Radius Agent is an online real estate brokerage focused on helping agents succeed

Radius

"How Many Colors Can the Human Eye See?": The Application

This Javascript Code Generates Random Quotes

এই জাভাস্ক্রিপ্ট কোড এলোমেলো উদ্ধৃতি তৈরি করে

Dieser Javascript-Code generiert zufällige Zitate

Este código Javascript genera citas aleatorias

Ce code Javascript génère des citations aléatoires

यह जावास्क्रिप्ट कोड यादृच्छिक उद्धरण उत्पन्न करता है

このJavascriptコードはランダムな引用を生成します

이 자바스크립트 코드는 무작위 인용문을 생성합니다

Este código Javascript gera citações aleatórias

Этот код Javascript генерирует случайные цитаты

Bu Javascript Kodu Rastgele Alıntılar Oluşturuyor

Mã Javascript này tạo ra các trích dẫn ngẫu nhiên

这段 JavaScript 代码可生成随机引号

Python Bokeh is one of the best Python packages for data visualization. Today, we are going to see some Python Bokeh Examples. I have also provided the Python Bokeh project source code on GitHub. Learn this easy visualization tool and add it to your Python stack. What is Python Bokeh? Python is a data visualization tool, or we can also say Python Bokeh is used to plot various types of graphs. There are various other graph plotting libraries like matplotlib, but Python Bokeh graphs are dynamic in nature, which means you can interact with the generated graph. See the below examples… Bokeh Installation 💻: Python Bokeh can be easily installed using PIP. You can install the Python Bokeh easily by running the command: pip install bokeh Now everything is ready, let’s go through the examples 🏃‍♂️… 1. LinePlot from bokeh.plotting import figure, show, output_notebook
x = [1, 2, 3, 4, 5]
y = [4, 5, 5, 7, 3]
p = figure(title="{LinePlot Python Bokeh Example")
p.line(x, y, line_width=2)
output_notebook()
show(p) | | Live Preview Source Code 🌿 Contribute 2. Scatter Plot from bokeh.plotting import figure, show, output_notebook
x = [1, 2, 3, 4, 5]
y = [4, 5, 5, 7, 3]
p = figure(title="Scatter Plot Python Bokeh Example by PratikPathak.com")
p.circle(x, y, size=10, color="navy", alpha=0.5)
output_notebook()
show(p) 3. Bar Chart from bokeh.plotting import figure, show, output_notebook
categories = ["A", "B", "C", "D", "E"]
values = [10, 15, 8, 12, 6]
p = figure(x_range=categories, title="Bar Chart Python Bokeh Example by PratikPathak.com")
p.vbar(x=categories, top=values, width=0.9)
output_notebook()
show(p) 4. Histogram from bokeh.plotting import figure, show, output_notebook
import numpy as np
data = np.random.normal(0, 1, 1000)
p = figure(title="Histogram Python Bokeh Example by PratikPathak.com")
p.hist(data, bins=30, color="navy", alpha=0.5)
output_notebook()
show(p) 5. Pie Chart from bokeh.plotting import figure, show, output_notebook
labels = ["A", "B", "C", "D"]
values = [10, 15, 8, 12]
p = figure(title="Pie Chart Python Bokeh Example by PratikPathak.com")
p.wedge(x=0, y=0, radius=0.4, start_angle=0.6, end_angle=2.6, color=["red", "green", "blue", "yellow"], legend_label=labels)
output_notebook()
show(p) | | Live Preview Source Code 🌿 Contribute 6. Time Series Plot from bokeh.plotting import figure, show, output_notebook
from datetime import datetime, timedelta
start = datetime(2023, 1, 1)
end = start + timedelta(days=30)
x = [start + timedelta(days=i) for i in range((end-start).days)]
y = [10, 15, 8, 12, 6, 18, 9, 14, 7, 11, 5, 16, 8, 13, 6]
p = figure(x_axis_type="datetime", title="Time Series Plot Python Bokeh Example by PratikPathak.com")
p.line(x, y, line_width=2)
output_notebook()
show(p) 7. Linked Brushing from bokeh.plotting import figure, show, output_notebook
from bokeh.models import ColumnDataSource
x1 = [1, 2, 3, 4, 5]
y1 = [4, 5, 5, 7, 3]
x2 = [2, 3, 4, 5, 6]
y2 = [2, 4, 6, 8, 4]
source = ColumnDataSource(data=dict(x1=x1, y1=y1, x2=x2, y2=y2))
p1 = figure(title="Scatter Plot 1")
p1.circle('x1', 'y1', source=source)
p2 = figure(title="Scatter Plot 2 Python Bokeh Example by PratikPathak.com")
p2.circle('x2', 'y2', source=source)
output_notebook()
show(p1, p2) 8. Hover Tooltips from bokeh.plotting import figure, show, output_notebook
from bokeh.models import HoverTool
x = [1, 2, 3, 4, 5]
y = [4, 5, 5, 7, 3]
p = figure(title="Hover Tooltips Python Bokeh Example by PratikPathak.com")
p.circle(x, y, size=15, fill_color="navy", line_color="white", alpha=0.5)
hover = HoverTool(tooltips=[("(x,y)", "(@x, @y)")])
p.add_tools(hover)
output_notebook()
show(p) 9. Annotations from bokeh.plotting import figure, show, output_notebook
from bokeh.models import Arrow, VectorRenderer, Label
x = [1, 2, 3, 4, 5]
y = [4, 5, 5, 7, 3]
p = figure(title="Annotations Python Bokeh Example by PratikPathak.com")
p.circle(x, y, size=15, fill_color="navy", line_color="white", alpha=0.5)
arrow = Arrow(x_start=2, y_start=4, x_end=3, y_end=5, line_width=2, line_color="red")
label = Label(x=3, y=6, text="This is a label", render_mode='css', border_line_color='black', border_line_alpha=1.0, background_fill_color='white', background_fill_alpha=0.5)
p.add_layout(arrow)
p.add_layout(label)
output_notebook()
show(p) 10. Custom Glyphs from bokeh.plotting import figure, show, output_notebook
from bokeh.models.glyphs import Asterisk
x = [1, 2, 3, 4, 5]
y = [4, 5, 5, 7, 3]
p = figure(title="Custom Glyphs Python Bokeh Example by PratikPathak.com")
p.add_glyph(x, y, Asterisk(size=20, line_color="red", fill_color="yellow"))
output_notebook()
show(p) | | Live Preview Source Code 🌿 Contribute 11. Gridlines and Axes from bokeh.plotting import figure, show, output_notebook
x = [1, 2, 3, 4, 5]
y = [4, 5, 5, 7, 3]
p = figure(title="Gridlines and Axes Python Bokeh Example by PratikPathak.com", x_range=(0, 6), y_range=(0, 8))
p.grid.grid_line_color = "grey"
p.grid.grid_line_dash = [6, 4]
p.xaxis.axis_label = "X-axis"
p.yaxis.axis_label = "Y-axis"
p.line(x, y, line_width=2)
output_notebook()
show(p) 12. Legend from bokeh.plotting import figure, show, output_notebook
x1 = [1, 2, 3, 4, 5]
y1 = [4, 5, 5, 7, 3]
x2 = [2, 3, 4, 5, 6]
y2 = [2, 4, 6, 8, 4]
p = figure(title="Legend Python Bokeh Example by PratikPathak.com")
p.line(x1, y1, line_width=2, color="red", legend_label="Line 1")
p.line(x2, y2, line_width=2, color="blue", legend_label="Line 2")
p.legend.location = "top_left"
output_notebook()
show(p) 13. Categorical Plots from bokeh.plotting import figure, show, output_notebook
fruits = ["Apples", "Pears", "Nectarines", "Plums", "Grapes", "Strawberries"]
counts = [5, 3, 4, 2, 4, 6]
p = figure(x_range=fruits, title="Categorical Plots Python Bokeh Example by PratikPathak.com")
p.vbar(x=fruits, top=counts, width=0.9)
p.xaxis.axis_label = "Fruit"
p.yaxis.axis_label = "Count"
p.xaxis.axis_label_text_font_size = "12pt"
p.yaxis.axis_label_text_font_size = "12pt"
output_notebook()
show(p) 14. Subplots from bokeh.plotting import figure, show, output_notebook
from bokeh.layouts import gridplot
x1 = [1, 2, 3, 4, 5]
y1 = [4, 5, 5, 7, 3]
x2 = [2, 3, 4, 5, 6]
y2 = [2, 4, 6, 8, 4]
p1 = figure(title="Scatter Plot 1 Python Bokeh Example by PratikPathak.com")
p1.circle(x1, y1, size=10, color="navy", alpha=0.5)
p2 = figure(title="Scatter Plot 2 Python Bokeh Example by PratikPathak.com")
p2.circle(x2, y2, size=10, color="red", alpha=0.5)
grid = gridplot([[p1, p2]], plot_width=400, plot_height=400)
output_notebook()
show(grid) 15. Interactive Plots from bokeh.plotting import figure, show, output_notebook
from bokeh.models import ColumnDataSource, HoverTool, BoxSelectTool
import numpy as np
x = np.random.random(1000)
y = np.random.random(1000)
source = ColumnDataSource(data=dict(x=x, y=y))
p = figure(title="Interactive Plots Python Bokeh Example by PratikPathak.com", tools="hover,box_select")
p.circle('x', 'y', source=source, size=3, color="navy", alpha=0.5)
hover = HoverTool(tooltips=[("(x,y)", "(@x, @y)")])
p.add_tools(hover)
output_notebook()
show(p) | | Live Preview Source Code 🌿 Contribute 16. Linked Panning and Zooming from bokeh.plotting import figure, show, output_notebook
from bokeh.models import Range1d
x1 = [1, 2, 3, 4, 5]
y1 = [4, 5, 5, 7, 3]
x2 = [2, 3, 4, 5, 6]
y2 = [2, 4, 6, 8, 4]
p1 = figure(title="Scatter Plot 1 Python Bokeh Example by PratikPathak.com", x_range=Range1d(0, 6), y_range=Range1d(0, 8))
p1.circle(x1, y1, size=10, color="navy", alpha=0.5)
p2 = figure(title="Scatter Plot 2 Python Bokeh Example by PratikPathak.com", x_range=p1.x_range, y_range=p1.y_range)
p2.circle(x2, y2, size=10, color="red", alpha=0.5)
output_notebook()
show(p1, p2) 17. Linked Axis Ranges from bokeh.plotting import figure, show, output_notebook
from bokeh.models import Range1d
x1 = [1, 2, 3, 4, 5]
y1 = [4, 5, 5, 7, 3]
x2 = [2, 3, 4, 5, 6]
y2 = [2, 4, 6, 8, 4]
p1 = figure(title="Scatter Plot 1", x_range=(0, 6), y_range=(0, 8))
p1.circle(x1, y1, size=10, color="navy", alpha=0.5)
p2 = figure(title="Scatter Plot 2", x_range=p1.x_range, y_range=p1.y_range)
p2.circle(x2, y2, size=10, color="red", alpha=0.5)
output_notebook()
show(p1, p2) 18. DateTime Axis from bokeh.plotting import figure, show, output_notebook
from datetime import datetime, timedelta
start = datetime(2023, 1, 1)
end = start + timedelta(days=30)
x = [start + timedelta(days=i) for i in range((end-start).days)]
y = [10, 15, 8, 12, 6, 18, 9, 14, 7, 11, 5, 16, 8, 13, 6]
p = figure(x_axis_type="datetime", title="Datetime Axis Python Bokeh Example by PratikPathak.com")
p.line(x, y, line_width=2)
output_notebook()
show(p) 19. Heatmap from bokeh.plotting import figure, show, output_notebook
import numpy as np
data = np.random.rand(10, 10)
p = figure(title="Heatmap Python Bokeh Example by PratikPathak.com")
p.image(image=[data], x=0, y=0, dw=10, dh=10, palette="Viridis256")
output_notebook()
show(p) 20. Streamgraph from bokeh.plotting import figure, show, output_notebook
from bokeh.models import ColumnDataSource
import numpy as np
# Generate some sample data
x = np.linspace(0, 10, 100)
y1 = np.cumsum(np.random.randn(100))
y2 = np.cumsum(np.random.randn(100))
y3 = np.cumsum(np.random.randn(100))
y4 = np.cumsum(np.random.randn(100))
y5 = np.cumsum(np.random.randn(100))
source = ColumnDataSource(data=dict(x=x, y1=y1, y2=y2, y3=y3, y4=y4, y5=y5))
p = figure(title="Streamgraph Python Bokeh Example by PratikPathak.com")
p.area(x='x', y1='y1', y2='y2', y3='y3', y4='y4', y5='y5', source=source, line_color=None)
output_notebook()
show(p) | | Live Preview Source Code 🌿 Contribute 21. Polar Plot from bokeh.plotting import figure, show, output_notebook
import numpy as np
r = np.linspace(0.1, 1, 10)
theta = np.linspace(0, 2*np.pi, 10)
p = figure(title="Polar Plot Python Bokeh Example by PratikPathak.com", plot_width=600, plot_height=600, x_range=(-1.2, 1.2), y_range=(-1.2, 1.2), toolbar_location=None)
p.polar(r, theta, color="navy", alpha=0.5, line_width=2)
output_notebook()
show(p) 22. Donut Chart from bokeh.plotting import figure, show, output_notebook
from bokeh.models import ColumnDataSource
labels = ["A", "B", "C", "D"]
values = [10, 15, 8, 12]
source = ColumnDataSource(data=dict(labels=labels, values=values))
p = figure(title="Donut Chart Python Bokeh Example by PratikPathak.com", x_range=labels)
p.wedge(x=0, y=1, radius=0.4, start_angle=0.6, end_angle=2.6, color=["red", "green", "blue", "yellow"], legend_field="labels")
p.wedge(x=0, y=1, inner_radius=0.3, outer_radius=0.4, start_angle=0.6, end_angle=2.6, color="white")
p.axis.visible = False
p.grid.grid_line_color = None
output_notebook()
show(p) 23. Treemap from bokeh.plotting import figure, show, output_notebook
from bokeh.models import TreemapRenderer, ColumnDataSource
import pandas as pd

# Sample data
data = pd.DataFrame({
    'label': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'],
    'parent': ['', 'A', 'A', 'B', 'B', 'C', 'C', 'D'],
    'value': [10, 5, 4, 3, 2, 1, 1, 1]
})

source = ColumnDataSource(data)
p = figure(title="Treemap Python Bokeh Example by PratikPathak.com")
treemap = TreemapRenderer(
    source=source,
    label='label',
    parent='parent',
    value='value',
    color_discrete_sequence=["#e6550d", "#3182bd", "#31a354", "#756bb1", "#636363", "#9e9ac8", "#de2d26", "#fd8d3c"],
)
p.add_layout(treemap)
output_notebook()
show(p) If you get any error, make sure you have installed Python pandas by using the “pip install pandas” command 24. Network Plot from bokeh.plotting import figure, show, output_notebook
from bokeh.models import ColumnDataSource, HoverTool, NodesAndLinkedEdges
import networkx as nx

# Sample data
nodes = ['A', 'B', 'C', 'D', 'E', 'F']
edges = [('A', 'B'), ('A', 'C'), ('B', 'D'), ('B', 'E'), ('C', 'F')]
G = nx.Graph()
G.add_nodes_from(nodes)
G.add_edges_from(edges)

node_positions = nx.spring_layout(G)
node_x = [node_positions[node][0] for node in G.nodes()]
node_y = [node_positions[node][1] for node in G.nodes()]
node_color = ['red', 'green', 'blue', 'yellow', 'purple', 'orange']

source = ColumnDataSource(data=dict(
    x=node_x,
    y=node_y,
    color=node_color,
    node=nodes
))

p = figure(title="Network Plot Python Bokeh Example by PratikPathak.com", x_range=(-1.1, 1.1), y_range=(-1.1, 1.1))
p.add_tools(HoverTool(tooltips=[("Node", "@node")]))
p.circle('x', 'y', size=15, color='color', source=source)

edge_x = []
edge_y = []
for start, end in edges:
    x0, y0 = node_positions[start]
    x1, y1 = node_positions[end]
    edge_x.append(x0)
    edge_x.append(x1)
    edge_x.append(None)
    edge_y.append(y0)
    edge_y.append(y1)
    edge_y.append(None)

p.multi_line(edge_x, edge_y, color="black", alpha=0.5, line_width=1)

output_notebook()
show(p) 25. Sankey Diagram from bokeh.plotting import figure, show, output_notebook
from bokeh.models import Sankey, ColumnDataSource

# Sample data
flows = [
    ('A', 'X', 5),
    ('B', 'X', 3),
    ('A', 'Y', 2),
    ('B', 'Y', 4),
    ('X', 'C', 4),
    ('X', 'D', 3),
    ('Y', 'C', 2),
    ('Y', 'D', 4)
]

source = ColumnDataSource(data=dict(
    source=[flow[0] for flow in flows],
    target=[flow[1] for flow in flows],
    value=[flow[2] for flow in flows]
))

p = figure(plot_width=800, plot_height=400, title="Sankey Diagram Python Bokeh Example by PratikPathak.com")
sankey = Sankey(source=source, label_text_color="white", label_text_font_size="8pt")
p.renderers.append(sankey)

output_notebook()
show(p) | | Live Preview Source Code 🌿 Contribute 26. Chord Diagram from bokeh.plotting import figure, show, output_notebook
from bokeh.models import ColumnDataSource, CategoricalColorMapper
import numpy as np

# Sample data
nodes = ['A', 'B', 'C', 'D', 'E', 'F']
connections = [
    ('A', 'B', 0.5), ('A', 'C', 0.3), ('A', 'D', 0.2),
    ('B', 'C', 0.4), ('B', 'D', 0.3), ('B', 'E', 0.3),
    ('C', 'D', 0.2), ('C', 'E', 0.3), ('C', 'F', 0.5),
    ('D', 'E', 0.2), ('D', 'F', 0.3), ('E', 'F', 0.4)
]

source = ColumnDataSource(data=dict(
    start=np.array([con[0] for con in connections]),
    end=np.array([con[1] for con in connections]),
    value=np.array([con[2] for con in connections])
))

p = figure(title="Chord Diagram Python Bokeh Example by PratikPathak.com", plot_width=800, plot_height=800)
chord = p.chord(
    source=source, 
    start_angle=np.pi / 2,
    direction="clockwise",
    colors=CategoricalColorMapper(factors=nodes, palette="Spectral11")
)

output_notebook()
show(p) How to Contribute? Feel free to open a PR request on our GitHub repo. Steps to contribute: Fork the repo Make changes in the Forked repo and save Open a Pull Request That’s it 😄! 🌿 Contribute Conclusion In this Repo, I have shared 25+ Python Bokeh examples that can help you learn Python Bokeh. Feel free to contribute to our GitHub repo and keep it updated. Also published . here

Getting Started With Python Bokeh: 25+ Data Visualization Examples With Source Code

I was recently inspired by some interesting performance characteristics for collection initializers and collection expressions in C#, and I wanted to put together an introductory article. This article will be part of a small series where I first introduce you to the syntax we have to work with for both collection expressions and collection initializers in C#. We’ll see the difference in style and readability — which the dotnet team has been progressing to make the language feel less heavy-handed while still maintaining expressiveness. Once you’ve got a feel for how collection initializers and collection expressions in C# work, you’ll be geared up to check out some of the performance benchmarks on them. There’s no point in hyper-optimizing for this stuff unless you understand the basics! Using List<T> with Collection Initializers in C# Collection initializers in C# allow for a concise and readable way to populate collections like upon instantiation. This feature simplifies code by enabling the initialization of a collection with a set of predefined elements without the need for multiple calls to the method. List<T> Add These next subsections will show examples of collection initializers with the type. Keep in mind that the entire point of these initializers is to define collections with elements in them to start with, which would save us from doing something like the following: List<T> List<string> devLeaderCoolList = new List<string>();
devLeaderCoolList.Add("Hello");
devLeaderCoolList.Add(", ");
devLeaderCoolList.Add("World!"); So, with this as a starting point, consider that the upcoming examples will make this feel more streamlined and concise. Example 1: Initializing a List of Integers List<int> primeNumbers = new List<int> { 2, 3, 5, 7, 11, 13, 17 }; This example demonstrates initializing a with a collection of prime numbers. The numbers are enclosed in braces and separated by commas, directly following the instantiation of the list. List<int> {} We can also use a slightly more short-hand syntax to drop the entire duplicated type definition from the right side of the equal sign: List<int> primeNumbers = new() { 2, 3, 5, 7, 11, 13, 17 }; Example 2: Combining Object and Collection Initializers public class Student
{
    public string Name { get; set; }
    public int Age { get; set; }
}

List<Student> students = new List<Student>
{
    new Student { Name = "Alice", Age = 22 },
    new Student { Name = "Bob", Age = 24 }
}; Here, we combine object and collection initializers to create a where each object is initialized with and properties. This approach streamlines the process of filling a collection with fully initialized objects. The important thing to pay attention to here is that the object initializer syntax is very much like the collection initializer syntax, but we are indeed doing two things: List<Student> Student Name Age Assigning values to properties of new objects Assigning the collection elements upon collection creation Example 3: Using Complex Expressions List<double> areas = new List<double>
{
    Math.PI * Math.Pow(3, 2),
    Math.PI * Math.Pow(5, 2)
}; This example initializes a with areas of circles (using ), where is the radius. It illustrates that expressions, including method calls, can be used within collection initializers — that is, there is no restriction on constants or pre-evaluated values. List<double> πr² r Example 4: Nested Collection Initializers public class Classroom
{
    public List<Student> Students { get; set; }
}

List<Classroom> classrooms = new List<Classroom>
{
    new Classroom
    {
        Students = new List<Student>
        {
            new Student { Name = "Alice", Age = 22 }
        }
    },
    new Classroom
    {
        Students = new List<Student>
        {
            new Student { Name = "Bob", Age = 24 }
        }
    }
}; This example shows how to use nested collection initializers to initialize a list of objects, each containing a list of objects. It is very much like Example 2, which we have already looked at, but this takes things up one more notch, showing multiple collection initializers and object initialization. Classroom Student Example 5: Simple List Initialization with Collection Expressions . This was a step forward in reducing the verbosity of collection declarations using more shorthand, similar to other languages. Microsoft says in its documentation: In C# 11, we start to get some new fancier syntax for collection expressions You can use a to create common collection values. A is a terse syntax that, when evaluated, can be assigned to many different collection types. A collection expression contains a sequence of elements between and brackets. collection expression collection expression [ ] Microsoft Let’s check out an example: List<int> evenNumbers = [2, 4, 6, 8, 10]; This example demonstrates the straightforward initialization of a using the new collection expressions syntax, making the code more concise and readable. List<int> Example 6: Combining Collections with Spread Operator And there are even more goodies in : C# 12 — we get the spread operator for collection initialization List<int> firstBatch = [1, 2, 3];
List<int> combinedList = [0, ..firstBatch, 4]; Here, the spread operator is used to include elements from an existing collection ( ) into a new list, showcasing the flexibility of the new syntax in combining collections seamlessly. .. firstBatch Where Are We Headed With These? As you read through the various code examples, you can decide for yourself which ones offer you the readability that you prefer. There’s not necessarily a right or wrong answer here, but with variety and choice, we are likely going to need to make decisions within our teams about how to stay consistent. Try to strike a balance between minimizing redundancy without hiding too much type information! But what’s next? Do we care THAT much about readability? I mean, I do. Honestly, I think it’s incredibly important to prioritize readability in code. But if you’re curious like me, you might see a post like this from on the interwebs and get very curious: Dave Callan And since this is what sparked my interest and caused me to write this article as a primer, you’ll perhaps be interested in the performance characteristics that I investigated! Wrapping Up C# Collection Initializers and Collection Expressions Now that you’ve seen various examples of the syntax that we have access to, you can make your own informed decisions about which are most readable to you. I think it’s always important to spend some time looking at alternatives so that you can understand different perspectives, even if it seems like the differences might be minor. Odds are you’re going to read and write collection initializers and collection expressions MANY times in your software engineering career, so why not optimize your choice? Speaking of optimizations… wait until you see ! the next article on the performance of collection initializers If you found this useful and you’re looking for more learning opportunities, consider and check out my ! subscribing to my free weekly software engineering newsletter free videos on YouTube Also published . here

C# Collection Expressions and Collection Initializers

The Bitcoin halving is slated for sometime around April 19th, 2024. As you might have heard, it follows the Bitcoin supply equation; which is a geometric series terminating after 32 divisions or halvings. In April 2024, we shall have the 4th halving, taking us from 6.25 to 3.125 mined per 10 minutes. BTC The last satoshi shall be mined 32 * 4 years from 2009, which shall be the year 2137. Below is a curve I made in MS Excel modeling the Bitcoin supply equation; Interestingly, however, 3 other equations look like the Bitcoin halving. One equation is behind the most profitable options trading algorithm in the world, one is behind the most powerful energy resource in the world, and one is behind the ability to find the energy in any physical system. More on these below: 1. The Black-Scholes equation The Black-Scholes equation is behind most of the profitable options trading in the world, including Exchange Traded Funds (ETFs) which can be traded like regular options. Multinational companies like BlackRock, which manages trillions of dollars in assets, recently launched a successful product for its investors. Bitcoin ETF Notice the term at the end, Assume an equilibrium situation with: Let the constant number be 5. Thus, we have: Let r be 2 and model as, When graphed, this behaves like the Bitcoin halving, as seen below. Here are similar graphs from other people’s research. 2. The Radioactive Decay equation Radioactivity is the spontaneous decay of heavy, unstable atomic nuclei to form stable nuclei. It is the power behind nuclear fission, the most powerful energy resource on the planet. Interestingly, while radioactivity is so good at releasing gargantuan amounts of energy, Bitcoin is good at absorbing it. But even more, both the Bitcoin halving and the radioactive decay process are exponential functions whose graphs grow in the same way. Consider the radioactive decay equation; The formula is easy enough to be taught to 17-year-olds studying A-level mathematics in High Schools. Now, represents the amount left. If this was Bitcoin, would be the bitcoins left to be mined. A A How about if we track the amount decayed, just like the bitcoins already mined? Easy enough. Subtract from thus; A A_0, Which we can see is similar to what we had before with the Black-Scholes equation. Taking A_0 = 5 and λ = 2, it is the same deal with us modelling y = 5 (1 - e^(-2x) ), hence a similar graph. 3. The Hamiltonian The Hamiltonian, of a mechanical system is defined as the amount of energy contained in the system. H While Bitcoin might be a digital computational system, from what Alan Turing describes in his thesis on a Universal Turing Machine, we can represent any computational system as a mechanical system. Therefore, Bitcoin can be represented as a mechanical computational system. Not that we have the resources to do it on earth. By further extension, classical mechanics can be described in terms of quantum mechanics, hence Bitcoin is a quantum-mechanical computational system. Thus, Bitcoin has a Hamiltonian unknown to us, that can describe its minimum workings absent external complexities and fluctuations in the number of users and miners joining and leaving the network. At the nanoscale, where Bitcoin’s digital dance of the halving resides, the simplest Hamiltonian is the quantum Hamiltonian, represented by hat{H} below. We can see this Hamiltonian operator is part of Schrödinger’s wave equation, fundamental to relating the Hamiltonian with the state of a quantum system at time ; t Notice the term: which is similar to: above. Using Euler’s formula, The introduction of the imaginary component has thrown us off the beaten path of a nice exponential leveling off like the Bitcoin supply equation.  We instead get a circle  with an angle given by and radius R = 1. i Ht Now let radius R = 1, and take |r| e^(-iθ) to be the common ratio of a geometric series with r being a complex number, |r| < 1 and first term a = 1. The resulting geometric series; can be modeled as a Fourier series hence the graphic below with r = 0.5,  a = 1 forming a circle of radius R = 4/3. https://en.wikipedia.org/wiki/File:Complex_geometric_series_animation.ogv?embedable=true#filelinks But what if radius R = 1, as we want? What would common ratio r be? First, we need to know that for the general form of a geometric progression; + + + + + … a ar ar^2 ar^3 ar^4 the sum to n terms, for |r| < 1. The sum to n terms then converges to a unique value as n to infinity. This is because r^n to 0. tends tends Hence, we can summarise as below; Note: Because Bitcoin's supply is capped at 21,000,000 it moves in a circle! This via circularity leveraging its monetary transactions velocity, V, in Irving Fischer's equation → MV = PT *** More wonders From the following are related to the Bitcoin halving; https://en.wikipedia.org/wiki/Geometric_series The expansion of the universe, where the common ratio r is defined by Hubble's constant. The decay of radioactive carbon-14 atoms, where the common ratio r is defined by the half-life of carbon-14. Last but not least, One of my Hackernoon post’s viewership statistics.

The Mathematical Mysteries of Bitcoin's Halving

বিটকয়েনের অর্ধেক হওয়ার গাণিতিক রহস্য

Die mathematischen Geheimnisse der Bitcoin-Halbierung

Los misterios matemáticos de la reducción a la mitad de Bitcoin

Les mystères mathématiques de la réduction de moitié du Bitcoin

बिटकॉइन को आधा करने का गणितीय रहस्य

ビットコインの半減期の数学的謎

비트코인 반감기의 수학적 미스터리

Os mistérios matemáticos da redução do Bitcoin pela metade

Математические тайны халвинга биткойна

Bitcoin Yarılanmasının Matematiksel Gizemleri

Những bí ẩn toán học về việc giảm một nửa Bitcoin

比特币减半的数学之谜

Affiliate marketing is a real powerhouse in the digital marketing realm and in recent years has gone through significant growth and transformation. Chances are, you’ve been on the receiving end of it yourself! Now, it is not the time to ignore this approach, since the power of social media, increased device usage, and the boom of creator-led media are all here to help your business thrive. According to _ __, the affiliate marketing industry is experiencing robust growth and there are approximately 9,600 global services and companies related to affiliate marketing in 2023 including agencies, platforms, and various other organizations or apps providing affiliate services. Additionally, forecasts that affiliate marketing spending will reach a staggering US$ 39,805.4 Mn by 2031. Influencer Marketing Hub Astute Analytica For context, reported that global affiliate revenue for affiliate networks amounted to $6.5 billion in 2006. MoreNiche Exciting numbers, huh? Here are some more. According to Performance marketing association survey data: 84% of businesses find affiliate marketing to be more profitable than other marketing methods. In 2021, affiliate marketing contributed to around $71 billion in ecommerce revenue in the United States. On average, every $1 spent on the affiliate channel resulted in $12 in ecommerce revenue across all industries. 84% of media publishers and bloggers create content for affiliate marketing. Retail brands were responsible for 76% of affiliate channel spending, with about one-third going to clothing affiliate programs. Again, number-heavy facts, but you and I know that marketing is nothing without numbers. The explosive growth of the affiliate marketing industry in the 21st century can be credited to a few key factors. First off, the surge in digital operations and the widespread use of mobile devices. Then, the subsequent digitalization of services, the advancements in digital marketing, and the increased volume of online purchases, fueled by a shift in consumer behavior, have all contributed to the flourishing landscape of affiliate marketing. Affiliate marketing's widespread appeal also stems from its affordability, and the high return on investment in terms of both time and cost when compared to alternative marketing approaches. Businesses caught on the wave, adapting their operations and creating affiliate marketing programs to drive their revenue. Then, the social media boom was exactly what gave affiliate marketing the kick in needed, coupled with the rise of influencer marketing and brand partnerships. Thanks to the significant increase of social media usage (from 5% in 2005 to 79% in 2019 according to ), platforms like Facebook and Instagram became key to affiliate marketing campaigns. Our World In Data That’s kind of how we got here. Now, it's not just something companies do on the side; it's a real way to make money. As we navigate the landscape, it's evident that the rise of Cost-Per-Action models is not just a trend but an exciting narrative for sellers on the global stage. So, what’s in plan? In this article I’d like to introduce to you current trends in affiliate marketing and most recent market breakthroughs, seen through the lens of a founder. Choose your fighter A growing market is nothing without innovation, and the very expected emergence of newer tools is a great indicator for market relevance. Just as with any increasing complexity, humans start to seek (and make) tools for dealing with the tools we already have. The rapidly growing affiliate marketing industry is no exception to the rool. Here are the purposes, and some of the tools we’ve got so far: This is software offered by Impact Radius, Awin, and Post Affiliate Pro and it provides advanced tracking and analytics for affiliate marketing campaigns, letting brands and their affiliates optimize their strategies based on performance data. Affiliate Tracking: Companies like AspireIQ, Upfluence, and CreatorIQ can help brands connect with influencers (including micro-influencers), streamlining the process of finding the right partners for affiliate marketing. Influencer Marketing Platforms: If you need a little help creating the visuals, tools like Canva and Adobe Spark let affiliates and marketers easily create high-quality, engaging content for promoting products across almost any channel of choice. Content Creation Tools: For managing affiliate marketing content across multiple social media platforms, doing things like scheduling posts, or analyzing engagement metrics – Hootsuite, Buffer, and Later are the way to go! Social Media Management Tools: Big-time players like Mailchimp and ConvertKit are well-known powerful tools for creating email lists and launching outreach email campaigns with personalized affiliate offers and content. You can also track opens, clicks, and conversions. Email Marketing Services: SEO-helpers such as SEMrush, Ahrefs, Moz and similar services provide affiliates with critical insights into keywords, competition, and performance, helping you optimize content and improve visibility in search engine results. SEO Tools: To conclude In recent years affiliate marketing has become not only a useful tool, but a robust solution for sales, bound to be a prominent player in the future of marketing as a whole. And for that, there are many reasons. Its low-risk nature provides a secure avenue for both businesses and marketers and the potential for high rewards and a scalable income adds an enticing element to the affiliate marketing landscape. With affiliate marketing you simultaneously build brand awareness and drive traffic, presenting itself as a holistic marketing solution and an attractive choice in the evolving landscape of digital marketing, making it a pivotal player in shaping the future of promotional strategies. So, are you in?

Inside the Affiliate Marketing Product Boom: A Founder's Perspective on Market Trends

Coding Patterns Revealed 

Authors: (1) Sha-Bo Lin, Center for Intelligent Decision-Making and Machine Learning, School of Management, Xi’an Jiaotong University; (2) Xingping Sun, Department of Mathematics, Missouri State University; (3) Di Wang, §Center for Intelligent Decision-Making and Machine Learning, School of Management, Xi’an Jiaotong University. Content Overview Abstract & Introduction Uncertainty Relation of Kernel Interpolation on Spheres Distributed Kernel Interpolation Operator Differences via Quadrature Rules Proofs Numerical Verifications References Abstract For radial basis function (RBF) kernel interpolation of scattered data, Schaback [30] in 1995 proved that the attainable approximation error and the condition number of the underlying interpolation matrix cannot be made small simultaneously. He referred to this finding as an “uncertainty relation”, an undesirable consequence of which is that RBF kernel interpolation is susceptible to noisy data. In this paper, we propose and study a distributed interpolation method to manage and quantify the uncertainty brought on by interpolating noisy spherical data of non-negligible magnitude. We also present numerical simulation results showing that our method is practical and robust in terms of handling noisy data from challenging computing environments. Kernel interpolation, distributed uncertainty mitigation, scattered spherical data Key words. Uncertainty Relation of Kernel Interpolation on Spheres 3. Distributed Kernel Interpolation. Corollary 2.2 shows that kernel interpolation performs poorly while confronting noisy data of non-negligible magnitude. To overcome this major drawback, we propose and study in this section a distributed kernel interpolation (DKI) method, which is motivated by the “distributed learning” in the literature [37, 19]. Figuratively speaking, this is a divide-and-conquer strategy for uncertainty quantification. To elaborate, we describe the method in three steps. 4. Operator Differences via Quadrature Rules. In this section, we first briefly exposit an integral-operator approach initiated in [8] and then derive tight upper bounds for differences of operators of our interest, obtaining a certain type of Sobolev sampling inequalities [12] as a byproduct. Highlights of the section include Proposition 4.5) and Lemma 4.8. 6. Numerical Verifications Four simulations are carried out in this section to verify the excellent performance of DKI. The first one shows that DKI succeeds in circumventing the uncertainty of kernel interpolation. The second one exhibits the role of m in DKI. The third one focuses on the role of the division strategy in DKI. The last one compares DKI with several popular spherical data fitting schemes including the distributed filtered hyperinterpolation (DFH) [21], sketching with s ∗ -designs [20], and distributed kernel ridge regression (DKRR) [8]. In this simulation, we show the role of the parameter m in DKI. We generate 10014 training samples (with 141-designs as inputs). The number of divisions, m, ranges from {5, 10, · · · , 200}. Figure 6.2 shows the relation between RMSE of DKI and the number of local machines under different levels of Gaussian noise, provided that the total number of training samples is given. From Figure 6.2, we can conclude the following assertions: 1) For training samples with higher levels of noise, the testing RMSE generally decreases at first and then increases slowly as the number of local machines increases. Moderate values of m are more conductive to good approximation property for DKI. The reason is that too small m does not successfully address the uncertainty issue in kernel interpolation; too large m increases the fitting error, resulting in slightly worse generalization performance. 2) The optimal number m with the lowest RMSE grows with increasing Gaussian noise. This verifies the equation (3.3) of Theorem 3.2, in which the approximation error is primarily concerned with the sample error for large noise (i.e., large M) and can be reduced using a large m. Simulation 2: REFERENCES [1] R. Bhatia, Matrix Analysis, vol. 169, Springer Science & Business Media, 2013. [2] J. S. Brauchart and K. Hesse, Numerical integration over spheres of arbitrary dimension, Constructive Approximation, 25 (2007), pp. 41–71. [3] G. Brown and F. Dai, Approximation of smooth functions on compact two-point homogeneous spaces, Journal of Functional Analysis, 220 (2005), pp. 401–423. [4] A. Chernih, I. H. Sloan, and R. S. Womersley, Wendland functions with increasing smoothness converge to a gaussian, Advances in Computational Mathematics, 40 (2014), pp. 185– 200. [5] F. Dai, Multivariate polynomial inequalities with respect to doubling weights and a∞ weights, Journal of Functional Analysis, 235 (2006), pp. 137–170. [6] F. Dai, On generalized hyperinterpolation on the sphere, Proceedings of the American Mathematical Society, 134 (2006), pp. 2931–2941. [7] H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems, vol. 375, Springer Science & Business Media, 1996. [8] H. Feng, S.-B. Lin, and D.-X. Zhou, Radial basis function approximation with distributively stored data on spheres, arXiv:2112.02499, (2021). [9] T. Hangelbroek, F. J. Narcowich, X. Sun, and J. D. Ward, Kernel approximation on manifolds ii: The l∞ norm of the l2 projector, SIAM Journal on Mathematical Analysis, 43 (2011), pp. 662–684. [10] T. Hangelbroek, F. J. Narcowich, and J. D. Ward, Kernel approximation on manifolds i: bounding the lebesgue constant, SIAM Journal on Mathematical Analysis, 42 (2010), pp. 1732–1760. [11] K. Hesse, I. H. Sloan, and R. S. Womersley, Radial basis function approximation of noisy scattered data on the sphere, Numerische Mathematik, 137 (2017), pp. 579–605. [12] K. Hesse, I. H. Sloan, and R. S. Womersley, Local rbf-based penalized least-squares approximation on the sphere with noisy scattered data, Journal of Computational and Applied Mathematics, 382 (2021), p. 113061. [13] S. Hubbert, Q. T. Le Gia, and T. M. Morton ˆ , Spherical radial basis functions, theory and applications, Springer, 2015. [14] M. A. King, R. J. Bingham, P. Moore, P. L. Whitehouse, M. J. Bentley, and G. A. Milne, Lower satellite-gravimetry estimates of antarctic sea-level contribution, Nature, 491 (2012), pp. 586–589. [15] Q. T. Le Gia, F. J. Narcowich, J. D. Ward, and H. Wendland, Continuous and discrete least-squares approximation by radial basis functions on spheres, Journal of Approximation Theory, 143 (2006), pp. 124–133. [16] P. Leopardi, A partition of the unit sphere into regions of equal area and small diameter, Electronic Transactions on Numerical Analysis, 25 (2006), pp. 309–327. [17] J. Levesley, Z. Luo, and X. Sun, Norm estimates of interpolation matrices and their inverses associated with strictly positive definite functions, Proceedings of the American Mathematical Society, (1999), pp. 2127–2134. [18] S.-B. Lin, X. Chang, and X. Sun, Kernel interpolation of high dimensional scattered data, arXiv preprint arXiv:2009.01514, (2020). [19] S.-B. Lin, X. Guo, and D.-X. Zhou, Distributed learning with regularized least squares, The Journal of Machine Learning Research, 18 (2017), pp. 3202–3232. [20] S.-B. Lin, D. Wang, and D.-X. Zhou, Sketching with spherical designs on spheres, SIAM Journal on Scientific Computation, in press (2023). [21] S.-B. Lin, Y. G. Wang, and D.-X. Zhou, Distributed filtered hyperinterpolation for noisy data on the sphere, SIAM Journal on Numerical Analysis, 59 (2021), pp. 634–659. [22] J. D. McEwen and Y. Wiaux, A novel sampling theorem on the sphere, IEEE Transactions on Signal Processing, 59 (2011), pp. 5876–5887. [23] H. Mhaskar, F. Narcowich, and J. Ward, Spherical marcinkiewicz-zygmund inequalities and positive quadrature, Mathematics of Computation, 70 (2001), pp. 1113–1130. [24] H. N. Mhaskar, Weighted quadrature formulas and approximation by zonal function networks on the sphere, Journal of Complexity, 22 (2006), pp. 348–370. [25] C. Muller ¨ , Spherical Harmonics, vol. 17, Springer, 1966. [26] F. J. Narcowich, N. Sivakumar, and J. D. Ward, Stability results for scattered-data interpolation on euclidean spheres, Advances in Computational Mathematics, 8 (1998), pp. 137– 163. [27] F. J. Narcowich, X. Sun, J. D. Ward, and H. Wendland, Direct and inverse sobolev error estimates for scattered data interpolation via spherical basis functions, Foundations of Computational Mathematics, 7 (2007), pp. 369–390. [28] F. J. Narcowich and J. D. Ward, Scattered data interpolation on spheres: error estimates and locally supported basis functions, SIAM Journal on Mathematical Analysis, 33 (2002), pp. 1393–1410. [29] A. Rudi, R. Camoriano, and L. Rosasco, Less is more: Nystr¨om computational regularization., in NIPS, 2015, pp. 1657–1665. [30] R. Schaback, Error estimates and condition numbers for radial basis function interpolation, Advances in Computational Mathematics, 3 (1995), pp. 251–264. [31] S. Smale and D.-X. Zhou, Shannon sampling and function reconstruction from point values, Bulletin of the American Mathematical Society, 41 (2004), pp. 279–305. [32] S. Smale and D.-X. Zhou, Shannon sampling ii: Connections to learning theory, Applied and Computational Harmonic Analysis, 19 (2005), pp. 285–302. [33] Y.-T. Tsai and Z.-C. Shih, All-frequency precomputed radiance transfer using spherical radial basis functions and clustered tensor approximation, ACM Transactions on Graphics (TOG), 25 (2006), pp. 967–976. [34] H. Wendland, Scattered data approximation, vol. 17, Cambridge university press, 2004. [35] M. A. Wieczorek and R. J. Phillips, Potential anomalies on a sphere: Applications to the thickness of the lunar crust, Journal of Geophysical Research: Planets, 103 (1998), pp. 1715–1724. [36] R. S. Womersley, Efficient spherical designs with good geometric properties, in Contemporary computational mathematics-A celebration of the 80th birthday of Ian Sloan, Springer, 2018, pp. 1243–1285. [37] Y. Zhang, J. Duchi, and M. Wainwright, Divide and conquer kernel ridge regression: A distributed algorithm with minimax optimal rates, The Journal of Machine Learning Research, 16 (2015), pp. 3299–3340. In this Appendix, we present the detailed implementation of the select-and-judge (SAJ) strategy. Our aim is to derive a series of subsets of similar Cardinality with separation radius not smaller than a given tolerance c0. There are two stages for SAJ. SM1. Appendix A: Select-and-Judge Strategy for Data Division. This paper is under CC0 1.0 DEED license. available on arxiv

Distributed Uncertainty Quantification of Kernel Interpolation on Spheres

গোলকের উপর কার্নেল ইন্টারপোলেশনের বিতরণ করা অনিশ্চয়তার পরিমাণ

Verteilte Unsicherheitsquantifizierung der Kernelinterpolation auf Kugeln

Cuantificación de la incertidumbre distribuida de la interpolación del kernel en esferas

Quantification distribuée de l'incertitude de l'interpolation du noyau sur les sphères

क्षेत्रों पर कर्नेल इंटरपोलेशन की वितरित अनिश्चितता मात्रा

球上のカーネル補間の分散不確実性の定量化

구에 대한 커널 보간법의 분산 불확실성 정량화

Quantificação de incerteza distribuída de interpolação de kernel em esferas

Количественная оценка распределенной неопределенности ядра интерполяции на сферах

Küreler Üzerindeki Çekirdek Enterpolasyonunun Dağıtılmış Belirsizliği Ölçümü

Định lượng độ không đảm bảo phân phối của phép nội suy hạt nhân trên hình cầu

球体核插值的分布式不确定性量化

RADIUS

radiusagent.com

-- employees

Since n.d.

COMPANY RANKING

RADIUS

EVERGREEN INDEX #8376

Representing this company? Click here to claim and customize this page!

Radius WIKI

Apply to get your Tech Company News Page live on HackerNoon.com today!

RADIUS

radiusagent.com

-- employees

Since n.d.

COMPANY RANKING

RADIUS

EVERGREEN INDEX #8376

RELATED COMPANIESRANK

STORIES ABOUT RADIUS

Representing this company? Click here to claim and customize this page!

Radius WIKI

Apply to get your Tech Company News Page live on HackerNoon.com today!