Heat capacities have been measured as a function of temperature for aluminum cluster cations with 16–48 atoms. Some clusters show peaks in their heat capacities that are attributed to melting transitions. The smallest cluster to show a well-defined melting transition is Al28 . For clusters with significant peaks in their heat capacities, the results can be fitted by a two-state model incorporat...

We consider two-variable first-order logic on finite words with a fixed number of quantifier alternations. We show that all languages with a neutral letter definable using the order and finite-degree predicates are also definable with the order predicate only. From this result we derive the separation of the alternation hierarchy of two-variable logic on this signature.

We consider a modified version of the situation calculus built using a two-variable fragment of the first-order logic extended with counting quantifiers. We mention several additional groups of axioms that need to be introduced to capture taxonomic reasoning. We show that the regression operator in this framework can be defined similarly to regression in the Reiter’s version of the situation ca...

In this paper, we compare four different Subspace Multiple Linear Regression methods for 3D face shape prediction from a single 2D intensity image. This problem is situated within the low observation-to-variable ratio context, where the sample covariance matrix is likely to be singular. Lately, efforts have been directed towards latent-variable based methods to estimate a regression operator wh...

The uniform one-dimensional fragment of first-order logic, U1, is a recently introduced formalism that extends two-variable logic in a natural way to contexts with relations of all arities. We survey properties of U1 and investigate its relationship to description logics designed to accommodate higher arity relations, with particular attention given to DLRreg . We also define a description logi...

In this paper, we propose an EXPSPACE tableaux-based algorithm for SHOIQ. The construction of this algorithm is founded on the standard tableauxbased method for SHOIQ and the technique used for designing a NEXPTIME algorithm for the two-variable fragment of first-order logic with counting quantifiers C.

We consider the two-variable fragment of first-order logic with counting, subject to the stipulation that a single distinguished binary predicate be interpreted as an equivalence. We show that the satisfiability and finite satisfiability problems for this logic are both NEXPTIME-complete. We further show that the corresponding problems for two-variable first-order logic with counting and two eq...

Fragments of first-order logic over words can often be characterized in terms of finite monoids, and identities of omega-terms are an effective mechanism for specifying classes of monoids. Huschenbett and the first author have shown how to use infinite Ehrenfeucht-Fra¨ıssé games on linear orders for showing that some given fragment satisfies an identity of omega-terms (STACS 2014). After revisi...

We study the finite satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers (C) and interpreted over linearly ordered structures. We show that the problem is undecidable in the case of two linear orders (in the presence of two other binary symbols). In the case of one linear order it is NExpTime-complete, even in the presence of the successor...