Assume that a maximum flow network comprises a node with no incoming arc other than the source node. Is it possible to remove this node without hurting the maximum flow? Is it possible to remove a node other than the sink node without causing an outgoing arc?

I am trying to execute the backward pass for a convolution network with layers (2 layer conv, relu, max pooling and linear, then softmax loss calculation). I have a hard time to retrieve x, y and probs at backward pass, the code does not recognize them as attributes. Please fix my code and show codes and output. Thank you   from .softmax_ce import SoftmaxCrossEntropyfrom .relu import ReLUfrom .max_pool import MaxPoolingfrom .convolution import Conv2Dfrom .linear import Linear class ConvNet:   """   Max Pooling of input   """   def __init__(self, modules, criterion):       self.modules = []       for m in modules:           if m['type'] == 'Conv2D':               self.modules.append(                   Conv2D(m['in_channels'],                          m['out_channels'],                          m['kernel_size'],                          m['stride'],                          m['padding'])               )           elif m['type'] == 'ReLU':               self.modules.append(…

Demonstrate that two red nodes in a route cannot be contiguous (e.g., parent and child). As a result, no more than half of the nodes in a path may be red.

Let f be an s,t-flow in an s, t-network D = (V, A) with capacities c : A → R>o, and assume that there is no augmenting path. Let X be the set of vertices that can be reached from s by unsaturated paths. Let (a, b) E A(X,V\ X). Explain why f(a,b) = c(a, b).