text:
## Tag: abelian-varieties

30 Why no abelian varieties over Z? 2010-01-05T22:59:34.470

28 Fontaine-Mazur for GL_1 2010-07-25T11:17:29.433

27 In which ways can the isogeny theorem fail for local fields? 2011-01-24T00:26:02.947

26 Over which fields does the Mordell-Weil theorem hold? 2012-10-01T13:01:11.950

25 Modern proof of Serre's open image theorem? 2012-09-26T15:02:32.520

24 Products of primitive roots of the unity 2013-07-04T14:39:32.490

23 Why do people think that abelian varieties are the hardest case for the Hodge conjecture? 2010-03-03T22:36:37.627

23 Is every abelian variety a subvariety of a Jacobian? 2018-07-05T11:30:37.020

22 Why polarization of abelian varieties? 2014-07-27T21:59:53.850

22 When is "independence of l" known? 2014-12-29T16:28:29.663

22 Is hyperelliptic cryptography "practical"? 2016-02-01T17:51:53.937

19 Are there Néron models over higher dimensional base schemes? 2010-01-25T11:17:05.137

18 Which curves can be found on Abelian varieties ? 2010-04-15T09:56:36.730

18 Torsion points of abelian varieties in the perfect closure of a function field 2011-08-27T20:56:01.353

17 Are Jacobians principally polarized over non-algebraically closed fields? 2009-12-01T21:00:37.367

17 Crystalline cohomology of abelian varieties 2010-04-05T11:48:26.797

17 Bhargava's work on the BSD conjecture 2018-03-13T22:54:53.353

16 Do all simple factors of jacobians of curves come from correspondences? 2015-10-19T22:30:27.933

16 On Tate's "Endomorphisms of Abelian Varieties over Finite Fields", sketch of proof of main result? 2016-11-12T23:37:55.230

15 Can we count isogeny classes of abelian varieties? 2009-11-07T07:21:50.657

15 non principally polarized complex abelian varieties 2010-03-03T18:53:56.120

15 Etale endomorphisms of abelian varieties in positive characteristic 2011-08-22T12:07:56.713

15 Elements of arbitrary large order in the first Galois cohomology of an elliptic curve 2016-05-21T15:29:04.523

14 Examples of rational families of abelian varieties. 2009-10-16T20:14:06.453

14 Characterizations of Abelian varieties (3-folds) in positive characteristic 2011-07-29T00:42:12.010

14 Status of Grothendieck's conjecture on homomorphisms of abelian schemes 2013-03-01T10:38:38.967

14 Infinitely many curves with isogenous Jacobians 2013-05-06T13:20:08.293

14 Counting abelian varieties over finite fields in a given isogeny class 2015-09-11T21:15:10.183

14 Albanese variety over non-perfect fields 2017-01-31T06:43:14.350

13 Lifting abelian varieties in (the closed fiber of) a fixed Neron model 2010-03-19T16:00:02.200

13 Torsion points in Abelian varieties over number fields 2011-02-19T03:50:45.017

13 Does every Abelian variety have a finite resolution by Jacobians? 2012-02-12T17:22:25.653

13 Katz--Mazur for abelian varieties 2013-12-28T19:48:13.267

13 Why study CM abelian varieties? 2014-01-21T11:29:18.360

13 Zeta function of Abelian variety over finite field 2017-09-29T10:12:37.070

12 "Albanese" schemes: When does an "initial abelian scheme" exist under a given scheme? 2009-10-26T01:17:13.010

12 When is an Albanese variety principally polarized? 2009-12-01T00:48:46.893

12 Complex torus, C^n/Λ versus (C*)^n 2010-04-06T16:01:25.190

12 isomorphism of abelian varieties 2010-04-08T21:56:00.717

12 Why were Abelian functions so important in the 19th century? 2010-05-31T09:56:28.813

12 Quotient of abelian variety by an abelian subvariety 2010-09-02T20:26:19.233

12 Generalizations of Belyi's theorem 2010-11-16T16:58:05.520

12 The torsion point count in higher dimension 2013-02-08T14:33:43.210

12 A frustrating cohomology class on the moduli of abelian surfaces 2013-08-30T07:46:39.750

12 Lifting Abelian Varieties to p-adic fields 2014-04-17T20:52:56.227

12 The Tate conjecture for abelian varieties 2014-04-30T16:32:13.983

12 Faltings height in short exact sequences 2014-11-01T03:28:20.597

12 Zariski vs etale torsors over abelian varieties 2016-12-23T15:33:21.310

12 Geometry underlying a comparison of Dieudonné theories 2017-02-10T00:36:40.047

12 What is known about abelian varieties with several principal polarizations? 2018-07-26T01:53:03.783

12 Is the complement of an affine open in an abelian variety ample? 2018-10-31T21:18:54.923

11 What classes am I missing in the Picard lattice of a Kummer K3 surface? 2010-02-16T18:52:57.660

11 Galois action on one-dimensional quotients of l-adic cohomology 2011-01-29T03:53:27.113

11 Is an abelian variety with a Galois invariant, rank one submodule of its Tate module, CM? 2011-02-16T21:30:30.740

11 Proofs of Mordell-Weil theorem 2011-08-07T15:08:52.660

11 What is the Brauer group of the moduli space of (p.p.) abelian varieties? 2012-09-27T05:23:48.297

11 Average ranks of abelian surfaces 2013-02-05T23:38:38.497

11 Purity for abelian schemes up to $p$-isogenies 2013-10-21T15:40:26.357

11 Can an abelian variety/Q have no non-trivial points over Q_sol? 2015-03-01T00:28:19.347

11 Are Hecke eigenvalues on the cohomology of the Newton polygon strata automorphic? 2015-10-31T20:44:51.613

11 Singular curve on an abelian surface 2016-06-16T17:39:21.600

11 Abelian variety with prescribed endomorphism ring 2016-08-11T15:05:32.360

11 When $k = \mathbb{F}_q$ finite field, $X$ always has $k$-rational point, and so $A \simeq X$? 2016-10-04T16:10:31.357

11 Points of abelian varieties over purely transcendental extensions 2018-02-20T14:20:25.097

10 Torsion of an abelian variety under reduction. 2010-01-02T03:08:01.643

10 Failure of Theorem of the Cube? 2010-12-05T23:34:22.677

10 Why can projective varieties just have abelian group operations? 2011-03-21T13:04:24.853

10 Mod m versions of the toric part of Tate modules 2011-05-16T13:36:54.747

10 About the Bloch conjecture on entire curves 2012-10-24T16:21:54.417

10 What are some consequences of the Mumford-Tate conjecture? 2012-11-19T18:42:58.207

10 Are automorphisms of abelian varieties detected by the formal group? 2014-01-03T16:27:35.780

10 On a proposition in Hartshorne's paper "Ample vector bundles on curves" 2014-11-14T14:09:27.313

10 What can we say about tropical maps $\mathbb{P}^1 \to A$ for an Abelian variety $A$? 2015-10-05T11:11:44.293

10 Does every Shimura variety contain a generic point defined over a number field? 2016-08-12T18:09:00.803

10 Surfaces with $q=2$ and generically finite Albanese map 2016-08-22T13:36:55.117

10 How to compute the formal group law of a Shimura variety (using its invariant differentials)? 2016-11-01T03:40:21.840

10 Orders of reductions of rational points on elliptic curves 2017-11-13T06:41:39.617

10 $K_0$-equivalence of varieties 2017-11-22T19:31:53.607

9 Is there any rational curve on an Abelian variety? 2009-12-16T03:32:00.290

9 Algebraic cycles of dimension 2 on the square of a generic abelian surface 2010-04-06T16:34:37.853

9 Galois orbits of newforms with prime power level 2010-05-16T19:57:03.317

9 Can we always find a curve which doesn't have semi-stable reduction 2011-10-12T21:35:29.377

9 finiteness of torsion points of an abelian variety over a totally real field？ 2011-11-26T23:46:06.740

9 Schottky locus in genus 2 2012-01-24T17:24:57.177

9 Obstructions to deforming an abelian variety 2012-06-15T02:32:15.683

9 Modularity of higher dimensional abelian varieties 2012-10-04T19:03:53.503

9 Motives over finite field not generated by hyperelliptic curves 2014-05-12T20:00:48.083

9 Is the compositum of all quadratic extensions of the rationals an ample field? 2015-08-03T09:53:09.990

9 Does bounded-degree base extension yield Zariski-dense Mordell-Weil group? 2015-09-03T17:18:19.923

9 Pull-back of an irreducible ample divisor via an isogeny of abelian varieties 2017-06-14T15:37:58.580

9 Geometry of Albanese image 2017-09-06T16:29:46.833

9 Endomorphism ring of simple ordinary abelian variety 2018-04-11T15:01:01.767

9 Do abelian varieties have Neron models over arbitrary valuation rings? 2018-08-05T17:39:49.297

8 Is there an intrinsic way to define the group law on Abelian varieties? 2010-05-19T18:14:05.163


text:
PartMC  2.6.1
Input File Format: Gas Profile

Read an array of gas states with associated times and rates from the file named on the line read from the given file.

Parameters
 [in,out] file Spec file. [in] gas_data Gas data. times Times (s). rates Rates (s^{-1}). gas_states Gas states.

A gas profile input file must consist of three or more lines, consisting of:

• the first line must begin with time and should be followed by space-separated real scalars, giving the times (in s after the start of the simulation) of the gas set points — the times must be in increasing order
• the second line must begin with rate and should be followed by space-separated real scalars, giving the values at the corresponding times
• the third and subsequent lines specify gas species, one species per line, with each line beginning with the species name and followed by space-separated scalars giving the gas state of that species at the corresponding times

The units and meanings of the rate and species lines depends on the type of gas profile:

• emissions gas profiles have dimensionless rates that are used to scale the species rates and species giving emission rates with units of mol/(m^2 s) — the emission rate is divided by the current mixing layer height to give a per-volume emission rate
• background gas profiles have rates with units s^{-1} that are dilution rates and species with units of ppb (parts per billion) that are the background mixing ratios

The species names must be those specified by the Input File Format: Gas Material Data. Any species not listed are taken to be zero.

Between the specified times the gas profile is interpolated step-wise and kept constant at its last value. That is, if the times are , the rates are , and the gas states are (all with ), then between times and the gas state is constant at . Before time the gas state is , while after time it is .

Example: an emissions gas profile could be:

 time   0       600     1800    # time (in s) after simulation start
rate   1       0.5     1       # scaling factor
H2SO4  0       0       0       # emission rate in mol/(m^2 s)
SO2    4e-9    5.6e-9  5e-9    # emission rate in mol/(m^2 s)

Here there are no emissions of , while starts out being emitted at at the start of the simulation, before falling to a rate of at 10 min (note the scaling of 0.5), and then rising again to after 30 min. Between 0 min and 10 min the emissions are the same as at 0 min, while between 10 min and 30 min they are the same as at 10 min. After 30 min they are held constant at their final value.

format: plain


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# Tag Info

11

Related answer: http://math.stackexchange.com/a/532746/24293 Looking at the comments, you seem to be asking why there are chiral 'pairs' and not chiral multiplets. Looking at the tag, it looks like you want an analysis of higher dimensions as well. TL;DR Short answer: In any number of dimensions, chiral objects come in pairs. This is because numbers ...

11

For spin measurements the original experiment was the Stern-Gerlach experiment in which you will see that a prior unpolarized beam will split up in two (Spin up and down) orientations. see: http://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment For helicity, a very ingenious and fascinating experiment is the famours Goldhaber experiment that uses a ...

9

No, it really is arbitrary. The reason we use the right hand rule today (although it may have been chosen for different reasons of convenience in the past) is simply that our coordinate system of choice is right-handed. Mathematically, this means that we define the directions of the axes so that you have to use the right-hand rule to evaluate this cross ...

8

The clockwise direction is normally defined by the right hand grip rule. When your thumb is pointing away from you, your fingers are curled clockwise. So when you look at a clock the axis of rotation is away from you through the clock. I'd guess the downvotes are because people believe your question is not physics related, but in fact this rule is how ...

7

Presumably you are asking about the communication ambiguity in physics: can we unambiguously specify what we mean by "a right handed coordinate system" to a correspondent far away without a pre-arrnage communications channel (i.e. using SETI)? For a long time the answer seemed to be "no", but the discovery of parity violation in 1957 changed the answer to ...

5

At first glance, chirality and helicity seem to have no relationship to each other. Helicity, as you said, is whether the spin is aligned or anti aligned with the momentum. Chirality is like your left hand versus your right hand. Its just a property that makes them different than each other, but in a way that is reversed through a mirror imaging - your left ...

5

There is no chiral anomaly/gauge anomaly if the spacetime dimension $2\ell+1$ is odd, partly because $SO(2\ell+1)$ has real or pseudo-real representations, but no complex representations. There may instead be parity anomalies in odd spacetime dimensions. In fact, there is a dimensional ladder of related anomalies $$\text{Abelian chiral anomaly in}~ ... 5 Your confusion arises because the term (anti)clockwise, when used by itself, is ambiguous, and should always be used with a statement like "as seen from the top" (unless that is absolutely obvious^1). The reason for this is that "clockwise" defines a direction of rotation within a plane, but does not specify which side the plane is observed from. (In more ... 3 The Majorana bound state inside a vortex of a topological superconductor is, indeed, not a chiral edge state. It does not follow that the topological superconductor does not have a chiral edge state. It does! Solve, for example, the BdG equations for a p+ip superconductor with open boundary conditions, and you'll see it. The existence of edge modes is ... 3 The importance of chiral symmetry breaking is a point that e.g. David Gross, a co-father of Quantum Chromodynamics, likes to make whenever some people suggest that the mass is entirely due to the Higgs field. In fact, most of the mass of visible matter is due to the QCD, especially chiral symmetry breaking, and it has nothing to do with the Higgs field. The ... 3 I agree with the answer of Quantum physicist , that zero mass for neutrinos was an input to the standard model , not a prediction, because measurements showed a mass compatible with zero. But I will add that the discovery that neutrinos must have mass does not destroy the Standard Model, just different Lagrangian for the neutrinos has to be included. ... 3 Standard model doesn't predict that neutrinos are massless. It's a "Model", where initially neutrinos are considered massless, because no mass was observed. The way we know, now, that neutrinos have masses, is through the mixing between the different neutrino types, through a matrix called the PMNS matrix (similar to the CKM matrix for quarks). This mixing ... 3 Tarek (OP) e-mailed me to contribute to this thread. Here's the response that I gave him (slightly edited for clarity). I see why this was confusing, my apologies! I was perhaps too glib in the post. Iwas implicitly talking about a chiral rotation but wanted to present it somewhat more intuitively. Let me try to spell it out more carefully, and hopefully ... 3 You seem want to introduce gauge invariance into a theory that doesn't appear to have the global symmetry need in the first place. One way to think of gauge invariance is that you 'gauge' the global symmetry, then you just change your derivative terms to covariant derivatives like you mentioned. In other words, we can only concern ourselves with the global ... 3 No, it's not true. Suppose I'm floating in outer space (presumably in a space suit or something else to keep me alive). I'm still me, and I still know that, for example, my left hand is the one on the left, and my right hand is the one I can write with. Even on Earth, we don't need environmental clues to distinguish left from right; it's more a matter of ... 3 Dear lurscher, the quote is the kind of C-physics described by the C-word which is a favorite word of mine but is discouraged on this server, so I won't use it - but you have used it. You don't misunderstand anything - quite on the contrary, you're right on the money. These comments about a non-existent test of parity in the equivalence principle are due to ... 2 I think what your frien talked about was chiral symmetry breaking, which was observe in particle physics experiments. In this sense, "right" and "left" may be absolutely defined, much like how positive and negative charges are absolutely defined although the names are arbitrary. 2 There is a very simple and enlightening explanation due to N.V.Gribov given in his following conference article and also beautifully explained by Dmitri Kharzeev in the following arxiv article(section 1). Gribov's argument doesn't involve the heavy machinery of quantum field theory. He actually proves that in the case of colinear electric and magnetic ... 2 Let me add a few comments to Michael Brown's answer/comment. As he mentioned, a QFT is well defined with an action and a regulator. We always wish to use regulators that preserve gauge invariance, since that is a redundancy of our description and should not be removed in our quantum theory. However, any regulator that preserves gauge invariance, ... 2 The charged current part of the Lagrangian of the electoweak interaction, for the first generation of leptons, is :$$L_c = \frac{g}{\sqrt{2}}(\bar \nu_L \gamma^\mu e_L W^+_\mu + \bar e_L \gamma^\mu \nu_L W^-_\mu )$$The first part corresponds to different versions of the same vertex : e_L + W^+ \leftrightarrow \nu_L \tag{1a} (\bar\nu)_R + W^+ ... 1 Apparently, there seems to be no agreed upon definition of clockwise in 3D space - but an a clear agreement regarding the meaning in a plane "seen from above" As I am starting to answer, I have no idea what is the correct answer, if any. It is the "if any" that gets me started on this topic. I am certainly not an expert, I never could tell my left from my ... 1 The angle 120 degrees is calculated as$$ \frac{360^\circ}{3} = 120^\circ because the full angle 360 degrees in the hexagon is divided to three equal parts. One may draw the "Mercedes logo" triplet of arms into the hexagon network in several ways – one of the arms may be vertical; or one of them may be horizontal, and so on – and one of these ways explains ...

1

The operator $S=\bar{q}\lambda_a q$ is the so-called scalar quark density, and together with its pseudoscalar counterpart, it enters the expressions for the divergence of the vector and axial-vector currents (see section 2.3.6). Spontaneous symmetry breaking occurs if $n$ generators of a symmetry transformation do not annihilate the ground state, resulting ...

1

The short answer is, yes, the chiral edge state is determined by bulk topological property. It is known as bulk-edge correspondence. The paper you should read is: Protected edge modes without symmetry - 1301.7355. Generically, to determine whether the edge states are robust is by determining whether the edge states are protected'' by any of the three ...

1

Left and Right can be used in different contexts. In most cases they work equally well in space but not quite always. Often when people talk about left or right they mean something relative to a person, e.g my left hand or my right eye or the book to my right. This works equally well in space because it is defined relative to the position of a person, not ...

1

I read in a book recently a theoretical conversation between an alien and and an earthling where the earthling was trying to explain which hand is the right hand (without any visual contact) and which the left. The alien would have to perform experiments to determine a reference left or right. It turns out after a whole chapter showing how there isn't ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
Determine the average % power in each sideband frequency in case of AM using sinusoidal modulating wave. Given that the percentage modulation = 20%

This question was previously asked in
UPPCL JE EC Official Paper (Held on 25 March 2021: Shift 1)
View all UPPCL JE Papers >
1. 10%
2. 5%
3. 1%
4. 18%

Option 3 : 1%
Free
CT 1: Network Theory 1
11608
10 Questions 10 Marks 10 Mins

Detailed Solution

Concept:

The power of a transmitted AM wave is given as:

$$P_t = {P_c}\left( {1 + \frac{{{μ ^2}}}{2}} \right)$$

$$P_t = {P_c} + P_c\frac{μ ^2}{2}$$

Power in the carrier = Pc

$$P_c=\frac{{A_m}^2}{2}$$

Power in both the sidebands is given by:

$$P_s= \frac{{{P_c}{μ^2}}}{2}$$

Since the power is distributed equally to the left and to the right side of the sideband, the power in one of the sidebands is given by:

$$P_{s1}= \frac{{{P_c}{u^2}}}{4}$$

Calculation:

Given μ = 20% = 0.2

$$P_c=\frac{{A_m}^2}{2}$$

Total Sideband power is:

$$P_{sb}=\frac{{A_m}^2\mu^2}{4}$$

Assume Am = 1

$$P_{sb}=\frac{0.2^2}{4} \ \times \ 100$$

Psb = 1%

Hence option (3) is the correct answer.


text:
### Generating Fullerenes

Today, we discuss “Generation of Fullerenes” by Brinkmann, Goedgebuer, and McKay, recently published in the Journal of Chemical Information and Modeling. A fullerene for our purposes is a cubic planar graph where every face has length 5 or 6. However, the definition of fullerene as a molecule is valuable as well (and why this paper was published in a chemistry journal). Since we previously discussed generating cubic graphs, we could use that algorithm and restrict our output to graphs that satisfy our requirements, but this method is wasteful as there are many more cubic graphs of order $n$ than fullerenes of order $n$. Since their method uses canonical deletion, we only need to describe our base objects and our augmentation step.

### Structural Properties of Fullerenes

Since fullerenes are planar, they satisfy Euler’s formula:
$n - e + f = 2$
where $n$ is the number of vertices, $e$ is the number of edges, and $f$ is the number of faces. Since $e = \frac{3}{2}n$ and $e = \frac{5}{2}f_5 + \frac{6}{2}f_6$ where $f_i$ is the number of faces of length $i$, we find that a fullerene contains exactly 12 5-faces and the rest are 6-faces.

A fullerene satisfies the independent pentagon rule (IPR) if no 5-faces are adjacent in the dual (i.e. no 5-faces share an edge). The smallest IPR fullerene is the buckyball (or buckminsterfullerene), named after Buckminster Fuller who started this whole mess. The buckyball has 60 vertices and is commonly known by the shape of some soccer balls. Something fun about the symmetry of the buckyball: the 5-faces are antipodal in the dual, but the faces are switched. See Figure 1, which shows the buckyball centered at a 5-face.

Figure 1. The buckyball centered on a 5-face. Source: Wikipedia.

### Generating Fullerenes

As when generating cubic graphs, we will perform canonical deletion subject to custom augmentation steps. These steps are designed such that at every point our current graph is a fullerene. We will replace certain connected induced subgraphs with larger connected subgraphs in expansion steps, and the reverse is a reduction step. It was shown by Brinkmann, Graver, and Justus that no finite set of replacements suffices to generate all fullerenes, so an infinite family must be used. However, the infinite family used can be generated algorithmically, and when a maximum order $n$ is given, the list of augmentations is finite.

#### $L$-type augmentations

The $L_i$-augmentation is an infinite family, where $i$ is a number corresponding to a path of length $i +2$ between two 5-faces in a fullerene. Suppose $p_1$ and $p_2$ are two 5-faces, and $P$ is a path of length $i+2$ between a vertex on $p_1$ and a vertex on $p_2$. In addition, suppose that every face incident to an edge in $P$ is a 6-face and every face shares at most two edges with $P$. If we imagine walking along $P$, we alternate between taking a left or right edge at every vertex. Let $f_1,\dots,f_{i+2}$ be the 6-faces along one side of $P$ and $g_1,\dots,g_{i+2}$ be the 6-faces on the other side of $P$, such that $g_{i}$ is adjacent to $f_{i-1}$ and $f_i$ (note $g_1$ is only adjacent to $f_1$).

With this path, the $L_i$ augmentation inserts $i$ 6-faces between the $f_i$‘s and $g_i$‘s, moves the 5-faces $p_1$ and $p_2$ closer together, and adds two 6-faces adjacent to the previous neighbors of $p_1$ and $p_2$. (The paper has a very nice figure that I won’t even try to replicate here.)

#### $B$-type augmentations

$B$-type augmentations are very similar to $L$-type augmentations since there is a path between two 5-faces bounded between faces $f_1, \dots, f_i$ and $g_1,\dots, g_i$ on either side of the path. However, for a $B$-type augmentation there is exactly one 6-face $f_j$ that is incident to this path on three edges and exactly one 6-face $g_j$ that is incident to the path on one edge. Essentially, this forms a “turn” in the path between the 5-faces. Similarly, we pull the 5-faces closer together and insert 6-faces on the outsides. (Again, the paper has a very nice figure. Seriously go look at it.)

#### $F$-augmentations

The $F$-augmentation is a single augmentation, but important, as this step by itself is required to generate the carbon nanotube structures. Let $p$ be a 5-face adjacent to five 6-faces $f_1,\dots,f_5$ and the five faces at distance two from $p$ are $g_1,\dots,g_5$, where $f_i$ is adjacent to $f, f_{i-1}, f_{i+1}, g_{i}, g_{i+1}$. To perform an $F$-augmentation on $p$, we add a ring of five 6-faces $h_1,\dots,h_5$ between the faces $f_i$ and faces $g_i$ such that $h_i$ is adjacent to $h_{i-1}, h_{i+1}, f_{i}, f_{i+1}, g_{i}, g_{i+1}$.

Observe that these augmentations have natural inversions, which I will call $L$-type contractions, $B$-type contractions, and $F$-contractions. It may not be obvious as to why every fullerene is generated by this family of augmentations, so I will sketch a short proof here. We shall consider a fullerene and test that some contraction exists within the graph. If an $F$-contraction exists, that suffices. We shall assume that no $F$-contraction exists.

Consider the fullerene embedded on a sphere as in the figure below.

Figure 2. A fullerene on the sphere, some 5-faces shown.

Now, start walking from one of the 5-faces, alternating left and right turns whenever reaching a new vertex until reaching a 5-face. If we reach a 5-face other than the one we started at, then we have an $L$-type contraction. Otherwise, we have made a closed curve about the sphere that starts and ends at a common 5-face, as in the figure below.

Figure 3. Walking from a 5-face back to itself.

However, every other 5-face lies to one side of this curve. Thus, there is some point where we can adjust our walk by making two right turns (or two left turns) in a row to then reach a distinct 5-face, as in the figure below.

Figure 4. Making one turn to form a $B$-type contraction.

### The Canonical Deletion

It takes some careful work to implement the given augmentations, and their inversions. However, once that has been dealt with, we can make a simple canonical deletion. Among all types of contractions in the graph, follow the filtering process below:

1. If some 5-face has a $F$-contraction, then select a 5-face using the canonical labels of the dual graph and contract on that face.
2. If both $B$-type and $L$-type contractions exist, then restrict to the $B$-type contractions.
3. If multiple contractions remain, then restrict to those of shortest length.
4. If multiple contractions remain, then restrict to contractions between two 5-faces of lowest lexicographic label in the canonical labeling of the dual graph.
5. If multiple contractions remain, then they are between the same pair of 5-faces, have the same length, and have the same type. Use the list of 6-faces surrounding the contraction to find the lexicographically-least tuple in the canonical labels of the dual graph.

This process of canonical deletion allows us to restrict our augmentations to be only $F$-augmentations if an $F$-contraction already exists, or only $F$-augmentations and $B$-type augmentations if a $B$-type contraction already exists. Finally, we can also restrict to augmentations that will form shortest contractions. This reduces the number of augmentations slightly.

The authors seem to use the dual graph as their generation tool, and I agree that this is the better option. Since the augmentations involve shifting faces and adding faces, and the canonical deletion uses the dual graph, it is only fitting that we use the dual graph. Thus, we are shifting vertices and adding vertices, a much more natural operation.

### Software

plantri and fullgen are Brinkmann and McKay’s software for generating certain classes of planar graphs, such as triangulations and fullerenes.

buckygen

### Online Resources

Fullerene on Wikipedia

Fullerene on MathWorld

Fullerense on House of Graphs

Shigeo Maruyama’s Fullerene and Carbon Nanotube Site

The Fullgen Page

### References

G. Brinkmann, J. Goedgebeur and B.D. McKay, Generation of Fullerenes, Journal of Chemical Information and Modeling, 52(11), pages 2910-2918 (2012). (arXiv version)

G. Brinkmann, A.W.M. Dress, A Constructive Enumeration of Fullerenes, Journal of Algorithms 23(2) 345-358, (1997).

J. R. Dias, Algorithm for generating fullerenes by circumscribing, Journal of Chemical Information and Computer Sciences 34 (2), pp 248-251 (1994).

B. Plestenjak, T. Pisanski, A. Graovac, Generating Fullerenes at Random, Journal of Chemical Information and Computer Sciences 36(4), pp 825-828 (1996).


text:
# Circle with a cross inside feynmp

The below code produces essentially what I want but there must be a more elegant way and more automatized way. I want a circle with a cross inside it at a vertex:

\fmfv{d.sh=circle,d.f=empty,d.si=.1w,l=$\times$,label.dist=0}{v3}% v3 is the name of the vertex

But notice that if the circle becomes big, the cross will remain small. I want a circle with a cross inside it that has the same diameter as the circle no matter how big the circle is.

Is there a simple way to achieve this?

-
Could you please provide a complete MWE for the community to work with? Something like \otimes might be what you want, but without knowing the surrounding code I am unable to test. – Paul Gessler May 6 '14 at 16:14
I tried \otimes, looked nice. Can one enlarge \otimes? – Faq May 6 '14 at 16:19
With the graphicx package, \scalebox{scalefactor}{code} will enlarge, if scale>1. If the code is math, $ delimiters will be needed around code. – Steven B. Segletes May 6 '14 at 16:32 That worked like a charm Steven! One solution to this problem is: \fmfv{l=\scalebox{2}{$\otimes\$},label.dist=0}{v3} So a combination of what you said and what @Paul Gessler suggested. Thanks. – Faq May 6 '14 at 16:42

Disclaimer: I have never used Metafont before, and I also have only ever touched feynmf once. Please comment if I did any of this completely wrong.

Since you never even provided a complete MWE, I had to just make this stuff up.

1. I used the \fmfcmd macro to define a path, which I named otimes, to draw a ⊗ shape.
It is made by rotating four copies of a ⌔ quadrant. (Thanks to egreg for the help.)

2. I turned on \fmfwizard according to footnote on page 17 of the feynmf manual:

If the variable feynmfwizard is true (e.g. after calling the \fmfwizard macro), it is also possible to specify [shape as] any METAFONT expression that evaluates to a path.

3. I set the vertex shape to otimes and the fill to empty. (Surprisingly, using another value for fill does not seem to break anything.)

\documentclass{minimal}
\usepackage{feynmp-auto}

\begin{document}
\begin{fmffile}{foo}
\begin{fmfgraph*}(80,80)

\fmfcmd{
% Please let me know if there’s a more efficient way to do this
quadrant = (0, 0) -- (0.5, 0) & quartercircle & (0, 0.5) -- (0, 0);
for i=1 upto 4: q[i] = quadrant rotated (45 + 90*i); endfor
otimes = q[1] & q[2] & q[3] & q[4] -- cycle;
}
\fmfwizard

\fmfleft{i1,i2}
\fmfright{r}

\fmf{fermion}{i1,c,i2}
\fmf{photon}{c,r}
\fmfdot{c}
\fmfv{d.sh=otimes,d.f=empty}{r}

\end{fmfgraph*}
\end{fmffile}

\end{document}

Notice how this scales “correctly” according to your requirements:

\fmfleft{a}
\fmfright{d}

\fmf{plain}{a,b,c,d}
\fmfv{d.sh=otimes,d.f=empty,d.si=.1w}{a}
\fmfv{d.sh=otimes,d.f=empty,d.si=.2w}{b}
\fmfv{d.sh=otimes,d.f=empty,d.si=.5w}{d}

-
Nice diagram,... – Faq May 6 '14 at 18:00


text:
# A quantum God ver 1

## Introduction

This page is  copy of a post I published February 1 2018.
I decided to transform it into a page in April 2019.

Jesus said once:

I still have many things to say to you, but you are not able to bear them now.” ( John 16:12  )

And to the jews he said “and you will know the truth, and the truth will set you free ”  (   John 8:32   )

These phrases raised two questions in me:

1. What were those many things he had to say?
2. Why couldn’t his audience “bear the many things” he had to say?

1 These “many things” may have not been so important to explain at his time as he would otherwise have talked about these “many things “with his intelligent use of metaphores.

2. Jesus is said to have talked galilean or hebraic aramaic with his disciples. The language could not have been the problem that made it  “unbearable”.  Maybe were the issues he wanted to talk about to difficult to understand at his time, when people did not have the knowledges we have today? Was it about understanding God?

In this article I focus on  the Quantum physics enigmas and the enigma of  Jesus’ miracles and how these miracles could be explained with some knowledge about Quantum Physics. I also look at definitions of God in holy books and how to get closer to a presumingly existing God.

The page has been updated with the issue  Human beings view of God inspired by Morgan Freemans documentary about God.

I also added the issue Omnipresence after listening to Dennis Zettings Youtube video from 2015.

INDEX

## About God in holy books

We find different definitions of God in the Bible.

” God is spirit, and his worshipers must worship in the Spirit and in truth.” (John 4:24  )

“I am the Alpha and the Omega,” says the Lord God, “who is, and who was, and who is to come, the Almighty.” ( Revelation 1:8  )

In the Quran God is defined as:

Allah, the Beneficent, the Merciful. (All Quran chapters of the Holy Book start with it except Al-Tawba (Chapter 9).  (Source : www.aljazeerah.info )

the Exalted in Might, the Wise ( Al-Naml, 27: 9 ).

iLord of the worlds ( Al-Qassas, 28: 30 ).

The One in the Beginning and in the End” (  urat Al-Ikhlas, Chapter 112, verse 1 )

“the Light of the Heavens and the Earth”

the Hearing, the Seeing  ( Al-Shoura, 42: 11 ).

full of forgiveness for the people despite their wrongdoing (    13: 6 and 41:43.   )

The Wisest of Judges

He is the swiftest of accountants  (   6: 62  )

give life to the dead, and He is over all things competent. (  Ar-rum 30: 50 and 41: 39. )

“… did certainly give Moses the Torah and followed up after him with messengers. And We gave Jesus, the son of Mary, clear proofs and supported him with the Pure Spirit”  ( al-Baqarah 2:87 )

(Source : www.aljazeerah.info )

Kyballion

To get an idea of what God is, it is interesting to read the Kybalion that were defined by the Egyptian Hermes trismegistus

in his 7 hermetic principles 4000 years ago. He was regarded a messenger of God and later, one of the Gods himself (Hermes in Greece and Toth in Egypt)  and a psychopomp.

among others he shared these principles:

• The all  is mental (mentalism, something the biocentrists accept)
• Everything vibrates and is rythm, reminding about physicists string theory

( Image source: www.truthinsideofyou.org )

.

## Human beings view of and connecting to  God

I decided to add this part after seeing Morgan Freemans docutmentary about God. He looked at views of God in different part of the world to find similarities. he raises for me important questions and try to find answers.

### Hindus view of God

“Behind all Gods there is single divine  energy the hindu believer try to get into” a energy that is neither female nor male, it has no name but they call it Brahman. Hinduism looked at superficially  seems to be a religion of many gods. But under the surface there is a single divine energy

Why one God in certain cultures and many in others?

### Stonehenge, The first monotheists

Stonehenge was build with a focus on the sun. The old stones at Durrington walls focusing on Beacon hill, where demolished after Stonehenge and rebuilt with a focus on the uprising midsummer sun.

Sun the main focus of worship and religious interest to establish a particular connection to the sun. The people of Stonehenge may hjave been the first people to worship a single God.  When the Gods were ancestors, a river, they were much more accessible. Woreshiping the Son, they missed this accessibility.

### worship the dog star, Sirius,

I were informed about another ancient temple.  the world’s oldest temple, #GobekliTepe, in Southern Turkey, may have been built to worship the dog star, Sirius, according to one researcher.

“How do you speak with a God that is so remote?”

He continued in Egypt

Anjali Kumar  shares about her search of God in a Ted.

### Atenism– the first monotheistic religion

Faraoh Akhenaton decided 1350 ad to worship the sun 100 years after Stonehenge.

His ideas was considered very dangerous. he thought there were to many Gods. He closed most of the temples. “We must have one important God that only I can channel. (Salima Ikram) There is a special God. The name of that God is Aton. You can worship Aton though me. “

That was not a popular move. All the important Gods priests were silenced. As oon as Akhenaton died the old priesthood struck back. His son Tuthankhamon was only 7 years when Akhenaton died and Tithankamon died when he was 19. The priesthood did their best to erase the memory of Akhenaton.

The Great Hymn to the Aten is the longest of one of a number of hymn-poems written to the sun-disk deity Aten. Composed in the middle of the 14th century BC, it is attributed to the 18th dynasty Pharaoh Akhenaten, who radically changed traditional forms of Egyptian religion by replacing them with Atenism.” (Wiki)

### Jerusalem

Half the people of the planet can trace their God to the ancient city of Jerusalem. it was in Jerusalem the belief in one single all powerful deity took root 2000 years ago.

How one God won out of many

Yoran Hazony, Jewish philosopher:

“Abrahams father owned a shop with God idols. The pagan Gods of that time represented anything people may need.  There was a God that brings the rain, a god of warfare. Some Gods wanted a party, they wanted wine, song and good food, some Gods wanted bloodshed’s. The Bible tell about Abraham wanting to shed  his son’s life. A voice stopped him telling to never sacrifice  lives again. Jews built a temple over that shedding site to commemorate that event. A temple that the Romans destroyed 70 ad. “

God is a single force that brings physical and moral order.

You could communicate with the God of Abraham without idols or temples. For Jews, Christians and Muslims,   the invisible God is always with them wherever and whenever they  turn to God.

How to connect to a God that has no physical form?

How do you knnow what is divine and what isn’t?

### Muslims

Al_Hussein Mosque, Cairo, Ahmed Ragab (islamolog)

The call to prayer,  For the faithful the song  of the Muezzzin is a manifestation of God itself.ed. Morgan Freeman says erroneously  “song ” but it is really a Quran recitation that you listen to in the video.)

At the end of the prayer one say “Ahsalamu Aleykum”. (e. “Piece with you”, something you say to people)
Morgan : “A prayer to Allah seems to be like a conversation with a person.”

Morgan to the Imam “In Christianity god is so manifest. There is not such thing in Islam. Who am I talking to?”

Al_Hussein Mosque, Cairo, Imam Al-Amir Mahfouz, (Mosque spiritual leader).

“You can not imagine God. God is beyond imagination. Whatever you would imagine , God is beyond that imagination”

Morgan “Mosques are designed to be filled with beautiful sounds and images that delights the senses, from elaborate architectures to verses of the Quran written with the fines calligraphy.

Many muslims sees this beauty as a manifestation of God itself. (ed. morgan says himself as god were a man. I prefer “itself” in Swedish one sould say “hensjälv”, hen that is neither han (him) nor hon (her) ).

Morgan: “Islam sees god in all things that are beautiful. As God as no form it can be experienced with any of the senses. But these experiences are only aspects of the divine. God is always more than we can imagine.

### Navajo God

Some faiths believe God can take a visible form. In a Navajo Hogan in Shiprock, where God and a human become one single being. a Navajo God start living in a  girl becoming a woman after a 4 day long kinaalda puberty ceremony, making a giant corn cake in honor of the sun over a fire outside the Hogan” it originates from the woman of change, Asdzaa Nadleehè. they wanted her to have children.

First man and first woman saw a cloud over Gobernador Knob and they hear a baby crying. the holy people instructed them to take care of the baby. In twelve days the baby grew up to a 12 year old girl. She was ready to become a woman. To become a woman the girls must connect to the Spirit of Asdzaa Nadleehè that the Navajo believes lives in the Nature. She must run each day toward tghe uprising sun

### Sufi islam

It is a pity Morgan hasn’t explored the Sufi meditative approach. Morgan that compared music with God should have done that.

## Neurotheology

“Dr. Andrew Newberg is a neuroscientist who studies the relationship between brain function and various mental states. He is a pioneer in the neurological study of religious and spiritual experiences, a field known as “neurotheology.”

( Source:   http://www.andrewnewberg.com   )

Understanding God through his Creation

Giordano Bruno was trying to understand  God through his Creation.

Giordano Bruno, who understood quite well Copernicus heliocentric model, said about God in his authobiography in page 35 that “the only bridge to understanding the infinity of God is to understand the infinity of the Universe.”

Giordano also said in his authobiography in page 20  that in the tiny bubbles in a cup of cuffy, you can see the reflection of the Universe.

My hypothesis is that we in the tiniest quantum particles can see a reflection of God and Jesus.

In the Romans 1:20-22 you can read about God that For his invisible qualities are clearly seen from the world’s creation onward, because they are perceived by the things made,  even his eternal power and Godship”

In James 4:8 you read that “Draw close to God, and he will draw close to you”

A conclusion of Romans 1:20 and James 4:8 is for me

“Study YHWHs (=Gods) Creation and gifts with the new technology we have today and you draw close to God And hopefully YHWH has time to draw close to you helping me in my searches.

Studying the Creation means today, to try to study what Biology, Chemistry and Physics today understand and know about our world e.g.:

Biology: Darwins theory of evolution, abiogenesis Biological anthropologyQuantum biology

Chemistry: the nucleosynthesis

Physics:  Quantum physics

I believe there is a God but I can not know.

If there is a God who created Universe and all the Creatures, then this God is able to control and use the unified force we had at the beginning of the Universe development. We do not know what can be done with this force. Of course such a God is able to take advantage of the capacity of the quantum particles he created.

I like this verse of Isaiah 40:26:

“Lift up your eyes to heaven and see. Who has created these things? It is the One who brings out their army by number; He calls them all by name. Because of his vast dynamic energy and his awe-inspiring power, Not one of them is missing

Now with my new knowledges about Quantum particles, I also think that God must master and be able to control the behaviour of the quantum particles, as God created these.

## Understanding God studying Quantum theory

Peter Baksa says: “there is a boundary between science and philosophy, between reality and fantasy. That boundary is Quantum Mechanics. ” and later in the same article: This insistence on discrete energy levels dictates how atoms interact with one another, which forms the chemistry of bulk matter — everything from the stars to ourselves. So it can be seen that the nature of the very littlest of things can have a tremendous impact on everything else, on the nature of our reality. …”

…Hence, for the first time in the history of man, ask and it shall be given is a biblical truism that can be explained using Quantum theory.”

One another article is about A Physicist Talks about God And The Quantum

“Quantum mysticism is growing up as a phenomena. Some scientists call this be pseudoscience or quackery.”

I may be a  quantum mysticist. But I am simply trying to get an idea of the nature of Jesus and God, like Giordano Bruno did.

I try to find a explanation of the mysteries of Jesus miracles with the help of Quantum theory.

To understand my idea of a “Quantum God” it is terefore important you have some basic  knowledge about the

• Quantum enigmas
• Jesus miracles

.

## The quantum enigmas

The physician   Domin Walliman after talking 5 minutes about the importance and difficulties to explain science, made a good explanation of some of the Quantum enigmas. Look at this Ted ed youtub from minute 5:33ew with

Before you continue reading me, I recommend to  listen to Dominic as  I am a novice in Quantum physics,

The single particle double slit experiment changed the way we look at materia.  This youtube video explain it very well.

.

1. Particle duality

Photons can be both particles and waves.

Thomas Young demonstrated with this experiment that light is a wave. But today we know that photons that gives us visual impulses in our retina, are particles as well.

just as Newton predicted in his  book Opticks.

Also big molecules as buckminsterfullerene can behave in the same way.

.

2. Quantum entanglement

Electrons have some kind of contact between them that is faster than light.

Electrons rotates like planets around their axes. Physicians call this rotation “spin”. Two electrons can be connected to each other through a so called entanglement. If one of the two electrons change its rotation from e.g. clockwise to counterclockwise the entangled electron will “know about this event” this and act accordingly changing its own rotation to clockwise so they are again in superposition, even if it the other electron is on the other side of the Universe or leaving the other with the speed of light.  Also a hydrogen proton can beentangled with its electron at 0 Kelvin.  “A spooky action at a distance” as Einstein called it.  According to Van Raamsdonk:”The Universe would not function in the same way without Quantum entanglement.” (Source:  Van Raamsdonk ).

two entangled aparticles may be seen “in some quantum sense  the same object”.

Philip Ball suggests min5:27 in his youtube “Understanding Quantum Entanglement

Many biological events (photosynthesis, many enzyme reactions, birds magnetic field sences etc) can not work well without entanglement. I wrote about it in my article about Quantum biology.

Some more enigmatic behaviours are:

.

3. quantum tunneling – a quantum particle can move through solid objects easily

Protons quantum tunnel into each other avoiding the rejection forces between these. This happens in the sun where two Hydrogen atoms (with one proton) fuse into Helium atoms (with 2 protons)  and release solar energy. (Source: Dominic Walliman)

4. A quantum particle can  go back in time and change the past.

5. Quantum superposition

A quantum particle can be in two  places in the same time (quantum superposition is used in photosynthesis)

Subatomic particles can to two opposite things in the same time, like e.g. spinning (rotating) in both direction at the same time. (Source: Dominic Walliman)
The physician Mark Van Raamsdonk explain this in https://youtu.be/GvRNV6Gmmzk?t=2m47s

To know more you find a lot of good videos in Youtube looking for “Quantum physics”. Another video I looked at is this one from Top5quantum.

Memphisastro explains these quantum enigma. I invite you therefore to look at this video from /www.memphisastro.org

Nils Bohr said once

or “if you are not astonished by the conclusions of quantum mechanics then you have not understood it.”

## Jesus miracles and quantum particle behaviours

Jesus miracles are well documented in the Gospels. And there are many

• Jesus walked on the water
• Jesus knew about what was going on elsewere
• Jesus cured sick mens
• Jesus resuscitated himself
• Jesus entered a house without opening the door

Even the Muslim Quran recognize Jesus as a messenger, Muslims says that Isa (Jesus ) is one of the greatest prophets and the only one who could make miracles. The Quran says:

“We gave ‘Îsa (jesus), the son of Maryam (Mary), clear signs and supported him with Ruh-ul-Qudus” (ed. english “holy Spirit”) (  Surah 2:87  )

Many people, especcially atheists, think that the stories about the  miracles of Jesus are fairy tales for childrens

but for these atheists the physicians stories bout the quantum particles are not controversial at all.

I will  below mention some of Jesus miracles together with the Quantum enigma that may explain it.

3. A quantum particle can become invisible

Mary: “They have taken the Lord out of the tomb, and we don’t know where they have put him!” (  John+20 )

After he said this, he was taken up before their very eyes, and a cloud hid him from their sight.

They were looking intently up into the sky as he was going, when suddenly two men dressed in white stood beside them. Men of Galilee,” they said, “why do you stand here looking into the sky?
“This same Jesus, who has been taken from you into heaven, will come backin the same way you have seen him go into heaven.” ( Acts1:9 )

### A quantum particle can move through solid objects easily (Quantum tunneling)

Jesus entered the house where the apostles where without knocking on and opening the door.

While they (ed. the apostles) were still talking about this, Jesus himself stood among them and said to them, “Peace be with you.”

They were startled and frightened, thinking they saw a ghost. He said to them, “Why are you troubled, and why do doubts rise in your minds?  Look at my hands and my feet. It is I myself! Touch me and see; a ghost does not have flesh and bones, as you see I have…. Do you have anything here to eat?” They gave him a piece of broiled fish,  and he took it and ate it in their presence.” (Luke 24:36-42  )

“Well, eight days later his disciples were again indoors, and Thomas was with them. Jesus came, although the doors were locked, and he stood in their midst and said: “May you have peace.”  Next he said to Thomas: “Put your finger here, and see my hands, and take your hand and stick it into my side, and stop doubting* but believe.”  In answer Thomas said to him: “My Lord and my God!”  Jesus said to him: “Because you have seen me, have you believed? Happy are those who have not seen and yet believe.”  (John 20:27-29 )

### A quantum particle can  go back in time and change the past.

People who suffered by Leprosy where previously infected by Mycobacterium_leprae. By curing people with Leprosy it is possible that Jesus went back in time and changed the past.

11 Now on his way to Jerusalem, Jesus traveled along the border between Samaria and Galilee. 12 As he was going into a village, ten men who had leprosy met him. They stood at a distance 13 and called out in a loud voice, “Jesus, Master, have pity on us!”

14 When he saw them, he said, “Go, show yourselves to the priests.” And as they went, they were cleansed.” Luke 17:11-14 )

### A quantum particle can be entangled with another

As explained above one particles behaviour <e.g. spin) impact on a entangled particle behaviour (spin in this case) even if the entangled particle is on the other side of the Universe.

here are two examples that according to me are examples of entaglement of God to Jesus

1. Luke 19:29-31 says:

29 Now it happened that when he was near Bethphage and Bethany, close by the Mount of Olives as it is called, he sent two of the disciples, saying, 30 ‘Go to the village opposite, and as you enter it you will find a tethered colt that no one has ever yet ridden. Untie it and bring it here. 31 If anyone asks you, “Why are you untying it?” you are to say this, “The Master needs it.”

2.  Luke 22,10-23: “share the second example:

Luke 22,10-23 says:

“He said to them, ‘Look, as you go into the city you will meet a man carrying a pitcher of water. Follow him into the house he enters 11 and tell the owner of the house,’ ‘The Master says this to you: ‘Where is the room for me to eat the Passover with my disciples?’ 12 The man will show you a large upper room furnished with couches. Make the preparations there.”

How could Jesus know about the colt and later the man carrying a pitcher? A hypohesis of mine is that  God is omnipresent and God may have been  entangled with jesus. What God saw, Jesus saw by entanglement.  Knowing about quantum physics, Jesus could maybe have said this metaphore: ” God choose who to become entangled with”. but at Jesus time he had to talk with metaphores for fishermen, shepherds and farmers and not for physicians.

the idea of two entangled objects as the same entity not matter the distance, is confirmed in Jesus words “I and the Father are one” ( John 10.30 ).

.

### Gods omnipresence

I see a possibility of omnipresence with entanglement.

With entanglement God can see with the eyes of those trillion species that have useful eyes, from insects to other animail around you.  In  the same way  is God able to hear with the help of all whose animals  and humans around us that have userful ears.

But God can also entange whoever of us  to listen to our brians.

I found Dennis Zettings who tries to explain omnipresence using knowledges about quantum physics .  I like his introducing with psalm 139:7-10 ). I have however yet difficulties to accept  his explanation as a proof of omnipresence.

We emit  light, like infrared light  that mosquitos can see. But I have never heard that our brains neurons by themselves emit some kind of electromagnetic  waves.  if you do not let the brain hydrogen atoms respond to cetain electromagnetic  frequencies MRI scanners  emit.

Even i  our neurons emit some strange electromagnetic waves, it doesnt prove God/Allah “is in us” btu possibly able to “listen to us”.

The Bible and the Quran say God is all-knowing.  But that could be a reality with entanglement  that is  a Quantum reality.

Dennis uses  a a simple  electromagnetical reality to describe a so called Omnipresence.  I agree with Dennis that electromagnetic waves from our body and brain  could be a way for God to listen to our brain activity and  understand our thoughts.
I am a little reluctant that he uses the word “Quantum physics” when his ecplanation is based on elementary Physics. Maybe Dennis uses these words  to attract attention and legitimate his conclusions. I see no need for him to do this. His argument about a all knowing God is good enough. I would give this title to his Youtube video “Human electromagnetic fields explain God’s allknowing.”

…. yes. But the neruons

Quantum computing with qubits

What can God calculate with quantum calculation?

All constants (cEulers eG, hLambda, pi, phi !,  Q, T ) that build up the Universe may have been calculated with this calculation power.

The constances of life

Einstein’s field equation

where

the cosmological constant is the value of the energy density of the vacuum of space

• ## To be on the same frequency

• Read about string theory and connection between parallell Universes at http://www.thewayofmeditation.com.au
• This article talks about meditation. But I am thinking about having contact with God as many believers thinks or believe they  have.
• I believe that  Mary. Jesus and all our near relatives who died may be in some parallell Universe. Another hypothesis of mine is that we may be able to talk with them if we succeed to set ourselves in in right mood/frequency.
• Some believe it is possible to get in touch with dead people.

This man is following my same path

.

Conclusion

“if you are not astonished by the miracles of Jesus,
then you have not understood God.”

[wpforms id=”4231″]

## Notebook of a pluralist

Insert math as
$${}$$


text:
# Image Processing I¶

This document was prepared at Caltech with support financial support from the Donna and Benjamin M. Rosen Bioengineering Center.

This tutorial was generated from an Jupyter notebook. You can download the notebook here.

In this tutorial, we will learn some basic techniques for image processing using scikit-image with Python. As usual, we will begin by importing the modules we will use.

In [1]:
import numpy as np

import skimage.io
import skimage.exposure
import skimage.filters
import skimage.morphology

import bokeh.io
import bokeh.plotting

import colorcet

import bi1x

bokeh.io.output_notebook()

Note: To run this tutorial, you may need to install the colorcet package. To do this, open a terminal and run conda install colorcet on the command line.

## Image processing tools for Python¶

There are many image processing tools available for Python. Some of them, such as ITK and OpenCV are mature image processing packages that have bindings for Python, allowing easy use of their functionality. Others were developed specifically for Python. Some of the many packages are

The first two packages are standard with Anaconda. They provide a set of basic image processing tools, with more sophisticated packages such as ITK and Fiji supplying many more bells and whistles. If in the future you have more demanding image processing requirements, the other packages can prove very useful.

We will almost exclusively use scikit-image along with the standard tools from NumPy. We will call is skimage for short (which is how the package is imported anyhow). A potential annoyance with skimage is that the main package has minimal functionality, and you must import subpackages as needed. For example, to load and view images, you will need to import skimage.io. Importantly, skimage is well-documented, and you can access the documentation at http://scikit-image.org/.

We will explore skimage’s capabilities and some basic image processing techniques through example. We will start with examining a graticule (stage micrometer), then put together an multi-color image, and finally analyze fluorescence and phase contrast images of growing bacteria.

## Calibrating an objective using a graticule¶

You should have downloaded the file 2014-03-24_graticule.tif. We will use this as our graticule sample image. Note that I have given it a descriptive name. A trick I find useful is to have the first 10 characters in the file name be the date. (I often include the time as well.) That way, images you are analyzing appear in chronological order when viewed on your computer. Following the date is a descriptive title for the image. I kept the name short for the purposes of this tutorial, but for my own files, I would name the file

2014-03-24-1456_graticule_10micron_increments_10x_wheels.tif

which specifies that I took this image at 2:56 PM on March 24, 2014 using the 10$\times$ objective on the microscope Wheels, and that the gradations on the graticule are ten microns apart. This is important to know going forward: we are calibrating a 10$\times$ objective using a graticule with 10 µm increments.

We load the image using the skimage.io.imread(). The image is stored as a NumPy array. Each entry in the array is a pixel value. This is an important point: a digital image is data. It is a set of numbers with spatial positions.

In [2]:
# Load images as NumPy array

# Show that grat_im is a NumPy array
print('grat_im is a', type(grat_im))

# Show that the data type is unsigned int
print('Data type is', grat_im.dtype)

# Let's look at grat_im (only works in the IPython console)
grat_im

grat_im is a <class 'numpy.ndarray'>
Data type is uint8

Out[2]:
array([[198, 201, 201, ..., 196, 195, 198],
[200, 198, 200, ..., 197, 197, 197],
[200, 198, 195, ..., 195, 196, 198],
...,
[199, 194, 197, ..., 193, 192, 193],
[197, 198, 195, ..., 193, 194, 193],
[199, 197, 197, ..., 193, 194, 194]], dtype=uint8)

An image is nothing more than a 2D array, or a matrix. Any operation we can do to a matrix, we can do to an image. That includes slicing, assignment, any mathematical operations; anything. Note also that the data type of grat_im is uint8, or unsigned 8 bit integer. This is the assumed bit depth of the image. Bit depth is the number of bits used to indicate the intensity of a single pixel in an image. For an 8-bit image, the pixel values for from $0$ to $2^8 − 1$, or from $0$ to $255$. (In general, low pixel values are dark and high pixel values are light.) skimage evaluates the pixel values in the image and then chooses which of its allowed data types are commensurate with the pixel values. skimage allows 8, 16, or 32 bit images, in addition to float images (with pixel values between 0 and 1). We will see the consequences of this later. For now, it suffices to know that our graticule image is 8 bit.

We have looked at the image as a set of numbers. As is often the case, it is useful to "plot" data. A common way to "plot" an image is to display it as we're used to seeing images. Bokeh allows us to do this with convenient zooming and scrolling. However, the interface is a bit low-level, so I wrote a higher level interface in the bi1x module.

In [3]:
bokeh.io.show(bi1x.viz.imshow(grat_im))