Events
Department of Mathematics and Statistics
Texas Tech University
Plasmodium falciparum is the most virulent malaria species that affects humans. During its lifecycle, the parasite exists in two forms, asexual and sexual. Within the human host, the asexual parasites primarily replicate in the bloodstream. During the replication cycle, some asexual parasites commit to produce sexual parasites, which cannot reproduce in the human host. The sexual parasites are necessary continue the malaria life-cycle through the mosquito host. The proportion of asexual parasites committed to forming sexual parasites in a given replication cycle is known as the “conversion rate.” The determination of the conversion rate is paramount to the understanding of the transmission and therefore control of Plasmodium falciparum. In 2000, Diebner et al. created a collection of deterministic models for the sexual parasite levels determined by conversion rate, asexual parasite levels, and sexual parasite mortality. Continuing this work in 2001, Eichner et al. determined a range of conversion rates through fitting their chosen best model from Diebner et al. to over 100 individual patient infections. The range of conversion rates generated from this work is used in some modelling studies. Here, we evaluate the practical identifiability of parameters for the chosen best model and simplifications of this model. Focusing on a small collection of well-documented patients, we fit all parameters of the model, including the conversion rates, and obtain predicted sexual parasite levels. Using these predicted trajectories as a baseline truth, we simulate a collection of sexual parasite trajectories with varying levels of noise. We fit all parameters for each simulated data set in the collection and then evaluate the measure of accuracy to our original parameters to determine if we have practical identifiability. We find that we do not have practical identifiability of parameters, except for one patient with the simplest model assumptions. Without parameter identifiability, the reported conversion rates may need to be reconsidered.
Zoom link:
https://texastech.zoom.us/j/94471029838?pwd=ZlJXR2JhU0ZjUHhYOUlmVGN3VFFJUT09
In this talk, I will talk about our recent work with Professor Chao Zhu on the mean-filed control problem with non-exponential discounting cost for general stochastic diffusions. Our problem exhibits two types of time-inconsistency at the same time: non-exponential discounting and mean-field interactions. By solving a backward equilibrium Hamilton--Jacobi--Bellman equation coupled with a forward distribution-dependent stochastic differential equation, we investigate the existence and uniqueness of a closed-loop Makovian equilibrium. Moreover, a special case of semilinear dynamics with a quadratic-type cost functional is considered due to its special structure.
Please attend this week's Statistics seminar at 4 PM (UT-6) Monday the 14th via this Zoom link.
Meeting ID: 916 8811 0314
Passcode: 477557
The origins of the Improved New Intersection Theorem can be traced
back to the following linear algebra exercise: let U,V and W be vector
spaces over a field such that U and V are contained in W, then the
dimension of of the intersection of U and V is at least dim U+dim
V-dim W. In their most modern forms, the intersection theorems are
concerned with bounding the length of finite free complexes over local
rings. In this talk, we will explore the history of these theorems,
culminating in a result due to L. Christensen and me.
Follow the talk this Zoom link
Meeting ID: 990 5902 7169
Passcode: 648002
It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN can accurately approximate any nonlinear continuous operator. This universal approximation theorem of operators is suggestive of the structure and potential of deep neural networks (DNNs) in learning continuous operators or complex systems from streams of scattered data. In this talk, I will present the deep operator network (DeepONet) to learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. I will also present several extensions of DeepONet, such as DeepM&Mnet for multiphysics problems, DeepONet with proper orthogonal decomposition (POD-DeepONet), MIONet for multiple-input operators, and multifidelity DeepONet. More generally, DeepONet can learn multiscale operators spanning across many scales and trained by diverse sources of data simultaneously. I will demonstrate the effectiveness of DeepONet and its extensions to diverse multiphysics and multiscale problems, such as nanoscale heat transport, bubble growth dynamics, high-speed boundary layers, electroconvection, and hypersonics.
Please attend this week's Applied Math seminar at 4 PM Wednesday via this Zoom link.
Meeting ID: 976 3095 1027
Passcode: applied
Statistical analysis and stochastic interest rate modelling for valuing the future
with implications in climate change mitigation
High future discounting rates favor inaction on present expending while lower rates advise
for a more immediate political action. A possible approach to this key issue in global
economy is to take historical time series for nominal interest rates and inflation,
and to construct then real interest rates and finally obtaining the resulting discount
rate according to a specific stochastic model. Extended periods of negative real interest rates,
in which inflation dominates over nominal rates, are commonly observed, occurring in many
epochs and in all countries.
This feature leads us to choose a well-known model in statistical physics,
the Ornstein-Uhlenbeck model, as a basic dynamical tool in which real interest rates
randomly fluctuate and can become negative, even if they tend to revert to a positive mean value.
By covering 14 countries over hundreds of years we suggest different scenarios and include
an error analysis in order to consider the impact of statistical uncertainty in our results.
We find that only 4 of the countries have positive long-run discount rates while the other ten
countries have negative rates.
Even if one rejects the countries where hyperinflation has occurred, our results support
the need to consider low discounting rates.
The results provided by these fourteen countries significantly increase the priority of
confronting global actions such as climate change mitigation.
We finally extend the analysis by first allowing for fluctuations of the mean level in
the Ornstein-Uhlenbeck model and secondly by considering modified versions of the Feller
and lognormal models.
In both cases, results remain basically unchanged thus demonstrating the robustness of
the results presented.