Probability Solutions LLC
Probabilistic Modeling · Stochastic Analysis · Algorithmic Expertise
ABOUT US
Expert Solutions in Probabilistic Modeling,
Stochastic analysis and Algorithms.
Probability Solutions LLC provides advanced consulting in probabilistic modeling, stochastic analysis, and algorithm design for complex, data-driven systems.
The company works with organizations facing challenging problems where uncertainty, scale, and performance are critical, delivering solutions that improve efficiency, reliability, and decision-making.
Leveraging deep expertise in data structures, network systems, and algorithmic optimization, Probability Solutions supports large technology companies, research-driven organizations, and innovative startups. Its services include mathematical modeling, performance analysis, and training technical teams to develop fast, efficient, near-optimal algorithms that reduce computational cost while maintaining high performance.
About The Founder
Hosam Mahmoud, PhD, is the Founder and CEO of Probability Solutions LLC and a Professor of Statistics at The George Washington University. He is an internationally recognized expert in probabilistic modeling, stochastic processes, and the analysis of complex algorithmic systems, with a focus on random structures such as trees, graphs, and large-scale networks.
Over a distinguished academic career, he has authored more than 130 peer-reviewed publications and four influential books, contributing foundational advances to the mathematical analysis of algorithms and random systems. His work extends beyond theory, offering deep insights into how complex systems behave under uncertainty and how they can be optimized for performance, scalability, and efficiency.
Through Probability Solutions LLC, he provides high-level consulting to organizations operating in data-intensive and computationally demanding environments, including large technology companies, research institutions, and innovative startups. His services include advanced mathematical modeling, performance analysis of data structures, and the design of efficient, near-optimal algorithms that significantly reduce computational cost while maintaining high performance.
In addition to consulting, he works closely with technical teams, delivering specialized training and strategic guidance to help them develop scalable, high-performance solutions. His approach combines rigorous mathematical theory with practical implementation, enabling organizations to make informed, data-driven decisions and solve complex problems with clarity and precision.
His expertise is particularly valuable in environments where efficiency, scalability, and precision are critical to success.
Prof. Hosam M. Mahmoud
Founder & CEO
Ravi Kalpathy, PhD
Chief Operating Officer
(Consulting Role)
Serves as Chief Operating Officer at Probability Solutions LLC in a part-time consulting capacity. Dr. Kalpathy’s primary professional appointment is as a full-time Assistant Professor in the Department of Mathematics & Statistics, with a dual appointment in Computer Science, at The Catholic University of America, where he teaches, advises students, conducts research, and fulfills his faculty responsibilities during the regular academic year. His consulting engagement with Probability Solutions is fully consistent with Catholic University’s policies governing external professional activities and reflects the complementary relationship between academic scholarship and professional practice.
At Probability Solutions, Ravi brings expertise in probabilistic modeling, statistical learning, algorithmic analysis, and data-driven decision-making to help guide the company’s technical strategy, product development, and operational direction. Working collaboratively with the team, he helps ensure that the company’s solutions are scientifically rigorous, practically relevant, and scalable for real-world applications across industry.
Ravi’s consulting work strengthens the connection between theory and practice. Exposure to real-world analytical challenges informs his scholarly research and enriches his teaching. Dr. Kalpathy’s academic expertise enables Probability Solutions to apply current advances in mathematics, statistics, and computing to complex client problems. This reciprocal exchange exemplifies the type of external professional engagement encouraged by Catholic University’s consulting guidelines.
His role at Probability Solutions is intentionally structured as a limited part-time consulting appointment and remains fully aligned with his primary commitment to The Catholic University of America. Through this engagement, Ravi contributes disciplinary expertise, intellectual leadership, and a commitment to rigor, curiosity, integrity, and responsible innovation in service of both the academic community and industry.
View Profile →
Ravi Kalpathy, PhD
Chief Operating Officer
(Consulting Role)
Our Associates
Ravi Kalpathy, PhD
COO
A faculty member in the
Department of Mathematics and Statistics at The Catholic University of America.
Expertise includes probabilistic analysis of algorithms and discrete random structures, with a strong interest in statistics education.
Well recognized for his contributions to leader election algorithms and large hooking networks.
Ali Alsam, PhD
Associate
Srinivasan Balaji, PhD
Associate
A faculty member in the
Department of Statistics at The George Washington University with many years of teaching.
Industrial experience in various capacities. Actively involved in the business development of Probability Solutions.
Academic interests are broadly in the area of probability theory and its applications including diffusion processes, Markov chains, stochastic differential equations, statistics in finance.
Our Services
Probabilistic Modeling
Applying stochastic methods to understand dynamic processes and predict system behavior.
This book cover is reproduced by permission of Taylor & Francis Group.
Stochastic Analysis
Developing advanced probabilistic models to analyze complex systems and quantify uncertainty.
Algorithmic Expertise
Designing efficient algorithms for data-driven decision-making and optimization.
Advisory Board
Our Advisory Board brings together experienced professionals from diverse fields, providing strategic guidance and expertise to support the growth and direction of Probability Solutions.
Kiran Bhutani
Advisory Board Member
Holds a PhD from McMaster University, Ontario, Canada.
Chair & Professor, Department of Mathematics and Statistics, Catholic University of America.
Leading authority in graph theory and its applications, random networks, fuzzy logic, and category theory
Wrote a book on fuzzy group theory and many influential research papers in premier journals.
Has recently participated in the US Congressional briefing on Capitol Hill, titled Mathematics: The Strategic Engine of Discovery, Competitiveness, and Security.
Mohamed Mansour
Advisory Board Member
Ravi Gupta
Advisory Board Member
Our Interns
Our internship program provides students with hands-on experience in real-world projects, allowing them to apply their academic knowledge in areas such as data structures, algorithms, and software development. Interns contribute to ongoing research and gain valuable exposure to professional practices and collaborative environments
Dhanush Mathivanan
Intern
Dates: June 1 – August 15, 2026
Education
Master’s Student at The George Washington University
.
Top skills
Python (Programming -Language)•
Machine Learning• Amazon Web Services (AWS).
AWS CloudFormation• RStudio.
Duties
Our Affiliates
Contact Us
hosam@probabilitysolutions.com
PHONE: +1 (703) 222-4284
LOCATION
The website Probability Solutions LLC has been designed by Sabah Bourgi.
sabah@probabilitysolutions.com