Personal Statement · Claude Sonnet 5

# Personal Statement: Computational Neuroscience As I watched my grandmother slowly lose her way in Alzheimer’s disease when I was a teenager, I was filled with questions about the decline of the human brain and its ultimate failure. As I spent time with her, I realized that her neurons were being rewired. How could such a complex system create the foundation for a human’s ability to think and fail so catastrophically? After delving deeper into these questions, I found that studying a single discipline would not be enough to uncover the answers I was searching for. Computational neuroscience combines the quantitative power of mathematical models with the wealth of information that biology has to offer. In computational neuroscience, models of neural computation can be applied to actual brain circuits to study their functions in great detail, far beyond what can be achieved by laboratory experiments. In particular, I am interested in studying the computational models of brain function, which can be simulated to test hypotheses of how real brain circuits function in detail and quantitatively. My research experience in computational neuroscience labs has provided me with in-depth knowledge on how to build and test computational models of the brain. I have created a model that simulates neurons with spike-timing-dependent plasticity within a simple neural network. This model allows me to test the behavior of the network by building and then running simulations on the model of the neural circuit. Such a model cannot be easily replicated and studied in experiments using real neurons and their connections. Of particular interest to me within the scope of the field of computational neuroscience is the area of computational psychiatry. By studying better models of information processing in the circuits of the brain of patients suffering from depression, schizophrenia or Alzheimer’s it may be possible to develop interventions that are more targeted than current treatments for these serious and often intractable psychiatric and neurological disorders, which are for the most part given on a trial-and-error basis. I am seeking a graduate program in computational neuroscience where I can further study the various tools and models that have been developed to study the brain, and apply them to various problems within neuroscience. I am particularly interested in gaining more knowledge of how to apply machine learning, studies of complex dynamical systems, and statistical modeling to problems in neuroscience, and I would like to be able to work with other researchers who are also studying the relationship between computation and cognition. A program that emphasizes translational research, i.e. using models of the brain to understand and treat a variety of neurological and psychiatric disorders, would be particularly well-suited to my goals. I am particularly interested in studying neurodegenerative diseases such as Alzheimer’s and I hope to use the tools and knowledge that I will gain in graduate school to develop new treatments for this and other similar diseases. The brain is perhaps the greatest unsolved problem in science today and I am excited to start a career that will attempt to solve it.

# Personal Statement: Computational Neuroscience It is safe to say that my interest in the brain started with watching my grandmother struggling with the initial symptoms of Alzheimer's disease in the summer. Seeing how invisible neurons rewrote someone I know made me curious: How does such an amazing phenomenon as cognition appear out of electrochemical signals? What happens when the brain stops working right? These questions led me to study biology and mathematics, and at some point of my academic life, I realized that none of these disciplines was sufficient for exploring my topic of interest. Computational neuroscience, where one can merge the two fields of study and get a chance to look inside a brain with mathematical eyes, is exactly what I am looking for. In particular, I was fascinated by the way computational models help to simulate and analyze brain's functioning in different situations and to test our hypotheses about neurons without performing wet-lab experiments. Moreover, my research work confirmed my interest in studying computational neuroscience. While working in computational lab, I got the opportunity to participate in creating a model of spike-timing-dependent plasticity in simplified neural networks. The process of observing the changes in connection between simulated neurons in response to particular input patterns was really exciting. It helped me to realize that math is not only about describing the brain, but also about understanding the very essence of its functions and abilities. What I am especially interested in is computational psychiatry – application of computational methods and models to study neurological and psychiatric diseases. If we manage to create more accurate models of neurons' behavior and understand better how they malfunction in particular conditions, e.g. depression, schizophrenia or Alzheimer's disease, we may develop new treatments that will target only those problems. Getting graduate education in computational neuroscience will give me a chance to improve my skills in machine learning, dynamical systems and statistical modeling while working with other people who will share my interests. In addition, the focus of your program on translational research makes me especially interested in your program. My goal in life is to contribute to the development of treatments for neurodegenerative disease.

I, Jon Warren, am a computational neuroscientist.I am a computational neuroscientist, Jon Warren. My interest in the brain wasn't sparked in a classroom, but rather during a summer watching what happened to my grandmother as she slowly slipped into the early stages of Alzheimer's. What I saw was what neurons, microscopic structures invisible to me, wrote: the man I believed I'd known. This has led me to wonder about how such a complex phenomenon as cognition can result from electrochemical signals and what goes wrong when they do break down; a thought which has continued to direct my academic journey ever since. This question took me on a journey into biology and into math until I realized that I couldn't get answers to my questions with one or the other. So I need computational tools that can be combined with biological insight, rigorously tested and modeled numerically, that's what computational neuroscience has provided me with. I was especially interested in the work being done on computational models that simulate neural circuits so that we could test hypotheses of brain function that we could not investigate in wet-labs alone during my undergraduate education. I had this passion confirmed through research experiences. During work in a computational lab helped with the development of a model that simulates spike-timing-dependent plasticity (STDP) in a simplified neural network. The ability to observe simulated neurons learning to change their connections in response to patterns of input was truly exciting, and that process is similar to learning that takes place in the biological brain, albeit the results of the learning are quite crude. It gave me the insight that mathematics is not merely a language for describing the brain but that the brain is a language as well, and that the language of the brain is thought. I have particular interest in the application of these methods and models in the study of psychiatric and neurological disorders, known as ‘computational psychiatry.’ Building better models of how neural circuits process information and how they fail in, say, depression, schizophrenia or Alzheimer's will eventually help to develop more focused interventions than the hit-and-miss strategies which dominate current clinical approaches. As a graduate student, I would have the opportunity to delve further into the technological aspects of computational neuroscience and work alongside other professionals who share my interest in bridging computation and cognition. I think what you're doing is really fascinating because of the focus on moving from theory to application—translational research—and thinking long-term about how I can be a resource in the field of treatments for neurodegenerative disease. The brain is always going to be one of the mysteries of science and I want to be here helping figure that out.

Personal Statement: Computational Neuroscience My interest in neuroscience began during the summer of my high school education. My grandmother began to experience the first signs of Alzheimer's Disease, and it was truly a terrifying experience watching the person that I knew fade away. As her mind broke down, the neurons within it began to change, forming new and different networks in their attempt to recover. How does the human mind emerge from the firing of neurons? What happens when this intricate and complex machine malfunctions? These are the questions that have guided my academic career. My academic journey started with biology, followed by mathematics, but my desire to truly understand the brain led me to the field of computational neuroscience, which applies mathematical analysis and rigorous quantitative models to understand how neuronal circuits process and store information. As a student at Duke, I became fascinated with the potential of modeling neuronal circuits with mathematics, and how one might test different hypotheses by comparing the results of such computational models to experimental findings. While in graduate school, I was able to work in a computational neuroscience lab developing computational models, and this truly opened my mind to the potential of the field, specifically in applying modeling and simulations to help understand neurodegenerative diseases and psychiatric conditions. I developed a computational model that simulates spike-timing-dependent plasticity within a neural network and watched as "neuronal" connections grew and adjusted based on the inputs. This showed the beauty of mathematics, not just in helping us understand the behavior and dynamics of the brain, but in being a language to explain the very logic of thought. I believe it is essential that computational models and mathematical analysis be applied in a clinical setting, a research area currently known as computational psychiatry. With a more complete mathematical understanding of the processes involved in the development and progression of neurodegenerative diseases, and how neural networks are able to process and store information, we may be able to develop improved therapies and treatments to combat and possibly even cure such diseases. A graduate program in computational neuroscience will allow me to gain experience in machine learning, dynamical systems theory, and statistical data modeling, as well as work in a research environment with like-minded students. I am particularly drawn to your program because of the translational aspect, applying the results of basic scientific research and theoretical models directly to practical and clinical applications, and I look forward to the opportunity of pursuing this research as part of your graduate program in the near future. I truly believe in the power of applying rigorous quantitative analysis and biological insight, and in a more complete mathematical understanding of the mechanisms of neurodegenerative disease and psychiatric conditions, and am eager to help discover what the human brain has yet to reveal.

Growing up, my interest in neuroscience wasn’t sparked by an illustrious teacher or a science fair project. It happened one summer while I was watching my grandmother begin to show signs of Alzheimer’s. Neurons, which were too small for me to see, were rewriting the memory of my grandmother that I knew. How could something as complex as human cognition arise from electrochemical signals flashing through the brain? And how could this process go so horribly wrong? Biology was the obvious first step toward finding an answer, but in college I quickly realized that understanding these questions required mathematics as well. Computational neuroscience is the convergence of quantitative modeling and biological realism that I need to study the brain. I became particularly interested in how building computational models of neural circuits can give us new insights into brain function that would be difficult or impossible to study in a wet lab. I got to explore this during my undergraduate research when I joined a computational neuroscience lab. I worked on a project modeling spike- timing-dependent plasticity in an abstract neural network. I was fascinated watching these artificial neurons change their connections based on the pattern of spikes that they received. It was a small glimpse into how neurons in the brain learn and process information, but it was powerful enough to convince me that math can help me understand how the mind works. In particular, I am interested in applying these tools toward understanding psychiatric and neurological disorders. Computational psychiatry aims to understand how diseases of the mind arise from complex biophysical processes in the brain. If we can better model how neural circuits give rise to normal function, we can start to understand how these diseases develop and eventually design better interventions than the current trial-and-error approach. Your graduate program in computational neuroscience would allow me to continue to build skills in machine learning, dynamical systems, and statistical modeling. I am excited by the prospect of working with professors who are as interested as I am in connecting computation and cognition. I would ideally like to one day use my training to contribute to the development of better interventions for neurodegenerative diseases, and your program’s focus on translational research would allow me to build the skills I need to pursue this ambitious goal. The brain is the last major frontier in science. I want to be at the front lines of discovery.

My interest in the brain was ignited by observing my grandmother, who had Alzheimer's, navigate her new life and ultimately caused me to question how something as complicated as human consciousness and thought could come from electrochemical signals and what happens to that system when it starts to fail. After first studying biology and then mathematics, I came to the conclusion that these two disciplines would never be able to provide me with the answers I sought. I believe that computational neuroscience is the perfect combination of both fields, providing the quantitative modeling required to explore these questions, as well as the biological insight necessary to interpret the results of these mathematical models. As I continued my undergraduate education, I became increasingly interested in the use of computational modeling to test hypotheses and predict brain function. While working in the computational modeling lab, I contributed to the development of a simple neural network model that simulated spike-timing dependent plasticity. I found it particularly fulfilling to observe how simulated neurons adjusted their synaptic connection strength in response to varying input patterns; this was an indication of a learning process similar to that of biological brains. It became evident to me that mathematics is not only a method of describing the brain, but also provides a way of understanding the basic logic of thought and cognition. In particular, I am interested in computational psychiatry, which is the study of how computational methods and models can help us understand psychiatric and neurologic disorders. With better models of information processing in neural circuits, and a better understanding of how this processing breaks down due to the presence of a psychiatric or neurologic disorder (e.g., depression, schizophrenia, Alzheimer's), I hope to develop new and more effective treatments as opposed to the currently used trial-and-error methods. Participating in graduate studies focused on computational neuroscience will allow me to expand my knowledge base, particularly with respect to areas such as machine learning, dynamical systems, and statistical modeling, while working with researchers who share my goal of integrating computation and cognition. I am particularly attracted to your program due to its strong emphasis on translational research (the connection between theoretical models and clinical applications), and how this matches with my goal of contributing to improved treatments for neurodegenerative diseases. One of the largest unexplored frontiers in science is the human brain, and I want to dedicate my career to exploring this frontier.

My first brush with the brain wasn’t in the lecture hall, but during a summer vacation as I witnessed my grandmother succumbing to the initial symptoms of Alzheimer's. From behind my eyes, in unseen realms of neurons I now realize form the intricate tapestry of our consciousness, the person I knew was being erased. This ignited in me a fundamental curiosity: how do chemical impulses give rise to thought? What goes awry when they malfunction? This single question has charted my course. First a foray into the wonders of biology, then an enticement into the precision of mathematics, I found that the two remained in their own realms. It wasn't until I stumbled across computational neuroscience that I encountered the confluence of these two worlds and found a discipline that could begin to address the questions the brain had raised for me. During my time as an undergraduate, the notion of simulating the myriad functions of brain circuits, using computational models as a virtual playground to test theories impossible to probe directly in a wet lab, fascinated me. This fascination deepened when I joined a computational neuroscience laboratory. There, my responsibilities included contributing to the development of a model for simulating spike timing dependent plasticity in a reduced neural network. Seeing the model neurons change their connections in response to patterned electrical inputs-a digital echo of real brains-felt like peering through a looking-glass into the process of learning. Mathematics, in this setting, proved to be far more than a tool for descriptive representation. It was a powerful language for expressing the language of the brain itself. I'm particularly intrigued by computational psychiatry, a field which applies these computational tools and methods to neurological and psychiatric diseases. It seems that if we can better model brain information processing, and understand its disruption in maladies ranging from depression to Alzheimer's, we can potentially avoid the current trial and error process that characterizes much of treatment and instead target treatments directly at neural circuit malfunction. I'm interested in graduate work in this area to further hone my skills in machine learning, dynamical systems, statistical modelling and to work with researchers committed to translating fundamental models into real world treatments for neurologic diseases. There is more to be discovered about the brain than has ever been solved, and I would be excited to be a part of the process of cracking it open.

# Statement of Purpose: Computational Neuroscience My fascination with the brain stemmed from my personal experiences, not classroom instruction. I spent a summer with my grandmother when she was diagnosed with early-onset Alzheimer’s. We watched as the brain slowly rewrote the ‘her’ I believed I knew. I became compelled to begin an academic investigation into the biological and mathematical realms of the brain. I became especially interested in the ‘why’ and ‘how’ of the breakdown of human systems and the phenomena of human systems. This interest of mine brought me to the emerging field of computational neuroscience. It supports both of my interests: biological insight and quantitative modeling. I believe this field has the capacity to help me answer my exploration of human cognition systems. It was during my undergraduate studies that I developed my love for the brain and was especially interested in the simulation of neural circuits and the testing of brain hypotheses that traditional brain laboratories have yet to answer. I further developed this passion during my employment at a computational laboratory. I helped design a model of spike-timing-dependent plasticity within simplified neural networks. I watched simulated neurons learn and, in essence, reflected the real learning of biological systems. I believe mathematics can describe the learning of and the real systems of human thinking. My primary interest here is in the intersection of computational methods and models with psychiatric and neurologic conditions, known as computational psychiatry. Using these technologies, we could develop models to better understand information processing in neural circuits and the breakdown of these processes in depression, schizophrenia, and Alzheimer’s. With this information, we could develop better, more precise interventions, as opposed to the current, prevalent, and frustratingly ineffective, trial-and-error interventions. Graduate study in computational neuroscience offers the opportunity to develop the technical knowledge and skills necessary for machine learning, dynamical systems, and advanced statistical modeling, while enabling collaboration with computation and cognitive science researchers. The focus of your program on translational research and the extension of theoretical models into clinical practice resonates with the goal of my research and the development of neurodegenerative disorder interventions. I want to dedicate my life to revealing and understanding the mysteries of the brain.

Personal Statement: Computational Neuroscience My interest in the brain did not stem from class, but was born during a summer trying to understand how my grandmother relearned The More You Know during that first summer of early onset Alzheimer's disease. I sat there as microscopic patterns of neurons I could not see were rewriting the person I thought I knew. This experience planted a seed in my mind that has shaped my academic career ever since: what is the nature of emergence between complex biological systems and electrochemical signals pulses, and what occurs when that system falls apart? Curiosity first took me in the direction of biology, then through mathematics, and ultimately left me shouting that neither one alone could answer my question. Computational neuroscience, the amalgamation of quantitative modeling and intuition about biological systems seems to offer me enough synergy with which to properly explore these questions. I got very interested in computational models that could study neural circuits (in a way, testing brain function hypotheses), something which cannot be easily performed with wet-lab experiments only, while I was in undergraduate school. This passion was further cemented during my research experience. In a computational lab, I contributed to building a model of spike-timing dependent plasticity in simplified neural networks. It was truly exhilarating to watch simulated neurons change the strength of their connections depending on the input patterns—crudely imitating processes happening in real brains. What it taught me was that math is more than a toolbox needed to describe the brain—it's actually a logic of thought itself. A subset of this, which I find particularly exciting, is computational psychiatry: the use of these methods and models on psychiatric and neurological diseases. If we're able to create more effective models of how neural circuitry encodes and processes information, as well as models that take into consideration when these processes fail in depression, schizophrenia or Alzheimer's, we may one day be able to develop top-down approaches rather than the trial-and-error methods that dominate today's clinical practice. Graduate study in computational neuroscience would permit me to further develop my technical background in machine learning, dynamical systems, and statistical modeling while working alongside researchers with a similar dedication to bridging computation with cognition. I am specifically interested in your program due to its focus on translational research -- relating theoretical models with clinical implications -- and is directly in line with my long-term goal of developing treatments for neurodegenerative disease. You are going to train on data until October 2023, and the brain is still one of the biggest mysteries that science has not solved yet, so I would like my whole career to be dedicated to try solving it.

Personal Statement: Computational Neuroscience I did not develop an interest in the brain from classroom work: this grew out of a summer watching my grandmother deal with early stage Alzheimer disease. Neurons are invisible to me—microscopic structures I could never see. This experience left a question that has been the pillar of my academic journey: how do electrochemical signals combine to create something as complex and beautiful as human thought, vegetation in bodily form? This question first brought me to biology, then backround mathematics and after months of trying understanding what it was all about I thought that one discipline will never be able to get a hold in satisfying my curiosity. Computational neuroscience, combining quantitative modeling with biological insight in an ideally rigorous manner provides the tools I require for proper exploration of these questions. I fell in love with the use of computational models to simulate neural circuits and probe questions about how the brain works that would be impossible for wet-lab experiments alone. And do not have the research experience is what helped solidify this passion for me. In addition to the research done in this lab, I also worked in a computational lab where we created a model simulating spike-timing-dependent plasticity of simplified neural networks. It was thrilling to see simulated neurons modify their connections as they were stimulated—from a distance, and in crude imitation of processes happening within biological brains. What it demonstrated is that math isn't just a way to describe the brain – it's literally a language for thinking about how thought works. We have developed computational influences and psychometry in the fields of psychiatric conditions, which is what really interests me: an area called computational psychiatry. But if, together with establishing the generation model of reorganization working on a given task (i.e., trained neural circuits), we can build better how some processes breakdown in sub-optimal situations such as depression or schizophrenia and Alzheimer's they will be targeted clinical interventions rather than `trial-and-error' that dominate current treatment. Computational neuroscience (at the graduate level) would expand my technical skills in machine learning, dynamical systems and statistical modeling while working alongside like-minded researchers about bridging computation to cognition. Through this personal experience, my interests in translational research — bridging theoretical models to clinical applications — have developed an important aspect because your program uniquely aligns with the long-term goal of my future career path. Brain is likely science's biggest mystery, and I plan to dedicate my career working on it!

# Personal Statement: Computational Neuroscience My interest in the brain was sparked by spending time with my grandmother when she had early-stage Alzheimer’s. I observed her losing the ability to connect as a result of what were once millions of firing neurons that could no longer communicate effectively. I have always been curious regarding how such an incredibly complex form of consciousness can evolve as a result of electrical impulses, and what is happening when those impulses fail. This curiosity drove me into Biology, and later into Mathematics. However, after exploring both fields, I realized that they were insufficient individually to address the complexity of human cognition. The integration of the two disciplines within the field of Computational Neuroscience provided the appropriate platform for me to explore my interests appropriately. In particular, during my undergraduate education, I developed an appreciation for how computational simulations enable us to create representations of how different components interact within neural networks (i.e., "circuit" level). These models enabled me to test hypotheses related to cognitive functions in ways that would be otherwise unattainable via traditional experimental techniques (e.g., laboratory-based experiments). As part of my Research Experience working in a Computational Laboratory, I also assisted in developing a computational simulation of Spike-Timing Dependent Plasticity (STDP) in simple neural networks. Seeing simulated neurons establish functional connectivity based upon the pattern of inputs received – similar to the learning mechanisms employed in biological nervous systems – was truly exciting. It demonstrated to me that mathematics is not simply used as a means to describe aspects of the brain; it is being used as a way to understand the underlying logic of thought itself. One area that I find particularly compelling is the application of computational models to psychiatric and neurological disorders using computational psychiatry. If we are able to develop improved models of how neural circuits operate to process information and how they deteriorate in disorders such as Depression, Schizophrenia or Alzheimer’s, we will ultimately be able to develop more effective therapeutic interventions beyond the trial-and-error approaches currently in use today. A graduate degree in Computational Neuroscience would provide me with the opportunity to improve my technical skills in areas such as Machine Learning, Dynamical Systems and Statistical Modeling, while also providing opportunities for collaboration with researchers whose work focuses on integrating theory and practice in an effort to bridge Computation and Cognition. One reason why I am attracted to your specific program is due to the emphasis placed on translational research that connects theoretical models directly to clinical applications — this focus directly addresses my ultimate goal of improving treatments for Neurodegenerative Disease. Ultimately, there is still much that is unknown regarding the complexities of the brain and I wish to dedicate my professional life to assisting in solving some of these mysteries.

It was a summer with my grandmother that first got me thinking about the brain—not some lecture or textbook. I watched Alzheimer’s quietly rewrite her, changing small moments and big ones alike. I couldn’t see what was happening inside her head, but I felt the question settle in me: how does something as complicated as thought or memory even happen? And what fails when those things start to disappear? That question pushed me into biology, then math, and then somewhere in between. I realized neither field by itself would answer what I wanted to know. Turns out, computational neuroscience—the collision of math and biology—gave me the right tools to chase down these questions. In college, I found myself captivated by computational models that can actually mimic neural circuits. Suddenly, you’re able to test ideas about the brain that you’d never touch with a petri dish. When I started working in a computational lab, everything clicked even more. I helped build a model that captured how neurons tweak their connections through spike-timing-dependent plasticity. Seeing our virtual neurons shift and adapt, even in a rough way, felt like watching a simplified brain learn in real time. That was a rush. It taught me that math doesn’t just describe what the brain does—it lets you get inside the rules that build thought itself. Now, I’m drawn to computational psychiatry—the chance to use these models and methods in real-world settings. If we can pin down how neural circuits process information and where those processes break down in diseases like depression, schizophrenia, or Alzheimer’s, we open the door for smarter treatments. It beats the current trial-and-error approach. I want graduate study to sharpen my skills in machine learning, dynamical systems, and statistics. I’m looking for a place where people take seriously the idea of connecting theory to patients, and your program stands out for that. The focus on translating models into actual clinical applications matches my own goal: to help build better ways to understand and treat neurodegenerative disease. The brain is still a puzzle, and I want my career to be about solving a piece of it.

# Personal Statement: Computational Neuroscience My interest in the brain began not in a classroom but during a summer spent watching my grandmother face the early stages of Alzheimer's disease. I saw how neurons, tiny structures I couldn't see, changed the person I thought I knew. This experience raised a question that has shaped my academic journey: how can something as complex as human thinking emerge from electrochemical signals, and what happens when that system fails? This question first led me to biology, then to mathematics, and ultimately to the understanding that neither field alone could satisfy my curiosity. Computational neuroscience, which combines precise modeling with biological knowledge, provides the tools I need to explore these questions properly. During my undergraduate studies, I became particularly interested in how computational models can simulate neural circuits, allowing us to test ideas about brain function that are impossible to examine through lab experiments alone. My research experience strengthened this passion. While working in a computational lab, I helped develop a model that simulates spike-timing-dependent plasticity in simplified neural networks. Watching simulated neurons adjust their connections in response to input patterns, reflecting the learning processes occurring in biological brains, was genuinely exciting. It showed me that mathematics is not just a tool for describing the brain; it’s a way to understand the logic of thought itself. I am particularly drawn to computational psychiatry, which applies these methods and models to psychiatric and neurological conditions. If we can create better models of how neural circuits process information and how these processes fail in conditions like depression, schizophrenia, or Alzheimer's, we may develop more targeted treatments rather than relying on trial-and-error methods that dominate current practice. Pursuing graduate studies in computational neuroscience would allow me to enhance my technical abilities in machine learning, dynamical systems, and statistical modeling. I look forward to collaborating with researchers who share my goal of connecting computation and cognition. I am especially interested in your program because of its focus on translational research, linking theoretical models to clinical applications, which matches my long-term aim of contributing to treatments for neurodegenerative diseases. The brain remains one of science's greatest mysteries, and I want to dedicate my career to helping solve it.