Is Pavlovian conditioning the same thing as Pavlovian conditioning? Though that question seems tautological, this article shows that it is not, because Pavlovian conditioning has at least three different meanings: Pavlovian conditioning is (1) a procedure, (2) the learning phenomenon observed in that same procedure and (3) the learning process explaining the phenomenon observed in that procedure. If we look at this third meaning from an evolutionary point of view, it seems extremely unlikely that a single Pavlovian conditioning process is responsible for learning in all procedures classified as Pavlovian conditioning -- a conclusion that supported by behavioral and neural data. In the end, it seems that it might be better to drop the term Pavlovian conditioning to designate a learning process and to stop the quest for a single process explaining all Pavlovian learning. Instead, it would be more fruitful to understand under which condition a particular model of Pavlovian learning holds. The same conclusion applies to other research field in the psychology of learning, notably operant conditioning and statistical learning.

This thesis is an experimental work, investigating how active matter can control the assembly of soft materials. We design a novel experimental system, combining sticky colloids sedimented on the bottom surface of a glass capillary with a bath of motile {\it E. coli}. The colloids diffuse and stick together, assembling into large, quasi - 2D aggregates. Motile {\it E. coli} generate forces and flows in the surrounding media: an active bath which injects energy into the system through mechanical work. In the active bath, aggregates exhibit a a persistent clockwise rotation, leading to a non-conventional aggregation mechanism. These aggregates form structures which are not accessible via conventional aggregation in a thermal bath. Aided by numerical simulation of spinning, sticky beads, we elucidate that the rotation and folding of aggregates is the salient feature driving the structural differences, and the activity of the bath controls the phase diagram of aggregation. Further experiments indicate that the bacteria collide with and then swim through the aggregates; additionally, the direction of rotation of the aggregates is correlated with the direction of the circular trajectories made by the {\it E. coli} bacteria. Based on these insights, we propose a simple model for the swimmer-aggregate interactions, and propose further experiments to test its validity. As a whole, this work constitutes a proof of concept that active matter can be harnessed to direct the assembly of soft materials. The experiments presented in this thesis lay the groundwork for the development of a new class active, soft materials, whose structure and mechanical properties are dictated by their assembly in an active bath.

A tight map is a map with some of its vertices marked, such that every vertex of degree \(1\) is marked. We give an explicit formula for the number \(N_{0,n}(d_1,\ldots,d_n)\) of planar tight maps with \(n\) labeled faces of prescribed degrees \(d_1,\ldots,d_n\), where a marked vertex is seen as a face of degree \(0\). It is a quasi-polynomial in \((d_1,\ldots,d_n)\), as shown previously by Norbury. Our derivation is bijective and based on the slice decomposition of planar maps. In the non-bipartite case, we also rely on enumeration results for two-type forests. We discuss the connection with the enumeration of non necessarily tight maps. In particular, we provide a generalization of Tutte's classical slicings formula to all non-bipartite maps.

Mathematics Subject Classifications: 05A15, 05A19

Keywords: Planar maps, bijective enumeration, slice decomposition

The Making of a Monetary Union: Evidence from the U.S. Discount Market 1914-1935

The decentralized structure of the Federal Reserve gave regional Reserve banks a large degree of autonomy in setting discount rates. This created repeated and continued periods of non-uniform discount rates across the 12 Federal Reserve districts. Commercial banks did not take full advantage of these differentials, reflecting the effectiveness of qualitative restrictions on the use of discount window liquidity in limiting the geographical movement of funds. While the choice of regional autonomy over complete financial integration was reasonable given the characteristics of the U.S. monetary union in the interwar period, the Federal Reserve failed to use this autonomy to stabilize regional economic activity relative to the national average. The diagnosis that the costs of decentralization outweighed the gains from regional differentiation motivated reforms that standardized and centralized control of Reserve bank discount policies.

Supply-Side Policies in the Depression: Evidence from France

The effects of supply-side policies in depressed economies are controversial. We shed light on this debate using evidence from France in the 1930s. In 1936, France departed from the gold standard and implemented mandatory wage increases and hours restrictions. Deflation ended but output stagnated. We present time-series and cross-sectional evidence that these supply-side policies, in particular the 40-hour law, contributed to French stagflation. These results are inconsistent both with the standard one-sector new Keynesian model and with a medium scale, multi-sector model calibrated to match our cross-sectional estimates. We conclude that the new Keynesian model is a poor guide to the effects of supply-side shocks in depressed economies.

Fiscal Policy in the Depression: Evidence from Digging Holes and Filling Them

I use historical data on military spending on a strategic defense system - the Maginot Line - during the interwar period in France to estimate the effect of fiscal policy in a depressed economy. Planning for the construction of the defense system took place in the 1920s, while actual spending mostly occurred in the 1930s. Factors such as the natural local terrain, and the location of military threat generated variations in spending across space and time that were not related to current or expected levels of economic activity in these areas. I exploit these variations to estimate a local government spending multiplier that controls for aggregate shocks and aggregate policy, such as changes in distortionary taxes and aggregate monetary policy. I find a local multiplier of 1. Given the likely bias introduced by the use of fiscal data to proxy local economic activity and by the \textit{ad-hoc} assumptions made to reconstruct a precise geographical allocation of border fortification spending, I see my result as evidence that the true local government spending multiplier is at least equal to 1.

We study the symplectic Howe duality using two new and independent combinatorial methods: via determinantal formulae on the one hand, and via (bi)crystals on the other hand. The first approach allows us to establish a generalised version where weight multiplicities are replaced by branching coefficients. In turn, this generalised Howe duality is used to prove the injectivity of induction for Levi branchings as previously conjectured by the last two authors.

Mathematics Subject Classifications: 17B10, 17B37, 05E05, 05E10

Keywords: Lie algebras, representation theory, Schur-Weyl duality, Howe duality, crystals, Schur functions, induced modules