The transition temperature of the dilute interacting Bose gas for NN internal degrees of freedom

We calculate explicitly the variation $\delta T_c$ of the Bose-Einstein condensation temperature $T_c$ induced by weak repulsive two-body interactions to leading order in the interaction strength. As shown earlier by general arguments, $\delta T_c/T_c$ is linear in the dimensionless product $an^{1/3}$ to leading order, where $n$ is the density and $a$ the scattering length. This result is non-perturbative, and a direct perturbative calculation of the amplitude is impossible due to infrared divergences familiar from the study of the superfluid helium lambda transition. Therefore we introduce here another standard expansion scheme, generalizing the initial model which depends on one complex field to one depending on $N$ real fields, and calculating the temperature shift at leading order for large $N$. The result is explicit and finite. The reliability of the result depends on the relevance of the large $N$ expansion to the situation N=2, which can in principle be checked by systematic higher order calculations. The large $N$ result agrees remarkably well with recent numerical simulations.Comment: 10 pages, Revtex, submitted to Europhysics Letter

Quantum phase transition in an atomic Bose gas near a Feshbach resonance

We study the quantum phase transition in an atomic Bose gas near a Feshbach resonance in terms of the renormalization group. This quantum phase transition is characterized by an Ising order parameter. We show that in the low temperature regime where the quantum fluctuations dominate the low-energy physics this phase transition is of first order because of the coupling between the Ising order parameter and the Goldstone mode existing in the bosonic superfluid. However, when the thermal fluctuations become important, the phase transition turns into the second order one, which belongs to the three-dimensional Ising universality class. We also calculate the damping rate of the collective mode in the phase with only a molecular Bose-Einstein condensate near the second-order transition line, which can serve as an experimental signature of the second-order transition.Comment: 8 pages, 2 figures, published version in Phys. Rev.

Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops

The shift of the Bose-Einstein condensation temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length `a' is computed for given particle density `n.' Variational perturbation theory is used to resum the corresponding perturbative series for Delta/Nu in a classical three-dimensional scalar field theory with coupling `u' and where the physical case of N=2 field components is generalized to arbitrary N. Our results for N=1,2,4 are in agreement with recent Monte-Carlo simulations; for N=2, we obtain Delta T_c/T_c = 1.27 +/- 0.11 a n^(1/3). We use seven-loop perturbative coefficients, extending earlier work by one loop order.Comment: 8 pages; typos and errors of presentation fixed; beautifications; results unchange

A global transcriptional network connecting noncoding mutations to changes in tumor gene expression.

Although cancer genomes are replete with noncoding mutations, the effects of these mutations remain poorly characterized. Here we perform an integrative analysis of 930 tumor whole genomes and matched transcriptomes, identifying a network of 193 noncoding loci in which mutations disrupt target gene expression. These 'somatic eQTLs' (expression quantitative trait loci) are frequently mutated in specific cancer tissues, and the majority can be validated in an independent cohort of 3,382 tumors. Among these, we find that the effects of noncoding mutations on DAAM1, MTG2 and HYI transcription are recapitulated in multiple cancer cell lines and that increasing DAAM1 expression leads to invasive cell migration. Collectively, the noncoding loci converge on a set of core pathways, permitting a classification of tumors into pathway-based subtypes. The somatic eQTL network is disrupted in 88% of tumors, suggesting widespread impact of noncoding mutations in cancer

Thermodynamic properties of confined interacting Bose gases - a renormalization group approach

A renormalization group method is developed with which thermodynamic properties of a weakly interacting, confined Bose gas can be investigated. Thereby effects originating from a confining potential are taken into account by periodic boundary conditions and by treating the resulting discrete energy levels of the confined degrees of freedom properly. The resulting density of states modifies the flow equations of the renormalization group in momentum space. It is shown that as soon as the characteristic length of confinement becomes comparable to the thermal wave length of a weakly interacting and trapped Bose gas its thermodynamic properties are changed significantly. This is exemplified by investigating characteristic bunching properties of the interacting Bose gas which manifest themselves in the second order coherence factor

The transition temperature of the dilute interacting Bose gas

We show that the critical temperature of a uniform dilute Bose gas must increase linearly with the s-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.Comment: 4 pages, Revtex, to be published in Physical Review Letter

Energy representation for out-of-equilibrium Brownian-like systems: steady states and fluctuation relations

Stochastic dynamics in the energy representation is employed as a method to study non-equilibrium Brownian-like systems. It is shown that the equation of motion for the energy of such systems can be taken in the form of the Langevin equation with multiplicative noise. Properties of the steady states are examined by solving the Fokker-Planck equation for the energy distribution functions. The generalized integral fluctuation theorem is deduced for the systems characterized by the shifted probability flux operator. There are a number of entropy and fluctuation relations such as the Hatano-Sasa identity and the Jarzynski's equality that follow from this theorem.Comment: revtex4-1, 18 pages, extended discussion, references adde

Association between remnant lipoprotein cholesterol levels and non-alcoholic fatty liver disease in adolescents

Background & Aims: Remnant lipoprotein cholesterol (RLP-C) is an atherogenic lipid profile associated with non-alcoholic fatty liver disease (NAFLD) and cardiovascular disease (CVD). With increased rates of CVD seen in adults with NAFLD, RLP-C has the potential to identify individuals with NAFLD who are at increased risk of CVD. This study examined in adolescents sex-different associations among RLP-C, NAFLD, and cardiometabolic risk factors, and whether RLP-C is associated with NAFLD beyond traditional cardiometabolic risk factors. Methods: Adolescents in the Raine Study had anthropometry, clinical, biochemistry and arterial stiffness measurements recorded at 17 years of age. Fatty liver, subcutaneous and visceral adipose thickness were assessed using abdominal ultrasound. Relationships among RLP-C, NAFLD, liver biochemistry, insulin resistance, adipokines, adiposity and arterial stiffness were assessed. Results: NAFLD was diagnosed in 15.1% (19.6% females and 10.7% males) of adolescents. Increasing RLP-C levels were associated with increasing severity of hepatic steatosis and metabolic syndrome. Adolescents with NAFLD and serum RLP-C levels in the highest quartile compared with the lowest quartile, had higher serum leptin, homeostatic model assessment of insulin resistance (HOMA-IR), high-sensitivity C-reactive protein, low-density-lipoprotein cholesterol, triglycerides, BMI, subcutaneous and visceral adipose thickness, systolic blood pressure and arterial stiffness, but lower adiponectin and high-density-lipoprotein cholesterol. Using multivariable logistic regression, RLP-C in the lowest quartile compared with the highest quartile was associated with 85% lower odds of NAFLD in males and 55% in females, after adjusting for waist circumference, leptin, ALT, adiponectin and HOMA-IR. Conclusions: There is an association between RLP-C and NAFLD beyond traditional risk factors of adiposity and insulin resistance in adolescents. Although raised serum RLP-C levels were associated with the severity of hepatic steatosis and markers of cardiometabolic risk, lower serum RLP-C might reflect reduced cardiovascular risk. Lay summary: Remnant lipoprotein cholesterol (RLP-C) is a part of the blood cholesterol that is linked with heart disease and non-alcoholic fatty liver disease (NAFLD) in adults. In the Raine Study, teenagers with high RLP-C levels had more severe fat accumulation in their liver. Thus, RLP-C might be the hidden link between NAFLD and future risk of heart disease

Thermodynamics of a trapped interacting Bose gas and the renormalization group

We apply perturbative renormalization group theory to the symmetric phase of a dilute interacting Bose gas which is trapped in a three-dimensional harmonic potential. Using Wilsonian energy-shell renormalization and the epsilon-expansion, we derive the flow equations for the system. We relate these equations to the flow for the homogeneous Bose gas. In the thermodynamic limit, we apply our results to study the transition temperature as a function of the scattering length. Our results compare well to previous studies of the problem.Comment: 14 pages, 5 figure

Predicting melanoma survival and metastasis with interpretable histopathological features and machine learning models

IntroductionMelanoma is the fifth most common cancer in US, and the incidence is increasing 1.4% annually. The overall survival rate for early-stage disease is 99.4%. However, melanoma can recur years later (in the same region of the body or as distant metastasis), and results in a dramatically lower survival rate. Currently there is no reliable method to predict tumor recurrence and metastasis on early primary tumor histological images.MethodsTo identify rapid, accurate, and cost-effective predictors of metastasis and survival, in this work, we applied various interpretable machine learning approaches to analyze melanoma histopathological H&E images. The result is a set of image features that can help clinicians identify high-risk-of-metastasis patients for increased clinical follow-up and precision treatment. We use simple models (i.e., logarithmic classification and KNN) and “human-interpretable” measures of cell morphology and tissue architecture (e.g., cell size, staining intensity, and cell density) to predict the melanoma survival on public and local Stage I–III cohorts as well as the metastasis risk on a local cohort.ResultsWe use penalized survival regression to limit features available to downstream classifiers and investigate the utility of convolutional neural networks in isolating tumor regions to focus morphology extraction on only the tumor region. This approach allows us to predict survival and metastasis with a maximum F1 score of 0.72 and 0.73, respectively, and to visualize several high-risk cell morphologies.DiscussionThis lays the foundation for future work, which will focus on using our interpretable pipeline to predict metastasis in Stage I & II melanoma