Brief Notes

Can computational hardness be mitigated by a local treatment of global information?

- It may help to get around the sign problem.

- Introduce auxiliary variables to deal with a global constraint by a local message passing algorithm.

- Map a loopy interaction graph to a tree interaction graph by introducing auxiliary local messages passing along the tree.

- Any complex system is connected to a computationally hard problem. Perhaps a complex system is solving a computationally hard problem. That is why it is difficult to find an efficient high-level representation (meaning) of such systems starting from the low-level representations (microstates).

- A reinforced (quantum) system with a state-dependent dynamics, which is in addition equipped with memory, is different.

Complexity of inferring a high-level language from a low-level one?

- Usually we start from a high-level (user-friendly) language like python to do a meaningful computation by using a number of local gates to change the state of basic units of information (bits). Suppose that instead we start from a low-level language, that is we observe the time evolution of the bits. Can we decide if the system is doing a meaningful computation? and infer the high-level language? How does the computational complexity of this problem depend on the computational complexity of the problem that is solved by the system (in case)? 

How diseases are defined, developed, and diagnosed?

- Diseases as emergent or macroscopic features of microscopic signs.

- Disease evolution is modeled by a reverse simulated annealing algorithm starting from a healthy state.

- More information about the relevant signs could result to a phase transition in a probabilistic model of signs and diseases which could make a diagnostic problem easier in an ordered phase.

What are the working principles of a city?

- A system of selfish and adaptable agents with limited information, energy, and time.

- There is no natural way of finding (learning) a Nash equilibrium.

- Interactions lead to unpredictability and thus to inefficient decisions which in turn result in more uncertainty. Energy is consumed to return the system back to its initial state.

- The two concepts of efficiency and payoff (utility) in a system of interacting and playing agents are different! The interplay between the two could have significant consequences. Considering both the agents' payoff and efficiency is important along with the whole system's payoff and efficiency.

- Consider a system of interacting agents. We may ask:

(i) why do the agents interact?

(ii) how are they interacting? (the nature and mechanism of interactions)

(iii) what do the interactions mean? (the effect and meaning of interactions)

(iv) how do the interactions (also with the environment) affect the efficiency of the system and its subsystems? how are these efficiencies correlated?

PS:

- A high-level algorithm (like evolution) can be used to optimize the performance of a low-level algorithm (like stochastic gradient descent) in an optimization problem (like learning and protein folding).  

- Any complex system is connected to a computationally hard problem; perhaps, a complex system is solving a computationally hard problem. That is why it is difficult to find an efficient high-level representation (meaning) of such systems starting from the low-level representations (time evolution of the microstates).

- “Emergent” laws and behaviors are effective and efficient representations of the “fundamental” laws.

-  Life (a cell) is on top of complexity hierarchy. Other “complex systems” or “models” in lower levels represent one or few aspects of complexity.