The kernel and the injectivity of the EPRL map

In this paper we prove injectivity of the EPRL map for |\gamma|<1, filling the gap of our previous paper.Comment: 17 pages, 3 figure

Coherent states, constraint classes, and area operators in the new spin-foam models

Recently, two new spin-foam models have appeared in the literature, both motivated by a desire to modify the Barrett-Crane model in such a way that the imposition of certain second class constraints, called cross-simplicity constraints, are weakened. We refer to these two models as the FKLS model, and the flipped model. Both of these models are based on a reformulation of the cross-simplicity constraints. This paper has two main parts. First, we clarify the structure of the reformulated cross-simplicity constraints and the nature of their quantum imposition in the new models. In particular we show that in the FKLS model, quantum cross-simplicity implies no restriction on states. The deeper reason for this is that, with the symplectic structure relevant for FKLS, the reformulated cross-simplicity constraints, in a certain relevant sense, are now \emph{first class}, and this causes the coherent state method of imposing the constraints, key in the FKLS model, to fail to give any restriction on states. Nevertheless, the cross-simplicity can still be seen as implemented via suppression of intertwiner degrees of freedom in the dynamical propagation. In the second part of the paper, we investigate area spectra in the models. The results of these two investigations will highlight how, in the flipped model, the Hilbert space of states, as well as the spectra of area operators exactly match those of loop quantum gravity, whereas in the FKLS (and Barrett-Crane) models, the boundary Hilbert spaces and area spectra are different.Comment: 21 pages; statements about gamma limits made more precise, and minor phrasing change

Holomorphic Factorization for a Quantum Tetrahedron

We provide a holomorphic description of the Hilbert space H(j_1,..,j_n) of SU(2)-invariant tensors (intertwiners) and establish a holomorphically factorized formula for the decomposition of identity in H(j_1,..,j_n). Interestingly, the integration kernel that appears in the decomposition formula turns out to be the n-point function of bulk/boundary dualities of string theory. Our results provide a new interpretation for this quantity as being, in the limit of large conformal dimensions, the exponential of the Kahler potential of the symplectic manifold whose quantization gives H(j_1,..,j_n). For the case n=4, the symplectic manifold in question has the interpretation of the space of "shapes" of a geometric tetrahedron with fixed face areas, and our results provide a description for the quantum tetrahedron in terms of holomorphic coherent states. We describe how the holomorphic intertwiners are related to the usual real ones by computing their overlap. The semi-classical analysis of these overlap coefficients in the case of large spins allows us to obtain an explicit relation between the real and holomorphic description of the space of shapes of the tetrahedron. Our results are of direct relevance for the subjects of loop quantum gravity and spin foams, but also add an interesting new twist to the story of the bulk/boundary correspondence.Comment: 45 pages; published versio

Physical boundary state for the quantum tetrahedron

We consider stability under evolution as a criterion to select a physical boundary state for the spinfoam formalism. As an example, we apply it to the simplest spinfoam defined by a single quantum tetrahedron and solve the associated eigenvalue problem at leading order in the large spin limit. We show that this fixes uniquely the free parameters entering the boundary state. Remarkably, the state obtained this way gives a correlation between edges which runs at leading order with the inverse distance between the edges, in agreement with the linearized continuum theory. Finally, we give an argument why this correlator represents the propagation of a pure gauge, consistently with the absence of physical degrees of freedom in 3d general relativity.Comment: 20 pages, 6 figure

Fractional derivatives of random walks: Time series with long-time memory

We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying autocorrelation functions. The relation between these correlated walks and the well-known fractionally integrated autoregressive (FIGARCH) models, commonly used in econometric studies, is discussed. The application of correlated random walks to simulate empirical financial times series is considered and compared with the predictions from FIGARCH and the simpler FIARCH processes. A comparison with empirical data is performed.Comment: 10 pages, 14 figure

Survey of Dairy Management Practices on One Hundred Thirteen North Central and Northeastern United States Dairies

The objective was to conduct a broad survey of dairy management practices that have an effect on animal well-being. Dairies were visited during the fall and winter of 2005 and 2006 in Wisconsin, Minnesota, Indiana, Iowa, and New York. Data were collected on 113 dairies on colostrum feeding, dehorning, tail-docking, euthanasia methods, producer statements about welfare, use of specialized calf-raising farms (custom), level of satisfaction with calf-raising by producers, and cow behavior. Calves were raised by the owner on 50.4% of dairies; 30.1% were raised on custom farms during the milk-feeding period, 18.6% were custom raised after weaning, and 1% sold calves with the option to buy them back as first-lactation heifers. A total of 51.8% of producers were very satisfied with their current calf-raising methods. Three feedings of colostrum were fed to the calves on 23.9% of dairies, 2 feedings on 39.8% of farms, 1 feeding on 31.0% of farms, and colostrum replacement products were fed on 5.3% of farms. Many farms (61.9%) provided 3.8 L at first feeding. Calves were dehorned at different ages by various methods. By 8 wk, 34.5% of calves were dehorned. By 12 wk, 78.8% of calves were dehorned. The majority of calves were dehorned by hot iron (67.3%). The remainder were dehorned by gouging (8.8%), paste (9.7%), saw (3.5%), or unknown by calf owner (10.6%). Anesthetic use was reported by 12.4% of dairy owners and analgesia use by 1.8%. Tail-docking was observed on 82.3% of dairies. The most common reported docking time was pre- or postcalving (35.2%). The second most commonly reported time was d 1 (15.4%). Rubber band was the most common method (92.5%), followed by amputation (7.5%). Three dairies amputated precalving, 1 at 2 mo and 3 at d 1 or 2. Cow hygiene was the most common reason given to dock (73.5%), followed by parlor worker comfort (17.4%) and udder health (1.0%). Producers reported 2.0% of cows obviously lame. Gun was the preferred euthanasia method (85.7%), followed by i.v. euthanasia (8.0%), live pick-up (1.8%), and nondisclosure (3.5%). Most producers (77.9%) stated that cows were in an improved environment as compared with 20 yr ago, whereas 8.0% stated conditions were worse, and 14.2% were undecided. Dairies with higher percentages of cows that either approached or touched the observer had lower somatic cell counts. The survey results showed management practices that were important for animal welfare

Proton Beam Energy Characterization

Introduction The Los Alamos Isotope Production Facility (IPF) is actively engaged in the development of isotope production technologies that can utilize its 100 MeV proton beam. Characterization of the proton beam energy and current is vital for optimizing isotope production and accurately conducting research at the IPF. Motivation In order to monitor beam intensity during research irradiations, aluminum foils are interspersed in experimental stacks. A theoretical yield of 22Na from 27Al(p,x)22Na reactions is cal-culated using MCNP6 (Monte Carlo N-Particle), TRIM (Transport of Ions in Matter), and Andersen & Ziegler (A&Z) [1] computational models. For some recent experiments, experimentally measured activities did not match computational predictions. This discrepancy motivated further experimental investigations including a direct time-of-flight measurement of the proton beam energy upstream of the target stack. The Isotope Production Program now tracks the beam energy and current by a complement of experimental and computational methods described below. Material and Methods A stacked-foil activation technique, utilizing aluminum monitor foils [2] in conjunction with a direct time-of-flight measurement helps define the current and energy of the proton beam. Theoretical yields of 22Na activity generated in the Al monitor foils are compared with experimental measurements. Additionally, MCNP, TRIM, and A&Z computational simulations are compared with one another and with experimental data. Experimental Approach Thin foils (0.254mm) of high purity aluminum are encapsulated in kapton tape and stacked with Tb foils in between aluminum degraders. Following irradiation, the Al foils are assayed using γ-spectroscopy on calibrated HPGe detectors in the Chemistry Division countroom at LANL. We use the well-characterized 27Al(p,x)22Na energy dependent production cross section [3] to calculate a predicted yield of 22Na in each foil. Details of the experimental activity determination and associated uncertainties have been addressed previously [4]. The nominally stated beam parameters are 100 MeV and 100–120 nA for the foil stack irradiation experiments. Time-of-flight measurements performed in the month of January 2014 revealed beam energy of 99.1 ± 0.5 MeV. Computational Simulations Andersen & Zeigler (A&Z) is a deterministic method and also the simplest of the three com-putational methods considered. While the mean energy degradation can be calculated using the A&Z formalism, the beam current attenuation cannot. Consequentially, A&Z will also lack the ability to account for a broadening in the beam energy that a stochastic method affords. Additionally, A&Z does not account for nuclear recoil or contributions from secondary interactions. TRIM uses a stochastic based method to calculate the stopping range of incident particles applying Bethe-Block formalisms. TRIM, like A&Z, does not include contributions from nuclear recoil or contributions from secondary interactions. Computationally, TRIM is a very expensive code to run. TRIM is able to calculate a broadening in the energy of the beam; however, beam attenuation predictions are much less reliable. TRIM determines the overall beam attenuation in the whole stack to be less than one percent, whereas 7–10 % is expected. MCNP6 is arguably the most sophisticated approach to modeling the physics of the experiment. It also uses a stochastic procedure for calculation, adopting the Cascade-Exciton Model (CEM03) to track particles. The physics card is enabled in the MCNP input to track light ion recoils. Contributions from neutron and proton secondary particle interactions are included, although their contribution is minimal. For both MCNP and TRIM, the proton beam is simulated as a pencil beam. To find the current, an F4 volumetric tally of proton flux from MCNP simulation is matched to the experimental current for the first foil in the stack. Subsequent foil currents are calculated relative to the first foil based on MCNP predictions for beam attenuation. The equation used for calculating the current from the experi-mental activity is [5]: where: is the cross section for the process, [mbarns] is the atomic mass of the target [amu] is the is the number of product nuclei pre-sent at End-of-Bombardment is the average beam current, [μA] is the density of the target material, [g/cc] is the target thickness, [cm] is the decay constant, [s−1] is the irradiation time, [s] For each foil in the experimental stack, we also have a statistically driven broadening of the incident energy. The beam energy is modeled as a Gaussian distribution, with the tallies for each energy bin determining the parameters of the fit. TABLE 1 and FIG. 3 summarize the mean energy and standard deviation of the energy for each aluminum monitor foil. To address the energy distribution, we calculate an effective or weighted cross-section. It is especially important to account for energy broadening in regions where the associated excitation function varies rapidly. In the excitation function, we see a strong variation in the energy range from 30–65 MeV, the energy region cov-ered by the last 3 foils in the stack. Cross section weighting also accounts for the mean energy variation within each foil. The excitation function will overlay the Gaussian shaped flux distribution, giving rise to a lateral distribution where incrementally weighted values of the cross section are determined by the flux tally of the corresponding energy bin. With the effective cross section and the current at each of the foils, it is straight-forward to calculate the number of 22Na atoms created and the activity of each foil using the previously stated equation. Results and Conclusion The general trend in the amount of activity produced follows the shape of the excitation func-tion for the 27Al(p,x)22Na reaction. Small shifts in the incident energy upstream trickle down to produce much more pronounced shifts in the energy range of foils towards the back of the foil stack. The characteristic “rolling over” of the activity seen in the experimental foils indicates that the 6th foil must be in the energy region below 45 MeV, where the peak of the excitation function occurs. Conservatively, computational simulations are able to accurately determine the proton beam’s energy for an energy range from 100 to 50 MeV. As the beam degrades below 50 MeV, computa-tional simulations diverge from experimentally observed energies by over-predicting the energy. This observation has been noted in past studies [6,7] that compare the stacked foil technique with stopping-power based calculations. A complement of experimental and computational predictions allows for energy determinations at several points within target stacks. While this study focuses on an Al-Tb foil stack, the analysis of a similar Al-Th foil stack resulted in the same conclusions. Although we do not have a concurrent time-of-flight energy measurement at the time of the foil stack experiments, it is reasonable to assume that the energy at the time of the stacked foil experiments was also lower than the assumed energy of 100 MeV. Computational simulations developed in this work firmly support this assumption. Various computational models are able to predict with good agreement the energy as a function of depth for complex foil stack geometries. Their predictions diverge as the beam energy distribution broadens and statistical uncertainties propagate. A careful inspection of the codes reveals that these discrepancies likely originate from minute differences between the cross sections and stopping power tables that MCNP and TRIM/A&Z use respectively

Scaling in the Bombay Stock Exchange Index

In this paper we study BSE Index financial time series for fractal and multifractal behaviour. We show that Bombay stock Exchange (BSE)Index time series is mono-fractal and can be represented by a fractional Brownian motion.Comment: 11 pages,3 figure

Motion in Quantum Gravity

We tackle the question of motion in Quantum Gravity: what does motion mean at the Planck scale? Although we are still far from a complete answer we consider here a toy model in which the problem can be formulated and resolved precisely. The setting of the toy model is three dimensional Euclidean gravity. Before studying the model in detail, we argue that Loop Quantum Gravity may provide a very useful approach when discussing the question of motion in Quantum Gravity.Comment: 30 pages, to appear in the book "Mass and Motion in General Relativity", proceedings of the C.N.R.S. School in Orleans, France, eds. L. Blanchet, A. Spallicci and B. Whitin