Monotone flows with dense periodic orbits

The main result is Theorem 1: A flow on a connected open set X ⊂ Rd is globally periodic provided (i) periodic points are dense in X, and (ii) at all positive times the flow preserves the partial order defined by a closed convex cone that has nonempty interior and contains no straight line. The proof uses the analog for homeomorphisms due to B. Lemmens et al. [27], a classical theorem of D. Montgomery [31, 32], and a sufficient condition for the nonstationary periodic points in a closed order interval to have rationally related periods (Theorem 2)

First-principles thermodynamic modeling of lanthanum chromate perovskites

Tendencies toward local atomic ordering in (A,A′)(B,B′)O_(3−δ) mixed composition perovskites are modeled to explore their influence on thermodynamic, transport, and electronic properties. In particular, dopants and defects within lanthanum chromate perovskites are studied under various simulated redox environments. (La_(1−x),Sr_x)(Cr_(1−y),Fe_y)O_(3−δ) (LSCF) and (La_(1−x),Sr_x)(Cr_(1−y),Ru_y)O_(3−δ) (LSCR) are modeled using a cluster expansion statistical thermodynamics method built upon a density functional theory database of structural energies. The cluster expansions are utilized in lattice Monte Carlo simulations to compute the ordering of Sr and Fe(Ru) dopant and oxygen vacancies (Vac). Reduction processes are modeled via the introduction of oxygen vacancies, effectively forcing excess electronic charge onto remaining atoms. LSCR shows increasingly extended Ru-Vac associates and short-range Ru-Ru and Ru-Vac interactions upon reduction; LSCF shows long-range Fe-Fe and Fe-Vac interaction ordering, inhibiting mobility. First principles density functional calculations suggest that Ru-Vac associates significantly decrease the activation energy of Ru-Cr swaps in reduced LSCR. These results are discussed in view of experimentally observed extrusion of metallic Ru from LSCR nanoparticles under reducing conditions at elevated temperature

Relational constraints in coalition formation

Equilibrium Theory;econometrics

Machine learning on quantum experimental data toward solving quantum many-body problems

Advancements in the implementation of quantum hardware have enabled the acquisition of data that are intractable for emulation with classical computers. The integration of classical machine learning (ML) algorithms with these data holds potential for unveiling obscure patterns. Although this hybrid approach extends the class of efficiently solvable problems compared to using only classical computers, this approach has been realized for solving restricted problems because of the prevalence of noise in current quantum computers. Here, we extend the applicability of the hybrid approach to problems of interest in many-body physics, such as predicting the properties of the ground state of a given Hamiltonian and classifying quantum phases. By performing experiments with various error-reducing procedures on superconducting quantum hardware with 127 qubits, we managed to acquire refined data from the quantum computer. This enabled us to demonstrate the successful implementation of classical ML algorithms for systems with up to 44 qubits. Our results verify the scalability and effectiveness of the classical ML algorithms for processing quantum experimental data.Comment: 25 pages, 5 figures; supplementary information 35 pages, 17 figures, 1 tabl

Coalition formation in large network economies

Organizational Structure;economic networks

Classification of Triadic Chord Inversions Using Kohonen Self-organizing Maps

In this paper we discuss the application of the Kohonen Selforganizing Maps to the classification of triadic chords in inversions and root positions. Our motivation started in the validation of Schönberg´s hypotheses of the harmonic features of each chord inversion. We employed the Kohonen network, which has been generally known as an optimum pattern classification tool in several areas, including music, to verify that hypothesis. The outcomes of our experiment refuse the Schönberg´s assumption in two aspects: structural and perceptual/functional