% Required packages:
% \usepackage{booktabs}
% \usepackage{tabularx}
% \usepackage{multirow}
% \usepackage{array}
% \usepackage[table]{xcolor} % optional, for alternating row colors

\section{Budget and Budget Justification}

\subsection{Budget Summary}

The proposed research will be conducted over three (3) years, 
corresponding to the expected completion timeline for the PhD 
dissertation. Table~\ref{tab:budget} provides a detailed breakdown 
of costs by category and year.

\begin{table}[htbp]
\centering
\caption{Proposed Budget by Year and Category}
\label{tab:budget}
\small
\begin{tabular}{@{}lrrrr@{}}
\toprule
\textbf{Category} & \textbf{Year 1} & \textbf{Year 2} & 
  \textbf{Year 3} & \textbf{Total} \\
\midrule
\multicolumn{5}{l}{\textbf{Senior Personnel}} \\
\quad Faculty (PI Advisor, 1 mo.) & \$12,083 & \$12,566 & 
  \$13,069 & \$37,718 \\
\addlinespace
\multicolumn{5}{l}{\textbf{Other Personnel}} \\
\quad Graduate Research Assistant & \$38,000 & \$39,520 & 
  \$41,101 & \$118,621 \\
\addlinespace
\multicolumn{5}{l}{\textbf{Fringe Benefits}} \\
\quad Faculty Fringe Benefits (29.6\%) & \$3,577 & \$3,720 & 
  \$3,868 & \$11,165 \\
\quad GRA Fringe Benefits (50\%) & \$19,000 & \$19,760 & 
  \$20,551 & \$59,311 \\
\cmidrule{2-5}
\quad \textit{Fringe Benefits Subtotal} & \$22,577 & \$23,480 & 
  \$24,419 & \$70,476 \\
\addlinespace
\multicolumn{5}{l}{\textbf{Equipment}} \\
\quad (No equipment over \$5,000) & --- & --- & --- & --- \\
\addlinespace
\multicolumn{5}{l}{\textbf{Travel}} \\
\quad Conference Travel (Domestic) & \$4,000 & \$4,000 & 
  \$4,000 & \$12,000 \\
\quad Industry Collaboration Visits & \$1,500 & \$1,500 & 
  \$1,500 & \$4,500 \\
\cmidrule{2-5}
\quad \textit{Travel Subtotal} & \$5,500 & \$5,500 & 
  \$5,500 & \$16,500 \\
\addlinespace
\multicolumn{5}{l}{\textbf{Participant Support Costs}} \\
\quad (Not applicable) & --- & --- & --- & --- \\
\addlinespace
\multicolumn{5}{l}{\textbf{Other Direct Costs}} \\
\quad \textit{Materials and Supplies:} & & & & \\
\quad \quad High-Performance Workstation & \$3,500 & --- & 
  --- & \$3,500 \\
\quad \quad Laboratory Materials \& Supplies & \$1,500 & \$1,000 & 
  \$1,000 & \$3,500 \\
\quad \textit{Publication Costs} & \$1,000 & \$1,500 & 
  \$2,000 & \$4,500 \\
\quad \textit{Computing/Cloud Services} & \$1,500 & \$1,500 & 
  \$1,500 & \$4,500 \\
\cmidrule{2-5}
\quad \textit{Other Direct Costs Subtotal} & \$7,500 & \$4,000 & 
  \$4,500 & \$16,000 \\
\addlinespace
\midrule
\textbf{Total Direct Costs} & \$85,660 & \$85,066 & 
  \$88,589 & \$259,315 \\
\addlinespace
\multicolumn{5}{l}{\textbf{H. Indirect Costs (F\&A)}} \\
\quad On-Campus Research (56\% MTDC) & \$35,326 & \$34,488 & 
  \$35,935 & \$105,749 \\
\addlinespace
\midrule
\textbf{TOTAL PROJECT COST} & \$120,986 & \$119,554 & 
  \$124,524 & \$365,064 \\
\bottomrule
\end{tabular}
\end{table}

\subsection{Budget Justification}

\subsubsection{Senior Personnel}

\paragraph{Faculty Advisor}
Funds are requested to support one month of summer salary per year 
for the faculty advisor (estimated at Associate Professor level, 
\$96,459/year base salary for 8 academic months = \$12,083/month). 
A 4\% annual salary increase is applied in subsequent years.

\subsubsection{Other Personnel}

\paragraph{Graduate Research Assistant (Principal Investigator)}
Funds are requested to support one full-time graduate research 
assistant (the PI) for the entire duration of the project at 
\$38,000 per year in Year 1. This represents a standard graduate 
research assistantship stipend at the University of Pittsburgh for 
a PhD student in the Swanson School of Engineering. A 4\% annual 
salary increase is included in Years 2 and 3 to account for 
cost-of-living adjustments.

\subsubsection{Fringe Benefits}

\paragraph{Faculty Fringe Benefits}
Faculty fringe benefits are calculated at 29.6\%, the University of 
Pittsburgh's approved rate for academic year faculty, covering 
retirement contributions, health insurance, and other benefits.

\paragraph{Graduate Research Assistant Fringe Benefits}
Fringe benefits for the GRA are calculated at 50\% of salary, 
consistent with University of Pittsburgh rates for graduate students 
on research assistantships. 

\subsubsection{Travel}

\paragraph{Conference Travel (\$4,000 per year)} Funds are requested for the PI
and faculty advisor to attend one major control systems conference annually to
disseminate research results. The budget assumes domestic conference attendance
with costs including: airfare, hotel, meals and incidentals, ground
transportation, and registration for both attendees per conference.
\paragraph{Industry Collaboration Visits (\$1,500 per year)} Funds are requested
for travel to industry partner sites and potential nuclear facilities to: (1)
validate reactor operating procedures with domain experts; (2) present research
progress to industry stakeholders; (3) gather feedback on practical
implementation considerations; and (4) explore deployment pathways for the
developed technology. 

\subsubsection{Other Direct Costs}

\paragraph{Materials and Supplies}

\textit{High-Performance Workstation (\$3,500, Year 1):} A dedicated
high-performance workstation is required for computationally intensive tasks
including. The workstation specifications include: Intel Core i9 or AMD Ryzen 9
processor (minimum 16 cores), 64 GB RAM, 2 TB NVMe SSD storage, and NVIDIA GPU
for potential acceleration of numerical computations. 

\textit{Laboratory Materials and Supplies (\$1,500 Year 1; \$1,000 Years 2--3):}
Funds are requested for laboratory supplies and materials including: electronic
components and sensors for hardware integration, cables and connectors for
hardware-in-the-loop setup, and miscellaneous computing accessories such as
external storage devices and backup media. 

\paragraph{Publication Costs}
Funds are requested to cover publication fees for disseminating 
research results in high-quality peer-reviewed venues. Budget 
includes:
\begin{itemize}
\item Year 1 (\$1,000): Conference proceedings fees and one journal 
  submission
\item Year 2 (\$1,500): Open-access publication charges for first 
  major journal paper
\item Year 3 (\$2,000): Open-access publication charges for 
  dissertation-culminating journal papers
\end{itemize}

Open-access publication is prioritized to maximize research impact 
and accessibility, particularly important for work with potential 
nuclear safety applications. Many high-impact journals (IEEE 
Transactions on Automatic Control, Automatica) charge 
\$1,000--\$2,000 for open access.

\paragraph{Computing and Cloud Services} Funds are requested for cloud computing
resources and online services. Cloud computing provides scalable
computational resources for particularly demanding verification problems without
requiring additional capital equipment purchases.

\subsubsection{H. Indirect Costs (Facilities \& Administrative)}

Indirect costs are calculated at 56\% of Modified Total Direct Costs 
(MTDC), which is the University of Pittsburgh's federally negotiated 
rate for on-campus research. MTDC includes all direct costs except 
equipment purchases over \$5,000, tuition remission, and certain 
other exclusions. The calculation base includes all personnel costs, 
travel, and other direct costs as shown in the budget table.
