text:
Theoretically...

magickc

Member
If you had a spare 4 channel mixer and 4 headsets that had seperate input/output lines could you wire all the mic's from the headsets into the mixer then put a 4-way splitter on the output to the mixer and put that into the input to the headsets to create an intercom/cans system?
Rob

avkid

Not a New User
Fight Leukemia
If you had a spare 4 channel mixer and 4 headsets that had seperate input/output lines could you wire all the mic's from the headsets into the mixer then put a 4-way splitter on the output to the mixer and put that into the input to the headsets to create an intercom/cans system?
Rob
If I understand you correctly, yes.
But you can't page and all the mics would be live.

erosing

The Royal Renaissance Man
if you have that much spare cable laying around that's actually a pretty cheap solution (read:free or mostly). and as was said, just wire in a few on off switches

mbenonis

Wireless Guy
Yes, in theory it would work. However, the line output of the mixer is not designed to be loaded by four line input devices, let alone speakers. You'd need a headphone amp type device, and by that point you may as well buy an inexpensive intercom power supply and a few beltpacks. Or just get radio's (NOT GMRS/FRS, needs to be either MURS or licensed UHF business two-way; see my previous thread on the legalities of radio's for theatre use).

Last edited:

Fight Leukemia

Andy_Leviss

Active Member
Actually, while I used to say that about FRS, I've done more recent research, and it IS legal to use them commercially, just with the same restrictions as on family use, and no special privelege. IE, if somebody else starts using the same channel, you have to either suck it up or move; you can't say, "We're using this for business, find another channel," or anything else to try to get the newcomers to move. It's an open band, and must be kept as such.

See, among other sources you can find via Google, http://wireless.fcc.gov/services/index.htm?job=service_home&id=family

avkid

Not a New User
Fight Leukemia
Actually, while I used to say that about FRS, I've done more recent research, and it IS legal to use them commercially, just with the same restrictions as on family use, and no special privelege. IE, if somebody else starts using the same channel, you have to either suck it up or move; you can't say, "We're using this for business, find another channel," or anything else to try to get the newcomers to move. It's an open band, and must be kept as such.
Cool, i'm not going to jail!!
(this time)

mbenonis

Wireless Guy
Actually, while I used to say that about FRS, I've done more recent research, and it IS legal to use them commercially, just with the same restrictions as on family use, and no special privelege. IE, if somebody else starts using the same channel, you have to either suck it up or move; you can't say, "We're using this for business, find another channel," or anything else to try to get the newcomers to move. It's an open band, and must be kept as such.
See, among other sources you can find via Google, http://wireless.fcc.gov/services/index.htm?job=service_home&id=family
Well, I stand corrected. I will point out that one must be careful when using dual FRS/GMRS radio's, through, to make sure one uses ONLY the FRS channels and not the GMRS channels (to use these channels one must have a license). Additionally, range and reliability will probably suffer due to the technical limitations of the FRS. That said, if it works for you, it works for you, end of story.

avkid

Not a New User
Fight Leukemia
Well, I stand corrected. I will point out that one must be careful when using dual FRS/GMRS radio's, through, to make sure one uses ONLY the FRS channels and not the GMRS channels (to use these channels one must have a license). Additionally, range and reliability will probably suffer due to the technical limitations of the FRS. That said, if it works for you, it works for you, end of story.
Mike, a GMRS licence is only about $75 US. mbenonis Wireless Guy Administrator Premium Member Mike, a GMRS licence is only about$75 US.
Yes, but the license prohibits use by people other than those in your immediate family. And you have to ID every so often with your call sign.

avkid

Not a New User
Fight Leukemia
Yes, but the license prohibits use by people other than those in your immediate family. And you have to ID every so often with your call sign.
Why must you always kill my fun?

mbenonis

Wireless Guy
Why must you always kill my fun?
I think it's in my job description

Wait, does GMRS actually have better range / quality? Or did I completely miss read that?
Yes, and yes. The primary difference between GMRS and FRS is the type of equipment you are permitted to use. FRS radio's cannot exceed 0.5W of output power, while GMRS radios are permitted to output up to 50W (though 4W is common). Additionally, FRS radio's must have built-in, non-detachable antennas, while GMRS radio's may use any kind of antenna. Essentially, this means one can use business-quality UHF radio's for GMRS, but must stick with the crappy \$20 radio's for FRS.

I thought I had mentioned this above, but I guess not. MURS is similar to GMRS, but does not require a license and can be used for any purpose. No identification is required. However, there are only five frequencies allowed for use, and total output power is limited to two watts (however external gain antennas are permissible). One can use VHF business radio's for MURS, but must make sure they put out no more than two watts. MURS frequencies are:

151.820 MHz
151.880 MHz
151.940 MHz
154.570 MHz (also part of the business band)
154.600 MHz (also part of the business band)

I would consider MURS to be the ideal radio band for theatre use, because it is simple to get up and running and does not require paperwork.

stantonsound

Active Member
Most restaurant drive thru's use the 154.600 band. Just an interesting fact. You can place an order from home via radio.

mbenonis

Wireless Guy
Most restaurant drive thru's use the 154.600 band. Just an interesting fact. You can place an order from home via radio.
Huh. I'll bring my scanner along next time I go to a drive through!

avkid

Not a New User
Fight Leukemia
Most restaurant drive thru's use the 154.600 band. Just an interesting fact. You can place an order from home via radio.
Oh sweet, we can terrorize the Wendy's down the block and possibly the McDonald's about a mile away.

mbenonis

Wireless Guy
Oh sweet, we can terrorize the Wendy's down the block and possibly the McDonald's about a mile away.
I can just see the order-taker person freaking out because someone's ordering food and there's no car on the screen.


text:
2013-06-29, 17:29   #3
lorgix

Sep 2010
Scandinavia

3×5×41 Posts

Quote:
 Originally Posted by VBCurtis I think we both would benefit from playing with settings and finding polys for a couple of smaller numbers. Perhaps some of the heavy hitters in this forum would like to supply you and I a couple of C155-180s to poly search? We can discuss settings, try to learn what stage1 bound produces the largest rate of useful nps hits per hour of gpu time, etc. I have a c147 in my own queue; I had just done -np for 5 days for a poly when this thread began. I tried to apply what we learned last week, and restarted the search. 24 hours of -np1 with stage1 set to 2e21 (default is 2.38e22) produced roughly 700MB of hits with a 460M, which will take almost a core-week to size optimize. This makes me wonder how -np manages to do all 3 steps with just one CPU thread without massively stalling the GPU. So, my first tentative guideline is to set stage 1 norm 10x tighter than default when running -np1 on its own, and even then the cpu has no chance to keep up. Or does the -nps step work with the -t threads command? If I understand previous advice, I should not bother to npr more than, say, 500 best nps hits? -Curtis
Here are a few 157-digit GNFS candidates:
Code:
(181^103-1)/((181-1)*7417*3386023*1622748672647*767015484026387551*1656939272001358583196903067208809)
(877^79-1)/((877-1)*4583*208520387347*96078130292657*103086319456710261705085017633872730943681601)
(5591^61-1)/((5591-1)*16556099215542617537*743213379283195327995487*11686924821525596917649777)
(421^101-1)/((421-1)*3637*52859291287277*15527015834461272375419*384360771211140230121323*3103491858106402597710257788494888754189303)
They are also listed at the OPN composites page. They have each had a t50.

format: plain


text:
906 views

Which packages come standard with Ubuntu's `texlive` package? [duplicate]

Is a list published somewhere of which macro packages come standard with texlive? Specifically, I am considering installing the texlive package (not texlive-full) in Ubuntu. I'd like to know if ...
1k views

Concerns on Switching to Plain LuaTeX or ConTeXt Mark IV

I am seriously considering to use Plain LuaTeX or ConTeXt MkIV. I will explain my expectations and worries to do so, and add several new questions. Before you mark me as duplicate, I know there are ...
824 views

How to compile the same input file for each of LaTeX font packages installed in our machine?

Inspired by my question How to create a PDF presentation for each available Beamer theme automatically?, now I want to compile my input file for each available LaTeX font package installed in my ...
1k views

Where can I find the changelog of TeX Live releases?

I know that TeX Live 2013 is now in beta and that there are already some new packages. I would like to know where the complete changelog will be available, when the new version will be released, and ...
7k views

tlmgr stopped working due to outdated repository [closed]

tlmgr used to work fine, but now I am getting the following error message for whatever I try to do: tlmgr: The TeX Live versions supported by the repository (20xx--20xx) do not include the ...
1k views

How do I list the available classes in my installation?

I am using TeXLive in Linux and want to learn and experiment. How can I list available document classes in my installation?
2k views

List of packages originally installed with Tex Live

Is there way to get a list of the packages which were installed when TeX Live was initially set up? I can get a list of all present packages with tlmgr list | grep '^i' but I do not see a way to ...
703 views

How many packages do MiKTeX and TeX Live contain? [duplicate]

Possible Duplicate: How many LaTeX classes and packages are there (say, on CTAN)? Where can I find the total package count for TeX Live 2012 and MiKTeX 2.9?
172 views

Transfer installed packages when installing a new TexLive release

Currently I have TexLive2016 with some packages installed via tlmgr. Now I would like to switch to the 2017 release and I was wondering if it is possible to somehow install the same packages in the ...
155 views

How to make a paper with zero margins and use the whole paper size for typesetting?

Inspired by solution of @kiss-my-armpit in How to print the list of packages installed on TeX Live to a file?, I decided to make a poster-like document to list all packages in a single page. So I made ...
92 views

texlive import packages from older installations

I've been using TeX Live 2018 and installed some packages to that, now that 2019 is out, I need to intall that new version (windows). I am using basis scheme install option (plain and latex) for ...


text:
Accelerating the pace of engineering and science

Documentation

Active Suspension Control Design

This example shows how to use robust control techniques to design an active suspension system for a quarter car body and wheel assembly model. In this example, you use H design techniques to design a controller for a nominal quarter-car model. Then, you use μ synthesis to design a robust controller that accounts for uncertainty in the model.

Conventional passive suspensions use a spring and damper between the car body and wheel assembly. The spring-damper characteristics are adjusted to emphasize one of several conflicting objectives such as passenger comfort, road holding, and suspension deflection. Active suspensions use a feedback-controller hydraulic actuator between the chassis and wheel assembly, which allows the designer to better balance these objectives.

Quarter-Car Suspension Model

This example uses the quarter-car model of the following illustration to design active suspension control laws.

The mass, mb, represents the car chassis (body) and the mass, mw, represents the wheel assembly. The spring, ks, and damper, bs, represent the passive spring and shock absorber placed between the car body and the wheel assembly. The spring, kt, models the compressibility of the pneumatic tire. The variables xb, xw, and r are the car body travel, the wheel travel, and the road disturbance, respectively. The force, fs, which is applied between the body and wheel assembly, is controlled by feedback. This force represents the active component of the suspension system.

The following state-space equations describe the quarter-car dynamics.

$\begin{array}{l}{\stackrel{˙}{x}}_{1}={x}_{2},\\ {\stackrel{˙}{x}}_{2}=-\frac{1}{{m}_{b}}\left[{k}_{s}\left({x}_{1}-{x}_{3}\right)+{b}_{s}\left({x}_{2}-{x}_{4}\right)-{f}_{s}\right],\\ {\stackrel{˙}{x}}_{3}={x}_{4},\\ {\stackrel{˙}{x}}_{4}=\frac{1}{{m}_{w}}\left[{k}_{s}\left({x}_{1}-{x}_{3}\right)+{b}_{s}\left({x}_{2}-{x}_{4}\right)-{k}_{t}\left({x}_{3}-r\right)-{f}_{s}\right].\end{array}$

The state variables in the system are defined as ${x}_{1}:={x}_{b}$, ${x}_{2}:={\stackrel{˙}{x}}_{b}$, ${x}_{3}:={x}_{w}$, and ${x}_{4}:={\stackrel{˙}{x}}_{w}$.

Define the physical parameters of the system.

```mb = 300;    % kg
mw = 60;     % kg
bs = 1000;   % N/m/s
ks = 16000 ; % N/m
kt = 190000; % N/m```

Use these equations and parameter values to construct a state-space model, qcar, of the quarter-car suspension system.

```A = [ 0 1 0 0; [-ks -bs ks bs]/mb ; ...
0 0 0 1; [ks bs -ks-kt -bs]/mw];
B = [0 0; 0 10000/mb ; 0 0; [kt -10000]/mw];
C = [1 0 0 0; 1 0 -1 0; A(2,:)];
D = [0 0; 0 0; B(2,:)];

qcar = ss(A,B,C,D);
qcar.StateName = {'body travel xb (m)';'body vel (m/s)';...
'wheel travel xw (m)';'wheel vel (m/s)'};
qcar.InputName = {'r';'fs'};
qcar.OutputName = {'xb';'sd';'ab'};```

The model inputs are the road disturbance, r, and actuator force, fs. The model outputs are the car body travel, ${x}_{b}$, suspension deflection ${s}_{d}={x}_{b}-{x}_{w}$, and car body acceleration ${a}_{b}={\stackrel{¨}{x}}_{s}$.

The transfer function from actuator to body travel and acceleration has an imaginary-axis zero. Examine the zero of this transfer function.

`tzero(qcar({'xb','ab'},'fs'))`
```ans =

-0.0000 +56.2731i
-0.0000 -56.2731i
```

The natural frequency of this zero, 56.27 rad/s, is called the tire-hop frequency.

The transfer function from the actuator to suspension deflection also has an imaginary-axis zero. Examine this zero.

`zero(qcar('sd','fs'))`
```ans =

0.0000 +22.9734i
0.0000 -22.9734i```

The natural frequency of this zero, 22.97 rad/s, is called the rattlespace frequency.

Plot the frequency response of the quarter-car model from inputs, (r,fs), to outputs, (ab,sd). Both zeros are visible on the Bode plot.

```bodemag(qcar({'ab','sd'},'r'),'b',qcar({'ab','sd'},'fs'),'r',{1 100});
title({'Gain from road dist (r) and actuator force (fs)';...
'to body accel (ab) and suspension travel (sd)'})```

Road disturbances influence the motion of the car and suspension:

• Small body acceleration influences passenger comfort.

• Small suspension travel contributes to good road handling. Further, limits on the actuator displacement constrain the allowable travel.

Because of the imaginary axis zeros, feedback control cannot improve the response from road disturbance (r) to body acceleration (ab) at the tire-hop frequency. Similarly, feedback control cannot improve the response from r to suspension deflection (sd) at the rattlespace frequency. Moreover, there is an inherent trade-off between passenger comfort and suspension deflection. Any reduction of body travel at low frequency results in an increase of suspension deflection. This trade-off arises because of the relationship xw = xb – sd and the fact that xw roughly follows r at low frequency (less than 5 rad/s).

Hydraulic Actuator Model

The hydraulic actuator used for active suspension control is connected between the body mass, mb, and the wheel assembly mass, mw. The nominal actuator dynamics can be represented by the first-order transfer function:

$ActNom\left(s\right)=\frac{1}{\frac{1}{60}s+1}.$

The maximum displacement is 0.05 m.

The nominal actuator model approximates the physical actuator dynamics. You can model variations between the actuator model and the physical device as a family of actuator models. You can also use this approach to model variations between the passive quarter-car model and actual vehicle dynamics. The resulting family of models comprises a nominal model with a frequency-dependent amount of uncertainty.

Create an uncertain model that represents this family of models.

```ActNom = tf(1,[1/60 1]);
Wunc = makeweight(0.40,15,3);
unc = ultidyn('unc',[1 1],'SampleStateDim',5);
Act = ActNom*(1 + Wunc*unc);
Act.InputName = 'u';
Act.OutputName = 'fs';```

At low frequency, below 3 rad/s, the model can vary up to 40% from its nominal value. Around 3 rad/s, the percentage variation starts to increase. The uncertainty crosses 100% at 15 rad/s, and reaches 2000% at approximately 1000 rad/sec. The weighting function, Wunc, reflects this profile and is used to modulate the amount of uncertainty as a function of frequency. The result Act is an uncertain state-space model of the actuator.

Examine the uncertain actuator model by plotting the frequency response of 20 randomly sampled models from Act.

```bodeplot(Act,'b',Act.NominalValue,'r+',logspace(-1,3,120))
title('Nominal and 20 random actuator models')```

The plus (+) marker denotes the nominal actuator model. The blue solid lines represent the randomly sampled models.

Design Objectives for H-Infinity Synthesis

To use H synthesis algorithms, you must express your design objectives as a single cost function to be minimized. For the quarter-car model, the main control objectives are formulated in terms of passenger comfort and road handling. These objectives relate to body acceleration, ab, and suspension travel, sd. Other factors that influence the control design include:

• Characteristics of the road disturbance

• Quality of the sensor measurements for feedback

• Limits on the available control force

Use weights to model external disturbances and quantify the design objectives, as shown in the following diagram.

The feedback controller uses the measurements y1 and y2 of the suspension travel, sd, and body acceleration, ab, to compute the control signal, u. This control signal drives the hydraulic actuator. There are three external sources of disturbance:

• The road disturbance, r, which is modeled as a normalized signal, d1, which is shaped by a weighting function Wroad.

• Sensor noise on both measurements. This noise is modeled as normalized signals, d2 and d3, which are shaped by weighting functions Wd2 and Wd3.

You can reinterpret the control objectives as a disturbance rejection goal. The goal is to minimize the impact of the disturbances, d1, d2, and d3, on a weighted combination of suspension travel (sd), body acceleration (ab), and control effort (u). You can consider the H norm (peak gain) as the measure of the effect of the disturbances. Then, you can meet the requirements by designing a controller that minimizes the H norm from the disturbance inputs, d1, d2, and d3, to the error signals , e1, e2, and e3.

Create the weighting functions that model the design objectives.

```Wroad = ss(0.07);

Wact = 8*tf([1 50],[1 500]);
Wact.u = 'u';
Wact.y = 'e1';

Wd2 = ss(0.01);
Wd2.u = 'd2';
Wd2.y = 'Wd2';

Wd3 = ss(0.5);
Wd3.u = 'd3';
Wd3.y = 'Wd3';```

The constant weight Wroad = 0.07 models broadband road deflections of magnitude 7 cm. Wact is a highpass filter. This filter penalizes high-frequency content in the control signal, and thus limits control bandwidth. Wd2 and Wd3 model broadband sensor noise of intensity 0.01 and 0.5, respectively. In a more realistic design, Wd2 and Wd3 would be frequency dependent to model the noise spectrum of the displacement and acceleration sensors. The inputs and outputs of all weighting functions are named to facilitate interconnection. The notation u and y are shorthand for the InputName and OutputName properties, respectively.

Specify target functions for the closed-loop response of the system from the road disturbance, r, to the suspension deflection, sd, and body acceleration, ab.

```HandlingTarget = 0.04 * tf([1/8 1],[1/80 1]);
ComfortTarget = 0.4 * tf([1/0.45 1],[1/150 1]);
Targets = [HandlingTarget;ComfortTarget];```

Because of the actuator uncertainty and imaginary-axis zeros, the targets attenuate disturbances only below 10 rad/s. These targets represent the goals of passenger comfort (small car body acceleration) and adequate road handling (small suspension deflection).

Plot the closed-loop targets and compare to the open-loop response.

```bodemag(qcar({'sd','ab'},'r')*Wroad,'b',Targets,'r--',{1,1000})
legend('Open-loop','Closed-loop target')```

The corresponding performance weights Wsd and Wab are the reciprocals of the comfort and handling targets. To investigate the trade-off between passenger comfort and road handling, construct three sets of weights, (βWsd,(1 – β)Wab). These weights use a blending parameter, β, to modulate the trade-off.

```beta = reshape([0.01 0.5 0.99],[1 1 3]);

Wsd = beta/HandlingTarget;
Wsd.u = 'sd';
Wsd.y = 'e3';

Wab = (1-beta)/ComfortTarget;
Wab.u = 'ab';
Wab.y = 'e2';```

Wsd and Wab are arrays of weighting functions that correspond to three different trade-offs: emphasizing comfort (β = 0.01), balancing comfort and handling (β = 0.5), and emphasizing handling (β = 0.99).

Connect the quarter-car plant model, actuator model, and weighting functions to construct the block diagram of the plant model weighted by the objectives.

```sdmeas = sumblk('y1 = sd+Wd2');
abmeas = sumblk('y2 = ab+Wd3');
ICinputs = {'d1';'d2';'d3';'u'};
ICoutputs = {'e1';'e2';'e3';'y1';'y2'};
sdmeas,abmeas,ICinputs,ICoutputs);```

qcaric is an array of three models, one for each value of the blending parameter, β. Also, the models in qcaric are uncertain, because they contain the uncertain actuator model Act.

Nominal H-Infinity Synthesis

Use hinfsyn to compute an H controller for each value of the blending parameter, β. hinfsyn ignores the uncertainty in the plant models and synthesizes a controller for the nominal value of each model.

```ncont = 1;
nmeas = 2;
K = ss(zeros(ncont,nmeas,3));
gamma = zeros(3,1);
for i=1:3
[K(:,:,i),~,gamma(i)] = hinfsyn(qcaric(:,:,i),nmeas,ncont);
end```

The weighted plant model has one control input (ncont), the hydraulic actuator force. The model also has two measurement outputs (nmeas), which give the suspension deflection and body acceleration.

Examine the resulting closed-loop H norms, gamma.

`gamma`
```gamma =

0.9410
0.6724
0.8877
```

The three H controllers achieve closed-loop H norms of 0.94 (emphasizing comfort), 0.67 (balancing comfort and handling), and 0.89 (emphasizing handling).

Construct closed-loop models of the quarter-car plant with the synthesized controller, corresponding to each of the three blending parameter values. Compare the frequency response from the road disturbance to xb, sd, and ab for the passive and active suspensions.

```K.u = {'sd','ab'}; K.y = 'u';
CL = connect(qcar,Act.Nominal,K,'r',{'xb';'sd';'ab'});

clf
bodemag(qcar(:,'r'),'b', CL(:,:,1),'r-.', ...
CL(:,:,2),'m-.', CL(:,:,3),'k:',{1,140})
grid
legend('Open-loop','Comfort','Balanced','Handling','location','SouthEast')
title('Body travel, suspension deflection, and body acceleration due to road')```

The solid blue line corresponds to the open-loop response. The other lines are the closed-loop frequency responses for the different comfort and handling blends. All three controllers reduce suspension deflection and body acceleration below the rattlespace frequency (23 rad/s).

Time-Domain Evaluation

To further evaluate the three designs, perform time-domain simulations using the following road disturbance signal r(t):

$r\left(t\right)=\left\{\begin{array}{c}a\left(1-\mathrm{cos}8\pi t\right),\text{ }0\le t\le 0.25\\ 0,\text{ }\text{otherwise}\text{.}\text{ }\text{ }\text{ }\text{ }\text{ }\end{array}$

This signal corresponds to a road bump of height 5 cm.

Create a vector that represents the road disturbance.

```t = 0:0.005:1;

Build the closed-loop model using the synthesized controller.

`SIMK = connect(qcar,Act.Nominal,K,'r',{'xb';'sd';'ab';'fs'});`

SIMK is a model array containing three closed-loop models, one for each of the three blending parameter values. Each model in the array represents a closed loop that is built from the original quarter-car plant model, the nominal actuator model, and the corresponding synthesized controller.

Simulate and plot the time-domain response of the closed-loop models to the road disturbance signal.

```p1 = lsim(qcar(:,1),roaddist,t);

clf
subplot(221)
title('Body travel')
ylabel('x_b (m)')

subplot(222)
title('Body acceleration')
ylabel('a_b (m/s^2)')

subplot(223)
title('Suspension deflection')
xlabel('Time (s)')
ylabel('s_d (m)')

subplot(224)
title('Control force')
xlabel('Time (s)')
ylabel('f_s (N)')

```

The simulations show that the body acceleration is smallest for the controller emphasizing passenger comfort. Body acceleration is largest for the controller emphasizing suspension deflection. The balanced design achieves a good tradeoff between body acceleration and suspension deflection.

Robust μ Design

So far you designed H controllers that meet the performance objectives for the nominal actuator model. However, this model is only an approximation of the true actuator. To make sure that controller performance is maintained even with model error and uncertainty, you must design the model to have robust performance. In this part of the example, you use μ-synthesis to design a controller that achieves robust performance for the entire family of actuator models that takes uncertainty into account.

Use D-K iteration to synthesize a controller for the quarter-car model with actuator uncertainty.

`[Krob,~,RPmuval] = dksyn(qcaric(:,:,2),nmeas,ncont);`

The model qcaric(:,:,2) is the weighted quarter-car model for the uncertain model that corresponds to the blending variable β = 0.5.

Examine the resulting μ-synthesis controller.

`size(Krob)`
`State-space model with 1 outputs, 2 inputs, and 11 states.`

Build the closed-loop model using the robust controller, Krob.

```Krob.u = {'sd','ab'};
Krob.y = 'u';
SIMKrob = connect(qcar,Act.Nominal,Krob,'r',{'xb';'sd';'ab';'fs'});```

Simulate and plot the nominal time-domain response to a road bump with the robust controller.

```p1 = lsim(qcar(:,1),roaddist,t);

clf

subplot(221)
title('Body travel'), ylabel('x_b (m)')

subplot(222)
plot(t,p1(:,3),'b',t,y1(:,3),'r')
title('Body acceleration'), ylabel('a_b (m/s^2)')

subplot(223)
plot(t,p1(:,2),'b',t,y1(:,2),'r')
title('Suspension deflection'), xlabel('Time (s)'), ylabel('s_d (m)')

subplot(224)
plot(t,zeros(size(t)),'b',t,y1(:,4),'r')
title('Control force'), xlabel('Time (s)'), ylabel('f_s (N)')

legend('Open-loop','Robust design','location','SouthEast')```

These responses are similar to those obtained with the balanced H controller.

Examine the effect of the robust controller on variability caused by model uncertainty. To do so, simulate the response to a road bump for 120 actuator models randomly sampled from the uncertain model, Act. Perform this simulation for both the H and the robust controllers, to compare the results.

Compute an uncertain closed-loop model with the balanced H controller, K. Sample this model, simulate the sampled models, and plot the results.

```CLU = connect(qcar,Act,K(:,:,2),'r',{'xb','sd','ab'});

nsamp = 120;
rng('default');
figure(1)
clf
title('Nominal "balanced" design')```

Compute an uncertain closed-loop model with the balanced robust controller, Krob. Sample this model, simulate the sampled models, and plot the results.

```CLU = connect(qcar,Act,Krob,'r',{'xb','sd','ab'});
figure(2)
clf
title('Robust "balanced" design')```

The robust controller reduces variability caused by model uncertainty, and delivers more consistent performance.

Controller Simplification

The robust controller Krob has eleven states. It is often the case that controllers synthesized with dksyn have high order. You can use the model reduction functions to find a lower-order controller that achieves the same level of robust performance. Use reduce to generate approximations of various orders. Then, use robustperf to compute the robust performance margin for each reduced-order approximation.

Create an array of reduced-order controllers.

```NS = order(Krob);
StateOrders = 1:NS;
Kred = reduce(Krob,StateOrders);```

Krob is a model array containing a reduced-order controller of every order from 1 up to the original 11 states.

Compute the robust performance margin for each reduced controller.

```CLP = lft(qcaric(:,:,2),Kred);
ropt = robustperfOptions('Sensitivity','off','Display','off','Mussv','a');
PM = robustperf(CLP,ropt);```

Compare the robust performance of the reduced- and full-order controllers.

```plot(StateOrders,[PM.LowerBound],'b-o',...
StateOrders,repmat(1/RPmuval,[1 NS]),'r');
title('Robust performance as a function of controller order')
legend('Reduced order','Full order','Location','SouthEast')```

There is no significant difference in robust performance between the 8th- and 11th-order controllers. Therefore, you can safely replace Krob by its 8th-order approximation.

`Krob8 = Kred(:,:,8);`

You now have a simplified controller, Krob8, that provides robust control with a balance between passenger comfort and handling.


text:
## Main Question or Discussion Point

How do I find the radius of the nucleus if given the mass? I am asked to compare it with the value found using the formula R= 1.2 A^(1/3)

Related High Energy, Nuclear, Particle Physics News on Phys.org
you have to take into assumption some stuff...
For example you'll have to assume that the nuclei have constant density....
and you'll have to assume that their shape is given (to be spherical)....

fzero
Homework Helper
Gold Member
Measured values for the radii of select nuclei are available from the IAEA.

That's what I was thinking using the relation mass=volume x density, but if I don't know the density how can I use this relation?

mfb
Mentor
I think all formulas are basically another way to calculate R= 1.2 A^(1/3) . Sure, you can replace A by the mass divided by the (average) mass of a nucleon, and get a formula like R= const* (mass/density)^(1/3), but that is nothing new.


text:
# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Definable hereditary families in the projective hierarchy

### Tom 140 / 1992

Fundamenta Mathematicae 140 (1992), 183-189 DOI: 10.4064/fm-140-2-183-189

#### Streszczenie

We show that if ℱ is a hereditary family of subsets of $ω^ω$ satisfying certain definable conditions, then the $Δ_1^1$ reals are precisely the reals α such that ${β:α ∈ Δ_1^1(β)} ∉ ∈ ℱ$. This generalizes the results for measure and category. Appropriate generalization to the higher levels of the projective hierarchy is obtained under Projective Determinacy. Application of this result to the $Q_{2n+1}$-encodable reals is also shown.

• R. Barua
• V. Srivatsa

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek


text:
# I Speed of time

Tags:
1. Feb 9, 2017

### Jens K Munk

Dear Forum,

The title "Speed of time" is the best I can come up with. We know that time isn't constant, rather it depends on the speed at which we move as well as the gravity we are subjected to (see https://en.wikipedia.org/wiki/Gravitational_time_dilation for a reference to the latter). As a consequence of the latter, and as stated on the Wikipiedia page, Earth is stated as being 2.5 years younger at its core (due to higher gravity in there).

Thoughts on this:
1. Isn't gravity zero at Earth's core (disregarding the gravity of the Sun)? I would argue that at the core, you have an equal amount of Earth at each side of you, so they cancel out.

2. Instead of "gravitational time dilation", do we experience "density-dependent time dilation"? Higher density (such as that in Earth's core) slows down time. This would explain why clocks in space record time going faster than at Earth's surface. It may also explain why extreme density such as that in black holes causes light to reach zero speed (relative to observer's perspective).

Let's stop here. Please comment. Thanks.

2. Feb 9, 2017

### Orodruin

Staff Emeritus
Gravitational time dilation depends on the gravitational potential, not the gravitational field.

No. Also, there is no such thing as light reaching zero speed and the Schwarzschild black hole is a vacuum solution to the Einstein field equations, i.e., the density is zero at the event horizon.

Also note that you should not be using the A-level tag unless you have knowledge in the subject equivalent to that of a graduate student or higher. It is clear from your post that you do not. The level system is in place for you to tell us your level of expertise so that the answers can be aimed at that level of understanding. <Moderator's note: level changed>

Last edited by a moderator: Feb 9, 2017
3. Feb 23, 2017

### Albrecht

I do not understand the comment to the time dilation and the speed of light in a gravitational field.
The Schwarzschild metrics say about the proper time in a gravitational field
d(tau) = (1 - r0/r)1/2dt where r0is the Schwarzschild radius.
This means that the flow of time stops completely at r = r0 where is the event horizon. Correspondingly the speed of light reaches zero at that range.

4. Feb 23, 2017

### Orodruin

Staff Emeritus
No it doesn't. It is just a matter of the coordinate t not being a good coordinate at the Schwarzschild radius. The "speed of light" that you are referring to is not the invariant speed of light - it is a coordinate velocity.

5. Feb 24, 2017

### Albrecht

So, what means: d(tau) = 0 ?
Doesn't it mean that the local, proper time stops at that point? Whatever the general meaning of t might be? - I have listened to a talk of nobel price winner Gerard t'Hoft about cosmology. And he just stated this. Was he wrong?

With respect to the speed of light I of course meant the coordiante velocity. The one which was for instance measured in the Shapiro experiment. That should go to zero. The invariant speed of light is the one measured by a local observer. It is easy to see that this observer will always measure the nominal speed of light as his tools (clocks and rulers) change accordingly in the gravitational field. - This is at least my understanding.

6. Feb 24, 2017

### Orodruin

Staff Emeritus
You do not generally get $d\tau = 0$ at $r = r_S$ - you only get this for null world lines. It is not any stranger than having a general null world line. The only locally peculiar thing is that you have chosen to use coordinates such that the coordinate lines for the $t$ coordinate are null world lines.

7. Feb 25, 2017

### Albrecht

So I understand that all points on the event horizon are world null lines. Which consequences?

An observer outside the black hole and outside the event horizon will see any motion stopping at the event horizon. For him (and so for us) there is c = 0 and as well any other motion and also - as a general conclusion - dτ = 0. From which the question follows how a black hole can collect material.

To say it again: We are the observers looking from outside and we have the expectation that material moves into the black hole. But how?

8. Feb 25, 2017

### Orodruin

Staff Emeritus
There is no local Lorentz frame where the event horizon is stationary. No observer can be stationary at the event horizon.

This is an empty statement. The observer is not located at the event horizon and does not measure the coordinate speed of light there. The symbol $c$ is the invariant speed of light in vacuum, not the coordinate speed of light.

9. Feb 27, 2017

### Albrecht

I think that it is just the other way around. If an observer would be located at the event horizon then for him anything would look normal. But seen from our view, so from our Lorentz frame, any speed at the event horizon goes to zero. That is what also Gerard t'Hoft has said in his talk which I have mentioned earlier.
If we transport a clock into a gravitational field and take it back later then this clock will have a delay compared to our clocks. That is according to General Relativity and also the result of measurements. If we would transport a clock close to the event horizon and would later be able to take it back that this clock would have a considerable delay. This is in my understanding a clear result of the Schwarzschild metric. What else could happen?

10. Feb 27, 2017

### Orodruin

Staff Emeritus
You do realise that this is a GR equivalent of referring to an observer travelling at the speed of light in SR? It simply does not make sense. The most probable is that t'Hooft was making some sort of popularisation or that you misunderstood him (or you took the popularisation too far). Without seeing the talk, there is no way we can tell.

11. Feb 27, 2017

### Albrecht

It is a clear result of the Schwarzschild metric that
dτ = dt*sqrt(1-rs/r) and c = c0*sqrt(1-rs/r) (for tangential motion)

It has in fact a singularity for r = rs.

One can of course avoid the singularity by introducing a coordinate system which adapts gradually with the approximation to the horizon so as to avoid a singularity (like Eddington-Finkelstein coordinates). But if we discuss the development of the universe we use our coordinates, for instance to say that its age since the Big Bang is 13 billion years. Such an adapted coordinate system will tell us something different. But what would be the use of that for our understanding?

12. Feb 27, 2017

### Orodruin

Staff Emeritus
No it won't. The physical predictions of GR are coordinate independent. This is the entire point.

13. Feb 27, 2017


text:
# Newton's Third Law, Speed of Light, and Relativity question

#### FattyRNL

Highschool physics student here with a thought experiment I would like some input on.

While learning about Newton's Third Law (are reactions are immediate and there is no delay) I had a thought about the speed of light and relativity. Imagine You have a stick with a length of one light-year. Person A and Person B are on either side of said stick, like so:

A ----------------- B

Let's say Person A moves the stick an inch or so to poke Person B. By Newton's third law, the entire stick moves instantaneously, meaning Person B feels the stick poke him instantaneously (ignoring the time it takes the end of the stick to travel an inch or two to get to him). Because the entire stick moves at once, he would see his end of the stick poke him at the same moment he was getting poked. However, if he looked down the stick at Person A (because he has eagle eyes), he would not see the stick near Person A move for another year. Would, given Person B's frame of reference, it appear the stick has stretched out to him, and that over the course of the next year the stick would look like it got smaller?

If this is so, is it safe to assume the opposite would occur to Person A? Would the stick contract into itself and get larger over the next year?

And if this is all stupid, I apologize. One quarter of honors physics and a couple of pop-sci books doesn't quite qualify me for good questions or explanations.

#### nicksauce

Homework Helper
Let's say Person A moves the stick an inch or so to poke Person B. By Newton's third law, the entire stick moves instantaneously, meaning Person B feels the stick poke him instantaneously (ignoring the time it takes the end of the stick to travel an inch or two to get to him).
This is false. The "poke" travels through the stick at the speed of sound - the pressure wave has to travel through the stick.

See: http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#4

#### FattyRNL

Code:
This is false. The "poke" travels through the stick at the speed of sound - the pressure wave has to travel through the stick.
QUOTE]

I may be wrong (please correct me if I am) but your link applies to hitting an object, and the waves that pass through it as a result. Imagine the end of the stick nearest Person A as DeltaXA. By Newton's third law, if DeltaXA were to move 2 inches, shouldn't DeltaXB amove two inches immediately?

If you are right, however, would that imply that Person B would see Person move the stick before the stick poked him? It would take a year for that light to get to him, and would take [However long it would take a sound wave to travel one light-year] to actually poke him?

#### Dale

Mentor
nicksauce is correct.

Note, this is not anything to do with relativity, even in classical Newtonian mechanics the poke travels at the speed of sound in the rod. The only difference between Newtonian mechanics and SR in this case is that in SR the speed of sound must be less than the speed of light.

#### Doc Al

Mentor
While learning about Newton's Third Law (are reactions are immediate and there is no delay)
By Newton's third law, the entire stick moves instantaneously,
By Newton's third law, if DeltaXA were to move 2 inches, shouldn't DeltaXB amove two inches immediately?
I think you have a misunderstanding of Newton's Third Law. If you push the stick, the stick pushes back on you. Those pushes are the 'action/reaction' pair that occur together. But the effect of your push on one part of the stick doesn't immediately affect the next part of the stick; As has been mentioned, the push travels along the stick at the speed of sound.

#### FattyRNL

Ah, thanks for the explanation on that.

However, would that then imply that Person B would see the stick being moved by Person A before he felt it?

#### grav-universe

Ah, thanks for the explanation on that.

However, would that then imply that Person B would see the stick being moved by Person A before he felt it?
Yes. Both A and B would see person A pushing the stick, then watch the pressure wave move down the stick to poke B.

#### mappy

Re: Newton's Third Law and the stick

hello i am new to this site, this long rod problem has been with me for a long time,
how dose newtons 2nd law hold up. if a and b know the mass of the rod and, have more than enough power to move it. can they double their expected rate of acceleration if singled by c at the middle of the rod and prearrange to move it one way? ie when A push and B pulls?

#### John232

I find it hard to beleive that the most rigid an object could be would be determined by the speed of sound. It would mean that if you spun any length of rod that was made of the most rigid material known to man would go completely flimsy if spun at the speed of sound.

A rod a foot long spun at the speed of sound would turn to jelly, lol, I have seen small rigid objects respond instantly to an end being moved, I don't see why they have to be a light year long.

Say a jet goes mach one, the back of the jet being pushed by the engines can only make the front of the ship be pushed forward to respond to the back as fast as it is moveing, the length contraction of going mach one would smash the jet and the sound barrier would never be able to be broken...

#### Fredrik

Staff Emeritus
Gold Member
I find it hard to beleive that the most rigid an object could be would be determined by the speed of sound.
It's the other way round. The speed of sound in the material is determined by how rigid it is. The most rigid an object could be (in principle, and according to SR) is determined by the speed of light. Of course, actual matter is composed of atoms, and the interactions between them ensure that the speed of sound is many orders of magnitude slower than the speed of light.

Say a jet goes mach one, the back of the jet being pushed by the engines can only make the front of the ship be pushed forward to respond to the back as fast as it is moveing, the length contraction of going mach one would smash the jet and the sound barrier would never be able to be broken...
The push from the engine propagates through the plane at the speed of sound in the material it's made of, which is a several times faster than the speed of sound in air. If you could make a plane out of a material in which the speed of sound is slower than the speed of sound in air, and you tried to accelerate it to a speed faster than the speed of sound in air, I think it would just be torn apart by all the vibrations.

#### DaleSwanson

I find it hard to beleive that the most rigid an object could be would be determined by the speed of sound.
Here, the "speed of sound" means the speed of sound in whatever material is being discussed. The speed of sound is much faster in a rigid material than it is in air. The term speed of sound, could probably be better described as the speed which particles in a material move. When you push a rod that movement begins moving down the rod in a wave at a certain speed which depends on how rigid the material is.

The speed of sound (or of particle movement in general) in steel is about 5000 m/s or 11,000 mph. That is why you will never see this wave of movement traveling through a rod. The time the wave would cover and distance you could reasonably see at once would be a tiny fraction of a second.

#### Dale

Mentor
Re: Newton's Third Law and the stick

hello i am new to this site, this long rod problem has been with me for a long time,
how dose newtons 2nd law hold up. if a and b know the mass of the rod and, have more than enough power to move it. can they double their expected rate of acceleration if singled by c at the middle of the rod and prearrange to move it one way? ie when A push and B pulls?
Hi mappy, welcome to PF!

Double the force will produce double the change in momentum, that is Newton's 2nd law.

#### John232

Then wouldn't that mean that any object that had one end move relative to another by a force would then always end up slightly bent because of its relative motion?

A rod a kilometer long would end up flopping the speed of sound less than the other end even if it was made of diamond?

The elasticity of an object would break down when ends of it had relative speeds close to the speed of sound. I don't think any object rotating at the speed of sound at the equater would have to be turned to jelly.

#### DaleSwanson

Then wouldn't that mean that any object that had one end move relative to another by a force would then always end up slightly bent because of its relative motion?

A rod a kilometer long would end up flopping the speed of sound less than the other end even if it was made of diamond?

The elasticity of an object would break down when ends of it had relative speeds close to the speed of sound. I don't think any object rotating at the speed of sound at the equater would have to be turned to jelly.
It would be deformed for however long it took for the motion to travel through the object. The speed of sound in diamond is 12 km per second. If you had a 1 km long diamond rod, and pushed one end towards the other end, the rod would contract in length while that movement traveled through it as a slight bulge. During that time (1/12 of a second) the far end of the rod would be motionless. Once the motion reached the far end the length would move however far the rod was pushed and the length would return to the original length.

Note all this is only limiting how fast movement can move through a solid object. Certainly an object as a whole can travel much faster than the speed of sound through it.

#### Dale

Mentor
Then wouldn't that mean that any object that had one end move relative to another by a force would then always end up slightly bent because of its relative motion?
Yes.

I don't think any object rotating at the speed of sound at the equater would have to be turned to jelly.
What do you mean here?

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving


text:
## Where communities thrive

• Join over 1.5M+ people
• Join over 100K+ communities
• Free without limits
##### Activity
P4tr1ck99
@P4tr1ck99
Hi everyone, I'm a Rookie at optuna and I would like to know how I can change the evaluation metrics for finding the most fitting hyperparameters. If I understood it corectly, the metric for on which optuna decide if a hyperparameter set is a good one is the accurency. Instead of the accurency I would prefere to use the F1-Score or the Recall.
How could that be implemented with optuna?
2 replies
Chris Fonnesbeck
@fonnesbeck
I'm running into an issue trying to optimize the hyperparameters for a TF Estimator model (specifically a DNNClassifier). When I set up and run an Optuna study it quickly uses up all of my session's resources and crashes (this is using either a high-memory GPU Colab session or an AWS Deep Learning AMI). I haven't had this problem using non-Estimator TF models, nor does it occur when I run my model outside of Optuna, so I'm wondering if there is something special that needs to be done with them.
17 replies
Dário Passos
@dario-passos
Hi! Is there a way of changing the color map that optuna.visualization.plot_contour uses by default? Thanks!
3 replies
Robin-des-Bois
@Robin-des-Bois

Hi :-)
Is there predefined way to nest trial parameters?
I would like to pass a trial object into a function and all the parameters that get added inside this function should be prefixed automatically by a string that I specify.

I imagine the interface to look something like this but did not find something similar in the API:

def configure_subsytem_a(trial: optuna.Trial) -> SubSystemA:
n_params = trial.suggest_int("n_params", 1,3)
return SubSystemA(n_params)

trial = ...

subsystem_a = configure_subsytem_a(trial.withPrefix('subsystem_a'))

This should result in a conifg like this:

{
'subsystem_a.n_parmas': 3
}

It would be quite easy to build this functionality myself, by wrapping the trial object, but if functionality like this is provided, I would prefer to use that.

MaximilianSamLickeAgdur
@MaximilianSamLickeAgdur

Hi,

What is the preferred way of dealing with trial/suggestions that have ranges that depend on each other, see below callfunction...
is the preferred way to do as below or is it better to set like a central value and penalize values outside of range?
Does this method even work with optuna, sampler being used: TPE. Are certain samplers better at this?
Tips on literature?

class Objectiveoptim(object):

def init(self, idmodelsdict, value):
self.idmodelsdict = idmodelsdict
self.value = value

def call(self, trial):
totalfactor = 0
totalvalueused = 0
valuedict = dict()

for id_, model in self.idmodelsdict.items():
model.eval()

valuedict[id_] = trial.suggest_float(id_, 0, self.value - totalvalueused)
totalvalueused += valuedict[id_]
totalfactor += model(torch.tensor([valuedict[id_]], dtype=torch.float32))

return totalfactor
Francesco Carli
@mr-fcharles_gitlab

Hi,

I'm having difficulties in understanding how i can use the command

optuna.visualization.plot_param_importances(study)

to visualize hyperparameters importance while performing multiple objectives optimization. I undestand that I should specify the metric wrt which I want the importances to be computed but I don't understand how to do so.

7 replies
Dário Passos
@dario-passos
Hey everyone. I've been using Optuna-dashboard for a couple of weeks now and I'm detecting a weird behaviour. I'm using Optuna 2.6 to optimize the hyperparameters of a relatively small (5 to 8 layers) tensorflow/keras convolution neural network in a Jupyter notebook and optuna-dashboard 0.3.1 (SQLAlchemy 1.3.22) to monitor the evolution of the optimization. My default browser is Chrome (version 89.0.4389.82) and my OS is Windows 10. The strange behaviour that I've started noticing is a very high RAM consumption by optuna-dashboard after a certain number of trial in my optimization studies, much larger than the database file being created by Optuna. For example I have a study.db file that has roughly 11Mb corresponding to 1563 trials points. Displaying this on the browser gobbles up around 4 Gb of RAM and this is if shutdown optuna-dashboard and reload the study.db from scratch. When I continuously monitor the optimization experiment from the beginning, optuna-dashboard reaches around 6 Gb of RAM (for the exactly same file). Around trial 500 (more or less), the browser starts to get unresponsive or very low in terms of selection buttons, etc. This difficults the results analysis and is quite annoying... I report this same behaviour in two different PCs with different graphic cards and memory configurations. My CPUs and GPUs are running always below 60% performance, so lack of resources do not seem to be the cause. Is this suppose to happen? What can I do make the process run faster?
yywangvr
@yywangvr
import optuna

def objective(trial):
x = trial.suggest_float("x", 0, 5)
y = trial.suggest_float("y", 0, 3)

v0 = 4 * x ** 2 + 4 * y ** 2
v1 = (x - 5) ** 2 + (y - 5) ** 2
v=v0+v1
return v
Hello!
Is it possible to log the value of v0 and v1 in some functions such asstudy.trials_dataframe. As I also wish to analyse the intermediate values from the objective function.
Miguel Crispim Romao
@romanovzky
Hi all. Quick question, when using optuna.multi_objective.samplers.NSGAIIMultiObjectiveSampler, which has by default 50 trials per generation, if I set the study to perform 1000 trials do I assume correctly that there will be 20 generations?
3 replies
yywangvr
@yywangvr
import optuna

def objective(trial):
x = trial.suggest_float("x", 0, 5)
y = trial.suggest_float("y", 0, 3)

v0 = 4 * x ** 2 + 4 * y ** 2
v1 = (x - 5) ** 2 + (y - 5) ** 2
v=v0+v1
return v

Hello!
Is it possible to log the value of v0 and v1 in some functions such asstudy.trials_dataframe. As I also wish to analyse the intermediate values from the objective function.

Solution is given by optuna author here: https://github.com/optuna/optuna/issues/2520#issuecomment-806578752

Chris Fonnesbeck
@fonnesbeck
Optuna is filling up my hard drive with what I assume are some sort of swap/temp files when running a study. My nearly empty (before running Optuna) 1TB drive is now almost full after 30 trials. Where are these files, and why doesn't Optuna get rid of them?
3 replies
Dário Passos
@dario-passos
In the Optuna documentation, there is a note in the "Key Features" section called "Which Sampler and Pruner Should be Used?" and that points to a possible very relevant document " Ozaki et al, Hyperparameter Optimization Methods: Overview and Characteristics, in IEICE Trans, Vol.J103-D No.9 pp.615-631, 2020" that describes the performance of samplers/pruners pairs for deep learning tasks. Unfortunately this document is in Japanese! Is anyone aware of a translation of this document to English or of some blog or webpage where its content is described in English? Since deep learning tasks are a very contemporary subject, it would be very useful to have this benchmark (or a summary of it) in English so researchers from different places can tap into that information.
James Y
@yuanjames
Hi, does any know whether the CMA-ES sampler will use n initial independent samplings to generate initial parameters for CMA-ES?
4 replies
Hideaki Imamura
@HideakiImamura
Thanks to your contributions, we’ve just released v2.7.0. Check out the highlights and release notes at https://github.com/optuna/optuna/releases/tag/v2.7.0 or with the Tweet https://twitter.com/OptunaAutoML/status/1378915791614058502?s=20. Highlights:
Optuna dashboard now has its own repository. Install with pip install optuna-dashboard and try it out with optuna-dashboard \$STORAGE_URL. The dashboard subcommand is now deprecated!
Deprecate n_jobs in Study.optimize keeping process-level parallelization. There should be one obvious way to do distributed optimization.
Lots of new tutorials and examples!
2403hwaseer
@2403hwaseer
Hey @c-bata , I wanted to ask where can I submit my GSoC proposal for review?
2 replies
Izabela Paulino
@izabfee_gitlab
Hi everyone! I would like to ask if there is any other documentation where I can find the explanation of each parameter of LightGBMTunerCV?
2 replies
I'm in doubt specifically regarding the difference of folds and nfold of LightGBMTunerCV.
Miguel Crispim Romao
@romanovzky
Hi all. In a given optimisation problem, I'm not only interested in the solutions, but getting as many non-duplicate solutions for a certain problem. So far, I have been using NSGAIISampler with multiple objectives, but I would like to encourage the evolution (or sample, if I use TPE instead) to "explore" more. Any advice? Thanks
3 replies
Hideaki Imamura
@HideakiImamura
Hi everyone! PR reviews and issue responses will be slow due to some maintainers taking a vacation from 4/24-5/6. Sorry for the inconvenience.
Michael Schlitzer
@michaelschlitzer
I have a very dumb question about Optuna. When I run a study and get study.best_trial.value and my objective function is returning the accuracy of the test / validation dataset, what is that best_trial.value? Is that the accuracy on the test / validation set, or is it the accuracy on the training set? Or is it some other number all together? I just can't seem to find or decipher the answer. Thank you.
2 replies
dumbjarvis
@dumbjarvis
Does optuna work on graphs? Like PyTorch geometric?
To be specific, tune params for community detection on graphs.
dlin1
@kdlin
The following command, optuna.visualization.plot_optimization_history(study), works on Jupyter notebook but not on Jupyer lab. What should I do to make it work on Jupyter lab? Thank you.
3 replies
MaximilianSamLickeAgdur
@MaximilianSamLickeAgdur
This message was deleted
3 replies
esarvestani
@esarvestani
Hi everyone. I want to use optuna for a simple multi-objective optimization problem. It works well, the only problem is that the process of retrieving of best trials takes too much time, even much more than the optimization itself. It's not clear for me why this simple python assignment should take so much time. This is a piece of code to do that, in which I have a function in two dimensions (x, y) and I want to find the value of y that minimizes the function for a given x.
def multi_objective(trial, X):
y = trial.suggest_float("y", -5., 5.)
result = []
for x in X:
result.append((x**2+y-11)**2 + (x+y**2-7)**2)

return result

optuna.logging.set_verbosity(optuna.logging.WARNING)
Y = np.linspace(start=-5., stop=5., num=500)
study = optuna.create_study(directions=['minimize']*len(Y))
study.optimize(lambda trial: multi_objective(trial, Y), n_trials=1000)

# the next line takes too much time to run
bests = study.best_trials

best_values = [trial.values for trial in bests]
best_params = [trial.params for trial in bests]
2 replies
Pedro Vítor
Hi there! I have some hyperparameters that are dependent on others. For example, I'm testing two different learning rate schedulers in AllenNLP: slanted_triangular and linear_with_warmup, and they each have their own hyperparameters. How can I tie these related hyperparameters to values that are related to each other? Also, is there any way to improve the sampler configuration to take these dependencies into consideration, to prevent combining and evaluating unnecessary scenarios?
6 replies
MaximilianSamLickeAgdur
@MaximilianSamLickeAgdur
Like above i have hyperparameters that are dependent on each other. Especially the last hyperparameter in the loop is dependent on all other hyperparameters, will the below code example be a problem? chosen sampler tpe(multivariate)
class Randomoptim(object):
def init(self, modelsdict):
self.modelsdict = modelsdict
self.value = 1.0
def __call__(self, trial):
totalfactor = 0
valuedict = dict()

for id_, model in self.modelsdict.items():
model.eval()
if id_ == list(self.modelsdict.keys())[-1]:
valuedict[id_] = trial.suggest_float(id_,
self.value,
self.value)
else:
valuedict[id_] = trial.suggest_float(id_,
0,
self.value)
self.value -= valuedict[id_]

totalfactor += model(valuedict[id_])
return totalfactor
3 replies
Dmitry
@Akkarine
Hello! Is there any way to prune study from failed/staled in RUNNING state trials?
Only manually in database?
Dmitry
@Akkarine
2 replies
Well, discovered, that you shouldn't do it, because of corruption for sampler history)
Pedro Vítor
I'm running a study with AllenNLP optuna testing 9 hyperparameters, with 8 categoricals and a float from 1 to 5 (with step 1). This would yield me around 576k different combinations. I'm around trial 26 now, and for some reason, trials from 21 to 25 were all using the exact same hyperparameters, which were "copied" from trial 11, which is the best one. Whis is this happening? Why isn't optuna trying other combinations? I'm using the default TPESampler (also default parameters) and SuccessiveHalvingPruner with min_resource 5 (other parameters are also default). I'm also running two processes, one for each GPU, but both sharing the same optuna database.
5 replies
Pedro Vítor
If i'm using a particular metric for a study, how do I setup the study so trials get pruned unless they reach a minimum x score after y epochs?
6 replies
TKouras
Hello, Im trying to do some regressions with optuna and after the 50 trials, i want to keep the best r2_score and a scatter plot of "actual vs predicted values". If I do the process inside the objective trial it will return 50 scatter plots, but i only want the best one. Is there any way you can do this?
4 replies
Alexander_Konstantinidis
@AlexanderKonstantinidis

Hi, I am running the following code and I get an error message, could you please help?
import optuna.integration.lightgbm as lgbm
best_params, tuning_history = dict(), list()
booster = lgbm.train(params, dtrain, valid_sets=dval,
verbose_eval=0,
best_params=best_params,
tuning_history=tuning_history)

The error message is:
TypeError Traceback (most recent call last)

<ipython-input-28-c0d324367a3c> in <module>
4 verbose_eval=0,
5 best_params=best_params,
----> 6 tuning_history=tuning_history)
7

~\Anaconda3\envs\tf2\lib\site-packages\optuna\integration_lightgbm_tunerinit.py in train(args, kwargs)
32 _imports.check()
33
---> 34 auto_booster = LightGBMTuner(args,
kwargs)
35 auto_booster.run()
36 return auto_booster.get_best_booster()

TypeError: init() got an unexpected keyword argument 'best_params'
Thank you.

Hiroyuki Vincent Yamazaki
@hvy

As always, thanks for all the feedback and contributions. We’ve just released v2.8.0 with several interesting features and improvements.

🙊Constant Liar (CL) for TPE improves distributed search
🌳Tree-structured search space support for multivariate TPE
🪞Copying Studies across storages
📞Callbacks to re-run a pre-empted trial

Check out the highlights and release notes at https://github.com/optuna/optuna/releases/tag/v2.8.0 or with the Tweet https://twitter.com/OptunaAutoML/status/1401799603154939908.

Patshin_Anton
@paantya

Hi All!

Can you please tell me if it is possible to run optuna.pruners together with n_jobs = 10 and how best to do it to get acceleration?

5 replies
Miguel Crispim Romao
@romanovzky
Hi all. I have an objective function that has a lot of invalid regions, which I inform the study by returning a nan. I notice that the TPE spends a lot of time/trials around invalid regions after a while. Is this by construction due to the "uncertainty driven" GP logic? Is there a way of preventing the TPE to spend so long trying points with high uncertainty due to previous nan in the vicinity? Cheers
5 replies
Hello,
I have a question about hyperparameter importance. When I use optuna.importance.get_param_importances(study) and optuna.visualization.plot_param_importances(study) , both on the same single-objective study and with default parameters, the results differ. Why it is like that? or maybe I am doing sht wrong? I tried to look for an explanantion in optuna doc but haven't found anything.
Krishna Bhogaonker
@00krishna
Hello there optuners, this is my first time using optuna and it works well except for one small thing. I am not exactly sure how to explain this. So I use Weights and Biases website (wandb.com) to track all of the model runs--the logs. And I am using pytorch-lightning to run my model. Now I am successfully able to create the objective() function and run the training, but it seems that the log on Weights and Biases is getting overwritten. So instead of different runs or experiments for each trial, I just see one really funky trial with training error and losses everywhere--because everything is mixed together.
Krishna Bhogaonker
@00krishna
Here is the code if it helps. I am not sure if there is a way to tell optuna to initiate a new experiment each time the trial runs.
def objective(trial: optuna.trial.Trial) -> float:

input_window_size = trial.suggest_categorical("input_window_size", [20, 30, 40])
output_window_size = trial.suggest_categorical("output_window_size", [ 20, 30, 40])
test_percentage = 0.20
val_percentage = 0.20
lags = [1, 2, 3, 365, 366, 367]
lag_combos = list(powerset(lags))
laglist = trial.suggest_categorical("lags", lag_combos)
drop_columns = ['pr', 'tmmx']
drop_column_combos = list(powerset(drop_columns))
remove_columns = trial.suggest_categorical("remove_columns", drop_column_combos)
batch_size = trial.suggest_categorical("batch_size",[16, 32, 64, 128])

datamodule = get_dataset('Sensor1')
datamodule = datamodule(input_window_size=input_window_size,
output_window_size=output_window_size,
test_percentage=test_percentage,
val_percentage=val_percentage,
laglist=laglist,
remove_columns=remove_columns,
batch_size=batch_size)

datamodule.prepare_data()
datamodule.setup()

hidden_dim = trial.suggest_categorical("hidden_dim", [16, 32, 64, 128])
num_layers = trial.suggest_int("num_layers", 1, 3)
dropout = trial.suggest_float("dropout", 0.2, 0.5, step=0.1)

optimizer_name = trial.suggest_categorical("optimizer", ["Adam", "RMSprop", "SGD"])
lr = trial.suggest_uniform("lr", 1e-5, 1e-1)

model = LitDivSensor(num_features = datamodule.num_features,
hidden_dim = hidden_dim,
num_layers = num_layers,
dropout = dropout,
debug = False,
learning_rate = lr,
batch_size = batch_size,
optimizer_name=optimizer_name)

tb_logger = pl_loggers.TensorBoardLogger('logs/', name='division-bell-rnn')
wandb_logger = pl_loggers.WandbLogger(name='division-bell-rnn'+ str(date_time),
save_dir='logs/',
project='division-bell',
entity='****',
offline=False)
trainer = pl.Trainer(
logger=[tb_logger, wandb_logger],
checkpoint_callback=False,
max_epochs=EPOCHS,
gpus=1 if torch.cuda.is_available() else None,
callbacks=[PyTorchLightningPruningCallback(trial, monitor="val_loss")])

hyperparameters = dict(input_window_size=input_window_size,
output_window_size=output_window_size,
laglist=laglist,
remove_columns=remove_columns,
batch_size = batch_size,
hidden_dim=hidden_dim,
num_layers=num_layers,
dropout=dropout,
optimizer_name=optimizer_name,
learning_rate=lr)

trainer.logger.log_hyperparams(hyperparameters)
trainer.fit(model, datamodule=datamodule)

return trainer.callback_metrics["val_loss"].item()
Philipp Dörfler
@phdoerfler
'sup! What RDBs does optuna support? The docs mention sqlite, mysql and postgresql but I can't find a complete list. I assume it uses some different library for the DB access which would have said list, right? Which one? Thanks!
alternatively: What exactly is the issue with sqlite and running optuna in parallel? I'm planning on running at most 4 instances of optuna in parallel (the machine has 4 GPUs). Is accessing sqlite simultaneously merely not as efficient or will it introduce inconsistencies? I'd be completely OK with, e.g., locking happening, that's still plenty fast for my use case obviously. I'm also on a system that isn't maintained by myself, so I can't easily install postgresql or some other RDB.
For that reason I was also looking into portable versions of Postgresql that would be self contained in a single directory but only found something for Windows (and this is a ubuntu machine I'm talking about)
Philipp Dörfler
@phdoerfler
fwiw I just realised that in https://optuna.readthedocs.io/en/stable/faq.html#how-can-i-use-two-gpus-for-evaluating-two-trials-simultaneously the code suggests that it is OK to use sqlite from multiple instances (on the same machine). Is this viable or just an oversimplification for the sake of easy to read documentation?
Renato Hermoza Aragonés
@renato145
Im using postgres while training in kubernetes and slurm cluster
I have one question, I have some clusters with limited time for execution, how do I resume a trial ?
2 replies
Shalini
@tomshalini
Hello everyone,
I want to plot history of trials using "plot_optimization_history". It is not working with multi-objectives. Is there something I can try to visualize multi objective sampler results?
2 replies
Evgeny Frolov
@evfro

Hi everyone. I have a three-level question about the best practices for skipping trials.

1. Is it possible to prohibit sampling of certain combinations of values from hyper-parameter distributions? I have a complex search space and there's an interplay between sampled hyper-parameter values. As an example, after params a, b, c are sampled the trial is allowed to run only if, e.g., a * b > c.

2. What is the most appropriate way to skip a trial before performing main calculations in an objective (e.g., defining model, running training, etc.)?
Currently, once I made all the necessary trial.suggest_* calls I also call my custom is_valid(trial.params) function, which tells me if the trial is allowed to run or not. Naïve implementation is to just call is_valid function within the objective body. But I would like to detach the objective from verification of trial parameters. I compose many models with different objectives and with different restrictions of the search space, so I'd like to avoid adding is_valid(trial.params) call to all objectives and would prefer a cleaner solution, something like a pre-trial check, so that I only define it once and register it for any objective whatever it is. Does optuna has such functionality? Or do I have to go with closures/decorators/custom objective classes?

3. After the way to skip a trial is found, what would be the correct approach for actually skipping it in the study? I'm specifically interested in the case of TPESampler, which uses history of trials for its next steps. There seems to be at least 2 ways to do so: either raise optuna.TrialPruned() if trial should be skipped, or generate a custom exception like raise ConfigError and add it to the catch list of study.optimize call. Which one is more appropriate in terms of ensuring the correct work of TPESampler?

Thanks!

8 replies
Khawaja Umair Ul Hassan
@umairkhawaja
I modified the pytorch simple code example given in this repo and replaced the training/validation loop with a code similar to the sample training loop given in a classifier training example in the pytorch docs. However, the study ends after a single trial. I'm assuming this has something to do with the return accuracy statement at the end of the objective function. Can someone explain the purpose of this statement, or better if someone has any idea what I could be doing wrong?


text:
# Why would a trader quickly flicker an order immediately preceding a tick away?

The Setup

Assume the inside market is $15.15 \times 15.16$ and there is a very large bid order imbalance. For example, 30,000 shares bid across 100+ orders, 200 shares offered across 1 order; however, it is not always this extreme.

Approximately 10-1000$\mu$s prior to a tick up I've seen numerous occasions where a single order is "flickered" at the bid very quickly. By flicker I mean an order with the same size is quickly added and canceled, over and over again.

The flickering persists until the spread widens and the market goes to $15.15 \times 15.17$. Orders then rush to improve the bid to $15.16$ narrowing the spread back down to $0.01$. I've noticed that an order with the same size as the order being flickered at $15.15$ joins the new bid level very quickly after the tick, often achieving a queue position of 3 or better. Sometimes the new level is joined with an $Add Order$ and sometimes with a $Replace Order$, presumably to coincide with the state of the order being managed at the time of the widening of ths spread ($Add Order$ if the order was deleted immediately prior the widening, $Replace Order$ if the order was added immediately prior to the widening).

1. While the flickering is happening the market is relatively quiet making it easy to "see" the effect if one is scanning data visually.

2. The venue involved seems to always be INET (Q). At least, when I have noticed or gone looking for the flicker this is where I always see it. I've not done an exhaustive search.

3. In line with the above, I've not searched across more than CSCO for the flicker. It may behave differently (or not be present) in other symbols.

My Question and Ideas

What purpose does flickering the order serve? Or perhaps it serves no purpose and it is simply an order execution algorithm unsure about where to place the next bid?

It would seem to be disadvantageous to do this because it resets the priority of your resting bid. Granted, the tick up is very probable given the imbalance at the inside, but it is not guaranteed. Further, resetting priority works against the trader if the midpoint reverts quickly after the tick up.

Perhaps there are latency advantages to doing the flicker, but I can't puzzle out what they might be. One could simply leave their order unmolested, wait for the tick, and proceed to do a $Replace Order$ improving the bid and joining the new level. However, perhaps there is a small latency advantage to using $Add Order$ over $Replace Order$ on INET and the flicker allows the trader to sometimes be able to do this: use $Add Order$ if the tick happens immediatley following a $Cancel Order$, and the flicker serves to allow the trader to stay at the bid while hoping for the right timing of the tick.

Finally, some might suggest quote stuffing, but the amount of traffic generated by this one order is inconsequential in the grand scheme. No ticker plant worth its salt would care about a few hundred more messages that might be caused by this flicker.

What other possibilities are there? What's the best motivation to flicker an order in this fashion? Of course there is the simplistic explanation of: it serves no purpose and happens due to negligence (bug in the trader's software) or is meant to be confusing, and without a better explanation I suppose I must accept this. However, I'm curious if there is a more positive motivation for this order execution behavior.

-
Does the quote flicker after the tick up? Or does it rest on the book waiting for execution? (I knew by the third paragraph that the venue had to be NASDAQ since most other exchange operators will get quite irritated by rapid cancelations like this.) –  chrisaycock Nov 17 '12 at 16:58
No, the quote stops flickering after the ask gives way and the spread widens. –  Louis Marascio Nov 17 '12 at 17:10
Another follow-up: Does the canceled quote reappear momentarily at $15.14$, or is this an out-right cancel? (I assume this order is not being removed because of an execution.) –  chrisaycock Nov 17 '12 at 17:43
No, I don't believe so. I just spot checked a few instances and did not see a case where the orders alternated back one level. They stayed at the current bid level. There are no executions, it is an out-right cancel. –  Louis Marascio Nov 17 '12 at 17:53
The flickered orders are postonly bid at 15.16. The exchange slides it back to 15.15 to avoid a locked market. Submitting firm sees the slideback and cancels. Then tries again. When the 15.16 offer is executed or cancelled out, the offer moves to 15.17 then the postonly bid at 15.16 goes through at the targeted price and gains good queue position. This tactic is pretty well known, not a mystery. –  Kevin Schmit Nov 18 '12 at 7:01


text:
# Leong Ying

In hmolscience, Leong Ying (c. 1960-) is a Asian-born American nuclear physicist noted, in literature thermodynamics, for his 2002 semi nonfictional "twin universes theory" about entropy and being, or something along these lines.

Overview
In 2002, Ying published an online semi-nonfiction idea called twin universes theory, an attempt to explain life, consciousness, dark matter, and cosmic expansion, second law, then in the form of a science fiction book Klystar, the latter of which incorporates Chinese principle of Yin-Yang with laws of thermodynamics to postulate the existence of a “single omnipotent consciousness” or god, bonded by a force akin to love, residing in the parallel universe. [1]

The book tells the story of a young man named Leo on his quest to discover his own origins and learn the truths of the universe. Ying's theory was originally conceived in 1995 in the context of the fictional sci-fi novel, but soon more of the theory began to emerge out of the writing, to which he now devotes more of his time to.

Ying’s theory, in theme, seems to be a cross between French philosopher Pierre Teilhard’s 1916 second law based omega point theory, American mathematician William Sidis’ 1920 entropy reversal theory, and American engineer Ronald Pearson's 1990 intelligent ether theory, possibly geared along the lines of Russian engineer Yevgeny Zamyatin's futuristic 1920 thermodynamics-based novel We. The following is the structural overview to Ying’s theory: [2]

 Laws of the Total Universe First law of thermodynamics Energy of the universe is conserved. Second law of thermodynamics Entropy of the universe is conserved. Law of Ying Yang There is a natural order in the universe acting as the foundation of all things, the mother of all change, and the root of life and death; whereby in healing, one must grasp the view that the root of disharmony is subject to the actions of Yin and Yang.

 Postulates of the Total Universe First postulate The total universe is composed of two symmetric systems, a positive universe and a negative universe. Both universal systems occupy the same space-time. Second postulate Energy can flow between both universe systems, but the total energy in the total universe is conserved:$E_{total-universe} = E_{positive-universe} + E_{negative-universe} \,$ Third postulate Entropy can flow between both universal systems, but the total entropy in the universe is conserved:$S_{total-universe} = S_{positive-universe} + S_{negative-universe} \,$ Fourth postulate Gravity dictates the direction of of entropy change (time). Fifth postulate Life on earth exists only in the positive universe.

 Formulae of the Total Universe Energy $E = Q + W \,$ Entropy $S = \frac{Q}{T}\,$ Entropy (statistical) $S = k \ln \Omega \,$ (where k is the Boltzmann constant and Ω is the number of microstates) Positive entropy $S = k \ln D \,$ Negative entropy $S = k \ln \frac{1}{D} \,$ (where D is a measure of disorder and 1/D is a measure of order).

In the positive universe, according to Ying, which is where earth is, the original second law states that "for irreversible processes, the entropy of the enclosed system must increase, or put another way, all real processes move towards a state of maximum disorder." [2]

Religion
Ying is a former atheist, who up until circa 2003 considered himself to be an anti-religious as well as a "religious bigot" who viewed religious people as "losers who needed to get a life", but has since, in his mind, discovered a bridge between science and faith, viewing god as a “single omnipotent consciousness”. His 2007 book, according to reviews, presents a scientific proof of God in an easy to understand, powerful way for non-scientists.

Education
Ying completed his BS in physics in 1983 and PhD in nuclear physics in 1987 both at the University of Liverpool.

References
1. (a) TwinUniverse.org (archives) – WayBack Machine.
(b) Ying, Leong. (2007). Klystar. Tate Publishing.
(c) Klystar (book overview) – Klystar.com.
2. Twin Universe Theory (overview) – TwinUniverse.org.

Videos
● Ying, Leong. (2010). “Twin Universes Love One God (1 of 2)” (V), Jan 24.


text:
# Which of the following function are increasing or decreasing on the interval given? $2x^{2}+3x$ on $[-\large\frac{1}{2} ,\frac{1}{2}]$

Note: This is part 2nd of a 5 part question, split as 5 separate questions here.

Toolbox:
• (i) If $f'$ is positive on an open interval $I$. Then $f$ is strictly increasing on $I$
• (ii) If $f'$ is negative on an open interval $I$, then $f$ is strictly decreasing on $I$
$f(x)= 2 x^2+3x$ on $\bigg[-\large\frac{1}{2}, \frac{1}{2}\bigg]$
$f'(x)=4x+3$
$f'(x) > 0\;where \; x > -\large\frac{3}{4}$
In $\bigg[-\large\frac{1}{2}, \frac{1}{2}\bigg] x > -\large\frac{3}{4}$
$\therefore f'(x) >0$
So $f(x)$ is strictly increasing


text:
svgnames Colors

svgnames Colors from the xcolor Package

This page lists all the colors provided when the svgnames option is used for the xcolor LaTeX package. This list is taken from the xcolor Package Documentation and is intended to be used as a reference for selecting a color to use within templates found on LaTeX Templates.

To use these colors in your LaTeX document, simply include `\usepackage[svgnames]{xcolor}` in your preamble and then select a color with the `\color{}` command (e.g. `\color{Navy}`) after which all text will be of the color you specify. Alternatively, you can specify a color inline with `\textcolor{Navy}{This text is Navy.}`.


text:
College Physics (4th Edition)

At the point $(4.0,~0)$, the electric potential is $-2.7\times 10^6~V$
We can find the electric potential at the point $(4.0, ~0)$: $V = \frac{k~q_1}{r_1}+ \frac{k~q_2}{r_2}$ $V = k~(\frac{q_1}{r_1}+ \frac{q_2}{r_2})$ $V = (9.0\times 10^9~N~m^2/C^2) (\frac{2.0\times 10^{-3}~C}{4.0~m} + \frac{-4.0\times 10^{-3}~C}{5.0~m})$ $V = -2.7\times 10^6~V$ At the point $(4.0,~0)$, the electric potential is $-2.7\times 10^6~V$.


text:
CMSA Geometry and Physics Seminar: Parabolic de Rham bundles: motivic vs periodic

CMSA EVENTS

View Calendar
July 27, 2020 9:30 pm - 10:30 pm
via Zoom Video Conferencing
Speaker:

Mao Sheng - USTC

Let $C$ be a complex smooth projective curve. We consider the set of parabolic de Rham bundles over $C$ (with rational weights in parabolic structure). Many examples arise from geometry: let $f: X\to U$ be a smooth projective morphism over some nonempty Zariski open subset $U\subset C$. Then the Deligne--Iyer--Simpson canonical parabolic extension of the Gauss--Manin systems associated to $f$ provides such examples. We call a parabolic de Rham bundle \emph{motivic}, if it appears as a direct summand of such an example of geometric origin. It is a deep question in the theory of linear ordinary differential equations and in Hodge theory, to get a characterization of motivic parabolic de Rham bundles. In this talk, I introduce another subcategory of parabolic de Rham bundles, the so-called \emph{periodic} parabolic de Rham bundles. It is based on the work of Lan--Sheng--Zuo on Higgs-de Rham flows, with aim towards linking the Simpson correspondence over the field of complex numbers and the Ogus--Vologodsky correspondence over the finite fields. We show that motivic parabolic de Rham bundles are periodic, and conjecture that they are all periodic parabolic de Rham bundles. The conjecture for rank one case follows from the solution of Grothendieck--Katz p-curvature conjecture, and for some versions of rigid cases should follow from Katz's work on rigid local systems. The conjecture implies that in a spread-out of any complex elliptic curve, there will be infinitely many supersingular primes, a result of N. Elkies for rational elliptic curves. Among other implications of the conjecture, we would like to single out the conjectural arithmetic Simpson correspondence, which asserts that the grading functor is an equivalence of categories from the category of periodic parabolic de Rham bundles to the category of periodic parabolic Higgs bundles. This is a joint work in progress with R. Krishnamoorthy.


text:
# Tag Info

## New answers tagged data-mining

1

The automated generation of pivot tables is a well-studied topic. In fact, Google has a patent on the technology. The general approach is: Identify low-cardinality, categorical data features that have many repetitions. Those features become the row and column candidates for the pivot table. Identify numerical data that are the candidates for the data (or ...

0

To answer your question we need to understand what the aim of the clustering analysis that you are doing. Some of goal's of clustering analysis are: Outlier Detection, Pattern Detection, Grouping Data together, etc Now depending on the type of data, we can choose the algorithm that best fits the data at hand. If you have only numerical features, then you ...

3

When it comes to choosing a threshold, I can see 3 approaches: Make an educated guess This is what you are currently doing. You pick a value and would need to argue why this is a reasonable threshold. Obviously, the argument is as strong as the assumptions you make. Unsupervised way If you compute the matching score for all pairs between A and B, you can ...

1

It is not the case that all data resembles some manifold, for most reasonable meanings of the phrase "resembles some manifold". Mathematically, zero dimensional manifolds are collections of points, and technically speaking all finite data sets can be thought of as zero dimensional manifolds. However, I'm quite sure that's not what you had in mind when you ...

0

I believe your Text version is outdated. Please update Text add-on. For issues with Orange, please always head over to the issue tracker and see if your issue already exists. If not, open a new issue.

0

This seems to me now to be a typical case of a bipartite graph. In the real world, this can be viewed with customers and products; where each customer is linked to a product that they bought, but node customers or product nodes cannot be linked to each other. I do not know the SOTA for that, but a useful tool to check with Python is NetworkX. Perhaps, you ...

0

From the top of my head I think you could build something similar to an autoencoder. $X$ as input, $Y$ as label: $Y' = f_\theta(X) \approx Y$ as label, $f_\theta$ is a Neural Network, $\theta$ the weights and your loss $\mathcal{L} = d(Y,Y')$, where $d$ is some convex distance measure like Mean-Squared-Error or Binary-Crossentropy (if you scale your ...

0

Make X as feature Y as Label Build a model on it with 80% example. Predict Y for 20% and check if it is very close to Y_actual. If you are getting a good score. Then you are good. Predict Y for new X If Y_pred is close to Y_actual. You may assume both are linked.

0

On the surface, There are feature selection methods type like filter, wrapper etc. which uses techniques like chi-sqaure, ANOVA,information gain etc. There also exists feature importance method in sklearn ExtraTreesClassifier which gives you the importance of the feature. here are some to give you a glimpse of- https://machinelearningmastery.com/feature-...

0

I too would fall back on parsing either the HTML or the entities using regular expressions. My experience is though that this always gets unelegant quickly. Do you have a somewhat clear idea of the relevant sources? If the better part of the relevant data comes from a limited number of pages, you could maintain a list of sources with matching wrappers. ...

0

You can split it into two dataframe containing only one of P1 and P2 first. df1 = df[df.index[df['Product'] == 'P1'].tolist()] df2 = df[df.index[df['Product'] == 'P2'].tolist()] And then marge df1 and df2 on Customer ID and Product df1.merge(df2, 'inner', left_on=['Customer ID', 'Product'], right_on=['Customer ID', 'Product'], copy=False)

0

Since the daily dataset does not contain labels, you could aggregate the daily data into annual and then do the join. It sounds like a (binary) classification problem, which can be done using methods such as logistic regression. You will however have to handle missing values caused by the left join, one method would be imputing them. Or just doing an inner ...

Top 50 recent answers are included