We show that the Vassiliev invariants of the knots contained in an embedding of a graph G into R 3 satisify certain equations that are independent of the choice of the embedding of G. By a similar observation we define certain edge-homotopy invariants and vertex-homotopy invariants of spatial graphs based on the Vassiliev invariants of the knots contained… (More)
BACKGROUND Extracapsular spread (ECS) of lymph node metastasis in head and neck cancers, including oral squamous cell carcinomas (OSCCs), is known to reflect tumour aggressiveness, and is significantly associated with high rates of loco-regional recurrence, distant metastasis, and poor outcome. The purpose of this study was to confirm ECS as an important… (More)
By the works of Gusarov  and Habiro , it is known that a local move called the Cn move is strongly related to Vassiliev invariants of order less than n. The coefficient of the z n term in the Conway polynomial is known to be a Vassiliev invariant of order n. In this note, we will consider to what degree the relationship is strong with respect to… (More)
We will determine the condition that a homogeneous quadratic equation with rank four becomes the Darboux-Halphen-Brioshi system in terms of the associated non-associative algebra.