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Information about this web version
Some mathematical preliminaries
0.1 Euclidean vectors
0.2 Vector spaces
0.3 Bras and kets
0.4 Daggers
0.5 Geometry
0.7 Outer products
0.8 The trace
0.9 Some useful identities
I Foundations
1 Quantum interference
1.1 Two basic rules
1.2 Quantum interference: the failure of probability theory
1.2.1 The double slit experiment
1.3 Superpositions
1.4 Interferometers
1.5 Qubits, gates, and circuits
1.6 Quantum decoherence
1.7 Computation: deterministic, probabilistic, and quantum
1.8 Computational complexity
1.9 Outlook
1.10 Remarks and exercises
1.10.1 A historical remark
1.10.2 Modifying the Born rule
1.10.3 Complex numbers
1.10.4 Many computational paths
1.10.5 Distant photon emitters
1.10.6 Physics against logic?
1.10.7 Quantum bomb tester
1.10.8 More time, more memory
1.10.9 Quantum Turing machines
1.10.10 Polynomial = good; exponential = bad
1.10.11 Big O
1.10.12 Imperfect prime tester
1.10.13 Imperfect decision maker
2 Qubits
2.1 Composing quantum operations
2.2 Quantum bits, called "qubits"
2.3 Quantum gates and circuits
2.4 Single qubit interference
2.5 The square root of NOT
2.6 Phase gates galore
2.7 Pauli operators
2.8 From bit-flips to phase-flips, and back again
2.9 Any unitary operation on a single qubit
2.10 The Bloch sphere
2.10.1 Drawing points on the Bloch sphere
2.11 Composition of rotations
2.12 A finite set of universal gates
2.13.1 Unknown phase
2.13.2 One of the many cross-product identities
3 Quantum gates
3.1 Physics against logic, via beamsplitters
3.2 Quantum interference, revisited (still about beam-splitters)
3.3 The Pauli matrices, algebraically
3.4 Unitaries as rotations
3.5 Universality, again
3.6 Some quantum dynamics
3.7 Remarks and exercises
3.7.1 Orthonormal Pauli basis
3.7.2 Pauli matrix expansion coefficients
3.7.3 Linear algebra of the Pauli vector
3.7.4 Matrix Euler formula
3.7.5 Special orthogonal matrix calculations
3.7.6 Phase as rotation
3.7.7 Geometry of the Hadamard
3.7.8 Swiss Granite Fountain
3.7.9 Dynamics in a magnetic field
4 Measurements
4.1 Hilbert spaces, briefly
4.2 Back to qubits; complete measurements
4.3 The projection rule; incomplete measurements
4.4 Example of an incomplete measurement
4.5 Observables
4.6 Compatible observables and the uncertainty relation
4.7 Quantum communication
4.8 Basic quantum coding and decoding
4.9 Distinguishability of non-orthogonal states
4.10 Wiesner's quantum money
4.11 Quantum theory, formally
4.11.1 Quantum states
4.11.2 Quantum evolutions
4.11.3 Quantum circuits
4.11.4 Measurements
4.12.1 Projector?
4.12.2 Knowing the unknown
4.12.3 Measurement and idempotents
4.12.4 Unitary transformations of measurements
4.12.5 Optimal measurement
4.12.6 Alice knows what Bob did
4.12.7 The Zeno effect
5 Quantum entanglement
5.1 A small history
5.2 One, two, many…
5.3 Quantum theory, formally (continued)
5.3.1 Tensor products
5.4 Back to qubits
5.5 Separable or entangled?
5.6 Controlled-NOT
5.6.1 The Bell states, and the Bell measurement
5.6.2 Quantum teleportation
5.6.3 Thou shalt not clone
5.7 Other controlled gates
5.7.1 Controlled-phase
5.7.2 Controlled-U
5.7.3 Phase kick-back
5.7.4 Universality, revisited
5.7.5 Density operators and the like
5.8 Why qubits, subsystems, and entanglement?
5.9.1 Entangled or not?
5.9.2 SWAP circuit
5.9.3 Controlled-NOT circuit
5.9.4 Measuring with controlled-NOT
5.9.5 Arbitrary controlled-U on two qubits
5.9.6 Entangled qubits
5.9.7 Quantum dense coding
5.9.8 Playing with conditional unitaries
5.10 Appendices
5.10.1 Tensor products in components
5.10.2 The Schmidt decomposition
6 Density matrices
6.2 Statistical mixtures
6.3 A few instructive examples, and some less instructive remarks
6.4 The Bloch ball
6.5 Subsystems of entangled systems
6.6 Partial trace, revisited
6.7 Mixtures and subsystems
6.8 Partial trace, yet again
6.9.1 Some density operator calculations
6.9.2 Purification of mixed states
6.9.3 Pure partial trace
6.9.4 Maximally Bell
6.9.5 Trace norm
6.9.6 Distinguishability and the trace distance
6.9.7 Spectral decompositions and common eigenbases
7 Quantum channels
7.1 Random evolution
7.1.1 Random unitaries
7.1.2 Random isometries
7.2 Evolution of open systems
7.3 Stinespring's dilation and Kraus's ambiguity
7.4 Single qubit channels
7.5 Composition of quantum channels
7.6 Completely positive trace-preserving maps
7.7 State-channel duality
7.8 The mathematics of "can" and "cannot"
7.9 Kraus operators, revisited
7.10 Correctable channels
7.11.1 Isometries
7.11.2 The Markov approximation
7.11.3 What use are positive maps?
7.11.4 The Choi–Jamiołkowski isomorphism
7.11.5 Block matrices and partial trace
7.12.1 Partial inner product
7.12.2 The "control" part of controlled-NOT
7.12.3 Surprisingly identical channels
7.12.4 Independent ancilla
7.12.5 Cooling down
7.12.6 Unchanged reduced density operator
7.12.7 Order matters?
7.12.8 Pauli twirl
7.12.9 Depolarising channel
7.12.10 Depolarising channel and the Bloch sphere
7.12.11 Complete positivity of a certain map
7.12.12 Toffoli gate
7.12.13 Duals
7.12.14 Trace, transpose, Choi
7.12.15 Purifications and isometries
7.12.16 Tricks with a maximally entangled state
7.12.17 Trace preserving and partial trace
7.12.18 Rotating Kraus operators
7.12.19 No pancakes
II Applications
8 Quantum cryptography
9 Bell's theorem
9.1 Quantum correlations
9.2 Hidden variables
9.3 CHSH inequality
9.4 Quantum correlations, revisited
9.5 Tsirelson's inequality
10 Quantum algorithms
10.1 Quantum Boolean function evaluation
10.1.1 Example
10.2 Hadamard and quantum Fourier transforms
10.3 More phase kick-back
10.4 Oracles and query complexity
10.4.1 Deutsch's algorithm
10.5 Three more quantum algorithms
10.5.1 The Bernstein-Vazirani algorithm
10.5.2 Grover's search algorithm
10.5.3 Simon's problem
10.6 Remarks and exercises
10.6.1 Shor's algorithm
10.6.2 RSA
10.6.3 More complexity classes
11 Decoherence and basic quantum error correction
11.1 Decoherence simplified
11.2 Decoherence and interference
11.3 Evolution of density operators under decoherence
11.4 Quantum errors
11.5 Same evolution, different errors
11.6 Some errors can be corrected on some states
11.7 Repetition codes
11.8 Quantum error correction
11.9 Turning bit-flips into phase-flips
11.10 Dealing with bit-flip and phase-flip errors
11.11 Remarks and exercises
12 Quantum error correction and fault tolerance
Introduction to Quantum Information Science
Chapter 3 Quantum gates
About understanding the square root of \texttt{NOT} via a physical implementation using symmetric beam-splitters. More about the Bloch sphere, via the omnipresent Pauli matrices, which can be described in a more algebraic way.
Before moving on, we first study two of the subjects from Chapter 2 in more depth: the square root of \texttt{NOT}, and the Bloch sphere.
The goal for the latter is to be able to visualise sequences of unitary operations on a qubit as sequences of rotations, and to see the action of some quantum circuits without getting engaged in lengthy calculations. The goal for the former is to study a way of implementing this gate using physical experiments, and then studying a related construction (the so-called Mach–Zehnder interferometer).
A symmetric beam-splitter is a cube of glass which reflects half the light that impinges upon it, while allowing the remaining half to pass through unaffected. For our purposes it can be viewed as a device which has two input and two output ports which we label as |0\rangle and |1\rangle, as in Figure 3.1.
Figure 3.1: A beam-splitter.
When we aim a single photon at such a beam-splitter using one of the input ports, we notice that the photon doesn't split in two: we can place photo-detectors wherever we like in the apparatus, fire in a photon, and verify that if any of the photo-detectors registers a hit, none of the others do. In particular, if we place a photo-detector behind the beam-splitter in each of the two possible exit beams, the photon is detected with equal probability at either detector, no matter whether the photon was initially fired from input port |0\rangle or |1\rangle.
It may seem obvious that, at the very least, the photon is either in the transmitted beam |0\rangle or in the reflected beam |1\rangle during any one run of this experiment. Thus we may be tempted to think of the beam-splitter as a random binary switch which, with equal probability, transforms any binary input into one of the two possible outputs. However, that is not necessarily the case. Let us introduce a second beam-splitter and place two normal mirrors so that both paths intersect at the second beam-splitter, resulting in something resembling the Mach-Zehnder interferometer (see 3.2).
Figure 3.2: Two beam-splitters with mirrors, so that a photon travels through both.
Now, the axiom of additivity in probability theory says that whenever something can happen in several alternative ways we add probabilities for each way considered separately. We might argue that a photon fired into the input port |0\rangle can reach the detector 0 in two mutually exclusive ways: either by two consecutive reflections or by two consecutive transmissions. Each reflection happens with probability 1/2 and each transmission happens with probability 1/2 thus the total probability of reaching detector 0 is a sum of the probability of the two consecutive reflections (1/2\times 1/2 = 1/4) and the probability of the two consecutive transmissions (1/2\times 1/2 = 1/4) which gives probability 1/2. This is summarised in Figure 3.3, and makes perfect sense — a random switch followed by a random switch should give nothing else but a random switch. However, if we set up such an experiment, that is not what happens!
There is no reason why probability theory (or any other a priori mathematical construct for that matter) should make any meaningful statements about outcomes of physical experiments.
Figure 3.3: The two possible classical scenarios. Note that this is not what actually happens in the real physical world!
In experimental reality, when the optical paths between the two beam-splitters are the same, the photon fired from input port |0\rangle always strikes detector 1 and never detector 0 (and the photon fired from input port |1\rangle always strikes detector 0 and never detector 1). Thus a beam-splitter acts as the square root of \texttt{NOT} gate.
The action of the beam-splitter — in fact, the action of any quantum device — can be described by tabulating the amplitudes of transitions between its input and output ports.44 B = \begin{bmatrix} B_{00} & B_{01}\\ B_{10} & B_{11} \end{bmatrix} = \begin{bmatrix} \frac{1}{\sqrt 2} & \frac{i}{\sqrt 2}\\ \frac{i}{\sqrt 2} & \frac{1}{\sqrt 2} \end{bmatrix}. The matrix element B_{lk}, where k,l=0,1, represents the amplitude of transition from input |k\rangle to output |l\rangle (watch the order of indices). Each reflection (entries B_{01} and B_{10}) happens with amplitude i/\sqrt{2} and each transmission (entries B_{00} and B_{11}) happens with amplitude 1/\sqrt{2}. Thus the total amplitude that a photon fired from input port |0\rangle will reach detector 0 is the sum of the amplitude of the two consecutive reflections (i/\sqrt{2}\times i/{\sqrt 2} = -1/2) and the amplitude of the two consecutive transmissions (1/{\sqrt 2}\times 1/{\sqrt 2} = 1/2) which gives the total amplitude 0. The resulting probability is then zero. Unlike probabilities, amplitudes can cancel out each other out. We can now go on and calculate the amplitude that the photon will reach detector 1. In this case we will get i, which gives probability 1. We can then switch to input |1\rangle and repeat our calculations. All possible paths and associated amplitudes are shown in 3.4.
Figure 3.4: All possible transitions and their amplitudes when we compose two beam-splitters B.
However, instead of going through all the paths in this diagram and linking specific inputs to specific outputs, we can simply multiply the transition matrices: BB = \begin{bmatrix} \frac{1}{\sqrt 2} & \frac{i}{\sqrt 2}\\ \frac{i}{\sqrt 2} & \frac{1}{\sqrt 2} \end{bmatrix} \begin{bmatrix} \frac{1}{\sqrt 2} & \frac{i}{\sqrt 2}\\ \frac{i}{\sqrt 2} & \frac{1}{\sqrt 2} \end{bmatrix} = \begin{bmatrix} 0 & i\\ i & 0 \end{bmatrix} = iX where X = \texttt{NOT} = \begin{bmatrix}0&1\\1&0\end{bmatrix}.
Recalling Chapter 2, we see that beam-splitters give a physical way of constructing the square root of \texttt{NOT}.
bit-flip \texttt{NOT}\equiv X \begin{bmatrix}0&1\\1&0\end{bmatrix}
beam-splitter \sqrt{\texttt{NOT}}\equiv B \frac{1}{\sqrt2}\begin{bmatrix}1&i\\i&1\end{bmatrix}
One of the simplest quantum devices in which quantum interference can be controlled is a Mach–Zehnder interferometer — see Figure 3.5.45
Figure 3.5: The Mach-Zehnder interferometer, with the input photon represented by the coloured dot. This experimental set-up is named after the physicists Ludwig Mach and Ludwig Zehnder, who proposed it back in 1890s.
It consists of two beam-splitters (the square boxes, bottom left and top right) and two slivers of glass of different thickness which are inserted into each of the optical paths connecting the two beam-splitters. The slivers are usually referred to as "phase shifters" and their thicknesses, \varphi_0 and \varphi_1, are measured in units of the photon's wavelength multiplied by 2\pi. The two inputs ports of the interferometer are labelled as |0\rangle and |1\rangle, and each of the two output ports, also labelled as 0 and 1, terminates in a photodetector.46
A photon (the coloured dot in the figure) impinges on the first beam-splitter from one of the two input ports (here input 1) and begins its journey towards one of the two photodetectors. Let47 U_{ij} denote the probability amplitude that the photon initially in input port j=0,1 ends up in detector i=0,1. At each of the two beam-splitters the photon is transmitted with the probability amplitude \sqrt{T} and reflected with the probability amplitude i\sqrt{R}, with R+T=1, and the two phase shifters modify the amplitudes by phase factors e^{i\varphi_0} and e^{i\varphi_1}, respectively. In quantum theory we almost always start with the amplitudes, and once we have a full expression for the amplitude of a given outcome we square its absolute value to get the corresponding probability.
For example, let us calculate U_{00}. We notice that there are two alternative ways for the photon in the input port 0 to end up in the output port 0. It can take the lower path, through the phase shifter \varphi_0, or the upper path, through the phase shifter \varphi_1. The lower path implies two consecutive transmissions at the beam-splitters and the phase factor e^{i\varphi_0}, whereas the upper path implies two consecutive reflections and the phase factor e^{i\varphi_1}. Once the photon ends in the output port 0 there is no way of knowing which path was taken, thus we add the amplitudes pertaining to each path. The resulting amplitude is U_{00} = \sqrt{T} e^{i\varphi_0} \sqrt{T} + i\sqrt{R} e^{i\varphi_1} i \sqrt{R}, and the corresponding probability P_{00}=|U_{00}|^2 reads \begin{aligned} P_{00} & = \left\vert \sqrt{T}e^{i\varphi_0}\sqrt{T} + i\sqrt{R}e^{i\varphi_1}i\sqrt{R} \right\vert^2 = \left\vert Te^{i\varphi_0} - Re^{i\varphi_1} \right\vert^2 \\& = T^2 + R^2 - 2TR\cos(\varphi_1-\varphi_0). \end{aligned}
The "classical" part of this expression, T^2+R^2, basically says that the photon undergoes either two consecutive transmissions with probability T^2, or two consecutive reflections with probability R^2. The probability of being transmitted through any phase shifter is always 1, hence the phase shifters play no role in the classical description of this process. But the classical description is not correct, as the experiments show, whence the interference term 2TR\cos(\varphi_1-\varphi_0) in which the phase shifters play the essential role. Depending on the relative phase \varphi=\varphi_1-\varphi_0 the probability that the detector 0 "clicks" can vary from (T-R)^2, for \varphi=0, to 1, for \varphi=\pi.
If we do not care about the experimental details, we can represent the action of the Mach–Zehnder interferometer in terms of a diagram: see 3.6.
Figure 3.6: The Mach-Zehnder interferometer represented as an abstract diagram.
Here we can follow, from left to right, the multiple different paths that a photon can take in between specific input and output ports. The amplitude along any given path is just the product of the amplitudes pertaining to the path segments (Rule 1), while the overall amplitude is the sum of the amplitudes for the many different paths (Rule 2). You can, for example, see that the probability amplitude U_{10} is given by U_{10} = \sqrt{T}e^{i\varphi_0}i\sqrt{R} + i\sqrt{R}e^{i\varphi_1}\sqrt{T} and the corresponding probability is \begin{aligned} P_{10} & = \left\vert \sqrt{T}e^{i\varphi_0}i\sqrt{R} + i\sqrt{R}e^{i\varphi_1}\sqrt{T} \right\vert^2 \\& = 2RT + 2RT\cos(\varphi_1-\varphi_0). \end{aligned} Again, the first term is of "classical" origin and represents probabilities corresponding to each path: one reflection followed by one transmission plus one transmission followed by one reflection, that is, RT+TR=2RT. The second term is the interference term. Clearly, the photon entering port 1 will end up in one of the two detectors, hence, P_{00} + P_{10} = R^2 + 2RT + T^2 = (T+R)^2 = 1. The action of the interferometer is thus fully described48 by the four probability amplitudes U_{ij} (i,j=0,1).
The most popular instance of a Mach–Zehnder interferometer involves only symmetric beam-splitters (R=T=\frac12) and is fully described by the matrix U = \begin{bmatrix} -\sin\varphi/2 & \cos\varphi/2 \\\cos\varphi/2 & \sin\varphi/2 \end{bmatrix} where \varphi=\varphi_1-\varphi_0. In fact, when you do all the calculations49 you obtain ie^{i\frac{\varphi_0+\varphi_1}{2}}U rather than U, but the global phase factor ie^{i\frac{\varphi_0+\varphi_1}{2}} is common to all the amplitudes in the matrix and as such it does not contribute to the resulting probabilities.
To better understand why we don't worry about global phase factors, think about the eigenvalues of a matrix A and of the matrix \mu A, where \mu is a complex number with |\mu|=1.
Matrices form a vector space: you can add them, and you can multiply them by a scalar. One possible choice of a basis in the vector space of (2\times 2) matrices is the set of matrices \{M_{00},M_{01},M_{10},M_{11}\}, where the entries of M_{ij} are all 0 except for the ij-th entry, which is 1 (e.g. M_{01}=\begin{bmatrix}0&1\\0&0\end{bmatrix}). However, it turns out that there is a different basis which offers lots of insights into the structure of the general single-qubit unitary transformations, namely \{\mathbf{1},X,Y,Z\}, i.e. the identity matrix and the three Pauli matrices.50 We have already defined the Pauli operators in Chapter 2, but we recall their definition here along with a different notation that we sometimes use.
Identity \mathbf{1}= \begin{bmatrix}1&0\\0&1\end{bmatrix}
Bit-flip X\equiv\sigma_x = \begin{bmatrix}0&1\\1&0\end{bmatrix}
Bit-phase-flip Y\equiv\sigma_y = \begin{bmatrix}0&-i\\i&0\end{bmatrix}
Phase-flip Z\equiv\sigma_z = \begin{bmatrix}1&0\\0&-1\end{bmatrix}
Recalling Chapter 2, we know that the Pauli operators (as well as the identity operator) are unitary and Hermitian, square to the identity, and anti-commute.51
Any (2\times 2) complex matrix A has a unique expansion in the form \begin{aligned} A &= \begin{bmatrix} a_0 + a_z & a_x - i a_y \\a_x +i a_y & a_0 - a_z \end{bmatrix} \\&= a_0\mathbf{1}+ a_x \sigma_x + a_y \sigma_y + a_z \sigma_z \\&= a_0\mathbf{1}+ \vec{a}\cdot\vec{\sigma}. \end{aligned} for some complex numbers a_0, a_x, a_y, and a_z. Here, \vec{a} is a vector with three complex components (a_x, a_y, a_z), and \vec{\sigma} represents the "vector" of Pauli matrices (\sigma_x,\sigma_y,\sigma_z). The algebraic properties of the Pauli matrices can be neatly compacted (see the exercises) into a single expression:
The multiplication rule: (\vec{a}\cdot\vec{\sigma})\,(\vec{b}\cdot\vec{\sigma}) = (\vec{a}\cdot\vec{b})\,\mathbf{1}+ i(\vec{a}\times \vec{b})\cdot\vec{\sigma}.
We also introduce the inner product of two matrices:
The Hilbert–Schmidt product:52 (A|B) = \frac12 \operatorname{tr}A^\dagger B.
Recall that the trace of a square matrix A, denoted by \operatorname{tr}A, is defined to be the sum of the elements on the main diagonal of A, and defines a linear mapping: for any scalars \alpha and \beta, \operatorname{tr}(\alpha A+\beta B) = \alpha\operatorname{tr}A +\beta\operatorname{tr}B. Moreover, the trace is invariant under cyclic permutations: e.g. \operatorname{tr}(ABC) = \operatorname{tr}(BCA) = \operatorname{tr}(CAB). Note, however, that this does not imply that e.g. \operatorname{tr}(ABC)=\operatorname{tr}(ACB).
Now we can finish off what we started in Chapter 2: we know how single-qubit state vectors correspond to points on the Bloch sphere, but now we can study how (2\times 2) unitary matrices correspond to rotations of this sphere.
Geometrically speaking, the group of unitaries \mathrm{U}(2) is a three-dimensional sphere S^3 in \mathbb{R}^4. We often fix the determinant to be +1 and express (2\times 2) unitaries as U = u_0\mathbf{1}+ i(u_x\sigma_x + u_y\sigma_y + u_z\sigma_z). Such matrices form a popular subgroup of \mathrm{U}(2); it is called the special (meaning the determinant is equal to 1) unitary group, and denoted by \mathrm{SU}(2). In quantum theory, any two unitary matrices that differ by some global multiplicative phase factor represent the same physical operation, so we are "allowed to" fix the determinant to be +1, and thus restrict ourselves to considering matrices in \mathrm{SU}(2). This is a sensible approach, practised by many theoretical physicists, but again, for some historical reasons, the convention in quantum information science does not follow this approach. For example, phase gates are usually written as P_\alpha = \begin{bmatrix}1&0\\0&e^{i\alpha}\end{bmatrix} rather than P_\alpha = \begin{bmatrix}e^{-i\frac{\alpha}{2}}&0\\0&e^{\,i\frac{\alpha}{2}}\end{bmatrix} Still, sometimes the T gate T = \begin{bmatrix}1&0\\0&e^{i\pi/4}\end{bmatrix} = \begin{bmatrix}e^{-i\pi/8}&0\\0&e^{i\pi/8}\end{bmatrix} is called the \pi/8 gate, because of its \mathrm{SU}(2) form.
So let us write any (2\times 2) unitary, up to an overall phase factor, as U = u_0\mathbf{1}+ i(u_x \sigma_x + u_y \sigma_y + u_z \sigma_z) = u_0\mathbf{1}+ i{\vec{u}}\cdot{\vec{\sigma}} where u_0^2+|\vec{u}|^2=1. This additional unitarity restriction allows us to parametrise u_0 and \vec{u} in terms of a real unit vector \vec{n}, parallel to \vec{u}, and a real angle \theta so that53 U = (\cos\theta)\mathbf{1}+ (i\sin\theta){\vec{n}}\cdot{\vec{\sigma}}.
An alternative way of writing this expression is54 U = e^{i\theta {\vec{n}}\cdot{\vec{\sigma}}}, as follows from the power-series expansion of the exponential. Indeed, any unitary matrix can always be written in the exponential form as \begin{aligned} e^{iA} &\equiv \mathbf{1}+ iA + \frac{(i A)^2}{1\cdot 2} + \frac{(i A)^3}{1\cdot 2\cdot 3} \ldots \\&= \sum_{n=0}^\infty \frac{(i A)^n}{n!} \end{aligned} where A is a Hermitian matrix.
Writing unitary matrices in the form e^{iA} is analogous to writing complex numbers of unit modulus as e^{i\alpha} (the so-called polar form).
Now comes a remarkable connection between two-dimensional unitary matrices and ordinary three-dimensional rotations:
The unitary U = e^{i\theta \vec{n}\cdot\vec{\sigma}} represents a clockwise rotation through the angle 2\theta about the axis defined by \vec{n}. (N.B. 2\theta, not \theta).
For example, \begin{aligned} e^{i\theta\sigma_x} &= \begin{bmatrix} \cos\theta & i\sin\theta \\i\sin\theta & \cos\theta \end{bmatrix} \\e^{i\theta\sigma_y} &= \begin{bmatrix} \cos\theta & \sin\theta \\-\sin\theta & \cos\theta \end{bmatrix} \\e^{i\theta\sigma_z} &= \begin{bmatrix}e^{i\theta}&0\\0&e^{-i\theta}\end{bmatrix} \end{aligned} represent rotations by 2\theta about the x-, y- and z-axis, respectively.
Figure 3.7: e^{i\theta\vec{n}\cdot\vec{\sigma}} rotates the vector \vec{s} about \vec{n} by angle 2\theta, sending it to a point on the blue circle, whose centre is passed through by \vec{n}.
Now we can show that the Hadamard gate \begin{aligned} H &= \frac{1}{\sqrt 2} \begin{bmatrix} 1& 1 \\1 & -1 \end{bmatrix} \\&= \frac{1}{\sqrt 2}(\sigma_x + \sigma_z) \\&= (-i)e^{i \frac{\pi}{2} \frac{1}{\sqrt 2}(\sigma_x+\sigma_z)} \end{aligned} (which, up to the overall multiplicative phase factor of -i, is equal to e^{i \frac{\pi}{2} \frac{1}{\sqrt 2}(\sigma_x+\sigma_z)}) represents rotation about the diagonal (x+z)-axis through the angle \pi.
In somewhat abstract terms, we make the connection between unitaries and rotations by looking how the unitary group \mathrm{U}(2) acts on the three-dimensional Euclidian space of (2\times 2) Hermitian matrices with zero trace. All such matrices S can be written as S=\vec{s}\cdot\vec{\sigma} for some real \vec{s}, i.e. each matrix is represented by a Euclidean vector \vec{s} in \mathbb{R}^3. Now, U\in \mathrm{U}(2) acts on the Euclidean space of such matrices by S\mapsto S' = USU^\dagger, i.e. \vec{s}\cdot\vec{\sigma} \longmapsto \vec{s'}\cdot\vec{\sigma} = U(\vec{s}\cdot\vec{\sigma})U^\dagger \tag{$\ddagger$} This is a linear map \mathbb{R}^3\to\mathbb{R}^3, and is thus given by some (3\times 3) real-valued matrix: R_U\colon \mathbb{R}^3\to\mathbb{R}^3. We note that this map is an isometry (a distance preserving operation), since it preserves the scalar product in the Euclidean space: for any two vectors \vec{s} and \vec{v}, \begin{aligned} \vec{s'}\cdot\vec{v'} &= \frac12\operatorname{tr}[S'V'] \\&= \frac12\operatorname{tr}[(USU^\dagger)(UVU^\dagger)] \\&= \frac12\operatorname{tr}[SV] \\&= \vec{s}\cdot\vec{v} \end{aligned} (where S=\vec{s}\cdot\vec{\sigma} and V=\vec{v}\cdot\vec{\sigma}) using the cyclic property of the trace. This means that the matrix R_U is orthogonal.55
Furthermore, we can show56 that \det R_U=1. But the only isometries in three dimensional Euclidian space (which are described by orthogonal matrices with determinant 1) are rotations.
Thus, in the mathematical lingo, we have established a homomorphism57 \begin{aligned} \mathrm{U}(2) &\longrightarrow \mathrm{SO}(3) \\U &\longmapsto R_U \end{aligned} where \mathrm{SO}(3) stands for the special orthogonal group in three dimensions (the group of all rotations about the origin of three-dimensional Euclidean space \mathbb{R}^3 under the operation of composition). It is quite clear from Equation (\ddagger) that unitary matrices differing only by a global multiplicative phase factor (e.g. U and e^{i\gamma}U) represent the same rotation.
Physicists, however, usually prefer a more direct demonstration, which goes roughly like this. Consider the map \vec{s} \mapsto \vec{s'} induced by U=e^{i \alpha \vec{n}\cdot\vec{\sigma}}. For small values of \alpha, we can write \begin{aligned} \vec{s'}\cdot\vec{\sigma} &= U(\vec{s}\cdot\vec{\sigma}) U^\dagger \\&= \Big( \mathbf{1}+i\alpha (\vec{n}\cdot\vec{\sigma})+\ldots \Big) (\vec{s}\cdot\vec{\sigma}) \Big( \mathbf{1}- i\alpha(\vec{n}\cdot\vec{\sigma})+\ldots \Big). \end{aligned} To the first order in \alpha, this gives \vec{s'} \cdot\vec{\sigma} = \Big( \vec{s} + 2\alpha (\vec{n}\times\vec{s}) \Big) \cdot \vec{\sigma} that is, \vec{s'} = \vec{s} + 2\alpha(\vec{n}\times\vec{s}) which we recognise as a good old textbook formula for an infinitesimal clockwise rotation of \vec{s} about the axis \vec{n} through the angle 2\alpha.
Although this may all seem tediously abstract, it is surprisingly useful. Take another look at the single qubit interference circuit
and the corresponding sequence of unitary operations \begin{aligned} H \left( e^{-i\frac{\varphi}{2}Z} \right) H &= e^{-i\frac{\varphi}{2}X} \\&= \begin{bmatrix} \cos\varphi/2 & -i\sin\varphi/2 \\-i\sin\varphi/2 & \cos\varphi/2 \end{bmatrix} \end{aligned}
The single qubit interference circuit has a simple geometrical meaning: it shows how a rotation about the z-axis, induced by the phase gate P_\varphi, is turned, by the two Hadamard gates, into a rotation about the x-axis.
Now, take a look at this circuit:
What does it represent? The central part is a rotation by \varphi about the x-axis, but is it is sandwiched between two rotations about the z-axis. Now we have to appeal to your knowledge of classical mechanics: you may recall that any rotation in the Euclidean space can be performed as a sequence of three rotations: one about z-axis, one about x-axis, and one more about the z-axis. In this context, this implies that any unitary U, up to a global phase factor, can be written as \begin{aligned} U(\alpha, \beta, \varphi) &= e^{-i\frac{\beta}{2}Z} e^{-i\frac{\varphi}{2}X} e^{-i\frac{\alpha}{2}Z} \\&= \begin{bmatrix} e^{-i\left(\frac{\alpha+\beta}{2}\right)}\cos\frac{\varphi}{2} & ie^{i\left(\frac{\alpha-\beta}{2}\right)}\sin\frac\varphi{2} \\ie^{-i\left(\frac{\alpha-\beta}{2}\right)}\sin\frac\varphi{2} & e^{i\left(\frac{\alpha+\beta}{2}\right)}\cos\frac\varphi{2} \end{bmatrix}. \end{aligned}
Thus once you are given a couple of Hadamard gates and an infinite supply of phase gates, so that you can choose the three phases you need, you can construct an arbitrary unitary operation on a single qubit. Needless to say, the two axes in question, z and x, do not have any special status, geometrically speaking — if we have rotations about any two orthogonal58 axes then we can create any one-qubit unitary that we want.
Figure 3.8: If we can move along the two families of circles, then from any point on the sphere we can reach any other point. The two axes do not even have to be orthogonal: any two different axes will do. Can you see why?
Consider the following circuit:
where both A and B are unitary operations. We claim that any unitary U can be represented in this form.
Again, we can prove this geometrically. The circuit represents two rotations by 180^\circ about two axes obtained by rotating the z-axis with unitaries A and B, respectively. Any rotation in the three-dimensional space is the composition of two rotations by 180^\circ, as shown in Figure 3.9. The resulting axis of rotation is perpendicular to the two axes about which rotations by 180^\circ are performed, and the angle of the composed rotation is twice the angle between the two axes.
Figure 3.9: Rotating by \alpha around the z-axis is the same as the composition of two rotations by 180^\circ around axes which both lie in the xy-plane, with angle \alpha/2 between them.
The time evolution of a quantum state is a unitary process which is generated by a Hermitian operator called the Hamiltonian, which we also59 denote by H. The Hamiltonian contains a complete specification of all interactions within the system under consideration. In an isolated system, the state vector |\psi(t)\rangle changes smoothly in time according to the Schrödinger equation: \frac{\mathrm{d}}{\mathrm{d}t} |\psi(t)\rangle =-\frac{i}{\hbar} H |\psi(t)\rangle.
For time-independent Hamiltonians (i.e. where |\psi(t)\rangle=|\psi\rangle has no t-dependence), the formal solution of this reads60 \begin{gathered} |\psi(t)\rangle = U(t)|\psi(0)\rangle \\\quad\text{where}\quad U(t) = e^{-\frac{i}{\hbar}Ht}. \end{gathered}
Now, to relate this to the earlier parts of this chapter, we note that the Hamiltonian of a qubit can always be written in the form H = E_0\mathbf{1}+\omega(\vec{n}\cdot\vec{\sigma}), hence \begin{aligned} U(t) &= e^{-i\omega t \vec n\cdot\vec\sigma} \\&= (\cos\omega t)\mathbf{1}- (i\sin\omega t)\vec{n}\cdot\vec{\sigma} \end{aligned} which is a rotation with angular frequency \omega about the axis defined by the unit vector \vec n.
!!!TO-DO!!! the 4\pi world of qubits
Show that \{\mathbf{1},\sigma_x,\sigma_y,\sigma_z\} is an orthonormal basis with respect to the Hilbert-Schmidt product in the space of complex (2\times 2) matrices.
Recall that any (2\times 2) complex matrix A has a unique expansion in the form \begin{aligned} A &= \begin{bmatrix} a_0 + a_z & a_x - i a_y \\a_x +i a_y & a_0 - a_z \end{bmatrix} \\&= a_0\mathbf{1}+ a_x \sigma_x + a_y \sigma_y + a_z \sigma_z \\&= a_0\mathbf{1}+ \vec{a}\cdot\vec{\sigma}. \end{aligned} \tag{$\star$} for some complex numbers a_0, a_x, a_y, and a_z.
Show that the coefficients a_k (for k=x,y,z) are given by the inner product a_k = (\sigma_k|A) = \frac12\operatorname{tr}\sigma_k A.
In these notes, we usually deal with matrices that are Hermitian (A=A^\dagger) or unitary (AA^\dagger=\mathbf{1}). It is easy to see that, if A is Hermitian, then a_0 and the three components of \vec{a} are all real. The (2\times 2) unitaries are usually parametrised as U = e^{i\gamma}\Big(u_0\mathbf{1}+ i(u_x\sigma_x + u_y\sigma_y + u_z\sigma_z)\Big) where e^{i\gamma} is an overall multiplicative phase factor, with \gamma real, and u_0 and the three components u_x, u_y, u_z are all real numbers.
Show that the unitarity condition implies that u_0^2 + u_x^2 + u_y^2 + u_z^2 = 1 and show, using this parametrisation, that the determinant of U is e^{i2\gamma}.
Show that \frac12\operatorname{tr}(\vec{a}\cdot\vec{\sigma})(\vec{b}\cdot\vec{\sigma}) = \vec{a}\cdot\vec{b}. (You may find a certain identity involving the cross product helpful.)
Show that any \vec{n}\cdot\vec{\sigma} has eigenvalues \pm|\vec{n}|.
Show that, if \vec{n}\cdot\vec{m}=0, then the operators \vec{n}\cdot\vec{\sigma} and \vec{m}\cdot\vec{\sigma} anticommute.
Show that, if A^2=\mathbf{1}, then we can manipulate the power series expansion of e^{iA} into a simple expression: for any real \alpha, e^{i\alpha A} = (\cos\alpha)\mathbf{1}+ (i\sin\alpha)A.
Show that any (2\times 2) unitary matrix U can be written, up to an overall multiplicative phase factor, as U = e^{i \theta \vec{n}\cdot\vec{\sigma}} = (\cos\theta)\mathbf{1}+ (i\sin\theta)\vec{n}\cdot\vec{\sigma}. (The argument here is the same as the argument that e^{i\theta}=\cos\theta +i\sin\theta).
Show that \operatorname{tr}\sigma_x\sigma_y\sigma_z = 2i.
Consider U(\vec e_k\cdot\sigma_k)U^\dagger=U\sigma_kU^\dagger={\vec f_k}\cdot\vec\sigma. So U maps the unit vectors \vec e_x, \vec e_y, and \vec z_z, (along the x-, y-, and z-axis, respectively), to new unit vectors \vec f_x, \vec f_y, and \vec f_z. We already know that, in Euclidean space, this transformation is described by a (3\times 3) orthogonal matrix R_U. How are the three vectors \vec f_x, \vec f_y, and \vec f_z related to the entries in matrix R_U?
Show that \begin{aligned} \operatorname{tr}\sigma_x\sigma_y\sigma_z &= \operatorname{tr}({\vec f_x}\cdot\vec\sigma)( {\vec f_y}\cdot\vec\sigma)({\vec f_z}\cdot\vec\sigma) \\&= 2i\det R_U \end{aligned} (which implies that \det R_U=1).
Use the orthonormality of the Pauli basis along with Equation (\ddagger) to show that the elements of the matrix R=R_U can be expressed in terms of those of the matrix U, in the form R_{ij}=\frac12\operatorname{tr}\left(\sigma_i U\sigma_j U^\dagger\right). Here, i and j take values in \{1,2,3\}, and \sigma_1\equiv\sigma_x, \sigma_2\equiv\sigma_y, \sigma_3\equiv\sigma_z.
Show that the phase gate P_\varphi = \begin{bmatrix}1&0\\0&e^{i\varphi}\end{bmatrix} represents an anticlockwise rotation about the z-axis through the angle \varphi.
Hint. It might be helpful to start with the \mathrm{SU}(2) version of the phase gate: \begin{aligned} P_\varphi &= e^{-i\frac{\varphi}{2}\sigma_z} \\&= \begin{bmatrix} e^{-i \frac{\varphi}{2}}& 0 \\0 & e^{i \frac{\varphi}{2}} \end{bmatrix} \quad\longrightarrow\quad R \\&= \begin{bmatrix} \cos \varphi & -\sin \varphi & 0 \\\sin \varphi & \cos \varphi & 0 \\0 & 0 & 1 \end{bmatrix} \end{aligned}
Express the Hadamard gate H in terms of \vec{n}\cdot\vec{\sigma}, and show that \begin{aligned} HZH&=X \\HXH&=Z \\HYH&=-Y. \end{aligned}
Show that the Hadamard gate H turns rotations about the x-axis into rotations about the z-axis, and vice versa. That is, \begin{aligned} H \left( e^{-i\frac{\varphi}{2}Z} \right) H &= e^{-i\frac{\varphi}{2}X} \\H \left( e^{-i\frac{\varphi}{2}X} \right) H &= e^{-i\frac{\varphi}{2}Z}. \end{aligned}
In the Singapore Botanic Gardens, there is a sculpture by Ueli Fausch called "Swiss Granite Fountain". It is a spherical granite ball which measures 80cm in diameter and weighs 700kg, and is kept afloat by strong water pressure directed through the basal block. It is easy to set the ball in motion, and it keeps rotating in whatever way you start for a long time. Suppose you are given access to this ball only near the top, so that you can push it to make it rotate around any horizontal axis, but you don't have enough of a grip to make it turn around the vertical axis. Can you make it rotate around the vertical axis anyway?
A qubit (spin one-half particle) initially in state |0\rangle (spin up) is placed in a uniform magnetic field. The interaction between the field and the qubit is described by the Hamiltonian H = \omega \begin{bmatrix} 0 & - i \\i & 0 \end{bmatrix} where \omega is proportional to the strength of the field.61 What is the state of the qubit after time t=\pi/4\omega?
Note that gate B is not the same square root of \texttt{NOT} as the one described previously. In fact, there are infinitely many ways of implementing this "impossible" logical operation.↩
You can play around with a virtual Mach–Zehnder interferometer at Quantum Flytrap. (There are also lots of other things you can do in this virtual lab: go have a look!).↩
The two diagonal objects in the top-left and bottom-right corners of 3.5 are simply mirrors to make the two possible paths meet at the second beam-splitter.↩
We will often use i as an index even though it is also used for the imaginary unit. Hopefully, no confusion will arise for it should be clear from the context which one is which.↩
In general, any isolated quantum device, including a quantum computer, can be described by a matrix of probability amplitudes U_{ij} that input j generates output i. Watch the order of indices.↩
That is, when you write down the matrices describing the action of the symmetric beam-splitters and the phase gates, and then multiply them all together (which is an exercise worth doing).↩
In this chapter we are concerned only with the single-qubit Pauli operators. There are analogous multi-qubit Pauli operators, but be careful: these do not satisfy all the same properties! For example, anti-commutativity (explained below) is special to the single-qubit case.↩
\begin{aligned}XY+YX&=0,\\XZ+ZX&=0,\\YZ+ZY&=0.\end{aligned}↩
The \frac12 coefficient here is simply the normalisation factor, which changes if we consider multi-qubit Pauli operators.↩
As you can see, we often make progress and gain insights simply by choosing a convenient parametrisation.↩
Although this looks neat and tidy, the normal convention is to parametrise so that U=e^{i\frac{-\theta}{2}\vec{n}\cdot\vec{\sigma}}, and then the direction follows from the right-hand rule, and the rotation corresponds to that in the Bloch sphere. It is a useful exercise to show that you can write U in this way as well.↩
Orthogonal transformations preserve the length of vectors as well as the angles between them.↩
We can also see that \det R_U=1 from the fact that any matrix in \mathrm{U}(2) can be smoothly connected to the identity.↩
Recall that a homomorphism is a structure-preserving map between two algebraic structures of the same type, in our case two groups. An isomorphism between algebraic structures of the same type is one-to-one homomorphism.↩
In fact, even this condition isn't necessary! See Figure 3.8↩
Hopefully it will always be clear from the context which H refers to Hamiltonian and which H to Hadamard. Don't confuse the two!↩
Here \hbar denotes Planck's constant, which has the value \hbar = 1.05\times 10^{-34}\,\text{ Js}. However, theorists always choose to work with a system of units where \hbar = 1.↩
In Earth's magnetic field, which is about 0.5 gauss, the value of \omega is of the order of 10^6 cycles per second.↩


Apple and Samsung, for example, are betting on the wrist; Google, the face. A slew of tech companies believeclothing will simply become electronic. Yet there's a whole new segment of start-ups that believe all of the above are destined for failure and that we humans will become the actual computers, or at least the place where the technology will reside.
Many of these technologies don't look anything like today's gadgets. Instead, they are stretchable, bendable and incredibly thin. They can also be given unique designs, to stand out like a bold tattoo, or to blend in to the color of your skin.
While these wearables raise novel privacy concerns, their advocates say there are numerous benefits. Attachable computers will be less expensive to make, provide greater accuracy because sensors will be closer to a person's body (or even inside us) and offer the most utility, as something people won't forget to wear.
MC10, a company based in Cambridge, Mass., is testing attachable computers that look like small rectangular stickers, about the size of a piece of gum, and can include wireless antennas, temperature and heart-rate sensors and a tiny battery.
MC10 recently teamed up with John A. Rogers, a professor of materials science and engineering at the University of Illinois at Urbana-Champaign, who has been working for nearly a decade to perfect flexible devices that can be worn on the skin or implanted internally.
How would these gadgets work? Imagine being able to slap a few Band-Aid-size sensors to your body when you go for a run, then seeing a micro-level reading of your exercise on your phone.
Maybe you want to figure out which deodorant would be best for you. This would be done with a sticker that tracks your sweat level, then emails you a few brand recommendations. Or if you want to monitor your baby's breathing, you would stick a little sensor on the baby's chest that will alert you to any problems.
The health applications are enormous. Over the past year, Mr. Rogers and his team of scientists have been working with patients with Parkinson's disease to monitor their motions, dermatologists to treat skin diseases, and beauty companies like L'Oréal to develop digital stickers that track skin hydration.
Wearable-computer advocates are also giddy about the infinite style possibilities. "It turns out that the mechanics of these devices are 100 percent compatible with kids' standard temporary tattoos," Mr. Rogers said. Meaning, they can be made to look like tattoos, with each segment containing different sensors.
On a more futuristic front, scientists at the University of Tokyo have been working on an "e-skin," which, as you may have guessed, is an electronic skin that sits on top of real skin. It looks like a flexible and stretchable sheet of plastic wrap, yet contains lots of health-related sensors.
In another iteration of e-skin, scientists are working to add a layer of LEDs, turning it into a functional screen that sits on the body.
But don't throw aside your smartwatch or say goodbye to Google Glass just yet. It will be a while before our wearable future becomes known.


The Career Center is excited to announce a shift in job search technology coming to K-State for the 2017-2018 school year.
Traveling abroad during summer break is an exciting opportunity to visit new places, try exotic foods and see unique things. It can also be an excellent chance to expand your experiences in a way that can positively affect your career journey.


It is proposed to establish inverted indexing for ontology-annotated outputs when services are registered in order to find the target services in a quick, accurate and efficient way. For each ontology-annotated output, there is a service list which records all the services in the registry that deliver the output. Based on the indexing, a composition-oriented service discovery algorithm is proposed, which greatly accelerates the filtering of irrelevant atomic services by making use of the inverted indexing, and increases the likelihood of finding a possible candidate by exploring service composition. The results of the extensive experiments show that the proposed algorithm provides better performance on response time than the sequential matchmaking, and better recall rate than the algorithms without the exploration of composition.


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AYER, MA and PHILADELPHIA, PA February 15, 2019 – Cambrooke Therapeutics, a member of Ajinomoto Group, and Trovita Health Science, a specialty medical nutrition company, announce a joint marketing and development partnership for ENU® Nutrition meal replacement shakes.
PHILADELPHIA, PA January 30, 2019 – Trovita Health Science, a specialty medical nutrition company, announces the sale of SAFE-T FEED, an FDA cleared device for the administration of enteral nutrition formulas. The US FDA granted pre-marketing authorization for the device in March 2017. The all equity transaction was valued at $6.3 million, and the company received a return of equity shares and convertible securities in a cashless transaction.
PHILADELPHIA, March 20, 2017 –Trovita Health Science, an emerging life science company specializing in medical nutrition, announces U.S. Food and Drug Administration marketing authorization of the new SAFE-T FEED™ device for administering tube feeding formulas. The nutrition delivery device is a novel, ready-to-feed pouch offering the first and only fully-closed system, pre-packaged with complete enteral formulas.
PHILADELPHIA, December 20, 2016 –Trovita Health Science, an emerging life science company specializing in clinical nutrition innovation, announces the 510(k) submission for clearance of a new tube feeding system offering the first and only method for administering bolus or gravity tube feeding in a fully closed system, without the need for pouring formulas through a syringe, or utilizing an electronic pump system.
Minneapolis, M.N., February 22, 2016 –Trovita Health Science, an emerging life science company focused in clinical nutrition innovation appointed Dr. Harold Smith, molecular biologist and Professor at University of Rochester School of Medicine and Dentistry, as a senior advisor on Trovita's Scientific Advisory Board. Additionally, Dr. Smith is CEO of OyaGen, Inc., a Rochester, New York based pre-clinical biotechnology company focused on developing new mechanisms of action to treat and cure a spectrum of diseases, including a platform for HIV/AIDS, ebola virus, and oncology.
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Minneapolis, M.N., February 16, 2016 –Trovita Health Science, an emerging life science company specializing in clinical nutrition innovation, appointed Dr. Roscoe M. Moore Jr., former U.S. Assistant Surgeon General as Senior Scientific Advisor and member of Trovita's Scientific Advisory Board.
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'Exercise' is universally recommended as a core treatment for knee and hip osteoarthritis (OA). However, there are very few head-to-head comparative trials to determine the relative efficacy between different types of exercise. The aim of this study is to benchmark different types of exercises against each other through the use of a common comparator in a network meta-analysis of randomised controlled trials (RCTs).
This study will include only RCTs published in peer-reviewed journals. A systematic search will be conducted in several electronic databases and other relevant online resources. No limitations are imposed on language or publication date. Participants must be explicitly identified by authors as having OA. Interventions that involved exercise or comparators in any form will be included. Pain is the primary outcome of interest; secondary outcomes will include function and quality of life measures. Quality assessment of studies will be based on the modified Cochrane's risk of bias assessment tool. At least two investigators will be involved throughout all stages of screening and data acquisition. Conflicts will be resolved through discussion. Conventional meta-analysis will be performed based on random effects model and network meta-analysis on a Bayesian model. Subgroup analysis will also be conducted based on study, patient and disease characteristics.
This study will provide for the first time comprehensive research evidence for the relative efficacy of different exercise regimens for treatment of OA. We will use network meta-analysis of existing RCT data to answer this question.
Osteoarthritis (OA) is the most common form of arthritis, characterised structurally by focal articular cartilage loss, subchondral bone remodelling and changes in the synovium, capsule and periarticular tissues . The aetiology of OA is multifactorial, and its prevalence is higher in the elderly and in women . The knee joint appears to be more commonly affected than the hip . It is a major health burden and has been ranked 11th out of all common causes of disability globally . Patients with symptomatic OA may experience substantial reduction in quality of life (QoL), limitation in mobility and higher mortality and morbidity [4, 5].
In the absence of any definitive cure [6, 7], non-pharmacological therapy with adjunctive pharmacological analgesic use are the mainstay of management in knee and hip OA, with joint replacement surgery being reserved for severe disease that is resistant to conservative management [8, 9]. Pain-related limitation in physical activity and lower limb muscle weakness are common problems in knee and hip OA but are potentially reversible. Hence, exercise therapy is one of the core non-pharmacological therapies universally recommended for all patients with OA. Exercise therapy is as effective as pharmacological agents in providing symptom relief and functional improvement, but without the serious side effects associated with systemic analgesics .
Physical activity is defined as body movement that is produced by the contraction of the skeletal muscles and that increases energy expenditure, whereas exercise is planned, structured and repetitive movement to improve or maintain one or more components of physical fitness . Exercise has proven benefits in the various components of health-related physical fitness—defined by the American College of Sports Medicine (ACSM) to consist of cardiorespiratory fitness, body composition, muscular strength, muscular endurance and flexibility .
Exercise programmes are complex interventions that vary with exercise type, frequency, intensity and duration, as well as the mode of delivery (individual-group, supervised-unsupervised or facility-home-based). There is a common tendency to pool clinical trial data on exercise as an indistinct entity when formulating conclusions on exercise effects . Such results can be misleading because the effects of exercise can be moderated by the nature of the exercise programmes itself and by both patient and disease characteristics [14, 15].
Most exercise interventions for OA conventionally fall into one of the following physical performance categories: strengthening, aerobic, flexibility and skills/balance. In theory, the health benefits accrued are specific to the type of exercise. For example, aerobic activity to improve cardiorespiratory fitness can improve sleep and well-being and reduce all-cause mortality, whereas strengthening primarily improves local muscle function and proprioception to improve joint stability and local biomechanical functioning. However, there is evidence that both forms of exercise can reduce pain and improve function so both are recommended in most recent guidelines [8, 11, 16].
Other than strengthening or aerobic exercises, range of motion (ROM) exercise is also believed to be beneficial in improving symptoms and function. This is especially useful when functional and structural properties of periarticular soft tissue have been compromised following acute knee swelling or prolonged joint immobilisation . Other types of exercise that incorporates 'mind and body' components such as Tai Chi and Yoga are also gaining interest for its role in improving symptoms and function . It is possible that these may have additional benefits such as modulation of the inflammatory response  and reduction of central sensitisation in people with OA .
As a result, an increasing number of exercise options are being recommended [8–10]. However, relative efficacy of different exercises (in terms of pain reduction, improvement of function and quality of life) still remains largely unknown. More interestingly, whether different types of exercise can be tailored to individual patient characteristics to maximise the benefits of exercise therapy has yet to be investigated.
Considering the complexity of trial designs involving exercise, it is unlikely that primary research can satisfactorily provide a good overview relating to the efficacy of each individual exercise—at least not without incurring a huge demand in resources in order to perform multiple head to head comparison trials. For these reasons, the comparisons between the effects of various exercises may be examined more efficiently through a network meta-analysis (NMA) using existing clinical trial data.
NMA is a method which attempts to estimate the difference between two treatments (A and B) through a common comparator (C) when the direct evidence between these two treatments is not available . There may be several common comparators (nodes) shared by different treatments at different levels. When common comparators (nodes) are identified, treatments from different trials can be networked. We will then be able to estimate the relative effects of the different treatments (exercises in this case) against each other through these common comparators. In other words, the effects of different types of exercises in improving symptoms, function and quality of life of patients with knee and hip OA can be determined by integrating evidence from existing comparison trials.
This protocol is prepared conforming to Preferred Reporting Items for Systematic Reviews and Meta-Analyses Protocols (PRISMA-P) as closely as possible (Additional file 1).
Randomised controlled trials (RCTs) (including cross-over and cluster randomised trials) which examine the effects of exercise interventions in adults with knee or hip OA in all settings will be included. Studies will be considered as RCT if authors had explicitly stated that it is randomised  or when randomisation cannot be ruled out. Quasi randomised trials are excluded.
People with symptomatic OA of the knee and hip joint, diagnosed clinically (e.g. American College of Rheumatology Criteria), or radiographically (e.g. Kellgren Lawrence grading), or by the use of other imaging (e.g. magnetic resonance imaging) will be included. There is no restriction on the severity or stage of the disease. Hence, studies involving patients from early to 'end-stage' OA, including participants with pain following joint replacement, will be considered.
Studies using mixed disease categories from which the subgroup of knee and/or hip OA cannot be identified or fail to explicitly specify the joint condition as OA will be excluded. Arbitrarily, >80 % of joint replacement patients need to have their surgery attributed to OA in order for the study to be included .
Interventions that involve exercise prescribed in any form, such as strengthening exercise, aerobic exercise or mind-body exercise (e.g. tai-chi, yoga), will be eligible for inclusion. In instances where the term 'exercise' is not used by the investigators, any physical training that fulfils the basic characteristics of exercise (i.e. a structured programme which is repeated/practised on a regular basis, e.g. three times a week) will also be included. Single and combined interventions will be included, for example exercise, ±adjunct treatment versus a non-exercise intervention such as education, manual therapy or electrotherapy. Additional file 2: Table S1 shows how the pairwise comparisons from a study will determine its eligibility.
Strengthening/resistance exercise: exercise that aims to improve the muscle's ability to exert force and involves applying resistance against a contracting muscle.
Aerobic exercise: exercise that aims to improve cardiorespiratory fitness and involves repetitive movement of large muscle groups, performed at moderate to vigorous intensity for prolonged periods of time.
Flexibility exercise: exercise that improves the ability to move a joint throughout its range of motion and includes various types of stretching exercises.
Neuromotor exercise: exercise that improves motor skills such as balance and coordination.
Mind-body exercise: exercise that combines a physical exercise with meditation or mindfulness. The latter is defined as the intention to be aware and engaged in the present moment, i.e. attention on your breath and movements without disturbed by other issues . It is a set of mindful movements with a primary purpose of relaxation. The prototype of this exercise includes Tai Chi, Qi Chong and Yoga.
If the authors had not clearly identified the exercise element of interest, intervention that includes more than one category of exercise will be categorised as mixed exercise. Other components (such as home based versus class based) will be added to each if necessary to flag out the difference. Further classifications may be made as appropriate. SLG (a sports physician) and MH (a physiotherapist) will be involved in classifying the exercise interventions.
All comparators which have been used in the exercise trials will be included. However, for the purpose of the network meta-analysis, we need to include a common comparator across different exercises. The common comparator is defined as the comparator which had been used by at least two trials for two different exercises. These could be a no treatment/attention control, a waiting list control, a leaflet/education control, a 'sham' exercise or an active control (another type of exercise or intervention).
The primary outcome will be pain. Secondary outcomes will include self-reported function, objective measured function/physical test and QoL. Except for outcomes based on physical testing, a hierarchical selection of measurement scale following Fransen  and Regnaux  will be adopted if more than one scale is being used for the same outcome. However, a lower ranked scale may be given priority over a higher ranked scale if (i) it is more comprehensively reported in the study or (ii) if the direction of effect of the higher ranked scale is unclear.
For objective performance-based outcomes, a different consideration is used and may involve identification of the commonest physical test through 'vote counting'—i.e. the test that is reported by most studies. This is because no physical tests, either singly or in combination, have been deemed to be sufficiently investigated or robust to warrant any definitive recommendations for the assessment of physical function in hip and knee OA patients . Alternatively, if the correlations between the tests are known, we may consider pooling the results and generate only one effect size estimate. In the event of any discrepancies, a consensus will be sought within the research team.
If widely reported by authors, additional measurements such as structural, biomechanical or physiological parameters, including features on imaging (radiographs, magnetic resonance imaging, ultrasound), will also be included.
There is no pre-specified study endpoint for eligibility. Outcomes at different time points during the follow-up period will be recorded, and the commonest point across all trials will be used as a primary outcome point. Additionally, outcome points during follow-up will be grouped into intervals (e.g. ≤1 month, 1–3 months, 3–6 months, 6–12 months, 12–24 months etc.) for a secondary analysis for the time-dependent effect.
This meta-analysis aims to include all studies for exercise therapy in OA published in peer-reviewed journals. The following electronic bibliographic databases will be systematically searched from their dates of inception: Allied and Complementary Medicine Database (AMED), The Cochrane Central Register of Controlled Trials (CENTRAL), Cumulative Index to Nursing and Allied Health Literature (CINAHL), Excerpta Medica Database (EMBASE), MEDLINE, Physiotherapy Evidence Database (PEDro), PubMed, SPORTDiscus and Google Scholar. There will be no restrictions on languages. An example of MEDLINE search is shown in Additional file 3.
The reference lists of systematic review protocols published in Cochrane Library since 2014 will be used to supplement the electronic database search. Abstracts may be included if sufficient information for data extraction with/without risk of bias assessment is provided. Publications of study protocols will be flagged pending the full publication of the trial.
Preliminary screening is by title and abstract. Full text of potential citations will be retrieved for final screening and data extraction. Study selection will be done by one reviewer with the second reviewer performing periodical validations at random. A third reviewer will be involved if any discrepancies arise—i.e. if either one of the reviewer is unsure or could not agree with each other.
A structured database is created in Microsoft Access for data entry. In situation where studies are able to contribute two pairwise comparisons, data from four intervention groups will be extracted, and the study will be considered as two separate comparisons. Conversely, studies that have produced companion publications may be combined to maximise the yield of data.
When pairing of multiple groups cannot be performed satisfactorily (such as when there are three groups in a study), then combining groups may be considered. Supposing that all intervention groups are eligible for inclusion, exercise groups may be combined as a single group to be compared against a single control group. The reverse will also be done if two control groups are eligible but only one exercise group is available to contribute to the comparison. Calculation of the standard deviation for the composite group will be performed as described by Cochrane Handbook  (Additional file 4). If there is no clinical or practical justification to combine the groups as described, the intervention or the comparator that is deemed to be the simplest/commonest will be chosen instead. The decision for adopting either approach will be described and explained in the table of summary.
The following data will be extracted.
An abridged data extraction form (Additional file 5) will be used for data validation. The data extraction will be performed by one reviewer while the second reviewer will independently perform validation. Discrepancies in data will be resolved through discussion between the two reviewers. A third reviewer may also be involved if needed.
If the required data cannot be extrapolated from the published article, attempts will be made to contact the authors for additional information. Where this is not possible, we will use statistical imputations as appropriate. Details of imputations and assumptions used will be reported.
As calculation of standard deviation is one of the commonly encountered situations, calculations for transforming other forms of summary data to standard deviation (SD) have been listed in Additional file 4. In studies where insufficient information is provided for calculation, the SD may be substituted with the widest SD obtained from other eligible studies.
Approach in analysis will flow from meta-analysis (MA) to NMA and individual patient data (IPD) if the data are available. The MA aims to confirm/update the efficacy of different exercises, whereas the NMA aims to determine the relative efficacy between different types of exercises. The IPD meta-analysis aims to examine who responds better to a specific exercise—that is, to determine predictors of response. Data will be processed using various softwares such as Microsoft Access, Excel, Stata and WinBUGS/SAS.
For calculation of effect size, the unit of analysis is the mean (and standard deviation) of each trial. Demographic features of participants that were randomised to each group at the commencement of studies will be described. For the summary of effect, independent pairwise comparisons will be the unit of analysis. This is to say, if a study has four independent arms which can be paired, the study will contribute two effect size estimates to the meta-analysis. If a study has only three independent arms, only one effect size will be synthesise for the summary of effect estimate.
Results of different outcomes and at different time point will be reported separately. Any aggregation of data will be indicated and justified.
The effect size of continuous data (pain, functional outcome and QoL) will be based on standardised means difference, Cohen d. Whenever possible, the post-treatment mean score will be used for calculation of effect size. If this is not available, the mean change score will be used instead.
From Cohen d, a correction factor will be used to obtain the unbiased effect size (Hedges' g). Unless these effect sizes are available by default in the statistical software, calculations will be based on the equations listed in Additional file 4. Point estimates of effect size will be reported with its 95 % confidence interval for pairwise meta-analysis and 95 % credibility intervals for NMA.
An exercise that is able to deliver minimal clinically important difference (MCID) for the respective outcome of interest (e.g. 30 % improvement in visual analogue score from baseline, 20 % improvement in WOMAC function from baseline) will be deemed as effective . An exercise that is able to deliver a predefined MCID compared to another (e.g. difference of 1 score on numerical rating scale) will be considered as more efficacious.
Empirical methods to assess publication bias are not considered to be better than visual assessment of funnel plots . Hence, we will use funnel plot to investigate for publication bias which can be easily detected by presence of gaps in the plot. This scatter plot of study size against treatment effect will demonstrate a void at the lower left section of the graph if the assumption that studies with small sample size and non-significant effect size tend to go unpublished is true.
We will use chi-squared (χ2) test to examine homogeneity where level of significance is set at p < 0.1. To quantify the impact of the heterogeneity on the pooled estimates, we will use I2 statistics. The value of I2 indicates the magnitude of heterogeneity in the analysis and is interpreted as: 0–40 %—might not be important; 30–60 %—may represent moderate heterogeneity; 50–90 %—may represent substantial heterogeneity; and 75–100 %—considerable heterogeneity . Assessment of similarity and consistency of the estimate will be performed to ensure that the direct and indirect estimates agree. If the direct and indirect evidence agree, the estimates will be pooled to increase the power of the point estimates.
A modified Cochrane risk of bias assessment tool will be used to assess the quality of studies  (Additional file 6). This is an assessment tool that considers the various sources of biases by examining the methods of randomisation, concealment, blinding and handling of missing data. Response for each criteria will either be yes, no or unclear following the predefined guidelines as outlined in Additional file 6.
Was the randomization procedure adequate?
Were there more than 100 subjects in each treatment group?
Was the treatment allocation adequately concealed?
Were physicians blinded to the intervention?
Were patients blinded to the intervention?
Were outcome assessors blinded to the intervention?
Was incomplete outcome data adequately assessed?
Were the treatment and control group similar at baseline?
Are all pre-specified outcomes of interest reported in the pre-specified way?
Wherever a published protocol for the included study is available, it will be used as a supplementary source of information to enhance the quality assessment of the trial protocol. Again, the assessment will be performed by one reviewer with a second review performing random validation in a sample of the included studies. Quality criteria will be used for extended subgroup analysis.
ITT and adjusted results will be extracted whenever possible. If final scores and change from baseline score are both reported, preference will be given to the final score. For data that needs to be extracted visually from graphs, the readings will be rounded to the nearest 0.5.
Random effects model will be used for all analyses. If there are discrepancies between the direct estimates from MA and indirect estimates from NMA—if the 95 % confidence interval of the difference between the direct and indirect does not cross 0—we will consider the network inconsistent. Further analysis will be performed to identify the reason. However, the presence or absence of incoherence will not be determined solely on statistical method since this method is also subjected to statistical errors. Type I error (falsely assuming that there is direct and indirect evidence are inconsistency) can occur in a complex network because multiple tests have to be performed. Type II error (falsely assuming that the direct and indirect evidence are consistent) can happen when the dataset in the network is small . Hence, the statistical significance of inconsistency will be weigh against its clinical significance.
Other than assessing the discrepancy of the estimates, the NMA will also be able to assess the strength and diversity of the treatment network. Comparisons that are supported by a large number of RCTs can be distinguished from those that are informed by only a small number of RCTs.
One major advantage of using Bayesian approach in NMA is that it is able to produce a result for all comparisons in a connected network without the presence of a common comparator. But on the other hand, different prior distributions can be used which can generate different results, and therefore, a sensitivity analysis is always required. As prior knowledge on exercise efficacy is inconclusive, a non-informative prior will be used in our analysis. Posterior distributions of the model parameters will be utilised to present the results of the NMA.
In IPD predictive regression modelling, only clinically meaningful treatment and covariate interaction terms at study and patient level will be investigated . If sample size is deemed sufficient, different predictive model may be explored for different subgroups. To minimise loss of data, we will avoid dichotomizing continuous predictors for analysis —checks for linearity of predictor-outcome relationship will be performed during modelling. If there is a need to convert continuous predictor to categorical nature, this will be performed prior to data analysis. Multiple imputations may be used to address missing data.
Extended subgroup analysis will be performed based on the quality criteria of the study (sample size, blinding etc.), patient characteristics (age, BMI, gender etc.), disease (severity, joint involved etc.), exercise and comparator types. Other subgroup analyses will also be undertaken as appropriate.
Sensitivity analysis will be performed to ascertain if the results are robust. Situations where sensitivity analysis will be indicated include (i) imputations of missing data has been employed; (ii) when some arbitrary decisions have been made with respect to study selection, subgroup data aggregation/segregation; and (iii) when outlying studies are suspected. Small-study effect will be specifically assessed as smaller studies tend to report larger effect size and distort the summary estimates of meta-analysis .
Meta-regression will be used to assess the association of various covariates in the model. This includes adjusting for study level covariates such as mean age, gender ratio, sample size, allocation concealment, blinding, duration of treatment and type of exercise. Baseline severity of the disease such as pain score may be included as a covariate when the post-treatment score has been used for analysis in lieu of change score.
Exercise is the cornerstone of treatment for patients with lower-limb osteoarthritis. The results of this study will provide evidence on relative efficacy of different types of exercises in OA. It will also provide evidence on which patient subgroup responds better to what type of exercise. This information will help guide clinical practice to optimise exercise therapy in people with OA.
There are several caveats for this study. Firstly, classification of exercise will be based on whatever the included trials have reported. Exercise is a complex intervention, and there is often overlap between the specific elements involved in each exercise intervention. For example, strengthening exercises often progress to involve an aerobic component and aerobic exercise involving lower limb activity may result in strengthening of muscles relevant to knee OA. Therefore, it is very difficult to have a clear cut difference between different types of exercises.
Secondly, this is not a direct head to head comparative study. The relative efficacy between exercises will be estimated from a common comparator indirectly using a network meta-analysis. Variations between studies would affect the estimate. We therefore aim to use Bayesian statistics to increase the precision of the estimate. Even so, we cannot guarantee that the relative efficacy of the difference between exercises is a 100 % true value. Further head to head comparison may still be needed to confirm the results.
Thirdly, heterogeneity is an inherent problem in meta-analysis because of the diversity in clinical and methodological characteristics. These variations include different study time point, different grade of severity and duration of intervention. Therefore, we will focus on identifying the reason for the heterogeneity by performing sensitivity analyses and subgroup analyses. By doing this, we will be grouping studies that are more homogenous together to synthesise a more precise summary of effect.
Another approach to assess the impact of heterogeneity is through the use of IPD which provides the means to subgroup patients according to their characteristics. Some of these subgroup characteristics may be the source of heterogeneity that can be controlled at the IPD level. IPD can also overcome the limitations of study-level meta-regression where individual characteristics are all averaged. However, IPD has some common limitations. It only provides some but not all individual characteristics for subgrouping, and these characteristics often vary from one trial to another. As a result, only limited information can be obtained from an IPD analysis . Furthermore, getting the IPD data from published trials is extremely difficult. The response rate is often low; hence, the selection bias may be introduced when only selective data are made available for the IPD analysis. We will assess the impact of this bias on the estimate by using aggregate data as substitute in both 1-stage and 2-stage analyses for studies without IPD. Lastly, for both NMA and IPD, our search strategy is relying heavily on electronic resources; publication bias may not be avoided. We will therefore estimate this bias in the analysis.
We acknowledge the administrative support from colleagues from the ARUK Pain Centre and ARUK Sports, Exercise and Osteoarthritis Centre. We also like to thank Professor Mark E. Batt, Professor Lin Jianhao and Dr. Hou Yunfei for their academic input.
This study is funded by Arthritis Research UK Pain Centre. However, the funding body will not be involved in the design, data analysis, data interpretation or writing of manuscript for this study.
Data generated from this study will be included with the relevant publication in future, and request for additional data can be made to the corresponding author.
WZ conceptualised the study and its design and revised search strategy and manuscript. MD conceptualised the project and revised the search strategy and the manuscript. MH conceptualised the project and revised the search strategy and the manuscript. AB provided the input for the statistical analysis and revised the search strategy and manuscript. MSMP drafted the manusript and designed the data extraction sheet. SLG drafted the manuscript and designed the search strategy and data extraction sheet. All authors reviewed and approved the manuscript for publication.
WZ is a Professor in Musculoskeletal Epidemiology.
MD is a Professor in Rheumatology and head of Academic Rheumatology Department.
MH is an Assistant Professor in Division of Physiotherapy and Rehabilitation Sciences.
AB is a Research fellow affiliated to ARUK Sports, Exercise and Osteoarthritis Centre.
MSMP, PhD, is a student funded by ARUK Pain Centre.
SLG is a Sports physician and PhD student funded by the Malaysian Ministry of Higher Education and University of Malaya.
Centers of Disease Control and Prevention. Disabilities and Limitations. Available from: http://www.cdc.gov/arthritis/data_statistics/disabilities-limitations.htm. Accessed 12 Feb 2016.
Singh JA, Tugwell P, Zanoli G, Wells GA. Total joint replacement surgery for knee osteoarthritis and other non-traumatic diseases: a network meta-analysis. Cochrane Database Syst Rev. 2015;(6). Art. No.: CD011765. doi:10.1002/14651858.CD011765.
Fransen M, McConnell S, Harmer AR, Van der Esch M, Simic M, Bennell KL. Exercise for osteoarthritis of the knee. Cochrane Database Syst Rev. 2015;(1). Art No.: CD004376. doi:10.1002/14651858.CD004376.pub3.
Regnaux JP, Lefevre-Colau MM, Trinquart L, Nguyen C, Boutron I, Brosseau L, Ravaud P. High-intensity versus low-intensity physical activity or exercise in people with hip or knee osteoarthritis. Cochrane Database Syst Rev. 2015;(10). Art No.: CD010203. doi:10.1002/14651858.CD010203.pub2.
Higgins JPT, Green S (editors). Cochrane handbook for systematic reviews of interventions version 5.1.0 [updated March 2011]. The Cochrane Collaboration. 2011. Available from www.cochrane-handbook.org.


text:
MCPL's Camden Point & Dearborn Branches Reopen
Published on Mon, 03/25/2019 - 07:26am
Mid-Continent Public Library is pleased to announce the completion of renovations at its Camden Point Branch (401 Hardesty St., Camden Point, MO 64018) and Dearborn Branch (206 Maple Leaf Ave., Dearborn, MO 64439), which both reopened to the public on January 22. An official Rededication Ceremony will be held at the Camden Point Branch on Friday, March 29, at 9:00 a.m. and at the Dearborn Branch on Friday, March 29, at 11:00 a.m. Each will include remarks from Library leadership as well as local officials, followed by a ribbon-cutting ceremony and reception.
"It's such an honor to be able to celebrate these improvements with the people who made it all possible―our community members!" said Tiara Dixon, manager of MCPL's Camden Point, Dearborn, and Edgerton Branches. "Residents reaffirmed their commitment to the Library when they passed Proposition L in 2016―making all these upgrades possible―and now the Library has demonstrated its commitment to our communities by reinvesting in our buildings as well as our resources and services."
In addition to the Rededication Ceremonies, the Camden Point and Dearborn Branches will each host an Open House on Saturday, March 30. The Dearborn open house will kick off at 10:00 a.m. on Saturday with live entertainment from juggler Brian Wendling at 10:30, and the Camden Point open house will begin at 1:00 p.m. with performances by KC Magic Man Brad Lynn. Both will also include refreshments, a selfie station, and an appearance from the Library's mascot, Marty the Martian.
At the ceremony on Friday and throughout the day on Saturday, the branches will give away special commemorative tokens (one per person) that can be used one time to clear all Library fines and fees up to $10. In addition, the Library will offer a mobile scavenger hunt through the free GooseChase app, which customers can participate in to qualify for a $50 gift certificate to Trex Mart. The Camden Point and Dearborn Branches Scavenger Hunt will kick off at the rededication ceremonies on March 29 and run through April 5 at 6:00 p.m.
Since the Camden Point and Dearborn Branches closed on November 8, they have each received a variety of interior and exterior upgrades, including new outdoor seating areas as well as upgraded technology, such as new computers and improved Wi-Fi coverage and access.
As part of MCPL's Capital Improvement Plan, the Camden Point and Dearborn Branches are two of many Library branches to receive upgrades, which have been made possible by increased funding from the passage of Proposition L by voters in 2016. While the upgrades at each branch vary based on individual community needs and the building's current condition, the Library's goal has been to create more intentional spaces and improve essential technology. Design work for the five-year Capital Plan is being completed by Sapp Design Architects and Helix Architecture + Design with JE Dunn assuming responsibility for construction contractor management.
In addition to all the physical upgrades, the increased funding approved by voters in 2016 has allowed MCPL to expand branch hours, enhance special services, augment early literacy efforts, and buy more materials.
More information about both reopening ceremonies can be found on each branch's page on mymcpl.org/Community.
Welcome Back to Your Reimagined Library
In recent months, the team at MCPL has been welcoming customers back to the first branches to be r
MCPL Opens Farview Neighborhood Library
As a way to better serve customers who live and work in eastern Independence, Mid-Continent
MCPL to Help Residents During 2020 Census
By April 1, 2020, all homes in America should receive a mailed invitation to participate in the 2020 Cen
Excelsior Springs Branch Reopens, Ribbon Cutting on Dec. 5
Mid-Continent Public Library is pleased to announce the completion of renovations at its Excelsior

redpajama_set_name: RedPajamaCommonCrawl


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text:
You're nothing but a pack of libertarian bloggers!
From Megan McArdle:
The other reason I don't necessarily trust elites is that they really like thinking big.
McArdle jumps on the newest right-wing meme, that the liberal elite are destroying America. This is after The Atlantic and Time and The New America Foundation got together and decided to promote McArdle as one of the nation's elite Big Thinkers.
Pfffft. It's useless. We're in Wonderland and we'll never wake up.
Which, of course, is so much better than thinking in black and white the way libertarians do.
Jesus God, the comment section.
It's like a big game of "why do you keep hitting yourself?"
Freshly Squeezed Cynic said...
Two thoughts and an obvious joke:
Thought 1: Megan "Argument from authority be the only argument I know" McArdle doesn't trust elites?
Thought 2: Does anyone - anyone - of sound mind consider the greatest failing of the American political class to be that they try to implement large-scale, radical plans as part of a grand, sweeping statement of intent and belief?
Obvious Joke: No-one can accuse McMegan of thinking big. She's one of the most small-minded people I've had the misfortune to read.
So, to MegaleBargle everyone "thinks big"?
Is she thinking of the interlinked Multi-national corporations openly trying to buy the election? They are thinking "big", all right.
More likely she means Liberals who want us to keep Social Security and Medicare; maybe even extend it to more people.
NonyNony said...
Jesus farking Christ. This woman is someone who is paid to write her opinions on business and politics for a political magazine. She got her undergrad degree at Penn and she has an MBA from Booth. And she's hating on "elites"?
I know she's mendacious, writes anything for money, and will latch on to whatever right-wing meme comes along and shout it from the rooftops, but even this is too much. I can't believe that she's just lying here - she has to be an idiot. Anyone who is as privileged as McArdle, and who is as lucky as McArdle and doesn't recognize that they are sitting among the elites is an idiot. Anyone who does recognize where they're sitting and still hatemongers against elites is also an idiot.
Either way I've now finally found my conclusive evidence. I've wondered for a long time if McArdle was just a liar who was willing to write anything - no matter how stupid - for the money, or if she was an idiot. This answers my question.
bulbul said...
Oh fuck me, she cites Douthat. And according to Douthat, Czech Republic, Austria and Germany are in Northern Europe.
I like this bit:
But the same figure for Britain (where Rush Limbaugh has relatively few listeners, I believe) was 48 percent
True, very few people listen to Rushbo in Britain. But Tokyo Rose Limbaugh is merely the loudest loudspeaker in the US; in Britain and elsewhere in Europe, conservatives have other outlets through which they influence the public, ehm, debate. In the Czech Republic, for example, the loudest voice for climate change denial is Václav Klaus, the motherfucking president of the country.
bulbul - I haven't gotten out of the boat, she (or Douthat) really says that?
Fuccccccccccccck, that's stupid, I mean, all you have to do is google "Melanie Phillips" or "Richard Littlejohn" to realise we Brits have our loathsome, scumsucking conservatives, too.
FSC,
those are Douthat's words. Stay in the boat, the stupid is strong with this one.
Nony,
She does footnote her post with the following:
"Yes, I am construing the word 'elite' broadly enough to include myself in it, as well as thousands of other people who make their living thinking about how we ought to run the country."
The irony of this being that, despite the education and upbringing she's so readily willing to brag about, she's an utterly mediocre, uninteresting, incurious person completely lacking in intelligence. If this person is considered one of the best "thinkers" in the US, then all that stuff grandpa used to moan about the place going to hell in a handbasket is genuinely true.
"I don't trust the big thinking elite although I am a member of the big thinking elite."
I will never understand why she thinks admitting a conflict of interest negates that conflict of interest.
Since one of her core, oft-repeated principles is that nobody can know anything about anything ever at any time, of course she's afraid of "elites" who "think big".
After all, "elites" might make her pay taxes, or register her car, or buy stamps, or some similarly tyrannical thing.
Clever Pseudonym -
That makes it worse because it sticks her firmly in the "I know I'm an elite but here's why you should hate elites" camp. Which is incredibly idiotic. You can get away with that kind of thing if you truly pulled yourself into the elite by your own bootstraps and sweat (see Nixon,Dick) or if you've stagemanaged your image to make people think you did (see Limbaugh,Pompous Boil on the Ass of Humanity).
But when you're a child of privilege, whose parents made sure you got every available opportunity when you were growing up, who got into college on the backs of your parents money, who has a job that you are obviously unqualified for, and whose own writing shows you to be an snob of the highest caliber, you are playing with fire when you're rousing the rabble into hating elites. The rabble aren't really stupid - eventually they will notice.
The thing about her snobbery and belief that she's genuinely a part of the elite is that it constantly manifests itself into her talking down her nose to her readers. She really does think she's so much smarter than most of us and that we're all so stupid and in need of her advice and guidance, she thinks she can get away with writing on stuff she knows absolutely nothing about, and that the rest of us little people will just be too dumb and ignorant to notice. I find that absolutely infuriating.
Though I'm lauging, picturing of one of her sycophants who actually eats her bloviating BS up, attempting to make mashed potatoes for the first time by boiling them in milk, per her recipe advice.
She really does think she's so much smarter than most of us and that we're all so stupid and in need of her advice and guidance, she thinks she can get away with writing on stuff she knows absolutely nothing about, and that the rest of us little people will just be too dumb and ignorant to notice.
That right there, a perfect description of nearly every journalist and pundit, especially those of the right-wing political slant.
"Boil potatoes in milk"? hmmm. I wonder if she boils spaghetti in spaghetti sauce- it might save time you know!
The Day The Brain Stood Still
Civil Discourse In The Age Of Unreason
The Wisdom Of The Marketplace
The Good German
I Know I Had A 2x4 Around Here Some Place---
Whom Do We Trust? What Is The Moral Thing To Do?
The Most Important Person In The History Of The World
Ignorance Is Bliss (II)
Shorter Megan McArdle: Life Is Wonderful
Bless Her Heart
Helping The Helpless
The Real Scandal
Why We Can't Have Nice Things
Argument By Assertion
Why Do Journalists Lie?
Sonnet #29 and 1/2
Women Who Stare At Men Who Stare At Goats
Trivial Nothings
Good Night And Good Luck
Defining Prosperity Downwards
K-Lo Goes To Confession: Another Brick In The Wall...


Socialist, trade unionist, and bitter critic of the Congress, Fernandes was, to those who didn't know him, a complex bundle of complex contradictions. He began life in Mangalore in a – relatively – middle-class Catholic family, and if life had led him where it wanted him to go, he would have become a priest. But being George Fernandes, he fought traditional trajectories. He got associated with the Socialist movement which itself was going through a trauma. Stalin's excesses and the resistance in Poland and Czechoslovakia had fired the Socialist imagination – Fernandes's too. At home, India's resounding defeat in the war against China had led to a split in the Communist movement and the branding of China as India's enemy number one. Indian Socialists might have been internally divided but they avoided the intellectually lazy trap of nationalism and instead embraced internationalism. As a member of the Socialist international, Fernandes absorbed and gave to the socialist movement ideas from India as he rubbed shoulders and discussed problems of society, class, democracy and international unequality with greats such as Olaf Palme of Sweden and Bruno Kriesky of Austria (both called for his release during the Emergency). In a sense, when Fernandes became a minister for the second time in the Atal Bihari Vajpayee government in 1998, he was, in an alliance of largely inward-looking forces, the only internationalist.
His opposition to the Congress brought him in close vicinity to the BJP and he defended his partner, even while disagreeing with the party on several issues. This was another side to Fernandes's famed duality. The attack on Christian missionary Graham Staines, his murder and killing of his two little sons in Orissa by a mob led by Bajrang Dal member Dara Singh saw Fernandes giving an extraordinary exculpation to the BJP (and the incident itself). He attributed the event to an international conspiracy mounted by those who wanted the BJP government in power at the Centre, to go. He saw no blame to the BJP, its Rath Yatra or the build-up of communal fervour in the events leading up to the demolition of the Babri Masjid. Instead, he charged that it was the Congress which was the biggest communalist, and had aided and abetted riots as a way of reminding minorities that they needed to be in its thrall or suffer the consequences. It was a point of view. Fernandes had had time to refine this view – he brought together disparate forces in Delhi and elsewhere by launching a loose group of civil liberty groups to protect Sikh families in the aftermath of Indira Gandhi's assassination.
Almost everything about his life is known – both as a prisoner during the emergency, the most enduring image being his raising his manacled shackled wrists when he was produced in court – his escape, disguised as a Sikh, the famous Bombay strike and the Baroda dynamite case (in which he was charged as a conspirator but the charges dropped when the Janata Party came to power).
But it is in his second coming as Minister of defence in successive Atal Behari Vajpayee governments that Fernandes really came of age. He left the strategic part of thinking of defence to his colleague and friend Jaswant Singh – except writing a letter to US president Bill Clinton in which he claimed that India had conducted the nuclear tests because its wanted to stay safe against enemy number one, China – a claim he later denied though no one was convinced. Instead, he did what came to him most easily – working on the 'soft' side of the defence, welfare of officers and the jawans. The armed forces scheme for health is Fernandes's contribution. His visits to Siachen made him one of the most visible, easily identified and beloved defence ministers in India's history, especially among the jawans.
Ironically, always the one to stand up for the underdog, Fernandes proceeded against and sacked Adm Vishnu Bhagwat, Chief of Naval Staff when as Chief, Bhagwat recorded that the elevation of one of his colleagues, recommended by the Cabinet, was a decision that was 'unimplementable'. Some 'corruption scandals' were reported during his ministership, but they rested on flimsy grounds: and the courts acquitted him in all.
Fernandes had to leave his Krishna Menon Marg (which had no gate – that he had broken and dismantled as a political statement) when his family reclaimed him after a long hiatus, the Congress came to power and he had lost the elections. Along with the house, had to go his dogs and his family of refugees who lived there – Burmese, Tibetans, Tamils, Manipuris and others. He fell and suffered a stroke, was diagnosed with Alzheimer's Disease and gradually could not recognize anyone. In his passing, many will mourn him – even those who disagreed vehemently with him.


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