Theworldwasweknowit

Thursday, 5 December 2013

Mandela

Nelson Mandela dies aged 95 http://www.dailymail.co.uk/news/article-2519062/BREAKING-NEWS-Nelson-Mandela-dies.html

Furax

http://www.foxnews.com/world/2013/08/04/fracking-fury-hits-idyllic-village/

Fracking fury hits idyllic village

By Judith EvansPublished August 04, 2013AFPPolice monitor protesters near a drill site operated by Cuadrilla Resources in Balcombe, England, on July 31, 2013. Protestors fear Cuadrilla will use the controversial method of hydraulic fracturing or 'fracking' of oil and gas from underground shale rock. (AFP)Protestors lie on the road to a drill site operated by Cuadrilla Resources in Balcombe, England, on July 31, 2013. Protesters against 'fracking' from around Britain have set up dozens of tents, loudspeakers and banners, while crowds surge forward with yells of fury to try to block each truck that drives towards the drilling site.(AFP)Police personnel escort a lorry to the entrance of a drill site operated by Cuadrilla Resources in Balcombe, England, on July 31, 2013. (AFP)Next SlidePrevious SlideBALCOMBE, UNITED KINGDOM (AFP) – Louisa Delpy had never protested before, but when she heard that shale gas extraction might begin in her leafy part of the English countryside, she was so furious that she took to the streets.The 36-year-old mother went with two friends and a home-made sign to the lonely site where test drilling for oil and gas has begun, close to her upmarket village of Balcombe in West Sussex, a fifty-minute train ride from central London.Three weeks later, the gaggle of demonstrators has mushroomed into a protest camp of hundreds, becoming the focus of a national campaign against the controversial extraction technique known as "fracking".Protesters from around Britain have set up dozens of tents, loudspeakers and banners, while crowds surge forward with yells of fury to try to block each truck that drives towards the drilling site."I've never protested against anything in my life, but look where we are now," Delpy said.Waving signs with slogans such as "Frack off!" and "Balcombe's not for shale", the campers say they will stay as long as it takes for Cuadrilla, the firm that has pioneered fracking in Britain, to reconsider its involvement.A prosperous commuter area in the home territory of Prime Minister David Cameron's Conservative party, Balcombe is an unlikely birthplace for a rowdy protest movement.But many residents say that having objected unsuccessfully through official channels, they feel forced into direct action."All the normal forms of democracy seem to have been ignored," said Stephen White, 59, a filmmaker from a nearby village. "It's like the Wild West."Cuadrilla -- whose chairman is former BP chief John Browne -- has tried to pacify the locals, holding open days and promising not to "ruin the countryside".It also says it is merely carrying out test drilling, which could lead to standard oil extraction, fracking, or nothing at all. The plan is to drill a 3,000-foot (915-metre) vertical well in a project lasting up to three months.But Cuadrilla's involvement elsewhere with fracking, or hydraulic fracturing -- using huge amounts of pressurised water mixed with chemicals to crack open rock and release natural gas -- has fuelled suspicion.Protesters bowed their heads for a minute's silence on Friday when news arrived that drilling had begun."It's a sad day for Balcombe -- but we will win!" declared 52-year-old Glayzer Frackman from Lancashire in the north, who turned activist and changed his name after his house was damaged by minor earthquakes blamed on test drilling.Like the other protesters, he also worries about potential chemical contamination of the air and water, and possible water shortages.The entertainer and DJ is one of dozens to arrive from Lancashire, a key testing area since the Conservative-led government took a strong stance in favour of fracking, which has led to a shale gas bonanza in the United States.Britain has proposed tax breaks for fracking companies, hoping to boost jobs and tax revenues while increasing energy security, although the technique has been banned in France and halted in Germany.Last week a Conservative member of parliament's House of Lords, David Howell, infuriated swathes of Britain when he suggested the "desolate" northeast as a good place to frack.He then corrected himself -- to say he had meant the "unloved" northwest.Balcombe's protest camp now has a kitchen, portable toilets and a children's play area. Demonstrators hold meditation sessions and concerts, and passing cars honk their horns in support.Dozens of police vans surround the camp, manned by up to 70 officers.There have been more than 30 arrests, amid scuffles with police and protest stunts including a group who locked themselves to an antique fire engine, blocking access to the site for six hours.Celebrity campaigners such as Bianca Jagger, ex-wife of Rolling Stones frontman Mick Jagger, have made appearances.The camp also includes well-heeled professionals, with some protesters brandishing academic studies on the dangers of fracking.In Balcombe itself, a village of immaculate brick houses, staff at the pub said they were "remaining neutral" while rumours circulated of a mystery thief taking down anti-fracking posters from local tea rooms.But it is hard to find anyone there who says they oppose the camp."It's polarising people a little bit," said trainee nutritionist Nancy Towers, 47. "But I think it's wonderful. They're very peaceful people."One 80-year-old villager, who asked not to be named, said she would protest on Saturday."I'm normally against protesting," she said. "I wouldn't go on marches, but this is important."
Via +Monica Yokubinas

Wednesday, 4 December 2013

Dick

http://elitedaily.com/news/world/which-country-has-the-biggest-this-world-map-is-color-coded-by-penis-size/

Dark energy

http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0080826

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Dark Energy from Discrete Spacetime

Aaron D. Trout mailPublished: December 03, 2013DOI: 10.1371/journal.pone.0080826ArticleAbout the AuthorsMetricsCommentsRelated ContentReader Comments (0)Figures

Abstract

Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies.Citation: Trout AD (2013) Dark Energy from Discrete Spacetime. PLoS ONE 8(12): e80826. doi:10.1371/journal.pone.0080826Editor: Garret Cotter, University of Oxford, United KingdomReceived: July 19, 2013;Accepted: October 15, 2013;Published: December 3, 2013Copyright: © 2013 Aaron D. Trout. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Funding: The author has no support or funding to report beyond his university salary.Competing interests: The author has declared that no competing interests exist.

Introduction

Multiple independent sets of empirical data [1]–[4]indicate that about 70% of the matter and energy in our universe comes from a mysterious repulsive gravitational effect known as “dark energy”. Understanding the origin of this energy is one of the most important problems in physics. Our only current theories involve speculative physical assumptions or finely tuned parameters. One popular assumption is the holographic principle: the idea that the degrees of freedom in a region of space are encoded on the region’s boundary [5]–[14]. Other explanations assume the existence of exotic matter fields or modify the Lagrangian defining general relativity. One recent theory[15] even hypothesizes a connection between dark matter and dark energy. See[16], [17] for reviews of various explanations of dark energy.Our work provides a simpler, better motivated model for dark energy set within the well-known dynamical triangulations (DT) approach to quantum gravity. This model assumes no holographic principle, uses no additional matter fields or finely tuned parameters, and does not modify general relativity beyond the geometric discretization inherent in dynamical-triangulations spacetimes. In our model, a positive vacuum energy of the correct observed magnitude spontaneously arises from the entropic bias toward negative curvature states inherent in DT geometries. Note that treating gravity as an emergent mean-field phenomenon driven by entropic forces is a popular research perspective at the moment [18]–[24].A reasonable prediction for dark-energy within a quantum-gravity theory is only significant if the theory approximates general relativity well at large distances. Why should we believe this about a theory that uses DT spacetime states? The progenitor of the DT theory, called the Regge calculus, has been used successfully in numerical general-relativity and quantum gravity for nearly five decades [25]–[31]. The DT model itself [32]–[36] and its descendent, causal dynamical triangulations(CDT) [32], [34], [35], [37]–[40]have been studied for nearly two decades. The numerous successes achieved by these theories give confidence that our model can describe general relativity at length-scales much larger than Planck’s length.The model presented in this paper uses the same discretization of geometry and the same action as the DT theory. However, it is not identical to DT because it puts restrictions on the set of triangulations which contribute to the partition function. These kind of restrictions are also what distinguish DT from CDT although our restrictions are distinct from those in CDT. Note that it is not our purpose to advocate “triangulations” as the ultimate structure of spacetime. Indeed, in our calculation the discrete nature of geometry may be removed at the end without altering the predicted vacuum energy. We suspect that the effect described in this paper is actually a generic feature of any quantum-gravity theory which predicts a discrete spacetime geometry and which has general relativity as its large-distance limit.

Background Material

General relativity can be written in the Lagrangian formalism using the Einstein-Hilbert action, which in natural units is(1)Here is a closed -manifold, a Lorentzian metric, scalar-curvature, the cosmological constant, the Lagrangian for matter and the standard volume element. See Table 1for a list of commonly used symbols. Note, both and depend on while does not. Also note that is the only term in this action with a physically distinguished zero value. In quantum field theory on a fixed background geometry, an arbitrary constant can be added to without changing the observed physics, allowing one to simply set to zero. Thus, it is reasonable to argue, as we do in this paper, that the observed non-zero value of arises from quantum effects related to the scalar-curvature field .Download:PPTPowerPoint slidePNGlarger image ()TIFForiginal image ()Table 1. Meaning of Commonly Used Symbols.doi:10.1371/journal.pone.0080826.t001Hilbert and Einstein showed that the critical points of this action satisfy the equations of motion(2)These are, of course, the field equations for general relativity. Here, is the Ricci curvature tensor and the stress-energy tensor for matter. In this work we restrict attention to the Einstein-Hilbert action for the vacuum with zero cosmological constant(3)The critical points of are metrics which satisfy the vacuum field equations. These metrics are Ricci flateverywhere ( at every point) and therefore alsoscalar flat everywhere (at every point.) Thus these metrics have action exactly zero. Finally, in dimensions less than four, the Ricci tensor determines the full curvature tensor , so critical points of in these dimensions must actually beflat everywhere ( at each point.).In his influential 1961 paper[25] Regge proposed a discretized version of which applies to triangulated piecewise-linear (PL) manifolds. A triangulation of a closed -manifold is a combinatorial -manifold homeomorphic to given as an abstract simplicial complex. Assigning a length to each edge in uniquely defines a piecewise-linear metric on provided these lengths satisfy some natural compatibility conditions. If we let denote the number of -simplices in , the Regge action is given by(4)In this equation, the sum runs over all codimension-2 simplices of (calledhinges), is the total dihedral angle around the hinge , and is that hinge’s volume. It is easy to insert a cosmological constant into this action, although here we do not. The possibility of incorporating matter fields into is a currently active topic of research. See [41]–[43].Note that has a nice geometric interpretation. The summand in this action is theangle defect in a small triangle enclosing and perpendicular to the hinge , weighted by the volume of that hinge. Given the close relationship in classical non-euclidean geometry between angle defect and curvature, it is natural to interpret as a discrete measure of total curvature. Because of the success of the Regge action in describing general relativity, we will interpret as a discrete measure corresponding to the Einstein-Hilbert action, and thus to total scalar-curvature. Interpreting as a total curvature is also supported by the fact that, like point-wise curvature bounds in Riemannian geometry, bounds on the angle-defect for all hinges have profound topological consequences for . See[44]–[47] for examples.

The Dynamical-Triangulation Action

Suppose we fix the abstract simplicial complex and consider as a function of the edge-lengths only. There is a large body of numerical evidence [26]–[29]that the critical points of this action define PL-metrics which behave like solutions to the vacuum field equations, at least at length scales much larger than the maximum edge-length. See[36] for a overview of this work, known as the Regge calculus. In this paper, however, we will require all edges to have a single fixed length so that the action is determined only by the structure of as an abstract simplicial complex, i.e. only on the way the simplices in are attached together. This form of the Regge action has been studied extensively as part of the dynamical triangulations (DT) approach to quantum gravity. We write this action as(5)where is the volume of a -simplex with all edges of length , is the dihedral angle in such a simplex, and , called the degree of , is the number of -simplices in with as a face. Usually, we will suppress the dependence on and write simply .Now for some terminology and preliminary results. Let denote the set of all triangulations of a fixed closed -manifold . We will write for the set of all triangulations of containing exactly -simplices, and for those with -simplices and DT-action . Since there are only finitely many ways to attach together the faces of a finite collection of -simplices, and are finite sets. We define to be the spacetime entropyof for -simplices and action . We will also need notation for the average hinge degree of a triangulation T,(6)By double-counting arguments we may alternately write this as(7)Proof. Suppose we examine each -simplex in and place a mark on each -simplex with as a face. Clearly we have placed marks. On the other hand, each -simplex has codimension-2 faces, so the number of marks is also . Dividing through by gives the first equality. Next, suppose we examine each -simplex in and place a mark on each of the two -simplices incident at . We have obviously placed marks. However, each -simplex has codimension-1 faces, so the number of marks is also and we have . Plugging into the previous equality and simplifying finishes the proof.The first part of equation (7) lets us nicely express as a function of the number of -simplices in and its average hinge-degree. We get(8)where is called the flat hinge-degree. Why do we call the flat hinge-degree? It is the number of regular -simplices needed around a hinge to provide a total dihedral angle of exactly , the expected quantity in a flat space. Note that, except in dimension two (where ) the quantity is not an integer.Proof of Equation (8). We begin with the DT action (5) and distribute the sum into the summand to obtain(9)By equation (7) we can replace with and the summation by to get(10)Finally, moving a factor of to the front finishes the derivation.

Mean Action Per Volume

The primary observable quantity of concern in this work is the mean action per volume, i.e. the average Lagrangian density over the manifold:(11)where is the PL-volume of . We use the symbol to remind us that this is a physically well-defined global observable with dimensions of energy per volume. Equation (8) gives a lovely formula for the mean action,(12)where depends only on the dimension . This tells us that for a fixed dimension and edge-length the mean-action depends only on the average hinge-degree . For notational convenience we will usually suppress the and dependence and simply write or .Finally, note that for a fixed number of -simplices we can use equations (7) and (12) to find the minimum possible separation between mean-actions. This corresponds to changing the number of hinges by one, resulting in a change to of(13)where and depend only on the dimension and is the total spacetime volume. The minimum possible separation between actions is then given by(14)

Action Spectrum in Dimension Three

From this point forward, we will restrict attention to dimension three. What can we say about the possible values of on when ? This is a formidable problem, since even for a small number of tetrahedra the set is quite large and complicated. We begin with an elementary result: for any triangulation of a closed 3-manifold we have(15)where and . This means that for a fixed number of 3-simplices, the effect of increasing (or equivalently, decreasing ) is to decrease both the number of vertices and the number of edges in the triangulation.Proof of Equation (15). We begin with a well-known topological fact: every closed 3-manifold has Euler characteristic zero. That is, for any triangulation of a closed 3-manifold we have . Now, we use equation (7) to replace by to get(16)Using equation (7) again to replace by and then rearranging gives(17)as desired. Finally, we plug this back into equation (16) and simplify to obtain(18)completing the proof.Equation (15) tells us that to understand the possible values for we must understand the possible combinations of and that can occur in a triangulation of a given closed 3-manifold. A 1970 paper [48] by Walkup tells us all we need to know.Theorem (Walkup). For every closed 3-manifold there is a smallest integer so that any two positive integers and which satisfy(19)are given by and for some . The quantity is a topological invariant which satisfies for all closed 3-manifolds .Note that is known for many manifolds , see [49], although we will not need this information.Walkup’s Theorem, together with equation (15) and some algebra suffice to prove the central mathematical result in this paper:Theorem. Let be a closed 3-manifold and a fixed number of tetrahedra. Then, there are mean actions(20)and(21)so that if is an integer for which lies in the interval then for some triangulation of with tetrahedra and edges. These are regularly spaced over the entire interval , each separated from the next by(22)where . This is the smallest possible separation given fixed , so these are all possible mean-actions on .Note that in most applications, the number of tetrahedra will be large and the energy densities given in the theorem will be approximately(23)Also note that when edges are Planck’s length ( in our units) the magnitude of these energy densities isenormous, about Joules per cubic meter.Proof of Main Theorem. Let be a closed 3-manifold. We start by showing that if two given integers and satisfy(24)then there is some triangulation of with and . We define . Note that by the first inequality in (24). A bit of algebra applied to the second inequality in (24) implies(25)Now, consider the upward opening parabola which has largest root . The first inequality in (24) implies which is just . Since is the largest root of an upward opening parabola, we conclude . By our definition of and , this tells us(26)By Walkup’s theorem, inequalities (25) and (26) imply that some triangulation has and . Finally, byequation (15), we know as desired.Next, we divide the inequality (24) by and take reciprocals to get(27)where . Thus, if is fixed and is an integer for which lies in this interval, then for some triangulation with tetrahedra. By equation (12) the change in mean-action for each increment of is as claimed in equation (22), completing the proof.

The -Action Model

The model used in this paper is designed to be dominated by states near a particular chosen target value for the mean-action. For a fixed number of tetrahedra let be the closest attainable mean-action to . For each , our model admits triangulations with mean-action along with those having one of the mean-action values on either side of . In this paper our target mean-action will be since the Einstein-Hilbert action for the vacuum in classical general-relativity is zero. Recall that, unlike actions in quantum field theory, the values of the Einstein-Hilbert and Regge actions are well-defined physical observables. This makes such a targeting strategy physically reasonable.Why not simply start with a model containing only those triangulation for which ? It turns out that there are no such triangulations. That is, for any triangulation of a closed 3-manifold we have , or equivalently . This follows from the irrationality of andequation (12). We know is irrational due to work [50] by Conway, Radin and Sadun on what are called calledgeodetic angles. Note that these angles are actually interesting mathematical objects on their own and are central to the solution to Hilbert’s third problem on thescissor-congruence of polyhedra.So, let be the mean-actions in the model and the corresponding total actions. Our main theorem implies that for any and spacetime volume there is an small enough so that all of the mean-action values lie within the range where attainable action-values are regularly spaced. For such our model has partition function(28)where is spacetime entropy at action . The expected action for this model is then(29)A Euclidean version of this expected value can be found by applying the standard Wick rotation to the expression above.It is currently impossible to write or as exact closed form expressions since the entropies are beyond our ability to compute. However, if we replace with its first order approximation for a constant, then a closed-form expression can be found. We used the computer-algebra package Mathematica to show(30)A closed form expression for can obtained as before by replacing with in the equation above.

Choosing

How are we to choose ? In an ideal world, we would have in hand a fully formed DT-style theory of quantum gravity coupled to matter, which provably reduced to general-relativity at large distances. From this theory we could derive an appropriate by computing how far a typical spacetime was from the classical action. We believe such a theory will eventually emerge, but it is not yet available. However, we have set up enough machinery to reasonably guess what such a theory would tell us about .Suppose we fix a total spacetime volume and consider the -action theory targeting mean-action zero. What happens as we let the edge-length approach zero? Because the separation between actions goes to zero and , if is left fixed as then even the most extreme action values in the theory, , would converge to zero. Since we wish to investigate quantum gravity, this is unacceptable and we are forced to choose an which diverges as . Now, suppose we make the affine entropy approximation . Equation (30) implies that if then for large enough and small enough the expected action is dominated by the final hyperbolic cotangent term and we have . This tells us that under these conditions, the model is completely dominated by entropy. The oscillating complex phase which suppresses the contribution of states far from is swamped by the entropy term involving .Thus, since is proportional to , it is natural to choose the dimensionless to be proportional to . For such a choice we can take the limit and the theory gives a finite non-zero value for the expected action. Therefore, we choose to use(31)mean-action values on either side of . Notice that by the approximations (23) even though diverges as , all actions in the model eventually lie within the “regularly spaced” range for small enough . Also note that as all the mean edge-degrees corresponding to these converge to the flat mean edge-degree .Finally, for any fixed we can use equation (30) to compute the limit, obtaining(32)For we get a purely imaginary standard expectation and a Euclidean expectation given by

Evidence for the Entropies

The calculation of the expected action as given by equation (32) depends on two assumptions about the entropies . First, for the states contributing to the model, spacetime entropy must be an approximately linear function of mean-action, i.e. , at least for large enough . Second, this must not approach zero as . In this section, we present evidence from Monte-Carlo simulations and small-enumerations that strongly supports these assumptions.

Monte-Carlo Sampling Results

To measure the dependence of entropy on mean-action we use a Metropolis-Hastings algorithm to take samples from near a given number of tetrahedra and mean-action. The algorithm wanders among the elements of by using the well-knownPachner moves to change from one triangulation to another, repeatedly choosing a random move and executing it with probability where is some non-negative objective function. Metropolis proved that if we wait long enough between samples, then each sample occurs with probability . Here, we use a quadratic objective function(33)with and fixed constants. This form for keeps the sampled triangulations near a target mean-action and number of tetrahedra .If there were equally many triangulations at each and then our sampled pairs would form a Gaussian distribution centered at the target point . If our samples have a Gaussian distribution but with mean significantly displaced from the target, this indicates a linear dependence of spacetime entropy on and with the magnitude of the dependence proportional to the size of this displacement. Since it is obvious that spacetime entropy is strongly dependent on and because the relative deviation from the mean for is at most in our data, we focus solely on deviation in mean-action . From this we can estimate the change entropy (per mean-action step) , in nats, using(34)The sampling trials conducted for this paper use the 3-sphere with target mean-action zero () and various targets for the number of tetrahedra . In all cases, we take and . In order to ensure independent samples, the algorithm attempts Pachner moves until accepted moves per tetrahedron have occurred. We checked that this wait time was sufficient using standard correlation tests. For these parameters, each sample was uncorrelated from the next. We also checked that the sampled and were independent. As desired, samples are approximately normally distributed with sample mean somewhat displaced from the target . This indicates that entropy is approximately a linear function of mean-action near , as was assumed in the previous section. See Figure 1 for a histogram of mean-actions for samples at . For each such distribution, we use equation (34) to infer the approximate change in entropy between mean-actions. These are comfortably negative and do not appear to approach zero as gets larger, validating our second assumption. SeeFigure 2. Copies of the code used for triangulation sampling are available on request.Download:PPTPowerPoint slidePNGlarger image ()TIFForiginal image ()Figure 1. Monte-Carlo sampling of triangulations of near mean-action zero.We plot the distribution of mean actions at for 2700 sampled triangulations of the 3-sphere . Samples were obtained from a Metropolis-Hastings algorithm using Pachner moves and a quadratic objective function targeting and with and . Waiting times were chosen so that accepted moves per tetrahedra occurred between successive samples. Observed means were with standard deviation and with standard deviation . Note that and are given in Planck units, and respectively.doi:10.1371/journal.pone.0080826.g001Download:PPTPowerPoint slidePNGlarger image ()TIFForiginal image ()Figure 2. Entropy remains a decreasing function of mean-action as the number of tetrahedra grows.We plot the change in spacetime entropy, in bits, due to each minimal increase in mean-action for the 3-sphere near , versus mean number of tetrahedra . Values were inferred from the bias seen in Monte-Carlo samples of triangulations near . See Figure 1. All data points except the last two were computed from 2700 samples. At the two largest values, we used 2394 and 1108 samples respectively. Error bars indicate 95% confidence intervals.doi:10.1371/journal.pone.0080826.g002

Triangulation Census Data

In addition to Monte-Carlo sampling evidence, one can also see a bias towards negative action states in computer-generated censuses of -manifolds triangulations. In particular, recent advances in enumeration algorithms have allowed for the creation of an explicit list of all triangulations of any closed 3-manifold using at most 11 tetrahedra. See [51], [52]. Unfortunately, the definition of a “triangulation” used in these censuses is slightly more general than ours. They define a triangulation of a closed 3-manifold as a space homeomorphic to obtained by identifying the faces of some finite set of tetrahedra. We believe this to be a largely technical distinction, and we expect this data to provide a good guide to the general features of our set of triangulations . See Figure 3 for a graph of spacetime entropy versus mean-action for the 3-sphere and . We observe two trends in the data. First, as we expect, the number of triangulations increases as the number of 3-simplices grows. However we also see the same effect as observed in the Monte-Carlo sampling experiments: the number of triangulations at a given action is adecreasing function of action.Download:PPTPowerPoint slidePNGlarger image ()TIFForiginal image ()Figure 3. Entropy versus mean-action from triangulation census data.We plot spacetime entropy in bits for the three-sphere at various numbers of tetrahedra , versus mean action at . Data come from a complete census [51],[52] of the million triangulations of with at most 9 tetrahedra. Note that and are given in Planck units, and respectively.doi:10.1371/journal.pone.0080826.g003

The Origin of Dark Energy

Taking and dividing through by in equation (32) gives(35)Let us briefly discuss the physical meaning of . Our goal was to construct a theory dominated by states close to the classical value of the mean-action, . We did this by “slicing” the partition function according to action-value, retaining only states whose actions lie within a certain distance of zero. If the volume of spacetime is large compared to Planck’s volume then we come very close to accomplishing our goal. That is, for we do indeed obtain in the limit. However, there is a small perturbation away from zero because of the relative entropy of action values. Notice that since action values are global observables, this effect is independent of the local details of the “metric”, i.e. the local structure of the triangulation. This leads us to expect that, for a typical triangulation at a given , the average action will appear very uniform at length-scales much larger than . Finally, recall that everything in the Einstein-Hilbert action exceptthe cosmological constant depends on the metric . Thus, the basic structure of almost demands we interpret our non-zero as an emergent cosmological constant given by(36)We now turn to the question of applying this result to our own universe. This is a somewhat speculative endeavor since our world appears to be both -dimensional and infinite in extent. However, as an entropic effect connected with the pattern of attachment between simplices, we expect the perturbation away from identified in this paper to occur quite generally. So, what is appropriate for assessing the magnitude of this effect in our particular universe? Considerations of causality give us a reasonable answer: take the volume of space which has had time to causally communicate with our point of observation. That is, we ought to use something like the current Hubble volume where is the Hubble constant. Plugging in in Planck units gives(37)which is in general agreement with observation.At this point, we feel obliged to briefly discuss the term “numerology”. It has long been known that the observed cosmological constant was approximately . This and many other unexplained approximate numerical relationships between cosmological parameters are often calledlarge number coincidences. Thinking of them as having explanatory power on their own is surely deserving of the label “numerology”. However, this epithet should not be applied to a physically well-motivated theory which predicts ab-initio such a numerical relationship, as our model does.

Discussion

Our derivation of has some interesting features. Using the Hubble parameter to define our characteristic volume means that the model actually predicts a time-varying cosmological constant(38)where is the Hubble parameter at proper time . That is, we predict that scales like the area of the cosmic horizon. Amazingly, although we made no holographic assumption, this is the same behavior that emerges from holographic dark energy (HDE) theories[5], [6], [10], [12], [13]. In fact, our model shares several other key features with these approaches, including the presence of two “cut-offs” in the theory which are removed in a coordinated fashion. HDE models typically contain both a UV and IR field cut-off which are removed in a way that saturates entropy in the Bekenstein bound. In our theory, the cut-offs and are chosen to keep the entropic perturbation on bounded as . While HDE theories are very different in detail from our model, the broad similarities are quite striking. Perhaps both approaches are pointing to the same underlying physical issues. We hope that the relative simplicity of our model can help elucidate these issues.We should also mention another explanation for which shares some features with our approach. In [53] it is argued that the true ground-state vacuum has but that we observe because the universe has not yet had time to decay into this ground state. The author considers a model in which the true ground state is given by the superposition of two degenerate states, one of which describes the universe’s present-day vacuum. Since the decay probability in a given volume and time period is related to the energy density , the requirement that no such decay has yet happened in the Hubble volume provides an estimate for which agrees with observation. This argument leads, as does our model, to a connection between the Hubble parameter and . Also note that both models contain states at or near which are suppressed compared to the states.Finally, we note that in the very early universe our model predicts large and hence rapid expansion. This raises the tantalizing possibility that big-bang inflation and dark-energy are manifestations of a common effect, though it is likely that a more sophisticated choice for the characteristic volume would be needed. See [54] for consideration of this idea in the HDE context.

Acknowledgments

The author would like to thank Cheryl Koester, C. Scott Wylie, Vadas Gintautas, Joe MacNeil, and Larry Viehland for their support and valuable advice. Also, many thanks to Henry Segerman for providing the triangulation census data used in this work and to Leah Langer for assisting in the collection and verification of triangulation sampling data.

Author Contributions

Conceived and designed the experiments: ADT. Performed the experiments: ADT. Analyzed the data: ADT. Wrote the paper: ADT.

References

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Curvature

Dark energy

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Entropy

General relativity

Origin of the universe

Physical cosmology

Quantum gravity

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Monday, 2 December 2013

Mm

http://blog.kissmetrics.com/master-mobile-marketing/

A BLOG ABOUT ANALYTICS, MARKETING AND TESTINGLEARN WHAT GOOGLE ANALYTICS CAN'T TELL YOUSHOW ME MY CUSTOMERS →

Master Mobile Marketing: 35 Resources to Help You Maximize Your Apps Visibility

Ask any technology investor what the hot area is today, and they’ll tell you “mobile”. Indeed, more people own a smartphone now than ever before, and that number is growing every day.Currently, the App Store has around 1 million apps, and it adds about 20,000 apps per month. In total, there have been over 50 billion app downloads. The Google Play Store has over 1 million apps, and there have been over 50 billion downloads. So, it’s a big market with a large user base for both iOS and Android.If you’re curious about how to promote your mobile app, this article is for you. In this post I’ve compiled a list of resources that you can learn from and use.

Complete Guides

1. How to Market Your Mobile App –Smashing Magazine gives a thorough guide for marketing a mobile app.2. A Marketer’s Complete Guide to Launching Mobile Apps – HubSpot lists 13 steps for introducing a mobile app, all the way from pre-launch to post-launch.3. Building an iOS App – Written by Apple, this article takes you step by step into making your first iOS app.4. Building an Android App – Written by the Android team, this article explains how you should go about making an Android app.5. App Promotion Guide – This in-depth article goes into detail about developing an app, assessing competition, building a quality app, initiating marketing, establishing a promotional budget, creating hype, and more.6. The iOS App Marketing Strategy Guide – Apptamin writes a thorough article covering a range of topics related to launching and promoting an app.7. Building an Audience of Fans for Your Mobile App’s Success – A free Moz account is required to view this webinar.8. Three Inbound Marketing Strategies – This post is an extension of the above-referenced webinar.9. 10 Inbound Marketing Tips – These 10 tips aren’t groundbreaking or even new, but they may help as a reminder. Also, they could be a good start for beginners.10. How do you Market a Mobile Application? – A few Quora answerers give their advice on approaches to take when marketing a mobile app.11. 20 Things Every iOS and Mobile Developer Should Consider in Their App Promotion Strategy – Kate Matsudaira breaks down all the details you need to know when forming your app strategy.12. FAQ Regarding Apps and Marketing – If you’re a beginner and thinking about launching a mobile app, read this article with common questions and answers.13. 6 Services to Help You With Mobile Marketing – If you’re a local business looking to expand your reach into mobile, these services may help.14. How to Use Snapguide to Promote Your Mobile App – Snapguide is an up-and-coming platform that people use to spread their apps. Want to try it yourself? Read this guide.15. 9 Tips for Promoting Your Mobile App – The Next Web runs through tips on promoting an iOS or Android app.16. How to Pitch Your App and Get it Reviewed – Getting your app reviewed on a popular site is an important aspect of marketing. This post runs down some of the basics you’ll need to know before you pitch.17. 10 Mistakes Startups Make When Promoting Their Apps – Companies make mistakes. The more you can avoid, the better. Run through this article to see if there are any potential mistakes you can avoid.18. Using Facebook to Promote Mobile Apps – Forrester has found that 19% of iOS (15% of Android) downloads come from people finding apps on social media. This 11 minute video gives tips on how to spread your app through Facebook.19. Seven Do’s and Don’ts for Mobile App Marketing – MarketingProfs’s infographic runs through seven tips to keep in mind when promoting your app.20. Thriving in an App Store World – Apple employee Michael Jurewitzgives a talk on strategies you can use to be successful in the App Store. A must watch.21. Understanding App Store Pricing – Part 1 – Being from Apple, Jurewitz understands the App Store quite well; he was formerly a developer tools evangelist. In this 5-part series he writes about understanding App Store pricing. Also check out part 2, part 3, part 4, and part 5.22. How to Use Updates to Promote Your App – App updates are a way to remind users that your app is still around on their mobile device. It’s also a chance to write great copy and entice users to check out the app again. This article tells us how to do that.23. Google Play: Marketing 101 For Developers – Patrick Mork, Marketing Director (former) for Google Play, presents ideas to help developers market their Android apps.24. 4 Tips on Designing an App Icon That Doesn’t Suck – Having a well-designed app starts with the icon. Learn what to avoid, and get tips on making a great icon.25. Tracking Your App Marketing – Understanding how your marketing is performing is key to refining it and eliminating wasteful ad expense. This article gives a list of tools and services you can use to track your app marketing efforts.26. Getting Featured on the App Store – Realmac Software breaks down the key attributes of apps that get featured on the App Store. Dave Addey gives us some of his research findings on the types of apps that get featured.27. Mobile App Tracking – If you want to track the effectiveness of your marketing, you’ll need to know which campaigns bring the most downloads. Mobile App Tracking is a service that helps you do just that.Tapstream is another service that does it, too.28. Growth Hacking Apps – Michael Patzer runs through the success he’s had in marketing his mobile apps.29. 10 Tips for Mobile App Landing Pages – Unbounce gives us 10 tips for creating effective landing pages.30. App Marketing Conversations – Apptentive holds video conversations covering various topics related to marketing a mobile app.31. Some Tips on Pricing – If you choose to charge for your app, the price you charge becomes integral.Bonus! 4 Mobile App Marketing Tips For a $0 Budget – Don’t have any money to promote your app? Read this article for some advice!

App Store and Google Play Store

32. Why is App Store Optimization Important? – Gives data and some background on why you need to be optimized for the App Store.33. App Store Optimization – Provides a background on App Store Optimization as well as helpful tips.34. Optimizing Your Google Play Store App Details Page – Article details the ins and outs of writing the summary of your android app. Even if you have an app on the Play Store, you’ll still want to view this as it may provide some good ideas.35. Getting Good App Reviews – Clearly, too many bad reviews can damage your app. This short post gives some ideas on structuring your app review process.

In Conclusion….

Mobile presents a unique challenge. People will willingly download a free app (assuming they’re interested) but getting them to regularly use and engage with the app is another conundrum. Pew Internet performed a study that showed of the people who had a mobile device with apps installed, more than half report using five or fewer apps on a regular basis.The app Color received a ton of buzz (primarily because of its $41 million round) and presumably got a lot of initial downloads (some say 1 million during launch) because of all the press and stir around the app. A year after launch, the app only had 30,000 daily users, which was far underperforming. The appannounced it would shut down at the end of year 2012. Overall, the app was active for 21 months.So while marketing can help people become aware of your app and even increase downloads, what determines if they’ll actually engage with it is the quality of the app and what the user gets out of it.I hope these resources give you some ideas for marketing and maybe some inspiration for building the best mobile app possible.About the Author: Zach Bulygo is a blogger for KISSmetrics, you can find him on Twitter here.Share on TwitterShare on FacebookSylvain GauchetOct 02, 2013 at 12:13 amThat’s a great compilation of app marketing resources (and I’m not saying this because you gave us some love).Congrats on putting all this together!ReplyZachOct 02, 2013 at 10:34 amThank you Sylvain for the comments and for helping us provide great resources.ReplyTom ManganOct 02, 2013 at 12:46 amThis is one of the reasons why KissMetrics has one of the best marketing blogs out there — I’m always finding tons of helpful & informative stuff here.ReplyZachOct 02, 2013 at 10:35 amWe aim to please, Tom!ReplyDeborah AndersonOct 06, 2013 at 6:25 pmVery helpful article and definitely one worth sharing and bookmarking for later reference.ReplyJames KayeOct 21, 2013 at 9:26 amWe’ve written an in-depth guide to app marketing which you might want to include http://glossi.com/dimoso/29060-top-10-tips-for-marketing-your-appReplyGuestOct 30, 2013 at 2:42 amHi,we offer FREE marketing for apps.. Pin your Mobile App or App related website, video, screenshot, app stor link…(no spam and no tricks)http://www.pincoolapps.com/ReplyEhsanNov 06, 2013 at 11:13 pmI am going to book mark this great helpful resource of mobile app marketing. ThanksReplyraviNov 25, 2013 at 9:43 pmZach,This is ton of information for app promotions, thanks a lot for putting it together.ReplybaidyanathNov 29, 2013 at 6:29 amThis is a large list for mobile apps promotion.Reply

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Sunday, 1 December 2013

Things

That's the real problem, envy of nothingness , greed of everything.. Human have lost their sense of value, I prefer people to things, everyone is unique. Things can be replaced.

Nsa

https://www.eff.org/deeplinks/2013/11/busting-eight-common-excuses-nsa-surveillance

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Search HOMEABOUTOUR WORKDEEPLINKS BLOGPRESS ROOMTAKE ACTIONSHOPNOVEMBER 25, 2013 | BY CINDY COHN AND TREVOR TIMM

Busting Eight Common Excuses for NSA Mass Surveillance

We’ve heard from lots of folks who are passionately concerned about the NSA’s mass spying, but are struggling to get their friends and family to understand the problem and join the over a half-million people who have demanded change throughstopwatching.us and elsewhere.Of course, you can show them the Stop Watching Us video and this great segment from Stephen Colbert. And if you’d like a detailed refresher on all the ways NSA is conducing mass surveillance, ProPublica has a handy explainer here.You can also check out this new video from filmmaker Brian Knappenberger (writer and director of We Are Legion: the Story of the Hacktivists):Note: clicking this thumbnail will take you to the New York Times' website.But you also need to be prepared to respond to the common refrains of folks confused, nonplussed, or simply exhausted from the headlines. So here’s a cheat sheet to help you talk about the NSA spying when you’re with family and friends.I have nothing to hide from the government, so why should I worry?There are a few ways to respond to this, depending on what you think will work best for the person raising the question.Point out how mass surveillance leaves you at the mercy of not only the NSA, but also to the DEA, the FBI and even the IRS. We know that the government claims that any evidence of a “crime” can be sent to the appropriate law enforcement agencies. Tell them that, even if youdon’t think you have something to hide, it’s possible the government thinks you do, or can create some concern about you (or your friends or loved ones). There are so many laws and regulations on the books, Rep. Jim Sensenbrenner said the Congressional Research Service did not have the resources to count them all. One legal expert has argued that the average person likely commits three felonies a day without ever realizing. So, you may be technically breaking a law you have no idea about.We all benefit from a system that allows privacy. For example, when journalists can speak to sources without the specter of surveillance, helping fuel investigative journalism and the free flow of information. And this is not just a hypothetical—the Department of Justicesubpoenaed the phone records of Associated Press journalists in an effort to track down government whistleblowers. And it’s not just journalists. Activists, political organizers, lawyers, individuals conducting sensitive research, businesses that want to keep their strategies confidential, and many others rely on secure, private, surveillance-free communication.Isn’t the NSA using the mass spying to stop terrorists?Even the NSA cannot point to a single terrorist attack they’ve stopped using the Patriot Act phone surveillance program that sweeps up virtually every phone record in the United States. They’ve thrown out many numbers claiming that the information was helpful in some capacity, including repeatedly claiming that it thwarted some 54 attacks, but those numbers have been thoroughly debunked.The only remaining example the NSA points to is known as the “Zazi case.” However, in that case, the Associated Press reportedthat the government could have easily stopped the plotwithout the NSA program, under authorities that comply with the Constitution. Sens. Ron Wyden and Mark Udall have been saying this for a long time.That’s the point here: we can stop terrorists with law enforcement authorities that this country has been using for decades. We don’t need to upend the Constitution to keep the nation safe.The government will not abuse its power.Some people believe that the government will never abuse its power, especially when the party they support is in office. You should remind these people that the government has a long history of overstretching its surveillance powers and using that information to try to blackmail people. Example of this include the NSA spying on Martin Luther King Jr., Muhammad Ali, and even some sitting senators in the 1960s. Imagine how Sen. Joe McCarthy’s investigations might have gone if he had access to this kind of spying.We already have evidence of abuse of power. We know that the NSA analysts were using their surveillance powers to track their ex-wives and husbands, and other love interests. They even had a name for it, LOVEINT. The FISA court has also cited the NSA for violating or ignoring court orders for years at a time. And those are just self-reported abuses. An independent investigation might reveal even more.Allowing mass spying is patriotic.Stopping untargeted seizure of information is one of the key reasons we fought the War of Independence and drafted the Fourth Amendment. During colonial times, the "crime" was tax evasion—remember the Boston Tea Party? The British crown issued Writs of Assistance, which were general warrants that allowed the British authorities to search through anyone’s papers in order to find those who were skirting the taxes. American patriot James Otis Jr. argued against the “hated writs” but lost his case in the British courts. John Adams noted that from that case, “the child independence was born.” Since that time, warrants have had to specify the persons and places searched. Mass surveillance by the NSA does neither. In short, one of our countries’ founding principles is the prohibition on mass searches and seizures.Kids today (or my friends) post everything they do on Facebook or Twitter, why should we care if the government can see too?What people choose to put on Facebook or Twitter (or Instagram or Tumblr or some other service) is almost always curated. People put the best or sometimes the worst things that happen to them online, but studies show they stillkeep things private, and restrict the audience for other information. A new poll shows young peoplemay even be more privacy conscious than older adults.We all know someone whose Facebook feed continued to show happy pictures even as they went through a terrible breakup or divorce. The point of privacy is control over the information that is available about you. Some people choose to share more, some choose to share less, but nearly everyone wants the power to pick and choose what information is available about them to their friends and to strangers, like future employers or NSA agents.Google and Facebook have my information, so why shouldn’t the NSA?There are many privacy problems with how the giant Internet companies gather and use so much of your personal data. However, Google and Facebook do not have the power to arrest you and, unlike government surveillance, there are other choices for communication tools. For example, you can use DuckDuckGo instead of Google search.Remember: while we may not like how companies collect a lot of our information, they are not under the same requirement to follow the Fourth Amendment. We need to protect the private information held by companies too, but the Constitution provides a foundation that always protects our communications from the prying eyes of government.It’s just metadata, so why should I care?For the mass phone record collection program, the NSA has said it is not “listening in” to telephone calls. Instead they are collecting a record of everyone you call, who calls you, when you’re on the phone, the length of your phone call, and at times, even your location.This "metadata" can be as invasive as the content of your conversations. It can reveal your religious and political views, who you are dating (and when you break up), who your spouse and children are, your movements, and even information your closest friends and family don’t know, such as medical conditions.Additionally, the government is getting more than just metadata. We also know the government has obtained online content, including email, under separate programs, and used the data based on a guess that you are 51 percent likely to be foreign, by scanning large a portion of the total number of emails entering and exiting the United States. Metadata is only a part of the government spying programs.This sucks, but there’s nothing I can do!Actually there is plenty you can do! First, join the over half-million others and sign our petition atstopwatching.us. Then call your representative in Congress—there are bills going through Congress right now that could curtail some of this spying and bring real transparency and accountability to the NSA. There are also some thatneed to be opposed so we don’t end up legalizing much of this illegal surveillance.There’s lots you can do to fight NSA surveillance. But one of the most important things you can do is explain why this issue is important to friends and family. So please share this guide widely.NSA Spying