Logic in the Tractatus

I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “form-series” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named. There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects is countably infinite, then the property of being a tautology is \Pi^1_1-complete. But third, it is only granted the assumption of countability that the class of tautologies is \Sigma_1-definable in set theory. Wittgenstein famously urges that logical relationships must show themselves in the structure of signs. He also urges that the size of the universe cannot be prejudged. The results of this paper indicate that there is no single way in which logical relationships could be held to make themselves manifest in signs, which does not prejudge the number of objects

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Entanglement of mechanical oscillators coupled to a non-equilibrium environment

Recent experiments aim at cooling nanomechanical resonators to the ground state by coupling them to non-equilibrium environments in order to observe quantum effects such as entanglement. This raises the general question of how such environments affect entanglement. Here we show that there is an optimal dissipation strength for which the entanglement between two coupled oscillators is maximized. Our results are established with the help of a general framework of exact quantum Langevin equations valid for arbitrary bath spectra, in and out of equilibrium. We point out why the commonly employed Lindblad approach fails to give even a qualitatively correct picture

Galactic emission at 19 GHz

We cross-correlate a 19 GHz full sky Cosmic Microwave Background (CMB) survey with other maps to quantify the foreground contribution. Correlations are detected with the Diffuse Infrared Background Experiment (DIRBE) 240, 140 and 100 micron maps at high latitudes (|b|>30degrees), and marginal correlations are detected with the Haslam 408 MHz and the Reich & Reich 1420 MHz synchrotron maps. The former agree well with extrapolations from higher frequencies probed by the COBE DMR and Saskatoon experiments and are consistent with both free-free and rotating dust grain emission.Comment: 4 pages, with 4 figures included. Accepted for publication in ApJL. Color figure and links at http://www.sns.ias.edu/~angelica/foreground.html#19 or from [email protected]

Acute kidney injury after ingestion of rhubarb: secondary oxalate nephropathy in a patient with type 1 diabetes

Background: Oxalosis is a metabolic disorder characterized by deposition of oxalate crystals in various organs including the kidney. Whereas primary forms result from genetic defects in oxalate metabolism, secondary forms of oxalosis can result from excessive intestinal oxalate absorption or increased endogenous production, e.g. after intoxication with ethylene glycol. Case presentation: Here, we describe a case of acute crystal-induced renal failure associated with excessive ingestion of rhubarb in a type 1 diabetic with previously normal excretory renal function. Renal biopsy revealed mild mesangial sclerosis, but prominent tubular deposition of oxalate crystals in the kidney. Oxalate serum levels were increased. Conclusion: Acute secondary oxalate nephropathy due to excessive dietary intake of oxalate may lead to acute renal failure in patients with preexisting renal disease like mild diabetic nephropathy. Attention should be payed to special food behaviors when reasons for acute renal failure are explored

Learning a Tracking Controller for Rolling μ\mubots

Micron-scale robots ($\mu$bots) have recently shown great promise for emerging medical applications. Accurate controlling $\mu$bots, while critical to their successful deployment, is challenging. In this work, we consider the problem of tracking a reference trajectory using a $\mu$bot in the presence of disturbances and uncertainty. The disturbances primarily come from Brownian motion and other environmental phenomena, while the uncertainty originates from errors in the model parameters. We model the $\mu$bot as an uncertain unicycle that is controlled by a global magnetic field. To compensate for disturbances and uncertainties, we develop a nonlinear mismatch controller. We define the model mismatch error as the difference between our model's predicted velocity and the actual velocity of the $\mu$bot. We employ a Gaussian Process to learn the model mismatch error as a function of the applied control input. Then we use a least-squares minimization to select a control action that minimizes the difference between the actual velocity of the $\mu$bot and a reference velocity. We demonstrate the online performance of our joint learning and control algorithm in simulation, where our approach accurately learns the model mismatch and improves tracking performance. We also validate our approach in an experiment and show that certain error metrics are reduced by up to $40\%$.Comment: 8 pages, 9 figure

The use of circulating cell-free tumor DNA in routine diagnostics of metastatic melanoma patients

Modern advances in technology such as next-generation sequencing and digital PCR make detection of minor circulating cell-free tumor DNA amounts in blood from cancer patients possible. Samples can be obtained minimal-invasively, tested for treatment-determining genetic alterations and are considered to reflect the genetic constitution of the whole tumor mass. Furthermore, tumor development can be determined by a time course of the quantified circulating cell-free tumor DNA. However, systematic studies which prove the clinical relevance of monitoring patients using liquid biopsies are still lacking. In this study, we collected 115 samples from 47 late stage melanoma patients over 1.5 years alongside therapy-associated clinical routine monitoring. Mutation status was confirmed by molecular analysis of primary tumor material. We can show that detectable levels of circulating cell-free tumor DNA correlate with clinical development over time. Increasing levels of circulating cell-free tumor DNA during melanoma treatment with either targeted therapy (BRAF/MEK inhibitors) or immunotherapy, during recovery time or the intervals between last treatment cycle and second-line treatment point towards clinical progression before the progression becomes obvious in imaging. Therefore, this is a further possibility to closely screen our patients for tumor progression during therapy, in therapy-free phases and in earlier stages before therapy initiation