Definition. The boundary map for a graph G is the v à e matrix defined by
â(ei) = head(ei) â tail(ei)
The graph Laplacian LG for a graph G is the symmetric v à v matrix defined by
LG := ââT
.
We proved in the notes that for any vector v â R
v
, we have
QLG
(v) = hv, LG vi =
Xe
i=1
vhead(ei) â vtail(ei)
2
.
- (10 points) Suppose that G and G0 have the same vertices and edges v1, . . . , vv = v
0
1
, . . . , v0
v0
and e1, . . . , ee = e
0
1
, . . . , e0
e
0, but the orientations of the edges may not agree.
Prove that LG = LG0.
Sample Solution
The Learning Trustâs Approach to SEN (2009) also then discusses the issue of disability and SEN, where there may be an overlap between the needs of both groups of students. âA disability might give rise to a learning difficulty that calls for SEN provision to be made for a child. Many children who have SEN will also be defined as being disabled under the EA. However, not all children who are defined as disabled under the EA will have SEN. For example, pupils with severe asthma, arthritis or diabetes may not have SEN but will have rights under the EA. Similarly not all children with SEN will be defined as having a disability under the EAâ. This therefore demonstrates clearly the overlap whereby a child may fall within either one or more of the definitions. The diagram below assists in explaining the difference between SEN and disability and where they overlap. According to The Learning Trustâs Approach to SEN (2009) demonstrates how useful this overlap can be when assessing the effect the EA has had on provisions made for those disabled students who require SEN considerations. As illustrated by OâMahony and R.Rieser (2001) a large number of students will be classified as both SEN and disabled. They will access the EA under the terms of anti-discrimination measures and reasonable adjustments. Data for SEN students Statistics from the Department of Education SFR (2013) indicate that there are 216,030 pupils who have statements who attend state-funded educational institutions in 2012/13. Statistics indicate that the most common primary type of need was autistic spectrum disorder which accounted for 21.9 per cent of all pupils with statements and the least common was multi-sensory impairment with 0.2 per cent of these students having statements. 462,045 pupils were identified as being at School Action Plus, where the most common types of need were behaviour, emotional and social difficulties, moderate learning difficulty and speech, language and communication needs the least common were multi-sensory impairment and profound and multiple learning difficulties.>
The Learning Trustâs Approach to SEN (2009) also then discusses the issue of disability and SEN, where there may be an overlap between the needs of both groups of students. âA disability might give rise to a learning difficulty that calls for SEN provision to be made for a child. Many children who have SEN will also be defined as being disabled under the EA. However, not all children who are defined as disabled under the EA will have SEN. For example, pupils with severe asthma, arthritis or diabetes may not have SEN but will have rights under the EA. Similarly not all children with SEN will be defined as having a disability under the EAâ. This therefore demonstrates clearly the overlap whereby a child may fall within either one or more of the definitions. The diagram below assists in explaining the difference between SEN and disability and where they overlap. According to The Learning Trustâs Approach to SEN (2009) demonstrates how useful this overlap can be when assessing the effect the EA has had on provisions made for those disabled students who require SEN considerations. As illustrated by OâMahony and R.Rieser (2001) a large number of students will be classified as both SEN and disabled. They will access the EA under the terms of anti-discrimination measures and reasonable adjustments. Data for SEN students Statistics from the Department of Education SFR (2013) indicate that there are 216,030 pupils who have statements who attend state-funded educational institutions in 2012/13. Statistics indicate that the most common primary type of need was autistic spectrum disorder which accounted for 21.9 per cent of all pupils with statements and the least common was multi-sensory impairment with 0.2 per cent of these students having statements. 462,045 pupils were identified as being at School Action Plus, where the most common types of need were behaviour, emotional and social difficulties, moderate learning difficulty and speech, language and communication needs the least common were multi-sensory impairment and profound and multiple learning difficulties.>
Is this question part of your Assignment?
We can help
Our aim is to help you get A+ grades on your Coursework.
We handle assignments in a multiplicity of subject areas including Admission Essays, General Essays, Case Studies, Coursework, Dissertations, Editing, Research Papers, and Research proposals
Header Button Label: Get Started NowGet Started Header Button Label: View writing samplesView writing samples