State-Dependent Demand Estimation with Initial Conditions Correction

The authors analyze the initial conditions bias in the estimation of brand choice models with structural state dependence. Using a combination of Monte Carlo simulations and empirical case studies of shopping panels, they show that popular, simple solutions that misspecify the initial conditions are likely to lead to bias even in relatively long panel data sets. The magnitude of the bias in the state dependence parameter can be as large as a factor of 2–2.5. The authors propose a solution to the initial conditions problem that samples the initial states as auxiliary variables in a Markov chain Monte Carlo procedure. The approach assumes that the joint distribution of prices and consumer choices is in equilibrium, which is plausible for the mature consumer packaged goods products commonly used in empirical applications. In Monte Carlo simulations, the approach recovers the true parameter values even in relatively short panels. Finally, the authors propose a diagnostic tool that uses common, biased approaches to bound the values of the state dependence and construct a computationally light test for state dependence.

A plausible solution to the problem of initial conditions for inflation

We propose yet another solution to the initial condition problem of inflation associated with homogeneity beyond the horizon at the onset of inflation, in cases where inflation is preceded by a radiation era. One may argue that causality will allow for smoothness over the causal horizon scale [Formula: see text], but for thermal inflationary scenarios, the background inflaton field will only be correlated over the thermal correlation length [Formula: see text] which is much smaller than [Formula: see text]. We argue, with examples, that if the number of relativistic degrees of freedom in the preinflationary era is very large [Formula: see text] then the thermal correlation length can be of the order of the causal horizon size alleviating the initial conditions problem of inflation.

Axion hilltops, Kahler modulus quintessence and the swampland criteria

We study the interplay among extrema of axion potentials, Kahler moduli stabilization and the swampland criteria. We argue that moving away from the minima of nonperturbatively generated axion potentials can lead to a runaway behavior of moduli that govern the couplings in the effective field theory. The proper inclusion of these degrees of freedom resolves the conflict between periodic axion potentials and the gradient de Sitter criterion, without the need to invoke the refined de Sitter criterion. We investigate the possibility of including this runaway direction as a model of quintessence that satisfies the swampland criteria. Using a single nonperturbative effect, the maximum along the axion direction provides such a runaway direction, which is unstable in the axion directions, sensitive to initial conditions and too steep to allow for a Hubble time of expansion without violating the field excursion criterion. Adding a second nonperturbative effect generates a saddle point in the potential satisfying the refined de Sitter criterion, which solves the steepness problem and improves the initial conditions problem although some fine-tuning remains required.

HARD WORK AND PROBLEM SOLVING BASED ON KRULIK-RUDNICK'S HEURISTIC THEORY ON PROJECT BASED LEARNING WITH OQALE APPROACH OF 5th GRADE ELEMENTARY SCHOOL STUDENTS

The study aimed to describe the state of early poblem solving, the effectiveness of learning, and discription the application of the learning to had work character and problem solving mathematics students. The research is the kind of research concurerent embedded. Technic the data with using interviews, observation, and tests. Technic data analysis using analysis discriptif and statistical tests influence regression, the appeal, and test an increase in the gain. The results of the study showed that the initial conditions problem solving students average be low; effectiveness of indicated by the average capability problem solving mathematical students experiment has reached KKM that is above 74,5%, the ability problem solving mathematical class experiment better than class control, hard work and skill problem solving mathematical students have had a positive impact of the ability of mathematical problem soling students, with big the influence of 88,7%, increased capacity problem solving mathematical class experiment higher than class control; the results of a description of this research is improving hard work students; skills literacy mathematics; and ability problem solving mathematical stdents with a score of the gain 0,59; 0,66; 0,70.

Initialization of Riemann-Liouville and Caputo Fractional Derivatives

Riemann-Liouville and Caputo fractional derivatives are fundamentally related to fractional integration operators. Consequently, the initial conditions of fractional derivatives are the frequency distributed and infinite dimensional state vector of fractional integrators. The paper is dedicated to the estimation of these initial conditions and to the validation of the initialization problem based on this distributed state vector. Numerical simulations applied to Riemann-Liouville and Caputo derivatives demonstrate that the initial conditions problem can be solved thanks to the estimation of the initial state vector of the fractional integrator.