We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length $l_P$. This suggests a Planck-size minimum ball of uncertainty in any measurement. Next, we study interferometers (such as LIGO) whose precision is much finer than the size of any individual components and hence are not obviously limited by the minimum ball. Nevertheless, we deduce a fundamental limit on their accuracy of order $l_P$. Our results imply a device independent limit on possible position measurements.

We construct genomic predictors for heritable but extremely complex human quantitative traits (height, heel bone density, and educational attainment) using modern methods in high dimensional statistics (i.e., machine learning). The constructed predictors explain, respectively, ∼40, 20, and 9% of total variance for the three traits, in data not used for training. For example, predicted heights correlate ∼0.65 with actual height; actual heights of most individuals in validation samples are within a few centimeters of the prediction. The proportion of variance explained for height is comparable to the estimated common SNP heritability from genome-wide complex trait analysis (GCTA), and seems to be close to its asymptotic value (i.e., as sample size goes to infinity), suggesting that we have captured most of the heritability for SNPs. Thus, our results close the gap between prediction R-squared and common SNP heritability. The ∼20k activated SNPs in our height predictor reveal the genetic architecture of human height, at least for common variants. Our primary dataset is the UK Biobank cohort, comprised of almost 500k individual genotypes with multiple phenotypes. We also use other datasets and SNPs found in earlier genome-wide association studies (GWAS) for out-of-sample validation of our results.

We show that in single scalar field models of the dark energy with equations of state satisfying $w\equiv p/\rho <-1$, the effective Lagrangian for fluctuations about the homogeneous background has a wrong sign spatial kinetic term. In most cases, spatial gradients are ruled out by microwave background observations. The sign of $w+1$ is not connected to the sign of the time derivative kinetic term in the effective Lagrangian.

We extend previous work showing that violation of the null energy condition implies instability in a broad class of models, including gauge theories with scalar and fermionic matter as well as any perfect fluid. Simple examples are given to illustrate these results. The role of causality in our results is discussed. Finally, we extend the fluid results to more general systems in thermal equilibrium. When applied to the dark energy, our results imply that $w=p/\rho$ is unlikely to be less than $-1$.

We investigate the effect of long range magnetic interactions on the renormalization group (RG) evolution of local Cooper pairing interactions near the Fermi surface in high density QCD. We use an explicit cut-off on momentum modes, with special emphasis on screening effects such as Landau damping, to derive the RG equations in a gauge invariant, weak coupling expansion. We obtain the Landau pole $\Delta \sim \mu g^{-5} \exp(- \frac{3 \pi^2}{\sqrt{2} g})$, although the structure of our equations differs from previous results. We also investigate the gap equation, including condensates of higher angular momentum. We show that rotational invariance is unbroken at asymptotically high density, and verify that $\Delta$ is the correct value of the gap when higher modes are included in the analysis.Comment: 17 pages, 3 figures, late

We construct risk predictors using polygenic scores (PGS) computed from common Single Nucleotide Polymorphisms (SNPs) for a number of complex disease conditions, using L1-penalized regression (also known as LASSO) on case-control data from UK Biobank. Among the disease conditions studied are Hypothyroidism, (Resistant) Hypertension, Type 1 and 2 Diabetes, Breast Cancer, Prostate Cancer, Testicular Cancer, Gallstones, Glaucoma, Gout, Atrial Fibrillation, High Cholesterol, Asthma, Basal Cell Carcinoma, Malignant Melanoma, and Heart Attack. We obtain values for the area under the receiver operating characteristic curves (AUC) in the range ~0.58–0.71 using SNP data alone. Substantially higher predictor AUCs are obtained when incorporating additional variables such as age and sex. Some SNP predictors alone are sufficient to identify outliers (e.g., in the 99th percentile of polygenic score, or PGS) with 3–8 times higher risk than typical individuals. We validate predictors out-of-sample using the eMERGE dataset, and also with different ancestry subgroups within the UK Biobank population. Our results indicate that substantial improvements in predictive power are attainable using training sets with larger case populations. We anticipate rapid improvement in genomic prediction as more case-control data become available for analysis.