Talks

Abstract This work connects models for virus spread on networks with their equivalent neural network representations. Based on this connection, we propose a new neural network architecture, called Transmission Neural Networks (TransNNs) where activation functions are primarily associated with links and are allowed to have different activation levels. This connection also leads to the discovery and the derivation of three new activation functions with tunable or trainable parameters. We show that TransNNs with a single hidden layer and a fixed non-zero bias term are universal function approximators. Moreover, we establish threshold conditions for virus spread on networks where the dynamics are characterized by TransNNs. Finally, we present new derivations of continuous time epidemic models on networks based on TransNNs. *This is joint work with Peter E. Caines.

Abstract Dengue virus is the most significant viral mosquito-borne infection in terms of its human impact. Mathematical modeling has contributed to our understanding of its transmission and control strategies aimed at halting its spread. We consider the spread of dengue at the level of a city. Because the Aedes aegypti mosquito that transmits dengue has relatively low dispersal over its lifetime, human movement plays a major role in its spread and the household is a key spatial scale on which transmission occurs. Simple multi-patch deterministic models---metapopulation models, which consider the population to be described as a network of well-mixed patches---have been used to model city-level spatial spread and can provide expressions for key epidemiological quantities such as the basic reproduction number, $R_0$. We compare dynamics predicted by such models with results from individual-based network models and illustrate several discrepancies. We argue that the small size of households and local depletion of susceptibles are key features of the dynamics that are not captured in the standard $R_0$ analysis of the ODE model. In order to gain analytic understanding, we propose the use of household-level models, which can be analyzed using branching process theory. Our work, which echoes results previously found for directly-transmitted infections, highlights the importance of correctly accounting for the relevant spatial scales on which transmission occurs

Abstract The ongoing COVID-19 pandemic has had devastating impacts on global public health and socioeconomic stability. Although highly efficacious COVID-19 vaccines were developed at an unprecedented rate, the ongoing evolution of SARS-CoV-2 and consequential changes in infectivity and immunological resistance of new variants continues to present challenges. Computing the growth rates of emerging variants is complicated by many issues, including vaccine uptake, regional levels of prior infection, viral resistance to protective antibodies, and the relative infectivity of new variants in complex populations. While epidemic forecasting has played an important role in decision-making, forecast accuracy has been limited, especially at key tipping points in the pandemic, by the inability to incorporate important factors, such as the emergence of phenotypically novel variants. In this talk, I will describe a flexible strategy to characterize variant transition dynamics through three simple summaries, the speed, the relative timing, and the magnitude of the variant transition. This foundational research is intended to better understand the implication of SARS-CoV-2 evolution to ultimately inform regional epidemiological forecasting.  

Bang Nucleosynthesis (BBN) is one of the greatest outcome of the Standard Model of Particle Physics when put next to ΛCDM cosmology. In this talk, I will first review the key aspects of standard BBN and illustrate a new code -- PRyMordial -- to make state-of-the-art predictions of primordial light-element abundances within and beyond the Standard Model. I will then highlight the latest measurements regarding the primordial abundance of helium-4 and deuterium, and present evidence at the 2 sigma level for a nonzero lepton asymmetry from BBN data jointly with the Cosmic Microwave Background. I will leave some final comments on how a large total lepton asymmetry can be consistently realized in the Early Universe.

Zoom Link: https://pitp.zoom.us/j/95011247645?pwd=S0EwZG9nSHQvTjV0QjBxeHNUWWtmUT09

Abstract Online social networks often mirror community formation in real-world networks (based on common demographics, interests, or affinities). Such patterns are often picked up and used by algorithms that leverage social data for the purpose of providing recommendations, diffusing information, or forming groups. In this talk, we'll discuss the influence maximization problem where multiple communities exist, showing that common centrality metrics may exclude minority communities from adopting the information diffused. Using the preferential attachment model with unequal communities, we'll characterize the relationship between homophily, network centrality, and bias through the power-law degree distributions of the nodes, and study the conditions in which diversity interventions can actually yield more efficient and equitable outcomes. We find a theoretical condition on the seedset size that explains the potential trade-off between outreach and diversity in information diffusion. To wrap up, we’ll discuss a novel set of algorithms that leverage the network structure to maximize the diffusion of a message while not creating disparate impact among participants based on community affiliation.

Abstract We study how communication platforms can improve social learning without censoring or fact-checking messages, when they have members who deliberately and/or inadvertently distort information. Message fidelity depends on social network depth (how many times information can be relayed) and breadth (the number of others with whom a typical user shares information). We characterize how the expected number of true minus false messages depends on breadth and depth of the network and the noise structure. Message fidelity can be improved by capping depth or, if that is not possible, limiting breadth, e.g., by capping the number of people to whom someone can forward a given message. Although caps reduce total communication, they increase the fraction of received messages that have traveled shorter distances and have had less opportunity to be altered, thereby increasing the signal-to-noise ratio.  

One fruitful strategy of tackling quantum gravity is to adapt quantum field theory to the situation where spacetime geometry is dynamical, and to implement diffeomorphism symmetry in a way that is compatible with regularization and renormalization. It has taken a while to address the underlying technical and conceptual challenges and to chart a quantum field-theoretic path toward a theory of quantum gravity that is unitary, essentially unique and can produce "numbers" beyond perturbation theory. In this context, the formulation of Causal Dynamical Triangulations (CDT) is a quantum-gravitational analogue of what lattice QCD is to nonabelian gauge theory. Its nonperturbative toolbox builds on the mathematical principles of “random geometry” and allows us to shift emphasis from formal considerations to extracting quantitative results on the spectra of invariant quantum observables at or near the Planck scale. A breakthrough result of CDT quantum gravity in four dimensions is the emergence, from first principles, of a nonperturbative vacuum state with properties of a de Sitter universe. I will summarize these findings, highlight the nonlocal character of observables in quantum gravity and describe the interesting physics questions that are being tackled using the new notion of quantum Ricci curvature.

Zoom Link: https://pitp.zoom.us/j/92791576774?pwd=VEg3MEdKOWsxOEhXOHVIQUhPcUt0UT09

Abstract Identifying the optimal set of individuals to first receive information (‘seeds’) in a social network is a widely-studied question in many settings, such as diffusion of information, spread of microfinance programs, and adoption of new technologies. Numerous studies have proposed various network-centrality based heuristics to choose seeds in a way that is likely to boost diffusion. Here we show that, for the classic SIR model of diffusion and some of its generalizations, randomly seeding s + x individuals can prompt a larger diffusion than optimally targeting the best s individuals, for a small x. We prove our results for large classes of random networks, and verify them in several small, real-world networks. Our results identify practically relevant settings under which collecting and analyzing network data to boost diffusion is not cost-effective.