On the kinetic Fokker-Planck equation in the half-space with absorbing barriers

Abstract

of 4T1 Metastatic Breast Cancer with Combined Hypofractionated Irradiation and Autologous T-Cell Infusion. Radiat. Res. 182, 163-169 (2014).The goal of this study was to determine whether a combination of local tumor irradiation and autologous T-cell transplantation can effectively treat metastatic 4T1 breast cancer in mice. BALB/c mice were injected subcutaneously with luciferase-labeled 4T1 breast tumor cells and allowed to grow for 21 days, at which time metastases appeared in the lungs. Primary tumors were treated at that time with 3 daily fractions of 20 Gy of radiation each. Although this approach could eradicate primary tumors, tumors in the lungs grew progressively. We attempted to improve efficacy of the radiation by adding autologous T-cell infusions. Accordingly, T cells were purified from the spleens of tumor-bearing mice after completion of irradiation and cryopreserved. Cyclophosphamide was administered thereafter to induce lymphodepletion, followed by T-cell infusion. Although the addition of cyclophosphamide to irradiation did not improve survival or reduce tumor progression, the combination of radiation, cyclophosphamide and autologous T-cell infusion induced durable remissions and markedly improved survival. We conclude that the combination of radiation and autologous Tcell infusion is an effective treatment for metastatic 4T1 breast cancer.

The model reduction of the Vlasov–Poisson–Fokker–Planck system to the Poisson–Nernst–Planck system via the Deep Neural Network Approach

“…The authors in [38] considered the global well-posedness of the nonlinear Fokker-Planck equation with the specular reflection boundary. Also, the well-posedness and regularity for different boundary conditions to the kinetic Fokker-Planck equation has been studied in [45][46][47][48][49][50][51][52].…”

“…Therefore, we introduce our second main theorem, Theorem 4.7, which shows that the DNN solutions converge to an analytic solution in a suitable function space when we minimize the total loss function Loss f p T otal . We assume that our compact domain V = [−10, 10] of the v-variable is chosen sufficiently large so that we can have (46) ||f…”

“…for some positive constant C 1 , C 2 , C 3 , and C 4 by the use of Young's inequality. Note that E L 1 x is also bounded as we have f ∈Ĉ (1,1,2) on the compact domain and we also have (46). Then, we can reduce (64) to (71) d dt…”

Pencil-beam approximation of fractional Fokker-Planck

“…Proof. We follow [21]. Let M = f ∞ and assume there exists α > 0 and a bounded set A ⊂ R n with positive measure such that (without loss of generality) u(x, θ) > M λ −1 0 + α in A.…”

Existence and Regularity of Solutions: Nonlocal and Nonlinear Models

“…The RTE (1.1) has been studied in the whole domain using slightly different approaches, based on hypo-ellipticity techniques [6], in the references [1,21]. References treating problems with boundaries are scarce in the context of kinetic equations with singular scattering, however, for the classical kinetic Fokker-Planck equation with absorbing boundary we refer to [26,27].…”