Search

Several attacks have been proposed against Proof-of-Work blockchains, which may increase the attacker's share of mining rewards (e.g., selfish mining, block withholding). A further impact of such attacks, which has not been considered in prior work, is that decreasing the profitability of mining for honest nodes incentivizes them to stop mining or to leave the attacked chain for a more profitable one. The departure of honest nodes exacerbates the attack and may further decrease profitability and incentivize more honest nodes to leave. In this paper, we first present an empirical analysis showing that there is a statistically significant correlation between the profitability of mining and the total hash rate, confirming that miners indeed respond to changing profitability. Second, we present a theoretical analysis showing that selfish mining under such elastic hash supply leads either to the collapse of a chain, i.e., all honest nodes leaving, or to a stable equilibrium depending on the attacker's initial share.

From the systemic point of view protein aggregation is a compensatory mechanism allowing transition of a system (protein solution) from an initially stable equilibrium, which became unstable under a stress, to another stable equilibrium, which bifurcates from the initial one because of the stress. The simplest bifurcation of this type is Logistic bifurcation with a positive small parameter.

While struggling as a third year graduate student to begin my thesis work in the spring of 1984, Hugo advised me to look into the possibility of refining sequential equilibrium by exploiting the implicit communication between the sender and the receiver. After working for a few additional months, I was able to produce an example in early July. I used it to explain to Hugo that the implicit communication can refine sequential equilibrium farther than David Kreps had proposed. At the end of the discussion, Hugo said “In-Koo, you have come a long way.” He asked me to polish the example so that he could send it to David.

Tinnitus is a symptom of perceiving phantom sounds. The majority of tinnitus cases are caused by misinterpreting null sounds from ears as significant nervous signals in the cerebral limbic system. There are two typical sound therapies for tinnitus: Tinnitus Masking (TM) and Tinnitus Retraining Therapy (TRT). Their effects have been discussed from clinical assessments. To account for the mechanism of perceiving tinnitus and the clinical effects from the viewpoint of engineering, this paper describes a neural oscillator model with a plastic coupling for a cerebral limbic system and its dynamic behavior. We observed a bi-stable state such that a stable equilibrium and a stable oscillation coexist in a certain range of parameters. It was also discovered that the value of the plastic coupling changes by external stimulation, and then the oscillation is inhibited. This could explain the fact that the retrained cerebral limbic system temporarily stops perceiving tinnitus after sound therapy.

In this paper, we investigate dynamical behavior of a general class of competitive or cooperative Lotka-Volterra systems with delays. Positive solutions and global stability of nonnegative equilibrium are discussed. Sufficient condition independent of delays guaranteeing existence of globally stable equilibrium is given. A Simulation verifying theoretical results is given, too.

Possible kinds of phase portraits. Evolution of the community with the growth of technologies and its dependence upon other parameters.

Possible types of motions — transient processes, stable equilibrium states and auto-oscillations.

The proposition that history matters is not new in the economic debate, but growing recognition that technological change matters for economic growth has renewed and rephrased that proposition in more formal if narrower terms. Rosenberg, Paul David and Brian Arthur are names associated with path-dependence. Ebeling et alit used Markov processes as a random walk, and de Araujo used a birth-and-death model as a stochastic equivalent of a diffusion equation for finite markets. The present paper further explores this line, with new results. By examining similarities and differences between the author’s results and those of others, we try to discern the implications of these assumptions for the results obtained on technology diffusion, and raise a few questions on the significance of stable equilibrium for analytic purposes. Finally, we discuss extensions to incorporate insights from other work aiming to arrive at a better understanding of the real processes of technology innovation and diffusion.

In this paper, we present a computational model for transforming discourses into Quasi-Mental Clusters (QMCs) through a convergence process. The process is interpreted as a particular transformation of a given set of discourse segments and concepts by examining the textual continuity. Examinations include testing the local cohesion in a cohesion parsing as well as the global coherence in semantic decomposition. In the convergence process, sentences in a discourse are represented as nodes in a spreading activation network. Competing coalitions of the nodes drive the network into a stable equilibrium. We argue the resulting QMCs are useful data structures in remembrance, summarization and knowledge discovery in discourses.

Early studies of the dynamics of biological populations tended to look for stable equilibrium points in spatially homogeneous contexts. Although such models are occasionally ridiculed today (usually for transparently careerist reasons), they represent a sensible first step toward understanding how populations interact, and how they respond to natural or human-created changes. And greater dynamical complexity has been hinted at from the earliest studies: witness Lotka and Volterra’s [1] neutrally stable cycles, or Skellam’s [2] work on what today would be called competitive coexistence of metapopulations.

Jigs and fixtures are devices used in manufacturing processes such as machining, welding, bonding and assembly. They are employed to locate and hold the workpiece firmly in position and to ensure that it is in a state of stable equilibrium (geometric control) and that dimensional accuracy is maintained during the manufacturing operation (dimensional control). Jigs and fixtures are generally referred to as “fixturing systems” or simply “fixtures”.

By differential equations with time delayed arguments, a predator-prey system is described where only older animals are predacious but hunt, besides a prey population, also juveniles of their own species. Increasing intraspecific predation first reduces the amplitudes of predator-prey oscillations; a further increase then causes damping. With a cannibalistic activity as measured for copepods, the system turns very fast into a stable equilibrium. This reduces the risk of extinction drastically.