Abstract:
We genotyped 142 women previously vaccinated with three doses of CMV gB for single nucleotide polymorphisms (SNPs) in TLR 1-4, 6, 7, 9, and 10, and their associated intracellular signaling genes. SNPs in the platelet-derived growth factor receptor (PDGFRA) and integrins were also selected based on their role in binding gB. Specific SNPs in TLR7 and IKBKE (inhibitor of nuclear factor kappa-B kinase subunit epsilon) were associated with antibody responses to gB vaccine. Homozygous carriers of the minor allele at four SNPs in TLR7 showed higher vaccination-induced antibody responses to gB compared to heterozygotes or homozygotes for the common allele. SNP rs1953090 in IKBKE was associated with changes in antibody level from second to third dose of vaccine; homozygotes for the minor allele exhibited lower antibody responses while homozygotes for the major allele showed increased responses over time.These data contribute to our understanding of the immunogenetic mechanisms underlying variations in the immune response to CMV vaccine.Infection with CMV is common in humans, causing severe morbidity and mortality in congenitally-infected newborns and in immunocompromised patients [1-3]. The importance of CMV as the leading infectious cause of mental retardation and deafness in children has been emphasized by its categorization by the Institute of Medicine as a level I vaccine candidate [4]. The rationale for developing a CMV vaccine is based on clinical and animal studies showing that immunity to CMV reduces the frequency and severity of disease [5,6]. In addition, animal studies demonstrated that immunization with subunit vaccines prevented disease and transplacental transmission of CMV [5-7]. Two recent phase II clinical trials with glycoprotein B (gB)-MF59 led to major enthusiasm and hope for the future success of CMV vaccine. The first was performed in young women recruited on postpartum wards [4], and showed 50% efficacy in preventing maternal CMV infection. Analysis of

Abstract:
The purpose of this note is to show that the solution to the Kantorovich optimal transportation problem is supported on a Lipschitz manifold, provided the cost is $C^{2}$ with non-singular mixed second derivative. We use this result to provide a simple proof that solutions to Monge's optimal transportation problem satisfy a change of variables equation almost everywhere.

Abstract:
Fix probability densities $f$ and $g$ on open sets $X \subset \mathbf{R}^m$ and $Y \subset \mathbf{R}^n$ with $m\ge n\ge1$. Consider transporting $f$ onto $g$ so as to minimize the cost $-s(x,y)$. We give a non-degeneracy condition (a) on $s \in C^{1,1}$ which ensures the set of $x$ paired with [$g$-a.e.] $y\in Y$ lie in a codimension $n$ submanifold of $X$. Specializing to the case $m>n=1$, we discover a nestedness criteria relating $s$ to $(f,g)$ which allows us to construct a unique optimal solution in the form of a map $F:X \longrightarrow \overline Y$, one level set at a time. This map is continuous if $spt(g)$ is connected. When $s,\log g$ (and $\log f$) are a derivative (or two) smoother and bounded, the Kantorovich dual potentials $(u,v)$ satisfy $v \in C^{1,1}_{loc}(Y)$, and the normal velocity $V$ of $F^{-1}(y)$ with respect to changes in $y$ is given by $V(x) = v"(F(x))-s_{yy}(x,F(x))$. Positivity (b) of $V$ locally implies a Lipschitz bound on $F$, moreover, $v \in C^2$ if ${F^{-1}(y)}$ intersects $\partial X \in C^1$ transversally (c). On subsets where (a)-(c) can be be quantified, for each integer $r \ge1$ the norms of $u,v \in C^{r+1,1}$ and $F \in C^{r,1}$ are controlled by these bounds, $||\log f,\log g, \partial X ||_{C^{r-1,1}}, ||\partial X||_{C^{1,1}}$, $||s||_{C^{r+1,1}}$, and the smallness of $F^{-1}(y)$. We give examples showing regularity extends from $X$ to part of $\overline X$, but not from $Y$ to $\overline Y$. We also show that when $s$ remains nested for all $(f,g)$, the problem in $\mathbf{R}^m \times \mathbf{R}$ reduces to a super- or submodular problem in $\mathbf{R} \times \mathbf{R}$.

Abstract:
Juvenile polyarteritis nodosa (PAN) is a rare, necrotizing vasculitis, primarily affecting small to medium-sized muscular arteries [1]. Recent classification criteria from EULAR/PRES require histopathology of necrotizing vasculitis or angiographic abnormalities (aneurysm, stenosis, or occlusion of small-medium arteries), plus one of five of the following: skin involvement, myalgia or muscle tenderness, hypertension, peripheral neuropathy, or renal involvement, for diagnosis [2]. Cardiac involvement amongst patients with PAN is not common. Well described cardiac manifestations in adults with PAN include pericarditis, arrhythmia and valvular disease. There are infrequent reports of coronary arteritis, stenosis [3], dissection [4], and occasionally aneurysms [5] associated with PAN, however renal and gastrointestinal aneurysms are more common [6,7]. There is a paucity of literature regarding coronary artery manifestations in juvenile PAN, with limited information on demographics, clinical characteristics, treatment, and outcomes. Herein we describe a case of coronary artery aneurysms in an adolescent with juvenile PAN.This is a report of a 16 year old girl from St. Croix, U.S. Virgin Islands, who had been previously diagnosed with juvenile idiopathic arthritis (JIA) at 5 years of age, based on reports of fever, arthritis, and chronic uveitis. She received no systemic immunosuppressant medication and appeared to be in remission for several years. In December 2009 she presented with three days of sharp, substernal chest pain, two days of fever, and one day of bilateral hip pain causing difficulty ambulating. Physical exam revealed a tall, slender girl with mild nasal congestion. On cardiac exam she had a regular rate and rhythm, normal S1 and S2, and no appreciable murmur. Examination of her extremities revealed tenderness over her bilateral greater trochanters and bilateral knee effusions. Initial laboratory testing demonstrated white blood cell count of 5.7 k/μl, hemog

Abstract:
We study a multi-marginal optimal transportation problem. Under certain conditions on the cost function and the first marginal, we prove that the solution to the relaxed, Kantorovich version of the problem induces a solution to the Monge problem and that the solutions to both problems are unique.

Abstract:
We study a form of optimal transportation surplus functions which arise in hedonic pricing models. We derive a formula for the Ma-Trudinger-Wang curvature of these functions, yielding necessary and sufficient conditions for them to satisfy \textbf{(A3w)}. We use this to give explicit new examples of surplus functions satisfying \textbf{(A3w)}, of the form $b(x,y)=H(x+y)$ where $H$ is a convex function on $\mathbb{R}^n$. We also show that the space of equilibrium contracts in the hedonic pricing model has the maximal possible dimension, a result of potential economic interest.

Abstract:
We study the principal-agent problem. We show that $b$-convexity of the space of products, a condition which appears in a recent paper by Figalli, Kim and McCann \cite{fkm}, is necessary to formulate the problem as a maximization over a convex set. We then show that when the dimension $m$ of the space of types is larger than the dimension $n$ of the space of products, this condition implies that the extra dimensions do not encode independent economic information. When $m$ is smaller than $n$, we show that under $b$-convexity of the space of products, it is always optimal for the principal to offer goods only from a certain prescribed subset. We show that this is equivalent to offering an $m$-dimensional space of goods.

Abstract:
We prove uniqueness and Monge solution results for multi-marginal optimal transportation problems with a certain class of surplus functions; this class arises naturally in multi-agent matching problems in economics. This result generalizes a seminal result of Gangbo and \'Swi\c{e}ch on multi-marginal problems. Of particular interest, we show that this also yields a partial generalization of the Gangbo-\'Swi\c{e}ch result to manifolds; alternatively, we we can think of this as a partial extension of McCann's theorem for quadratic costs on manifolds to the multi-marginal setting. We also show that the class of surplus functions considered here neither contains, nor is contained in, another class of surpluses studied by the present author, which also generalized Gangbo and \'Swi\c{e}ch's result.

Abstract:
In this note, we study an optimal transportation problem arising in density functional theory. We derive an upper bound on the semi-classical Hohenberg-Kohn functional derived by Cotar, Friesecke and Kl\"{u}ppelberg (2012) which can be computed in a straightforward way for a given single particle density. This complements a lower bound derived by the aforementioned authors. We also show that for radially symmetric densities the optimal transportation problem arising in the semi-classical Hohenberg-Kohn functional can be reduced to a 1-dimensional problem. This yields a simple new proof of the explicit solution to the optimal transport problem for two particles found by Cotar, Friesecke and Kl\"{u}ppelberg (2012). For more particles, we use our result to demonstrate two new qualitative facts: first, that the solution can concentrate on higher dimensional submanifolds and second that the solution can be non-unique, even with an additional symmetry constraint imposed.