Talks

The phase diagram of a material is of central importance in describing the properties and behaviour of a condensed matter system. Indeed, the study of quantum phase transitions has formed a central part of 20th and 21st Century physics. We examine the complexity and computability of determining the phase diagram of a general Hamiltonian. We show that in the worst case it is uncomputable and in more restricted cases, where the Hamiltonian is “better behaved”, it remains computationally intractable even for a quantum computer. Finally, we take a look at the relations between the Renormalization Group and uncomputable Hamiltonians.

Zoom Link: https://pitp.zoom.us/j/96048987715?pwd=WGtwWk1SUnFsanNIVTZVYjNmbTh3Zz09

Abstract The dynamics of an infectious disease is usually approached at the population scale. However, the event of an epidemic outbreak depends on the existence of an active infection at the level of the  individual. A full study of the interaction between the infection of hosts and its transmission in the population requires the incorporation of many factors such as physiological age, age of infection, risk conditions, contact structures and other variables involving different spatial and temporal scales. Nevertheless, simple models can still give some insight on the intricate mechanisms of interactions necessary for the occurrence of an epidemic outbreak, in particular, one can explore the role that the reproductive numbers at the between-host and within-host levels play. In this talk I will review some results on the epidemiology of between-host, within host interactions.

Abstract We will discuss some adaptations of the standard epidemic models to incorporate various kinds of restrictions on the interaction between susceptible and infected individuals and study the effect of such restrictions on the prognosis of an epidemic. In one case, we study the effect of avoiding known infected neighbors on the persistence of a recurring infection process. In another case, we develop a flexible mathematical framework for pool-testing and badging protocol in the context of controlling contagious epidemics and tackling the far-reaching associated challenges, including understanding and evaluating individual and collective risks of returning prior infected individuals to normal society and other economic and social arrangements and interventions to protect against disease.

Abstract TBA

Zoom link:  https://pitp.zoom.us/j/91804523922?pwd=M0NBa21NVklLUjBiY2pPR1ExdXZxQT09

Abstract The novel coronavirus that emerged in December 2019, COVID-19, is the greatest public health challenge humans have faced since the 1918 influenza pandemic (it has so far caused over 615 million confirmed cases and 6.5 million deaths). In this talk, I will present some mathematical models for assessing the population-level impact of the various intervention strategies (pharmaceutical and non-pharmaceutical) being used to control and mitigate the burden of the pandemic. Continued human interference with the natural ecosystems, such as through anthropogenic climate change, environmental degradation, and land use changes, make us increasingly vulnerable to the emergence, re-emergence and resurgence of infectious diseases (particularly respiratory pathogens with pandemic potential). I will discuss some of the lessons learned from our COVID-19 modeling studies and propose ways to mitigate the next respiratory pandemic.

Models of dark sectors with a mass threshold can have important cosmological signatures. If, in the era prior to recombination, a relativistic species becomes non-relativistic and is then depopulated in equilibrium, there can be measurable impacts on the CMB as the entropy is transferred to lighter relativistic particles. In particular, if this "step'" occurs near z = 20,000, the model can naturally accommodate larger values of $H_0$. If this stepped radiation is additionally coupled to dark matter, there can be a meaningful impact on the matter power spectrum as dark matter can be coupled via a species that becomes non-relativistic and depleted. This can naturally lead to suppressed power at scales inside the sound horizon before the step, while leaving conventional CDM signatures for power outside the sound horizon. We study these effects and show such models can naturally provide lower values of $S_8$ than scenarios without a step. This suggests these models may provide an interesting framework to address the $S_8$ tension, both in concert with the $H_0$ tension and without.

Zoom Link:  https://pitp.zoom.us/j/96399847158?pwd=RkNHMkJHeEo5Q1Q2MkhHSHZ6c1BoQT09

Abstract Throughout the coronavirus disease 2019 (COVID-19) pandemic, countries have relied on a variety of ad hoc border control protocols to allow for non-essential travel while safeguarding public health, from quarantining all travellers to restricting entry from select nations on the basis of population-level epidemiological metrics such as cases, deaths or testing positivity rates. Here we report the design and performance of a reinforcement learning system, nicknamed Eva. In the summer of 2020, Eva was deployed across all Greek borders to limit the influx of asymptomatic travellers infected with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), and to inform border policies through real-time estimates of COVID-19 prevalence. In contrast to country-wide protocols, Eva allocated Greece’s limited testing resources on the basis of incoming travellers’ demographic information and testing results from previous travellers. By comparing Eva’s performance against modelled counterfactual scenarios, we show that Eva identified 1.85 times as many asymptomatic, infected travellers as random surveillance testing, with up to 2–4 times as many during peak travel, and 1.25–1.45 times as many asymptomatic, infected travellers as testing policies that utilize only epidemiological metrics. We demonstrate that this latter benefit arises, at least partially, because population-level epidemiological metrics had limited predictive value for the actual prevalence of SARS-CoV-2 among asymptomatic travellers and exhibited strong country-specific idiosyncrasies in the summer of 2020. Our results raise serious concerns on the effectiveness of country-agnostic internationally proposed border control policies that are based on population-level epidemiological metrics. Instead, our work represents a successful example of the potential of reinforcement learning and real-time data for safeguarding public health. Joint work with Kimon Drakopoulos, Vishal Gupta, Ioannis Vlachogiannis, Christos Hadjichristodoulou, Pagona Lagiou, Gkikas Magiorkinis, Dimitrios Paraskevis and Sotirios Tsiodras.

Abstract Motivated by the discovery of hard-to-find social networks (such as MSM or A natural and well-known way to dPWIDs) or by finding contact-tracing strategies, we consider the question of exploring the topology of random structures (such as a random graph G) by random walks. The usual random walk jumps from a vertex of G to a neighboring vertex, providing information on the connected components of the graph G. The number of these connected components is the Betti number beta0. To gather further information on the higher Betti numbers that describe the topology of the graph, we can consider the simplicial complex C associated to the graph G: a k-simplex (edge for k=1, triangle for k=2, tetrahedron for k=3 etc.) belongs to C if all the lower (k-1)-simplices that constitute it also belong to the C. For example, a triangle belongs to C if its three edges are in the graph G. Several random walks have already been propose recently to explore these structures, mostly in Informatics Theory. We propose a new random walk, whose generator is related to a Laplacian of higher order of the graph, and to the Betti number betak. A rescaling of the walk for k=2 (cycle-valued random walk) is also detailed when the random walk visits a regular triangulation of the torus. We embed the space of chains into spaces of currents to establish the limiting theorem. Joint work with T. Bonis, L. Decreusefond and Z. Zhang.

Abstract We study a non-Markovian individual-based stochastic spatial epidemic model where the number of locations and the number of individuals at each location both grow to infinity while satisfying certain growth condition. Each individual is associated with a random infectivity function, which depends on the age of infection. The rate of infection at each location takes an averaging effect of infectivity from all the locations. The epidemic dynamics in each location is described by the total force of infection, the number of susceptible individuals, the number of infected individuals that are infected at each time and have been infected for a certain amount of time, as well as the number of recovered individuals. The processes can be described using a time-space representation. We prove a functional law of large numbers for these time-space processes, and in the limit, we obtain a set of time-space integral equations together with the limit of the number of infected individuals tracking the age of infection as a time-age-space integral equation. Joint work with G. Pang (Rice Univ)

Abstract People's interaction networks play a critical role in epidemics. However, precise mapping of the network structure is often expensive or even impossible. I will show that it is unnecessary to map the entire network. Instead, contact tracing a few samples from the population is enough to estimate an outbreak's likelihood and size. More precisely, I start by studying a simple epidemic model where one node is initially infected, and an infected node transmits the disease to its neighbors independently with probability p. In this model, I will present a nonparametric estimator on the likelihood of an outbreak based on local graph features and give theoretical guarantees on the estimator's accuracy for a large class of networks. Finally, I will extend the result to the general SIR model with random recovery time: Local graph features are enough to predict the time evolution of epidemics on a large class of networks.