Closed classes of functions, generalized constraints and clusters

Classes of functions of several variables on arbitrary non-empty domains that are closed under permutation of variables and addition of dummy variables are characterized in terms of generalized constraints, and hereby Hellerstein's Galois theory of functions and generalized constraints is extended to infinite domains. Furthermore, classes of operations on arbitrary non-empty domains that are closed under permutation of variables, addition of dummy variables and composition are characterized in terms of clusters, and a Galois connection is established between operations and clusters.Comment: 21 page

Explicit kinetic heterogeneity: mechanistic models for interpretation of labeling data of heterogeneous cell populations

Estimation of division and death rates of lymphocytes in different conditions is vital for quantitative understanding of the immune system. Deuterium, in the form of deuterated glucose or heavy water, can be used to measure rates of proliferation and death of lymphocytes in vivo. Inferring these rates from labeling and delabeling curves has been subject to considerable debate with different groups suggesting different mathematical models for that purpose. We show that the three models that are most commonly used are in fact mathematically identical and differ only in their interpretation of the estimated parameters. By extending these previous models, we here propose a more mechanistic approach for the analysis of data from deuterium labeling experiments. We construct a model of "kinetic heterogeneity" in which the total cell population consists of many sub-populations with different rates of cell turnover. In this model, for a given distribution of the rates of turnover, the predicted fraction of labeled DNA accumulated and lost can be calculated. Our model reproduces several previously made experimental observations, such as a negative correlation between the length of the labeling period and the rate at which labeled DNA is lost after label cessation. We demonstrate the reliability of the new explicit kinetic heterogeneity model by applying it to artificially generated datasets, and illustrate its usefulness by fitting experimental data. In contrast to previous models, the explicit kinetic heterogeneity model 1) provides a mechanistic way of interpreting labeling data; 2) allows for a non-exponential loss of labeled cells during delabeling, and 3) can be used to describe data with variable labeling length

Improved Bounds on Quantum Learning Algorithms

In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum black-box queries which are required to exactly identify an unknown function from C is $O(\frac{\log |C|}{\sqrt{{\hat{\gamma}}^{C}}})$, where $\hat{\gamma}^{C}$ is a combinatorial parameter of the class C. We essentially resolve this conjecture in the affirmative by giving a quantum algorithm that, for any class C, identifies any unknown function from C using $O(\frac{\log |C| \log \log |C|}{\sqrt{{\hat{\gamma}}^{C}}})$ quantum black-box queries. We consider a range of natural problems intermediate between the exact learning problem (in which the learner must obtain all bits of information about the black-box function) and the usual problem of computing a predicate (in which the learner must obtain only one bit of information about the black-box function). We give positive and negative results on when the quantum and classical query complexities of these intermediate problems are polynomially related to each other. Finally, we improve the known lower bounds on the number of quantum examples (as opposed to quantum black-box queries) required for $(\epsilon,\delta)$-PAC learning any concept class of Vapnik-Chervonenkis dimension d over the domain $\{0,1\}^n$ from $\Omega(\frac{d}{n})$ to $\Omega(\frac{1}{\epsilon}\log \frac{1}{\delta}+d+\frac{\sqrt{d}}{\epsilon})$. This new lower bound comes closer to matching known upper bounds for classical PAC learning.Comment: Minor corrections. 18 pages. To appear in Quantum Information Processing. Requires: algorithm.sty, algorithmic.sty to buil

Accelerated in vivo proliferation of memory phenotype CD4+ T-cells in human HIV-1 infection irrespective of viral chemokine co-receptor tropism.

CD4(+) T-cell loss is the hallmark of HIV-1 infection. CD4 counts fall more rapidly in advanced disease when CCR5-tropic viral strains tend to be replaced by X4-tropic viruses. We hypothesized: (i) that the early dominance of CCR5-tropic viruses results from faster turnover rates of CCR5(+) cells, and (ii) that X4-tropic strains exert greater pathogenicity by preferentially increasing turnover rates within the CXCR4(+) compartment. To test these hypotheses we measured in vivo turnover rates of CD4(+) T-cell subpopulations sorted by chemokine receptor expression, using in vivo deuterium-glucose labeling. Deuterium enrichment was modeled to derive in vivo proliferation (p) and disappearance (d*) rates which were related to viral tropism data. 13 healthy controls and 13 treatment-naive HIV-1-infected subjects (CD4 143-569 cells/ul) participated. CCR5-expression defined a CD4(+) subpopulation of predominantly CD45R0(+) memory cells with accelerated in vivo proliferation (p = 2.50 vs 1.60%/d, CCR5(+) vs CCR5(-); healthy controls; P<0.01). Conversely, CXCR4 expression defined CD4(+) T-cells (predominantly CD45RA(+) naive cells) with low turnover rates. The dominant effect of HIV infection was accelerated turnover of CCR5(+)CD45R0(+)CD4(+) memory T-cells (p = 5.16 vs 2.50%/d, HIV vs controls; P<0.05), naïve cells being relatively unaffected. Similar patterns were observed whether the dominant circulating HIV-1 strain was R5-tropic (n = 9) or X4-tropic (n = 4). Although numbers were small, X4-tropic viruses did not appear to specifically drive turnover of CXCR4-expressing cells (p = 0.54 vs 0.72 vs 0.44%/d in control, R5-tropic, and X4-tropic groups respectively). Our data are most consistent with models in which CD4(+) T-cell loss is primarily driven by non-specific immune activation

Increased Turnover of T Lymphocytes in HIV-1 Infection and Its Reduction by Antiretroviral Therapy

The mechanism of CD4+ T cell depletion in human immunodeficiency virus (HIV)-1 infection remains controversial. Using deuterated glucose to label the DNA of proliferating cells in vivo, we studied T cell dynamics in four normal subjects and seven HIV-1–infected patients naive to antiretroviral drugs. The results were analyzed using a newly developed mathematical model to determine fractional rates of lymphocyte proliferation and death. In CD4+ T cells, mean proliferation and death rates were elevated by 6.3- and 2.9-fold, respectively, in infected patients compared with normal controls. In CD8+ T cells, the mean proliferation rate was 7.7-fold higher in HIV-1 infection, but the mean death rate was not significantly increased. Five of the infected patients underwent subsequent deuterated glucose labeling studies after initiating antiretroviral therapy. The lymphocyte proliferation and death rates in both CD4+ and CD8+ cell populations were substantially reduced by 5–11 weeks and nearly normal by one year. Taken together, these new findings strongly indicate that CD4+ lymphocyte depletion seen in AIDS is primarily a consequence of increased cellular destruction, not decreased cellular production