Contains the gene: e. Coli K-12 MG1655 gene thrL.
Subset of the longer E. Coli K-12 MG1655 transcription unit thrLABC.
A good definition is that the sparse matrix has non-zero entries proportional the number of rows. Therefore this is Big O notation less than something that has non zero entries. Of course, this only makes sense when generalizing to larger and larger matrices, otherwise we could take the constant of proportionality very high for one specific matrix.
Of course, this only makes sense when generalizing to larger and larger matrices, otherwise we could take the constant of proportionality very high for one specific matrix.
A Cartesian product that carries over some extra structure of the input groups.
E.g. the direct product of groups carries over group structure on both sides.
Like the U.S.' spring term.
We don't need to understand a super generalized version of tensor products to know what they mean in basic quantum computing!
Intuitively, taking a tensor product of two qubits simply means putting them together on the same quantum system/computer.
The tensor product is called a "product" because it distributes over addition.
E.g. consider:
Intuitively, in this operation we just put a Hadamard gate qubit together with a second pure qubit.
And the outcome still has the second qubit as always 0, because we haven't made them interact.
The quantum state is called a separable state, because it can be written as a single product of two different qubits. We have simply brought two qubits together, without making them interact.
If we then add a CNOT gate to make a Bell state:we can now see that the Bell state is non-separable: we've made the two qubits interact, and there is no way to write this state with a single tensor product. The qubits are fundamentally entangled.
Surely You're Joking, Mr. Feynman chapter An Offer You Must Refuse (a play on words on The Godfather (1972)) has an interesting historical mention from the early 1950s while at Caltech:
The next day, I had the greatest luck in making a decision. God must have set it up to help me decide. I was walking to my office, and a guy came running up to me and said, "Hey, Feynman! Did you hear what happened? Baade found that there are two different populations of stars! All the measurements we had been making of the distances to the galaxies had been based on Cephid variables of one type, but there's another type, so the universe is twice, or three, or even four times as old as we thought!"I knew the problem. In those days, the earth appeared to be older than the universe. The earth was four and a half billion, and the universe was only a couple, or three billion years old. It was a great puzzle. And this discovery resolved all that: The universe was now demonstrably older than was previously thought. And I got this information right away - the guy came running up to me to tell me all this.
Just like computers, biological systems can be seen as being composed of several different layers of complexity.
The Evolution of Bacteria on a 'Mega-Plate' Petri dish by Kishony Lab (2016)
Source. They've made a huge Petri dish with bands of different concentrations of antibiotic, and then they visualize Escherichia coli mutations as new strains manage to make their way into the highest antibiotic concentration strip. mind blowing.Specifies fixed values.
Can be used for elliptic partial differential equations and parabolic partial differential equations.
Numerical examples:
Our notation: , called "dihedral group of degree n", means the dihedral group of the regular polygon with sides, and therefore has order (all rotations + flips), called the "dihedral group of order 2n".
Where is Anatomy Encoded in Living Systems? by Michael Levin (2022)
Source. - we are very far from full understanding. End game is a design system where you draw the body and it compiles the DNA for you.
- some cool mentions of regeneration
NP-intermediate as of 2020 for similar reasons as integer factorization.
An important case is the discrete logarithm of the cyclic group in which the group is a cyclic group.
Does not have any non-trivial normal subgroup.
And therefore, going back to our intuition that due to the fundamental theorem on homomorphisms there is one normal group per homomorphism, a simple group is one that has no non-trivial homomorphisms.
Unlisted articles are being shown, click here to show only listed articles.