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Full-Text Articles in Physical Sciences and Mathematics

Characterizing Stiffness Dynamics Of Normal And Malignant Breast Spheroids Using Brillouin Microscopy, Razanne Rafat Zaghloul, Karlin Hilai, Chenjun Shi, Jitao Zhang May 2026

Characterizing Stiffness Dynamics Of Normal And Malignant Breast Spheroids Using Brillouin Microscopy, Razanne Rafat Zaghloul, Karlin Hilai, Chenjun Shi, Jitao Zhang

Medical Student Research Symposium

Background: Breast cancer progression and metastasis are closely linked to alterations in the mechanical properties of tumor cells and their microenvironment. Softer, more deformable cells are often associated with higher metastatic potential. While atomic force microscopy (AFM) is the current gold standard for mechanical characterization, it is limited to surface measurements and can damage 3D cultures. It remains unclear how the mechanical properties evolve over time in normal versus malignant spheroids. This study utilizes Brillouin light-scattering microscopy, a non-contact and label-free optical technique, to assess stiffness changes in normal and malignant breast epithelial spheroids over time. Understanding these mechanical signatures …


Environmental Mercury Alters Immune Pathways Linked To Autoimmune Risk In Mice Mirroring Humans, Maurgan Lee, Paul Stemmer, Randall Gill, Allen Rosenspire, Anil Aranha, Heather Gibson May 2026

Environmental Mercury Alters Immune Pathways Linked To Autoimmune Risk In Mice Mirroring Humans, Maurgan Lee, Paul Stemmer, Randall Gill, Allen Rosenspire, Anil Aranha, Heather Gibson

Medical Student Research Symposium

Background and Purpose: Mercury is a pervasive environmental contaminant, and human epidemiologic studies have linked chronic low-level exposure to increased autoimmune disease-risk. Dysregulated lymphocyte activation and impaired signaling tolerance are central mechanisms in human autoimmunity. Protein phosphorylation governs lymphocyte differentiation and function, alterations in phosphoproteomic networks may represent a signature of immune disruption. This study evaluates how low dose mercury exposure modifies B and T cell abundance and intracellular signaling patterns in BALB/c and Diversity Outbred (DO) mice.

Methods: BALB/c and DO mice were exposed to low dose HgCl2 in their water for two weeks or provided standard water controls. …


Identifiability, Sequentiality And Infinity, Jose L. Menaldi May 2026

Identifiability, Sequentiality And Infinity, Jose L. Menaldi

Mathematics Faculty Research Publications

Abstract: A definition of identifiable-sets is used with sequential analysis to establish a realm of mathematics. Within this imaginary world, a specific consonant between infinite sets and sequentiality is reached.  This consonant allows some mathematical constructions to model pieces of the reality, based on dual philosophy and physics itself.  There is an effort made to render this understandable for the scientific community.


Balanced Multi-Party Tournament Designs, Parsa Nematollahe Jan 2026

Balanced Multi-Party Tournament Designs, Parsa Nematollahe

Honors College Theses

This paper introduces Multi-Party Tournament (MPT) designs that generalize established combinatorial structures, including Whist, Pitch, and Generalized Whist tournament designs. This work will formally define MPTs, establish the fundamental properties of resolvability, fullness, and balance, and formulate a mathematical and algorithmic foundation for multi-party tournament scheduling. The primary contributions of this research are the presentation of necessary and sufficient existence conditions for MPTs across various properties and parameters, the identification of connections between MPTs and other fields of mathematics such as combinatorial design theory, graph theory, and probability theory, and the investigation of MPT construction algorithms, including tree-search, finite-field constructions, …


Investigating Resilience Of Cyberattack Detection Using Lyapunov-Based Economic Model Predictive Control To Data Poisoning, Helen Durand, Akkarakaran Francis Leonard Aug 2025

Investigating Resilience Of Cyberattack Detection Using Lyapunov-Based Economic Model Predictive Control To Data Poisoning, Helen Durand, Akkarakaran Francis Leonard

Chemical Engineering and Materials Science Faculty Research Publications

Cyberattacks may be performed on process control systems due to their integration of networking and computing with physical systems. Prior work in our group has developed detection strategies for nonlinear systems under sensor, actuator, and combined sensor and actuator attacks which can ensure, under characterizable conditions, that attacks can be detected before they cause safety issues. However, this work did not take into account the potential that an attacker could attempt to provide data to a process that causes an attack to remain undetected but that also is consistent with different process dynamics than those which the process has. This …


Response Of Dynamic Processes With Control Implemented On A Noisy Quantum Computer, Shilpa Narashimhan, Dominic Messina, Henrique Oyama, Helen Durand Aug 2025

Response Of Dynamic Processes With Control Implemented On A Noisy Quantum Computer, Shilpa Narashimhan, Dominic Messina, Henrique Oyama, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

A major challenge to determining the applicability (and potential outperformance over classical computers) of a quantum computer (QC) within chemical manufacturing processes is quantum noise. Computations by a QC are error-prone due to the influence of quantum noise inherent to the hardware. Errors in control inputs may destabilize a chemical process and lead to unsafe conditions for manufacturing personnel and the environment. The response of a process with control implemented on a QC to errors due to noise must be investigated thoroughly. In this work, the impacts of control input errors due to quantum noise on a process are modeled …


Heuristic Strategies For Process Stabilization Using Proportional Control Implemented By A Noisy Quantum Simulator, Keshav Kasturi Rangan, Helen Durand Aug 2025

Heuristic Strategies For Process Stabilization Using Proportional Control Implemented By A Noisy Quantum Simulator, Keshav Kasturi Rangan, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

Processing and storage demands of industrial processes are causing fields such as optimization, scheduling, and control to assess the effectiveness of quantum devices in their applications. A key objective of control systems is to ensure process safety. This paper focuses on the potential of quantum devices to compute control inputs that maintain system safety despite sources of nondeterminism inherent to currently available quantum devices (quantum noise). In our previous work, we employed a quantum simulator to assess whether a quantum implementation of a proportional (P) control law could stabilize a single-input/single-output system under quantum noise approximated from a real quantum …


Tools To Design Algorithms For Implementing Control Over Quantum Computers, Shilpa Narashimhan, Jihan Abou Halloun, Kip Nieman, Helen Durand Aug 2025

Tools To Design Algorithms For Implementing Control Over Quantum Computers, Shilpa Narashimhan, Jihan Abou Halloun, Kip Nieman, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

Quantum computers (QCs) may find future applications within control systems that operate manufacturing processes. For application within control engineering, quantum algorithm development must be led by control engineers. However, control engineers may face challenges in designing quantum algorithms for control engineering problems. In this work, we provide several path-finding studies that leverage engineering tools such as optimization, encryption, and computational "short-cuts" toward making algorithm design for QC easier for control engineers.


Opioid Vs. Money Choice Preference Patterns In Regular Heroin Users, Amolak S. Jhand, Mark Greenwald Apr 2025

Opioid Vs. Money Choice Preference Patterns In Regular Heroin Users, Amolak S. Jhand, Mark Greenwald

Medical Student Research Symposium

About two-thirds of people treated for opioid use disorder (OUD) return to opioid use within the first-year post-treatment, and about 10% report use while on agonist therapy. Understanding determinants of opioid-seeking is vital to reducing recurrence and its risks. We assessed individual differences in effortful choices between opioid and money amounts, modeling real-world choices.

Our lab conducted studies in which regular heroin-users were stabilized on buprenorphine to suppress withdrawal. Within experimental sessions, the participant could choose repeatedly across 12 trials between units of hydromorphone (HYD, 1 or 2 mg IM) vs. money ($2 or $4); HYD and money amounts differed …


Demand Characterization For Real-Time Cyber-Physical Systems: Algorithms, Analysis, And Applications To Control Systems, Aaron Thomas Willcock Jan 2025

Demand Characterization For Real-Time Cyber-Physical Systems: Algorithms, Analysis, And Applications To Control Systems, Aaron Thomas Willcock

Wayne State University Dissertations

This work adds novel co-design, demand characterization, and utilization bounding tools to the real-time community toolbox for the effective deployment of real-time, safety-critical cyber-physical systems. Specifically, this work exploits system dynamics for improved real-time analysis in: software-based short circuit detection, intelligent power distribution systems (IPDSes), robotic arm motion, and internal combustion engines (ICEs). In short detection, inductor sub-saturation back-EMF is exploited to link circuit size and task utilization. In the IPDS, sub-maximal loading is used to bound system utilization for variable-frequency current monitoring tasks. For the robotic arm, repeated motion and error-dependent worst-case execution time are leveraged for faster schedulability …


Finite Hybrid- And Semi-Markov Chains, Jose L. Menaldi, Maurice Robin Jan 2025

Finite Hybrid- And Semi-Markov Chains, Jose L. Menaldi, Maurice Robin

Mathematics Faculty Research Publications

The ergodic behaviour of finite Markov chains having also instantaneous transition are considered. Some estimates are obtained which complement our previous work [29]. Also, an optimal switching control model for semi-Markov chains is analysed, without any particular assumptions on the recurrent classes.


Transition Metal Alkoxide Complexes Synthesis Using Thallium Reagents And Design Of Iron(Ii)-Alkoxide Carbene Complexes And Their Reactivity, Lakshani Wathsala Kulathungage Jan 2025

Transition Metal Alkoxide Complexes Synthesis Using Thallium Reagents And Design Of Iron(Ii)-Alkoxide Carbene Complexes And Their Reactivity, Lakshani Wathsala Kulathungage

Wayne State University Dissertations

ABSTRACTTRANSITION METAL ALKOXIDE COMPLEXES SYNTHESIS USING THALLIUM REAGENTS AND DESIGN OF IRON(II)-ALKOXIDE CARBENE COMPLEXES AND THEIR REACTIVITY by LAKSHANI WATHSALA KULATHUNGAGE May 2025 Advisor: Dr. Stanislav Groysman Major: Chemistry (Inorganic) Degree: Doctor of Philosophy

This dissertation focuses on the synthesis and reactivity of transition metal and main group metal alkoxide complexes. The dissertation began with exploring a novel, efficient synthetic route towards transition metal alkoxides involving thallium reagents. A novel dimeric Tl2(OCtBu2Ph)2 complex was synthesized in the reaction between a lithium alkoxide and thallium precursor TlPF6. Tl2(OCtBu2Ph)2 served as a convenient precursor to the formation of old and new transition …


Structural Impacts Of Canonical And Non-Canonical Oligonucleotide Modifications, Deepak Shrestha Jan 2025

Structural Impacts Of Canonical And Non-Canonical Oligonucleotide Modifications, Deepak Shrestha

Wayne State University Dissertations

Nucleic acids, including DNA (deoxyribonucleic acid) and RNA (ribonucleic acids), are the fundamental building blocks of living organisms. The events that cause modification of DNA/RNA are of interest because they impact the nucleic acid function. Targeting DNA is important for treating diseases such as cancer. Cisplatin (cisPt) is a well-studied drug that targets DNA and blocks replication, but its use is limited by adverse side effects and cellular resistance. Prevoius research addressed some of these challenges through development of platinum analogues such as carboplatin and oxaliplatin. Amino acid-linked platinum analogues (AAPt) are the focus of this thesis work. AAPt complexes …


Mass Spectrometry Combined With Chemical Biology To Study Human Ailments, Eric Thomas Jacquerio Davis Jan 2025

Mass Spectrometry Combined With Chemical Biology To Study Human Ailments, Eric Thomas Jacquerio Davis

Wayne State University Dissertations

Post-translational modifications (PTMs) are essential as chemical changes that regulate protein function, activity, stability, interactions, and localization after protein synthesis. PTMs, such as phosphorylation, acetylation, and ubiquitination, can activate or deactivate proteins, influence their interactions with other molecules, and determine their cellular location. This regulation is vital for numerous biological processes, such as cell cycle control, signal transduction, and gene expression. Abnormal PTMs are linked to various diseases in humans, including parasitic infection, blood disorders, cancers, and neurodegenerative diseases, making their study crucial for understanding disease mechanisms and developing targeted therapies. In the Pflum lab, we are interested in the …


Ergodic Switching Control For Markov-Feller Processes Ii, Jose L. Menaldi, Maurice Robin Jan 2025

Ergodic Switching Control For Markov-Feller Processes Ii, Jose L. Menaldi, Maurice Robin

Mathematics Faculty Research Publications

This is the continuation of Part I [14], where we considered control problems with long term average (or ergodic) cost for Markov switching processes (zt , nt ), nt being a discrete component with values in a finite set N . The control acts only on this discrete component and consists of immediate switching actions. We solve the ergodic problem in several situations extending previous works, mainly when zt is a reflected diffusion with or without jumps and when the set of control values is strictly smaller than N . In this Part II, we conclude our theoretical analysis with …


Ergodic Switching Control For Markov-Feller Processes I, Jose L. Menaldi, Maurice Robin Jan 2025

Ergodic Switching Control For Markov-Feller Processes I, Jose L. Menaldi, Maurice Robin

Mathematics Faculty Research Publications

We consider control problems with long term average (or ergodic) cost for Markov switching processes (zt, nt ), nt being a discrete component with values in a finite set N . The control acts only on this discrete component and consists of immediate switching actions. We solve the ergodic problem in several situations extending previous works, mainly when zt is a reflected diffusion with or without jumps and when the set of control values is strictly smaller than N .


Optimization Of Free-Time Controlled Constrained Sweeping Processes And Applications, Thi Dai Trang Nguyen Jan 2025

Optimization Of Free-Time Controlled Constrained Sweeping Processes And Applications, Thi Dai Trang Nguyen

Wayne State University Dissertations

Optimization and optimal control have a wide range of applications across fields like engineering, biology, data science, and economics. This dissertation is devoted to advanced optimal control problems discontinuous constrained differential inclusions of the sweeping type involving the duration of the dynamic process into optimization, which are truly challenging and underinvestigated in control theory while being highly important for various applications. To attack such problems, we use the method of discrete approximation while establishing its well-posedness and strong convergence to optimal solutions of the controlled sweeping process. This approach, married to advanced tools of variational analysis, enables this research to …


Neutron Star Low-Mass X-Ray Binaries In And Out Of Focus: Nustar Stray Light, Songwei Li Jan 2025

Neutron Star Low-Mass X-Ray Binaries In And Out Of Focus: Nustar Stray Light, Songwei Li

Wayne State University Dissertations

Neutron star low-mass X-ray binaries (NS LMXBs) provide crucial insights into the physics of accretion under extreme gravity. In this dissertation, we explore the capabilities of NuSTAR’s stray light (SL) observations to supplement, and in some cases, surpass focused data in spectral studies of bright LMXBs. Utilizing the use of SL datasets, we perform detailed spectral analyses of two Z sources: GX 340+0 and Sco X-1.

For GX 340+0, we compare 7 focused and 25 SL observations across multiple spectral states, demonstrating that SL data significantly expand temporal coverage and allow for the detection of long-term spectral evolution not evident …


Toward Biocompatible Assessment Of N-15 Hyperpolarized Metronidazole For Hypoxia Sensing, Faisal Asif Jan 2025

Toward Biocompatible Assessment Of N-15 Hyperpolarized Metronidazole For Hypoxia Sensing, Faisal Asif

Wayne State University Theses

Recent advances in hyperpolarization, particularly Signal Amplification by Reversible Exchange (SABRE), have enhanced molecular magnetic resonance imaging (MRI) for in vivo applications. This study investigates [15N3]metronidazole, a tri-nitrogen-labeled derivative of an FDA-approved antibiotic, as a hypoxia-sensitive imaging agent. Under hypoxic conditions, the nitroimidazole group undergoes stepwise reduction to an amino group, inducing significant 15N chemical shift changes (30–600 ppm). We aim to develop an iridium catalyst-free, biocompatible hyperpolarized (HP) [15N3]metronidazole formulation exhibiting robust polarization (up to 15%) and extended T1 lifetimes (~10 min). Three specific objectives guide this work: (1) formulation of a HP injectable with enhanced 15N detection, (2) …


Lead Bioaccessibility And Commonly Measured Soil Characteristics (Detroit, Mi, Usa) Phase Ii, Conor T. Gowan, Sabrina R. Good, Allison R. Harris, Patrick Crouch, Shawn P. Mcelmurry Jan 2025

Lead Bioaccessibility And Commonly Measured Soil Characteristics (Detroit, Mi, Usa) Phase Ii, Conor T. Gowan, Sabrina R. Good, Allison R. Harris, Patrick Crouch, Shawn P. Mcelmurry

Open Data at Wayne State

Urban soil contaminated with anthropogenic sources of Pb is a major contributor to child Pb exposure. To assess the Pb risk in urban areas, composite samples were collected from 142 voluntary privately owned 142 residential parcels in Detroit, Hamtramck, and Highland Park, Michigan. Samples were collected at two time periods, before and after treatment applied for those denoted as treatment sites. Samples were collected from areas covered with turf grass on the parcels from the front, middle and rear sections. Soils were collected with a bulb planter at approximately 10cm depth and were cleaned with a tap water-Liquinox detergent solution …


Fault And Cyberattack Diagnosis And Handling Via Large Language Models And State Prediction For Manufacturing And Quantum Systems, Jihan Abou Halloun Jan 2025

Fault And Cyberattack Diagnosis And Handling Via Large Language Models And State Prediction For Manufacturing And Quantum Systems, Jihan Abou Halloun

Wayne State University Dissertations

In the digitalization era and Smart Manufacturing, companies are harnessing the power of artificial intelligence (AI) and machine learning (ML) across multiple sectors, including process engineering optimization, process control and fault detection, to enhance efficiency and engineering decision making. Although AI and ML are widely used in anomaly detection and handling, there are still areas where it has been less explored. One of the major areas where AI’s potential in manufacturing needs to be characterized is with respect to the applications of large language models (LLMs) in manufacturing troubleshooting for fault/attack handling. A second major area where the potential of …


How Do Selected Biomedical And Health Sciences Journals React To Submissions Of Artificial Intelligence (Ai) Assisted Manuscripts?, Misa Mi, Lin Wu, Yingting Zhang, Wendy Wu Jan 2025

How Do Selected Biomedical And Health Sciences Journals React To Submissions Of Artificial Intelligence (Ai) Assisted Manuscripts?, Misa Mi, Lin Wu, Yingting Zhang, Wendy Wu

Library Scholarly Publications

Background and Objectives: Generative artificial intelligence (GenAI) increasingly impacts research and scholarly communication. Given the evolving application of ChatGPT and other AI tools in scholarly communications, health sciences librarians must become cognizant of any existing journal publishing guidelines for AI-created or assisted manuscripts. The study aims to examine how scholarly biomedical and health sciences journals and publishers respond to submissions of these manuscripts and what requirements or policies have been put in place to guide and instruct authors on AI use.

Methods: We first retrieved and consolidated a list of journals representing disciplines in biomedical and health sciences from four …


Leveraging Large-Language Models As Collaborative Reasoning Partners To Enhance Scientific Workflow, Douglas B. Craig Jan 2025

Leveraging Large-Language Models As Collaborative Reasoning Partners To Enhance Scientific Workflow, Douglas B. Craig

Wayne State University Dissertations

The rise of Large Language Models (LLMs) has transformed artificial intelligence, offering advanced capabilities in text generation, natural language understanding, and multi-modal interactions. However, their use as standalone tools or as perceived repositories of static knowledge has limited their potential in real-world applications, especially in critical domains like healthcare and scientific research, where transparency, explainability, and accountability are paramount. This research addresses these limitations by conceptualizing LLMs as reasoning engines within a hybrid framework that integrates retrieval-augmented generation (RAG) and case-based reasoning (CBR) within a note-taking application.

The study introduces a novel system, LmRaC, designed to enhance the reliability, explainability, …


Advancing Road Safety Through Software-Defined Vehicles, Raef Abdallah Jan 2025

Advancing Road Safety Through Software-Defined Vehicles, Raef Abdallah

Wayne State University Dissertations

Road traffic accidents are a significant global concern, claiming approximately 1.3 million lives annually and causing non-fatal injuries to 20–50 million people, many of which result in long-term disabilities. They are the leading cause of death for individuals aged 5–29 and impose a substantial economic burden, costing most countries 3% of their Gross Domestic Product (GDP). In addition to car accidents, other types of road incidents, such as collisions involving tall vehicles and overpasses, also pose significant risks. These accidents result in numerous fatalities and cause millions of dollars in damages annually. Environmental conditions like wet or icy roads and …


Advancing Generative Ai In 3d And 4d Spaces, Hasan Iqbal Jan 2025

Advancing Generative Ai In 3d And 4d Spaces, Hasan Iqbal

Wayne State University Dissertations

Generative Artificial Intelligence (AI) has transformed how we synthesize, edit, and manipulate complex data, opening new possibilities for immersive digital content. This dissertation, titled “Advancing Generative AI in 3D and 4D Spaces,” investigates the capabilities and limitations of state-of-the-art generative models in static 3D scenes and time-aware 4D environments. In the 3D setting, scene editing is hindered by multi-view inconsistency and the high computational cost of per-scene retraining. To address these issues, the work introduces Free-Editor, a training free approach that utilizes an Edit Transformer to propagate a single edited view across all camera perspectives without additional optimisation, delivering prompt …


Cyberattack Detection And Handling For Neural Network-Approximated Economic Model Predictive Control, Jihan Abou Halloun, Helen E. Durand Sep 2024

Cyberattack Detection And Handling For Neural Network-Approximated Economic Model Predictive Control, Jihan Abou Halloun, Helen E. Durand

Chemical Engineering and Materials Science Faculty Research Publications

Cyberattacks on control systems can create unprofitable and unsafe operating conditions. To enhance safety and attack resiliency of control systems, cyberattack detection strategies can be developed. Prior work in our group has sought to develop cyberattack detection strategies that are integrated with an advanced control formulation known as Lyapunov-based economic model predictive control (LEMPC), in the sense that the controller properties can be used to analyze closed-loop stability in the presence or absence of undetected attacks. In this work, we consider neural network-approximated control laws, concepts for mitigating cyberattacks on such control laws, and how these ideas elucidate concepts in …


Lyapunov-Based Cyberattack Detection For Distinguishing Between Sensor And Actuator Attacks, Dominic Messina, Helen E. Durand Sep 2024

Lyapunov-Based Cyberattack Detection For Distinguishing Between Sensor And Actuator Attacks, Dominic Messina, Helen E. Durand

Chemical Engineering and Materials Science Faculty Research Publications

Control-theoretic cyberattack detection strategies are control strategies where control theory can be used in the design of the detection policies and analysis of stability properties with and without cyberattacks. This work provides a step toward understanding how to diagnose cyberattacks using control-theoretic cyberattack detection mechanisms. Specifically, we analyze the conditions under which a control-theoretic cyberattack detection strategy developed in our prior work to handle detection of simultaneous actuator and sensor attacks can be extended to distinguish between whether attacks are occurring on sensors or actuators. We present and evaluate heuristic concepts for attempting to diagnose sensor attacks; these again demonstrate …


Profit Considerations For Nonlinear Control-Integrated Cyberattack Detection On Process Actuators, Keshav Kasturi Rangan, Helen E. Durand Sep 2024

Profit Considerations For Nonlinear Control-Integrated Cyberattack Detection On Process Actuators, Keshav Kasturi Rangan, Helen E. Durand

Chemical Engineering and Materials Science Faculty Research Publications

Prior research from our group developed a control-integrated active actuator cyberattack detection strategy. This strategy continuously probed for cyberattacks by updating target steady-states at every sampling time and then moving the process state toward these over the subsequent sampling period. Attacks were fagged if a Lyapunov function around the target steady-state did not decrease over a sampling period. This strategy had the benefit of ensuring safety of the process until an attack was detected. However, the continuous probing for attacks could decrease profit from the process compared to not probing for the attacks, which could limit the attractiveness of the …


Synchronicity: An Analysis Of Einstein's Halfway Rule, Preslava Nikolova Jan 2024

Synchronicity: An Analysis Of Einstein's Halfway Rule, Preslava Nikolova

Rushton Journal of Undergraduate Humanities Research

For the modern world to function, Global Positioning System satellites must synchronize to clocks on Earth. This paper examines a concept that underlies GPS systems, namely Albert Einstein’s halfway rule—the idea that a line of simultaneity exists between two events in different systems. This essay discusses how Einstein used conventionalist methods to establish ½ as a constant value for σ to take advantage of the property of symmetry.


Computing The Roots Of Twisting Sheaves Over The Projective Line Arising From Monodromy Representations, Diego Yepez Jan 2024

Computing The Roots Of Twisting Sheaves Over The Projective Line Arising From Monodromy Representations, Diego Yepez

Wayne State University Dissertations

Given a monodromy representation of the projective line minus a finite number of points, one can extend the resulting vector bundle with connection map canonically to a vector bundle with logarithmic connection map over all of the projective line. Now, since vector bundles split as twisting sheaves over the projective line, the focus of this work regards knowing the exact decomposition.