Change license, add Makefile, add image caching control

21 files changed, 94 insertions, 47 deletions

diff --git a/source/know/concept/bernstein-vazirani-algorithm/index.md b/source/know/concept/bernstein-vazirani-algorithm/index.md
index 85017dc..5f224dc 100644
--- a/source/know/concept/bernstein-vazirani-algorithm/index.md
+++ b/source/know/concept/bernstein-vazirani-algorithm/index.md
@@ -36,7 +36,8 @@ However, the Bernstein-Vazirani algorithm
 allows a quantum computer to do it with only a single query.
 It uses the following circuit:
 
-{% include image.html file="bernstein-vazirani-circuit.png" width="52%" alt="Bernstein-Vazirani circuit" %}
+{% include image.html file="bernstein-vazirani-circuit.png" width="52%"
+    alt="Bernstein-Vazirani circuit" %}
 
 Where $$U_f$$ is a phase oracle,
 whose action is defined as follows,
diff --git a/source/know/concept/bloch-sphere/index.md b/source/know/concept/bloch-sphere/index.md
index 0ca6f1b..99ac45d 100644
--- a/source/know/concept/bloch-sphere/index.md
+++ b/source/know/concept/bloch-sphere/index.md
@@ -13,7 +13,8 @@ In quantum mechanics, particularly quantum information,
 the **Bloch sphere** is an invaluable tool to visualize qubits.
 All pure qubit states are represented by a point on the sphere's surface:
 
-{% include image.html file="sketch-full.png" width="67%" alt="Bloch sphere" %}
+{% include image.html file="sketch-full.png" width="67%"
+    alt="Bloch sphere" %}
 
 The $$x$$, $$y$$ and $$z$$-axes represent the components of a spin-1/2-alike system,
 and their extremes are the eigenstates of the Pauli matrices:
diff --git a/source/know/concept/deutsch-jozsa-algorithm/index.md b/source/know/concept/deutsch-jozsa-algorithm/index.md
index 5f2f268..44b06ad 100644
--- a/source/know/concept/deutsch-jozsa-algorithm/index.md
+++ b/source/know/concept/deutsch-jozsa-algorithm/index.md
@@ -41,7 +41,8 @@ In other words, we only need to determine if $$f(0) = f(1)$$ or $$f(0) \neq f(1)
 To do this, we use the following quantum circuit,
 where $$U_f$$ is the oracle we query:
 
-{% include image.html file="deutsch-circuit.png" width="48%" alt="Deutsch circuit" %}
+{% include image.html file="deutsch-circuit.png" width="48%"
+    alt="Deutsch circuit" %}
 
 Due to unitarity constraints,
 the action of $$U_f$$ is defined to be as follows,
@@ -141,7 +142,8 @@ We are promised that $$f(x)$$ is either constant or balanced;
 other possibilities are assumed to be impossible.
 This algorithm is then implemented by the following quantum circuit:
 
-{% include image.html file="deutsch-jozsa-circuit.png" width="52%" alt="Deutsch-Jozsa circuit" %}
+{% include image.html file="deutsch-jozsa-circuit.png" width="52%"
+    alt="Deutsch-Jozsa circuit" %}
 
 There are $$N$$ qubits in initial state $$\Ket{0}$$, and one in $$\Ket{1}$$.
 For clarity, the oracle $$U_f$$ works like so:
diff --git a/source/know/concept/dispersive-broadening/index.md b/source/know/concept/dispersive-broadening/index.md
index 9642737..55a31e6 100644
--- a/source/know/concept/dispersive-broadening/index.md
+++ b/source/know/concept/dispersive-broadening/index.md
@@ -62,7 +62,8 @@ This phenomenon is illustrated below for our example of a Gaussian pulse
 with parameter values $$T_0 = 1\:\mathrm{ps}$$, $$P_0 = 1\:\mathrm{kW}$$,
 $$\beta_2 = -10 \:\mathrm{ps}^2/\mathrm{m}$$ and $$\gamma = 0$$:
 
-{% include image.html file="simulation-full.png" width="100%" alt="Dispersive broadening simulation results" %}
+{% include image.html file="simulation-full.png" width="100%"
+    alt="Dispersive broadening simulation results" %}
 
 The **instantaneous frequency** $$\omega_\mathrm{GVD}(z, t)$$,
 which describes the dominant angular frequency at a given point in the time domain,
diff --git a/source/know/concept/fabry-perot-cavity/index.md b/source/know/concept/fabry-perot-cavity/index.md
index c013f1d..c88e62d 100644
--- a/source/know/concept/fabry-perot-cavity/index.md
+++ b/source/know/concept/fabry-perot-cavity/index.md
@@ -19,7 +19,8 @@ We divide the $$x$$-axis into three domains: left $$L$$, center $$C$$, and right
 The cavity $$C$$ has length $$\ell$$ and is centered on $$x = 0$$.
 Let $$n_L$$, $$n_C$$ and $$n_R$$ be the respective domains' refractive indices:
 
-{% include image.html file="sketch-full.png" width="70%" alt="Cavity structure" %}
+{% include image.html file="sketch-full.png" width="70%"
+    alt="Cavity structure" %}
 
 
 
diff --git a/source/know/concept/feynman-diagram/index.md b/source/know/concept/feynman-diagram/index.md
index ace8dbc..1f1c957 100644
--- a/source/know/concept/feynman-diagram/index.md
+++ b/source/know/concept/feynman-diagram/index.md
@@ -38,7 +38,8 @@ Let the subscript $$I$$ refer to the
 and $$\mathcal{T}\{\}$$ denote the
 [time-ordered product](/know/concept/time-ordered-product/):
 
-{% include image.html file="fermion-light.png" width="60%" alt="Fermion line diagram" %}
+{% include image.html file="fermion-light.png" width="60%"
+    alt="Fermion line diagram" %}
 
 $$\begin{aligned}
     = i \hbar G_{s_2 s_1}^0(\vb{r}_2, t_2; \vb{r}_1, t_1)
@@ -58,7 +59,8 @@ Less common is a **heavy fermion line**, representing
 a causal Green's function $$G$$ for the entire Hamiltonian $$\hat{H}$$,
 where the subscript $$H$$ refers to the [Heisenberg picture](/know/concept/heisenberg-picture/):
 
-{% include image.html file="fermion-heavy.png" width="60%" alt="Heavy fermion line diagram" %}
+{% include image.html file="fermion-heavy.png" width="60%"
+    alt="Heavy fermion line diagram" %}
 
 $$\begin{aligned}
     = i \hbar G_{s_2 s_1}(\vb{r}_2, t_2; \vb{r}_1, t_1)
@@ -72,7 +74,8 @@ which we assume to be instantaneous, i.e. time-independent
 hence it starts and ends at the same time,
 and no arrow is drawn:
 
-{% include image.html file="boson.png" width="60%" alt="Boson/interaction line diagram" %}
+{% include image.html file="boson.png" width="60%"
+    alt="Boson/interaction line diagram" %}
 
 $$\begin{aligned}
     = \frac{1}{i \hbar} W_{s_2 s_1}(\vb{r}_2, t_2; \vb{r}_1, t_1)
@@ -94,7 +97,8 @@ $$\begin{aligned}
 One-body (time-dependent) operators $$\hat{V}$$ in $$\hat{H}_1$$
 are instead represented by a special vertex:
 
-{% include image.html file="impurity.png" width="35%" alt="One-body perturbation (e.g. impurity) diagram" %}
+{% include image.html file="impurity.png" width="35%"
+    alt="One-body perturbation (e.g. impurity) diagram" %}
 
 $$\begin{aligned}
     = \frac{1}{i \hbar} V_s(\vb{r}, t)
@@ -171,7 +175,8 @@ Working in Fourier space allows us to simplify calculations.
 Consider the following diagram and the resulting expression,
 where $$\tilde{\vb{r}} = (\vb{r}, t)$$, and $$\tilde{\vb{k}} = (\vb{k}, \omega)$$:
 
-{% include image.html file="example.png" width="40%" alt="Example: fermion-fermion interaction" %}
+{% include image.html file="example.png" width="40%"
+    alt="Example: fermion-fermion interaction" %}
 
 $$\begin{aligned}
     &= (i \hbar)^3 \sum_{s s'} \!\!\iint \dd{\tilde{\vb{r}}} \dd{\tilde{\vb{r}}'}
diff --git a/source/know/concept/metacentric-height/index.md b/source/know/concept/metacentric-height/index.md
index 3d81d44..97afff6 100644
--- a/source/know/concept/metacentric-height/index.md
+++ b/source/know/concept/metacentric-height/index.md
@@ -26,7 +26,8 @@ does not coincide with the origin in general,
 as is illustrated in the following sketch
 of our choice of coordinate system:
 
-{% include image.html file="sketch-full.png" width="75%" alt="Boat's coordinate system" %}
+{% include image.html file="sketch-full.png" width="75%"
+    alt="Boat's coordinate system" %}
 
 Here, $$B$$ is the **center of buoyancy**, equal to
 the center of mass of the volume of water displaced by the boat
diff --git a/source/know/concept/modulational-instability/index.md b/source/know/concept/modulational-instability/index.md
index f1c246c..d646503 100644
--- a/source/know/concept/modulational-instability/index.md
+++ b/source/know/concept/modulational-instability/index.md
@@ -185,7 +185,8 @@ $$\begin{aligned}
     = \sqrt{P_0} \sech\!\Big(\frac{t}{T_0}\Big)
 \end{aligned}$$
 
-{% include image.html file="simulation-full.png" width="100%" alt="Modulational instability simulation results" %}
+{% include image.html file="simulation-full.png" width="100%"
+    alt="Modulational instability simulation results" %}
 
 Where $$L_\mathrm{NL} = 1/(\gamma P_0)$$ is the characteristic length of nonlinear effects.
 Note that no noise was added to the simulation;
diff --git a/source/know/concept/optical-wave-breaking/index.md b/source/know/concept/optical-wave-breaking/index.md
index 3509bc2..1b6b558 100644
--- a/source/know/concept/optical-wave-breaking/index.md
+++ b/source/know/concept/optical-wave-breaking/index.md
@@ -34,7 +34,8 @@ Shortly before the slope would become infinite,
 small waves start "falling off" the edge of the pulse,
 hence the name *wave breaking*:
 
-{% include image.html file="frequency-full.png" width="100%" alt="Instantaneous frequency profile evolution" %}
+{% include image.html file="frequency-full.png" width="100%"
+    alt="Instantaneous frequency profile evolution" %}
 
 Several interesting things happen around this moment.
 To demonstrate this, spectrograms of the same simulation
@@ -51,7 +52,8 @@ After OWB, a train of small waves falls off the edges,
 which eventually melt together, leading to a trapezoid shape in the $$t$$-domain.
 Dispersive broadening then continues normally:
 
-{% include image.html file="spectrograms-full.png" width="100%" alt="Spectrograms of pulse shape evolution" %}
+{% include image.html file="spectrograms-full.png" width="100%"
+    alt="Spectrograms of pulse shape evolution" %}
 
 We call the distance at which the wave breaks $$L_\mathrm{WB}$$,
 and want to predict it analytically.
@@ -189,7 +191,8 @@ $$\begin{aligned}
 This prediction for $$L_\mathrm{WB}$$ appears to agree well
 with the OWB observed in the simulation:
 
-{% include image.html file="simulation-full.png" width="100%" alt="Optical wave breaking simulation results" %}
+{% include image.html file="simulation-full.png" width="100%"
+    alt="Optical wave breaking simulation results" %}
 
 Because all spectral broadening up to $$L_\mathrm{WB}$$ is caused by SPM,
 whose $$\omega$$-domain behaviour is known,
diff --git a/source/know/concept/quantum-fourier-transform/index.md b/source/know/concept/quantum-fourier-transform/index.md
index 1c68ad0..217596b 100644
--- a/source/know/concept/quantum-fourier-transform/index.md
+++ b/source/know/concept/quantum-fourier-transform/index.md
@@ -172,13 +172,15 @@ The quantum circuit to execute the mentioned steps is illustrated below,
 excluding the swapping part to get the right order.
 Here, $$R_m$$ means $$R_\phi$$ with $$\phi = 2 \pi / 2^m$$:
 
-{% include image.html file="qft-circuit-noswap.png" width="100%" alt="QFT circuit, without final swap" %}
+{% include image.html file="qft-circuit-noswap.png" width="100%"
+    alt="QFT circuit, without final swap" %}
 
 Again, note how the inputs $$\Ket{x_j}$$ and outputs $$\Ket{k_j}$$ are in the opposite order.
 The complete circuit, including the swapping at the end,
 therefore looks like this:
 
-{% include image.html file="qft-circuit-swap.png" width="85%" alt="QFT circuit, including final swap" %}
+{% include image.html file="qft-circuit-swap.png" width="85%"
+    alt="QFT circuit, including final swap" %}
 
 For each of the $$n$$ qubits, $$\mathcal{O}(n)$$ gates are applied,
 so overall the QFT algorithm is $$\mathcal{O}(n^2)$$.
diff --git a/source/know/concept/quantum-gate/index.md b/source/know/concept/quantum-gate/index.md
index e8ff579..9704e53 100644
--- a/source/know/concept/quantum-gate/index.md
+++ b/source/know/concept/quantum-gate/index.md
@@ -204,7 +204,8 @@ but not always in the basis of $$\Ket{0}_1$$, $$\Ket{1}_1$$, $$\Ket{0}_2$$ and $
 With that said, the first two-qubit gate is $$\mathrm{SWAP}$$,
 which simply swaps $$\Ket{\psi_1}$$ and $$\Ket{\psi_2}$$:
 
-{% include image.html file="swap.png" width="22%" alt="SWAP gate diagram" %}
+{% include image.html file="swap.png" width="22%"
+    alt="SWAP gate diagram" %}
 
 $$\begin{aligned}
     \boxed{
@@ -231,7 +232,8 @@ $$\begin{aligned}
 Next, there is the **controlled NOT gate** $$\mathrm{CNOT}$$,
 which "flips" (applies $$X$$ to) $$\Ket{\psi_2}$$ if $$\Ket{\psi_1}$$ is true:
 
-{% include image.html file="cnot.png" width="22%" alt="CNOT gate diagram" %}
+{% include image.html file="cnot.png" width="22%"
+    alt="CNOT gate diagram" %}
 
 $$\begin{aligned}
     \boxed{
@@ -256,7 +258,8 @@ More generally, from every one-qubit gate $$U$$,
 we can define a two-qubit **controlled U gate** $$\mathrm{CU}$$,
 which applies $$U$$ to $$\Ket{\psi_2}$$ if $$\Ket{\psi_1}$$ is true:
 
-{% include image.html file="cu.png" width="22%" alt="CU gate diagram" %}
+{% include image.html file="cu.png" width="22%"
+    alt="CU gate diagram" %}
 
 $$\begin{aligned}
     \boxed{
diff --git a/source/know/concept/random-phase-approximation/index.md b/source/know/concept/random-phase-approximation/index.md
index 0d0b428..03fd302 100644
--- a/source/know/concept/random-phase-approximation/index.md
+++ b/source/know/concept/random-phase-approximation/index.md
@@ -71,17 +71,20 @@ leaving only the single most divergent one at each order $$n$$,
 i.e. the ones where all $$n$$ interaction lines
 carry the same momentum and energy:
 
-{% include image.html file="self-energy.png" width="92%" alt="RPA self-energy definition" %}
+{% include image.html file="self-energy.png" width="92%"
+    alt="RPA self-energy definition" %}
 
 Where we have defined the **screened interaction** $$W^\mathrm{RPA}$$,
 denoted by a double wavy line:
 
-{% include image.html file="interaction.png" width="95%" alt="RPA screened interaction definition" %}
+{% include image.html file="interaction.png" width="95%"
+    alt="RPA screened interaction definition" %}
 
 Rearranging the above sequence of diagrams quickly leads to the following
 [Dyson equation](/know/concept/dyson-equation/):
 
-{% include image.html file="dyson.png" width="55%" alt="Dyson equation for screened interaction" %}
+{% include image.html file="dyson.png" width="55%"
+    alt="Dyson equation for screened interaction" %}
 
 In Fourier space, this equation's linear shape
 means it is algebraic, so we can write it out:
@@ -98,7 +101,8 @@ with an internal wavevector $$\vb{q}$$, fermionic frequency $$i \omega_m^F$$, an
 Abbreviating $$\tilde{\vb{k}} \equiv (\vb{k}, i \omega_n^B)$$
 and $$\tilde{\vb{q}} \equiv (\vb{q}, i \omega_n^F)$$:
 
-{% include image.html file="pairbubble.png" width="45%" alt="Internal variables of pair-bubble diagram" %}
+{% include image.html file="pairbubble.png" width="45%"
+    alt="Internal variables of pair-bubble diagram" %}
 
 We isolate the Dyson equation for $$W^\mathrm{RPA}$$,
 which reveals its physical interpretation as a *screened* interaction:
diff --git a/source/know/concept/repetition-code/index.md b/source/know/concept/repetition-code/index.md
index 89e6f4d..fa039a3 100644
--- a/source/know/concept/repetition-code/index.md
+++ b/source/know/concept/repetition-code/index.md
@@ -77,7 +77,8 @@ $$\begin{aligned}
 Such a transformation is easy to achieve with the following sequence
 of [quantum gates](/know/concept/quantum-gate/):
 
-{% include image.html file="bit-flip-encode.png" width="32%" alt="Bit flip code encoder" %}
+{% include image.html file="bit-flip-encode.png" width="32%"
+    alt="Bit flip code encoder" %}
 
 So, a little while after encoding the state $$\Ket{\psi}$$ like that,
 a bit flip occurs on the 2nd qubit:
@@ -180,7 +181,8 @@ without affecting $$\ket{\overline{\psi}}$$ itself,
 by applying $$\mathrm{CNOT}$$s to some ancillary qubits
 and then measuring those:
 
-{% include image.html file="bit-flip-detect.png" width="62%" alt="Bit flip code decoder" %}
+{% include image.html file="bit-flip-detect.png" width="62%"
+    alt="Bit flip code decoder" %}
 
 The two measurements, respectively representing $$ZZI$$ and $$IZZ$$,
 yield $$\Ket{1}$$ if a bit flip definitely occurred,
@@ -231,14 +233,16 @@ $$\begin{aligned}
     = \alpha \Ket{+\!+\!+} + \beta \Ket{-\!-\!-}
 \end{aligned}$$
 
-{% include image.html file="phase-flip-encode.png" width="40%" alt="Phase flip code encoder" %}
+{% include image.html file="phase-flip-encode.png" width="40%"
+    alt="Phase flip code encoder" %}
 
 A phase flip along the $$Z$$-axis
 corresponds to a bit flip along the $$X$$-axis $$\Ket{+} \to \Ket{-}$$.
 In this case, the stabilizers are $$XXI$$ and $$IXX$$,
 and the error detection circuit is as follows:
 
-{% include image.html file="phase-flip-detect.png" width="70%" alt="Phase flip code decoder" %}
+{% include image.html file="phase-flip-detect.png" width="70%"
+    alt="Phase flip code decoder" %}
 
 This system protects us against all single-qubit phase flips,
 but not against bit flips.
@@ -281,7 +285,8 @@ This encoding is achieved by the following quantum circuit,
 which simply consists of the phase flip encoder,
 followed by 3 copies of the bit flip encoder:
 
-{% include image.html file="shor-code-encode.png" width="55%" alt="Shor code encoder" %}
+{% include image.html file="shor-code-encode.png" width="55%"
+    alt="Shor code encoder" %}
 
 We thus use 9 physical qubits to store 1 logical qubit.
 Fortunately, more efficient schemes exist.
diff --git a/source/know/concept/rutherford-scattering/index.md b/source/know/concept/rutherford-scattering/index.md
index 6f5a21f..edf391c 100644
--- a/source/know/concept/rutherford-scattering/index.md
+++ b/source/know/concept/rutherford-scattering/index.md
@@ -19,7 +19,8 @@ Let 2 be initially at rest, and 1 approach it with velocity $$\vb{v}_1$$.
 Coulomb repulsion causes 1 to deflect by an angle $$\theta$$,
 and pushes 2 away in the process:
 
-{% include image.html file="two-body-full.png" width="50%" alt="Two-body repulsive 'collision'" %}
+{% include image.html file="two-body-full.png" width="50%"
+    alt="Two-body repulsive 'collision'" %}
 
 Here, $$b$$ is called the **impact parameter**.
 Intuitively, we expect $$\theta$$ to be larger for smaller $$b$$.
@@ -67,7 +68,8 @@ then by comparing $$t > 0$$ and $$t < 0$$
 we can see that $$v_x$$ is unchanged for any given $$\pm t$$,
 while $$v_y$$ simply changes sign:
 
-{% include image.html file="one-body-full.png" width="60%" alt="Equivalent one-body deflection" %}
+{% include image.html file="one-body-full.png" width="60%"
+    alt="Equivalent one-body deflection" %}
 
 From our expression for $$\vb{r}$$,
 we can find $$\vb{v}$$ by differentiating with respect to time:
diff --git a/source/know/concept/self-energy/index.md b/source/know/concept/self-energy/index.md
index f233466..4120011 100644
--- a/source/know/concept/self-energy/index.md
+++ b/source/know/concept/self-energy/index.md
@@ -204,7 +204,8 @@ that exactly $$2^m m!$$ diagrams at each order are topologically equivalent,
 so we are left with non-equivalent diagrams only.
 Let $$G(b,a) = G_{ba}$$:
 
-{% include image.html file="expansion.png" width="90%" alt="Full expansion of G in Feynman diagrams" %}
+{% include image.html file="expansion.png" width="90%"
+    alt="Full expansion of G in Feynman diagrams" %}
 
 A **reducible diagram** is a Feynman diagram
 that can be cut in two valid diagrams
@@ -215,7 +216,8 @@ At last, we define the **self-energy** $$\Sigma(y,x)$$
 as the sum of all irreducible terms in $$G(b,a)$$,
 after removing the two external lines from/to $$a$$ and $$b$$:
 
-{% include image.html file="definition.png" width="90%" alt="Definition of self-energy" %}
+{% include image.html file="definition.png" width="90%"
+    alt="Definition of the self-energy" %}
 
 Despite its appearance, the self-energy has the semantics of a line,
 so it has two endpoints over which to integrate if necessary.
@@ -234,7 +236,8 @@ Thanks to this recursive structure,
 you can convince youself that $$G(b,a)$$ obeys
 a [Dyson equation](/know/concept/dyson-equation/) involving $$\Sigma(y, x)$$:
 
-{% include image.html file="dyson.png" width="95%" alt="Dyson equation in Feynman diagrams" %}
+{% include image.html file="dyson.png" width="95%"
+    alt="Dyson equation in Feynman diagrams" %}
 
 This makes sense: in the "normal" Dyson equation
 we have a one-body perturbation instead of $$\Sigma$$,
diff --git a/source/know/concept/self-phase-modulation/index.md b/source/know/concept/self-phase-modulation/index.md
index 931e10b..bc5a103 100644
--- a/source/know/concept/self-phase-modulation/index.md
+++ b/source/know/concept/self-phase-modulation/index.md
@@ -69,7 +69,8 @@ $$\begin{aligned}
     A(z, t) = \sqrt{P_0} \exp\!\Big(\!-\!\frac{t^2}{2 T_0^2}\Big) \exp\!\bigg( i \gamma z P_0 \exp\!\Big(\!-\!\frac{t^2}{T_0^2}\Big) \bigg)
 \end{aligned}$$
 
-{% include image.html file="simulation-full.png" width="100%" alt="Self-phase modulation simulation results" %}
+{% include image.html file="simulation-full.png" width="100%"
+    alt="Self-phase modulation simulation results" %}
 
 The **instantaneous frequency** $$\omega_\mathrm{SPM}(z, t)$$,
 which describes the dominant angular frequency at a given point in the time domain,
diff --git a/source/know/concept/self-steepening/index.md b/source/know/concept/self-steepening/index.md
index fd48e0f..f96c020 100644
--- a/source/know/concept/self-steepening/index.md
+++ b/source/know/concept/self-steepening/index.md
@@ -126,7 +126,8 @@ $$L_\mathrm{shock} = 0.847\,\mathrm{m}$$,
 which turns out to be accurate,
 although the simulation breaks down due to insufficient resolution:
 
-{% include image.html file="simulation-full.png" width="100%" alt="Self-steepening simulation results" %}
+{% include image.html file="simulation-full.png" width="100%"
+    alt="Self-steepening simulation results" %}
 
 Unfortunately, self-steepening cannot be simulated perfectly: as the
 pulse approaches $$L_\mathrm{shock}$$, its spectrum broadens to infinite
diff --git a/source/know/concept/shors-algorithm/index.md b/source/know/concept/shors-algorithm/index.md
index 5ae5077..678d5d2 100644
--- a/source/know/concept/shors-algorithm/index.md
+++ b/source/know/concept/shors-algorithm/index.md
@@ -48,7 +48,8 @@ The period $$s$$ is the smallest integer satisfying $$f(x) = f(x+s)$$.
 To do this, the following $$2q$$-qubit quantum circuit is used,
 with $$q$$ chosen so that $$N^2 \le 2^q < 2 N^2$$:
 
-{% include image.html file="shors-circuit.png" width="70%" alt="Shor's circuit" %}
+{% include image.html file="shors-circuit.png" width="70%"
+    alt="Shor's circuit" %}
 
 Here, $$\mathrm{QFT}_q$$ refers to the $$q$$-qubit
 [quantum Fourier transform](/know/concept/quantum-fourier-transform/),
diff --git a/source/know/concept/simons-algorithm/index.md b/source/know/concept/simons-algorithm/index.md
index 294912b..63bb808 100644
--- a/source/know/concept/simons-algorithm/index.md
+++ b/source/know/concept/simons-algorithm/index.md
@@ -52,7 +52,8 @@ A quantum computer needs to query $$f$$ only $$\mathcal{O}(n)$$ times,
 although the exact number varies due to the algorithm's probabilistic nature.
 It uses the following circuit:
 
-{% include image.html file="simons-circuit.png" width="52%" alt="Simon's circuit" %}
+{% include image.html file="simons-circuit.png" width="52%"
+    alt="Simon's circuit" %}
 
 The XOR oracle $$U_f$$ implements $$f$$,
 and has the following action for $$n$$-bit $$a$$ and $$b$$:
diff --git a/source/know/concept/step-index-fiber/index.md b/source/know/concept/step-index-fiber/index.md
index 210a339..2d049a1 100644
--- a/source/know/concept/step-index-fiber/index.md
+++ b/source/know/concept/step-index-fiber/index.md
@@ -269,7 +269,8 @@ $$\begin{aligned}
     \end{cases}
 \end{aligned}$$
 
-{% include image.html file="bessel-full.png" width="100%" alt="First few solutions to Bessel's equation" %}
+{% include image.html file="bessel-full.png" width="100%"
+    alt="First few solutions to Bessel's equation" %}
 
 Looking at these solutions with our constraints for $$R_o$$ in mind,
 we see that for $$\mu > 0$$ none of the solutions decay
@@ -429,7 +430,8 @@ An example graphical solution of the transcendental equation
 is illustrated below for a fiber with $$V = 5$$,
 where red and blue respectively denote the left and right-hand side:
 
-{% include image.html file="transcendental-full.png" width="100%" alt="Graphical solution of transcendental equation" %}
+{% include image.html file="transcendental-full.png" version="2" width="100%"
+    alt="Graphical solution of transcendental equation" %}
 
 For the ground state the light is well-confined in the core,
 but for higher modes it increasingly leaks into the cladding,
diff --git a/source/know/concept/toffoli-gate/index.md b/source/know/concept/toffoli-gate/index.md
index 9a99e69..23dc81e 100644
--- a/source/know/concept/toffoli-gate/index.md
+++ b/source/know/concept/toffoli-gate/index.md
@@ -16,29 +16,35 @@ of which it returns $$A$$ and $$B$$ unchanged,
 and flips $$C$$ only if both $$A$$ and $$B$$ are true.
 In circuit logic diagrams, its representation is:
 
-{% include image.html file="toffoli.png" width="19%" alt="Toffoli gate symbol" %}
+{% include image.html file="toffoli.png" width="19%"
+    alt="Toffoli gate symbol" %}
 
 This gate is reversible because $$A$$ and $$B$$ are preserved,
 and it is universal because we can make a NAND gate from it:
 
-{% include image.html file="nand.png" width="38%" alt="NAND gate made of Toffoli gate" %}
+{% include image.html file="nand.png" width="38%"
+    alt="NAND gate made of Toffoli gate" %}
 
 A NAND is enough to implement every conceivable circuit.
 That said, we can efficiently implement NOT, AND, and XOR using a single Toffoli gate too.
 Note that NOT is a special case of NAND:
 
-{% include image.html file="not.png" width="32%" alt="NOT gate made of Toffoli gate" %}
+{% include image.html file="not.png" width="32%"
+    alt="NOT gate made of Toffoli gate" %}
 
-{% include image.html file="and.png" width="35%" alt="AND gate made of Toffoli gate" %}
+{% include image.html file="and.png" width="35%"
+    alt="AND gate made of Toffoli gate" %}
 
-{% include image.html file="xor.png" width="35%" alt="XOR gate made of Toffoli gate" %}
+{% include image.html file="xor.png" width="35%"
+    alt="XOR gate made of Toffoli gate" %}
 
 Using these, we can, as an example, make an OR gate
 from three Toffoli gates,
 thanks to the fact that $$A \lor B = \neg (\neg A \land \neg B)$$,
 i.e. OR is NAND of NOT $$A$$ and NOT $$B$$:
 
-{% include image.html file="or.png" width="50%" alt="OR gate made of Toffoli gates" %}
+{% include image.html file="or.png" width="50%"
+    alt="OR gate made of Toffoli gates" %}
 
 Thanks to its reversibility and universality,
 the Toffoli gate is interesting for quantum computing.