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My question is: what is the difference between DC motor with encoder and DC without encoder? As long as I can control the speed of DC motor using PWM, for example on the Arduino, what is the fundamental difference?
$\begingroup$ Fundamental difference in terms of what? Open loop control, closed loop control, price, construction, etc... $\endgroup$– Ben ♦Nov 25, 2016 at 14:37
As @szczepan mentions, the difference is one of feedback.
There are many ways to get feedback regarding the motion of a dc motor. People implementing a control system will often put a mark on the motor's shaft, or attach a "flag" of masking tape, so that they can visually see the turning of the shaft. This helps to ensure the direction of motion is correct (otherwise the dc polarity needs to be reversed). It also helps for observing motion at slow speeds - but is otherwise not appropriate for an automated system.
If you want to automate the observations of the motor's rotation, you must implement some type of sensor that provides appropriate information to the control computer. There are many ways to do this. For example, you can monitor the current being consumed by the motor's windings, and use the motor constant $k_\tau$, to infer the torque generated by the motor. This can be related to acceleration of the shaft by using an appropriate dynamic model of the system. This method, however, is not very accurate and is prone to modelling errors and signal noise. This method is similar to you monitoring the PWM output and inferring motion dynamics - neither is robust to changing dynamics of the system. Another approach is to glue a magnet to the shaft, and monitor it with a Hall effect sensor. This will provide a single pulse to the computer for each rotation of the shaft. This is frequently a solution for high-temperature, or dirty, environments (such as in automotive applications). However, often you need finer granularity of the motion. That is where encoders come in.
There are two basic types of encoders: incremental and absolute. They can be further characterized as quadrature, or non-quadrature encoders. A non-quadrature incremental encoder provides a single pulse to the controller for every incremental motion of the motor shaft. As the previous answer makes clear, this position feedback can be interpreted to infer velocity, acceleration, and possibly jerk (although three derivatives of a sensed value are "spikey" in most applications). This type of encoder, however, only provides information when the position changes, and it does not provide any information about the direction of motion. A quadrature encoder provides two pulses, out of phase, that can be used to detect direction also.
An absolute encoder can provide not only the same information as the incremental encoder does, but it also has many more bits of information from which you can know the angular position of the shaft, in addition to detecting the incremental changes in position.
You can make a very simple encoder by using a disc with slots cut into it. Place a photodiode on one side of the disc, and a photodetector on the opposite side. You will get one pulse each time a slot passes between the sensor elements. As you can see, the accuracy of motion detection is determined by the number of slots in the disc. Encoders are available with many different numbers of pulses per revolution.
I suggest reading a book such as this one if you want to know more about motion metrology:
Fundamental difference is closed loop feedback. Without encoder you just know how much speed you sent to engine, but have no information about speed that is on it - lower battery voltage will decrease your speed. Encoder gives you ability to measure engine
speed position, from which you can calculate speed, and regulate those parameters, for example with PID regulator. Usage example can be micromouse robots, where odometry is crucial in moving through maze.
$\begingroup$ The encoder gives you angular position and speed can be calculated from this. $\endgroup$– 50k4Nov 24, 2016 at 8:56
$\begingroup$ @50k4 Not every encoder gives angular position. AS5040 can measure angular position and speed, while this kind of encoder gives only quadrature output (A and B channel) and measuring impulse count in certain time gives angular velocity. $\endgroup$– SzczepanNov 24, 2016 at 8:59
$\begingroup$ The link you have provided clearly states (in the title) that is it a rotary position sensor. Every other output (e.g. speed) is computed not measured. $\endgroup$– 50k4Nov 24, 2016 at 9:51
$\begingroup$ Okay, I'll update my answer as soon as I get home. As You said, AS5040 is rotary position sensor. $\endgroup$– SzczepanNov 24, 2016 at 12:48
$\begingroup$ Encoders are not the only way of closing the loop, for example you can sense changes in back emf (certain model railway controllers do this for DC motors, most 'sensorless' BLDC controllers do this). $\endgroup$ Jul 27, 2017 at 12:07 | <urn:uuid:7a028f3e-5ddc-4341-883a-08ba831d6ee7> | CC-MAIN-2023-14 | https://robotics.stackexchange.com/questions/11108/what-is-the-difference-between-dc-motor-with-encoder-and-dc-with-out-encoder/11109 | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943704.21/warc/CC-MAIN-20230321162614-20230321192614-00000.warc.gz | en | 0.913547 | 1,134 | 3.03125 | 3 |
9.10: Chapter Review
- Page ID
9.1 Null and Alternative Hypotheses
In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we:
- Evaluate the null hypothesis, typically denoted with H0. The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality (=, ≤ or ≥)
- Always write the alternative hypothesis, typically denoted with \(H_a\) or \(H_1\), using not equal, less than or greater than symbols, i.e., (\(neq\), <, or > ).
- If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis.
- Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.
9.2 Outcomes and the Type I and Type II Errors
In every hypothesis test, the outcomes are dependent on a correct interpretation of the data. Incorrect calculations or misunderstood summary statistics can yield errors that affect the results. A Type I error occurs when a true null hypothesis is rejected. A Type II error occurs when a false null hypothesis is not rejected.
The probabilities of these errors are denoted by the Greek letters \(\alpha\) and \(\beta\), for a Type I and a Type II error respectively. The power of the test, \(1 – \beta\), quantifies the likelihood that a test will yield the correct result of a true alternative hypothesis being accepted. A high power is desirable.
9.3 Distribution Needed for Hypothesis Testing
In order for a hypothesis test’s results to be generalized to a population, certain requirements must be satisfied.
When testing for a single population mean:
- A Student's \(t\)-test should be used if the data come from a simple, random sample and the population is approximately normally distributed, or the sample size is large, with an unknown standard deviation.
- The normal test will work if the data come from a simple, random sample and the population is approximately normally distributed, or the sample size is large.
When testing a single population proportion use a normal test for a single population proportion if the data comes from a simple, random sample, fill the requirements for a binomial distribution, and the mean number of successes and the mean number of failures satisfy the conditions: \(np > 5\) and \(nq > 5\) where \(n\) is the sample size, \(p\) is the probability of a success, and \(q\) is the probability of a failure.
9.4 Full Hypothesis Test Examples
The hypothesis test itself has an established process. This can be summarized as follows:
- Determine \(H_0\) and \(H_a\). Remember, they are contradictory.
- Determine the random variable.
- Determine the distribution for the test.
- Draw a graph and calculate the test statistic.
- Compare the calculated test statistic with the \(Z\) critical value determined by the level of significance required by the test and make a decision (cannot reject \(H_0\) or cannot accept \(H_0\)), and write a clear conclusion using English sentences. | <urn:uuid:a52c0134-060a-4b5d-b2c7-605f366d8377> | CC-MAIN-2023-14 | https://stats.libretexts.org/Bookshelves/Applied_Statistics/Introductory_Business_Statistics_(OpenStax)/09%3A_Hypothesis_Testing_with_One_Sample/9.10%3A_Chapter_Review | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945376.29/warc/CC-MAIN-20230325222822-20230326012822-00400.warc.gz | en | 0.869652 | 727 | 4.21875 | 4 |
It’s been way too long since my last posting. A combination of wanting to do some additional research to support the post I was working on, and real life interfering,
So in the meantime I thought I’d do a quick post on a question that pops up here and there on the internet as it’s a fun little calculation: What happens (theoretically) if you fall into a hole that goes all the way through the earth?
As usual in introductory physics problems, we make some simplifying assumptions and ignore some practicalities. We’re not going to worry about the heat that would fry you as you descend to the core, we’re not going to worry about the fact that you would smash into the sides of the hole due to the rotation of the earth, and we’re definitely not going to worry about the fact that the earth is not technically a sphere.
Our idealized earth is non-rotating, a perfect sphere, and has the same density throughout. And doesn’t have any of that pesky volcanic
The calculation is pretty simple once you lay the groundwork on two concepts: Simple Harmonic Motion and Gauss’s Law.
Simple Harmonic Motion
Suppose you have a quantity which obeys the following differential equation:
The general solution to this equation is known to be a sine wave, where and are arbitrary constants. Plugging this back into the differential equation:
oscillates sinusoidally with time. Any motion that has this sinusoidal behavior is called simple harmonic motion. If we define then is the frequency of the oscillation. For any wave, the period is the reciprocal of . From this we can conclude that if we have a variable which obeys a differential equation of the form , then will be simple harmonic motion with period .
The constants and are the amplitude and phase, respectively, of the sine wave. The fact that the equation is satisfied no matter what the values of those constants means that the system can have any amplitude and phase.
Example: Mass on a spring
The standard model of a mass on a spring is that there is a constant called the spring constant, such that if you displace the spring by an amount from its equilibrium position, the spring pulls back with a force . The negative sign indicates that the force is opposite to the displacement. If you pull the spring down, the force pulls up and vice versa.
That force acts on the mass to accelerate it . And so we see that the mass on the spring follows the equation:
and we can see immediately that this motion meets the conditions for simple harmonic motion with , and its period is therefore
If you swing a pendulum out of its equilibrium position by an angle , gravity will tend to pull it back down. The component of gravity pulling outward on the string has no effect as we assume the pendulum isn’t free to move in that direction. The component of gravitational force which is perpendicular to the string is $-mg \sin \theta$.
If we set this equal to as usual, the in that equation refers to distance along the arc, where is the length of the pendulum. So we have the equation
Because of the sine, this doesn’t at first glance look like it meets the conditions for simple harmonic motion. But for small angles, with in radians. What does “small” mean? As with any approximation in physics, there’s no firm definition. It depends on what level of accuracy you need. The smaller the angle, the better the approximation. For introductory physics calculations, is often taken as a rule of thumb for “small enough”. is about radians, and , an error of about .
If we use the small angle approximation then the equation of motion becomes
and now we see that does (approximately) follow simple harmonic motion, with period .
The mathematician Carl Friedrich Gauss discovered a very powerful theorem that simplifies many otherwise very difficult calculations. There is a form for the electrostatic force and for the gravitational force, and it arises from certain mathematical properties these two forces share, most especially that they are both inverse square-law forces, proportional to .
The general form for the electric field is this somewhat intimidating notation:
This relates an integral of the electric field over a closed surface , to the total charge enclosed inside that surface. It doesn’t matter what charge is outside, only inside. The constant comes from the electric field of a point charge, .
The analogous result for gravitational fields, where we define the gravitational field of a point mass to be is
where M is the total mass enclosed by the surface S. The minus sign expresses the fact that the gravitational field of a mass points inward (masses attract) while the direction of electric field from a positive charge is outward.
Note that “electric field” is defined as “force per unit charge”, while “gravitational field” is analogously defined as “force per unit mass”. But because , then “force per unit mass” is simply acceleration.
Gravity Inside the Earth
We don’t need to do a complete exploration of Gauss’s Law, we only need to cover the case of a uniform sphere, our model of the earth. To calculate the gravitational field at distance from the center of the earth, we take as the surface S the sphere of radius . The field will be the same at every point on the surface of this sphere, which means the left hand side of Gauss’ Law reduces to the field times the area of the sphere: .
On the right hand side we have the mass enclosed inside the radius . We’ll call this . So
The gravitational field at radius looks like the gravitational field of a point whose mass is , all the mass enclosed by the sphere of radius .
How much mass is that? We are assuming a constant density for the earth, so is times the volume of the sphere, . Thus
Everything on the right besides is a constant. So this says that the gravitational field at distance from the center is proportional to .
Jumping Into the Hole
As we noted above, the gravitational field is simply the acceleration, . So the equation above says that is a negative constant times , which we know means that will follow simple harmonic motion.
We’re almost done, but it will be convenient to put it in terms of different constants. The average density of the earth is equal to total mass over total volume. Using for the total mass of the earth and for the radius,
We know that this describes simple harmonic motion, and from the previous analysis we can immediately conclude that the period is Using values of , (the polar radius, as I think we should drill the hole pole-to-pole to avoid the rotation), and this gives seconds, which means the one way trip is 2522 seconds or almost exactly 42 minutes.
Fans of Douglas Adams (Hitchhiker’s Guide to the Galaxy) will appreciate the cosmic significance of the number 42.
Conclusion: Ignoring rotation, air drag, and the minor annoyance of core temperatures, if you jump into a hole that goes straight through the earth, you will oscillate from one end of the hole to the other forever, taking 42 minutes to go from one end to the other.
Leave a Reply | <urn:uuid:a35cb8e5-1c00-43cc-8027-99719dadc057> | CC-MAIN-2023-14 | https://terra-phy.com/2022/08/30/drilling-a-hole-through-the-earth/ | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948620.60/warc/CC-MAIN-20230327092225-20230327122225-00600.warc.gz | en | 0.921016 | 1,540 | 3.046875 | 3 |
TL;DR: If by “analogue computers”, you mean differential analysers, the answer is adders, constant units and integrator. Bournez, Campagnolo, Graça and Hainry have shown in 2006 (paywalled / free reprint) that an idealized model of it allows to compute all the computable functions in the framework of computable analysis, and this model only needs these 3 kind of units.
The set of operation you propose (addition, multiplication, subtraction, and division), even completed by root equation is by definition not sufficient to compute any transcendental function. Transcendental functions includes very common functions, like $\sin$, $\exp$, $\log$. However, as discussed below, some analogue computer model allow to compute transcendental functions and, basically all real functions computable by a Turing machine.
Analogue computing models
As stressed by others, the concept of “universal computation” is less clear for analogue computers than for standard computer, where different natural notion of computability in different computing models where found equivalent in the 1930’s (see Wikipedia page on Church Turing Thesis for details).
In order to define such a universality, one should first define a good model for analogue computation, and it is a difficult task, since the model should be idealized and and natural enough to be useful, but its idealization should not give unrealistic power to the model. An example of such a good idealization is the infinite tape of Turing machines. The problem with analogue computers comes with real numbers which could allow to build unreasonable stuff like the Zeno machine. However, several such models have been proposed and used in the literature (The GPAC is the main subject of this answer, but I try to be complete in the list below, without any hypercomputer):
Power of the GPAC model
In his 1941 paper, Shanon introduced the GPAC to model differential analysers.This model only needs 3 kinds of interconnected units (constant units, adders and integrators. Multipliers can be built from integrators and adders.)
He showed that the set of functions which it generates is the set of algebraic differential functions, but excludes the hypertranscendental functions. It means that the $\Gamma$ and $\zeta$, which are Turing-computable cannot be generated. In other words, no differential analyser will ever have an output $y(t)=\Gamma(t)$, ant it seemed for a long time that such an analogue computer is not “universal”, since it cannot generate some reasonable computable functions, used by mathematicians.
However, in 2004, Daniel Silva Graça showed that the previous model, based on instantaneous computation is too restrictive. If one define the computability of a function $f$ differently, allowing $y(t)$ to converge towards $f(x)$, for an input $x$, then the $\gamma$ and $\zeta$ functions are computable by a GPAC. Bournez, Campagnolo, Graça and Hainry then showed in 2006 (paywalled / free reprint) that an idealized model of it allows to compute all the computable functions in the framework of computable analysis.
Bournez, Graça and Pouly then showed in 2013 that these analogue computers can efficiently simulate a Turing machine (p.181 of a big pdf) and, in 2014, that the P and NP complexity classes are equivalent in this model. | <urn:uuid:4b37137b-2e55-4330-984c-b0b4ccba51e7> | CC-MAIN-2023-14 | https://cs.stackexchange.com/questions/1292/what-is-required-for-universal-analogue-computation | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943589.10/warc/CC-MAIN-20230321002050-20230321032050-00000.warc.gz | en | 0.909528 | 731 | 2.578125 | 3 |
The island municipality of Soteholm is required to write a plan of action for their work with emission of greenhouse gases. They realize that a natural first step is to decide whether they are for or against global warming. For this purpose they have read the IPCC report on climate change and found out that the largest effect on their municipality could be the rising sea level.
The residents of Soteholm value their coast highly and therefore want to maximize its total length. For them to be able to make an informed decision on their position in the issue of global warming, you have to help them find out whether their coastal line will shrink or expand if the sea level rises. From height maps they have figured out what parts of their islands will be covered by water, under the different scenarios described in the IPCC report, but they need your help to calculate the length of the coastal lines.
You will be given a map of Soteholm as an $N\times M$ grid. Each square in the grid has a side length of 1 km and is either water or land. Your goal is to compute the total length of sea coast of all islands. Sea coast is all borders between land and sea, and sea is any water connected to an edge of the map only through water. Two squares are connected if they share an edge. You may assume that the map is surrounded by sea. Lakes and islands in lakes are not contributing to the sea coast.
The first line of the input contains two space separated integers $N$ and $M$ where $1\leq N,M\leq 1000$. The following $N$ lines each contain a string of length $M$ consisting of only zeros and ones. Zero means water and one means land.
Output one line with one integer, the total length of the coast in km.
|Sample Input 1||Sample Output 1|
5 6 011110 010110 111000 000010 000000 | <urn:uuid:289cbcac-5832-4ec1-97a2-0157c3b7c1fa> | CC-MAIN-2023-14 | https://ru.kattis.com/courses/T-414-AFLV/aflv21/assignments/hd5o83/problems/coast | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943625.81/warc/CC-MAIN-20230321033306-20230321063306-00200.warc.gz | en | 0.936491 | 418 | 3.984375 | 4 |
By Anusha Nagabandi and Ignasi Clavera
Humans have the ability to seamlessly adapt to changes in their environments: adults can learn to walk on crutches in just a few seconds, people can adapt almost instantaneously to picking up an object that is unexpectedly heavy, and children who can walk on flat ground can quickly adapt their gait to walk uphill without having to relearn how to walk. This adaptation is critical for functioning in the real world.
Robots, on the other hand, are typically deployed with a fixed behavior (be it hard-coded or learned), allowing them succeed in specific settings, but leading to failure in others: experiencing a system malfunction, encountering a new terrain or environment changes such as wind, or needing to cope with a payload or other unexpected perturbations. The idea behind our latest research is that the mismatch between predicted and observed recent states should inform the robot to update its model into one that more accurately describes the current situation. Noticing our car skidding on the road, for example, informs us that our actions are having a different effect than expected, and thus allows us to plan our consequent actions accordingly (Fig. 2). In order for our robots to be successful in the real world, it is critical that they have this ability to use their past experience to quickly and flexibly adapt. To this effect, we developed a model-based meta-reinforcement learning algorithm capable of fast adaptation.
Figure 2: The driver normally makes decisions based on his/her model of the world. Suddenly encountering a slippery road, however, leads to unexpected skidding. Online adaptation of the driver’s world model based on just a few of these observations of model mismatch allows for fast recovery.
Prior work has used (a) trial-and-error adaptation approaches (Cully et al., 2015) as well as (b) model-free meta-RL approaches (Wang et al., 2016; Finn et al., 2017) to enable agents to adapt after a handful of trials. However, our work takes this adaptation ability to the extreme. Rather than adaptation requiring a few episodes of experience under the new settings, our adaptation happens online on the scale of just a few timesteps (i.e., milliseconds): so fast that it can hardly be noticed.
We achieve this fast adaptation through the use of meta-learning (discussed below) in a model-based learning setup. In the model-based setting, rather than adapting based on the rewards that are achieved during rollouts, data for updating the model is readily available at every timestep in the form of model prediction errors on recent experiences. This model-based approach enables the robot to meaningfully update the model using only a small amount of recent data.
Fig 3. The agent uses recent experience to fine-tune the prior model into an adapted one, which the planner then uses to perform its action selection. Note that we omit details of the update rule in this post, but we experiment with two such options in our work.
Our method follows the general formulation shown in Fig. 3 of using observations from recent data to perform adaptation of a model, and it is analogous to the overall framework of adaptive control (Sastry and Isidori, 1989; Åström and Wittenmark, 2013). The real challenge here, however, is how to successfully enable model adaptation when the models are complex, nonlinear, high-capacity function approximators (i.e., neural networks). Naively implementing SGD on the model weights is not effective, as neural networks require much larger amounts of data in order to perform meaningful learning.
Thus, we enable fast adaptation at test time by explicitly training with this adaptation objective during (meta-)training time, as explained in the following section. Once we meta-train across data from various settings in order to get this prior model (with weights denoted as ) that is good at adaptation, the robot can then adapt from this at each time step (Fig. 3) by using this prior in conjunction with recent experience to fine-tune its model to the current setting at hand, thus allowing for fast online adaptation.
At any given time step , we are in state , we take action , and we end up in some resulting state according to the underlying dynamics function . The true dynamics are unknown to us, so we instead want to fit some learned dynamics model that makes predictions as well as possible on observed data points of the form . Our planner can use this estimated dynamics model in order to perform action selection.
Assuming that any detail or setting could have changed at any time step along the rollout, we consider temporally-close time steps as being able to inform us about the “task” details of our current situation: operating in different parts of the state space, enduring disturbances, attempting new goals/reward, experiencing a system malfunction, etc. Thus, in order for our model to be the most useful for planning, we want to first update it using our recently observed data.
At training time (Fig. 4), what this amounts to is selecting a consecutive sequence of (M+K) data points, using the first M to update our model weights from to , and then optimizing for this new to be good at predicting the state transitions for the next K time steps. This newly formulated loss function represents prediction error on the future K points, after adapting the weights using information from the past K points:
In other words, does not need to result in good dynamics predictions. Instead, needs to be such that it can use task-specific (i.e. recent) data points to quickly adapt itself into new weights that do result in good dynamics predictions. See the MAML blog post for more intuition on this formulation.
Fig 4. Meta-training procedure for obtaining a $\theta$ such that the adaptation of $\theta$ using the past $M$ timesteps of experience produces a model that performs well for the future $K$ timesteps.
We conducted experiments on simulated robotic systems to test the ability of our method to adapt to sudden changes in the environment, as well as to generalize beyond the training environments. Note that we meta-trained all agents on some distribution of tasks/environments (see paper for details), but we then evaluated their adaptation ability on unseen and changing environments at test time. Figure 5 shows a cheetah robot that was trained on piers of varying random buoyancy, and then tested on a pier with sections of varying buoyancy in the water. This environment demonstrates the need for not only adaptation, but for fast/online adaptation. Figure 6 also demonstrates the need for online adaptation by showing an ant robot that was trained with different crippled legs, but tested on an unseen leg failure occurring part-way through a rollout. In these qualitative results below, we compare our gradient-based adaptive learner (‘GrBAL’) to a standard model-based learner (‘MB’) that was trained on the same variation of training tasks but has no explicit mechanism for adaptation.
Fig 5. Cheetah: Both methods are trained on piers of varying buoyancy. Ours is able to perform fast online adaptation at run-time to cope with changing buoyancy over the course of a new pier.
Fig 6. Ant: Both methods are trained on different joints being crippled. Ours is able to use its recent experiences to adapt its knowledge and cope with an unexpected and new malfunction in the form of a crippled leg (for a leg that was never seen as crippled during training).
The fast adaptation capabilities of this model-based meta-RL method allow our simulated robotic systems to attain substantial improvement in performance and/or sample efficiency over prior state-of-the-art methods, as well as over ablations of this method with the choice of yes/no online adaptation, yes/no meta-training, and yes/no dynamics model. Please refer to our paper for these quantitative comparisons.
Fig 7. Our real dynamic legged millirobot, on which we successfully employ our model-based meta-reinforcement learning algorithm to enable online adaptation to disturbances and new settings such as traversing a slippery slope, accommodating payloads, accounting for pose miscalibration errors, and adjusting to a missing leg.
To highlight not only the sample efficiency of our meta reinforcement learning approach, but also the importance of fast online adaptation in the real world, we demonstrate our approach on a real dynamic legged millirobot (see Fig 7). This small 6-legged robot presents a modeling and control challenge in the form of highly stochastic and dynamic movement. This robot is an excellent candidate for online adaptation for many reasons: the rapid manufacturing techniques and numerous custom-design steps used to construct this robot make it impossible to reproduce the same dynamics each time, its linkages and other body parts deteriorate over time, and it moves very quickly and dynamically as a function of its terrain.
We meta-train this legged robot on various terrains, and we then test the agent’s learned ability to adapt online to new tasks (at run-time) including a missing leg, novel slippery terrains and slopes, miscalibration or errors in pose estimation, and new payloads to be pulled. Our hardware experiments compare our method to (a) standard model-based learning (‘MB’), with neither adaptation nor meta-learning, and well as (b) a dynamic evaluation (‘MB+DE’) comparison having adaptation, but performing the adaptation from a non-meta-learned prior. These results (Fig. 8-10) show the need for not only adaptation, but adaptation from an explicitly meta-learned prior.
Fig 8. Missing leg.
Fig 9. Payload.
Fig 10. Miscalibrated Pose.
By effectively adapting online, our method prevents drift from a missing leg, prevents sliding sideways down a slope, accounts for pose miscalibration errors, and adjusts to pulling payloads. Note that these tasks/environments share enough commonalities with the locomotion behaviors learned during the meta-training phase such that it would be useful to draw from that prior knowledge (rather than learn from scratch), but they are different enough that they do require effective online adaptation for success.
Fig 11. The ability to draw from prior knowledge as well as to learn from recent knowledge enables GrBAL (ours) to clearly outperform both MB and MB+DE when tested on environments that (1) require online adaptation and/or (2) were never seen during training.
This work enables online adaptation of high-capacity neural network dynamics models, through the use of meta-learning. By allowing local fine-tuning of a model starting from a meta-learned prior, we preclude the need for an accurate global model, as well as allow for fast adaptation to new situations such as unexpected environmental changes. Although we showed results of adaptation on various tasks in both simulation and hardware, there remain numerous relevant avenues for improvement.
First, although this setup of always fine-tuning from our pre-trained prior can be powerful, one limitation of this approach is that even numerous times of seeing a new setting would result in the same performance as the 1st time of seeing it. In this follow-up work, we take steps to address precisely this issue of improving over time, while simultaneously not forgetting older skills as a consequence of experiencing new ones.
Another area for improvement includes formulating conditions or an analysis of the capabilities and limitations of this adaptation: what can or cannot be adapted to, given the knowledge contained in the prior? For example, consider two humans learning to ride a bicycle who suddenly experience a slippery road. Assume that neither of them have ridden a bike before, so they have never fallen off a bike before. Human A might fall, break their wrist, and require months of physical therapy. Human B, on the other hand, might draw from his/her prior knowledge of martial arts and thus implement a good “falling” procedure (i.e., roll onto your back instead of trying to break a fall with the wrist). This is a case when both humans are trying to execute a new task, but other experiences from their prior knowledge significantly affect the result of their adaptation attempt. Thus, having some mechanism for understanding limitations of adaptation, under the existing prior, would be interesting.
We would like to thank Sergey Levine and Chelsea Finn for their feedback during the preparation of this blog post. We would also like to thank our co-authors Simin Liu, Ronald Fearing, and Pieter Abbeel. This post is based on the following paper:
- Learning to Adapt in Dynamic, Real-World Environments Through Meta-Reinforcement Learning
A Nagabandi*, I Clavera*, S Liu, R Fearing, P Abbeel, S Levine, C Finn
International Conference on Learning Representations (ICLR) 2019
Arxiv, Code, Project Page
This article was initially published on the BAIR blog, and appears here with the authors’ permission. | <urn:uuid:39a8ca22-1e43-4288-ae06-b9825fb21d43> | CC-MAIN-2023-14 | https://robotics.ee/2019/05/13/robots-that-learn-to-adapt/ | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945315.31/warc/CC-MAIN-20230325033306-20230325063306-00200.warc.gz | en | 0.939574 | 2,728 | 3.265625 | 3 |
Game of Throwns
Daenerys frequently invents games to help teach her second grade Computer Science class about various aspects of the discipline. For this week’s lesson she has the children form a circle and (carefully) throw around a petrified dragon egg.
The $n$ children are numbered from $0$ to $n - 1$ (it is a Computer Science class after all) clockwise around the circle. Child $0$ always starts with the egg. Daenerys will call out one of two things:
a number $t$, indicating that the egg is to be thrown to the child who is $t$ positions clockwise from the current egg holder, wrapping around if necessary. If $t$ is negative, then the throw is to the counter-clockwise direction.
the phrase undo $m$, indicating that the last $m$ throws should be undone. Note that undo commands never undo other undo commands; they just undo commands described in item $1$ above.
For example, if there are $5$ children, and the teacher calls out the four throw commands 8 -2 3 undo 2, the throws will start from child $0$ to child $3$, then from child $3$ to child $1$, then from child $1$ to child $4$. After this, the undo 2 instructions will result in the egg being thrown back from child $4$ to child $1$ and then from child $1$ back to child $3$. If Daenerys calls out $0$ (or $n, -n, 2n, -2n$, etc.) then the child with the egg simply throws it straight up in the air and (carefully) catches it again.
Daenerys would like a little program that determines where the egg should end up if her commands are executed correctly. Don’t ask what happens to the children if this isn’t the case.
Input consists of two lines. The first line contains two positive integers $n$ $k$ ($1\leq n \leq 30$, $1 \leq k \leq 100$) indicating the number of students and how many throw commands Daenerys calls out, respectively. The following line contains the $k$ throw commands. Each command is either an integer $p$ ($-10\, 000 \leq p \leq 10\, 000$) indicating how many positions to throw the egg clockwise or undo $m$ ($m \geq 1$) indicating that the last $m$ throws should be undone. Daenerys never has the kids undo beyond the start of the game.
Display the number of the child with the egg at the end of the game.
|Sample Input 1||Sample Output 1|
5 4 8 -2 3 undo 2
|Sample Input 2||Sample Output 2|
5 10 7 -3 undo 1 4 3 -9 5 undo 2 undo 1 6 | <urn:uuid:923dd795-d672-4a6d-bcc0-f19dc6926003> | CC-MAIN-2023-14 | https://nus.kattis.com/courses/IT5003/IT5003_S2_AY2223/assignments/pe7tbg/problems/throwns | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296944452.74/warc/CC-MAIN-20230322180852-20230322210852-00600.warc.gz | en | 0.915059 | 646 | 3.390625 | 3 |
نوع مقاله : پژوهشی
1 بخش مهندسی صنایع، دانشگاه تربیت مدرس
2 پژوهشگاه بین المللی زلزله شناسی و مهندسی زلزله
عنوان مقاله [English]
Iran is known as one of the high risk seismic regions of the world. Over the past 50 years, many destructive earthquakes have occurred in this area, causing much human loss and financial damage. So, from the perspective of emergency-management and hazard preparedness, it is essential to make an effort to predict earthquake occurrence. Earthquake prediction is an instance of
interdisciplinary research, which is a concern of many scientists in various fields, such as geology, seismology, engineering, mathematics, computer science and even social sciences, who study different aspects of the matter to find new solutions. Efforts in this field are divided into long-term and short-term predictions. The short-term predictions are based on precursors such as foreshock, seismic quiescence, decrease in radon concentrations and other geochemical phenomenon. Due to numerous complexities and unknown factors inside the earth, exact prediction of earthquakes is difficult and practically impossible. During the last two decades, many techniques have been developed to discover the pattern of seismic data and predict three earthquake parameters, namely; time of occurrence, location and magnitude of future earthquakes. Soft computing and data mining techniques, such as neural networks, fuzzy logic and clustering methods are appropriate tools for problems, such as earthquake
prediction, that suffer from inherent complexities. Many researchers have used these approaches to reduce uncertainty in results.
In this paper, the b-value of the Gutenberg Richter law has been considered as a precursor to earthquake prediction. Prior to earthquakes equal to or greater than $M_w$ = 6.0, temporal variation of the b-value has been examined in Qeshm island and neighboring areas in the south of Iran, from 1995 to 2012. The clustering method, by the k-means algorithm, and a self-organizing map (SOM) have been undertaken to find a pattern of variation of the b-value. Three clusters are obtained as an optimum number of clusters by the Silhouette Index and the Davis-Bouldin index. Prior to all the mentioned earthquakes $(M_w\geq 6.0)$ a cluster, known as a decrease in b-value, has been seen; so, a decrease in the b-value before main shocks has been considered as a distinctive pattern. Also, an approximate time of decrease has been determined. | <urn:uuid:7accd3ff-6c23-4341-8b71-b5638ea3eff2> | CC-MAIN-2023-14 | http://sjce.journals.sharif.edu/article_1014.html | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945242.64/warc/CC-MAIN-20230324020038-20230324050038-00600.warc.gz | en | 0.914645 | 674 | 3.078125 | 3 |
Multivariate metamodelling is a way to make simplified models of mechanistic models that can be run faster and are more interpretable. This opens up a set of possibilities for how to use already existing mechanistic models to optimize processes and improve understanding.
Our Multivariate Metamodelling methods allow our customers to:
Mechanistic, or theory driven models, are widely used to describe behavior of a system based on known theory. These mathematical models could be for furnaces in the metallurgy industry, wind turbines, spread of infectious diseases, or the cardiovascular system. Examples: Finite element models of heat diffusion or electrical fields, differential equations of reaction kinetics, or computational fluid dynamic models of turbulence in gases or liquids.
A good mechanistic model describes essential properties and behaviors, according to the laws of physics within the selected process design. Such a model is a valuable source of prior knowledge, especially about how the system will behave under conditions where you don’t even WANT to have observational data, for example situations that cause harm to equipment or personnel.
Mechanistic mathematical models often encapsulate deep prior knowledge of domain experts. However, mechanistic models may be slightly oversimplified – they often do not take all possible interactions between the parameters into account. Still, they do describe valuable insight about how the laws of physics determine the input-output relationships of the system, and how the system was intended to function.
One other issue is that many of the coefficients that are built into the mechanistic/first principle models are estimated from certain experiments that might not have a general applicability, but represent a “best estimate”. This might introduce some bias in the models, so that they cannot be extrapolated uncritically to other similar but not identical applications.
Mechanistic models are often used for design of processes and assets. But today, they are seldom used in the operations phase. One reason is that they are often slow to compute and difficult to fit to streams of process measurements. Another reason is that a model is no longer trusted – maybe there were discrepancies between the planned “design” in the model and what was actually “built”, or perhaps the model has not been updated with later furnace modernizations. Raw materials and operating conditions also change over time, reducing fit with the original mechanistic model.
So, theory-driven mechanistic models might not be perfect. But they can be supplemented by data-driven models based on actual process measurements. This is called “hybrid modelling”, and combine mechanistic- and data driven modelling, using the advantage of each and avoiding the disadvantage of each.
A multivariate metamodel is a simplified description of the output behavior of a mechanistic model under different input conditions. When building a metamodel, we need to describe the mechanistic model’s behavior. This means running the mechanistic model repeatedly under different conditions, making sure that the relevant range of conditions are included.
The model inputs (various combinations of relevant system design descriptions, parameter values, initial conditions and computational controls), are chosen so that the model outputs will be is representative for the use case of interest as well as for unwanted, but possible deviations from these. This set of computer simulations with the mechanistic model needs only to be done only once.
In Idletechs we do this through our highly efficient experimental designs, to make the most cost-effective computer simulations of parameter combinations, spanning the whole relevant range of behavior with respect to the important statistical properties. Read more in Design of Experiments
The input-output relationship from the simulated data from the mechanistic model are described with the same methods that are used for modelling the relationship between empirical measurements of input and output. These so-called subspace regression methods, extensions of methods originally developed in the field of chemometrics (ref H. Martens & T Næs (1989) Multivariate Calibration. J. Wiley & Sons Ltd. Chichester UK), are fast to compute, give good input-output prediction models and are designed to give users a graphical overview and provide insight.
The laws of physics as implemented in the mechanistic model still apply in the obtained metamodels of the mechanistic model’s behavior. Only now the computations of outputs from inputs can run thousands of times faster, and without risk of local minima or lack of convergence.
Multivariate metamodelling can be used for a range of applications:
Most mechanistic models define how a system’s outputs depend on its inputs according to theory:
\(Outputs \approx F(Inputs)\)
The metamodel of such a theoretical, mechanistic mathematical model is a simpler statistical approximation model:
\(Outputs \approx f(Inputs)\)
A metamodel in this causal direction is guaranteed to give good descriptions of the mechanistic model’s outputs from its combination of inputs. Such a metamodel gives quantitative predictions and graphical insight into what are the most critical elements and stages hidden inside the mechanistic model itself. The user gets information at three levels:
Example: The known operating conditions of a furnace (e.g. electrode control, input current, raw material charge and cooling rate) predicts the inner, hidden position of the electrode tip, or the outer surface temperature and electromagnetic field.
Example: How certain combinations of operating conditions of the furnace should be able to predict its inner or outer properties.
Example: Why a combination of electrode control, input current and raw material charge seem to affect a combination of electrode tip and outer electromagnetic field, while a different combination of input current and cooling capacity seem to affect the surface temperature distribution.
In other words: The many input/output variations form distinct patterns of causalities that can monitored in real time, in particular if the model is fitted fast enough to relevant measurements.
Many mechanistic mathematical models are highly informative, but too slow for real-time updating. Examples: Nonlinear spatiotemporal dynamics of e.g. metallurgical reactions, or heating and cooling processes. A metamodel of such a slow mechanistic model may be developed to mimic its input/output behavior and make the computations much faster and more understandable.
To establish a metamodel of a mechanistic model requires some computer simulation work (mostly automatic) and some multivariate data analysis (requires our expertise). But this work is done once and for all. Once established, our metamodels run very fast, due to their mathematical form (low-dimensional bilinear subspace regressions).
Moreover, each time the original non-linear model is applied, it may give computational problems, such as local minima and lack-of-convergence. In contrast, its bilinear metamodel do not suffer in this way, for those problems were already dealt with during the metamodel development.
Various predicted Outputs predicted from a metamodel, e.g. the surface temperature distribution of an engine, may be compared to actually measured profiles of these Outputs, e.g. continuous thermal video monitoring of that engine. This allows us to infer the unknown causal Inputs – inner states and parameter values like unwanted changes in the inner combustion, heat conductivity or cooling of the engine.
One way to attain this is to search for already computed Output combinations that resemble the measured Output profile, starting with the previous simulation results.
But an even faster approach is also possible. In many cases it may be even more fruitful to invert the modelling direction, compared to the causal direction Output=f(Inputs):
\(Inputs \approx g(Outputs)\)
That can give an exceptionally fast way to predict unknown input conditions and inner process states from real-time output measurements.
In addition, the metamodel will automatically give warning of abnormality if it detects discrepancies between the predicted and measured temperature distribution of the engine surface. This facility is very sensitive, since it ignores patterns of variation that have already been determined to be OK.
Combine metamodel outputs with empirical measurements for a hybrid modelling approach that combines “the best of both worlds” and models the process as it really is.
Improving the process knowledge and also the mechanistic model.
It is generally a good idea to bring background knowledge into the interpretation of process measurements. Even though the boundary conditions may have changed, the laws of physics are the same.
Improving your old mechanistic model. The so-called subspace regression models also provide automatic outlier detection if and when new, unexpected process variation patterns are seen to develop in the measurements. These new pattern developments are used for generating warnings to the operators. Moreover, process properties that have changed are revealed and corrected in terms of model parameter settings that appear to change compared to what you expected. Thereby the combined meta-/data-modelling process helps you update the parameter values in your old mechanistic model.
But in addition, your old mechanistic model may not only be updated, but also expanded in this process: Unexpected, new variation patterns in the hybrid can be analyzed more depth, in terms of mechanistic mathematical equations, e.g. differential equation between the inner states, known or known, of your process. These model elements may be grafted onto the original mechanistic model, just like a new branch may be grafted onto the trunk of an old fruit tree. Thereby, your old mechanistic model becomes fully adapted to more modern times.
Some mechanistic models display an apparent weakness: Several different combinations of Input conditions can give more or less the same Output profile:
\(F(Inputs_1) \approx F(Inputs_2) \approx … F(Inputs_N) = Outputs\)
This means that the mechanistic model is mathematically ambiguous, in the sense that different input combinations may cause the system to behave in the same way.
Such a collection of parameter combinations with more or less equal effects on the system is called a “neutral parameter set”. And a mechanistic model with neutral parameter sets is called “mathematically sloppy”.
However, in an industrial setting, this apparent weakness may be turned into a great advantage. Assume that this ambiguity is a property of the physical system itself (e.g. a furnace or an engine), and not just due to an error in its mechanistic model.
Assume also that there are multiple key performance indicators (KPIs) for a given system. May be there are ways to optimize one key KPI, KPIKey, without sacrificing the other KPIs, KPIOther?
Then, for a process where a good mechanistic model shows such an ambiguity, its metamodel may list a range of different input combinations that may change KPIKey while not affecting KPIOther.
Seeing this type of ambiguity may allow you to find ways to optimize the Input conditions with respect to KPIKey without affecting the other desired process Output significantly. For instance, by studying the sloppiness of the mechanistic model (its many-inputs-to-one-output, e.g. discovered via its metamodel) you may find new ways to run an engine that reduce CO2 or fuel cost without sacrificing engine power. Or new and less risky ways to control the electrode positioning in a furnace without affecting its productivity.
Idletechs helps you to combine valuable information from both the mechanistic model (via its metamodel) and from modern measurements (e.g. thermal cameras etc), in a way that is understandable for operators and experts alike.
One of the essential tools in meta- and hybrid- modelling is Design of Experiments (DoE). Proper use of DoE ensures that the parameter space in the mechanistic and simulation-based models is described with a minimum number of combinations of the parameters of interest, i.e. the best subset of experimental runs. The traditional analysis of results from DoE, ANalysis Of VAriance (ANOVA) yields statistical inference w.r.t the importance of the parameters, and to distinguish real effects from noise. The multivariate subspace models gives detail insight into the relationship between samples and variables from experimental designs, specifically in situations with multiple outputs. Yet another important aspect in this context it that one can a priori estimate the danger of overlooking real effects by means of power estimation. No experiments should be performed before there exists an estimate of the uncertainty in the outputs of the model.
Furthermore, DOE will also clarify possible interaction effects which initially may not have been the considered in the mechanistic models. Derived input and output parameters might be added by so-called feature engineering; adding transforms of the initial parameters based on domain specific knowledge and theory. Temperature is e.g. rarely affecting a process in a linear way. The modern optimal designs also offer the definition of constraints as known in the system under observation, e.g. that some combinations of parameters will be give fatal outcome of the process. After the initial model has been established, the model can be numerically and graphically optimized, which is the basis for one or more confirmation runs for verification. | <urn:uuid:db7eb7fc-6a12-4cd6-861b-f5931fa04ecb> | CC-MAIN-2023-14 | https://idletechs.com/metamodelling/ | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948756.99/warc/CC-MAIN-20230328011555-20230328041555-00600.warc.gz | en | 0.907242 | 2,737 | 2.5625 | 3 |
Graphing Systems of Linear Inequalities
Graphing Systems of Linear Inequalities involves two inequalities in two variables x and y.
For graphing systems of inequalities we use a Cartesian plane or XY -plane. In that vertical line divides the plane in left and right part and slanting or oblique line divides the plane in upper and lower part. A point in the Cartesian plane will either lie on a line or will lie in either of the part.
Steps to graph the systems of inequality
(i) Solve the given inequality for y by following the rules of inequality of signs.
(ii) Graph the equation either using function table or using slope and y-intercept.
(iii) If the inequality is strict (< or >), graph a dotted line and if the inequality is not strict ($\geq or \leq$ ), draw a solid line.
(iv) Apply the Origin test
| Origin Test : Put x = 0 and y = 0 in the given equation after solving if the equation is true then origin (0,0) is included in the region and if false then set the region in which the origin is not included.
Lightly shade the half-plane that is the graph of the inequality. Colored
pencils may help you distinguish the different half-planes
Graph both the equations using the above rules, mark the region accordingly.For marking use the two different color pencils or dark and light shade to distinguish the two different region.The intersection or overlapping region formed by both the inequalities is the solution region.
Examples on graphing systems of linear inequalities
Example 1 :
Graph the system : y $\geq$ -3x - 2 and y < x + 3
y $\geq$ -3x - 2 ---------(1)
and y < x + 3 ------- (2)
Graph the 1st and 2nd equation using slope and y intercept.
Now put x = 0 and y = 0 in the 1st equation ,
0 $\geq$ - 3(0) -2
0 $\geq$ -2
Which is true, so origin is included for the 1st inequality.
So after graphing an equation we will mark right region of the line which includes origin.
2nd equation ⇒
0 < 0 + 3
0 < 3
which is also true, so origin is also included in 2nd inequality.
So after graphing an equation we will mark the lower region of the line which includes origin.
From the above graphs we can see that in A region from 1st graph, there is a solid line as the inequality is not strict. In region B, 2nd graph there is a dotted line as there is strict inequality. The 3rd graph both region A and B are overlapped and region c is intersection region. So region C is the solution.
11th grade math
From graphing systems of linear inequalities to Home | <urn:uuid:39f64b3b-ac37-4cff-a3e9-e2b6acb19bd3> | CC-MAIN-2023-14 | https://www.ask-math.com/graphing-systems-of-linear-inequalities.html | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949009.11/warc/CC-MAIN-20230329151629-20230329181629-00001.warc.gz | en | 0.929625 | 619 | 4.53125 | 5 |
There is a multi-billion dollar global industry dedicated to feeding wild birds in residential gardens. This extraordinary boost to food resources is almost certainly reshaping entire bird communities, yet the large-scale, long-term impacts on community ecology remain unknown. Here we reveal a 40-year transformation of the bird communities using garden bird feeders in Britain, and provide evidence to suggest how this may have contributed to national-scale population changes. We find that increases in bird diversity at feeders are associated with increasing community evenness, as species previously rarely observed in gardens have increasingly exploited the growing variety of foods on offer over time. Urban areas of Britain are consequently nurturing growing populations of feeder-using bird species, while the populations of species that do not use feeders remain unchanged. Our findings illustrate the on-going, gross impact people can have on bird community structure across large spatial scales.
Food availability may be the single most important factor determining the size and distribution of animal populations. Winter food availability, in particular, plays a critical role in regulating bird populations in seasonal environments1, with over-winter survival a key cause of population change for many terrestrial bird species2,3,4. In much of Europe and North America, the deliberate provision of food in domestic gardens and yards (garden bird feeding) has modified the winter resource base for birds extensively5, helping to buffer against environmental drivers that operate through changes in natural food abundance6. In Britain, for example, homeowners are reportedly providing enough supplementary food to support approximately 196 million birds, far exceeding the combined, total population of many common garden species7. This massive human intervention is likely to be having profound repercussions on the bird communities around us5.
Early feeding pioneers attracted a relatively simple bird community to gardens using kitchen scraps and home-made table feeders5. However, the practice has changed substantially since becoming commercialised in the mid-20th century8. It now seemingly benefits a much broader bird community, although it is unclear whether or not some species may have lost out due to heightened interspecific competition for access to supplementary foods9,10. Previous research has demonstrated that the distribution of feeders across a city can predict avian abundance patterns for some species11, with bird community composition also reacting promptly to the introduction and removal of feeding stations12. This would suggest that garden bird feeding is capable of supporting local populations and enhancing bird numbers, at least in the short-term. The availability and nutritional value of anthropogenic foods are also likely to have substantial impacts (both positive and negative) on the health, survival and breeding outputs of wild birds3,13,14. But ultimately, how these effects scale up to influence bird community dynamics and population trajectories across entire landscapes is still unknown.
In Britain, gardens cumulatively account for approximately one quarter of all urban land cover15 and play an important role in supporting the national populations of many bird species16,17,18. Given our awareness that at least half of British homeowners feed the birds in their gardens7,19, and our growing understanding of the extensive ecological and evolutionary impacts of supplementary food use, it is reasonable to predict that garden bird feeding might also be influencing bird communities across large spatial scales. The supply and uptake of garden bird food during winter has been monitored throughout Britain since the 1970s, via the Garden Bird Feeding Survey (GBFS, Supplementary Fig. 1), providing a unique opportunity to study long-term shifts in bird communities in response to large-scale food supplementation. Here, first, we characterise real-time growth and innovation within the garden bird feeding industry. Then, using data extracted over a 40-year time series, we demonstrate that, over time, food resources provided by the British public have altered the composition of bird communities utilising garden bird feeders and, consequently, have helped to shape the national populations of birds in Britain today.
Results and Discussion
Garden bird feeding industry
To quantify long-term changes to garden bird feeding in Britain, we conducted a comprehensive review of advertising in Birds—a charity membership magazine reaching more than 2 million readers20—published between 1973 and 2005. By definition, the magazine’s audience have a keen interest in birds and their conservation, thus representing the target market for companies selling popular and novel feeding products. Since brand advertising is known to impact total industry demand21, advertising patterns in Birds are expected to provide meaningful indices of consumers’ garden bird feeding habits.
The proportion of advertising space dedicated to the bird feeding industry increased significantly over time (\(\chi _1^2\) = 26.19, df = 2.62, p < 0.001; Supplementary Fig. 2), indicating the rising popularity of feeding wild birds. After accounting for changes to advertising practices, we revealed upward trajectories in the total numbers of food (F = 178.1, df = 3.15, p < 0.001) and feeder (F = 187.9, df = 3.70, p < 0.001) products on offer, including exponential increases from 1980 onwards (Fig. 1; Supplementary Fig. 2). The number of food types available (\(\chi _1^2\) = 8.06, p = 0.005) and their diversity (Simpson’s Index, \(\chi _1^2\) = 7.26, p = 0.007) also grew significantly (Supplementary Table 1; Supplementary Fig. 2). Specialist foods, such as sunflower hearts and fat balls, first appeared in the 1990s (Fig. 1) as companies, supported by conservation bodies, deliberately diversified their products to attract more species5. This broadening of food resources, added to the potential for selective provisioning by homeowners, may have both influenced and complicated bird community responses to increases in food quantity.
Community changes at garden bird feeders
Using 40 years of GBFS data from 1973/74 to 2012/13, we identified 133 bird species using garden feeders during winter, equating to 52.6% of all species, excluding vagrants, found in Britain22 (Supplementary Table 2). We analysed the long-term trends in community composition, nationally (using a single, rarefied time-series) and within individual gardens (using mixed effects modelling), to examine evidence of bird community adaptation in response to evolving feeding practices (see Methods section).
Across Britain, there has been a highly significant increase in the diversity of birds using garden bird feeders since the 1970s, according to Simpson’s Diversity Index (F = 355.0, df = 3.52, p < 0.001; Fig. 2a). Although, nationally, the same suite of species have continued to use feeders over time (\(\chi _1^2\) = 0.00, p = 0.99; Fig. 2c), homeowners are encountering an increasingly species-rich (F = 143.5, df = 2.99, p < 0.001; Fig. 2d) and diverse (F = 123.0, df = 2.92, p < 0.001; Fig. 2b) community of birds visiting the feeders in their individual gardens.
This combination of large- (national-) and small- (garden-) scale patterns suggests that many species have become more abundant at garden feeders over time, potentially resulting in a change in species dominance within the feeder-using community. Indeed, a comparison of k-dominance curves from each year revealed a clear pattern of increasing evenness over time (Fig. 2e). Most notably for example, approximately half of all birds using feeders belonged to just two species in the 1970s, but by the 2010s, the number of species making up the same proportion of the community had more than tripled. We examined the possibility that this finding might purely reflect the changing spatial ranges of British birds23, potentially influencing community trends by bringing more wintering bird species in contact with monitored feeders over time. However, the median net change in the proportion of GBFS gardens located within a species’ range between 1981 and 2011 was only 2.49% (n = 130)24,25. This suggests that garden bird feeders, specifically, could be responsible for attracting more individuals across a greater species range as time has passed.
We used GBFS data on the numbers of hanging, table and ground feeding units (collectively termed feeders) to evaluate the importance of garden bird food availability in driving community patterns directly. As expected, individual homeowners supplied an increasing number of feeders (F1,6431 = 195.6, p < 0.001), particularly hanging feeders (F1,6431 = 297.2, p < 0.001), over time (Supplementary Fig. 3). It is reasonable to assume that this increase in feeder numbers also reflects the greater variety in food types that became available during the same timeframe, since homeowners are likely to aim to attract more species by diversifying food provision, rather than simply increasing provision of the same foods.
Changes in bird communities across the British countryside have previously been shown to be at least partially linked to climate change and urbanisation26,27. Indeed, variation in garden use by birds is also known to be associated with winter temperatures and local habitat characteristics18,28. But interestingly, when we included all of these potential drivers as covariates in the modelling of bird community temporal trends, we found that the number of feeders provided in a garden had a greater influence on species richness and diversity than either winter temperature or local habitat (Supplementary Fig. 4). It therefore seems that the broad temporal changes observed at garden bird feeders could be the result of the cumulative changes in food provisioning across multiple gardens, allowing species rarely observed at the start of the time-series to take better advantage of feeders over time.
Well-defined interspecific dominance hierarchies are known to exist at bird feeders, as species of different sizes and competitive strengths fight for to access food supplements9,29. Our findings suggest that, by increasing the number of feeders available in gardens, this has reduced the capacity for resource monopolisation by any one species. Concurrent increases in the diversity of food and feeder types on offer are also likely to have led to greater opportunities for species with more specialist foraging requirements. To this end, the continuing modifications made by homeowners to their feeding practices appear to have contributed significantly to the changing composition of bird communities in gardens.
Links to national population change
It would seem that the composition of bird communities exploiting garden bird food has changed in parallel with evolving feeding practices. More generally, community changes in terrestrial birds are likely to be the product of many different factors, including climate, habitat change, resource availability, conditions in breeding/wintering grounds or on migration, disease, competition and predation. Indeed, as previously mentioned, wider community changes have occurred across Britain27, and therefore it is feasible that apparent increases in feeder use could merely reflect the greater detection of birds whose populations have grown through a mechanism unrelated to garden bird feeding. So, are changing feeder communities simply reflecting these wider patterns18, or could feeding actually be a driver of population change?
To answer this, first, we needed evidence that there is a real association between the use of garden bird feeders during winter and concurrent changes in species’ population sizes. Species that regularly visit garden feeders are most likely to experience population-level impacts of supplementary food use. Therefore, we identified 39 species that regularly visit garden feeders (feeder-users) and tested whether independent estimates of their national breeding population trends, derived from Massimino et al.30, could be linked to shifting winter feeder usage. Feeder use—the proportion of gardens where each species used feeders—increased by an average of 14.9% (s.e.m. 4.0%) between 1973 and 2012, with two thirds of species showing a significant positive change (Fig. 3a; Supplementary Table 3). Further, these changes were found to be significantly associated with national population changes over the same timeframe (r2 = 0.43, F1,29 = 21.82, p < 0.001; Fig. 3b). We accounted for phylogeny in our analysis, under the assumption that more closely related species would be more similar in their tendency to use feeders and in the extent to which their populations change. Indeed, the estimate of Pagel’s lambda (a measure of the phylogenetic signal) for species population change was significantly different from zero (λ = 0.94, p = 0.014). However, there was no evidence that feeder use was influenced by phylogeny (λ < 0.001, p = 0.15), and the optimised lambda value from the regression model (λ < 0.001) denotes very limited covariance between feeder use and species’ population change (distinct from the explanatory power of feeder use per se). Feeder use is typically associated with passerine birds5, but, with use of supplementary food evident across the phylogenetic tree (Supplementary Fig. 5), these findings give a strong indication that the proliferation of feeder use within bird communities is independent of species’ inter-relatedness.
Previous research has demonstrated that, across species, bird population trends are significantly reduced in urban areas compared to other habitats31. Therefore, to understand whether feeding, specifically, could be contributing to the wider population changes reported, we needed to be able to separate the influence of feeder use from other co-varying drivers of garden bird numbers that also operate along a gradient of urbanisation32. To achieve this, we focused our analysis on the changes in bird populations occuring in urban areas of Britain only, where garden bird feeders are widely accessible to all birds19, allowing us to test the effect of feeding independently of any other potential influences associated with the urban gradient32. Using all available trends for species (n = 72) occurring in urban areas of Britain (namely, all urban, suburban and rural human-dominated habitats31) we tested for a difference in the urban population trends for the species that regularly use garden feeders (n = 33), compared to those which do not (n = 39). Compellingly, feeder-users had significantly different population trajectories from those species with equal access to, but which do not commonly visit, feeders (F1,70 = 7.43, p = 0.008; Fig. 3c), with no phylogenetic influence (Pagel’s λ < 0.001). In fact, while there was no overall directional change for the species that do not use feeders, by comparison populations of feeder-users increased significantly (Fig. 3c).
Since these results do not distinguish cause and effect between increasing supplementary food use and population growth definitively, we checked whether or not similar differences between the two species groups also occured throughout the rest of Britain (i.e. non-urban areas). Finding the same pattern would suggest that the differences observed in urban areas are reflecting broader population changes, with birds moving into gardens in approximate proportion to their availability by area, following something like an ideal free distribution across the wider countryside33. However, we found no difference between the non-urban trends for these groups (F1,70 = 1.71, p = 0.196), implying that the relationship is more likely to have resulted from birds choosing to use garden feeders than from them expanding their habitat use due to population growth. While many other factors are certain to influence interspecific variation in trends, these findings provide the first landscape scale evidence consistent with garden bird feeding having influenced population change.
Wild bird feeding has become engrained into human culture across many areas of the world within the last half-century, to the extend that this seemingly small-scale activity is now frequently acknowledged for its demonstrable benefits to human well-being5,34,35,36,37. Nonetheless, the historical basis for feeding wild birds began with the perception that, by providing food during winter, one can improve the survival prospects of vulnerable individual birds5. Changes to bird feeding activities conducted in gardens are already reported to have resulted in stark ecological and evolutionary responses within some individual bird species38,39. Our findings indicate that the consequences of feeding reach further still, with evidence that this habitual human activity is also associated with the national-scale restructuring of bird communities.
Intuitively, the types of food provided should affect the types of species attracted10,12. Our results indicate that the diversifying commercial bird food market has enabled a growing number of species to exploit supplementary foods over time, while some appear to have lost out as a result of behaviourally dominant or better adapted species becoming more common within the community. Indeed, the bird assemblage that commonly uses feeders (Fig. 3a) includes species of high conservation concern30, species capable of promoting human well-being40 and species considered common pests41. Feeding is, therefore, highly likely to have already had important effects, and greater coordination of feeding activities, across networks of gardens and at multiple spatial scales, could be an innovative way of delivering large-scale conservation or species management outcomes in the future42.
Feeding birds is a growing practice throughout the world, with many people shifting from traditional, winter-only feeding to provisioning all year round5. If feeding continues to intensify, it will likely exacerbate the species- and community-level consequences observed here. Greater food diversity, innovation in feeder design, variation in food quality and behavioural adaptation by birds all have the potential to influence the frequency of feeder use and the benefits or detrimental impacts accrued, with downstream consequences for population sizes and community structure. The positive influences of feeder use on population size reported here are likely to be the product of a combination of improved survival3,4, better physiological condition13,43 and increased productivity44 among the individuals frequenting feeders. However, negative impacts of supplementary feeding have been widely reported, particularly those associated with increased disease transmission at feeders and the poor nutritional quality of food supplements45,46,47,48. Further research is needed to determine whether, and how, these might limit population growth. Individual decisions by homeowners to feed wild birds can impact cumulatively upon bird communities across large spatial scales. As such this growing, global phenomenon has profound potential to influence biodiversity further and should not be underestimated.
Evidence of garden bird feeding industry change
Garden bird feeding industry data were derived from advertisements featured in Birds magazine; a free publication, widely distributed to members of the Royal Society for the Protection of Birds (RSPB; recent membership figures totalled over 1.2 million49). Our assessment focused on all advertisements promoting garden bird food and/or feeder products in the Autumn editions of Birds from 1973 to 2005. After 2005, advertising was biased toward RSPB-branded products. Over the 33-year period considered, the number of pages featuring all forms of advertising in Birds increased linearly (GLS \(\chi _1^2\) = 26.19, p < 0.001), correlated with a general increase in magazine length (r = 0.901, n = 33, p < 0.001). For every advertisement (n = 179), we extracted data for its size (proportion of page covered), and the names and descriptions of individual food and feeder products. Foods were also allocated to one of 21 different food type categories (see Supplementary Table 1) using product descriptions, images and online information.
To test for temporal changes in supplementary food quantites, the food and feeder product ranges from all advertisements were summed (respectively) per magazine (n = 33). To test for temporal changes in supplementary food diversity, we quantified the number and diversity (using Simpson’s diversity index) of food types represented in each magazine. We ruled out the possibility that observed patterns were confounded by increased advertising space by controlling for the total number of pages featuring bird feeding industry advertisements (advertising pages). Number of bird food products and number of feeder products were modelled seperately as a function of a year smooth using generalised linear models (GAMs), with a Poisson error distribution. Advertising pages was also log-transformed and included as an offset, since the numbers of products advertised was expected to be proporitional the the total amount fo advertising space available. The number of different food types and food diversity over time were modelled as a function of year using generalised least squares (GLS) with advertising pages included as a covariate. Food type number was log-transformed to reach normality of the residuals. In a further test for overall growth in the bird food industry, we modelled the proportion of total advertising space dedicated to feeding products as a function of a year smooth using a GAM. Full details about model specifications are given below.
Garden Bird Feeding Survey
Data from the Garden Bird Feeding Survey (GBFS) were used to investigate changes in bird communities at feeders in mainland Britain between winter 1973/4 and winter 2012/13 (40 years). GBFS is an annual survey monitoring the number of birds visiting feeders in domestic gardens over a 26-week period from October to March (www.bto.org/gbfs). The survey comprises an average of 217.8 (s.e.m. 7.1) gardens each year, covering a representative range of garden types (suburban/urban and rural) and a consistent geographic distribution. Participants leaving the scheme are replaced with new volunteers from the same region, and with gardens of a similar type and size.
Survey participants record the maximum number of each bird species observed simultaneously using feeders (i.e. at/on feeders and in their vicinity) each week or, in the case of sparrowhawk, feeding on birds using feeders. Data for all species known to occur in Britain according to the British Bird List22, except vagrants (n = 6 species), were used to estimate community indices (n = 133; Supplementary Table 2). Scarce migrants, summer migrants (recorded at the beginning or end of the winter period) and species not traditionally considered as garden visitors (e.g. wetland birds) were retained to avoid removing evidence of community change. Records for domestic and aviary species were excluded (n = 21). Species with ambiguous identification, such as marsh tit and willow tit, were combined. Changes in community composition are unlikely to have been biased by long-term changes in the arrival and departure of British breeding migrants, since estimated phenological shifts are not large enough to have noticibly increased the probablity of these migrants being recorded by GBFS50. Similarly, although volunteer field-skills are not formally controlled, there is no reason to suspect spatial biases or temporal change in the accuracy of species’ identification and counts.
Since diversity estimates are influenced by sampling effort51, the data were restricted to gardens with at least 20 weekly submissions for a given winter (mean = 25.13 weeks), as this number of replicates was seen to produce reliable species richness and species-specific abundance measures. More specifically, species accumulation curves, averaged across gardens each winter, reached an asymptote with 20 weeks of surveying. Further, we used general linear mixed models (GLMMs) controlling for garden and year random effects to verify that increasing sampling effort over 20 weeks had no effect on winter abundance (defined as the maximum count observed in a garden across all weeks surveyed). Winter abundance was independent of sampling effort in 94% of species (n = 125/133), significantly more than expected by chance (z-test, χ2 = 101.2, p < 0.001, 95% CI = 89.2 – 100.0%). We note that maximum counts provide an accurate (asymptotic) means of comparing changes in relative abundances across species, but probably under-represent true abundance.
The filtered data set used to conduct the analyses comprised 1,001 GBFS gardens in mainland Britain (mean ± s.e.m. per year = 185.8 ± 6.1) that contributed a total of 186,825 weekly submissions over the 40-year survey period (Supplementary Fig. 1). We do not expect the data set to contain any biases that might influence the observed findings, given that the data were collected across a consistent set of gardens using structured sampling to a defined protocol, and that the species list has been carefully validated and sampling effort controlled. Any erroneous data, for example due to species misidentification, should be a source of noise rather than bias.
Potential drivers of bird community change
To estimate the potential for species’ spatial range shifts to impact measures of community temporal change, distribution data from the 1981/82–1983/84 Winter Atlas25 were compared with equivalent data from Bird Atlas 2007–201124 to identify areas where a species had apparently colonised or apparently disappeared at a 10-km resolution. Data were available for 98% (n = 130) of all species represented in the GBFS data set (Supplementary Table 2); three species were not recorded during either winter atlas period. GBFS gardens were assigned data from the 10-km squares in which they were located, allowing the net change in the number of GBFS gardens located within a species’ range to be calculated and averaged across all species (using the median due to data skew).
In addition to examining bird community changes through time, three potential drivers of garden bird feeder use were also considered: number of feeders, winter temperature18 and local habitat28. The numbers of hanging feeders, bird tables and ground feeding stations (collectively termed feeders) were recorded each week in surveyed gardens. Weekly feeder numbers were averaged annually by feeder type and in total, to provide an indicator of supplementary food availability throughout winter in each garden. To examine changes in the provision of garden bird feeders over time, numbers of feeders, in total and by feeder type, were log-transformed and fitted separately against year using linear mixed models (LMM) with garden identity included as a random effect. The log-linear functional relationship, which specifies the percentage change in numbers of feeders over time, was applied to achieve normality of the residuals.
Gardens were classified as either suburban/urban or rural according to their surrounding habitat. Suburban/urban includes gardens in areas with a mix of built cover and green space, or in dense urban areas with little vegetation, such as town centres. Rural includes gardens in areas away from towns, with just a few scattered houses, farms or other isolated buildings. The difference in garden habitat types was verified using Land Cover Map 199052, which showed that rural gardens were located in 1-km squares with significantly less urban cover on average than suburban/urban gardens (rural = 12.04% ± 0.70 s.e.m.; suburban/urban = 42.66% ± 1.06; χ2 = 40265, p < 0.001). Gardens were re-classified from rural to suburban/urban if urban encroachment occurred (n = 6 gardens), but garden identity remained unchanged.
We expected that weather conditions throughout the whole bird data collection period would have a greater influence feeder use than extreme weather events. Therefore, annual measures of average winter temperature were estimated using mean monthly temperature for October – March and used to test for climatic effects on feeder use. Mean monthly temperature (°C) data were extracted from the UK Meteorological Office Climate Projections (UKCP09) 5 × 5-km resolution gridded data set53. Gardens were assigned averaged winter temperature data for the 5-km square in which they were located.
Evidence of bird community change
We used annual measures of species richness, Simpson’s diversity index and k-dominance to examine bird community patterns. Species richness was the total number of species observed throughout the winter. Simpson’s diversity index was used to provide a robust and meaningful measure of community diversity per winter51. Since Simpson’s diversity incorporates both the number of species present and their relative abundances, its comparison with species richness was also used to infer changes in bird community evenness. k-dominance curves—which plot the cumulative abundances of all species in a community (as percentages) against their species rank (logged)—were used to study changes in community evenness over time51. We used species abundance and rank, averaged annually across gardens, to compare k-dominance curves from each year of the time-series. The higher the curve, the less diverse and more uneven the community it represented.
To estimate national indices of species richness and Simpson’s diversity, we compiled data from all gardens into a single time-series, then applied sample-based rarefaction to standardise sampling effort through time54. Specifically, 115 gardens (equivalent to the minimum number surveyed in a single year) were randomly resampled without replacement from the total pool of gardens surveyed per year to achieve a consistent sample size over time. For each year, data from all resampled gardens were pooled and species richness and Simpson’s diversity calculated. Resampling was repeated for 1000 iterations and diversity measures averaged. Confidence intervals were not generated, since estimates derived from rarefaction are dependent on the size of the subsample and are therefore not informative about sample variability. The rarefied measures of Simpson’s diversity and species richness were modelled separately to quantify national-scale bird community trends. Simpson’s diversity was fitted against a year smooth using a GAM, and species richness was fitted against year using GLS regression.
To assess bird community trends at the garden scale, annual measures of species richness and Simpson’s diversity per garden were fitted using generalised additive mixed models (GAMMs) with garden identity included as a random term (n = 7433 garden-years). To evaluate the influence of other garden use drivers on bird community change, we also included number of feeders, winter temperature and habitat as fixed effects. These terms were standardised to a mean of 0 and s.d. of 0.5 to enable effect sizes to be compared directly55.
Linking feeder use to national population change
Since feeder use would need to be reasonably prevalent within a population to incur national-scale impacts, we focused on species that regularly used feeders when testing for associations between changing feeder use and changes to population size. Data were combined across all gardens per year to derive a single, intuitive index of overall feeder use per species in Britain, defined as the proportion of GBFS gardens in which a species was observed using feeders. Using site occupancy to derive feeder use, as opposed to species abundance, produces an easily interpreted measure of the scale of feeder use nationally, while also minimising the influence of stochastic variation in species counts. We conservatively defined species that regularly used feeders (feeder-users) as those with a mean feeder use of ≥ 0.1 (i.e., observed in an average of 10% of surveyed gardens per year across the study period; n = 39 species; Supplementary Table 3).
For all feeder-users, a binomial generalised linear model, testing the difference in feeder use between the first and last three years in the time-series (1973/4–1975/6 vs. 2010/11–2012/13), was used to estimate the value and significance of net change in feeder use. This approach was used as it could produce a measure of change that was analogous with estimates of national breeding population change over the same timeframe, while also minimising any influence of inter-annual stochasticity and avoiding assumptions about the shape of the temporal trend. More specifically, breeding population changes for feeder-users were similarly calculated as the difference between smoothed annual indices for 1974 and 2013 (i.e. the breeding seasons immediately following the beginning and end of the time-series), derived from the joint Common Bird Census/Breeding Bird Survey (CBC/BBS) trends for England30. CBC and BBS use structured, stratified protocols to monitor national bird populations and inform the UK Biodiversity Indicators. Trends were not available for eight feeder-user species, which included winter migrants and species not well covered by the CBC.
Phylogenetic generalised least squares regression (PGLS) was used to test the relationship between changes in feeder use and national population size (n = 31 species) while accounting for phylogenetic structure. Bird phylogeny was based on a pruned consensus tree produced by majority rules using 100 phylogenetic trees randomly extracted from the avian phylogenies developed by Jetz et al.56 (Supplementary Fig. 5). Within the pruned tree, Eurasian nuthatch (Sitta europaea) was represented by phylogenetically similar white-tailed nuthatch (S. himalyensis)57 and lesser redpoll (Carduelis cabaret) by common redpoll (C. flammea)58 since these species were absent from the global avian tree. Maximum likelihood was used to estimate the PGLS model’s Pagel’s lambda, giving a measure of the phylogenetic covariation between the predictor and response. Pagel’s lambda values of zero indicate that the predictor-response relationship is unrelated to phylogeny, whereas high lambda values indicate a strong similarity in the relationship between closely related species. To ensure that the error associated with each annual index value was accounted for within the final model outcome, we used a bootstrap procedure to produce 95% confidence limits around the PGLS regression line. For each bootstrap sample (n = 1000), new values of feeder use and population index for the beginning and end of the time series were drawn at random from the confidence limits around their original estimates, and then used to recalculate estimates of change. The PGLS model was fitted to each bootstrap sample with lambda set at the value estimated for the original model, then 95% confidence limits were calculated from the set of regression coefficients produced.
PGLS, using the pruned consensus tree and maximum likelihood to estimate Pagel’s lambda, was also used to test for differences in population trends between feeder-users and non-feeder users. Here, we used the 1994-2012 habitat-specific trends from Sullivan et al.31 for all breeding birds that are associated with urban areas of Britian and therefore have frequent access to garden bird feeders. These trends were available for 72 species, 33 (46%) of which had been defined as feeder-users. Feeder-users without trends were either winter migrants or did not have suitable data for population estimation. We aggregated the trends for 12 individual habitats to derive two broader trends of interest, urban and non-urban. More specifically, urban trends were estimated using a weighted average of the trends for suburban/urban settlements and rural settlements, accounting for their habitat availability. Non-urban trends were estimated using an weighted average of the trends from all other habitat types (deciduous woodland, mixed woodland, coniferous woodland, upland semi-natural open habitats, lowland semi-natural open habitats, arable farmland, pasture, mixed farming, wetlands and flowing water), accounting for their availability31.
To account for temporal auto-correlation, all trend analyses (described above) included an AR(1) correlation structure. The AR(1) correlation structure was found to be optimal for time series modelling across the different response variables, based on the comparison of models with and without different autocorrelation structures (AR1 or AR2) using AIC and the examination of auto-correlation plots for the model residuals. There was no evidence of spatial autocorrelation in bird community indices across gardens within years, according to spline correlograms fitted to the raw data using the ncf R package59. When using GAM(M)s to investigate non-linear temporal trends, year was always fitted in the form of a thin-plate regression spine with a maximum of five degrees of freedom and the gamma parameter was fixed at 1.4 to reduce over-fitting. Generalised least squares (GLS, national-scale data) and linear mixed models (LMM, garden-scale data) were used to determine the significance of linear temporal trends when GAM(M)s fitted to the same data did not indicate non-linearity (e.g. the smoothed trend had one degree of freedom, was not significant, or did not deviate enough from the linear trend to be deemed ecologically meaningful). Significance was determined using maximum likelihood, Wald statistics, χ2 and F-tests as appropriate with alpha set at 0.0560. To identify periods of significant change within non-linear trends, where the rate of change (the slope) was distinguishable from zero given the uncertainty of the model, we estimated the first derivatives of the GAM temporal smooth61,62. A significant change was assumed where the 95% confidence intervals of the first derivatives excluded zero61. All analyses were performed using R version 3.4.363. Trend analyses used the packages mgcv64 and nlme65, and phylogenetic comparative analyses used APE66, phytools67 and caper68.
The Garden Bird Feeding Survey data and the bird feeding industry data that support the findings of this study are available upon reasonable request from the British Trust for Ornithology, https://www.bto.org/research-data-services. The UKCP09 temperature data used are available under licence from the British Met Office, https://www.metoffice.gov.uk/climate. The avian phylogeny data used are publicly available from BirdTree.org, https://www.BirdTree.org.
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We thank all the amateur ornithologists who have contributed to the collection of bird data; the past and present GBFS administrative team, particularly A. Prior, and C. Simm for overseeing the survey; K.W. Smith and L. Smith for discussions about and help with collecting the bird food industry data; D. Massimino for sharing the CBC/BBS bird trend annual indices; S. Gillings for help with examining bird spatial range shifts; J.W. Pearce-Higgins, S. Bearhop and K. Metcalfe for comments and suggestions on previous versions of the manuscript. This paper is the product of an institutional fellowship award (to K.E.P.), made possible thanks to a generous legacy donation to the BTO from Maxwell Hoggett.
The authors declare no competing interests.
Journal peer review information: Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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Plummer, K.E., Risely, K., Toms, M.P. et al. The composition of British bird communities is associated with long-term garden bird feeding. Nat Commun 10, 2088 (2019). https://doi.org/10.1038/s41467-019-10111-5
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Educational Codeforces Round 68 B Yet Another Crosses Problem
memory limit per test : 256 megabytes
input : standard input
output : standard output
You are given a picture consisting of $nn$ rows and $m$ columns. Rows are numbered from $1$ to $n$ from the top to the bottom, columns are numbered from $1$ to $m$ from the left to the right. Each cell is painted either black or white.
You think that this picture is not interesting enough. You consider a picture to be interesting if there is at least one cross in it. A cross is represented by a pair of numbers $x$ and $y$ , where $1≤x≤n$ and $1≤y≤m$, such that all cells in row $x$ and all cells in column $y$ are painted black.
For examples, each of these pictures contain crosses:
The fourth picture contains 4 crosses: at $(1,3)$ , (1,5)(1,5), $(3,3)$ and $(3,5)$ .
Following images don’t contain crosses:
You have a brush and a can of black paint, so you can make this picture interesting. Each minute you may choose a white cell and paint it black.
What is the minimum number of minutes you have to spend so the resulting picture contains at least one cross?
You are also asked to answer multiple independent queries.
The first line contains an integer $q$ (1≤q≤5⋅1041≤q≤5⋅104) — the number of queries.
The first line of each query contains two integers $nn$ and $m$ (1≤n,m≤5⋅1041≤n,m≤5⋅104, n⋅m≤4⋅105n⋅m≤4⋅105) — the number of rows and the number of columns in the picture.
Each of the next $nn$ lines contains $m$ characters — ‘.’ if the cell is painted white and ‘*’ if the cell is painted black.
It is guaranteed that $\sum n\le5\times10^4, \sum n\times m \le 4 \times 10^5$.
Print $q$ lines, the $i$-th line should contain a single integer — the answer to the $i$-th query, which is the minimum number of minutes you have to spend so the resulting picture contains at least one cross.
The example contains all the pictures from above in the same order.
The first 5 pictures already contain a cross, thus you don’t have to paint anything.
You can paint $(1,3)$ , $(3,1)$ , $(5,3)$ and $(3,5)$ on the 66-th picture to get a cross in $(3,3)$ . That’ll take you 44 minutes.
You can paint $ (1,2)$ on the $7$-th picture to get a cross in $(4,2)$ .
You can paint $(2,2)$ on the 88-th picture to get a cross in $(2,2)$. You can, for example, paint $(1,3)$ , $(3,1)$ and $(3,3)$ to get a cross in $(3,3)$ but that will take you 33 minutes instead of $1$ .
There are 9 possible crosses you can get in minimum time on the 99-th picture. One of them is in $ (1,1)$ : paint $ (1,2)$ and $(2,1)$ .
对我来说毒瘤题目啊，B 题，难受。一开始用的暴力的方法，wa 在了 2，一直找不到自己错在了哪里。眼看着别人一个一个过了这题，自己还一直卡在这，真的难受。几乎卡了整场比赛，最后没有时间看 D 题，赛后几乎秒出了Ｄ题。诶，还是太菜了，如果不卡这题的话应该能上很多分。
分别统计出每行每组 ‘.’ 的数量，最后遍历每个符号，用
r[i] + r[j] - (maze[i][j] == '.') 来更新最小值。 | <urn:uuid:94fc34c8-bc48-440b-a3ad-a758eb35f74a> | CC-MAIN-2023-14 | http://zhiyi.live/2019/07/21/Educational-Codeforces-Round-68-B-Yet-Another-Crosses-Problem/ | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945144.17/warc/CC-MAIN-20230323100829-20230323130829-00601.warc.gz | en | 0.784393 | 1,203 | 2.9375 | 3 |
These are some unfinished notes that I have taken while reading the Children’s Machine by Seymour Papert. Hope that someday I will weave them into something more fluid.
Why, though a period when so much human activity has been
revolutionized, have we not seen comparable change in the way we
help our children learn?
One could indeed make kitchen math part of the School by making School part of the kitchen.
Are there any snakes in the house?
Yes there are, there are zero snakes in the house!
So. negative numbers are numbers too, and their reality grows in the course of playing with turtle.
You can’t retire from a good project simply because it has succeeded.
Constructionism: It does not call in question the value of instruction as such
The kind of knowledge that children most need is the knowledge that will help them get more knowledge.
If the children really want to learn something, and have the opportunity to learn it in its use, they do so even if the teaching is poor.
Constructionism looks more closely than other educational -isms at the idea of mental construction. It attaches a special importance to role of constructions in the world as a support for those in the head, thereby becoming less of a purely mentalistic doctrine. It also takes the idea of constructing in the head more seriously by recognizing more than one kind of construction and by asking questions about the methods and materials used.
How can one become expert in constructing knowledge?
What skills are required?
Are these skills different for different kinds of knowledge?
School math, like the ideology, though not necessarily the practice, of modern science, is based on the idea of generality – the single, universally correct method that will work for all problems and for all people.
Use what you’ve got, improvise, make do.
The natural context for learning would be through particiaption in other activities other than math itself.
The reason is that the educators who advocate imposing abstract ways of thinking on students almost practice what they preach – as I tried to do in adopting a concrete style of writing – but with very different effects.
But however concrete their data, any statistical question about “the effect” of “the computer” is irretrievably abstract. This is because all such studies depend on use of what is known as the “scientific method,” in form of experiments designed to study the effect of one factor which is varied while taking great pains to
keep everything else same. … But nothing could be more absurd than an experiment in which computers are placed in a classroom where nothing else has changed. The entire point of all the examples I have given is that the computers serve best when they allow everything to change.
The concept of highly rigorous and formal scientific method that most of us have been taught in school is really an ideology proclaimed in books, taught in schools and argued by philosophers but widely ignored in actual practice of science.
They count the same, but it’s more eggs.
My overarching message to anyone who wishes to influence, or simple understand, the development of educational computing is that it is not about one damn product after another (to paraphrase a saying
about how school teaches history). Its essence is the growth of a culture, and it can be influenced constructively only through understanding and fostering trends in this culture.
I would be rather precisely wrong than vaguely right.
– Patrick Suppes
It had been obvious to me for a long time that one of the major difficulties in school subjects such as mathematics and science is that School insists on the student being precisely right. Surely it is necessary in some situations to be precisely right. But these situations cannot be the right ones for developing the kind of thinking that I most treasure myself and many creative people I know.
What computers had offered me was exactly what they should offer children! They should serve children as instruments to work with and to think with, as means to carry out projects, the source of concepts to think new ideas. The last thing in the world I wanted or needed was a drill and practice program telling me to do this sum of spell that word! Why should we impose such a thing on children?
The opportunity for fantasy opens the to a feeling of intimacy
with the work and provides a peep at how emotional side of
children’s relationship with science and technology could be very
different from what is traditional in School. Fantasy has always
been encouraged in good creative writing and art
classes. Excluding it from science is a foolish neglect of an
opportunity to develop bonding between children and science.
Errors can become sources of information.
Although the ultimate goal was the same, the means were more than
just qualitatively different; they were episte,mologically
different in that they used a different way of thinking.
Traditional epistemology is an epistemology of precision:
Knowledge is valued for being precise and considered inferior if
it lacks precision. Cybernetics creates an epistemology of
The real problem was that I was still thinking in terms of how to
“get the children to do something.” This is the educator’s
instinctive way of thinking: How can you get children to like
math, to write wonderfully, to enjoy programming, to use
higher-order thinking skills? It took a long time for me to
understand in my gut, even after I was going around saying it,
that Logo gaphics was successful because of the powet it /gave/ to
children, not because of the performance it /got from/ them.
Children love constructing things, so let’s choose a construction
set and add to it whatever is needed for these to make cybernetic
What will they [children] learn from it [Logo]? And won’t it favor
boys over girls?
The first question concerns what piece of the school curriculum is
being learned but I attach the most importance to such issues as
children’s relationship with technology, then idea of learning,
their sense of self. As for the gender issue, I am thinking more
about, how in the long run comoutational activities will affect
gender than how the gener will affect the activities.
Their work provies good examples of material that overlaps with
School science and math, and of an alternative style applied to
these subjects – ins
tead of formal style that uses rules, a
concrete style that uses objects.
It is worth noting that the students appreciated the
self-organizing nature of the traffic jam only because they had
written the programs themselves. Had they been using a packaged
simulation, they would have had no way of knowing the elegant
simplicity of the programs underlying the jam.
Emergent stuctures often behave very differently than the elements
that compose them.
The cathedral model of education applies the same principle to
building knowledge structures. The curriculum designer in cast in
the role of a “knowledge architect” who will specify a plan, a
tight progra, for the placement of “knowledge brick’s” in
What is typical of emergently programmed systems is that
deviations from what was expected do not cause the wholw to
collapse but provoke adaptive responses.
We are living with an edicational systsem that is fundamentally as
irrational as the command economy and ultimately for the same
reason. It does not have capacity for local adaptation that is
necessary for a complex system even to function effieciently in a
changing environment, and is doubly necessary for such a system to
be able to evolve.
Defininf educational success by test scores is not very different
from couting nails made rather than nails used.
But calling hierarchy into question is the crux of the problem if
Each of these cases suggests ways in which a little school created
in a militant spirit can mobilize technology as an assertion of
I could continue in this spirit, but this may be enough to make
the point that little schools could give themselves a deeper and
more conscious specific identity. Everything I have said in this
book converges to suggest that this would produce rich
intellectual environments in which not only children and teachers
but also new ideas about learning would develop together.
I see little schools as the most powerful, perhaps an essential,
route to generating variety for the evolution of education.
The prevailing wisdom in the education establishment might agree
with the need for variety but look to other sources to provide
it. For example, many – let us call them the Rigorous
Researchers – would say that the proper place for both variation
and selection is in the laboratory. On their model, researchers
should develop large numbers of different ideas, test them
rigorously, select the best, and disseminate them to schools.
In my view this is simply Gosplan in disguise.
The importance of the concept of the little school is that it
provides a powerful, perhaps by far the most powerful, strategy to
allow the operation of the principle of variation and selection.
This objection depends on an assumption that is at the core of the
technicalist model of education: Certain procedures are the best,
and the people involved can be ordered to carry them out. But even
if there were such a thing as “the best method” for learning, it
would still only be the best, or even mildly good, if people
believed in it. The bueracrat thinks that you can make people
beleive in something by issuing orders.
The design of learning environment has to take account of the
cultural environment as well, anad its implementation must make
serious effort at involvement of the communities in which it is to
It is no longer necessary to bring a thousand children together in
one building and under one administration in order to develop a
sense of community.
I do not see that School can be defended in its social role. It
does not serve the functions it claims, and will do so less and
Talking about megachange feels to them like fiddling when Rome
burns. Education today is faced with immediate, urgent
problems. Tell us how to use your computer to solve some of the
many immediate practical problems we have, they say.
Impediments to change in education such as, cost, politics, the
immense power of the vested interests of school bureaucrats, or lack
of scientific research on new forms of learning.
Large number of teachers manage to create within the walls of their
own classrooms oases of learning profoundly at odds with the
education philosophy espoused by their administrators…
But despite the many manifestations of a widespread desire for
something different, the education establishment, including most of
its research community, remains largely committed to the educational
philosophy of the late nineteenth and early twentieth centuries, and
so far none of those who challenge these have hallowed traditions
has been able to loosen the hold of the educational establishement
on how children are taught.
Do children like games more than homework because, the later is
harder than the former?
Most [games] are hard, with complex information – as well as
techniques – to be mastered, in the information often much more
difficult and time consuming to master than the technique.
These toys, by empowering children to test out ideas about working
within prefixed rules and structures in a way few other toys are
capable of doing, have proved capable of teaching students about the
possibilities and drawbacks of a newly presented system in ways many
adults should envy.
In trying to teach children what adults want them to know, does
School utitlize the way human beings most naturally learn in
If it has so long been so desperately needed, why have previous
calls for it not caught fire?
Is reading the principal access route to knowledge?
Ask a symapathetic adult who would reward her curiosity with praise.
Literacy is being able to read and write. Illiteracy can be
remedied by teaching children the mechanical skill of decoding black
marks on white paper.
/Letteracy/ and /Letterate/
Reading from Word to Reading from World
… the Knowledge Machine offers children a transition between
preschool learning and true literacy in way that is more personal,
more negotiational, more gradual, and so less precarious thant the
abrupt transition we now ask chidlrento malke as they move from
learning through direct experience to using the orinted word as a
source of important information.
…. School’s way is the only way beacause they have never seen or
imagined convincing alternatives in the ability to impart certain
kinds of knowledge.
* Babies learn to talk without curriculum or formal lessson
develop hobbies at skills without teachers
* social behavior is picked up other than through classroom
Parable of the Automobile:
… certain problems that had been abstract and hard to grasp
became concrete and transparent, and certain projects that had
seemed interesting but too complex to undertake became
Paulo Freire: “Banking model” information is deposited in
child’s mind like money in a savings account.
/Tools/ for creating new experiments in effective fashion.
* Dewey: children would learn better if learning were truly a
part of living experience
* Freire: chidlren would learn better if they were truly in
charge of their own learning processes
* Piaget: intelligence emerges from an evolutionary process in
which many factors must have time to find their equilibrium.
* Vygotsky: Conversation plays a crucial role in learning.
Why did the discovery method fail?
By closing off a much larger basis of knowledge that should
serve as a foundation for formal mathematics taught in school
and perhas a minimal intuitive basis directly connected with
The central problem of mathematics education is to find ways
to draw on the child’s vast experience of oral
mathematics. Computers can do this.
Giving chidlren opportunity learn and use mathematics in a
nonformalized way of knowing encourages rather than inhibits
the eventual adoption of formalized way, just as the XO,
rather than discouraging reading, would eventually stimulate
children to read.
The design process is not used to learn more formal geometry.
Traditionally teh art and writing classes are for fantasy but
science deals with facts; union of technology with biology.
It allows them to enter science through a region where
scientific thinking is most like there own thinking.
Reading biographies and iterrogating friends has convinced me
that all successful learners find ways to take charge of their
early lives sufficiently to develop a sense of intellectual
Piaget’s first article: a paradox?
Schools have inherent tendency to infantilize the children by
placing them in a position of have to do so as they are told,
to occupy themselves with work dictated by someone else and
that, morever, has no intrinsic value – school work is done only
because the designer of the curriculum decided that doingthis
work would shape the doer into a desirable form[for the
NatGeo: Kidnet??Robert Tinker
Researchers, following the so-called scientific method of
using controlled experiments, solemnly expose the children to
a “treatment” of some sort and then look at measurable
results. But this flies in the face of all common knowledge
of how human beings develop.
The method of controlled experimentation that evaluates an
idea by implementing it, taking care to keep everything else
the same, and measuring the result, may be an appropriate way
to evaluate the effects of a small modification. However, it
can tell us nothing about ideas that might lead to deep
change… It will be steered less by the outcome of tests and
measurements than by its participant’ intuitive understanding.
The prevalent literal-minded, “what you see is what you get”
approach measuring the effectiveness of computers in learning
by teh achievements in present-day classroons makes it certain
that tomorrow will always be prisoner of yesterday.
Example of Jet attached to horse wagon.
… most people are more interested in what they learn than in how
the learning happens.
But math is not about feeling the relationship of your body to
Turtle lets you do this!
Intellectual work is adult child’s play.
Example that if observation of schools in some country where
only one writing instrument could be provided for every fifty
students suggested that writing does not significantly help
The change requires a much longer and more social computer
experience than is possible with two machines at the back of
/Balkanized Curriculum and impersonal rote learning/
What had started as a subversive instrument of change was
neutralized by the system and converted into an instrument of
Schools will not come to use computers “properly” because
researchers tell it how to do so.’
It is characteristic of a conservative systems that
acoomodation will come only when the opportunities of
assimilation have been exhausted.
* Immediate Feedback
* Individualized instruction
* Neutrality *
CAI will often modestly raise test scores, especially at the low end
of the scale. But it does without questioning the structure or the
educational goals of the traditional School.
Today, because it is the 15th Monday of your 5th grade year,
you have to do this sum irrespective of who you are or what
you really want to do; do what you are told and do it the
way you are told to do it.
Piaget was the theorist of learning without curriculum;
School spawned the projectof developing a Piagetian curriculum.
The central issue of change in education is the tension
between technicalizing and not technicalizing, and here the teacher
occupies the fulcrum position.
Shaw: He who can, does; he who cannot, teaches.
The system defeats its own purpose in attempt to enforce them.
School has evolved a heirarchical system of control that
sets narrow limits within which the actors – administators
as well as teachers – are allowed to exercise a degree of
Hierarchy vs. Heterarchy
The major obstacle in the way of teachers becoming learners
is inhibition about learning.
The problem with `developed’ countries as opposed to `developing’ ones
is that the developed countries are already there, there is no further
In education, the highest mark of success is not having imitators but
inspiring others to do something else.
As long as there is afixed curriculum, a teacher has no need to become
in the question what is and what is not mathematics.
Society cannot afford to keep back its potentially best teachers
simply because some. or even most, are unwilling.
The how-to-do-it literature in the constructivist subculture is almost
as strongly biased to the teacher side as it is in the instructionist
/Mathematikos/ disposed to learn
/mathema/ a lesson
/manthanein/ to learn
\ldots mathetics is to learning what heuristics is to problem solving.
What is that feeling when you look at a familiar object, with a sense
that you are looking at the object for the first time?
It is /jamais vu/.
Attempts by teachers and textbook authors to connect school fractions
with real life via representations as pies simply reuslyed in a new
* What is the difference in learning at school and all other learning?
Generally in life, knowledge is acquired to be used. But school
learning more often fits Freire’s apt metaphor: Knowledge is treated
like money, to be put away in a bank for the future.
* What does /Computer Literacy/ mean?
* The Technology of the Blackboard and The Technology of The Computer
* Lines You can use:
The computer to program the student…
The student to program the computer…
Computer as an expensive set of flash cards.
If the students scores improve, our approach must be right.
Self-directed activities versus carefully guided ones
If the scores improve does it mean that the strategy is effective/
approach is right?
Heterarchical versus Hierarchical
Totalitarian Education or Trivialized Education | <urn:uuid:1d669837-8c25-41b7-9a94-0728b02f6906> | CC-MAIN-2023-14 | https://damitr.org/category/xo/ | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949355.52/warc/CC-MAIN-20230330163823-20230330193823-00601.warc.gz | en | 0.951936 | 4,521 | 2.953125 | 3 |
More often than I care to admit, I find myself sitting in the audience of a maths lecture or seminar completely and utterly lost as to what the speaker is going on about. What are they talking about? How does this relate to stuff I know about? Where does this fit within the sphere of mathematics as a whole? In fact, most of the time I am lost beyond the first slide of a presentation. In an endeavour to minimise the possibility that audience members would experience this feeling that I know all too well, I recently introduced myself at the start of a talk with this slide:
You could be forgiven for remarking “My, what a beautiful Venn diagram you have there!” Indeed, I too was under the impression that what I had created was in fact a Venn diagram.
You almost certainly will have come across Venn diagrams before. Though in case you have not, allow me to briefly introduce them. Venn diagrams are widely-used visual representation tools that show logical relationships between sets. Popularised by John Venn in the 1880s, they illustrate simple relations between sets, and are nowadays used across a multitude of scenarios and contexts. And no one can be blamed for their wide usage—they truly are things of beauty. But who was John Venn? And how did he come to create such an iconic tool that’s used so broadly today?John Venn (1834–1923) was an English mathematician, logician and philosopher during the Victorian era. In 1866, he published The Logic of Chance, a groundbreaking book which advocated the frequency theory of probability—the theory that probability should be determined by how often something is forecast to occur, as opposed to ‘educated’ assumptions.
The Victorian era in general saw significant shifts in the way that science and experimental measurements were thought about. It was at this point in history that science began to shift towards a new paradigm of statistical models, rather than exact descriptions of reality. Previously, scientists had believed that mathematical formulas could be used to describe reality exactly. But nowadays, we talk about probabilities and distributions of values, and not about certainties. We now interpret individual experimental measurements knowing that, no matter how precise or controlled an experiment is, some degree of randomness always exists. Using statistical models of distributions is what enables us to describe the mathematical nature of that randomness.
But I digress—back to Venn diagrams. When Venn actually first created his namesake diagrams, he referred to them as Eulerian circles, after everyone’s favourite Swiss mathematician Leonard Euler, who created similar diagrams in the 1700s. And this is where, I regret to inform you, the thing is—and I’m very sorry to be the one to tell you—that Venn diagram up there? Not actually a Venn diagram.
By definition, in a Venn diagram, the curves of all the sets shown must overlap in every possible way, showing all possible relations between the sets, regardless of whether or not the intersection of the sets is empty: $\emptyset$. Venn diagrams are actually a special case of a larger group of visual representations of sets: Euler diagrams. Euler diagrams are like Venn diagrams, except they do not necessarily show all relations.
When thinking about Venn diagrams, we normally picture something like my beautiful introductory slide above, right? Namely, there are circles, and they overlap. The interior of each of the circles represents all of the elements of that set, while the exterior represents things that are not in that set. For example, in a two-set Venn diagram, one circle may represent the group of all Chalkdust readers, while the other circle may represent the set of tea drinkers. The overlapping region, or intersection, would then represent the set of all Chalkdust readers that drink tea (a verifiably non-empty set). It is common for the size of the circles to represent relative size of the set that circle is representing (eg one’s undergraduate maths education being much (much) smaller compared with the sphere of mathematics as a whole).
We also commonly see nested Venn diagrams, where one set is completely situated within another set (again, one’s undergraduate maths education being entirely nested in the realm of mathematics as a whole [though this is debatable—I’ll save this for the next Chalkdust article]). But in a traditional, true-to-definition Venn diagram, every single possible combination of intersections of the sets must be visually displayed…
(While we cannot verify whether or not there exist cats that are also Chalkdust readers and/or tea drinkers, the Venn diagram insists we show all possible intersections.)
It is actually mathematically impossible to draw a Venn diagram exclusively with circles for more than three sets. If we add a fourth set below, no matter how you move the four circles around, you can never find a region that isolates only the intersection of diagonally opposite sets—cats and tea drinkers (or Chalkdust readers and accordion players). Formal mathematical proof is LeFt aS An eXeRcIsE fOr ThE rEaDeR.
As you can see then on the right, for high numbers of sets (‘high numbers’ $=$ greater than three), unfortunately some loss of symmetry in the diagrams is unavoidable. John Venn experimented with ellipses for the four-set case in an attempt to cling onto some diagrammatic elegance and symmetry. He also devised Venn’s constructions which gave a construction for Venn diagrams for any number of sets. These constructions started with the three-set circular Venn diagram and added arc-like shapes which weaved between each of the previous sets to create every possible logical intersection. These constructions quickly become quite dizzying (see the loopiness of Venn’s construction for six sets):
So what can we do if we don’t want to weave back and forth so dizzyingly for higher numbers of sets? Enter: Edwards–Venn diagrams. Anthony William Fairbank Edwards (1935–) constructed a series of Venn diagrams for higher numbers of sets. He did this by segmenting the surface of a sphere.
For example—as you can see on the right—three sets can be easily represented by taking three hemispheres of the sphere at right angles ($x = 0$, $y = 0$ and $z = 0$). He then added a fourth set to the representation, by taking a curve similar to the seam on a tennis ball, which winds up and down around the equator, and so on.
The resulting sets can then be projected back to a plane, to give cogwheel diagrams, with increasing numbers of teeth for more and more sets represented:
So finally, to conclude this article, I present to you my new and improved introductory (actually-a-Venn) diagram:
While I appreciate the poetic implication that the realms of my respective research groups (fluid dynamics and behavioural genomics) weave in and out of my PhD project, which is nested neatly in the centre, in reality the fact is that many many of these intersections are quite empty.
Please consider this article in support of my upcoming petition to make it mandatory for academics to introduce themselves at the start of every talk with a Venn (or Euler) diagram.
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In conversation with Dominique SleetEllen Jolley learns how to run a maths outreach programme | <urn:uuid:72482170-80cd-4086-b80d-2f0f0b7f6361> | CC-MAIN-2023-14 | https://chalkdustmagazine.com/features/on-the-cover-vhat-vhere-venn/ | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949533.16/warc/CC-MAIN-20230331020535-20230331050535-00202.warc.gz | en | 0.946868 | 1,647 | 3.25 | 3 |
DNS Lookup tool finds all DNS records of a given domain name. The records include but not limited to A, AAAA, CNAME, MX, NS, PTR, SRV, SOA, TXT, CAA. Enter a domain name and select record type to get a specific record or keep default to fetch all DNS records.
Jul 09, 2020 · The network settings for your computer, router, or access point allow you to specify which DNS servers—primary and secondary—to use. By default, these are likely set by your internet service provider , but there may be faster ones you can use. The next very popular DNS Service on our list is “Level3”. It is considered as the best after Google and Open DNS service provider. In order to use this level3 DNS server, one should configure their Domain Name System settings to the following IP addresses. Favored DNS Server: 220.127.116.11; Exchange DNS Server: 18.104.22.168 ABOUT DNS LOOKUP. This test will list DNS records for a domain in priority order. The DNS lookup is done directly against the domain's authoritative name server, so changes to DNS Records should show up instantly. By default, the DNS lookup tool will return an IP address if you give it a name (e.g. www.example.com) Jul 27, 2017 · Hi All, I'm having some fun with a power-shell script for setting the DNS settings of clients $dnsserver = (,"W.X.Y.Z") $Computer = Get-Content "c:\users\path\to\my.csv"
Gather DNS settings from remote servers using PowerShell This script is a continuation of the script in the “Performing Advanced Server Management” chapter in theWindows PowerShell 2.0 Bible., which itself was a modified version of a script I presented on my blog on May 12th, 2010: PowerShell WMI Gather DNS settings for all ServersThis
This command gets a DNS server configuration. Example 2: Get local DNS server configuration and then export it. PS C:\> Get-DnsServer | Export-Clixml -Path "c:\config\DnsServerConfig.xml" This command gets the DNS server configuration on the local server and passes it to the Export-Clixml cmdlet to be translated into an XML file. Parameters How (and Why) to Change Your DNS Server | PCMag May 17, 2019
Jun 18, 2020
Use Powershell or CMD to list DNS Servers in Domain. A sample way out is open CMD or Powershell and start the NSLOOKUP utilitiy. Next, In order to get the list of DNS Servers in domain, set the type to NS and finally, type your Root Domain Name and press Enter. Above list will list DNS Server in your domain. How to Fix DNS Server Not Responding Errors Jun 17, 2020 How to Double Your Internet Speed With One Settings Change Jul 09, 2020 | <urn:uuid:1da49682-1cda-49b9-8c41-eab11f41e88e> | CC-MAIN-2023-14 | https://goodvpnfeltgs.netlify.app/galinol6302vana/get-dns-settings-706.html | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949533.16/warc/CC-MAIN-20230331020535-20230331050535-00202.warc.gz | en | 0.8113 | 620 | 2.515625 | 3 |
Knights in Fen
There are black and white knights on a 5 by 5 chessboard. There are twelve of each color, and there is one square that is empty. At any time, a knight can move into an empty square as long as it moves like a knight in normal chess (what else did you expect?).
Given an initial position of the board, the question is: “what is the minimum number of moves in which we can reach the final position”, which is:
First line of the input file contains an integer $N$ ($N<14$) that indicates how many sets of inputs are there. The description of each set is given below:
Each set consists of five lines; each line represents one row of a chessboard. The positions occupied by white knights are marked by $0$ and the positions occupied by black knights are marked by $1$. The space corresponds to the empty square on board.
There is no blank line between the two sets of input.
The first set of the sample input below corresponds to this configuration:
For each set your task is to find the minimum number of moves leading from the starting input configuration to the final one. If that number is bigger than $10$, then output one line stating
Unsolvable in less than 11 move(s).
otherwise output one line stating
Solvable in $n$ move(s).
where $n \leq 10$.
The output for each set is produced in a single line as shown in the sample output.
|Sample Input 1||Sample Output 1|
2 01011 110 1 01110 01010 00100 10110 01 11 10111 01001 00000
Unsolvable in less than 11 move(s). Solvable in 7 move(s). | <urn:uuid:f341288c-d430-4879-9785-08f2c7b04ba6> | CC-MAIN-2023-14 | https://open.kattis.com/contests/ma2nhe/problems/knightsfen | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945472.93/warc/CC-MAIN-20230326111045-20230326141045-00202.warc.gz | en | 0.911431 | 383 | 3.4375 | 3 |
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