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RSS Feed for Wolfram Community showing any discussions in tag Graphics and Visualization sorted by activeStationary dynamics in DNA: a nonlinear Klein-Gordon approach
https://community.wolfram.com/groups/-/m/t/3137876
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/24692edf-0555-4097-80ce-1958ebe919fdAthanasios Paraskevopoulos2024-03-08T23:25:24ZFinding critical points with NMaximize[] and Solve[] yielding different results query
https://community.wolfram.com/groups/-/m/t/3142452
I have two codes which carry out the same task, that is finding the maxima of a function. The function I am considering is a log-likelihood function. Since I am modelling a quantum process, I am using a random number generator to generate to measurement outcomes {m1,m1,m2} which then defines the log-likelihood function. The codes follow identical mathematical approaches, but In Code 1 I use the Mathematica built-in function NMaximize[] to find the critical points (which maximize the function) directly from the log-likelihood function, and in Code 2 I first take the derivative of the function and analytically solve for the points which yield the a zero derivative using the built-in Mathematica Solve[] function. I would expect these two approaches to yield identical results (or very similar results) for large iteration counts. But Code 1 does not converge to the expected value of 1.5, but instead maintains a negative bias by converging to about 1.475 (regardless of the number of trials). Code 2 converges to 1.5 as expected. Could anyone advise on the cause of the discrepancy. Many thanks for any assistance.
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/b6ae5ce0-c597-4764-853e-788ca73b2e4d
**Note**: I have tried setting different Methods in the NMaximum function but still get a negative bias. There also does not seem to be an appreciable difference when considering the built-in Maximum function as opposed to NMaximum, one still gets a negative bias.Byron Alexander2024-03-18T11:49:37ZNew volcano discovered on Mars hidden in plain sight
https://community.wolfram.com/groups/-/m/t/3142811
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=435wg54qg.jpg&userId=11733
[2]: https://www.wolframcloud.com/obj/d7970f5e-ccd6-4048-b300-debe32b1bb56Jeffrey Bryant2024-03-18T16:23:11ZAPI access to Claude 3 and use cases: image processing, conversation and programming
https://community.wolfram.com/groups/-/m/t/3142280
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1917Main.png&userId=20103
[2]: https://www.wolframcloud.com/obj/42516f06-2e9d-4dc9-8974-2be640577d3bMarco Thiel2024-03-17T18:00:41ZWhere half of the world lives: 69 of top 100 cities in Valeriepieris circle
https://community.wolfram.com/groups/-/m/t/3142243
[![enter image description here][1]][2]
&[Wolfram Notebook][3]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=VC691002.jpg&userId=11733
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=VC691002.jpg&userId=11733
[3]: https://www.wolframcloud.com/obj/9ac23d46-7d76-4298-be53-3f28e77338efVitaliy Kaurov2024-03-17T08:06:37ZConfidence regions with nuisance parameters
https://community.wolfram.com/groups/-/m/t/3141897
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/c78dfa86-f81a-4e43-80ce-cc2e2b7b6976Jan Vrbik2024-03-17T02:29:58ZSupposed "antenna null" isn't?
https://community.wolfram.com/groups/-/m/t/3141376
UPDATE: This turned out to be a trivial error on my part. See the response.
I thought that [in the far field of a Hertzian dipole the reason there is no E field because the scalar and vector potential contributions to the E field cancel in the far field][1].
The following notebook *seems* to indicate that the E field of an antenna "null" isn't null at all -- it doesn't fall off as 1/r^3 nor even off as 1/r^2. It falls off as 1/r! What's going on with this ultra-simple calculation based not on an antenna but a simple point charge moving back and forth in a line?
&[Wolfram Notebook][2]
PS: The comments are a bit off. They should have said the numerator goes as the cube of z and denominator as the fourth power of z.
[1]: https://physics.stackexchange.com/questions/206631/vector-potential-oscillating-e-field-of-the-null-field-of-a-hertzian-dipole
[2]: https://www.wolframcloud.com/obj/24042a98-6003-4c02-b6b0-7214d84b07f7James Bowery2024-03-16T02:32:07ZShowing histogram and PDF of normal distribution in a plot?
https://community.wolfram.com/groups/-/m/t/2225208
Hi,
How do I show complete normal distribution over its histogram?
list = {0.014952084292167656`, -0.0011142109478073092`, \
-0.03200699329376222`, 0.02610873317718504`, -0.007922259316024804`,
0.02329423863175964`,
0.0034785055449905455`, -0.007747760345867161`,
0.003986198148096087`,
0.031948672158741004`, -0.01922689853585434`, 0.0232439658404808`,
0.009156392455101026`, 0.05302010750555419`, 0.025142071231658958`,
0.0116075829784546`, -0.001449418525741597`,
0.029618730201622007`,
0.005921508633949274`, -0.0180861548626976`, -0.00510255607675171`,
0.018578990326231004`, 0.017420623630748748`,
0.003315652924846646`,
0.005526839598472583`, -0.023282105739082348`, 0.0474595471466141`,
0.000629691585357639`, 0.005254308208282488`,
0.0323716812689209`, -0.007494270578567497`, \
-0.019957153216545107`, 0.0009755785364255892`, 0.012999416718997955`,
0.016312600450492862`, -0.022726446137008666`,
0.007457557185943597`, -0.021121406314605712`,
0.020816311136428844`,
0.018826234340667714`, -0.026312034792572048`,
0.016020506724174488`, -0.06359624135386657`, \
-0.012528348147869107`, 0.018086951234972`,
0.0009406040330610273`, -0.010624625399940489`,
0.001383440169586178`, -0.03254843844527436`, \
-0.023731778793663033`, -0.029474470123107915`,
0.017707966601989755`, -0.011709554448547377`, \
-0.02584689544087218`, 0.010129309176322931`, -0.06913883297091293`,
0.017521978981166843`, 0.014526618114977838`,
0.038873448773523334`, -0.0259937403719101`, \
-0.020663881794158942`, 0.016251452890144347`, 0.019502766982261666`,
0.0248790234506836`, -0.029827586532714834`,
0.0028897048234939604`, -0.0015713386704406807`, \
-0.0029079686403274546`, -0.012514878168525697`, \
-0.004687818520397187`, -0.003439080581300734`, -0.00081486164625931`,
0.009277975678443906`, -0.060646119527069095`,
0.007911314948852527`, -0.020871743782455432`, \
-0.034051828420303354`, -0.018067103608901985`, \
-0.019255875162330627`, -0.03503792834281921`, -0.035022689569067`,
0.0060782724170112615`,
0.04824767377845382`, -0.03138784995280075`,
0.006499843955039969`, -0.01786340096987915`, 0.02081189918518067`,
0.01398221559014895`, -0.03275392018168641`, 0.02883601571673583`,
0.05740358064871215`, -0.0009542576516227697`,
0.07298482561545772`};
fitDist =
EstimatedDistribution[list, NormalDistribution[\[Alpha], \[Beta]],
ParameterEstimator -> MethodOfMoments]
Show[Histogram[list, Automatic, PDF],
Plot[Evaluate@PDF[fitDist][x], {x, 0, 15},
PlotStyle -> Directive[Blue, Thick], Filling -> Axis]]M.A. Ghorbani2021-03-20T21:14:07ZIterate Delay-Difference Equations efficiently
https://community.wolfram.com/groups/-/m/t/3141331
I have a system of delay-difference equations which I would like to iterate in an efficient fashion. Just using Table[] will iterate the system but as the size of the system grows the execution time gets long. I think the inefficiency comes from re-computing values multiple times instead of re-using the results. I thought RecurrenceTable[] would be more efficient, but I can't seem to find the correct usage that doesn't result in me getting an error message. If you have suggestion(s) I would be happy to listen.
Thanks,
Robert Buchanan
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/91125527-13fe-4cd5-b5ad-fb08c2b3e916Robert Buchanan2024-03-15T14:54:03ZEclipses and conic sections
https://community.wolfram.com/groups/-/m/t/3139774
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/4b76105e-4900-49e7-a1b5-0087078a02a0Brad Klee2024-03-12T22:46:17ZMIni-Series: What's New in 14?
https://community.wolfram.com/groups/-/m/t/3139036
New Mini-Series on the [Wolfram R&D YouTube channel][1]!
Curious about what's new in Version 14? This mini-series features videos that provide a 6-minute summary of the WTC 2023 talks. The first [two episodes focus on Visualization and System Modeler][2].
Don't miss out on the latest updates and exciting content -- subscribe now and become a part of our community!
[![enter image description here][3]][2]
[1]: https://youtube.com/playlist?list=PLdIcYTEZ4S8SIK-S-9JGYAZgohaV7cB0t&si=9-arFCq9EbHkIipm
[2]: https://youtube.com/playlist?list=PLdIcYTEZ4S8SIK-S-9JGYAZgohaV7cB0t&si=9-arFCq9EbHkIipm
[3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=MiniSeries_Newin14_2.png&userId=1660606Keren Garcia2024-03-11T17:37:50ZPrincipal component analysis of grasp force and pose during in-hand manipulation
https://community.wolfram.com/groups/-/m/t/3141582
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=345sdfdfa.jpg&userId=11733
[2]: https://www.wolframcloud.com/obj/1c1c0549-477c-44db-ba57-be9538dff8beJoshua Schultz2024-03-15T21:41:27ZPi, the Golden Ratio and the Tribonacci Constant
https://community.wolfram.com/groups/-/m/t/3140342
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2024-03-13at2.27.01%E2%80%AFPM.jpg&userId=11733
[2]: https://www.wolframcloud.com/obj/11fd58aa-a010-486d-bc09-a5d351c6d025Ed Pegg2024-03-13T18:06:26ZImproving the longitudinal spot width of an optimizingly designed transcranial ultrasonic lens
https://community.wolfram.com/groups/-/m/t/3139057
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2225Mainimage.png&userId=20103
[2]: https://www.wolframcloud.com/obj/08416228-31c3-4062-859d-6421984843a2Ueta Tsuyoshi2024-03-11T18:02:48ZDSolve has reached the maximum number of calculations
https://community.wolfram.com/groups/-/m/t/3138820
I reached the maximum number of calculations when using *DSolve* to calculate differential equations, which makes it impossible to fully solve. How can I expand the number of calculations of *DSolve*?
Here is my codeļ¼
system = {vi q[t] == l iL'[t] + vC[t],
vC'[t] == iL[t]/c - vC[t]/(r c), vC[0] == 0, iL[0] == 0};
control = {q[0] == 1,
WhenEvent[Mod[t, \[Tau]] == (2/3) \[Tau], q[t] -> 0],
WhenEvent[Mod[t, \[Tau]] == 0, q[t] -> 1]};
pars = {vi -> 24, r -> 22, l -> 2 10^-2,
c -> 1 10^-4, \[Tau] -> 2.5 10^-5};
sol = DSolve[{system, control} /. pars, {vC, iL, q}, {t, 0, .2},
DiscreteVariables -> q];
a = Evaluate[iL[t] /. sol];
b = Evaluate[vC[t] /. sol];
Plot[a, {t, 0, 0.2}, AxesLabel -> {"s", "il[t]/A"},
PlotLegends -> {"LinearlyImplicitEuler"}, PlotStyle -> {Red},
PlotRange -> All]
Plot[b, {t, 0, 0.2}, AxesLabel -> {"s", "vc[t]/V"},
PlotLegends -> {"LinearlyImplicitEuler"}, PlotStyle -> {Blue},
PlotRange -> All]James James2024-03-11T06:01:41Z