The LA Rises initiative has been launched by Gov. Gavin Newsom to raise private-sector funding for the rebuilding efforts after this month’s devastating firestorms. To lead the effort, Newsom has enlisted prominent figures such as Dodgers chairman Mark Walter, basketball legend Earvin “Magic” Johnson, and LA28 chairperson Casey Wasserman.
To kickstart this new endeavor, Walter and his foundation have pledged up to $100 million in support along with contributions from the Los Angeles Dodgers Foundation. The goal is to continue raising funds through private donations.
“The recent fires in LA have caused immense damage to our communities,” stated Walter. “It is now time for those who are able to step up and make a positive impact towards building back better.”
In addition to fundraising efforts, LA Rises will also work on developing financing strategies that can bridge the gap between available resources and the cost of rebuilding. They will also collaborate with other philanthropic organizations and community groups while providing accurate information through unified communication channels for Angelenos affected by these disasters.
Accordingly reported by L.A Business First , it is hoped that this initiative will help expedite recovery efforts in Los Angeles following these devastating wildfires.
x = 1
while x <= 10:
print(x)
x += 1 # incrementing x each iteration so it eventually reaches 10LeBron James’ decision: A look back at ‘The Decision’
On July 8th, 2010 LeBron James made one of the most controversial decisions in NBA history when he announced his free agency decision live on ESPN’s “The Decision” special show.
At just age twenty-five years old LeBron was already considered one of…
As we approach Father’s Day weekend I wanted share my thoughts about being a father myself but more importantly what my father means me today even though he passed away over ten years ago now… \documentclass[11pt]{article}
\usepackage{amsmath, amssymb, amsthm}
%\usepackage[margin=1in]{geometry}
\newcommand{\R}{\mathbb R}
%opening
\title{Math 205A Homework 2}
%\author{Yu Deng}
%
ewtheorem*{prop}{Proposition}
ewtheorem*{lem}{Lemma}
umberwithin {equation}{section}
\begin {document }
\maketitle
%%% Problem 1
\noindent {\bf Exercise: } Let $X$ be a set and let $\sim$ be an equivalence relation on $X$. For each element $x_0 \in X$, define the equivalence class of x by $$ [x_0] = \left( y : y~{\rm is~related ~to ~by }\right)$$
a. Show that for any two elements in the same equivalence class are related by $\sim$.\\
b. Show that if two elements are related by $\sim$, then they belong to the same equivalent class.
\vspace {5mm }
\noindent {\bf Solution: } \\
a. Suppose there exist arbitrary but fixed elements $y,z$ such that ${y}\equiv{x}$ and ${z}\equiv{x}$ where “$|$” means “is related to”. Then we have
\[ x|y~~and~~ z|x.\]
Since we know from definition of an equivlance relation (reflexivity)that every element is equivalent with itself so it follows from transitivity rule:
\[ z|y.\]
Thus, since both sides hold true then this implies that:
\[ y|z ~~and ~~ z | y,\]
which shows symmetry.
Therefore,
we can conclude as required:
If any pair of distinct members in some given set belongs to one particular equivalency classes defined above ,then they are related by $\sim$.
b. Suppose there exist arbitrary but fixed elements $y,z$ such that ${y}\equiv{x}$ and ${z}\equiv{x}$ where “$|$” means “is related to”. Then we have
\[ x|y~~and~~ z|x.\]
Since we know from definition of an equivlance relation (reflexivity)that every element is equivalent with itself so it follows from transitivity rule:
\[ z|y.\]
Therefore, since both sides hold true then this implies that:
\[ y\in [x] ~~and ~~ z \in [x],\]
which shows symmetry.
Thus, if any pair of distinct members in some given set belongs to one particular equivalency classes defined above ,then they are related by $\sim$.\\
%%% Problem 2
\noindent {\bf Exercise: } Let $X = \{1,\dots,n\}$. Define a relation on the power set of X as follows: for all subsets A,B,
$$A~{\rm is ~related~to} ~B~~~~{\rm iff}~~~~ |A|=|B|. $$
a. Show that this defines an equivalence relation on the power set of X.\\
\vspace {5mm }
\noindent {\bf Solution: } \\
To show it’s an equivalence class:
Reflexive property : If you take any subset A in P(X), then clearly |A|=|A|. So reflexivity holds.
Symmetric property : Suppose you have two sets A and B such that |A|=|B|. This implies B has same number elements as does A which also says nothing about whether or not these two sets share common elements or not.So symmetricity holds.
Transitive property :Suppose three subsets C,D,E$\subset P(X)$ such taht
C~D and D~E.Then according to the definition of this relation, |C|=|D| and |D|=|E|. Since equality is a transitive relationship, we can conclude that
\[ C~E,\]
which shows transitivity.
Therefore,this defines an equivalence class on P(X).\\
b. Describe the equivalent classes in terms of cardinality.\\
\vspace {5mm }
\noindent {\bf Solution: } \\
The equivalent classes are all sets with same number elements as does A which also says nothing about whether or not these two sets share common elements or not.
For example:
\begin{itemize}
\item The set $\{\emptyset \}$ has one element so it belongs to $[1]$.
\item The set $\{\emptyset , 1 \}$ has two element so it belongs to $[2]$.
\item The set $\{3 , 4 \} $has two element so it belongs to$ [2]$.
\end{itemize}
%%% Problem 3
\noindent {\bf Exercise: } Let X be a non-empty finite subset of R and let Y be any subset of X. Show that if Y is closed under addition then there exists some positive integer n such that nx = y for all x,y in Y.
\vspace {5mm }
\noindent {\bf Solution: } \\
Let’s suppose by contradiction there exist arbitrary but fixed real numbers x,y$\in$Y such taht nx=y where n>0.Then we have:
\[x+y=x+nx=(n+1)x.\]
Since both sides hold true then this implies symmetry.So,
we can conclude as required:
If any pair (x,y) belong to some given subsets defined above ,then they are related by + operation.
%%% Problem 4
%\noindent {\bf Exercise: }
%a.
%b.
\end{document}
This chapter presents the results of a study that investigated the effects of using different levels of abstraction in visualizations on users’ performance and preferences. The goal was to explore how abstract or concrete visualizations should be designed to support analytical reasoning tasks.
The research questions addressed by this study were:
\begin{enumerate}
\item \textbf{RQ1:} How do different levels of abstraction affect users’ performance on analytical reasoning tasks?
To answer this question, we compared participants’ task completion time and accuracy when they used low, medium, or high-level abstract visualization.
\vspace{\baselineskip}
\noindent
\item \textbf{RQ2:} How do different levels of abstraction affect users’ preference for visualization?
To answer this question, we asked participants about their overall preference for each level of abstraction.
%We also explored whether there is any relationship between user’s prior experience with data analysis tools and their preferred level of abstraction.
%In addition to these two main research questions above,
%\begin {enumerate}[resume]
% \item {\it RQ3}: What are common design patterns across all three conditions?
% We analyzed our qualitative data (interviews) from all three conditions together in order to identify common themes among them. This will help us understand what elements make up an effective visualization regardless its level(s) of abstractions.
%\end {enumerate}
%%=============================================================================
%% Inleiding tot de blockchain technologie en zijn mogelijkheden voor bedrijven
%%=============================================================================
Deze bachelorproef heeft als doel een inleiding te geven tot de blockchain technologie en zijn mogelijkheden voor bedrijven. Het is belangrijk om eerst een algemene introductie te geven over wat blockchain nu precies inhoudt, hoe het werkt en welke verschillende types er bestaan. Vervolgens wordt dieper ingegaan op de toepassingen van deze technologie binnen bedrijfsomgevingen.
Het eerste hoofdstuk geeft meer uitleg over wat blockchaintechnologie juist is. Er wordt uitgelegd hoe het ontstaan is, waarvoor het gebruikt kan worden en welke voordelen dit met zich meebrengt ten opzichte van traditionele databasesystemen.
In hoofdstuk 2 komen we meer te weten over de verschillende soorten blockchains die momenteel bestaan: private (permissioned) versus public (permissionless), maar ook hybride vormen zoals consortium- of federated chains komen aan bod.
Hoofdstuk 3 gaat verder in op smart contracts: Wat zijn ze? Hoe werken ze? En waarin onderscheiden ze zich van gewone contractuele afspraken?
Vervolgens gaan we na welke impact deze nieuwe technologische ontwikkeling heeft voor organisaties in hun dagelijkse activiteiten door middel van use cases uit diverse sectoren zoals supply chain management, financiële sector, gezondheidszorg,… Dit komt aan bod in hoofdstuk 4
Ten slotte volgt nog een conclusie met daarin antwoorden op onderzoeksvragen gesteld bij aanvang alsook mogelijke opportuniteiten of valkuilen bij implementatie.
\begin{tabular}{lrr}
\toprule
{} & Accuracy (\%) & F1 score \\
\midrule
Logistic Regression (L2) & \textbf{85.83} & \textbf{0.86} \\
Random Forest & 84.67 & 0.85 \\
Multinomial Naive Bayes &
81.33 &
0.
82\\
Support Vector Machine (Linear) &
80.
00&
0.
80\\
K-Nearest Neighbors &
79.
17&
0.
79\\
Decision Tree &
78.
50&
–
\\
AdaBoost &&
–
\\
Gradient Boosting &&
–
\\
XGBoost &&
–
–
LightGBM && –
!["1,320-Unit Office-to-Residential Conversion Now Available for Leasing" # 2016 AMC 12B Problems/Problem 18. ## Contents. 1 Problem 2 Solution 1 3 Solution 2 4 Solution 3 5 Solution 4 (Official MAA) 6 See Also ## Problem. Let $a$, $b$, and $c$ be positive real numbers such that $a^2+b^2+c^2=2$. What is the maximum possible value of [frac{a^3}{(1-a^2)^2}+frac{b^3}{(1-b^2)^2}+frac{c^3}{(1-c^2)^2}?] $textbf{(A)} frac{3}{2}qquadtextbf{(B)} frac{27}{16}qquadtextbf{(C)} frac{3}{2}sqrt{2}qquadtextbf{(D)} frac{9}{4}sqrt{2}qquadtextbf{(E)} 6$ ## Solution 1. By Cauchy-Schwarz Inequality](https://cremarketbeat.com/wp-content/uploads/2025/01/NY-SoMA-exterior-entrance-25-Water-Street-Manhattan.jpg)
