Long-time Behavior of State Functions for Badyko Models

In this note we examine the long-time behavior of state functions for a climate energy balance model (Budyko Model) in the strongest topologies of the phase and the extended phase spaces. Strongest convergence results for all weak solutions are obtained. New structure and regularity properties for global and trajectory attractors are justified

Uniform global attractors for non-autonomous dissipative dynamical systems

In this paper we consider sufficient conditions for the existence of uniform compact global attractor for non-autonomous dynamical systems in special classes of infinite-dimensional phase spaces. The obtained generalizations allow us to avoid the restrictive compactness assumptions on the space of shifts of non-autonomous terms in particular evolution problems. The results are applied to several evolution inclusions

Radiation and the Risk of Chronic Lymphocytic and Other Leukemias among Chornobyl Cleanup Workers

Background: Risks of most types of leukemia from exposure to acute high doses of ionizing radiation are well known, but risks associated with protracted exposures, as well as associations between radiation and chronic lymphocytic leukemia (CLL), are not clear.
 Objectives: We estimated relative risks of CLL and non-CLL from protracted exposures to low-dose ionizing radiation.
 Methods: A nested case–control study was conducted in a cohort of 110,645 Ukrainian cleanup workers of the 1986 Chornobyl nuclear power plant accident. Cases of incident leukemia diagnosed in 1986–2006 were confirmed by a panel of expert hematologists/hematopathologists. Controls were matched to cases on place of residence and year of birth. We estimated individual bone marrow radiation doses by the Realistic Analytical Dose Reconstruction with Uncertainty Estimation (RADRUE) method. We then used a conditional logistic regression model to estimate excess relative risk of leukemia per gray (ERR/Gy) of radiation dose.
 Results: We found a significant linear dose response for all leukemia [137 cases, ERR/Gy = 1.26 (95% CI: 0.03, 3.58]. There were nonsignificant positive dose responses for both CLL and non-CLL (ERR/Gy = 0.76 and 1.87, respectively). In our primary analysis excluding 20 cases with direct in-person interviews less than 2 years from start of chemotherapy with an anomalous finding of ERR/Gy = –0.47 (95% CI: less than –0.47, 1.02), the ERR/Gy for the remaining 117 cases was 2.38 (95% CI: 0.49, 5.87). For CLL, the ERR/Gy was 2.58 (95% CI: 0.02, 8.43), and for non-CLL, ERR/Gy was 2.21 (95% CI: 0.05, 7.61). Altogether, 16% of leukemia cases (18% of CLL, 15% of non-CLL) were attributed to radiation exposure.
 Conclusions: Exposure to low doses and to low dose-rates of radiation from post-Chornobyl cleanup work was associated with a significant increase in risk of leukemia, which was statistically consistent with estimates for the Japanese atomic bomb survivors. Based on the primary analysis, we conclude that CLL and non-CLL are both radiosensitive.

PROCESSING NETWORK CONTROLS VIA DEEP REINFORCEMENT LEARNING

173 pagesNovel advanced policy gradient (APG) algorithms, such as proximal policy optimization (PPO), trust region policy optimization, and their variations, have become the dominant reinforcement learning (RL) algorithms because of their ease of implementation and good practical performance. This dissertation is concerned with theoretical justification and practical application of the APG algorithms for solving processing network control optimization problems. Processing network control problems are typically formulated as Markov decision process (MDP) or semi-Markov decision process (SMDP) problems that have several unconventional for RL features: infinite state spaces, unbounded costs, long-run average cost objectives. Policy improvement bounds play a crucial role in the theoretical justification of the APG algorithms. In this thesis we refine existing bounds for MDPs with finite state spaces and prove novel policy improvement bounds for classes of MDPs and SMDPs used to model processing network operations. We consider two examples of processing network control problems and customize the PPO algorithm to solve them. First, we consider parallel-server and multiclass queueing networks controls. Second, we consider the drivers repositioning problem in a ride-hailing service system. For both examples the PPO algorithm with auxiliary modifications consistently generates control policies that outperform state-of-art heuristics

Lyapunov Functions for Weak Solutions of Reaction-Diffusion Equations with Discontinuous Interaction Functions and its Applications

In this paper we investigate additional regularity properties for global and trajectory attractors of all globally defined weak solutions of semi-linear parabolic differential reaction-diffusion equations with discontinuous nonlinearities, when initial data uτ ∈ L2(Ω). The main contributions in this paper are: (i) sufficient conditions for the existence of a Lyapunov function for all weak solutions of autonomous differential reaction-diffusion equations with discontinuous and multivalued interaction functions; (ii) convergence results for all weak solutions in the strongest topologies; (iii) new structure and regularity properties for global and trajectory attractors. The obtained results allow investigating the long-time behavior of state functions for the following problems: (a) a model of combustion in porous media; (b) a model of conduction of electrical impulses in nerve axons; (c) a climate energy balance model; (d) a parabolic feedback control problem