From constructive field theory to fractional stochastic calculus. (II) Constructive proof of convergence for the L\'evy area of fractional Brownian motion with Hurst index α∈(1/8,1/4)\alpha\in(1/8,1/4)

{Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\alpha<1/4$, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of $B$ is a difficult task because of the low H\"older regularity index of its paths. Yet rough path theory shows it is the key to the construction of a stochastic calculus with respect to $B$, or to solving differential equations driven by $B$. We intend to show in a series of papers how to desingularize iterated integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using "standard" tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates, and call for an extension of Gaussian tools such as for instance the Malliavin calculus. After a first introductory paper \cite{MagUnt1}, this one concentrates on the details of the constructive proof of convergence for second-order iterated integrals, also known as L\'evy area

Quantum Bubble Nucleation beyond WKB: Resummation of Vacuum Bubble Diagrams

On the basis of Borel resummation, we propose a systematical improvement of bounce calculus of quantum bubble nucleation rate. We study a metastable super-renormalizable field theory, $D$ dimensional O(N) symmetric $\phi^4$ model ($D<4$) with an attractive interaction. The validity of our proposal is tested in D=1 (quantum mechanics) by using the perturbation series of ground state energy to high orders. We also present a result in D=2, based on an explicit calculation of vacuum bubble diagrams to five loop orders.Comment: 19 pages, 5 figures, PHYZZ

The N-component Ginzburg-Landau Hamiltonian with cubic anisotropy: a six-loop study

We consider the Ginzburg-Landau Hamiltonian with a cubic-symmetric quartic interaction and compute the renormalization-group functions to six-loop order in d=3. We analyze the stability of the fixed points using a Borel transformation and a conformal mapping that takes into account the singularities of the Borel transform. We find that the cubic fixed point is stable for N>N_c, N_c = 2.89(4). Therefore, the critical properties of cubic ferromagnets are not described by the Heisenberg isotropic Hamiltonian, but instead by the cubic model at the cubic fixed point. For N=3, the critical exponents at the cubic and symmetric fixed points differ very little (less than the precision of our results, which is $\lesssim 1$ in the case of $\gamma$ and $\nu$). Moreover, the irrelevant interaction bringing from the symmetric to the cubic fixed point gives rise to slowly-decaying scaling corrections with exponent $\omega_2=0.010(4)$. For N=2, the isotropic fixed point is stable and the cubic interaction induces scaling corrections with exponent $\omega_2 = 0.103(8)$. These conclusions are confirmed by a similar analysis of the five-loop $\epsilon$-expansion. A constrained analysis which takes into account that $N_c = 2$ in two dimensions gives $N_c = 2.87(5)$.Comment: 29 pages, RevTex, new refs added, Phys. Rev. B in pres

Critical Exponents of the N-vector model

Recently the series for two RG functions (corresponding to the anomalous dimensions of the fields phi and phi^2) of the 3D phi^4 field theory have been extended to next order (seven loops) by Murray and Nickel. We examine here the influence of these additional terms on the estimates of critical exponents of the N-vector model, using some new ideas in the context of the Borel summation techniques. The estimates have slightly changed, but remain within errors of the previous evaluation. Exponents like eta (related to the field anomalous dimension), which were poorly determined in the previous evaluation of Le Guillou--Zinn-Justin, have seen their apparent errors significantly decrease. More importantly, perhaps, summation errors are better determined. The change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values. Finally, because an error has been discovered in the last order of the published epsilon=4-d expansions (order epsilon^5), we have also reanalyzed the determination of exponents from the epsilon-expansion. The conclusion is that the general agreement between epsilon-expansion and 3D series has improved with respect to Le Guillou--Zinn-Justin.Comment: TeX Files, 27 pages +2 figures; Some values are changed; references update

On the nature of the finite-temperature transition in QCD

We discuss the nature of the finite-temperature transition in QCD with N_f massless flavors. Universality arguments show that a continuous (second-order) transition must be related to a 3-D universality class characterized by a complex N_f X N_f matrix order parameter and by the symmetry-breaking pattern [SU(N_f)_L X SU(N_f)_R]/Z(N_f)_V -> SU(N_f)_V/Z(N_f)_V, or [U(N_f)_L X U(N_f)_R]/U(1)_V -> U(N_f)_V/U(1)_V if the U(1)_A symmetry is effectively restored at T_c. The existence of any of these universality classes requires the presence of a stable fixed point in the corresponding 3-D Phi^4 theory with the expected symmetry-breaking pattern. Otherwise, the transition is of first order. In order to search for stable fixed points in these Phi^4 theories, we exploit a 3-D perturbative approach in which physical quantities are expanded in powers of appropriate renormalized quartic couplings. We compute the corresponding Callan-Symanzik beta-functions to six loops. We also determine the large-order behavior to further constrain the analysis. No stable fixed point is found, except for N_f=2, corresponding to the symmetry-breaking pattern [SU(2)_L X SU(2)_R]/Z(2)_V -> SU(2)_V/Z(2)_V equivalent to O(4) -> O(3). Our results confirm and put on a firmer ground earlier analyses performed close to four dimensions, based on first-order calculations in the framework of the epsilon=4-d expansion. These results indicate that the finite-temperature phase transition in QCD is of first order for N_f>2. A continuous transition is allowed only for N_f=2. But, since the theory with symmetry-breaking pattern [U(2)_L X U(2)_R]/U(1)_V -> U(2)_V/U(1)_V does not have stable fixed points, the transition can be continuous only if the effective breaking of the U(1)_A symmetry is sufficiently large.Comment: 30 pages, 3 figs, minor correction

Critical behavior of the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy

We study the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy. We compute and analyze the fixed-dimension perturbative expansion of the renormalization-group functions to four loops. The relations of these models with N-color Ashkin-Teller models, discrete cubic models, planar model with fourth order anisotropy, and structural phase transition in adsorbed monolayers are discussed. Our results for N=2 (XY model with cubic anisotropy) are compatible with the existence of a line of fixed points joining the Ising and the O(2) fixed points. Along this line the exponent $\eta$ has the constant value 1/4, while the exponent $\nu$ runs in a continuous and monotonic way from 1 to $\infty$ (from Ising to O(2)). For N\geq 3 we find a cubic fixed point in the region $u, v \geq 0$, which is marginally stable or unstable according to the sign of the perturbation. For the physical relevant case of N=3 we find the exponents $\eta=0.17(8)$ and $\nu=1.3(3)$ at the cubic transition.Comment: 14 pages, 9 figure

Cell-Free DNA Genomic Profiling and Its Clinical Implementation in Advanced Prostate Cancer.

Most men with prostate cancer (PCa), despite potentially curable localized disease at initial diagnosis, progress to metastatic disease. Despite numerous treatment options, choosing the optimal treatment for individual patients remains challenging. Biomarkers guiding treatment sequences in an advanced setting are lacking. To estimate the diagnostic potential of liquid biopsies in guiding personalized treatment of PCa, we evaluated the utility of a custom-targeted next-generation sequencing (NGS) panel based on the AmpliSeq HD Technology. Ultra-deep sequencing on plasma circulating free DNA (cfDNA) samples of 40 metastatic castration-resistant PCa (mCRPC) and 28 metastatic hormone-naive PCa (mCSPC) was performed. CfDNA somatic mutations were detected in 48/68 (71%) patients. Of those 68 patients, 42 had matched tumor and cfDNA samples. In 21/42 (50%) patients, mutations from the primary tumor tissue were detected in the plasma cfDNA. In 7/42 (17%) patients, mutations found in the primary tumor were not detected in the cfDNA. Mutations from primary tumors were detected in all tested mCRPC patients (17/17), but only in 4/11 with mCSPC. AR amplifications were detected in 12/39 (31%) mCRPC patients. These results indicate that our targeted NGS approach has high sensitivity and specificity for detecting clinically relevant mutations in PCa

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, that corresponds to the limit $N\to 0$ of an $N$-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions concerning the critical crossover functions, finding a good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal lscrossover behavior of our data for any finite range.Comment: 43 pages, revte

The power of perturbation theory

We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach based on the PicardLefschetz theory we characterize the conditions under which perturbative expansions lead to exact results. Even when such conditions are not met, we explain how to define a different perturbative expansion that reproduces the full answer without the need of transseries, i.e. non-perturbative effects, such as real (or complex) instantons. Applications to several quantum mechanical systems are presented

Coordinated changes in energy intake and expenditure following hypothalamic administration of neuropeptides involved in energy balance

OBJECTIVE: The hypothalamic control of energy balance is regulated by a complex network of neuropeptide-releasing neurons. Whilst the effect of these neuropeptides on individual aspects of energy homeostasis has been studied, the coordinated response of these effects has not been comprehensively investigated. We have simultaneously monitored a number of metabolic parameters following ICV administration of 1nmol and 3nmol of neuropeptides with established roles in the regulation of feeding, activity and metabolism. Ad libitum fed rats received the orexigenic neuropeptides neuropeptide Y (NPY), agouti-related protein (AgRP), melanin-concentrating hormone (MCH) or orexin-A. Overnight food deprived rats received an ICV injection of the anorectic peptides α-MSH, corticotrophin releasing factor (CRF) or neuromedin U (NMU). RESULTS: Our results reveal the temporal sequence of the effects of these neuropeptides on both energy intake and expenditure, highlighting key differences in their function as mediators of energy balance. NPY and AgRP increased feeding and decreased oxygen consumption, with the effects of AgRP being more prolonged. In contrast, orexin-A increased both feeding and oxygen consumption, consistent with an observed increase in activity. The potent anorexigenic effects of CRF were accompanied by a prolonged increase in activity whilst NMU injection resulted in significant but short-lasting inhibition of food intake, ambulatory activity and oxygen consumption. Alpha-MSH injection resulted in significant increases in both ambulatory activity and oxygen consumption, and reduced food intake following administration of 3nmol of the peptide. CONCLUSION: We have for the first time, simultaneously measured several metabolic parameters following hypothalamic administration of a number of neuropeptides within the same experimental system. This work has demonstrated the interrelated effects of these neuropeotides on activity, energy expenditure and food intake thus facilitating comparison between the different hypothalamic systems