A Quasi-Random Approach to Matrix Spectral Analysis

Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of Hermitian matrices. The result is a completely new, efficient and stable, parallel algorithm to compute an approximate spectral decomposition of any Hermitian matrix. The algorithm can be implemented by Boolean circuits in $O(\log^2 n)$ parallel time with a total cost of $O(n^{\omega+1})$ Boolean operations. This Boolean complexity matches the best known rigorous $O(\log^2 n)$ parallel time algorithms, but unlike those algorithms our algorithm is (logarithmically) stable, so further improvements may lead to practical implementations. All previous efficient and rigorous approaches to solve the Eigen-Problem use randomization to avoid bad condition as we do too. Our algorithm makes further use of randomization in a completely new way, taking random powers of a unitary matrix to randomize the phases of its eigenvalues. Proving that a tiny Gaussian perturbation and a random polynomial power are sufficient to ensure almost pairwise independence of the phases $(\mod (2\pi))$ is the main technical contribution of this work. This randomization enables us, given a Hermitian matrix with well separated eigenvalues, to sample a random eigenvalue and produce an approximate eigenvector in $O(\log^2 n)$ parallel time and $O(n^\omega)$ Boolean complexity. We conjecture that further improvements of our method can provide a stable solution to the full approximate spectral decomposition problem with complexity similar to the complexity (up to a logarithmic factor) of sampling a single eigenvector.Comment: Replacing previous version: parallel algorithm runs in total complexity $n^{\omega+1}$ and not $n^{\omega}$. However, the depth of the implementing circuit is $\log^2(n)$: hence comparable to fastest eigen-decomposition algorithms know

Functional roles for noise in genetic circuits

The genetic circuits that regulate cellular functions are subject to stochastic fluctuations, or ‘noise’, in the levels of their components. Noise, far from just a nuisance, has begun to be appreciated for its essential role in key cellular activities. Noise functions in both microbial and eukaryotic cells, in multicellular development, and in evolution. It enables coordination of gene expression across large regulons, as well as probabilistic differentiation strategies that function across cell populations. At the longest timescales, noise may facilitate evolutionary transitions. Here we review examples and emerging principles that connect noise, the architecture of the gene circuits in which it is present, and the biological functions it enables. We further indicate some of the important challenges and opportunities going forward

Catheter-induced mechanical trauma to accessory pathways during radiofrequency ablation: incidence, predictors and clinical implications

AbstractOBJECTIVESTo evaluate the incidence, predictors and clinical implications of nonintentionally catheter-induced mechanical trauma to accessory pathways during radiofrequency ablation procedures.BACKGROUNDData on the incidence and significance of catheter-induced trauma to accessory pathways are scarce.METHODSConsecutive patients (n = 381) undergoing radiofrequency ablation of accessory pathways at two different institutions were closely monitored for appearance of mechanical block of accessory pathways during catheter manipulation.RESULTSMechanical trauma to accessory pathways was observed in 37 (9.7%) patients. According to a multivariate analysis, the only independent variable associated with this phenomenon was the anatomical pathway location (p = 0.0001). The incidence of trauma of either right anteroseptal (38.5%) or right atriofascicular pathways (33.3%) was significantly greater than that of pathways (≤10%) at all remaining locations (p < 0.0001). The duration of conduction block observed ranged from ≤1 min to >30 min in 19% and 35% of patients, respectively. “Immediate” application of radiofrequency pulses at sites of mechanical block (<1 min after occurrence) was associated with a 78% long-term success rate at follow-up. This contrasted with a 25% long-term success rate in patients in whom pulses were delivered 30 min after occurrence of block (“delayed pulses”). Finally, in 24% of patients persistent trauma-induced conduction block led to discontinuation of the ablation procedure.CONCLUSIONSTrauma to accessory pathways is more common than previously recognized and frequently results in prolongation or discontinuation of the ablation procedure and in lower success rates. The only independent predictor of catheter-trauma to accessory pathways is the pathway location

IRAS versus POTENT Density Fields on Large Scales: Biasing and Omega

The galaxy density field as extracted from the IRAS 1.2 Jy redshift survey is compared to the mass density field as reconstructed by the POTENT method from the Mark III catalog of peculiar velocities. The reconstruction is done with Gaussian smoothing of radius 12 h^{-1}Mpc, and the comparison is carried out within volumes of effective radii 31-46 h^{-1}Mpc, containing approximately 10-26 independent samples. Random and systematic errors are estimated from multiple realizations of mock catalogs drawn from a simulation that mimics the observed density field in the local universe. The relationship between the two density fields is found to be consistent with gravitational instability theory in the mildly nonlinear regime and a linear biasing relation between galaxies and mass. We measure beta = Omega^{0.6}/b_I = 0.89 \pm 0.12 within a volume of effective radius 40 h^{-1}Mpc, where b_I is the IRAS galaxy biasing parameter at 12 h^{-1}Mpc. This result is only weakly dependent on the comparison volume, suggesting that cosmic scatter is no greater than \pm 0.1. These data are thus consistent with Omega=1 and b_I\approx 1. If b_I>0.75, as theoretical models of biasing indicate, then Omega>0.33 at 95% confidence. A comparison with other estimates of beta suggests scale-dependence in the biasing relation for IRAS galaxies.Comment: 35 pages including 10 figures, AAS Latex, Submitted to The Astrophysical Journa

Prognostication after out-of-hospital cardiac arrest, a clinical survey

Background: Numerous parameters and tests have been proposed for outcome prediction in comatose out-of-hospital cardiac arrest survivors. We conducted a survey of clinical practice of prognostication after therapeutic hypothermia (TH) became common practice in Norway. Methods: By telephone, we interviewed the consultants who were in charge of the 25 ICUs admitting cardiac patients using 6 structured questions regarding timing, tests used and medical specialties involved in prognostication, as well as the clinical importance of the different parameters used and the application of TH in these patients. Results: Prognostication was conducted within 24–48 hours in the majority (72%) of the participating ICUs. The most commonly applied parameters and tests were a clinical neurological examination (100%), prehospital data (76%), CCT (56%) and EEG (52%). The parameters and tests considered to be of greatest importance for accurate prognostication were prehospital data (56%), neurological examination (52%), and EEG (20%). In 76% of the ICUs, a multidisciplinary approach to prognostication was applied, but only one ICU used a standardised protocol. Therapeutic hypothermia was in routine use in 80% of the surveyed ICUs. Conclusion: Despite the routine use of TH, outcome prediction was performed early and was mainly based on prehospital information, neurological examination and CCT and EEG evaluation. Somatosensory evoked potentials appear to be underused and underrated, while the importance of prehospital data, CCT and EEG to appear to be overrated as methods for making accurate predictions. More evidence-based protocols for prognostication in cardiac arrest survivors, as well as additional studies on the effect of TH on known prognostic parameters are needed

Political influence through microtargeting

Political actors routinely target custom audiences on social media in order to influence elections. We model this process, focusing on the way in which it induces voters to learn about their own preferences. This differs from the past literature, which has focused on party platforms and the effects of bias. We find that the optimal strategy based on some empirically estimated parameters is to target groups favoring one’s opponents, providing a rational explanation for negative campaigning. More generally, log-concave cost of voting distributions can give rise to a non-convex set being targeted—weak supporters of the politician and strong sup porters of their opponent. We make use of this setup to provide a novel analysis of the effects of micro-targeting on turnout, and find a sense in which lower costs of voting encourage negative campaigning

Successful use of therapeutic hypothermia in an opiate induced out-of-hospital cardiac arrest complicated by severe hypoglycaemia and amphetamine intoxication: a case report

The survival to discharge rate after unwitnessed, non-cardiac out-of-hospital cardiac arrest (OHCA) is dismal. We report the successful use of therapeutic hypothermia in a 26-year old woman with OHCA due to intentional poisoning with heroin, amphetamine and insulin

Partial penetrance facilitates developmental evolution in bacteria

Development normally occurs similarly in all individuals within an isogenic population, but mutations often affect the fates of individual organisms differently. This phenomenon, known as partial penetrance, has been observed in diverse developmental systems. However, it remains unclear how the underlying genetic network specifies the set of possible alternative fates and how the relative frequencies of these fates evolve. Here we identify a stochastic cell fate determination process that operates in Bacillus subtilis sporulation mutants and show how it allows genetic control of the penetrance of multiple fates. Mutations in an intercompartmental signalling process generate a set of discrete alternative fates not observed in wild-type cells, including rare formation of two viable 'twin' spores, rather than one within a single cell. By genetically modulating chromosome replication and septation, we can systematically tune the penetrance of each mutant fate. Furthermore, signalling and replication perturbations synergize to significantly increase the penetrance of twin sporulation. These results suggest a potential pathway for developmental evolution between monosporulation and twin sporulation through states of intermediate twin penetrance. Furthermore, time-lapse microscopy of twin sporulation in wild-type Clostridium oceanicum shows a strong resemblance to twin sporulation in these B. subtilis mutants. Together the results suggest that noise can facilitate developmental evolution by enabling the initial expression of discrete morphological traits at low penetrance, and allowing their stabilization by gradual adjustment of genetic parameters