We prove that the amalgamated product of free groups with cyclic amalgamations satisfying certain conditions are virtually free-by-cyclic. In case the cyclic amalgamated subgroups lie outside the derived group such groups are free-by-cyclic. Similarly a one-relator HNN-extension in which the conjugated elements either coincide or are independent modulo the derived group is shown to be free-by-c...

In this paper, we analyze four typical sequential Hopfield neural network (HNN) based algorithms for image restoration and reconstruction, which are the modified HNN (PK) algorithm, the HNN (ZCVJ) algorithm with energy checking, the eliminating-highest-error (EHE) algorithm, and the simulated annealing (SA) algorithm. A new measure, the correct transition probability (CTP), is proposed for perf...

Conceptual cost estimates are important to project feasibility studies and impact upon final project success. Such estimates provide significant information that can be used in project evaluations, engineering designs, cost budgeting and cost management. This study proposes an artificial intelligence approach, the evolutionary fuzzy hybrid neural network (EFHNN), to improve conceptual cost esti...

Lymph node segmentation is an important yet challenging problem in medical image analysis. The presence of enlarged lymph nodes (LNs) signals the onset or progression of a malignant disease or infection. In the thoracoabdominal (TA) body region, neighboring enlarged LNs often spatially collapse into “swollen” lymph node clusters (LNCs) (up to 9 LNs in our dataset). Accurate segmentation of TA L...

An extraordinary theorem of Gromov, [4], characterizes the finitely generated groups of polynomial growth; a group has polynomial growth iff it is nilpotent by finite. This theorem went a long way from its roots in the class of discrete subgroups of solvable Lie groups. Wolf, [11], proved that a polycyclic group of polynomial growth is nilpotent by finite. This theorem is primarily about linear...

Due to the existence of membrane potential differences, electromagnetic induction flows can be induced in interconnected neurons Hopfield neural network (HNN). To express flows, this paper presents a unified memristive HNN model using hyperbolic-type memristors link neurons. By employing theoretical analysis along with multiple numerical methods, we explore effects on three Three cases are clas...