Blitiri

Structural Analysis of Colloidal Titania-Based Ribbons and Their Self-Assembly upon Drying

2025-04-23T10:45:00.004+02:00

Our paper has been published in Small Structures!

Synchrotron-based small- and wide-angle X-ray scattering is used to elucidate the structure of low-dimensional lepidocrocite–titanate-based nanofilaments. In the colloidal state, they consist of quantum-confined 1D NFs, loosely associated into nanoribbons, one lepidocrocite sheet thick (about 4 Å), 30–40 Å wide (5–8 NFs), and more than 300 Å long. In the dry state, they reach a final state of extended sheets, stacked three to about twenty high, whose crystallinity increases with stack height, in parallel with a decrease in photocatalytic activity. These findings suggest a kinetic pathway for the self-assembly of initially 1D titanate nanoribbons into 2D and ultimately 3D structures, providing context for a recent body of work on these low-dimensional materials.

Two-Step Reshaping of Acicular Gold Nanoparticles

2025-01-14T14:50:00.000+01:00

Our paper has been published in Nano Letters!

Anisometric plasmonic nanoparticles find applications in various fields, from photocatalysis to biosensing. However, exposure to heat or to specific chemical environments can induce their reshaping, leading to loss of function. Understanding this process is therefore relevant both for the fundamental understanding of such nano-objects and for their practical applications. We followed in real time the spontaneous reshaping of gold nanotetrapods in solution via optical absorbance spectroscopy, revealing a two-step kinetics (fast tip flattening into {110} facets, followed by slow arm shortening) with characteristic times a factor of 6 apart but sharing an activation energy around 1 eV. Synchrotron-based X-ray scattering confirms this time evolution, which is much faster in solution than in the dry state, highlighting the importance of the aqueous medium and supporting a dissolution–redeposition mechanism or facilitated surface diffusion. High-temperature transmission electron microscopy of the dry particles validates the solution kinetics.

CNRS positions - the 2024 campaign

2024-01-11T17:28:00.002+01:00

The 2024 campaign for permanent research positions at the CNRS (Centre national de la recherche scientifique) is open (see the submission site). The deadline is February 9th 2024 (13:00 Paris time). There are 254 open positions at the CR level, 314 for DR2 and 1 for DR1, as detailed here. The official texts are here: CRCN, DR2, DR1 and the evolution of these numbers over the last twenty years is shown in the graph below:

Good luck to all the candidates!

Shedding Light on the Birth of Hybrid Perovskites

2023-10-10T14:57:00.000+02:00

Our paper has been published in Chemistry of Materials!

We combined synchrotron SAXS and environmental TEM to reveal the pathway leding from precursors to MAPI perovskites. This result was also featured on the cover.

Confinement Effects on the Structure of Entropy-Induced Supercrystals

2023-07-01T11:27:00.001+02:00

Our paper has just been published in Small. Using LCTEM we were able to follow the desorption kinetics of gold nanoparticles from a 2D supercrystal deposited on a solid substrate.

The time and dose dependence of the process reveals that the desorption is due to loss of adhesion between the particles and the substrate, presumably due to charge buildup under the electron beam.

de Gennes narrowing

2023-04-28T12:07:00.003+02:00

In colloidal solutions, a widely-used relation connects the scale-dependent collective diffusion constant and the structure factor:
\begin{equation}
D_c(q) =\frac{D_0}{S(q)}
\label{eq:dGn}
\end{equation} and is generally known as de Gennes narrowing since its use by de Gennes in the context of quasi-elastic neutron scattering from liquids [1].

Intuitively, equation \eqref{eq:dGn} makes sense: if \(S(q)\) is high for a certain value of \(q\) then fluctuations with that particular \(q\) are frequent, meaning that their energetic cost is low and that they will decay slowly. However, I have not yet found in the literature a simple yet rigorous derivation. This is what I will attempt below.

Consider a system characterized by a conserved scalar parameter \( \phi(\mathbf{r})\) (for instance, the local particle concentration in a suspension \( \phi(\mathbf{r}) = \rho(\mathbf{r}) - \rho_0\), with \(\rho_0\) the equilibrium value). We are interested in the excess free energy due to inhomogeneities of this field: \(\mathcal{F} - \mathcal{F}_0 = \mathcal{F}[\phi(\mathbf{r})]\) or, in terms of its Fourier components: \(\mathcal{F} - \mathcal{F}_0 = \mathcal{F}[\phi(\mathbf{q})]\).

For an isotropic system in the absence of applied fields, all fluctuations \( \phi(\mathbf{q})\) with \( \left |\mathbf{q} \right | > 0\) will eventually decay to zero. To fix the ideas, we will consider an overdamped relaxation (model B in the Hohenberg-Halperin classification [2], but of course far from criticality).

Let us write Fick's laws, with \( \mathbf{j} \) and \( \mu\) the current and chemical potential associated to \( \phi\) (this is similar to the presentation in [2], Eqs. (2.2)-(2.9)):
\begin{equation}
\label{eq:defs}
\frac{\partial \phi(\mathbf{r},t)}{\partial t} = - \nabla \mathbf{j} \, ; \quad \mathbf{j} = - \lambda \nabla \mu \, ; \quad \mu = \frac{\delta \mathcal{F}}{\delta \phi(\mathbf{r},t)} \, \Rightarrow \, \frac{\partial \phi(\mathbf{r},t)}{\partial t} = \lambda \nabla ^2 \frac{\delta \mathcal{F}}{\delta \phi(\mathbf{r},t)}\end{equation} where \( \delta\) denotes the functional derivative. The second relation in \eqref{eq:defs} serves as a definition for the transport coefficient \(\lambda\).
Introducing the Fourier components yields: \begin{equation}
\label{eq:relax}
\frac{\partial \phi(\mathbf{r},t)}{\partial t}= \lambda \nabla ^2 \frac{\delta \mathcal{F}}{\delta \phi(\mathbf{r},t)} \Rightarrow \frac{\partial \phi(\mathbf{q},t)}{\partial t} = - \lambda q^2 \frac{\text{d} \mathcal{F}}{\text{d}\phi(\mathbf{q},t)}
\end{equation} If the different Fourier modes are uncoupled, we can write the equipartition relation:
\begin{equation}
\label{eq:equi}
\mathcal{F} = \mathcal{F}_0 + \sum_{\mathbf{q}} \frac{A(\mathbf{q})}{2} |\phi(\mathbf{q})| ^2 \Rightarrow \frac{\text{d} \mathcal{F}}{\text{d}\phi(\mathbf{q},t) } = A(\mathbf{q}) \phi(\mathbf{q})
\end{equation} Let us introduce the time-dependent structure factor \begin{equation}
\label{eq:Sqt}
S(\mathbf{q},t) = \left \langle \phi(\mathbf{q},t) \phi(\mathbf{-q},0) \right \rangle
\end{equation} with \( \left \langle \cdot \right \rangle\) the ensemble average.

Plugging \eqref{eq:equi} into \eqref{eq:relax}, multiplying by \(\phi(-\mathbf{q},0)\) and averaging yields the evolution of mode \(\mathbf{q}\): \begin{equation}
\label{eq:evol}
\frac{\partial}{\partial t} \left \langle \phi(\mathbf{q},t) \phi(-\mathbf{q},0) \right \rangle =- \lambda q^2 A(\mathbf{q}) \left \langle \phi(\mathbf{q},t) \phi(-\mathbf{q},0) \right \rangle \Rightarrow \frac{S(\mathbf{q},t)}{S(\mathbf{q},0)} = \exp \left \lbrace - D_c(q) q^2 t \right \rbrace
\end{equation} where we invoked the isotropy of the system. The collective diffusion coefficient is given by: \begin{equation}
\label{eq:Dc}
D_c(q) = \lambda A(q)
\end{equation} On the other hand,equipartition also implies: \begin{equation}
S(\mathbf{q}) = S(\mathbf{q},0) = \left \langle \phi(\mathbf{q},0) \phi(\mathbf{-q},0) \right \rangle = \frac{k_B T}{A(\mathbf{q})} .
\label{eq:Sq}
\end{equation} From \eqref{eq:Dc} and \eqref{eq:Sq} we finally obtain:
\begin{equation}
\label{eq:final}
D_c(q) = \frac{\lambda k_B T}{S(q)}
\end{equation}
[1] P. G. de Gennes, Liquid dynamics and inelastic scattering of neutrons, Physica A 25, 825-839 (1959).
[2] P. C. Hohenberg and B. Halperin, Theory of dynamic critical phenomena, Rev. Mod. Phys. 49, 435-479 (1977).

Power laws in small-angle scattering - part II

2023-04-27T15:39:00.001+02:00

In the first part I showed that the SAXS intensity scattered by a platelet system goes like \( I(q) \sim q^{-2}\), at least in some intermediate (but as yet unspecified) q range. Here I will show that for thin rods this dependence becomes \( q^{-1}\), I will then derive the terminal (Porod) behaviour \( q^{-4}\) and briefly consider the transition between these two regimes.

Rods: α = 1

For a rod, the Patterson function:
\[ P (\mathbf{r}) = \delta(x) \delta(y) \mathrm{Cst}(z)\] with the same notations as in part I. Its Fourier transform, and thus the intensity, are then given by \(I(\mathbf{q}) = \tilde{P} (\mathbf{q}) = \mathrm{Cst}(q_x) \mathrm{Cst}(q_y) \delta(q_z)\). The "dual" object of a rod under Fourier transform is a platelet:

Fourier transform of a rod.

When spreading this intensity over reciprocal space we must keep in mind that the intersection of the plane with a sphere of constant \(q\) is a great circle (shown in red in the figure above). Thus, the total contribution \( 2 \pi q I_0\) increases with \(q\), but it must also be divided by the surface area of the sphere, yielding for the two spheres: \[ I(q_0) = \frac{2 \pi q_0 I_0}{4 \pi q_0^2} = \frac{I_0}{2 q_0} \quad \mathrm{and} \quad I(2 q_0) = \frac{4 \pi q_0 I_0}{4 \pi (2 q_0)^2} = \frac{I_0}{4 q_0} \] so that \( I(2 q_0) = I(q_0) /2\) and \( \alpha = 1\).

Interfaces: α = 4 (Porod)

This case is a bit more complicated, since \(P(\mathbf{r})\) diverges for all \(\mathbf{r}\). We will thus work with the density profile of an interface, which is invariant under \(x\) and \(y\) translations and is a Heaviside (step) function along \(z\): \[ \rho (\mathbf{r}) = \mathrm{Cst}(x) \mathrm{Cst}(y) H(z)\] The (quick and dirty) Fourier transform of \( H(z)\) is \( \frac{1}{i q_z} \), as one can see either by direct evaluation or by noting that the derivative of \( H(z)\) is the Dirac delta. It ensues that \[ \left | \tilde{\rho}(\mathbf{q}) \right |^2 = \delta(q_x) \delta(q_y) {q_z}^{-2}\] As for the platelet in part I, the scattering is confined along a rod perpendicular to the interface, but its intensity, instead of being constant, decreases along its length. Further spreading this signal over the sphere adds an additional \( {q}^{-2}\) factor, for a final \( {q}^{-4}\) dependence.

Crossover

Although both are infinitely extended in the plane, a single interface (Porod) and two interfaces very close together (thin plate) exhibit very different scattering laws. However, at high enough scattering vector, all objects reach the Porod regime. We will discuss this crossover for the case of a plate with finite thickness. The Fourier transform of this object along its normal is easily shown to be a cardinal sine, so that: \( \left | \tilde{\rho}(q_z) \right |^2 = \left [ \frac{\sin(q_z a)}{q_z a} \right ] ^2\). Close to the origin, ie. for \(q_z a \ll 1\), this function is flat, hence the approximation \(\sim \mathrm{Cst}(q_z)\) we used for the platelet in part I. At high \(q\), on the other hand, it behaves as \(q^{-2}\), yielding the Porod law. To put it differently, when the typical scale \(L = 2\pi/q\) over which we observe the object is much larger than its thickness, we are in the "platelet" regime and do not resolve the two interfaces. When \(L \ll 2a\), on the other hand, we only observe "one interface at a time", justifying the treatment above and thus the \( q^{-4} \) law. This regime is "terminal" insofar there is no smaller typical length scale in the system, until that of the composing atoms or molecules.

Power laws in small-angle scattering - part I

2023-04-27T15:19:00.002+02:00

The small-angle X-ray scattering (SAXS) spectrum of particles with a well-defined shape (such as rods or platelets) is often characterized by a power-law dependence: \( I(q) \sim q^{-\alpha}\), where the exponent \( \alpha \) is directly related to the particle geometry. For "compact" particles, the large-\( q \) intensity scales as \( q^{-4}\) (Porod regime). Below, I'll give the most compact and yet -hopefully- understandable derivation I can think of for these power laws.

To simplify the derivation, we'll consider these objects as infinitely thin and infinitely large, meaning that we'll be looking at them on length scales much larger than their thickness and much smaller than their lateral extension. The approximation is legitimate, since it is in this range of length (or, conversely, scattering vector) that the power-law regimes are encountered.
As discussed above, the Patterson function is similar to the density and thus we will apply the same approximation to \(P(\mathbf{r})\), which is the natural descriptor of the system, due to its intimate relation with the intensity \(I(\mathbf{q}) = \left | \tilde{\rho}(\mathbf{q}) \right |^2\).

Platelets: α = 2

For a platelet, this simplification yields for the Patterson function:
\[ P (\mathbf{r}) = \mathrm{Cst}(x) \mathrm{Cst}(y) \delta(z)\]
where "Cst" (constant) means that the density does not vary as a function of \(x\) and \(y\). Of course, a constant does not need an argument, but we will specify it in order to keep track of the space dimensions.

We now need the Fourier transform of \(P (\mathbf{r})\), \(\mathcal{F}^{-1} [P (\mathbf{r})] = \tilde{P} (\mathbf{q})\). Since the Fourier transform of a constant is a Dirac delta and viceversa, we simply have:
\[ \tilde{P} (\mathbf{q}) = \delta(q_x) \delta(q_y) \mathrm{Cst}(q_z)\] From the Wiener-Khinchine theorem, the intensity scattered at a given wave vector is precisely \( I(\mathbf{q}) = \tilde{P} (\mathbf{q})\). Thus, the intensity scattered by a platelet perpendicular to the \(z\) axis is a thin rod parallel to \( q_z\), as shown in the Figure below.

Fourier transform of a platelet.

In solution, colloidal particles assume all possible orientations, so that this intensity is spread evenly over the sphere of constant \( q\). Consider two such spheres, with radii \( q_0\) and \( 2 q_0\). The rod contributes to each sphere the same amount, namely twice its (constant) intensity \( 2 I_0\), shown as red dots at the poles. This signal must however be divided by the surface area of the sphere, an area that increases as the square of the radius: \[ I(q_0) = \frac{2 I_0}{4 \pi q_0^2} \quad \mathrm{and} \quad I(2 q_0) = \frac{2 I_0}{4 \pi (2 q_0)^2}\] so that \( I(2 q_0) = I(q_0) /4\) and, finally, \( \alpha = 2\).

More power laws coming in part II of this post...

Patterson functions

2023-04-27T14:46:00.001+02:00

Fourier transforms

We will use the following convention for the Fourier transforms:\begin{equation} \begin{split} \rho(\mathbf{q}) = \mathcal{F} [\rho(\mathbf{r})](\mathbf{q}) & \triangleq \int_{\mathcal{V}} \rho(\mathbf{r}) \exp(-i \mathbf{q} \mathbf{r}) {\textrm d} \mathbf{r} \\ \rho(\mathbf{r}) = \mathcal{F}^{-1} [\tilde{\rho}(\mathbf{q})](\mathbf{r}) & \triangleq \dfrac{1}{(2\pi)^3}\int_{\mathbb{R}^3} \tilde{\rho}(\mathbf{q}) \exp(i \mathbf{q} \mathbf{r}) {\textrm d} \mathbf{q} \end{split} \label{eq:Fourierdef} \end{equation} where we integrate in real space over the (as yet unspecified) volume of interest \(\mathcal{V}\) and in reciprocal space over the entire \(\mathbb{R}^3\).

Wiener-Khinchine theorem

The autocorrelation of the real-space density function is \(\Gamma_{\rho \rho} = \int_{\mathcal{V}} \rho(\mathbf{r}') \rho(\mathbf{r}'+\mathbf{r}) {\textrm d} \mathbf{r}'\), which can be developed (using the second line of \eqref{eq:Fourierdef}) into:\begin{equation} \begin{split} \Gamma_{\rho \rho}(\mathbf{r}) & = \dfrac{1}{(2\pi)^6} \int_{\mathcal{V}} {\textrm d} \mathbf{r}' \rho(\mathbf{r}') \int_{\mathbb{R}^3} {\textrm d} \mathbf{q} \, \tilde{\rho}(\mathbf{q}) \exp(i \mathbf{q} \mathbf{r}') \int_{\mathbb{R}^3} {\textrm d} \mathbf{q}' \tilde{\rho}(\mathbf{q}') \exp[i \mathbf{q}' (\mathbf{r}' + \mathbf{r})] \\ & = \dfrac{1}{(2\pi)^6} \int_{\mathbb{R}^3} {\textrm d} \mathbf{q} \int_{\mathbb{R}^3} {\textrm d} \mathbf{q}' \tilde{\rho}(\mathbf{q}) \tilde{\rho}(\mathbf{q}') \exp(i \mathbf{q}' \mathbf{r}) \underbrace{\int_{\mathcal{V}} {\textrm d} \mathbf{r}' \exp[i (\mathbf{q} + \mathbf{q}') \mathbf{r} ]}_{(2\pi)^3 \delta (\mathbf{q} + \mathbf{q}')} \\ & = \dfrac{1}{(2\pi)^3} \int_{\mathbb{R}^3} {\textrm d} \mathbf{q}' \exp(i \mathbf{q}' \mathbf{r}) \tilde{\rho}(\mathbf{q}') \underbrace{\int_{\mathbb{R}^3} {\textrm d} \mathbf{q} \, \tilde{\rho}(\mathbf{q}) \delta (\mathbf{q} + \mathbf{q}')}_{\tilde{\rho}(-\mathbf{q}')} \end{split} \end{equation} where we assumed that everything converges, and thus we can interchange the integration order at will. Dropping the prime and noting that \(\tilde{\rho}(-\mathbf{q}) = \overline{\tilde{\rho}(\mathbf{q})}\) (Friedel's law) we finally prove the Wiener-Khinchine theorem: the autocorrelation function of the scattering length density is the inverse Fourier transform of its spectral density: \begin{equation} \Gamma_{\rho \rho}(\mathbf{r}) = \dfrac{1}{(2\pi)^3} \int_{\mathbb{R}^3} {\textrm d} \mathbf{q} \exp(i \mathbf{q} \mathbf{r}) \left | \tilde{\rho}(\mathbf{q}) \right |^2 = \mathcal{F}^{-1} [|\tilde{\rho}(\mathbf{q})|^2] \label{eq:WK} \end{equation}

The Patterson function

As discussed during the lecture, the scattered intensity is precisely the spectral density of \(\rho(\mathbf{r})\): \(I(\mathbf{q}) = \left | \tilde{\rho}(\mathbf{q}) \right |^2\). Unlike \(\rho(\mathbf{r})\) itself, its autocorrelation \(\Gamma_{\rho \rho}(\mathbf{r})\) is directly accessible via Fourier transform from the experimental data, provided their quality and \(q\)-range are sufficient. Since it is frequently used in crystallography, it has a specific name: the Patterson function, denoted by \(P(\mathbf{r})\).

Correlation and convolution

2023-04-26T15:59:00.012+02:00

In reciprocal space, the signal recorded by the detector at position \(\mathbf{q}\) is characterized by the electric field amplitude \(E(\mathbf{q})\), but the experimentally accessible quantity is its modulus squared, the intensity \(I(\mathbf{q}) = |E(\mathbf{q})|^2\). In real space, the structure is described by the density function \(\rho(\mathbf{r})\) but, as we will see in the next post, it is useful to define two new types of functions "of the type of the square", but where the two instances of \(\rho\) are evaluated in different space points.

The first such combination is the convolution:
\begin{equation}
f(\mathbf{r}) * g(\mathbf{r}) \triangleq \int_{\mathcal{V}} f(\mathbf{r}')\overline{g(\mathbf{r}-\mathbf{r}')} {\textrm d} \mathbf{r}'
\label{eq:conv}
\end{equation}
where the overbar \(\overline{\cdot}\) denotes the complex conjugation.

The second one is the correlation:
\begin{equation} \Gamma_{fg}(\mathbf{r}) \triangleq \int_{\mathcal{V}} f(\mathbf{r}')\overline{g(\mathbf{r}'-\mathbf{r})} {\textrm d} \mathbf{r}' \label{eq:corr} \end{equation} There is an obvious similarity between \eqref{eq:conv} and \eqref{eq:corr}, which can be formalized by noting that:\begin{equation}
\Gamma _{fg}(\mathbf{r}) = f(\mathbf{r}) * g(-\mathbf{r}) \label{eq:convcorr}
\end{equation}and the two operations are identical if \(g\) is symmetric with respect to the origin (\(g(\mathbf{r}) = g(-\mathbf{r})\)). Nevertheless, if this symmetry does not hold the results can be quite different, as we will see in the following (one-dimensional) example.

Let us consider:
\begin{equation}f(x) = g(x) = \left\lbrace \begin{array}{cc} \dfrac{1}{\lambda} \exp \left (-\dfrac{x}{\lambda} \right )& x \geq 0 \\ 0 & \text{ otherwise.} \\ \end{array} \right.\end{equation}
For the convolution \(h(x) = f(x) * g(x) = \int_{-\infty}^{\infty} f(x')g(x-x') {\textrm d} x'\), the integration variable \(x'\) appears in the argument of \(g\) with a minus sign. The second factor in the integrand is thus the same as the first, but reversed with respect to the origin and shifted to the right by the amount \(x\). We dropped the complex conjugation since the functions are real.

Figure 1: The two functions to be convolved \(f\) and \(g\) and their product \(h\) for a given shift \(x = \lambda\).

Figure 1 shows functions \(f(x')\) (in red) and \(g(x-x')\) (in blue) for a shift \(x = \lambda\). Their product is shown as purple line, and the area under this curve is precisely the value of their convolution for this particular shift \(h(x)\).
It is easy to show that:
\begin{equation}h(x) = \left\lbrace \begin{array}{cc} \dfrac{x}{\lambda^2} \exp \left (-\dfrac{x}{\lambda} \right )& x \geq 0 \\ 0 & \text{ otherwise.} \\ \end{array} \right. \end{equation}
with a maximum \(h(x_{\text{max}}) = (\lambda \text{e})^{-1}\) at \(x_{\text{max}} = \lambda\). Figure 2 shows how this function is built up.


Figure 2: Convolution of two decaying exponentials (purple line) and the way it is built up from the superposition of the two factors.

If \(x<0\) the supports of these two terms do not overlap, and thus \(h(x) = 0\). They start overlapping for \(x = 0\) and their product increases rapidly with increasing \(x\) until \(x_{\text{max}}\), after which it decreases as the two maxima shift away from each other. As for the convolution factors \(f\) and \(g\), the result \(h(x) \geq 0\), its support is the range of positive \(x\) and its integral is 1.

The autocorrelation, on the other hand, is obviously symmetric with respect to the origin: shifting one instance of \(f\) to the left or to the right by the same amount yields the same result, which is once again positive and normalized to 1:
\begin{equation}\Gamma_{ff} = \int_{-\infty}^{\infty} f(x')g(x'-x) {\textrm d} x'= \dfrac{1}{2 \lambda} \exp \left (-\dfrac{|x|}{\lambda} \right )\end{equation}
As shown in Figure 3, the product \(f(x')g(x'-x)\) decays twice faster than the individual factors, and its amplitude decreases rapidly with the (absolute value of) the shift.

Figure 3: The two functions to be correlated \(f\) and \(g\) and their product \(h\) for a given shift \(x = -\lambda\).

Polymorphous Packing of Pentagonal Nanoprisms

2023-02-12T15:47:00.012+01:00

Our paper has just been published in Nano Letters.

Pentagonal packing is a long-standing and rich mathematical topic: in two dimensions, the optimal (highest packing fraction η=0.921) packing of regular pentagons is a double-lattice arrangement, called the "pentagonal ice ray".

We pack pentagonal nanoprism into long-range mesocrystals by evaporation induced self-assembly and find the ice-ray structure, but also an arrangement devised by Albrecht Dürer in the 16^th century, with a slightly lower packing fraction (η=0.854), as well as intermediate polymorphs that can be obtained by a continuous sliding transformation between these two configurations.

We discuss the subtle relation between the orientational and positional order, as well as the presence of defects in the lattices.

Extracting the morphology of gold bipyramids from SAXS experiments

2023-01-25T13:37:00.004+01:00

Our paper has just been published in Journal of Applied Crystallography.

We validate the use of the bicone model for extracting the form factor of gold bipyramids in solution from SAXS data.

The salary of CNRS researchers - update

2022-05-07T13:43:00.002+02:00

This is a quick update to a previous post, first published in 2013 and with some additions in 2018-2019. If any details are unclear, please refer back to that post.

In France, the salary of state employees is calculated by multiplying the number of index points associated with a given position with the value of the index point. The idea behind this system is that the number of points is fixed and the point value is adjusted, e.g. to compensate for inflation. One small problem is that this value has been practically unchanged from 2010: an increase is planned for 2022 (it is an election year, after all!) but its quantum is unknown.

This simple revaluation mechanism was therefore replaced by a much more complicated one, the PPCR (the gory details can be found here - in French) and somewhat compensated by a bonus system (the RIPEC).

Some changes since my 2013 post are:

The CR2 and CR1 ranks were merged into one (CRCN). Young researchers can thus acceed to higher seniority levels without the 4-year wait for promotion to CR1.
The hors classe (HC) rank for CRs was created. This rank extends the CR pay scale to greater seniority, but is not a prerequisite for promotion to a DR position.
The number of index points for the various pay grade levels increased. The new values are available here.
In 2021 the statutory bonus increased, to 1620 €/year for DR and 2200 €/year for CR positions. As of 2022, it stands at 2800 € for all researchers.
As of 2022, the performance bonus (formerly known as PEDR) still starts at 3500 €/year, but is only awarded for three years (instead of four), with a mandatory waiting period of one year before one can reapply.

I have updated the graph with the evolution of my net salary, including the statutory bonus, but not the performance bonus. I have also left out any extra income (from teaching or expertise work).

The Dawn of Everything - IV

2022-04-15T12:15:00.001+02:00

Chapter 12 starts by reviewing the competing theories for the origin of human society: either a fall-from-grace story or the progressive alternative. The authors argue against a (purportedly dominant) view of history, with an essential split between pre- and post-Enlightenment phases. The former consisted of traditional societies, and any revolutionary movement was either regressive or religiously inspired. Only in the latter would human beings really have agency.

The difference is illustrated by Mircea Eliade's distinction between cyclical and linear time, quoting the Sacred and Profane [I believe they are completely off on this one: for Eliade, the two kinds of time were not in historical succession, but rather represented different structures in the life of religious people]. Eliade's statement that the perception of sacred time as cyclical changed with Judaism is taken as his own political position and, combined with his far-right sympathies, leads to a view of history which is rather sinister (in particular, antisemitic) and completely absurd [I tend to agree, but mainly because G&W's construction is itself absurd].

Social science is presented as technologically dominated and dismissive of any attempt at earning collective freedom. G&W propose a more organic and "playful" pattern of discovery throughout most of history, with a (speculatively) substantial female participation. This evolution was accompanied by social experiments, among them large-scale egalitarian societies based not on some abstract concept of liberty, but on the three concrete individual freedoms discussed in Chapter 2. Unfortunately, in the course of history they were gradually lost to the point of becoming incomprehensible.

This evolution occurred through division of human societies via schismogenesis, through hierarchical stratification, but also through warfare, which is however not inevitable (either psychologically or historically). Was it connected to the loss of freedom? Indeed, each of the elements of the modern state curtails one of the basic freedoms. Ancient political systems started with only one or two of these elements, but they all shared a connection between patriarchal household and military force.

For G&W, conceiving social alternatives faces a conceptual difficulty due to the discussion always being carried out in the framework of Roman Law. They see it as based on the individual's power over things and persons, in particular over the slaves, which are both household members and (formally) war-conquered property. This essential connection between care and domination (see Chapter 10) separates Western societies from more egalitarian ones, such as the Wendat. The latter also used violence, but not against their own: war captives were either put to death or adopted into the winning tribe. From this, G&W infer [a bit hastily, I think] that Wendat households and tribes were harmonious and free of violence and hierarchical structure, in stark contrast with France under the Ancien Régime.

One of the misconceptions the authors are trying to correct is the hasty inference from the size of a society to its complexity and from the latter to hierarchy. This reasoning is neither theoretically essential nor historically accurate: some early cities went from egalitarian to authoritarian, while others moved in the opposite direction. This diversity of urban structures is due to their emergence not from the coalescence of small isolated groups, but rather from the "compression" of complex large-scale networks.

Returning to the fundamental connection between "systems of violence and systems of care" and to its role in the establishment of power-based societies, the authors find a possible explanation (and many historical examples) in the work of Franz Steiner, with its focus on 'pre-servile institutions': for Steiner, slavery is a perversion of charity and not, as for Lowie and Clastres (see Chapter 3), a consequence of religious authority.

Finally, this book is supposed to fill a gap in the literature concerning early egalitarian structures, which were more common than previously thought and did not necessarily evolve towards hierarchical ones (in fact, the change often went the other way). A more diverse past means more options for the present, and many elements of modern Western society that we take for granted might have come into existence accidentally. Recognizing this truth could lead to profound changes in the social sciences and in society itself.

Conclusion

The Dawn of Everything is clearly not a dispassionate account of how society may have evolved. It is a selective reading of the available material, combined with (sometimes wild) extrapolations in order to support the conclusion that large-scale decentralized societies can exist, and in fact have existed. In itself, this is not a big problem: Graeber and Wengrow speculate a lot, but it is (as far as I can tell) very intelligent speculation. What I found annoying is their tendency of deriding other authors for speculating to different conclusions.

Another issue that bothered me from the outset was the authors' strange insistence that the concept of social equality was lacking in Western thought until the 17th century. To prove it, they simply ignore any antecedent: it's like Ancient Greece, Roman law or the Reformation never existed. The argument is not even crucial for the thesis of the book: the Amerindians could have had a sophisticated understanding of freedom and equality without needing to teach them to the Europeans!

The schismogenesis concept is also too strong for my taste: if a certain organization existed at a certain time in a given group, then we can argue that its opposite also existed at the same time among its neighbors, without restriction, qualification or nuance. This is a bit too convenient when your goal is to challenge established ideas, because in some sense each sociological result becomes proof of its contrary - one village over.

Finally, although I find interesting the connection they make between violence and care, I am amazed they fail to distinguish in the second term the care of the king for widows and orphans from the service of the slave to the master (Chapter 10). While the former does seem significant for the evolution of society, the latter is forced and not a sign of nurture.

The Dawn of Everything - III

2022-04-15T12:15:00.000+02:00

Chapter 10 deals with the origins of the state (or lack thereof). The first difficulty is giving a general definition for the state, which applies throughout history. At a nodal point of the argument, the authors unfortunately use a sleight of hand: after exposing the difficulties of such a definition, they conclude that many complex social and cultural systems existed in the absence of a state. This sounds like an ontological argument in reverse: "We cannot conceive of a state, so it must not exist".

They prefer instead to focus on three elementary forms of domination, de-emphasizing property rights, which are a "peculiarly Western phenomenon", but they still illustrate the three types of control (of violence, of information and individual charisma) on a case of private property. At any rate, they state that each of these forms has given rise to fundamental institutions of the modern state. Democracy (at least in its modern, representative form) cannot balance the domination institutions. Moreover, its competitive aspect has more in common with the archaic 'heroic societies' than with the ancient democracies, where public functions were assigned by lottery.

We finally get to the definition of the modern state: "a combination of sovereignty, bureaucracy and a competitive political field" each item corresponding to one of the forms of domination above. [I do not understand the use of super- and inter-statal institutions (EU, WTO, IMF etc.) as counterexamples, i.e. bureaucracies without sovereignty. They only get their authority from sovereign states, through well-defined mechanisms, not by any independent process.] This ternary framework is used to understand both history and other people's reading of it. The discussion is rather long, so I'll only list a few salient points for each example.

At the arrival of the conquistadors, America was the scene of two highly centralized states: the Aztec Empire (an aristocratic confederation) and the Inca Empire (where the king concentrated all authority). Both were easily taken over by the invaders once the center of power was captured. In contrast, the Mayan territories were divided between various regional structures, and thus much more resilient against invasion. Women played a more important role than in the two former civilizations.

Warning against reading the history of other societies through a Western grid and dismissing periods (or territories) without identifiable central rulers as insignificant or chaotic. On the contrary, focusing on these in-between times and places can help understand some "anomalous" cases of societies based almost exclusively on one of the three forms of domination:

The Olmecs (predecessors of all later Central Americal civilizations) were ruled by elites, but the latter's power was mostly cultural and centered around games (personal charisma).
The Chavín de Huántar Peruvian civilization (before the Incas) used elaborate art to describe shamanic, mescaline-induced journeys. It maintained its power by control over some esoteric knowledge.
The Natchez tribe, in 18th century Louisiana, was organized around the strong (albeit narrowly localized) personal monopoly on violence of the king.

[I see no convincing arguments for this neat separation]. However, these "first-order" regimes did not restrict the three basic freedoms very much and some of these social organizations were seasonal.

Ancient Egypt is closer to what we would nowadays call a "state". It shares with other early kingdoms the presence of human sacrifices after the death of a ruler, highlighting the connection between violence and kinship that has an important role in establishing the hierarchy. Like Mesopotamia, Maya or China, it combined two of the three forms of domination (although which two specifically changes from state to state.) In Egypt, it was the first two principles, seemingly confirming accepted theories of social evolution: scale engenders leaders and bureaucracy. However, the first systems of administrative control appeared very early (c. 6000 BC) and in much smaller settlements (around 150 people) in the Middle East. [I am not sure this proves what the authors hope it would: size could be sufficient, but not necessary for the emergence of bureaucracy.]

I will not try to summarize the last part of the Chapter, which is a rather confusing summary of the above, interrupted by a discussion of Minoan Crete. I may still do this later...

Chapter 11: TO DO

Packing spindles

2022-03-27T16:55:00.001+02:00

Our paper Double-Lattice Packing of Pentagonal Gold Bipyramids in Supercrystals with Triclinic Symmetry has just been published in Advanced Materials! Congratulations to all involved, and in particular to first author Jieli Lyu for her unrelenting focus (and the countless hours spent!) on improving the quality of the nanoparticle batches and of their assemblies.

We solve the fundamental packing problem for this particular object and, guided by numerical simulations, we try to extend the result to similar shapes in order to understand the delicate balance between the inversion symmetry (or lack thereof) of the particles, the complexity of the supercrystal lattice and the packing fraction. Unexpectedly, we detect a strongly facet-dependent optical response of the assemblies.

The Dawn of Everything - II

2022-01-20T22:01:00.002+01:00

In the first half of the book (reviewed here), Graeber and Wengrow argued against the widely accepted idea that social inequality was a (necessary or contingent) result of the Agricultural Revolution. What did then happen in the communities that adopted farming? Chapter 7 tries to show that sustainable agriculture can be (and has been) based on schemes of communal land sharing, which do not require inequality or hierarchy.

The Neolithic adoption of agriculture was slow and meandering, in contrast with the European conquest of the New World (which was aided by guns, germs and steel), and was conditioned by the climate, viz. the onset of the Holocene. Sometimes it was unsuccessful (as in central Europe, where it went through a boom and bust because of an overreliance on cereals), but the farmers always avoided already settled territories, meaning that they often had to make do with less productive environments.

The Amazonian case is interesting, since there were no domestic animals (except pets) and farming activities remained seasonal for thousands of years. However, far from being an incarnation of the state of nature, this region was in fact quite diverse in terms of modes of production and of social organization.

Farming was generally adopted in the areas with the least resources, but due to its growth potential it left the most archaeological traces. This does not mean that other type of societies did not create large edifices and even cities, as discussed in Chapter 8. The exposition begins with a purported citation from Elias Canetti's Crowds and Power, "Cities begin in the mind", which I cannot find in the text. [If it is from the "Invisible Crowds" chapter, then it refers to people's communion with their ancestors, not to large assemblies being different in nature from small ones.] Nevertheless, the transition from the family (or village) to the city does pose a question: are social hierarchies inevitable above a certain size?

The common sense view that cohesive social groups cannot have more than about 150 members is supposedly challenged by the very extended networks of tribal kinship in modern hunter-gatherer peoples [I do not understand how, since recognition and living together are very different situations]. These large-scale virtual communities would then be the precursors of (or even "squeezed into") actual cities.

In Eastern Europe, the Kurgan culture takes its name from the monumental tombs of warrior-kings but also featured vast "mega-sites" that deserve the title of "cities". What was their organization? Apparently, they combined small-scale farming with foraging and herding and had a relatively flat social structure, as the authors infer from the archaeological evidence and by comparison with modern Basque settlements with the same circular arrangement.

Elements of democracy were also present in Sumerian cities since before 3000 BC, as illustrated by the case of Uruk: the presence of a large public space is taken as proof of governing by popular assembly (moreso than in classical Athens, based on the principle "the wider the space, the larger the participation"). This changed around 2600 BC, when evidence of city rulers begins to appear. How did this change occur?

The smaller settlement at Arslantepe, in eastern Turkey, was roughly contemporary with Uruk, but provides a clearer record of political developments: a warrior aristocracy took over a previous bureaucracy, in a first example of a 'heroic society' (using H. M. Chadwick's term). These cultures always appeared on the margins of urban civilizations, lacked centralized authority, rejected commerce and writing, relying instead on oral transmission (and left behind epic poems around the world).

The story then skips 1000 years forward in time to Mohenjo-daro, in the Indus valley. This city's organization prefigures the caste system documented another thousand years later in the Rig Veda and serves as an example of a hierarchical system where the social rank was not correlated to material possessions (or even anti-correlated for the top caste, the brahmins). On the other hand, Mohenjo-daro lacks evidence for a class of warrior-nobles, with the associated feasts and tournaments. This lack of a clear aristocratic structure opens the possibility that the society was organized on egalitarian principles, the caste hierarchy notwithstanding.

The conclusion would be that some ancient Eurasian cities developed systems of "communal self-governance", but based on two quite different conceptions of egalitarianism:

all humans are fundamentally identical, or
individuals are so different as to be incommensurate.

which the authors assign to Uruk and the Ukrainian cities, respectively. Two Chinese sites, Shimao and Taosi, are counterexamples, with a presumably hierarchical structure. More interestingly, the latter might have undergone a dramatic transition from a rigid class system to self-governance.

Chapter 9 presents other examples of social upheaval, this time in central Mexico: Aztec cities were inspired by the ruins of Teotihuacan, a metropolis with at least 100 000 inhabitants (ten times larger than the towns discussed in the previous chapter), and which was also self-governed, unlike the contemporary Classic Mayan cities (schismogenesis at work, once again).

After an authoritarian period, Teotihuacan switched to an egalitarian organization around 300 AD. This did not prevent (or maybe even motivated!) some of its residents to try their luck in Mayan cities such as Tikal (1000 km away, in current Guatemala) where they became rulers. Teotihuacan itself started by a period of intense construction effort, which left behind several large buildings but also hundreds of victims of ritual killings. However, after a sudden upheaval the building activity focused on housing for all the population, not only the wealthy part of it. In this latter period authority was probably decentralized, if we judge by later examples such as the city-state of Tlaxcala, which (democratically!) allied with Hernàn Cortés against the Aztec Empire.

The Dawn of Everything - I

2021-12-30T15:53:00.001+01:00

Is anarchy¹ a realistic social organization? Based on its absence in the modern world one would be tempted to answer in the negative, at least for communities above the size of indigenous tribe (a few thousands, say.) Showing that complex and large-scale societies can function (or, even better, that they have already functioned) without a strong state and its inherent dangers would be a powerful argument in favor of attempting such a decentralized system in our time. This is exactly the argument that David Graeber and David Wengrow are trying to make in The Dawn of Everything: A New History of Humanity. Unfortunately, they are trying too hard. Below the fold, I'll give a synopsis of the first part of the book (chapters 1 to 6). A second post will summarize chapters 7-12 and a third one will conclude the review.

In Chapter 1, the authors lay out their case against the Rousseau/Hobbes alternative: prehistorical humans were neither intrinsically good nor inherently evil, and much more interesting than we (i.e. our current understanding of early humanity, as exemplified by a few popular authors: Fukuyama, Diamond, Pinker) give them credit for. In the process, they manage to work in a few recent events (e.g. the 2008 financial crisis and reactions to it, among the general public or the financial elites) and end the chapter by promising a new understanding of ancient history and (by implication) new insight into our current situation.

They start the work in Chapter 2, by rewriting the intellectual history of equality in the West, and trying to prove that it was strongly influenced by contacts with other cultures, in particular with the Native American tribes in the Great Lakes region. Their point of view is clearly stated:

'Social equality' -and, therefore, its opposite, inequality- simply did not exist as a concept.

until the seventeenth century, by their estimate. This sad state of affairs was improved by the contact with intellectually sophisticated and socially mature tribes such as the Wendat. Kandiaronk, a particularly brilliant member of the latter, introduced his revolutionary ideas on equality, freedom and rationality to the French colonists in a "proto-Enlightenment salon" (that's an exact quote). These ideas were then disseminated in Europe by a certain Lahontan in the early 1700s, they were adopted by the major French Enlightenment figures (Montesquieu, Voltaire, and later Rousseau) and the rest is history. A history, that is, shaped by a fundamental misunderstanding: Rousseau (and other culprits) fail to understand that individual liberty can coexist with a sense of community and sharing beyond the idyllic originary state. After the French Revolution, the right wing first repudiated Rousseau before adopting his 'myth of the stupid savage'.

Chapter 3 goes deeper into this concept of a primordial age, which should be carefully distinguished from our view of prehistory and from the actual state of affairs during the hundreds of millennia between the separation of humans from animals and the beginning of written history. There is very little information about social organization during this time, but based on the presumed physical diversity the authors conclude that:

social organization among our earliest ancestors [...is] likely to have been extraordinarily diverse.

so there was in fact no uniform originary state, and at any rate not one of small egalitarian bands, as shown by the existence of large (even monumental) constructions and by highly elaborate graves. The latter evidence would point towards a very large degree of inequality (since, after all, it would have been impossible to give sumptuous burials to all members of society). A large part of the chapter is thus spent using anthropological evidence on contemporary primitive society to argue for a prehistorical "sweet spot" between a highly hierarchical organization and no organization at all. One line of argument relies on the acceptance of "extreme" (in behavior or physical appearance) individuals and on the fact that most ceremonial graves hold difform individuals. This is used as proof against the existence of hereditary elites (although, on the face of it, it is an argument for them!)
A second observation concerns the seasonal variations in social organization: in some tribes authority only lasts for part of the year, opening the possibility that chiefs had little coercive power and ruled by shrewdly building consensus.

Taking for granted the hypothesis that seasonal changes in structure were fundamental for the organization of prehistorical societies, in Chapter 4 the authors recast their basic question:

What is the origin of social inequality?

as "how did we get stuck in the authoritarian phase of the social cycle?" One element of response is the gradual reduction in the scale over which social interaction takes place [is this not simply sedentarization?]

The definition of egalitarianism depends on the important value in that society (which should be equally distributed). In modern European thinking, this would be material property and, per Rousseau, inequality followed the adoption of agriculture and lead to the rise of the state. Is this sequence of events inevitable? Here, Graeber and Wengrow once again shift focus, this time from equality to individual liberty, which in modern society is severely reduced, or at best reduced to formal freedoms.

Ancient monumental complexes such as Poverty Point (Louisiana) and others across the world show that farming is not a necessary condition: foraging peoples were capable of complex organization and of gathering enough resources to build such earthworks or to keep large standing armies or rich royal courts. The argument does hinge on a very specific definition of foragers: "populations which don't rely on biologically domesticated plants and animals as their primary sources of food".

Finally, all this discussion is supposed to reveal [but I have trouble finding the line of reasoning] a sacred origin of private property, still visible in contemporary primitive tribes and even (in trace form) in modern society.

Chapter 5 tries to explain how such foraging societies in Northern California rejected agriculture, even as neighboring tribes were practicing it. Such an explanation is important for understanding the process of cultural differentiation. Following Marcel Mauss, the authors insist that civilizations define themselves to a large extent by contrast with their neighbors, whose culture they refuse. They return here to the concept of schismogenesis (already alluded to in Chapter 2) and apply it to the relation between northern Californian tribes and those on the Northwest Coast. Are the variations between these two types of societies due to economical or cultural factors or simply to the need of self-defining with respect to an Other?

Major differences are that the latter tribes were much more socially stratified (with a clearly delimited aristocracy) and practiced slavery on a fairly large scale. The two features are related, since the aristocracy needed a "dependable workforce", beyond what the free subjects were willing to contribute. Northern Californian populations would then have defined themselves in opposition with the above and adopted a frugal and egalitarian way of life.

The take-home message of the chapter seems to be twofold:

inequality "starts small", at the domestic level
rather than being successive moments in history separated by an arbitrary threshold (such as the adoption of agriculture), egalitarian and hierarchic arrangements can be contemporary and influence each other in complex ways via the schismogenic tendencies of the populations that adopt them.

Chapter 6 uses the concept of schismogenesis to explain the difference between the highlands (e.g. Göbekli Tepe) and the lowlands (e.g. Çatalhöyük) of the Fertile Crescent. The latter were Neolithic farmers, but had a different relation with agriculture (and Nature in general) than modern humans: less clinical and forceful, more concrete and imaginative (invoking Lévi-Strauss and his The Savage Mind).

The authors try to resurrect the Neolithic matriarchy hypothesis of Marija Gimbutas and, in the case of Çatalhöyük, they argue for significant sequality between families and between sexes (with some feminine ascendance?) and for seasonal variations of social structure (as in Chapter 3) [this seems to derive from the seasonal character of farming and herding, but the claim is much stronger.] This society was more egalitarian and less violent than the highlands settlements (which probably relied less on farming), disproving the assumed causality relation between agriculture and inequality. Moreover, "the Agricultural Revolution" is not a very useful phrase for explaining the very long and complex process.

¹ I am using this term in the broad sense of social organization without a central government. It also corresponds to Graeber's political sympathies, although Wengrow avoids it in interviews.^↩

CNRS positions - the 2022 campaign

2021-12-08T21:14:00.001+01:00

The 2022 campaign for permanent research positions at the CNRS (Centre national de la recherche scientifique) is open (see the submission site). The deadline is January 11th 2022 (13:00 Paris time). There are 238 open positions at the CR level, 260 for DR2 and 2 for DR1. The official texts are here: CRCN, DR2, DR1 and the evolution of these numbers over the last twenty years is shown in the graph below:

Two changes are worth mentioning this year:

The significant increase in DR2 positions (13 in 2022, up from 3 over the last few years!) for section 50, "research management". This section's purpose is to promote (no external hire possible) CNRS researchers who undertake heavy administration tasks, such as directing a large organization (e.g. a laboratory or a large facility)¹.
The emphasis on "big data" and AI, with the creation of the new interdisciplinary section 55 (5 DR2 and 5 CRCN positions), but also with targeted positions in other sections (e.g. 15, 17, 51, 53).

Good luck to all the candidates!

1. This is probably part of the larger tendency of reducing the count of staff blocked at the "junior" CRCN level, by promotion to the DR rank and by the creation of the "hors-classe" CR rank in 2017. A similar strategy is announced for the universities, with more promotions from associate professor "maître de conférences" (MdCf) to full professor and to "MdCf hors classe".^↩

Conservatorismul în România şi în Occident

2021-11-28T14:42:00.002+01:00

O discuție pe Reddit despre un mesaj al lui Dan Alexe pentru Adrian Papahagi m-a făcut să reflectez la definiția conservatorismului, la modul cum ea se aplică în România şi la eventualele diferențe față de Occident.

Dincolo de presupusul caracter universal al conservatorismului şi de eventualele lui legături cu iluminismul şi liberalismul, cred că definiția lui Alexe este corectă şi că unul din principiile fundamentale ale conservatorilor (aşa cum e formulat spre exemplu de Burke) e următorul: tradiția socială este valoroasă şi trebuie în principiu respectată dacă nu există motive foarte întemeiate de schimbare.

În țările occidentale, unde s-a instaurat de-a lungul secolului XX consensul în jurul unor valori "moderne" (din lipsă de alt termen mai bun): egalitate în drepturi pentru femei, toleranță față de anumite practici sexuale, separare între stat şi biserică şi, în general, nivelarea (măcar aparentă) a ierarhiei sociale, argumentul lui Dan Alexe este valabil: cei care vor să revină la situația dinainte de 1968, sau 1939, sau (în cazuri extreme) 1789 nu sunt conservatori, ci mai degrabă reacționari: ei vor să schimbe tradiția existentă, care le este (moral vorbind) insuportabilă, fiind motivați nu de prudență ci de indignare (ca şi progresiştii, cu care nu au nimic altceva în comun!)

Putem aplica acelaşi raționament în cazul României? Dacă acceptăm că valorile moderne de mai sus au început să fie introduse în anii 90 şi că situația socială anterioară (inclusiv sub regimul comunist) era caracterizată de conformism social, de respect față de ierarhie (a cărei structură s-a schimbat în timp, bineînțeles), de atitudini tradiționale față de sex şi de reproducere (inclusiv interzicerea avortului), de importanța bisericii (în ciuda caracterului declarat ateu al statului comunist), poziția conservatorilor ca reprezentanți ai unei "majorități tăcute" care nu a acceptat evoluția ultimelor trei decenii devine mai convingătoare.

Problema conservatorilor occidentali este că propun schimbarea, deşi principiul lor de bază este continuitatea: a celor români este că programul lor se aseamănă prea mult cu perioada dinainte de 1989, de care ar dori probabil să se distanțeze.

Bernard Henri-Lévy is the anti-Forrest Gump

2021-09-16T10:27:00.000+02:00

They both get their photo taken at major historical events, but FG has short hair, buttons his shirts all the way up and is wise without being smart.

The Pareto distribution and Price's law

2021-08-29T22:07:00.003+02:00

As detailed in the previous post, the ratio \(f\) of the top authors that publish a fraction \(v\) of all publications is independent from the total number of authors \(N_0\). Of course, this result is incompatible with Price's law (that for \(v=0.5\), \(f = 1/\sqrt{N_0}\)). This issue has been discussed by Price and co-workers [1], but I will take here a slightly different approach.

I had assumed in my derivation that he domain of the distribution was unbound above (\(H = \infty\)), and that the exponent \(\alpha\) was higher than 1. One can relax these assumptions and check their effect on \(f\) by:

imposing a finite upper bound \(H\) and
by setting \(\alpha = 1\). Note that 2. also requires 1.

Role of the upper bound

In the finite \(H\) case one must use the full expressions (containing \(H\) and \(L\)) for the various quantities. In this section, we will continue to assume that \(\alpha > 1\). Since \(L\) acts everywhere as a scale factor for \(x\) (and \(H\)) I will set it to 1 in the following. It is also reasonable to assume that the least productive authors have one publication (why truncate at a higher value?!) Consequently, all results will also depend on \(H\), but presumably not explicitly on \(N_0\), which is a prefactor for the PDF and should cancel out of all expectation calculations. It is, however, quite likely that \(H\) itself will depend on \(N_0\), since more authors will lead to a higher maximum publication number!

In my opinion, the most reasonable assumption is that there is only one author with \(H\) publications, so that \(N_0 p(H) = 1 \Rightarrow H \simeq (N_0 \alpha)^{\frac{1}{\alpha + 1}}\), neglecting the normalization prefactor of \(p(x)\).

The threshold number \(x_f\) is easy to obtain directly from \(S(x)\):

\[x_f = \left [ f + (1-f) H^{-\alpha}\right ]^{-1/\alpha}\]

From its definition, the fraction \(v\) is given by: \(v = \dfrac{\alpha}{\mu} \dfrac{1}{1-H^{-\alpha}} \dfrac{1}{\alpha - 1} \left ( x_f^{1-\alpha} - H^{1-\alpha} \right )\). Note that we need here the complete expression for the mean [2]:

\[\mu = \dfrac{\alpha}{\alpha - 1} L \dfrac{1-H^{1-\alpha}}{1-H^{-\alpha}}\]

Plugging \(x_f\) and \(\mu\) in the definition of \(v\) and setting \(v = 1/2\) yields:

\begin{equation} f = f_{\infty} \dfrac{\left ( 1 + H^{1-\alpha}\right )^{\frac{\alpha}{\alpha - 1}} - 2^{\frac{\alpha}{\alpha - 1}}H^{-\alpha}}{1-H^{-\alpha}}, \quad \text{with } f_{\infty} = \left( \dfrac{1}{2} \right )^{\frac{\alpha}{\alpha - 1}},\end{equation}

and we assume that the upper bound is given by:

\begin{equation} H = (N_0 \alpha)^{\frac{1}{\alpha + 1}}. \end{equation}

Exponent \(\alpha = 1\)

Let us rewrite the PDF, CDF and survival function in this particular case:

\[p(x) = \dfrac{1}{1 - H^{-1}} \dfrac{1}{x^2}; \, F(x) = \dfrac{1- x^{-1}}{1 - H^{-1}} ; \, S(x) = 1 - F(x) = \dfrac{x^{-1}- H^{-1}}{1 - H^{-1}}\]

\[x_f = S^{-1}(f) = \dfrac{1}{f + (1-f) H^{-1}}\]

\[v = \dfrac{1}{2} = 1 - \dfrac{\ln(x_f)}{\ln(H)} \Rightarrow x_f = \sqrt{H} \quad \text{and, since } H = \sqrt{N_0}, \, x_f = N_0^{1/4}\]

Putting it all together yields \(f = \dfrac{N_0^{1/4} - 1}{N_0^{1/2} - 1}\) and, in the high \(N_0\) limit, \(f \sim N_0^{-1/4}\), so the number of "prolific" authors \(N_p = f N_0 = N_0^{3/4}\), a result also obtained by Price et al. [1] using the discrete distribution. They also showed that other power laws (from \(N_0^{1/2}\) to \(N_0^{1}\)) can be obtained, depending on the exact dependence of \(H\) on \(N_0\).

Fraction \(f\) of the most prolific authors that contribute \(v = 1/2\) of the total output, as a function of the total number of authors, \(N_0\), for various exponents \(\alpha\). The unbound limit \(f (H \rightarrow \infty)\), calculated in the previous post is also shown for \(\alpha > 1\). With my choice for the relation between \(N_0\) and \(H\), this also corresponds to \(N_0 \rightarrow \infty\). The particular value \(\alpha = 1.16\) yields the 20/80 rule, but also the 0.6/50 rule shown as solid black line. Note that the curve for \(\alpha = 1\) is computed using a different formula than the others and does not reach a plateau: its asymptotic regime \(f \sim N_0^{-1/4}\) is shown as dotted line.

The graph above summarizes all these results: for \(\alpha = 1\), \(f\) reaches the asymptotic regime \(f \sim N_0^{-1/4}\) very quickly (\(N_0 \simeq 100\)). For \(\alpha > 1\), \(f\) leaves this asymptote and saturates at its unbound limit \(f (H \rightarrow \infty)\), calculated in the previous post. This regime change is very slow for \(\alpha < 2\): the plateau is reached for \(N_0 > 10^6\).

In conclusion, an attenuated version of Price's law is indeed obtained for \(\alpha = 1\)(where it holds for any \(N_0\)) but also for reasonably low \(\alpha > 1\), in particular for \(\alpha = 1.16\) (of 20/80 fame) where it applies for any practical number of authors! As soon as \(\alpha\) exceeds about 1.5, the decay is shallow and saturates quickly so \(f\) is relatively flat.

¹ Allison, P. D. et al., Lotka's Law: A Problem in Its Interpretation and Application Social Studies of Science 6, 269-276, (1976).↩

² https://en.wikipedia.org/wiki/Pareto_distribution ↩

The Pareto distribution and the 20/80 rule

2021-08-28T19:51:00.001+02:00

I mentioned in the previous post Pareto's 20/80 rule. Here, I will discuss Pareto's distribution, insisting on how (and in what conditions) it gives rise to this result. I had some trouble understanding the derivation as presented in various sources, so I will go through it in detail.

The functional form of the Pareto distribution is a power law, over an interval \((L,H)\) such that \(0<L<H\leq \infty\). I will use the notations of the Wikipedia page unless stated otherwise. Its probability density function (PDF) \(p(x)\) and cumulative distribution function (CDF) \(F(x)\) are (\(\alpha\) is real and strictly positive):

\[p(x) = \dfrac{\alpha}{1-(L/H)^{\alpha}} \dfrac{1}{x} \left ( \dfrac{L}{x} \right ) ^{\alpha}\quad ; \quad F(x) = \dfrac{1-(L/x)^{\alpha}}{1-(L/H)^{\alpha}}\]

One often uses the complementary CDF (or survival function) defined as:

\[S(x) = 1 - F(x) = \dfrac{1}{1-(L/H)^{\alpha}}\left [ \left ( \dfrac{L}{x} \right )^{\alpha} - \left ( \dfrac{L}{H} \right )^{\alpha}\right ]\]

Note that the survival function is very similar to the PDF multiplied by \(x\): \(S(x) \simeq \dfrac{x}{\alpha} p(x)\), the difference being due only to the final truncation term. However, this is only true for power laws, as one can easily check by writing \(p(x) = F'(x)\) and solving the resulting ODE. We should therefore carefully distinguish \(x p(x)\) (which is, for instance, the integrand to use for computing the mean of the distribution) and \(S(x)\) which "has already been integrated", so to speak.

Let us use this continuous model to describe the distribution of publications (neglecting for now its intrinsically discrete character). \(x\) stands for the number of publications by one author, bounded by \(L\) and \(H\). The number of authors that published \(x\) books is given by \(N_0 \, p(x)\). \(N_0\) is the total number of authors.

The first question is: who are the first \(f\) more prolific authors (in Pareto's case, \(f = 0.2 = 20\)%)? More precisely, what is the threshold number of publications \(x_f\) separating them from the less prolific ones?

This is quite easy: if we go through the list of authors (ordered by increasing \(x\)) when we reach \(x_f\) we will have counted the lower fraction, so \(\int_{L}^{x_f} p(x) \text{d}x = F(x_f) = 1-f\). Thus, the survival function is \(S(x_f) = \int_{x_f}^{H} p(x) \text{d}x = f\) and we can simply invert this dependency to get \(x_f =S^{-1}(f)\).

The second question is: how many publications did these top \(f\) authors contribute?

We need to count the authors again, but with an additional factor of \(x\), since there are \(N_0 \, p(x)\) authors with exactly \(x\) publications, for a total contribution of \(x \, N_0 \, p(x)\). The fraction of publications contributed by the top \(f\) authors \(v\) is then:

\[v = \dfrac{\int_{x_f}^{H} x \, N_0 \, p(x) \text{d}x}{\int_{L}^{H} x \, N_0 \, p(x) \text{d}x} = \dfrac{\int_{x_f}^{H} x \, p(x) \text{d}x}{ \mu}\]

where \(\mu\) is the mean of the distribution and \(N_0 \mu\) is the total number of publications.

In the simple case \(H = \infty\) (which requires \(\alpha > 1\)), one has:

\[p(x) = \dfrac{\alpha}{x} \left ( \dfrac{L}{x} \right )^{\alpha}, \quad \text{with} \quad \mu = \dfrac {\alpha}{\alpha-1} L\]

\[f = S(x_f) =\left ( \dfrac{L}{x_f} \right )^{\alpha} \Rightarrow x_f = L f^{-1/\alpha}\]

Plugging the above into the equation for \(v\) yields:

\[v = \dfrac{1}{\mu} \int_{x_f}^{\infty} x \, p(x) \text{d}x = \dfrac{\alpha}{\mu} \int_{x_f}^{\infty} \left ( \dfrac{L}{x} \right ) ^{\alpha} \text{d}x = \left ( \dfrac{L}{x_f} \right ) ^{\alpha-1} =f^{\frac{\alpha-1}{\alpha}} \Rightarrow f = v^{\frac{\alpha}{\alpha-1}}\]

Pareto's rule \(f=0.2\) and \(v=0.8\) requires \(\alpha \simeq 1.161\): a power law with this exponent will obey the rule, irrespective of the values of \(L\) and \(N_0\). Despite the neat coincidence in the established statement of the principle, there is absolutely no need that \(f+v=1\)! For instance, the same \(\alpha\) implies that, for \(v=0.5\), \(f \simeq 0.065\), a result I have already used in the previous post.

Price's law is not intensive

2021-08-27T09:17:00.002+02:00

Price's law was proposed in the context of scientific publishing:

The square root of the total number of authors contribute half of the total number of publications.

It is a more extreme version of Pareto's 20/80 rule, which would state that 20% of authors contribute 80% of the total number of publications (see next post for the relation between the two). Unlike Pareto's rule, however, Price's law is not stable under extension. This is a trivial observation, but I have not yet seen it in the literature, just like I have not seen much empirical evidence for Price's law.

Let us denote by \(N\) the total number of authors and by \(N_p\) the number of "productive" authors (the top authors that provide half of all publications). As the ratio of two extensive quantities, \(p\) should be independent of the system size \(N\): consider ten systems (e.g. the research communities in different countries, different subjects, etc.), each of size \(N\), with the same publication distribution and hence the same \(N_p\). Half of the total number of publications is published by \(10 \, N_p\) contributors, so the overall productivity is \(p' = \dfrac{10 N_p}{10 N} = p\). According to Price's law, it should however be \(p' = p/\sqrt{10}\) ! The situation is similar to having ten identical vessels, all under the same pressure \(p\). If we connect them all together the pressure does not change, although both the volume and energy increase by a factor of ten.

Price's law does have a "convenient" feature: simply by selecting the representative size \(N\) one can obtain any productivity, since \(p = 1/\sqrt{N}\). For instance, the same Pareto distribution that yields the 20/80 rule predicts that 0.7% of causes yield half of the effects. This result is reproduced by Price's law with \(N \simeq 23000\).

Outside of bibliometry, Price's law has been invoked in economics, for instance by Jordan Peterson in (at least) one of his videos. What I find amusing is that it seems to contradict the principle of economies of scale: if there is a connection between the productivity \(p\) and the economic efficiency (and this is the more likely the higher the personnel costs are) then an increase in the size of a company decreases its efficiency. For instance, a chain of ten supermarkets would be less effective than ten independent units, which would be less effective than many small shops. Since the market is supposed to select for efficiency, we should witness fragmentation, rather than consolidation.

References:

https://subversion.american.edu/aisaac/notes/pareto-distribution.pdf Clear derivation of the 20/80 principle from the general Pareto distribution.

Heuristic derivation of physical laws - II

2021-03-03T18:35:00.010+01:00

In the previous post I presented the main result of Trachenko et al. [1] concerning the speed of sound in solids and a possible fundamental upper bound for this parameter. Here, I will add a couple of observations.

Clean derivation

The heuristic formula for the speed of sound in elemental solids, \( \frac{v_{\text{est}}}{c} = \alpha \sqrt{\frac{m_e}{2 m_p} } A^{-1/2}\) arises quite naturally; in particular, the ratio \(\frac{m_e}{m_p}\) intervenes because the Ry contains the mass of the electron, but the density is given by that of nucleons. In contrast, Press and Lightman [2] put this factor in "by hand", noting that the electron is bound, but the whole molecule vibrates (see the paragraph above Eq. (9)) and neglect the mass number dependence. This line of reasoning is also presented by Ref. [1] as a second option.

Large experimental scatter

The experimental values in Fig. 1 are rather scattered around the theoretical prediction; this is to be expected for such a simple approach, and even agreement within a factor of two for all points is remarkable; however, this should be taken into account in the following discussion. For instance, when mentioning the excellent agreement (within 3%) between the theoretically predicted maximum and the fitted value I would have expected the authors to give the uncertainty on the latter, as well as on the exponent of the variation with the mass number. How close is it to \(-1/2\)?

At what pressure?

The most serious difficulty of the universality claim has to do with the conditions under which the speed of sound is measured (or evaluated numerically). The upper value \( v_{u} = \alpha \sqrt{\frac{m_e}{2 m_p} \, c} \) should apply for solid hydrogen, and the authors further limit this to metallic hydrogen, but this putative phase only occurs at high pressure, above 400 GPa (note that the speed of sound in solid hydrogen at a few GPa is much lower than \( v_{u}\), see e.g. [3]). Simulations then yield good agreement with the \( v_{u}\), but one is now confused: why compare hydrogen at 600 GPa with all the other elements at standard pressure? Could the speed of sound in high-pressure diamond exceed \( v_{u}\)?

¹ Trachenko, K. et al., Speed of sound from fundamental physical constants Science Advances 6, eabc8662, (2020).↩

² Press, W. H. and Lightman, A. P., Dependence of macrophysical phenomena fundamental constants Phil. Trans. R. Soc. Lond. A 310, 323-336, (1983); two lines above Eq. (10).↩
³ Guerrero, C. L. and Perlado, J. M., Speed of sound in solid molecular hydrogen-deuterium: Quantum Molecular Dynamics Approximation Journal of Physics: Conference Series 717, 012018, (2016).↩