Generalized Differentiation and Characterizations for Differentiability of Infimal Convolutions

This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas obtained unify several known results and allow us to characterize the differentiability of the infimal convolution which plays an important role in variational analysis and optimization

Electrospun antibody-functionalized poly(dimethyl siloxane)-based meshes for improved T cell expansion

Adoptive cell transfer (ACT) has garnered significant interest in recent years within the medical field due to its potential in providing an effective form of personalized medicine for patients suffering from a wide range of chronic illnesses, including but not limited to cancer. By leveraging the patient’s own cells as the therapeutic agent, concerns over patient compatibility and adverse reactions are significantly reduced. Central to this therapy is the ability to optimize cell quantity and cell activation in order to produce a more robust infusion to the patient. This thesis focuses on two main aspects. The first is the materials synthesis and development of a novel platform for the ex vivo expansion of human T cells for ACT, while the second aims to elucidate the underlying structural mechanics of this platform. This platform, which consists of an electrospun mesh of micron and sub-micron diameter poly (dimethyl siloxane)-based fibers, aims to maintain the high surface-area to volume ratio characteristic of the current clinical gold standard. This also simultaneously allows for effective leveraging of T cell mechanosensing, a phenomenon previously discovered by our lab that is the ability of a human T cell to respond differently to surface mechanical cues. By modulating the concentration of poly (ε-caprolactone) in these fibers, a biocompatible polymer, the mesh mechanical rigidity was varied: this effectively allowed for the leverage of T cell mechanosensing by maintaining a low and tunable Young’s modulus throughout. Additionally, safety concerns involving transfusion of the expansion platform into the patient were addressed by having a single continuous substrate instead of an array of disjoint ferromagnetic beads. Our results thus far indicate that this soft mesh platform can produce upwards of 5.6-12.5 times more T cells in healthy patients than the clinical gold standard while maintaining comparable levels of cellular activation and phenotypic distributions as measured through IFNγ secretion and expression of surface proteins CD107b, CD45RO, and CCR7, respectively. Additionally, this platform demonstrates the ability to produce improved expansion of exhausted (PD-1high) T cells from CLL patients compared to the clinical gold standard across all analyzed Rai stages. Finally, experiments have shown our platform to be scalable to produce clinically relevant levels of cells (> 50 million) from a given starting population, thus indicating its potential in adaptation in larger scale in vitro systems. The currently demonstrated capabilities of our mesh platform thus hold significant promise in the clinical development and adoption of ACT, as well as the development of larger scale in vitro systems. In order to elucidate the underlying structural mechanics of our platform, quantitative AFM studies have indicated a force-dependency in rigidity measurement, thus indicating that standard Hertzian contact models and their derivatives (DMT, Sneddon, etc.), may not be ideal in calculating the rigidity of this material. In order to better model the effective Young’s modulus (E_eff) of the mesh and account for cantilever beam-bending type mechanical deformation, a modification of Euler-Bernoulli theory was established. This mathematical model was subsequently used to correlate fiber geometry parameters to bending stiffness, thus allowing for us to estimate E_eff for a range of meshes. Subsequent T cell expansions and comparison of data to previous expansions on planar surfaces provided verification of our model

Quasi-Relative Interiors for Graphs of Convex Set-Valued Mappings

This paper aims at providing further studies of the notion of quasi-relative interior for convex sets introduced by Borwein and Lewis. We obtain new formulas for representing quasi-relative interiors of convex graphs of set-valued mappings and for convex epigraphs of extended-real-valued functions defined on locally convex topological vector spaces. We also show that the role, which this notion plays in infinite dimensions and the results obtained in this vein, are similar to those involving relative interior in finite-dimensional spaces.Comment: This submission replaces our previous version

Optimizing the cooling parameters for annealing of glass bottles by stress simulation according to the viscoelastic theory

The anneahng process of glass bottles was calculated by means of the stress Simulation according to Narayanaswamy, a finite element method coded in ANSYS. The glass characteristics were described according to the viscoelastic theory. The change of glass properties was computed with the help of the fictive temperature, which is described by the relaxation function of the glass structure. For a successful anneahng process, the heating of the entire glass bottle to the annealing temperature is fundamental. The heating-up time depends strongly on the initial temperature and the wall thickness of the bottles. The maximum cooling stresses in the bottle are located at the bend between bottle wall and bottom. The residual stress depends particularly on the cooling rate in the critical cooling zone and for the smaller part on the cooling rate in the cooling-down zone. The maximum residual stress in the bottle was fitted as an exponendal function of the cooling time

Duality Theory on Vector Spaces

In this paper, we study the Fenchel-Rockafellar duality and the Lagrange duality in the general frame work of vector spaces without topological structures. We utilize the geometric approach, inspired from its successful application by B. S. Mordukhovich and his coauthors in variational and convex analysis (see \cite{CBN21,CBNC,CBNG22,CBNG,m-book,mn-book}). After revisiting coderivative calculus rules and providing the subdifferential maximum rule in vector spaces, we establish conjugate calculus rules under qualifying conditions through the algebraic interior of the function's domains. Then we develop sufficient conditions which guarantee the Fenchel-Rockafellar strong duality. Finally, after deriving some necessary and sufficient conditions for optimal solutions to convex minimization problems, under a Slater condition via the algebraic interior, we then obtain a sufficient condition for the Lagrange strong duality.Comment: 21 pages. arXiv admin note: text overlap with arXiv:2106.1577