Rademacher-Carlitz Polynomials

We introduce and study the \emph{Rademacher-Carlitz polynomial} \RC(u, v, s, t, a, b) := \sum_{k = \lceil s \rceil}^{\lceil s \rceil + b - 1} u^{\fl{\frac{ka + t}{b}}} v^k where $a, b \in \Z_{>0}$, $s, t \in \R$, and $u$ and $v$ are variables. These polynomials generalize and unify various Dedekind-like sums and polynomials; most naturally, one may view \RC(u, v, s, t, a, b) as a polynomial analogue (in the sense of Carlitz) of the \emph{Dedekind-Rademacher sum} \r_t(a,b) := \sum_{k=0}^{b-1}\left(\left(\frac{ka+t}{b} \right)\right) \left(\left(\frac{k}{b} \right)\right), which appears in various number-theoretic, combinatorial, geometric, and computational contexts. Our results come in three flavors: we prove a reciprocity theorem for Rademacher-Carlitz polynomials, we show how they are the only nontrivial ingredients of integer-point transforms $$\sigma(x,y):=\sum_{(j,k) \in \mathcal{P}\cap \Z^2} x^j y^k$$ of any rational polyhedron $\mathcal{P}$, and we derive a novel reciprocity theorem for Dedekind-Rademacher sums, which follows naturally from our setup

R Package distrMod: S4 Classes and Methods for Probability Models

Package distrMod provides an object oriented (more specifically S4-style) implementation of probability models. Moreover, it contains functions and methods to compute minimum criterion estimators - in particular, maximum likelihood and minimum distance estimators.

L_2 Differentiability of Generalized Linear Models

We derive conditions for $L_2$ differentiability of generalized linear models with error distributions not necessarily belonging to exponential families, covering both cases of stochastic and deterministic regressors. These conditions induce smoothness and integrability conditions for corresponding GLM-based time series models.Comment: 10 page

Performance Measures in Binary Classification

We give a brief overview over common performance measures for binary classification. We cover sensitivity, specificity, positive and negative predictive value, positive and negative likelihood ratio as well as ROC curve and AUC

Dextran sulfate activates contact system and mediates arterial hypotension via B2 kinin receptors

To define some of the mechanisms underlying dextran sulfate (DXS)-induced hypotension, we investigated the effects of either the plasma kallikrein inhibitor des-Pro2-[Arg15] aprotinin (BAY x 4620) or the specific bradykinin B2-receptor antagonist Hoe-140 on the hypotensive response to DXS. In the first study, anesthetized miniature pigs were given DXS alone, DXS plus BAY x 4620 in various doses, or saline. As expected, DXS alone produced a profound but transient systemic arterial hypotension with a concomitant reduction in kininogen. Circulating kinin levels, complement fragment des-Arg-C3a, and fibrin monomer were all increased. Treatment with BAY x 4620 produced a dose-dependent attenuation of these effects with complete blockade of the hypotension as well as the observed biochemical changes at the highest dose (360 mg). In a second study, two groups of pigs were given either DXS alone or DXS plus Hoe-140. DXS-induced hypotension was completely blocked by Hoe-140 pretreatment; however, kininogen was again depleted. We conclude, therefore, that DXS-induced hypotension is produced by activation of plasma kallikrein that results in the production of bradykinin and that liberation of bradykinin and its action on B2 receptors in the vasculature are both necessary and sufficient to produce the observed effects on circulatory pressure