that can be used to compute all the observables in these spin chains, known as Functional Separation of Variables. Then, we generalise our methods and results to a class of integrable spin chains with more general boundary conditions, known as open integrable spin chains.In the second part, we study a cusped Maldacena-Wilson line in N “ 4 SYM with insertions of scalar fields at the cusp, in a simplifying limit called the ladders limit. We derive a rigorous duality between this observable and an open integrable spin chain, the open Fishchain. We solve the Baxter TQ relation for the spin chain to obtain the exact spectrum of scaling dimensions of this observable involving cusped Maldacena-Wilson line.The open Fishchain and the application of Functional Separation of Variables to it form a very promising road for the study of the three-point functions of non-local operators in N “ 4 SYM via integrability
The infrared structure of perturbative gauge theories
Infrared divergences in the perturbative expansion of gauge theory amplitudes and cross sections have been a focus of theoretical investigations for almost a century. New insights still continue to emerge, as higher perturbative orders are explored, and high-precision phenomenological applications demand an ever more refined understanding. This review aims to provide a pedagogical overview of the subject. We briefly cover some of the early historical results, we provide some simple examples of low-order applications in the context of perturbative QCD, and discuss the necessary tools to extend these results to all perturbative orders. Finally, we describe recent developments concerning the calculation of soft anomalous dimensions in multi-particle scattering amplitudes at high orders, and we provide a brief introduction to the very active field of infrared subtraction for the calculation of differential distributions at colliders. © 2022 Elsevier B.V
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Model-Predictive Control with New NUV Priors
Normals with unknown variance (NUV) can represent many useful priors
including norms and other sparsifying priors, and they blend well with
linear-Gaussian models and Gaussian message passing algorithms. In this paper,
we elaborate on recently proposed discretizing NUV priors, and we propose new
NUV representations of half-space constraints and box constraints. We then
demonstrate the use of such NUV representations with exemplary applications in
model predictive control, with a variety of constraints on the input, the
output, or the internal stateof the controlled system. In such applications,
the computations boil down to iterations of Kalman-type forward-backward
recursions, with a complexity (per iteration) that is linear in the planning
horizon. In consequence, this approach can handle long planning horizons, which
distinguishes it from the prior art. For nonconvex constraints, this approach
has no claim to optimality, but it is empirically very effective
Non-perturbative renormalization group analysis of nonlinear spiking networks
The critical brain hypothesis posits that neural circuits may operate close
to critical points of a phase transition, which has been argued to have
functional benefits for neural computation. Theoretical and computational
studies arguing for or against criticality in neural dynamics largely rely on
establishing power laws or scaling functions of statistical quantities, while a
proper understanding of critical phenomena requires a renormalization group
(RG) analysis. However, neural activity is typically non-Gaussian, nonlinear,
and non-local, rendering models that capture all of these features difficult to
study using standard statistical physics techniques. Here, we overcome these
issues by adapting the non-perturbative renormalization group (NPRG) to work on
(symmetric) network models of stochastic spiking neurons. By deriving a pair of
Ward-Takahashi identities and making a ``local potential approximation,'' we
are able to calculate non-universal quantities such as the effective firing
rate nonlinearity of the network, allowing improved quantitative estimates of
network statistics. We also derive the dimensionless flow equation that admits
universal critical points in the renormalization group flow of the model, and
identify two important types of critical points: in networks with an absorbing
state there is Directed Percolation (DP) fixed point corresponding to a
non-equilibrium phase transition between sustained activity and extinction of
activity, and in spontaneously active networks there is a \emph{complex valued}
critical point, corresponding to a spinodal transition observed, e.g., in the
Lee-Yang model of Ising magnets with explicitly broken symmetry. Our
Ward-Takahashi identities imply trivial dynamical exponents in
both cases, rendering it unclear whether these critical points fall into the
known DP or Ising universality classes
Machine learning applications in search algorithms for gravitational waves from compact binary mergers
Gravitational waves from compact binary mergers are now routinely observed by Earth-bound detectors. These observations enable exciting new science, as they have opened a new window to the Universe.
However, extracting gravitational-wave signals from the noisy detector data is a challenging problem. The most sensitive search algorithms for compact binary mergers use matched filtering, an algorithm that compares the data with a set of expected template signals. As detectors are upgraded and more sophisticated signal models become available, the number of required templates will increase, which can make some sources computationally prohibitive to search for. The computational cost is of particular concern when low-latency alerts should be issued to maximize the time for electromagnetic follow-up observations. One potential solution to reduce computational requirements that has started to be explored in the last decade is machine learning. However, different proposed deep learning searches target varying parameter spaces and use metrics that are not always comparable to existing literature. Consequently, a clear picture of the capabilities of machine learning searches has been sorely missing.
In this thesis, we closely examine the sensitivity of various deep learning gravitational-wave search algorithms and introduce new methods to detect signals from binary black hole and binary neutron star mergers at previously untested statistical confidence levels. By using the sensitive distance as our core metric, we allow for a direct comparison of our algorithms to state-of-the-art search pipelines. As part of this thesis, we organized a global mock data challenge to create a benchmark for machine learning search algorithms targeting compact binaries. This way, the tools developed in this thesis are made available to the greater community by publishing them as open source software.
Our studies show that, depending on the parameter space, deep learning gravitational-wave search algorithms are already competitive with current production search pipelines. We also find that strategies developed for traditional searches can be effectively adapted to their machine learning counterparts. In regions where matched filtering becomes computationally expensive, available deep learning algorithms are also limited in their capability. We find reduced sensitivity to long duration signals compared to the excellent results for short-duration binary black hole signals
Emergence of common concepts, symmetries and conformity in agent groups—an information-theoretic model
© 2023 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/The paper studies principles behind structured, especially symmetric, representations through enforced inter-agent conformity. For this, we consider agents in a simple environment who extract individual representations of this environment through an information maximization principle. The representations obtained by different agents differ in general to some extent from each other. This gives rise to ambiguities in how the environment is represented by the different agents. Using a variant of the information bottleneck principle, we extract a ‘common conceptualization’ of the world for this group of agents. It turns out that the common conceptualization appears to capture much higher regularities or symmetries of the environment than the individual representations. We further formalize the notion of identifying symmetries in the environment both with respect to ‘extrinsic’ (birds-eye) operations on the environment as well as with respect to ‘intrinsic’ operations, i.e. subjective operations corresponding to the reconfiguration of the agent’s embodiment. Remarkably, using the latter formalism, one can re-wire an agent to conform to the highly symmetric common conceptualization to a much higher degree than an unrefined agent; and that, without having to re-optimize the agent from scratch. In other words, one can ‘re-educate’ an agent to conform to the de-individualized ‘concept’ of the agent group with comparatively little effort.Peer reviewe
"What if?" in Probabilistic Logic Programming
A ProbLog program is a logic program with facts that only hold with a
specified probability. In this contribution we extend this ProbLog language by
the ability to answer "What if" queries. Intuitively, a ProbLog program defines
a distribution by solving a system of equations in terms of mutually
independent predefined Boolean random variables. In the theory of causality,
Judea Pearl proposes a counterfactual reasoning for such systems of equations.
Based on Pearl's calculus, we provide a procedure for processing these
counterfactual queries on ProbLog programs, together with a proof of
correctness and a full implementation. Using the latter, we provide insights
into the influence of different parameters on the scalability of inference.
Finally, we also show that our approach is consistent with CP-logic, i.e. with
the causal semantics for logic programs with annotated with disjunctions
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