The Zagreb eccentricity indices are the eccentricity reformulation of the Zagreb indices. Let H be a simple graph. The first Zagreb eccentricity index (E1(H)) is defined to be the summation of squares of the eccentricity of vertices, i.e., E1(H) = ∑u∈V(H) Symmetry 2016, 9, 7; doi: 10.3390/sym9010007 www.mdpi.com/journal/symmetry Article First and Second Zagreb Eccentricity Indices of Thorny Gra...

Strategies to reduce excess salt consumption play an important role in preventing cardiovascular disease, which is the largest contributor to global mortality from non-communicable diseases. In many countries, voluntary food reformulation programs seek to reduce salt levels across selected product categories, guided by aspirational targets to be achieved progressively over time. This paper eval...

We show that Connes’ embedding conjecture (CEC) is equivalent to a real version of the same (RCEC). Moreover, we show that RCEC is equivalent to a real, purely algebraic statement concerning trace positive polynomials. This purely algebraic reformulation of CEC had previously been given in both a real and a complex version in a paper of the last two authors. The second author discovered a gap i...

We study a general framework for query rewriting in the presence of an arbitrary first-order logic ontology over a database signature. The framework supports deciding the existence of a safe-range first-order equivalent reformulation of a query in terms of the database signature, and if so, it provides an effective approach to construct the reformulation based on interpolation using standard th...

The attributional reformulation of the learned helplessness model claims that an explanatory style in which bad events are explained by internal, stable, and global causes is associated with depressive symptoms. Furthermore, this style is claimed to be a risk factor for subsequent depression when bad events are encountered. We describe a variety of new investigations of the helplessness reformu...

BACKGROUND AND OBJECTIVES The Tick programme of the National Heart Foundation (NHF) is the longest standing voluntary front of pack signpost nutrition logo in New Zealand. It provides a platform for collaboration with the food industry to encourage development of healthier products. This study evaluated the impact of the Tick programme on sodium in processed food. METHODS AND STUDY DESIGN Fif...

We propose a reformulation algorithm as well as a set of re-formulation rules for models of constraint satisfaction problems written in our high-level constraint programming language esra, which is more expressive than opl and is compiled into opl. For the class of mapping problems, the reformulation algorithm achieves models that integrate a constraint programming formulation and an integer pr...

Specification by reformulation is a general interface paradigm. It is an abstraction of retrieval by reformulation, a paradigm used in previous systems for assisting users in formulating database queries. Specification by reformulation serves as a general foundation upon which domain specific applications can be built. To illustrate its usage, we describe three services built within it: a datab...

We are concerned with the compatible gauge reformulation for H(div) equations and the design of fast solvers of the resulting linear algebraic systems as in [5]. We propose an algebraic reformulation of the discrete H(div) equations along with an algebraic multigrid (AMG) technique for the reformulated problem. The reformulation uses discrete Hodge decompositions on co-chains to replace the dis...

Society today is calling for optimized lipid content in meat products line with health recommendations and nutritional guidelines. The product reformulation strategies offering the biggest advantages improving are based on replacing animal fat materials featuring solid-fat characteristics that created using gelling procedures containing vegetable and/or marine oils. From among different materia...