Corporate Hierarchies and the Size of Nations: Theory and Evidence

Corporate organization varies within a country and across countries with country size. The paper starts by establishing some facts about corporate organization based on unique data of 660 Austrian and German corporations. The larger country (Germany) has larger firms with flatter more decentral corporate hierarchies compared to the smaller country (Austria). Firms in the larger country change their organization less fast than firms in the smaller country. Over time firms have been introducing less hierarchical organizations by delegating power to lower levels of the corporation. We develop a theory which explains these facts and which links these features to the trade environment that countries and firms face. We introduce firms with internal hierarchies in a Krugman (1980) model of trade. We show that international trade and the toughness of competition in international markets induce a power struggle in firms which eventually leads to decentralized corporate hierarchies. We offer econometric evidence which is consistent with the models predictions

Enhanced van der Waals interaction at interfaces

Using a recently obtained (general) formula for the interaction energy between an excited and a ground-state atom (Sherkunov Y 2007 Phys. Rev. A 75 012705), we consider the interaction energy between two such atoms near the interface between two media. We demonstrate that under the circumstances of the resonant coupling of the excited atom to the surface polariton mode of a vacuum-medium system the nonretarded atom*-atom interaction energy can be enhanced by (several) orders of magnitude in comparison with the van der Waals interaction energy of the two isolated atoms.Comment: 8 pages, 5 figures, local-field corrections included and improved presentatio

Glassy Phase of Optimal Quantum Control

We study the problem of preparing a quantum many-body system from an initial to a target state by optimizing the fidelity over the family of bang-bang protocols. We present compelling numerical evidence for a universal spin-glass-like transition controlled by the protocol time duration. The glassy critical point is marked by a proliferation of protocols with close-to-optimal fidelity and with a true optimum that appears exponentially difficult to locate. Using a machine learning (ML) inspired framework based on the manifold learning algorithm t-SNE, we are able to visualize the geometry of the high-dimensional control landscape in an effective low-dimensional representation. Across the transition, the control landscape features an exponential number of clusters separated by extensive barriers, which bears a strong resemblance with replica symmetry breaking in spin glasses and random satisfiability problems. We further show that the quantum control landscape maps onto a disorder-free classical Ising model with frustrated nonlocal, multibody interactions. Our work highlights an intricate but unexpected connection between optimal quantum control and spin glass physics, and shows how tools from ML can be used to visualize and understand glassy optimization landscapes.Comment: Modified figures in appendix and main text (color schemes). Corrected references. Added figures in SI and pseudo-cod

Universality of Tip Singularity Formation in Freezing Water Drops

A drop of water deposited on a cold plate freezes into an ice drop with a pointy tip. While this phenomenon clearly finds its origin in the expansion of water upon freezing, a quantitative description of the tip singularity has remained elusive. Here we demonstrate how the geometry of the freezing front, determined by heat transfer considerations, is crucial for the tip formation. We perform systematic measurements of the angles of the conical tip, and reveal the dynamics of the solidification front in a Hele-Shaw geometry. It is found that the cone angle is independent of substrate temperature and wetting angle, suggesting a universal, self-similar mechanism that does not depend on the rate of solidification. We propose a model for the freezing front and derive resulting tip angles analytically, in good agreement with observations.Comment: Letter format, 5 pages, 3 figures. Note: authors AGM and ORE contributed equally to the pape

Broken symmetry in a two-qubit quantum control landscape

We analyze the physics of optimal protocols to prepare a target state with high fidelity in a symmetrically coupled two-qubit system. By varying the protocol duration, we find a discontinuous phase transition, which is characterized by a spontaneous breaking of a $\mathbb{Z}_2$ symmetry in the functional form of the optimal protocol, and occurs below the quantum speed limit. We study in detail this phase and demonstrate that even though high-fidelity protocols come degenerate with respect to their fidelity, they lead to final states of different entanglement entropy shared between the qubits. Consequently, while globally both optimal protocols are equally far away from the target state, one is locally closer than the other. An approximate variational mean-field theory which captures the physics of the different phases is developed

Reinforcement Learning in Different Phases of Quantum Control

The ability to prepare a physical system in a desired quantum state is central to many areas of physics such as nuclear magnetic resonance, cold atoms, and quantum computing. Yet, preparing states quickly and with high fidelity remains a formidable challenge. In this work we implement cutting-edge Reinforcement Learning (RL) techniques and show that their performance is comparable to optimal control methods in the task of finding short, high-fidelity driving protocol from an initial to a target state in non-integrable many-body quantum systems of interacting qubits. RL methods learn about the underlying physical system solely through a single scalar reward (the fidelity of the resulting state) calculated from numerical simulations of the physical system. We further show that quantum state manipulation, viewed as an optimization problem, exhibits a spin-glass-like phase transition in the space of protocols as a function of the protocol duration. Our RL-aided approach helps identify variational protocols with nearly optimal fidelity, even in the glassy phase, where optimal state manipulation is exponentially hard. This study highlights the potential usefulness of RL for applications in out-of-equilibrium quantum physics.Comment: A legend for the videos referred to in the paper is available on https://mgbukov.github.io/RL_movies

Simulação do efeito combinado de palhada e adubação na modelagem da cana-de-açúcar.

O objetivo geral do trabalho foi modelar o crescimento da cana-de-açúcar em sistemas de colheita de cana crua e queimada, com diferentes doses de adubação nitrogenada 60, 120 e 180 Kg.ha-1

Spatio-temporal variability of sugarcane yield efficiency in the state of São Paulo, Brazil.

The objective of this work was to assess the spatial and temporal variability of sugarcane yield efficiency and yield gap in the state of São Paulo, Brazil, throughout 16 growing seasons, considering climate and soil as main effects, and socioeconomic factors as complementary. An empirical model was used to assess potential and attainable yields, using climate data series from 37 weather stations. Soil effects were analyzed using the concept of production environments associated with a soil aptitude map for sugarcane. Crop yield efficiency increased from 0.42 to 0.58 in the analyzed period (1990/1991 to 2005/2006 crop seasons), and yield gap consequently decreased from 58 to 42%. Climatic factors explained 43% of the variability of sugarcane yield efficiency, in the following order of importance: solar radiation, water deficit, maximum air temperature, precipitation, and minimum air temperature. Soil explained 15% of the variability, considering the average of all seasons. There was a change in the correlation pattern of climate and soil with yield efficiency after the 2001/2002 season, probably due to the crop expansion to the west of the state during the subsequent period. Socioeconomic, biotic and crop management factors together explain 42% of sugarcane yield efficiency in the state of São Paulo

Discovery of Blue Hook Stars in the Massive Globular Cluster M54

We present BV photometry centered on the globular cluster M54 (NGC 6715). The color-magnitude diagram clearly shows a blue horizontal branch extending anomalously beyond the zero age horizontal branch theoretical models. These kinds of horizontal branch stars (also called ``blue hook'' stars), which go beyond the lower limit of the envelope mass of canonical horizontal branch hot stars, have so far been known to exist in only a few globular clusters: NGC 2808, Omega Centauri (NGC 5139), NGC 6273, and NGC 6388. Those clusters, like M54, are among the most luminous in our Galaxy, indicating a possible correlation between the existence of these types of horizontal branch stars and the total mass of the cluster. A gap in the observed horizontal branch of M54 around T(eff)= 27000 K could be interpreted within the late helium flash theoretical scenario, a possible explanation for the origin of those stars.Comment: 10 pages, 2 figures, accepted for publication in the Astrophysical Journa

Eficiência da produção agrícola de cana-de-açúcar no Estado de São Paulo entre as safras 1990/1991 a 2005/2006.

O objetivo do presente trabalho foi mapear a eficiência produtiva ao longo de 16 safras agrícolas, analisando a importância relativa do clima e do solo e inferindo sobre os aspectos socioeconômicos e conjunturais que interferem na sua composição. Admitiu-se que a energia disponível pode ser dada pela produtividade atingível estimada por modelos de simulação baseados em variáveis ambientais, enquanto que a produtividade observada representaria a energia efetivamente utilizada no processo. Os elementos climáticos explicaram 43% da variabilidade da eficiência da produção agrícola de cana-de-açúcar, na seguinte ordem de importância: radiação solar, deficiência hídrica, temperatura máxima, precipitação e temperatura mínima. Observou-se que o solo explicou 15% da variabilidade da eficiência, na média de todas as safras. Analisando a variação temporal dessa correlação, notou-se uma alteração no padrão de correlação a partir da safra 2001/2002. Em média, 42% da variabilidade da eficiência da produção de cana-de-açúcar no Estado de São Paulo foram explicadas por outros fatores, além do clima e do solo.CBA 2009