Chapter 357 - 294: This Is a Response 60 Years Late

Chapter 357: Chapter 294: This Is a Response 60 Years Late

"Teacher Wu."

"Teacher Lu."

He sounded a little unnatural as he said it.

Wu Kai glanced up at him and smiled.

"Hey, Xiaoguo, you’re back?"

"Just put that stuff over there for now. Xiaosu will bring it over later so we can calibrate everything together."

Wu Kai’s voice was calm.

It was as if Guo Han had never left, as if he had just popped into the next room to grab something.

Guo Han grunted in acknowledgment, quickly hefting the lock-in amplifier onto the table. He then turned and ran back downstairs; there was still another piece of equipment to bring up.

Wu Kai watched Guo Han’s retreating back but said nothing.

To be honest.

That email had bothered him.

But it was just a fleeting irritation.

When Wu Kai himself was young, he had been with his advisor when their research group went through a major crisis.

He knew better than anyone what it felt like to lie awake at night, staring at your inbox the next morning, wondering whether or not you should hit ’send’.

Students, after all, have to think about their future.

What was past was past.

Wu Kai silently moved his own teacup on the main console to the side.

He was making space for Guo Han to put down his own cup when he returned.

Just then, Lu Mingyuan beckoned to Li Dong.

"Li Dong, come take a look at this section."

Li Dong walked over to the screen.

Lu Mingyuan brought up the calibration curve they had just generated that morning.

It was an energy calibration spectrum for the manganese and iron thin films.

The horizontal axis represented the monochromator’s set energy.

The vertical axis represented the sample-side current after being demodulated by the lock-in amplifier.

Normally, the standard absorption edges of manganese and iron should be as reliable as a steel ruler, ready to use as a benchmark.

But on the current spectrum, the "shoulders" of the two absorption edges were smeared and blurry.

The edges weren’t sharp, and the tails of several kappa curves were overlapping, making them difficult to distinguish.

Lu Mingyuan pointed at the blurry edge.

"The system response... it hasn’t been tuned properly since we rebuilt the chamber."

"After the light spot comes through, there’s a small convolution happening somewhere between the energy axis and the current output."

"The convolution itself isn’t large, but it’s smearing the tails of the kappa curves we need to measure later all together."

Wu Kai was also looking at the screen from the side.

"Old Lu already tried a simple Gaussian deconvolution."

"It didn’t work. The moment the parameters fluctuate, artifacts pop up."

"We’ve calibrated this machine three times this morning already."

Li Dong studied the graph for a moment.

He asked casually.

"Teacher Lu, are you trying to solve an inverse problem here?"

Lu Mingyuan nodded.

"You could say that."

"It’s a small inverse problem. We’re trying to deduce the convolution kernel from the measured current spectrum."

"It’s not a huge issue, just an annoying one."

"This is already our third attempt this morning."

Li Dong thought for a moment, then spoke.

"For this part, you can just use Upper Gihonov regularization."

The room suddenly fell silent.

Lu Mingyuan turned and stared at Li Dong for two seconds.

Wu Kai also looked up from the main console.

The corner of his mouth twitched.

"Li Dong."

"We’re on the physical path here."

"As for the mathematical inversion approach..."

"Didn’t you already prove that path was a dead end?"

Wu Kai genuinely couldn’t wrap his head around it.

In his mind, the two words "mathematical inversion" were inextricably linked to the main path that had already been proven to be a dead end.

Li Dong knew what he was getting stuck on.

To be honest...

If it hadn’t been for that bonus money arriving last night, the distinction between ’using inversion as the main path’ and ’using inversion as a tool’ might not have been so clear even in his own mind.

"Teacher Wu."

"The path we ruled out before was one where mathematical inversion was used as the main approach."

"Using inversion to extract that cluster of peak positions in the third coordination shell."

"The operator for that particular inversion was inherently ill-posed."

"The condition number was sky-high, and the coefficient for the Li Criterion was stuck firmly within the anchoring interval."

"That path is truly impossible."

"But what my ’Comment’ paper invalidated was the use of inversion as the main path."

"It didn’t completely discredit the very concept of inversion."

He raised his hand and pointed at the calibration spectrum on the screen.

"Now, take another look at this current problem."

Lu Mingyuan was the first to understand, his eyes lighting up.

Li Dong continued.

"The convolution kernel here is the chamber response."

"The operator is bounded, and the condition number is small enough to be negligible."

"In terms of the problem’s structure, it’s a simple, well-posed inverse problem."

"It’s completely different from the inversion problem on the main path we were dealing with before."

He smiled.

"Our ’Comment’ paper established the criterion as a yardstick."

"When it was established, its purpose was to measure which inversions *couldn’t* be done."

"Conversely..."

"It also tells us, loud and clear, which inversions *can* be done."

"As long as the Li Criterion coefficient doesn’t fall within the anchoring interval, you can apply the inversion cleanly."

He lifted his chin slightly.

"If you measure this current convolution inversion with the criterion, you’ll see it’s nowhere near the anchoring region."

"Upper Gihonov will work just fine."

"As for alpha, the regularization parameter, you can find it just by plotting the L-curve with the current condition number."

"It won’t even take half an hour."

Wu Kai was stunned for several seconds.

Then it dawned on him.

Mathematical inversion itself had never been a path.

It was a tool.

The inversion on the main path had led to a dead end because that specific inversion was inherently flawed.

It wasn’t as if the very word "inversion" was a crime.

Wu Kai gave a wry smile.

This idea of "using the criterion in reverse"—if he’d thought about it a little longer, he could have figured it out himself.

But the problem was that the person who’d figured it out was Li Dong, who was still just a PhD student—even if no one really treated him like one.

And he was a Changjiang Scholar. It was, all things considered, a bit embarrassing.