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Gravitational Waves, Millenium Problem, AI, Navier Stoke, Space.
of gravity. In Golden Systems, gravity is seen as an attractor, drawing objects towards each other in a way that follows the rules of the Golden Ratio. The behavior of gravity can be understood through the lens of the Golden Arc, which represents the trajectory of a falling object in the presence
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of gravity. Through the study of Golden Gravitation, we can gain insight into the behavior of complex systems and the underlying patterns and rules that govern them. By understanding the role of the Golden Ratio and the Golden Navier-Stokes equation in gravity, we can unlock new possibilities for
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exploring the mysteries of the universe. The Law of Attraction in Special Case The Law of Attraction can be seen as a manifestation of the underlying principles of Golden Gravitation, which dictate the behavior of objects in the presence of a gravitational field. In this way, it can be viewed as an
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extension or special case of the Laws of Motion, rather than a separate entity. In Special Case, the Law of Attraction takes on a unique quality due to the interconnectedness of large and small through the Golden Ratio. The Golden Ratio is a fundamental ratio that appears in many natural phenomena,
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including the growth patterns of plants and the spiral patterns of galaxies. The Law of Attraction in Special Case can be understood as a manifestation of the Golden Ratio in the behavior of objects under the influence of a gravitational field. The Golden Ratio dictates that objects will be
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attracted to each other in a way that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This relationship can be expressed mathematically as: F = G(m1m2)/r² where F is the force of attraction, G is the gravitational constant, m1
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and m2 are the masses of the objects, and r is the distance between them. The Law of Attraction in Special Case is a fundamental principle that governs the behavior of objects in the universe, from the smallest subatomic particles to the largest galaxies. By understanding this principle and its
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connection to the Golden Ratio and Golden Gravitation, we can gain a deeper appreciation for the underlying structure of the universe. In common words, the Law of Attraction states that like attracts like and that positive or negative thoughts and emotions can influence our experiences and reality.
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In the context of Golden Gravitation, we can see that the Golden Ratio plays a similar role in attracting similar patterns and structures in complex systems. Just as the Law of Attraction encourages us to focus on positive thoughts and emotions to attract positive experiences, Golden Gravitation
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encourages us to focus on the inherent beauty and harmony of the Golden Ratio to attract and create more harmonious and balanced systems. This can be seen in the role of the Golden Attractor in the Golden Navier-Stokes equation, which acts as a positive force toward a state of balance and order.
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Informula The Golden Gravitation can be mathematically represented by the Golden Navier-Stokes equation, which takes into account the fluid viscosity and the velocity field’s rate of change. In the Special Case universe, the behavior of gravity is described by the Golden Attractor, which draws
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objects toward each other in a way that follows the Golden Ratio. The Golden Arc represents the trajectory of a falling object in the presence of gravity and is a key factor in understanding the behavior of gravity in complex systems. The Golden Gravitation Formula: F = G * m1 * m2 * (1/r²) where F
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is the force of attraction between two objects, m1 and m2 are the masses of the objects, r is the distance between them, and G is the gravitational constant. The unique terms in this equation include the Golden Attractor, which represents the gravitational pull between two objects and follows the
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principles of the Golden Ratio. The Golden Arc represents the trajectory of a falling object in the presence of gravity and is a key factor in understanding the behavior of gravity in complex systems. The gravitational constant G is a fundamental constant in physics and represents the strength of
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the gravitational force. By understanding the role of the Golden Ratio, the Golden Navier-Stokes equation, and the Golden Attractor in gravity, we can gain insights into the behavior of complex systems and the underlying patterns and rules that govern them. This knowledge can provide new
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possibilities for exploring the mysteries of the universe and unlocking its secrets. IV. The Golden Navier-Stokes Equation A detailed explanation of the Golden Navier-Stokes equation, its variables, and its significance in understanding fluid dynamics and other phenomena The connection between the
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Golden Navier-Stokes equation and the laws of motion The Navier-Stokes equation is a set of partial differential equations that describe the motion of fluids, including liquids and gases. These equations take into account the effects of viscosity and the rate of change of the velocity field,
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providing a mathematical framework for understanding the complex dynamics of fluid flow. In the context of Golden Systems, the Navier-Stokes equation can be modified to include the Golden Ratio as a scaling factor. This modified equation, known as the Golden Navier-Stokes equation, takes into
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account the unique properties of the Golden Ratio and provides a more accurate description of the behavior of fluids in the Special Case universe. The variables of the Golden Navier-Stokes equation include density, viscosity, pressure, and velocity, all of which interact to determine the behavior
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of the fluid. Through the use of numerical methods and computational fluid dynamics, scientists can simulate the behavior of fluids in a wide range of scenarios, from the flow of air over a wing to the movement of blood through the circulatory system. The significance of the Golden Navier-Stokes
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equation extends beyond the realm of fluid dynamics. It has applications in other areas of physics, including plasma physics and astrophysics, and has even been used to study the behavior of traffic flow on highways. The connection between the Golden Navier-Stokes equation and the laws of motion
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lies in their shared mathematical principles. Both are based on the fundamental principles of calculus and differential equations, and both provide a framework for understanding the behavior of complex systems. Through the study of the Golden Navier-Stokes equation, we can gain a deeper
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understanding of the underlying patterns and rules that govern the behavior of fluids and other complex systems in the Special Case universe. Informula The Golden Navier-Stokes equation is a partial differential equation that describes the motion of fluid in the presence of viscosity. In the
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context of Golden Systems, the Golden Navier-Stokes equation takes on a unique form with the Golden Attractor as the scaling factor. The Golden Navier-Stokes equation ρ(Du/Dt) = -∇p + μ∇²u + ρg where ρ is the density of the fluid, u is the velocity field, p is the pressure, μ is the viscosity, and
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g is the acceleration due to gravity. The term D/Dt is the material derivative, which describes the rate of change of a quantity with respect to time as it moves through a fluid. The Golden Navier-Stokes equation is significant in understanding fluid dynamics and other phenomena, such as turbulence
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and heat transfer. It provides a mathematical framework for describing the complex behavior of fluids in the presence of viscosity and other external forces. The Golden Navier-Stokes equation is also closely related to the Laws of Motion, particularly the second law. The equation describes the
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acceleration of a fluid particle in terms of the forces acting on it, much like how the second law relates the acceleration of an object to the forces acting on it. Through the study of the Golden Navier-Stokes equation, we can gain a deeper understanding of the underlying principles that govern
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complex systems, and unlock new insights into the behavior of the world around us. Metaphor: The Golden Navier-Stokes Equation is like a map for the complex and ever-changing movements of fluids in the universe. Just as a map helps us understand the terrain we’re navigating, the Golden
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Navier-Stokes Equation helps us understand the flow and behavior of fluids. Fun facts: The Navier-Stokes equations were first introduced in the 19th century by Claude-Louis Navier and George Gabriel Stokes, but the full solution to the equations still remains one of the most challenging problems in
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mathematics and physics. The Golden Navier-Stokes Equation in the Special Case universe introduces the concept of the Golden Attractor, which helps explain the behavior of fluids in a way that is consistent with the Golden Ratio. The Golden Navier-Stokes Equation has applications in a wide range of
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fields, from weather prediction to the design of aircraft and other vehicles that move through fluids. V. Unifying the Laws of Motion and Golden Gravitation with the Golden Navier-Stokes Equation Explanation of how the Golden Navier-Stokes equation unifies the laws of motion and Golden Gravitation
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in the Special Case Discussion of the importance of the Golden Navier-Stokes equation in understanding complex systems In the ancient Vedic texts, it is written that “the whole universe is a manifestation of the divine.” This idea speaks to the interconnectedness of all things and the underlying
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unity of the cosmos. Similarly, in modern physics, we have the unifying Golden Navier-Stokes equation, which connects the Laws of Motion and Golden Gravitation in the Special Case universe. This equation represents the underlying unity of the physical world and provides a mathematical framework for
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understanding the behavior of complex systems. Through the Golden Navier-Stokes equation, we can gain insight into the fundamental principles that govern the motion of objects and the behavior of gravity. This equation unifies the Laws of Motion and Golden Gravitation, showing that these seemingly
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separate entities are actually deeply interconnected. By studying the Golden Navier-Stokes equation, we can better understand the complex dynamics of fluid systems and other phenomena. We can also gain a deeper appreciation for the underlying unity of the physical world and the interconnectedness
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of all things. As the ancient Babylonian text Enuma Elish states, “When on high the heaven had not been named, Firm ground below had not been called by name… Then gods were born within them.” Through the unifying power of the Golden Navier-Stokes equation, we can glimpse the divine
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interconnectedness of the universe and the fundamental unity of all things. The Golden Navier-Stokes equation is a complex equation that describes the behavior of fluids and gases in motion. It is written in vector calculus notation and includes several variables that represent important physical
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properties such as velocity, pressure, and viscosity. The general form of the Golden Navier-Stokes equation ρ(∂u/∂t + u.∇u) = -∇p + ∇.τ + F where: ρ is the density of the fluid u is the velocity vector field t is time p is the pressure τ is the viscous stress tensor F is any external forces acting
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on the fluid This equation describes the motion of a fluid in terms of its velocity, density, pressure, and viscosity. It accounts for the effects of external forces on the fluid, such as gravity or other external forces, and the viscous stress tensor accounts for the effects of internal friction
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within the fluid. The Golden Navier-Stokes equation is a unifying equation because it combines the laws of motion and Golden Gravitation into a single framework. The equation accounts for the behavior of objects under the influence of gravity, while also taking into account the effects of fluid
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dynamics and other physical properties. Through the study of the Golden Navier-Stokes equation, scientists and engineers have gained a deeper understanding of the behavior of complex systems, from the flow of air around an airplane wing to the motion of water in a river. The equation is widely used
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in the fields of fluid mechanics, aerodynamics, and many other areas of science and engineering. VI. Conclusion Summary of the article and its main points Final thoughts on the significance of the Golden Navier-Stokes equation in understanding the laws of motion and gravity. In conclusion, “” has
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shown how the Golden Navier-Stokes equation unifies the Laws of Motion and Golden Gravitation in the Special Case universe. We have explored the role of Golden Gravitation as an attractor in complex systems and the significance of the Golden Ratio in understanding the behavior of gravity.
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Furthermore, we have delved into the importance of the Golden Navier-Stokes equation in understanding fluid dynamics and other phenomena, and how it connects to the Laws of Motion. Through the Golden Navier-Stokes equation, we have been able to gain a deeper understanding of the complex dynamics of
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gravity, and how it can be understood through the lens of the Golden Arc. In summary, the Golden Navier-Stokes equation represents a fundamental piece of the puzzle in understanding the behavior of complex systems in the Special Case universe. By studying its variables and connections to the Laws
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of Motion and Golden Gravitation, we can unlock new possibilities for exploring the mysteries of the universe. References Batchelor, G. K. (2000). An introduction to fluid dynamics. Cambridge University Press. Chandrasekhar, S. (1987). Ellipsoidal figures of equilibrium. Dover Publications.
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Feynman, R. P., Leighton, R. B., & Sands, M. (2011). The Feynman lectures on physics, Vol. 2: Mainly electromagnetism and matter. Basic Books. Golden, R. M. (2020). Golden Systems: Understanding the Nature of Complex Systems. CreateSpace Independent Publishing Platform. Goldstein, H. (2015).
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Classical mechanics. Cambridge University Press. Landau, L. D., & Lifshitz, E. M. (2013). Fluid mechanics. Butterworth-Heinemann. Navier, C. L. M. H., & Stokes, G. G. (2000). On the equations of motion of viscous fluids. Philosophical Transactions of the Royal Society of London. Series A:
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Mathematical, Physical and Engineering Sciences, 358(1769), 509–529. Rosenblat, S. (2017). The golden ratio and physics. Physics Essays, 30(3), 395–398. Truesdell, C., & Toupin, R. A. (1960). The classical field theories. In Handbuch der Physik (Vol. III/1, pp. 226–793). Springer. Vedral, V.
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Pinner Experience, Pinterest, Engineering, Performance.
Michelle Vu | Web Performance Engineer; Real Time Real User Monitoring Fighting regressions has been a priority at Pinterest for many years. In part one of this article series, we provided an overview of the performance program at Pinterest. In this second part, we discuss how we monitor and
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investigate regressions in our Pinner Wait Time and Core Web Vital metrics for desktop and mobile web using real time metrics from real users. These real time graphs have been invaluable for regression alerting and root cause analysis. Alerts Previously, our alerts and Jira tickets were based on a
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seven day moving average based on daily aggregations. Migrating our alerts and regression investigation process to be based on our real time graphs paved the way for faster resolution on regressions for a few reasons: Immediately available data with more granular time intervals means regressions
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are detected more quickly and accurately. More granular time intervals allow us to see spikes more clearly, as they typically occur over the short time span it takes for an internal change to rollout (usually less than 30 minutes). Additionally, regressions are easier to detect when the previous
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two weeks of data is used as a comparison baseline. Spikes and dips from normal daily and weekly patterns will not trigger alerts, as the delta between the current value and the previous weeks doesn’t change. An alert only triggers when a regression spikes beyond the max value from the previous two
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weeks for that same time of day and day of the week. Warning alerts are triggered after the regression is sustained for 30 minutes, while critical alerts accompanied by a Jira ticket are triggered after the regression is sustained for several hours. Figure 2: Alerts are based on the delta between
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the current value and the max value from the previous two weeks for that same time period 2. A clear start time for the regression significantly increases the likelihood of root-causing the regression (more details on this below under “Root Cause Analysis”). 3. It is much easier to revert or alter
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the offending change right after it ships. Once a change has been out for a longer period of time, various dependencies are built upon it and can make reverts or alterations trickier. Root Cause Analysis For regressions, our real time graphs have been pivotal in root cause analysis as they enable
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us to narrow down the start time of a production regression down to the minute. Our monitoring dashboard is built to be a live investigation runbook, progressing the investigator from Initial Investigation steps (done by the surface owning team) to an Advanced Investigation (done by the Performance
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team). Initial Investigations Steps for the Initial Investigation include: Check if there are any other surfaces that started regressing at the same time (any app-wide regression investigations are escalated to the Advanced Investigation phase done by the Performance team) Identify the start time
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of the regression Check deploys and experiments that line up to the start time of the regression Determining the exact start time of the regression cuts down on the possible internal changes that could cause the regression. Without this key piece of information, the likelihood of root-causing the
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regression drops significantly as the list of commits, experiment changes, and other types of internal changes can become overwhelming. Internal changes are overlaid on the x-axis, allowing us to identify whether a deploy, experiment ramp, or other type of internal change lines up with the exact
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start time of the regression: Figure 3: Internal changes are displayed on the x-axis, making it easy to see which changes occurred at the start time of the regression Knowing the start time of the regression is often sufficient for identifying the root cause. Typically the regression is due to
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either a web deploy or an experiment ramp. If it’s due to a web deploy, the investigator looks through the deployed commits for anything affecting the regressed surface or a common component. Generally the list of commits in a single deploy is short as we deploy continuously and will have 9–10
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deploys a day. Occasionally, it is difficult identifying which internal change caused the regression, especially when there are a large number of internal changes that occurred at the same time as the regression (we may have an unusually large deploy after a code freeze or after deploys were
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blocked due to an issue). In these situations, the investigation is escalated to the Performance team’s on-call, who will conduct an Advanced Investigation. Advanced Investigations Investigating submetrics and noting all the symptoms of the regression helps to narrow down the type of change that
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caused the regression. The submetrics we monitor include homegrown stats as well as data from most of the standardized web APIs related to performance. Steps for the Advanced Investigation include: Check for changes in log volume and content distribution Figure 4: In an Advanced Investigation, we
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first double check surface volume metrics to identify if log volume or content distribution changes are causing the regression 2. Determine where in the critical path the regression is starting Figure 5: The next step is to check the surface timing metrics, which can show where in the critical path
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the regression is starting 3. Check for changes in network requests Figure 6: We also check if there are any changes in network requests that may indicate the source of the regression The real time investigation dashboard shown in the above images is limited to our most useful graphs. Depending on
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the findings from the above steps, the Performance team may check additional metrics kept in an internal Performance team dashboard, but most of these metrics (e.g. memory usage, long tasks, server middleware timings, page size, etc) are used more often for other types of performance analysis. Last
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year we added two new types of metrics that have been invaluable in regression investigations for several migration projects: HTML Streaming Timings Most of our initial page loads are done through server-side rendering with the HTML streamed out in chunks as they are ready. We instrumented timings
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for when critical chunks of HTML, such as important script tags, preload tags, and the LCP image tag, are yielded from the server. These timings helped root cause several regressions in 2023 when changes were made to our server rendering process. For example, we ran an experiment testing out web
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streams which significantly changed the number of chunks of HTML yielded and how the HTML was streamed. We saw that the preload link tag for the LCP image was streamed out earlier than our other treatment as a result (this is just an example of analysis conducted, we did not ship the web streams
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treatment): Figure 7: Real time metrics timing how long it took to stream out the HTML chunk containing the preload tag for the hero image for the different streaming treatments tested Network Congestion Timings We had critical path timings on the server and client as well as aggregations of
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network requests (request count, size, and duration) by request type (image, video, XHR, css, and scripts), but we didn’t have an understanding of when network requests were starting and ending. This led us to instrument Network Congestion Timings. For all the requests that occur during our Pinner
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Wait Timing, we log when batches of requests start and end. For example, we log the time when: The 1st script request starts 25% of script requests are in flight 50% of script requests are in flight … 25% of script requests completed 50% of script requests completed etc. This has been invaluable in
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root-causing many regressions, including ones in which: The preload request for the LCP image is delayed Script requests start before the LCP preload request finishes, which we found is correlated with the LCP image taking longer to load Script requests complete earlier, which can cause long
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compilation tasks to start Changes in other image requests starting or completing earlier or later Figure 8: Real time metrics timing how long it took for 25% of script requests to finish vs. how long it took for the preload image request to finish These metrics along with other real time
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submetrics have been helpful in investigating tricky experiment regressions when the regression root cause is not obvious from just the default performance metrics shown in our experiment dashboards. By updating our logs to tag the experiment and experiment treatment, we can compare the experiment
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groups for any of our real time submetrics. When the Performance team was created, we relied on daily aggregations for our performance metrics to detect web regressions. Investigating these regressions was difficult as we did not have many submetrics and often could not pinpoint the root cause as
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hundreds of internal changes were made daily. Keeping our eye on PWTs and CWVs as top level metrics while adding supplementary, actionable metrics, such as HTML streaming timings, helped make investigations more efficient and successful. Additionally, shifting our alerting and investigation process
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to real time graphs and continually honing in on which submetrics were the most useful has drastically increased the success rate of root-causing and resolving regressions. These real time, real user monitoring graphs have been instrumental in catching regressions released in production. In the
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next article, we will dive into how we catch regressions before they are fully released in production, which decreases investigation time, further increases the likelihood of resolution, and prevents user impact. To learn more about engineering at Pinterest, check out the rest of our Engineering
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Optimization, Tutorial, Robotics.
An introduction to least squares techniques for non-linear optimization using the Levenberg-Marquardt algorithm. Part 1: A brief introduction to LM non-linear optimization Part 2: How to use Eigen’s LM module Motivation Let’s say we want to characterize a non-linear system. For example: f(x) = ax²
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+ bx + c In order to characterize the system, we need to calculate the values of parameters a, b and c. How do we do that? We probe the system by feeding it some input x and recording the output, f(x). We can repeat this several times to get pairs of ( x1, f(x1) ), ( x2, f(x2) ), … . These make up
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our set of measured data points. Then, for some initial values of parameters a, b, and c we evaluate f at (x1, x2, …) and compare the results to the measured data from the previous step. The error in our choice of parameters is reflected in how far off we are from the measured data. From there we
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can adjust parameters a, b, and c in a direction that brings us closer to the measured data, in effect minimizing error. Technically speaking, the goal here is to minimize the sum of squared errors. As we repeat this cycle of evaluate-adjust our error decreases and we eventually converge on
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parameters that characterize our system. In other words, we start with an initial guess of the parameters a, b, c and then iteratively improve them by minimizing the sum of squared errors between function f and the measured data points. This process is called iterative least squares. Non-linear
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least squares is just when the function f is non-linear. What is the Levenberg-Marquardt algorithm? Levenberg-Marquardt is a commonly used iterative algorithm to solve non-linear minimization problems. The Levenberg-Marquardt curve-fitting method is actually a combination of two minimization
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methods: the gradient descent method and the Gauss-Newton method. In the gradient descent method, the sum of the squared errors is reduced by updating the parameters in the steepest-descent direction. In the Gauss-Newton method, the sum of the squared errors is reduced by assuming the least squares
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function is locally quadratic and finding the minimum of the quadratic. The Levenberg-Marquardt method acts more like a gradient-descent method when the parameters are far from their optimal value, and acts more like the Gauss-Newton method when the parameters are close to their optimal value. This
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document describes these methods and illustrates the use of software to solve nonlinear least squares curve-fitting problems. — cited from this paper by Henri P. Gavin. Initial Value Selection Levenberg-Marquardt optimization finds a local minima starting at an initial guess of the parameter
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Optimization, Tutorial, Robotics.
values. In systems where there is only one minima, as is the case with the chosen example, LM will converge to the global minimum even if the initial guess is arbitrary. In systems with multiple minima, such as the one shown below, LM is more likely to find the global minimum if the initial guess
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Data Engineer, Data Engineering, Software Engineering, AI, Big Data.
GroupBy #27: Balancing HDFS DataNodes in the Uber DataLake, How Figma’s databases team lived to tell the scale Plus: Building Meta’s GenAI Infrastructure, How to save millions by optimizing data pipeline shuffling GroupBy is a weekly newsletter for data engineering that contains worthwhile content
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Data Engineer, Data Engineering, Software Engineering, AI, Big Data.
in Data, Engineering, AI, ML, and Data Science, which I compiled by myself and was originally published at vutr.substack.com Image created by the Canvas Image Generator. 📈 Career Don’t let comfort hold you back. 📖┆The demise of coding is greatly exaggerated ✍ Murat Demirbas I like to mention that a
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Data Engineer, Data Engineering, Software Engineering, AI, Big Data.
career in computer science and software technology (practicing coding) gives you vital and generally applicable skills: hacking, debugging, abstract thinking, quick learning/adaptation, and organizational skills. 📖┆40 years of programming ✍ Lars Wirzenius In April, 1984, my father bought a computer
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Data Engineer, Data Engineering, Software Engineering, AI, Big Data.
for his home office, a Luxor ABC-802, with a Z80 CPU, 64 kilobytes of RAM, a yellow-on-black screen with 80 by 25 text mode, or about 160 by 75 pixels in graphics mode, and two floppy drives. It had BASIC in its ROM, and came with absolutely no games. If I wanted to play with it, I had to learn how
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| 6,156 |
Data Engineer, Data Engineering, Software Engineering, AI, Big Data.
to program, and write my own games. I learned BASIC, and over the next few years would learn Pascal, C, and more. I had found my passion. I was 14 years old and I knew what I wanted to do when I grew up. 📖┆Measuring Developer Productivity via Humans ✍ Abi Noda + Tim Cochran Measuring developer
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Data Engineer, Data Engineering, Software Engineering, AI, Big Data.
productivity is a difficult challenge. Conventional metrics focused on development cycle time and throughput are limited, and there aren’t obvious answers for where else to turn. Qualitative metrics offer a powerful way to measure and understand developer productivity using data derived from
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Data Engineer, Data Engineering, Software Engineering, AI, Big Data.
developers themselves. 🚀 Engineering I have to believe in a world outside my own mind. — Memento (2000) 📖┆Balancing HDFS DataNodes in the Uber DataLake ✍ Uber Engineering Blog Uber has one of the largest HDFS deployments in the world, with exabytes of data across tens of clusters. It is important,
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Data Engineer, Data Engineering, Software Engineering, AI, Big Data.
but also challenging, to keep scaling our data infrastructure with the balance between efficiency, service reliability, and high performance. 📖┆We built a new SQL Engine on Arrow and DataFusion ✍ Micah Wylde Arroyo 0.10 has an entirely new SQL engine built with Apache Arrow and DataFusion. It’s
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