eriksywu

Objective

Find a mapping $DS$ (cumulative downsampler) such that $$DS : {X} \longrightarrow {Y} \times {R}, \quad where \quad {X} = \mathbb{R}^N, \quad {Y} = \mathbb{R}^M, \quad M \le N,\quad N \gt 1, \quad M \gt 1 \quad \text{and} \quad M \text{ is a cost to minimize.}$$

$DS$ has these constraints:

1. $\exists {m} in {M} \text{such that } Increase(X) = Increase(D(X)) ; \text{for all } x \in X$
   • The increase observed in the input and output must be equal
2. $\forall x \in X, ; y = DS(x) ; => y_1 = x_1 ; and ; y_m = x_n$

eriksywu

Objective

Prove that there exists a mapping $DS$ (cumulative downsampler) such that $$DS : {X} \longrightarrow {Y}, \quad where \quad {X} = \mathbb{R_{\ge 0}}^N, \quad {Y} = \mathbb{R_{\ge 0}}^M, \quad M \le N,\quad N \gt 1, \quad M \gt 1 \quad \text{and} \quad M \text{ is a cost to minimize.}$$

$DS$ has these constraints:

1. $\exists {m} \in M, \text{ such that } Increase(X) = Increase(D(X)) ; \text{for all } x \in X$
   • The increase observed in the input and output must be equal
2. $\forall x \in X, \quad y = DS(x) \quad => y_1 = x_1 \quad and \quad y_m = x_n$

eriksywu

apiVersion: apps/v1
kind: Deployment
metadata:
  name: otelcollector-deployment
spec:
  replicas: 1
  selector:
    matchLabels:
      app: otelcollector-deployment
  template:

eriksywu

apiVersion: apps/v1
kind: Deployment
metadata:
  name: promtest
  labels:
    app: promtest
spec:
  replicas: 1
  selector:
    matchLabels:

eriksywu

kind: DaemonSet
apiVersion: apps/v1
metadata:
  name: downgradecontainerd
  namespace: kube-system
  labels:
    app: downgradecontainerd
spec:
  selector:
    matchLabels:

eriksywu

kind: DaemonSet
apiVersion: apps/v1
metadata:
  name: downgradecontainerd
  namespace: kube-system
  labels:
    app: downgradecontainerd
spec:
  selector:
    matchLabels:

eriksywu

kind: DaemonSet
apiVersion: apps/v1
metadata:
  name: ensure-no-dup
  namespace: kube-system
  labels:
    app: ensure-no-dup
spec:
  selector:
    matchLabels:

eriksywu

kind: DaemonSet
apiVersion: apps/v1
metadata:
  name: snat-exemption
  namespace: kube-system
  labels:
    app: snat-exemption
spec:
  selector:
    matchLabels:

eriksywu

apiVersion: v1
kind: Pod
metadata:
  name: busybox1
  labels:
    app: busybox1
spec:
  containers:
  - image: busybox
    command:

eriksywu

{
	"apiVersion": "vlabs",
	"location": "",
	"properties": {
		"orchestratorProfile": {
			"orchestratorType": "Kubernetes",
			"orchestratorRelease": "1.17",
			"kubernetesConfig": {
                "components": [{
                    "name": "kube-addon-manager",