Simultaneous determination of two unknown thermal coefficients through a mushy zone model with an overspecified convective boundary condition

The simultaneous determination of two unknown thermal coefficients for a semi-infinite material under a phase-change process with a mushy zone according to the Solomon-Wilson-Alexiades model is considered. The material is assumed to be initially liquid at its melting temperature and it is considered that the solidification process begins due to a heat flux imposed at the fixed face. The associated free boundary value problem is overspecified with a convective boundary condition with the aim of the simultaneous determination of the temperature of the solid region, one of the two free boundaries of the mushy zone and two thermal coefficients among the latent heat by unit mass, the thermal conductivity, the mass density, the specific heat and the two coefficients that characterize the mushy zone. The another free boundary of the mushy zone, the bulk temperature and the heat flux and heat transfer coefficients at the fixed face are assumed to be known. According to the choice of the unknown thermal coefficients, fifteen phase-change problems arise. The study of all of them is presented and explicit formulae for the unknowns are given, beside necessary and sufficient conditions on data in order to obtain them. Formulae for the unknown thermal coefficients, with their corresponding restrictions on data, are summarized in a table.Comment: 27 pages, 1 Table, 1 Appendi

Efficient approaches for escaping higher order saddle points in non-convex optimization

Local search heuristics for non-convex optimizations are popular in applied machine learning. However, in general it is hard to guarantee that such algorithms even converge to a local minimum, due to the existence of complicated saddle point structures in high dimensions. Many functions have degenerate saddle points such that the first and second order derivatives cannot distinguish them with local optima. In this paper we use higher order derivatives to escape these saddle points: we design the first efficient algorithm guaranteed to converge to a third order local optimum (while existing techniques are at most second order). We also show that it is NP-hard to extend this further to finding fourth order local optima

Estimating ordered categorical variables using panel data: a generalized ordered probit model with an autofit procedure

Estimation procedures for ordered categories usually assume that the estimated coefficients of independent variables do not vary between the categories (parallel-lines assumption). This view neglects possible heterogeneous effects of some explaining factors. This paper describes the use of an autofit option for identifying variables that meet the parallel-lines assumption when estimating a random effects generalized ordered probit model. We combine the test procedure developed by Richard Williams (gologit2) with the random effects estimation command regoprob by Stefan Boes.generalized ordered probit; panel data; autofit, self-assessed health

Estimating ordered categorical variables using panel data: a generalized ordered probit model with an autofit procedure

Estimation procedures for ordered categories usually assume that the estimated coefficients of independent variables do not vary between the categories (parallel-lines assumption). This view neglects possible heterogeneous effects of some explaining factors. This paper describes the use of an autofit option for identifying variables that meet the parallel-lines assumption when estimating random effects generalized ordered probit model. We combine the test procedure developed by Richard Williams (gologit2) with the random effects estimation command regoprob by Stefan Boes.Generalized ordered probit; panel data; autofit, self-assessed health.

Attribute preference and priming in reference production : experimental evidence and computational modeling

Referring expressions (such as the red chair facing right) often show evidence of preferences (Pechmann, 1989; Belke & Meyer, 2002), with some attributes (e.g. colour) being more frequent and more often included when they are not required, leading to overspecified references. This observation underlies many computational models of Referring Expression Generation, especially those influenced by Dale & Reiter’s (1995) Incremental Algorithm. However, more recent work has shown that in interactive settings, priming can alter preferences. This paper provides further experimental evidence for these phenomena, and proposes a new computational model that incorporates both attribute preferences and priming effects. We show that the model provides an excellent match to human experimental data.peer-reviewe