In recent years, various intervention strategies have reduced malaria morbidity and mortality, but further improvements probably depend upon development of a broadly protective vaccine. To better understand immune requirement for protection, we examined liver-stage immunity after vaccination with irradiated sporozoites, an effective though logistically difficult vaccine. We identified a population of memory CD8 T cells that expressed the gene signature of tissue-resident memory T (Trm) cells and remained permanently within the liver, where they patrolled the sinusoids. Exploring the requirements for liver Trm cell induction, we showed that by combining dendritic cell-targeted priming with liver inflammation and antigen recognition on hepatocytes, high frequencies of Trm cells could be induced and these cells were essential for protection against malaria sporozoite challenge. Our study highlights the immune potential of liver Trm cells and provides approaches for their selective transfer, expansion, or depletion, which may be harnessed to control liver infections or autoimmunity.

This paper presents novel algorithms that iteratively converge to a local minimum of a real-valued function () subject to the constraint that the columns of the complex-valued matrix are mutually orthogonal and have unit norm. The algorithms are derived by reformulating the constrained optimization problem as an unconstrained one on a suitable manifold. This significantly reduces the dimensionality of the optimization problem. Pertinent features of the proposed framework are illustrated by using the framework to derive an algorithm for computing the eigenvector associated with either the largest or the smallest eigenvalue of a Hermitian matrix. Index Terms-Constrained optimization, eigenvalue problems, optimization on manifolds, orthogonal constraints. I. INTRODUCTION T HIS paper derives novel algorithms for numerically minimizing a cost function , subject to the orthogonality constraint , where denotes Hermitian transpose, and is the identity matrix. The complex-valued case is considered for generality; the results in this paper remain valid if all quantities are restricted to being real-valued. It has been shown recently [8] that the geometrically correct setting for this constrained minimization problem is on the Stiefel manifold in general and on the Grassmann manifold if possesses the symmetrical property that for any unitary (that is,) matrix. However, not only did [8] consider only the real-valued case, the approach therein relied on endowing the Stiefel manifold with a Riemannian structure. The present paper presents a simpler framework for orthogonally constrained optimization problems. Orthogonally constrained optimization problems tend to occur in signal processing problems involving subspaces. This is because the constraint requires the columns of to form an orthonormal basis, meaning that the cost function can be interpreted as a function of an ordered set of orthonormal basis vectors. Similarly, if for any unitary matrix , then is a function of the subspace spanned by the columns of , or equivalently, the range space of. This is because the range spaces of and are the same.

Barrier tissues such as the skin contain various populations of immune cells that contribute to protection from infections. These include recently identified tissue-resident memory T cells (T RM ). In the skin, these memory CD8 + T cells reside in the epidermis after being recruited to this site by infection or inflammation. In this study, we demonstrate prolonged persistence of epidermal T RM preferentially at the site of prior infection despite sustained migration. Computational simulation of T RM migration within the skin over long periods revealed that the slow rate of random migration effectively constrains these memory cells within the region of skin in which they form. Notably, formation of T RM involved a concomitant local reduction in dendritic epidermal γδ T-cell numbers in the epidermis, indicating that these populations persist in mutual exclusion and may compete for local survival signals. Accordingly, we show that expression of the aryl hydrocarbon receptor, a transcription factor important for dendritic epidermal γδ T-cell maintenance in skin, also contributes to the persistence of skin T RM . Together, these data suggest that skin tissue-resident memory T cells persist within a tightly regulated epidermal T-cell niche. T he skin is a complex organ that acts as a primary barrier between the body and the environment. Multiple leukocyte subsets reside within the main compartments of the skin, the dermis and the epidermis, as well as the hair follicles that are contiguous with the epidermis. Populations of macrophages, dendritic cells, mast cells, γδ T cells and αβ T cells are present in the dermis, and Langerhans cells (LCs) and dendritic epidermal γδ T cells (DETCs) lie in a strategic network in the epidermis (1). We recently described a population of memory CD8 + T cells that enter the epidermis and hair follicles during infection or inflammation and become long-lived populations of tissue-resident memory T cells (T RM ) (2-5). These memory T cells are sequestered in this site and are distinct from circulating effector memory (T EM ) and central memory (T CM ) populations (3, 6). Memory CD8 + T cells in the epidermis display a dendritic morphology and move at a slower velocity than T cells within the dermis. These memory T cells are sequestered in the skin epithelial layer and do not recirculate to other tissues. In contrast, memory CD4 + T cells are found within the dermis and at least a proportion of these cells are capable of recirculating around the body (3, 7).In this study, we sought to further examine the mechanisms of T RM persistence within the skin. We reveal that skin T RM persist at the site of their formation and despite displaying a sustained mode of random migration, the slow rate of this movement locally constrains these memory cells. Examination of other cells in this environment showed that although epidermal T RM regularly interact with LC, these interactions were not required for persistence. In contrast, skin tissue-resident memory T cells replaced DETCs in the epidermis, seem...

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