Alpha- and beta-adrenergic mediation of changes in metabolism and Na/K exchange in rat brown fat

Double- and triple-barreled ion-sensitive microelectrodes were used to measure changes in extracellular K+ and Na+ concentrations ([K+]o, [Na+]o) in brown fat. Redox states of different respiratory enzymes were measured simultaneously in order to correlate ion movements with metabolic activity. Trains of stimuli applied to the efferent nerves evoked two distinct increases in [K+]o. A first, small, rapid increase occurred within 10 s and accompanied a first, rapid membrane depolarization. A second, slow increase of [K+]o occurred several minutes after stimulation and accompanied a second, slow depolarization. A few seconds after stimulation onset, while the membrane was repolarizing and shifts in redox states indicated increases in lipolysis and respiration, [K+]o decreased. The [K+]o decrease was accompanied by an increase in [Na+]o, and could be partly blocked by ouabain. Phentolamine, an alpha-antagonist that blocks the first depolarization, also blocked the first, rapid [K+]o increase and part of the subsequent decrease. Propranolol, a beta-antagonist, had little effect on the first depolarization and the first increase in [K+]o, but blocked part of the subsequent [K+]o decrease and the second, slow [K+]o increase. The changes in [K+]o were almost completely abolished in the presence of both antagonists. It is concluded that brown adipocytes take up K+ and simultaneously lose Na+ in response to the interaction of noradrenaline with alpha- and beta-receptors, and this indicates a very early stimulation of the Na+ pump

The real Ginibre ensemble with k=O(n)k = O(n) real eigenvalues

We consider the ensemble of Real Ginibre matrices with a positive fraction $\alpha>0$ of real eigenvalues. We demonstrate a large deviations principle for the joint eigenvalue density of such matrices and we introduce a two phase log-gas whose stationary distribution coincides with the spectral measure of the ensemble. Using these tools we provide an asymptotic expansion for the probability $p^n_{\alpha n}$ that an $n\times n$ Ginibre matrix has $k=\alpha n$ real eigenvalues and we characterize the spectral measures of these matrices.Comment: 19 pages, 3 figure

Algebra of Theoretical Term Reductions in the Sciences

An elementary algebra identifies conceptual and corresponding applicational limitations in John Kemeny and Paul Oppenheim’s (K-O) 1956 model of theoretical reduction in the sciences. The K-O model was once widely accepted, at least in spirit, but seems afterward to have been discredited, or in any event superceeded. Today, the K-O reduction model is seldom mentioned, except to clarify when a reduction in the Kemeny-Oppenheim sense is not intended. The present essay takes a fresh look at the basic mathematics of K-O comparative vocabulary theoretical term reductions, from historical and philosophical standpoints, as a contribution to the history of the philosophy of science. The K-O theoretical reduction model qualifies a theory replacement as a successful reduction when preconditions of explanatory adequacy and comparable systematicization are met, and there occur fewer numbers of theoretical terms identified as replicable syntax types in the most economical statement of a theory’s putative propositional truths, as compared with the theoretical term count for the theory it replaces. The challenge to the historical model developed here, to help explain its scope and limitations, involves the potential for equivocal theoretical meanings of multiple theoretical term tokens of the same syntactical type

New Deterministic Algorithms for Solving Parity Games

We study parity games in which one of the two players controls only a small number $k$ of nodes and the other player controls the $n-k$ other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite parity games in time $k^{O(\sqrt{k})}\cdot O(n^3)$, and general parity games in time $(p+k)^{O(\sqrt{k})} \cdot O(pnm)$, where $p$ is the number of distinct priorities and $m$ is the number of edges. For all games with $k = o(n)$ this improves the previously fastest algorithm by Jurdzi{\'n}ski, Paterson, and Zwick (SICOMP 2008). We also obtain novel kernelization results and an improved deterministic algorithm for graphs with small average degree

A variant of the Johnson-Lindenstrauss lemma for circulant matrices

We continue our study of the Johnson-Lindenstrauss lemma and its connection to circulant matrices started in \cite{HV}. We reduce the bound on $k$ from $k=O(\epsilon^{-2}\log^3n)$ proven there to $k=O(\epsilon^{-2}\log^2n)$. Our technique differs essentially from the one used in \cite{HV}. We employ the discrete Fourier transform and singular value decomposition to deal with the dependency caused by the circulant structure