College Football Playoff Predictions

Based on the optics of maintaining a lead over #1 Alabama for 50 minutes, perhaps Georgia can argue for a #4 spot, but based on cold, hard facts, Oklahoma has the best argument for that #4 spot. Nobody outside of the CFP selection room knows the official rules, but we know that the Power-5 get automatic bids with all things being equal, i.e. number of losses. To elaborate, conference champions are automatically in with 0 losses, but the committee has to look at quality of losses and wins after the 1st loss. We know that the quality of those losses is more important than quality of wins, with quality of wins being the tiebreaker. Rather than going through a bunch of gyrations to justify quality, I will assume that the committee will assume any ranked team is quality, and they can argue the details in tiebreaker discussions. That being said, I cannot see any arguments for putting Georgia higher than #6.

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Quantum Cryptography, Day 5: Axioms of Quantum Mechanics, Hilbert Spaces

Axioms of Quantum Mechanics

Quantum mechanics models represent the states, observables, measurements, and dynamics of quantum theory.

Quantum states

In quantum mechanics, the state is a ray in a Hilbert space. According to Wolfram, A Hilbert space is a vector space \left < f,g\right > such that the norm is defined by |f|= (\left < f,g\right >)^{0.5} . A Hilbert space is a vector space over the complex numbers C with an inner product \left <\psi | \phi\right > that maps an ordered pair of vectors to C. The inner product is defined by the following properties:

  • Positivity: \left < \psi | \psi \right > > 0 \ for \left | \psi \right > = 0
  • Linearity: \left < \phi | (\alpha | \psi_1 \right>  + \beta \left | \psi_2 \right >) = \alpha \left < \phi | \psi_1 \right > + \beta \left < \phi | \psi_2 \right >
  • Skew symmetry: \left < \psi | \phi \right >  = \left < \psi | \phi \right > \star 

wmgpf

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Week 13: #11 Florida Gators 41, FSU Seminoles 14 – Nov 24, 2018

Preview

The #13 Florida Gators take on the Florida State Seminoles in the Sunshine State Showdown this Saturday at noon (Eastern Time) at Ron Zook Field in Tallcrappy, Florida. The Gators are somehow favored by 4 points over that dumpster fire of a prison football team. Florida leads the series 34-26-2 all-time, but is 0-5 with shitty coaches these past few years. Florida can end FSU’s season with a victory, and end their 41-year streak of cheating in order to preserve their bowl game streak.

Result

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Quantum Cryptography, Day 4: Hadamard Gates & Pauli Gates

Hadamard Gate

In quantum information processing the Hadamard transformation, more often called Hadamard gate in this context (cf. quantum gate), is a one-qubit rotation, mapping the qubit-basis states \left | 0 \right> and \left | 1 \right> to two superposition states with equal weight of the computational basis states \left | 0 \right> and \left | 1 \right>

H = \frac{\left | 0 \right> + \left | 1 \right>}{\sqrt{2}}  \left < 0 \right | + \frac{\left | 0 \right> - \left | 1 \right>}{\sqrt{2}}  \left < 1 \right |

The transformation matrix is H_1=\frac{1}{\sqrt{2}}\begin{pmatrix}1&1\\1&-1 \end{pmatrix}

\frac{\left | 0 \right> + \left | 1 \right>}{\sqrt{2}}   and \frac{\left | 0 \right> - \left | 1 \right>}{\sqrt{2}}   are known as \left | + \right> and \left | - \right>

The Hadamard gate is the one-qubit version of the quantum fourier transform.

Pauli-X Gate

The Pauli-X gate is a one-qubit equivalent of the NOT gate, and equates to a rotation of the Block sphere around the X-axis by \pi radians. The Pauli-X gate maps \left | 0 \right > to \left | 1 \right > and \left | 1 \right > to \left | 0 \right >

X=\begin{bmatrix}0&1\\1&0\end{bmatrix}

Pauli-Y Gate

The Pauli-Y gate is a one-qubit rotation around the Y-axis of the Bloch sphere by \pi radians. The Pauli-Y gate maps \left | 0 \right > to i \left | 1 \right > and \left | 1 \right > to -i \left | 0 \right >

Y=\begin{bmatrix}0&-i\\i&0\end{bmatrix}

Pauli-Z Gate

The Pauli-Z gate, or R_{\pi} is a one-qubit rotation around the Z-axis of the Bloch sphere by \pi radians. This is also called a phase shift gate with \phi = \pi . This gate leaves the basis state \left | 0 \right > unchanged and maps \left | 1 \right > to \left | -1 \right >

Z=\begin{bmatrix}1&0\\0&-1\end{bmatrix}

 

 

Week 12: #13 Florida Gators 63, Idaho Vandals 10 – (Senior Day) November 17, 2018

The Florida Gators dominated the overmatched Idaho Vandals 63-10 in front of a modest crowd of 80,000. Today’s game was played in honor of our Gator veterans, as well as the 20 seniors who participated in Senior Day celebration. The veterans were represented by retired Major General Dave Kratzer, who was instrumental in the $90 million renovation to the Reitz Union Center upon returning from recall to duty in Operation DESERT STORM.

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