He drew two lines by the third and fifth lines of the equation, followed by a question mark.

His expression was thoughtful:

"Seems like..."

"Could the composite system of equations on this piece of paper be calculated in three parts?"

It's well known.

Regularization theory was first proposed to solve ill-posed problems.

For a long time, it was believed that mathematical problems derived from practical problems were always well-posed.

As early as the early 20th century.

Hadamard observed a phenomenon:

In some very general circumstances, solving linear equations can be ill-posed.

Even if the equation has a unique solution, a small disturbance on the right side of the equation can cause a large change in the solution.

In this situation.

Minimizing a norm function of the difference between both sides of an equation doesn't yield an approximate solution to the equation.

By the 1960s.

Tikhonov, Ivanov, and Phillips discovered the addition of regularization terms to minimize error norms.

That is, the regularized norm, not just minimizing the error norm, can obtain a sequence of solutions to an ill-posed problem that tends towards the correct solution.

In other words.

The first part of the equations is actually a sequence set describing the gradient change region.

It might even be...

Images?

With this thought.

Xu Yun suddenly became interested.

Judging from 4D/B2, this should be a problem involving rotational surfaces.

The second line's ∑(jik=S)∏(jik=q)(Xi)(ωj) determines the surface at a fixed angle to the meridian.

Since it's a fixed angle, one can assume the fixed model λ=( A , B ,π), and the observation sequence O =( o1 , o2 ,..., oT ).

Then there is α1(i)=πibi(o1), i=1,2,...,N

αt+1(i)=[j=1∑Nαt(i)aji]bi(ot+1), i=1,2,...,N

Fifteen minutes later.

Looking at the results before him, Xu Yun was contemplative:

"Maximized model parameters..."

Then he pondered for a moment and continued writing an equation on paper:

Q(λ,λ)=I∑logπi1P(O,I|λ)+I∑(t=1∑T−1logaitit+1)P(O,I|λ)+I∑(t=1∑Tlogbit(ot))P(O,I|λ).

This is a very simple projection curve, and the arc length at any point of a conic logarithmic spiral is inversely proportional to the distance from that point to the axis.

Thus it can be simplified into another expression.

δt(i)=i1i2,...,it−1maxP(it=i,t−1,...,i1,ot,...,o1|λ), i=1,2,...,N

While solving, Xu Yun's expression became increasingly grave.

Two hours later.

Xu Yun looked at the drawings in front of him, his brows tightly knit:

"Goodness, the reduced terms of the first set of equations turned out to be a state of observation equation?"

A state of observation equation is quite an odd thing, its mathematical interpretation is rather complex, but its physical interpretation is quite simple:

It represents a time sequence non-probability model, referring to a non-random process passing through state space from one state to another state.

Seeing this.

Might some students feel very familiar?

That's right.

This is a model definition that is entirely contrary to the Markov chain, describing a definite possibility within a very small interval.

And such models will generally only appear in.....

Extremely, extremely small microscopic fields.

With this thought.

Xu Yun suddenly had a flash of inspiration.

"Micro-scale, decay integral?"

He swiftly picked up a pen and quickly wrote a line on another piece of paper:

y(xn+1)−y(xn)/h≈f(xn,y(xn))

y(xn+1)=y(xn)+hf(xn,y(xn))

After finishing writing.

Xu Yun took out his notebook and opened a customized physics software.

This is a quantitative computational program that graduate students at Ke Da can apply for, based on Gauss's quantitative calculations as the core foundation, capable of calculating models with limited precision, named Aurora.

Aurora includes the trajectories of all discovered particles so far, connected to a secondary server over at Keda Tongfu.

Subsequently, Xu Yun used Mathpix to recognize and input the formulas he wrote, pressing the Enter key.

Twelve seconds later.

A number appeared before Xu Yun:

0.

This 0 isn't the unreliable 0, it signifies that the system didn't find a result matching this eigenvalue.

"Strange..."

Looking at the 0 before him, Xu Yun was spinning his pen as he puzzledly talked to himself:

"No result matching the eigenvalue... the equation set wasn't input wrong, could it be that my idea is flawed?"

According to his thought process.

The first part of the set of equations produced an observation state equation after simplification, he then tentatively performed an integral simplification.

Finally, he derived a period from a finite difference approximation derivative that seemed to correspond to the magnitude of the decay in the microscale field of particles.

In other words....

It seems to match a certain particle's trajectory.

Yet the result from Aurora is a 0?

Or maybe...

Is this a new particle not previously discovered?

It's commonly understood.

Currently in the particle physics standard model, we temporarily believe there are 61 fundamental particles divided into four parts:

Quarks.

Leptons.

Gauge bosons.

And Higgs particles.

Of course.

There's also an unconfirmed particle, the "graviton."

It is a hypothetical particle used to mediate gravitational interactions, thus won't be elaborated here.

Among them, the matter is constituted by fermions, including quarks and leptons.

Quarks form baryons and mesons through strong interactions, baryons like protons and neutrons form the atomic nucleus, and the atomic nucleus is fermions too.

Simultaneously, the atomic nucleus and electrons can form atoms, thereby creating the world we see.

The mediators of interactions are gauge bosons, used to transmit interaction forces between fermions.