IMMUNOLOGICAL MEMORY IN VITRO

The immune responses to sheep erythrocytes of mouse spleen cell suspensions from immune and nonimmune donors were compared in vitro. In vivo immunity was only transiently reflected in vitro, and 8 wk after in vivo immunization the responses of cultures from immunized and nonimmunized mice were virtually identical. There appeared to be two mechanisms for an antibody response to sheep erythrocytes. The first was responsible for the early primary response and is unmodified in the immune animal though contributing little to subsequent in vivo responses due to its suppressibility by specific antibody. The second was expressed in the in vivo secondary response but not on in vitro challenge of spleen cells from mice immunized many weeks previously; spleen cell cultures from such immune mice, freed from the antibody of the in vivo environment, once again demonstrate a pure primary-type response

Capsule-Based Dropwise Additive Manufacturing with Pharmaceutical Suspensions

Current manufacturing of pharmaceutical products focuses on creating a standard dosage of the active pharmaceutical ingredient (API); however, dosages often need to be altered or customized to account for a patient’s age, weight, comorbidity, and other genetic factors. A potential method for dispensing precise dosages of API suspensions through dropwise addition is detailed in the following paper. By using a drop-on-demand printing rig, a series of suspensions comprised of varying volume fractions of a micron-scale API in a carrier fluid were printed, and individual drop volumes were analyzed using high-resolution imaging. From this, capsules with 1 mg dosages and 100 mg dosages were manufactured. Completed trials yielded respective means of 1.043 mg and 99.946 mg of API being deposited across varying suspension compositions. The relative standard deviations of the 1 mg capsules averaged to be 1.51% and 0.30% for the 100 mg capsules. Further combinations of APIs and carrier fluids are continuing to be tested. The relative standard deviations of both dosage sizes are well under the 6% maximum variability imposed by the US Food and Drug Administration to regulate dosages of API, which provides evidence for the feasibility of printing pharmaceutical suspensions to create customized dosages for patient consumption

Nowhere to Hide: Radio-faint AGN in the GOODS-N field. I. Initial catalogue and radio properties

(Abridged) Conventional radio surveys of deep fields ordinarily have arc-second scale resolutions often insufficient to reliably separate radio emission in distant galaxies originating from star-formation and AGN-related activity. Very long baseline interferometry (VLBI) can offer a solution by identifying only the most compact radio emitting regions in galaxies at cosmological distances where the high brightness temperatures (in excess of $10^5$ K) can only be reliably attributed to AGN activity. We present the first in a series of papers exploring the faint compact radio population using a new wide-field VLBI survey of the GOODS-N field. The unparalleled sensitivity of the European VLBI Network (EVN) will probe a luminosity range rarely seen in deep wide-field VLBI observations, thus providing insights into the role of AGN to radio luminosities of the order $10^{22}~\mathrm{W\,Hz^{-1}}$ across cosmic time. The newest VLBI techniques are used to completely cover an entire 7'.5 radius area to milliarcsecond resolutions, while bright radio sources ($S > 0.1$ mJy) are targeted up to 25 arcmin from the pointing centre. Multi-source self-calibration, and a primary beam model for the EVN array are used to correct for residual phase errors and primary beam attenuation respectively. This paper presents the largest catalogue of VLBI detected sources in GOODS-N comprising of 31 compact radio sources across a redshift range of 0.11-3.44, almost three times more than previous VLBI surveys in this field. We provide a machine-readable catalogue and introduce the radio properties of the detected sources using complementary data from the e-MERLIN Galaxy Evolution survey (eMERGE).Comment: 15 pages, 8 figures, accepted in A&A. Machine-readable table available upon reques

Neighborhood Variants of the KKM Lemma, Lebesgue Covering Theorem, and Sperner's Lemma on the Cube

We establish a "neighborhood" variant of the cubical KKM lemma and the Lebesgue covering theorem and deduce a discretized version which is a "neighborhood" variant of Sperner's lemma on the cube. The main result is the following: for any coloring of the unit $d$-cube $[0,1]^d$ in which points on opposite faces must be given different colors, and for any $\varepsilon>0$, there is an $\ell_\infty$ $\varepsilon$-ball which contains points of at least $(1+\frac{\varepsilon}{1+\varepsilon})^d$ different colors, (so in particular, at least $(1+\frac{2}{3}\varepsilon)^d$ different colors for all sensible $\varepsilon\in(0,\frac12]$).Comment: 18 pages plus appendices (30 pages total), 3 figure

Geometry of Rounding: Near Optimal Bounds and a New Neighborhood Sperner's Lemma

A partition $\mathcal{P}$ of $\mathbb{R}^d$ is called a $(k,\varepsilon)$-secluded partition if, for every $\vec{p} \in \mathbb{R}^d$, the ball $\overline{B}_{\infty}(\varepsilon, \vec{p})$ intersects at most $k$ members of $\mathcal{P}$. A goal in designing such secluded partitions is to minimize $k$ while making $\varepsilon$ as large as possible. This partition problem has connections to a diverse range of topics, including deterministic rounding schemes, pseudodeterminism, replicability, as well as Sperner/KKM-type results. In this work, we establish near-optimal relationships between $k$ and $\varepsilon$. We show that, for any bounded measure partitions and for any $d\geq 1$, it must be that $k\geq(1+2\varepsilon)^d$. Thus, when $k=k(d)$ is restricted to ${\rm poly}(d)$, it follows that $\varepsilon=\varepsilon(d)\in O\left(\frac{\ln d}{d}\right)$. This bound is tight up to log factors, as it is known that there exist secluded partitions with $k(d)=d+1$ and $\varepsilon(d)=\frac{1}{2d}$. We also provide new constructions of secluded partitions that work for a broad spectrum of $k(d)$ and $\varepsilon(d)$ parameters. Specifically, we prove that, for any $f:\mathbb{N}\rightarrow\mathbb{N}$, there is a secluded partition with $k(d)=(f(d)+1)^{\lceil\frac{d}{f(d)}\rceil}$ and $\varepsilon(d)=\frac{1}{2f(d)}$. These new partitions are optimal up to $O(\log d)$ factors for various choices of $k(d)$ and $\varepsilon(d)$. Based on the lower bound result, we establish a new neighborhood version of Sperner's lemma over hypercubes, which is of independent interest. In addition, we prove a no-free-lunch theorem about the limitations of rounding schemes in the context of pseudodeterministic/replicable algorithms

Geometry of Rounding

Rounding has proven to be a fundamental tool in theoretical computer science. By observing that rounding and partitioning of $\mathbb{R}^d$ are equivalent, we introduce the following natural partition problem which we call the {\em secluded hypercube partition problem}: Given $k\in \mathbb{N}$ (ideally small) and $\epsilon>0$ (ideally large), is there a partition of $\mathbb{R}^d$ with unit hypercubes such that for every point $p \in \mathbb{R}^d$, its closed $\epsilon$-neighborhood (in the $\ell_{\infty}$ norm) intersects at most $k$ hypercubes? We undertake a comprehensive study of this partition problem. We prove that for every $d\in \mathbb{N}$, there is an explicit (and efficiently computable) hypercube partition of $\mathbb{R}^d$ with $k = d+1$ and $\epsilon = \frac{1}{2d}$. We complement this construction by proving that the value of $k=d+1$ is the best possible (for any $\epsilon$) for a broad class of ``reasonable'' partitions including hypercube partitions. We also investigate the optimality of the parameter $\epsilon$ and prove that any partition in this broad class that has $k=d+1$, must have $\epsilon\leq\frac{1}{2\sqrt{d}}$. These bounds imply limitations of certain deterministic rounding schemes existing in the literature. Furthermore, this general bound is based on the currently known lower bounds for the dissection number of the cube, and improvements to this bound will yield improvements to our bounds. While our work is motivated by the desire to understand rounding algorithms, one of our main conceptual contributions is the introduction of the {\em secluded hypercube partition problem}, which fits well with a long history of investigations by mathematicians on various hypercube partitions/tilings of Euclidean space

Memetic Multilevel Hypergraph Partitioning

Hypergraph partitioning has a wide range of important applications such as VLSI design or scientific computing. With focus on solution quality, we develop the first multilevel memetic algorithm to tackle the problem. Key components of our contribution are new effective multilevel recombination and mutation operations that provide a large amount of diversity. We perform a wide range of experiments on a benchmark set containing instances from application areas such VLSI, SAT solving, social networks, and scientific computing. Compared to the state-of-the-art hypergraph partitioning tools hMetis, PaToH, and KaHyPar, our new algorithm computes the best result on almost all instances

Algebraic analysis of a model of two-dimensional gravity

An algebraic analysis of the Hamiltonian formulation of the model two-dimensional gravity is performed. The crucial fact is an exact coincidence of the Poisson brackets algebra of the secondary constraints of this Hamiltonian formulation with the SO(2,1)-algebra. The eigenvectors of the canonical Hamiltonian $H_{c}$ are obtained and explicitly written in closed form.Comment: 21 pages, to appear in General Relativity and Gravitatio

IQ and Blood Lead from 2 to 7 Years of Age: Are the Effects in Older Children the Residual of High Blood Lead Concentrations in 2-Year-Olds?

Increases in peak blood lead concentrations, which occur at 18–30 months of age in the United States, are thought to result in lower IQ scores at 4–6 years of age, when IQ becomes stable and measurable. Data from a prospective study conducted in Boston suggested that blood lead concentrations at 2 years of age were more predictive of cognitive deficits in older children than were later blood lead concentrations or blood lead concentrations measured concurrently with IQ. Therefore, cross-sectional associations between blood lead and IQ in school-age children have been widely interpreted as the residual effects of higher blood lead concentrations at an earlier age or the tendency of less intelligent children to ingest more leaded dust or paint chips, rather than as a causal relationship in older children. Here we analyze data from a clinical trial in which children were treated for elevated blood lead concentrations (20–44 μg/dL) at about 2 years of age and followed until 7 years of age with serial IQ tests and measurements of blood lead. We found that cross-sectional associations increased in strength as the children became older, whereas the relation between baseline blood lead and IQ attenuated. Peak blood lead level thus does not fully account for the observed association in older children between their lower blood lead concentrations and IQ. The effect of concurrent blood level on IQ may therefore be greater than currently believed