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We use the recent observations of Cosmic Microwave Background temperature and polarization anisotropies provided by the Planck satellite experiment to place constraints on the running $α_\mathrm{s} = \mathrm{d}n_{\mathrm{s}} / \mathrm{d}\log k$ and the running of the running $β_{\mathrm{s}} = \mathrm{d}α_{\mathrm{s}} / \mathrm{d}\log k$ of the spectral index $n_{\mathrm{s}}$ of primordial scalar fluctuations. We find $α_\mathrm{s}=0.011\pm0.010$ and $β_\mathrm{s}=0.027\pm0.013$ at $68\%\,\mathrm{CL}$, suggesting the presence of a running of the running at the level of two standard deviations. We find no significant correlation between $β_{\mathrm{s}}$ and foregrounds parameters, with the exception of the point sources amplitude at $143\,\mathrm{GHz}$, $A^{PS}_{143}$, which shifts by half sigma when the running of the running is considered. We further study the cosmological implications of such preference for $α_\mathrm{s},β_\mathrm{s}\sim0.01$ by including in the analysis the lensing amplitude $A_L$, the curvature parameter $Ω_k$, and the sum of neutrino masses $\sum m_ν$. We find that when the running of the running is considered, Planck data are more compatible with the standard

Running is part of almost every sport, and requires a great amount of stamina, endurance, mental toughness and overall strength. At every step, the foot experiences ground reaction forces necessary to support the motion of the body. With the advancements in shoe technology, running shoes have grown in popularity among runners, as well as non-runners, because they reduce the risk of injuries from the impact felt by the foot. The purpose of this report is to analyze the effect of running shoes on impact forces on the foot. This is achieved through the use of three force pads fixed at different locations on the foot The force measured by each sensor is then used to estimate the vertical ground reaction force, using the sensors' calibrations equations . Based on the ground reaction force, the effective mass corresponding to the momentum change occurring during the transient phase of the impact is estimated. The results show that running at 9 miles per hour without running shoes generates an effective mass of (14.9 +/- 4.8)% of the total body mass, while running at the same speed with running shoes generates an effective mass of (7.8 +/- 1.5 )% of the total body mass. The values highlig

We provide a game-theoretic analysis of the problem of front-running attacks. We use it to distinguish attacks from legitimate competition among honest users for having their transactions included earlier in the block. We also use it to introduce an intuitive notion of the severity of front-running attacks. We then study a simple commit-reveal protocol and discuss its properties. This protocol has costs because it requires two messages and imposes a delay. However, we show that it prevents the most severe front-running attacks while preserving legitimate competition between users, guaranteeing that the earliest transaction in a block belongs to the honest user who values it the most. When the protocol does not fully eliminate attacks, it nonetheless benefits honest users because it reduces competition among attackers (and overall expenditure by attackers).

We calculate running coupling corrections for the lowest-order gluon production cross section in high energy hadronic and nuclear scattering using the BLM scale-setting prescription. At leading order there are three powers of fixed coupling; in our final answer, these three couplings are replaced by seven factors of running coupling: five in the numerator and two in the denominator, forming a `septumvirate' of running couplings, analogous to the `triumvirate' of running couplings found earlier for the small-x BFKL/BK/JIMWLK evolution equations. It is interesting to note that the two running couplings in the denominator of the `septumvirate' run with complex-valued momentum scales, which are complex conjugates of each other, such that the production cross section is indeed real. We use our lowest-order result to conjecture how running coupling corrections may enter the full fixed-coupling k_T-factorization formula for gluon production which includes non-linear small-x evolution.

We calculate running coupling corrections for the lowest-order gluon production cross section in high energy hadronic and nuclear scattering using the BLM scale-setting prescription. In the final answer for the cross section the three powers of fixed coupling are replaced by seven factors of running coupling, five in the numerator and two in the denominator, forming a 'septumvirate' of running couplings, analogous to the 'triumvirate' of running couplings found earlier for the small-x BFKL/BK/JIMWLK evolution equations. It is interesting to note that the two running couplings in the denominator of the 'septumvirate' run with complex-valued momentum scales, which are complex conjugates of each other, such that the production cross section is indeed real. We use our lowest-order result to conjecture how running coupling corrections may enter the full fixed-coupling kT-factorization formula for gluon production which includes non-linear small-x evolution.

Current data from the Planck satellite and the BICEP2 telescope favor, at around the $2 σ$ level, negative running of the spectral index of curvature perturbations from inflation. We show that for negative running $α< 0$, the curvature perturbation amplitude has a maximum on scales larger than our current horizon size. A condition for the absence of eternal inflation is that the curvature perturbation amplitude always remain below unity on superhorizon scales. For current bounds on $n_{\rm S}$ from Planck, this corresponds to an upper bound of the running $α< - 4 \times 10^{-5}$, so that even tiny running of the scalar spectral index is sufficient to prevent eternal inflation from occurring, as long as the running remains negative on scales outside the horizon. In single-field inflation models, negative running is associated with a finite duration of inflation: we show that eternal inflation may not occur even in cases where inflation lasts as long as $10^4$ e-folds.

The new model for the QCD analytic running coupling, proposed recently, is extended to the timelike region. This running coupling naturally arises under unification of the analytic approach to QCD and the renormalization group (RG) formalism. A new method for determining the coefficients of the "analytized" RG equation is elaborated. It enables one to take into account the higher loop contributions to the new analytic running coupling (NARC) in a consistent way. The expression for the new analytic running coupling, independent of the normalization point, is obtained by invoking the asymptotic freedom condition. It is shown that the difference between the values of the NARC in respective spacelike and timelike regions is rather valuable for intermediate energies. This is essential for the correct extracting of the running coupling from experimental data. The new analytic running coupling is applied to the description of the inclusive $τ$ lepton decay. The consistent estimation of the parameter $Λ_{QCD}$ is obtained here.

Next generation of cosmological observations are expected to improve the measurements of several quantities connected to the primordial inflation in the early Universe. These quantities include for example improved measurements for the spectral index of the scalar curvature of the primordial power spectrum and to also bring a better understanding on the scaling dependence of the primordial spectrum. This includes the running of the tilt and, possibly, also the running of the running. In this paper, we investigate the possibility of generating large runnings in the context of warm inflation. Useful analytical expressions for the runnings are derived in the context of warm inflation in the strong dissipation regime. The results are compared to and discussed for some well motivated primordial inflaton potentials that have recently been of interest in the literature.

Physical activity is known to help improve and maintain one's health. In particular, recreational running has become increasingly popular in recent years. Yet, lack of motivation often interferes with people's routines and thus may prohibit regular uptake. This is where running tracking applications are frequently used to overcome one's weaker self and offer support. While technology artifacts, such as sport watches or running applications, usually count as extrinsic drivers, they can also impact one's intrinsic motivation levels. The aim of this study was thus to investigate upon the motivational impact of distinct features found within applications specifically used for running. Focusing on the 22 most famous running applications, a semi-structured, problem-centered interview study with $n=15$ recreational runners showed that intrinsic motivation is stimulated from diverting runners, aiding them in their goal setting, decreasing their efforts, improving and sharing their run performance, allowing them to receive acknowledgements, as well as providing them with guidance, information, and an overall variety in their training routines.

We discuss the running couplings in the standard model, SU(3$)_C \times $SU(2$)_L \times $U(1$)_Y$, when the Higgs sector is replaced by SU($N_{TC})$ technicolor. Particular attention is given to the running of the couplings at momentum scales where technicolor is nonperturbative, and in this region we apply a relativistic constituent technifermion model. This model has been tested against the known running of the QED coupling due to nonperturbative QCD. An understanding of this low momentum running allows the calculation of the couplings at a higher scale, $Λ_{pert}$, where technicolor becomes perturbative. We provide numerical values for the changes in the three standard model couplings between $m_Z$ and $Λ_{pert}$ due to technicolor, assuming separately ``one doublet'' and ``one family'' technicolor models. The distinction between a running and walking technicolor coupling is also considered.

We explore some thermodynamical consequences of accelerated universes driven by a running cosmological constant (CC) from the renormalization group (RG). Application of the generalized second law (GSL) of gravitational thermodynamics to a framework where the running of the CC goes at the expense of energy transfer between vacuum and matter, strongly restricts the mass spectrum of a (hypothetical) theory controlling the CC running. We find that quantum effects driving the running of the CC should be dominated by a trans-planckian mass field, in marked contrast with the GUT-scale upper mass bound obtained by analyzing density perturbations for the running CC. The model shows compliance with the holographic principle.

The first year WMAP measurement of the CMB temperature anisotropy is intriguingly consistent with a larger running of the inflationary scalar spectral index than would be expected for single-field inflation. We revisit the issue of a large running spectral index, first by reexamining the evidence from the data, and then by reconstructing the inflationary potential, using an improved method based upon the Hamilton-Jacobi formulation. We note that a spectrum which runs only over 1.5 decades of k space provides as good a fit to the CMB data as one which runs at all k, that significant evidence for running comes from multipoles l near 40, and that large running gives a better fit than a flat spectrum primarily if the tensor-to-scalar ratio $r$ is large, r ~ 0.5, and the field values are at the Planck scale. This allows one to break the large degeneracy of potentials which would be consistent with the scalar power alone. Large running, should it be confirmed, is thus linked to a high scale of inflation and the possibility of seeing effects of tensor modes in the CMB and Planck-scale physics. Nevertheless, we show that the reconstructed inflaton potential is well-described by a renormali

Three-year data of WMAP implies not only a negative running of the spectral index with large absolute value, but also a large positive running of running of the spectral index with order of the magnitude $10^{-2}$. We calculate the running of running in usual inflation model and noncommutative inflation model. A large tensor-scalar ratio $r\geq 1.23$ is needed in order to fit the WMAP data in the noncommutative inflation model, which roughly saturates the observational upper bound on it.

The amount of dark matter in the Milky Way and beyond is examined by taking into account the possible running of the gravitational constant $G$ as a function of distance scale. If the running of $G$, as suggested by the Asymptotically-Free Higher-Derivative quantum gravity, is incorporated into the calculation of the total dark matter in the galactic halo, the amount of dark matter that is necessary to explain the rotation curve is shown to be reduced by one third compared with the standard calculations. However, this running of $G$ alone cannot reproduce the observed flat behavior of the rotation curve. It is also shown that the running of $G$ cannot explain away the presence of most of the dark matter beyond the scale of $ \sim 10$ Mpc in the Universe. We also present a pedagogical explanation for the running of $G(r)$ in the region of large scales which is clearly a classical domain.

Despite the many outstanding cosmological observations leading to a strong evidence for a nonvanishing cosmological constant (CC) term in the gravitational field equations, the theoretical status of this quantity seems to be lagging well behind the observational successes. It thus seems timely to revisit some fundamental aspects of the CC term in Quantum Field Theory (QFT). We emphasize that, in curved space-time, nothing a priori prevents this term from potentially having a mild running behavior associated to quantum effects. Remarkably, this could be the very origin of the dynamical nature of the Dark Energy, in contrast to many other popular options considered in the literature. In discussing this possibility, we also address some recent criticisms concerning the possibility of such running. Our conclusion is that, while there is no comprehensive proof of the CC running, there is no proof of the non-running either. The problem can be solved only through a deeper understanding of the vacuum contributions of massive quantum fields on a curved spacetime background. We suggest that such investigations are at the heart of one of the most important endeavors of fundamental theoretical

A simplified higher dimensional Randall-Sundrum-like model in 6 dimensions is considered. It has been observed previously by Goldberger and Wise that in such a self-interacting scalar theory on the bulk with a conical singularity there is mixing of renormalization of 4d brane couplings with that of the bulk couplings. We study the influence of the running bulk couplings on the running of the 4d brane couplings. We find that bulk quantum effects may completely alter the running of brane couplings. In particular, the structure of the Landau pole may be drastically altered and non-asymptotically free running may turn into asymptotically safe (or free) behavior.

We argue that a large negative running spectral index, if confirmed, might suggest that there are abundant structures in the inflaton potential, which result in a fairly large (both positive and negative) running of the spectral index at all scales. It is shown that the center value of the running spectral index suggested by the recent CMB data can be easily explained by an inflaton potential with superimposed periodic oscillations. In contrast to cases with constant running, the perturbation spectrum is enhanced at small scales, due to the repeated modulations. We mention that such features at small scales may be seen by 21 cm observations in the future.

We investigate the scale-dependence, or the runnings, of linear and second order density perturbations generated in various curvaton scenarios. We argue that the second order perturbations, i.e. non-Gaussianity, can strongly depend on the scale, even when the linear perturbations are nearly scale-invariant. We present analytic formulae for the runnings from curvatons with general energy potentials, and clarify the conditions under which fNL becomes strongly scale-dependent. From the point of view of the fNL running, curvaton potentials can be classified into roughly two categories by whether the potential flattens or steepens compared to a quadratic one. As such examples, we study pseudo-Nambu-Goldstone curvatons, and self-interacting curvatons, respectively. The dynamics of non-quadratic curvatons and the behaviors of the resulting density perturbations are clarified by analytical methods. Then we also study models where multiple source can be responsible for density perturbations such as the multi-curvaton, and mixed curvaton and inflaton models where the running of fNL can also be large due to their multi-source nature. We make quantitative analysis for each curvaton scenario an

Based on a study of the analytic running coupling obtained from the standard perturbation theory results up to four-loop order, the QCD ``synthetic'' running coupling α_{syn} is built. In so doing the perturbative time-like discontinuity is preserved and nonperturbative contributions not only remove the nonphysical singularities of the perturbation theory in the infrared region but also decrease rapidly in the ultraviolet region. In the framework of the approach, on the one hand, the running coupling is enhanced at zero and, on the other hand, the dynamical gluon mass m_g arises. Fixing the parameter which characterize the infrared enhancement corresponding to the string tension σand normalization, say, at M_τcompletely define the synthetic running coupling. In this case the dynamical gluon mass appears to be fixed and the higher loop stabilization property of m_g is observed. For σ= (0.42 GeV)^2 and α_{syn}(M^2_τ) = 0.33 \pm 0.01 it is obtained that m_g = 530 \pm 80 MeV.