Like Path A but cut the steps the things that you think won’t be necessary.
Like B but with some additions
Endnote: I think there are still quite a lot more other topics like the Algorithms and Data Structure rabbit hole. I still can’t figure it out how to put those in each path without making them feel so daunting. Feel free to discuss your thoughts.
Most of these I learned from Mr. Aiviet Nguyen and some parts of the blog is the direct translation of his writings in Vietnamese.
]]>Fortunately, an educator in Vietnam already came up with a Physics curriculum for CS majors. Here are the main notes I took from his blog post written in Vietnamese.
Learning Physics even if you are a CS major will be beneficial because:
You don’t need to study Physics the traditional way(which is almost impossible if you are also majoring CS), just focus on the core ideas, concepts and their applications. After the having a grasp of the basics, you can try to focus more on the topics that you are interested in. Moreover, the following curriculum should be sufficient for giving you a decent Physics foundation, which will help you grasp the big picture of Physics, while providing you with enough foundational knowledge to help you be open to new computing technology(that are deeply Physics) like Quantum Computing or Brain Simulation.
Oscillation and motion
Deep dive: Structures in the universe
Electromagnetic radiation and light
Relativity theory and Positioning technology
Quantum theory and Quantum World
Energy and Spectroscopy
Semiconductor and Microprocessor
MOSFET technology
Magnetic Materials
Computer Memory
Measurement
Electronic Microscope, medical imaging
Pressure and heat sensor
Abnormal sound detection and noise filtering
Chemical sensor
Material analysis and environmental protection
Magnetic sensor
Radar signal analysis and environment monitoring
Laser
Design and making microchip
Graphic Display and Lighting
Advertising display and decoration
Fiber-optic
Application of Photonics Technology
The Physics foundations of Quantum Computing
Shor’s algorithm
Quantum Information
Quantum Cryptography
The Physics foundation of Brain Simulation and Computing
Hopfield network and Spin glass
I’ll try to include the materials, but for now I’ll just leave it here. (May 10 2023)
]]>Our biological existence, social world, economy, and religious traditions tell a compelling story of interrelatedness. As the great Argentinean author Jorge Luis Borges put it,“everything touches everything.”
We have taken apart the universe and have no idea how to put it back together. After spending trillions of research dollars to disassemble nature in the last century, we are just now acknowledging that we have no clue how to continue—except to take it apart further. This was the humble start of what’s behind many of the greatest scientific discoveries - the idea of Reductionism. Reductionism was the driving force behind much of the twentieth century’s scientific research. To comprehend nature, it tells us, we first must decipher its components. The assumption is that once we understand the parts, it will be easy to grasp the whole. But as we go deeper, the more we separate the already separated parts, the more we know that we know less than we have always thought. Perhaps it’s time to think of how we can pull all of the things back together, and try to study them as a whole, which implies that we now need a new paradigm for thinking that is different from the old-school Reductionism. Here, networks might have the answer.
In a network(also called Graph), there are nodes. These nodes thing are connected to each other through links, which together create a network of nodes interconnected to the others. Simple as that, but very often, a simple idea can be a total game-changer. Networks have properties, hidden in their construction, that limit or enhance our ability to do things with them. If the network is large, despite the links’ completely random placement, almost all nodes will have approximately the same number of links. Our society has somewhat the same properties where most of us, on average, will have the same numbers of social links, and the extremely social individuals are considered outliers.
“Everybody on this planet is separated by only six other people. Six degrees of separation. Between us and everybody else on this planet. The president of the United States. A gondolier in Venice…. It’s not just the big names. It’s anyone. A native in a rain forest. A Tierra del Fuegan. An Eskimo. I am bound to everyone on this planet by a trail of six people. It’s a profound thought…. How every person is a new door opening up into other worlds.” Not only are we connected, but we live in a world in which no one is more than a few handshakes from anyone else.
Even so, weak ties play a crucial role in our ability to communicate with the outside world. Hence, do value the those you are not so close with!
As there are several types of person when it comes to sociability, Node has different types too. Let’s now talk about the extrovert nodes - The Connectors or alternatively, The Hubs. These extrovert nodes are just nodes with lots of friends, lots of connections, in short, lots of links. Connectors are present in very diverse complex systems, ranging from the economy to the cell. They are a fundamental property of most networks, a fact that intrigues scientists from disciplines as disparate as biology, computer science, and ecology. In the case of our social network, Connectors(Hubs) are an extremely important component of it. They create trends and fashions, make important deals, spread fads, or help launch a restaurant. From Instagram(YouTube, TikTok, whatever) Influencers, Industry Leaders, Celebrity Tech CEO(Elon Musk), Worrying Billionaire(Bill Gates), Loved Politicians(ugh!, can’t think of anyone), Renowned Researchers, Nobel laureates, to Podcast Owners, etc., these people are the thread of society, smoothly bringing together different races, levels of education, and pedigrees. This is why hubs are so important when it comes to spreading the innovations. Innovations spread from innovators to hubs. The hubs in turn send the information out along their numerous links, reaching most people within a given social or professional network. Hubs, the integral components of scale-free networks(which we will discuss right away!), are the statistically rare, highly connected individuals who keep social networks together. With their numerous social contacts, they are among the first to notice and use the experience of the innovators. Though not necessarily innovators themselves, their conversion is the key to launching an idea or an innovation. If the hubs resist a product, they form such an impenetrable and influential wall that the innovation can only fail. If they accept it, they influence a very large number of people. As we will see, hubs are changing nearly everything we know regarding the spread of ideas, innovations, and viruses.
“Hubs cannot be explained by either of the graph models we have seen so far. Therefore, hubs force us to reconsider our knowledge of networks and to ask three fundamental questions: How do hubs appear? How many of them are expected in a given network? Why did all previous models fail to account for them? …..hubs are not rare accidents of our interlinked universe. Instead, they follow strict mathematical laws whose ubiquity and reach challenge us to think very differently about network.”
For sometimes, network was modeled as some sort of a static model, where nodes and their links are all randomly generated. That may sound simple, but this model was quite enough for a young research field at the time. But randomly generated static model does can hardly reflect reality. We need something new. Real networks are governed by two laws: growth and preferential attachment. Each network starts from a small nucleus and expands with the addition of new nodes. Then these new nodes, when deciding where to link, prefer the nodes that have more links. By discovering and incorporating the two mentioned new laws, network modeling had stepped one more step further, we are now talking about a network that grows and the links between its nodes are meaningful. Behold, we can now model a network in which new nodes stem from another, the most extrevert nodes get more and more links. The whole network can be described the by a few concentrated collections of Hubs and their fellow nodes. We see a concentration here, if you think that the more links one node has, the weathier it is becoming. In other words, as wealth concentrates at one place, the person who has that stock pile is getting richer over time. Does that sound familiar to you?
The static nature of the classical models had gone unnoticed until we were forced to incorporate growth. Similarly, randomness had not been a problem until the power laws required us to introduce preferential attachment. Understanding that structure and network evolution couldn’t be divorced from one another made it difficult to revert to the static models that dominated our thinking for decades. These shifts in thinking created a set of opposites: static versus growing, random versus scale-free, structure versus evolution.
The theory of evolving networks, developed in the past three years, represents a one-way sign in network modeling. By viewing networks as dynamical systems that change continuously over time, the scale-free model embodies a new modeling philosophy. The classic static models starting with Erdős-Rényi sought simply to arrange a fixed number of nodes and links such that the final web conforms to the network being modeled. This process is similar to drawing. Seated in front of a Ferrari, our task is to draw a picture that will allow anyone to recognize the car. Having a faithful drawing, however, doesn’t bring us any closer to understanding the processes that created the car in the first place. For that we need to know how to build one just like the original. This is exactly what the various evolving network models aim to accomplish. They capture how networks are assembled by reproducing the steps followed by nature when it created its various complex systems. If we correctly model the network assembly, our final network should closely match the reality. Thus our goals have shifted from describing the topology to understanding the mechanisms that shape network evolution.
Networks are not en route from a random to an ordered state. Neither are they at the edge of randomness and chaos. Rather, the scale-free topology is evidence of organizing principles acting at each stage of the network formation process. There is little mystery here, since growth and preferential attachment can explain the basic features of the networks seen in nature. No matter how large and complex a network becomes, as long as preferential attachment and growth are present it will maintain its hub-dominated scale-free topology.
But the scale-free model raised new questions. One in particular kept resurfacing: How do latecomers make it in a world in which only the rich get richer? The quest for the answer took us to a very unlikely place: the birth of quantum mechanics at the beginning of the twentieth century.(which I suggest you should get the book if you want to know more about)
In a competitive environment each node has a certain fitness. Fitness is your ability to make friends relative to everybody else in your neighborhood; a company’s competence in luring and keeping consumers compared to other companies; an actor’s aptitude for being liked and remembered relative to other aspiring actors; a Webpage’s ability to bring us back on a daily basis relative to the billions of other pages competing for our attention. It is a quantitative measure of a node’s ability to stay in front of the competition. Fitness may have genetic roots in people; it may be related to product and management quality for companies, to talent for actors, or to content for Websites. We can assign a fitness to each node in a network, mimicking its ability to compete for links.
In a competitive environment, fitness also plays a role: Nodes with higher fitness are linked to more frequently. A simple way to incorporate fitness into the scale-free model is to assume that preferential attachment is driven by the product of the node’s fitness and the number of links it has. Each new node decides where to link by comparing the fitness connectivity product of all available nodes and linking with a higher probability to those that have a higher product and therefore are more attractive. Between two nodes with the same number of links, the fitter one acquires links more quickly. If two nodes have the same fitness, however, the older one still has an advantage. In some networks the fittest node could theoretically grab all the links, leaving none for the rest of the nodes. The winner takes all.
Every network has its own fitness distribution, which tells us how similar or different the nodes in the network are. In networks where most of the nodes have comparable fitness, the distribution follows a narrowly peaked bell curve. In other networks, the range of fitnesses is very wide such that a few nodes are much more fit than most others.
Errors and failures typically corrupt all human designs. Natural systems are different. In general, natural systems have a unique ability to survive in a wide range of conditions. We can think of this ability as the robustness of the system. Although internal failures can affect their behavior, they often sustain their basic functions under very high error rates. This is in stark contrast to most products of human design, in which the breakdown of a single component often handicaps the whole device. For this reason, scientists from all disciplines have recognized the resilience of nature’s designs, raising the hope that we can exploit that convenience in human-made structures. Therefore, robustness—rooted in the Latin word robus, meaning“oak,” the symbol of strength and longevity in the ancient world—is an increasingly investigated topic in many fields.
Summary: As long as we thought of networks as random, we modeled them as static graphs. The scale-free model reflects our awakening to the reality that networks are dynamic systems that change constantly through the addition of new nodes and links. The fitness model allows us to describe networks as competitive systems in which nodes fight fiercely for links.
In the presence of fitness, the early bird is not necessarily the winner. Rather, fitness is in the driver’s seat, making or breaking the hubs. In the scale-free model the connectivity of nodes in the network increases as a square root of time. The fitness model predicts a very different behavior. It tells us that nodes still acquire links following a power law, tβ. But the dynamic exponent, β, which measures how fast a node grabs new links, is different for each node. It is proportional to the node’s fitness, such that a node that is twice as fit as any other node will acquire links faster because its dynamic exponent is twice as large. Therefore, the speed at which nodes acquire links is no longer a matter of seniority. Independent of when a node joins the network, a fit node will soon leave behind all nodes with smaller fitness. Google is the best proof of this: A latecomer with great search technology, it acquired links much faster than its competitors, eventually outshining all of them. Beauty over age.
Removing only a few nodes will have little impact on the scale-free dynamic network’s integrity. Yet, if the number of removed nodes reaches a critical point, the system abruptly breaks into tiny unconnected islands. These removed nodes, or in other words, node failures can easily break a net work into isolated, noncommunicating fragments. Failures in random networks offer an example of an inverse phase transition: There is a critical error threshold below which the system is relatively unharmed. Above this threshold, however, the network simply falls apart. Still, removing just some insignificant nodes might not be a big deal for the network, given that it has the robustness, and resilience originated from its scale-free nature. But sometimes, we do not need to remove a large number of nodes to reach the critical point. Disable a few of the hubs and a scale-free network will fall to pieces in no time. For example: ecosystems can easily survive random species deletions. If, however, the highly connected keystone species are removed, the ecosystem dramatically collapses. Therefore, hidden within their structure, scale-free networks harbor an unsuspected Achilles’ heel, coupling a robustness against failures with vulnerability to attack. The coexistence of robustness and vulnerability plays a key role in understanding the behavior of most complex systems.
When a network acts as a transportation system, a local failure shifts loads or responsibilities to other nodes.We call these cascading failures. If the extra load is negligible, it can be seamlessly absorbed by the rest of the system, and the failure remains effectively unnoticed. If the extra load is too much for the neighboring nodes to carry, they will either tip or again redistribute the load to their neighbors. Either way, we are faced with a cascading event, the magnitude and reach of which depend on the centrality and capacity of the nodes that have been removed in the first round. Cascading failures are frequent phenomena in the economy.
However, our understanding of cascading failures is rather limited. Topological robustness is a structural feature of networks. Cascading failures, however, are a dynamic property of complex systems, a relatively uncharted territory.
Most illnesses, ranging from manic depression to cancer, are not caused by a single malfunctioning gene. Rather, several genes interacting through a complex network hidden within our cells are simultaneously responsible. If we want to understand life—and ultimately cure disease—we must think networks. The behavior of living systems can seldom be reduced to their molecular components. Our inability to find a single gene responsible for manic depression is the best illustration. In fact, there are no ‘good’ genes or ‘bad’ genes, but only networks that exist at various levels. Genes are known to play a structural role, determining the scope and make of proteins and passing this information in a hereditary manner to subsequent generations. Recently, however, scientists have discovered that genes also play an important functional role as members of a complex cellular network. This functional role is apparent only in the dynamic context in which an individual gene interacts with many other cellular components. The cell, like the Internet, appears to be a ‘scale-free network’: a small subset of proteins is highly connected(linked) and controls the activity of a large number of other proteins, whereas most proteins interact with only a few others. The proteins in this network serve as the nodes, and the most highly connected nodes are the hubs. In such a network, performance is almost unchanged by random removal of nodes. But such systems contain an Achilles’ heel.” The“Achilles’ heel” of a network, you’ll recall, refers to the vulnerability of its hubs. The inactivation of less connected molecules does not have draconian effects on the cell, whereas a mutation in the p53 molecule, one of the clear hubs of the cellular network, turns the cell cancerous and eventually kills the organism. This explains why combined pharmaceutical attacks on molecules that interact with the p53 molecule(a protein that acts as a tumor suppressor) have progressively more severe effects on the cell, resembling an attack on the p53 molecule itself.
More on p53: The p53 protein, created by the p53 gene, is a tumor suppressor. Just as your brakes allow you to stop your car, tumor suppressor genes act to slow and halt DNA replication and division into new cells. Healthy cells keep a small number of p53 molecules around. If radiation or some other injury damages the cell, more p53 is produced, preventing the progression of the cell through cell division. This gives the cell time to repair the damage before further copies of the malfunctioning cell can be produced. However, if the damage is irreparable, the p53 protein will activate a group of genes to kill the cell. If the cell’s brake—the p53 protein—malfunctions, the cell can run amok.
Changing the concentration of a chemical in your body via a drug could reduce the symptoms of a particular disease. However, since the cell is controlled by a complex network with small-world properties, a drug-induced perturbation inevitably affects many other chemicals, possibly creating undesired side effects. Patients treated for manic depression might die of heart disease, a condition they had never experienced before. Furthermore, the drug that causes heart disease for you could have no side effects on another individual. We all have different eye and hair colors and facial features, after all, so it is not surprising that we metabolize drugs differently as well. With the map of life in hand and with tools such as the recently developed DNA chips that monitor the links between the genes, doctors will be able to obtain a detailed list of all molecules and genes affected by a given drug. Exploring side effects will no longer be guesswork. We will have personalized medicine, allowing the marketing and approval of drugs that are effective for only 10 percent of the population and potentially lethal for everybody else.
A sparse network of a few powerful directors controls all major appointments in Fortune 1000 companies; a network of alliances determines the success in the biotech industry; the structure of the network within the firm is responsible for the organization’s ability to adapt to rapidly changing market conditions; and strategies taking advantage of the network nature of the consumer base lead to phenomenal successes in marketing. To comprehend how an economy truly works, we need to understand how corporations and other economic institutions run by these highly connected directors interact with each other. To accomplish such thing, understanding network effects become the key to survival in a rapidly evolving new economy.
As research, innovation, product development, and marketing become more and more specialized and divorced from each other, we are converging to a network economy in which strategic alliances and partnerships are the means for survival in all industries. The interfirm linkages of suppliers and subcontractors are well documented in southwestern Germany and north central Italy; Japanese business has long relied on interfirm collaborations to diffuse responsibilities for technological innovations; the Korean business model marries a whole array of diverse companies under the umbrella of large conglomerates; Silicon Valley regularly takes advantage of technology transfers by pairing up startups with established companies. These fluid alliances, which are periodically renegotiated as the marketplace shifts or the focus of the participants changes, offer a glimpse of the future of the world’s business environment.
In reality, the market is nothing but a directed network. Companies, firms, corporations, financial institutions, governments, and all potential economic players are the nodes. Links quantify various interactions between these institutions, involving purchases and sales, joint research and marketing projects, and so forth. In such networks, the actions of one node affect other nodes easily cripples whole segments of the network. The weight of the links captures the value of the transaction, and the direction points from the provider to the receiver. The structure and evolution of this weighted and directed network determine the outcome of all macroeconomic processes. Understanding macroeconomic interdependencies in terms of networks can help us to foresee and limit future crises. Thinking networks can teach us to monitor the path of the damage and to set firewalls by identifying and strengthening the nodes that can stop the spread of macroeconomic fires.
Walter W. Powell writes in Neither Market nor Hierarchy: Network Forms of Organization,“in markets the standard strategy is to drive the hardest possible bargain on the immediate exchange. In networks, the preferred option is often creating indebtedness and reliance over the long haul.” Therefore, in a network economy, buyers and suppliers are not competitors but partners. The relationship between them is often very long lasting and stable. The stability of these links allows companies to concentrate on their core business. If these partnerships break down, the effects can be severe. Most of the time failures handicap only the partners of the broken link. Occasionally, however, they send ripples through the whole economy.
Hierarchical thinking does not fit a network economy. In traditional organizations, rapid shifts can be made within the organization, with any resulting losses being offset by gains in other parts of the hierarchy. In a network economy each node must be profitable. Failing to understand this, the big players of the network game exposed themselves to the risks of connectedness without benefiting from its advantages. When problems arose, they failed to make the right, tough decisions, for example shutting down the supply line, and got into even bigger trouble.
All twentieth century corporations has the same structure: It is a tree, where the CEO occupies the root and the bifurcating branches represent the increasingly specialized and non-overlapping tasks of lower-level managers and workers. Responsibility decays as you move down the branches, ending with the drone executors of orders conceived at the roots. There are many problems with the corporate tree.
Apparently, companies aiming to compete in a fast-moving marketplace are shifting their organization structure from a static and optimized tree into a dynamic and evolving web, flat and with a lots of cross-links between the nodes, offering a more malleable, flexible command structure. Those that resist this change could easily be forced to the periphery. As valuable resources shift from physical assets to bits and information, operations move from vertical to virtual integration, the reach of businesses increasingly expands from domestic to global, the lifetime of inventories decreases from months to hours, business strategy changes from top-down to bottom-up, and workers transform into employees or free agents.
Innovations and products with a higher spreading rate have a higher chance of reaching a large fraction of the network. Hotmail enhanced its spreading rate by eliminating the adoption threshold individuals experience. First, it is free; thus you do not have to think about whether you are making a wise investment. Second, the Hotmail interface makes it very easy to sign up. In two minutes you have an account; thus there is no time investment. Third, once you sign up, every time you send an e-mail, you offer free advertisement for Hotmail. Combine these three features, and you get a service that has a very high infection rate, a built-in mechanism to spread.
Most startups were based on the simple philosophy that offering things online was sufficient to replicate the success stories of the new economy. Yet, apart from a few early starts, such as Amazon.com, AOL, or eBay, most failed. The real legacy of the Internet is not the birth of thousands of new online companies but the transformation of existing businesses. Networks do not offer a miracle drug, a strategy that makes you invincible in any business environment. The truly important role networks play is in helping existing organizations adapt to rapidly changing market conditions. The very concept of network implies a multidimensional approach.(End of Notes)
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