Abstract:
We derive a general formulation of the self-organized branching process by considering sandpile dynamics in an evolving population characterized by "birth" (excitation) and "death" (de-excitation) of active sites ($z=1$). New active sites are born in empty sites ($z=0$) with a probability of $\eta$, whereas active sites die, thus becoming empty, with a probability $\lambda$. Subsequently, when an active site becomes unstable ($z=2$), it topples by transferring two grains to two randomly chosen sites with probability $\alpha$ or, by transferring only one grain to a randomly selected site (while retaining the other) with probability $\beta=1+\frac{\lambda}{\eta}-2\alpha$, thus remaining active after toppling. We show that when sandpile dynamics occurs in an evolving population, self-organized criticality, characterized by a power-law avalanche size distribution with exponent $\tau_s=3/2$ and power-law avalanche duration distribution with exponent $\tau_T=2$ at very high dimension $n >> 1$, is achieved even in the presence of dissipation ($\epsilon = 1-\alpha - \beta > 0$), contrary to previous claims.

Abstract:
We evolve topology of a network of N fully-coupled nodes that interact according to repulsion-attractiondynamics within a confining wall. The dynamics portrays each node’s tendency to keep distance from itscompetitors while maintaining a lighter tendency to resist relative isolation. Each node is characterizedby two parameters: an intrinsic mobility μ and a preferred neighboring distance ρ. Onset of clustering isfound to occur at a critical variance in mobility, σμ2 = 1, and in preferred neighboring distance, σμ2 = 10.This result implies that small-world behavior manifested in clustering can be triggered by the diversity ofnode population.

Abstract:
We examine avalanche statistics of rain- and vibration-driven granular slides in miniature sand mounds. A crossover from power-law to non power-law avalanche-size statistics is demonstrated as a generic driving rate $\nu$ is increased. For slowly-driven mounds, the tail of the avalanche-size distribution is a power-law with exponent $-1.97\pm 0.31$, reasonably close to the value previously reported for landslide volumes. The interevent occurrence times are also analyzed for slowly-driven mounds; its distribution exhibits a power-law with exponent $-2.670\pm 0.001$.

Abstract:
A self-organising model is proposed to explain the criticality in cortical networks deduced from recent observations of neuronal avalanches. Prevailing understanding of self-organised criticality (SOC) dictates that conservation of energy is essential to its emergence. Neuronal networks however are inherently non-conservative as demonstrated by microelectrode recordings. The model presented here shows that SOC can arise in non-conservative systems as well, if driven internally. Evidence suggests that synaptic background activity provides the internal drive for non-conservative cortical networks to achieve and maintain a critical state. SOC is robust to any degree $\eta \in (0,1]$ of background activity when the network size $N$ is large enough such that $\eta N\sim 10^3$. For small networks, a strong background leads to epileptiform activity, consistent with neurophysiological knowledge about epilepsy.

Abstract:
A mean-field sandpile model that exhibits self-organized criticality (SOC) despite violation of the grain-transfer conservation law during avalanches is proposed. The sandpile consists of $N$ agents and possesses background activity with intensity $\eta\in[0,1]$. Background activity is characterized by transitions between two stable agent states. Analysis employing theories of branching processes and fixed points reveals a transition from sub-critical to SOC phase that is determined by $\eta N$. The model is used to explain the school size distribution of free-swimming tuna as a result of population depletion.

Abstract:
The "social-networking revolution" of late (e.g., with the advent of social media, Facebook, and the like) has been propelling the crusade to elucidate the embedded networks that underlie economic activity. An unexampled synthesis of network science and economics uncovers how the web of human interactions spurred by familiarity and similarity could potentially induce the ups and downs ever so common to our economy. Zeroing in on the million-strong global industry known as multi-level marketing, this study finds that such a socially-powered enterprise can only work stably through discrimination about who to make entrepreneurial connections with.

Abstract:
The allelomimesis clustering model is based on only two parameters a and p, which represent the probability of nearest-neighbor copying and the fraction of unresponsive agents, respectively. The model results into the formation of clusters of agents, the sizes of which obey a distribution that is determined by the values of a and p. Several experimental data are fitted by tuning the two parameters. In particular, the significance of the value of a that corresponds to an experimental data is discussed and justified according to ecological context. Recommendations for possible extensions of the model are also enumerated.

Abstract:
The allelomimesis clustering model is based on only two parameters: a local parameter $\alpha$ that represents the probability of nearest-neighbor copying and a global parameter $p$ that represents the fraction of unresponsive agents. The model results into the formation of clusters of agents, the sizes of which obey a distribution that is determined by the values of $\alpha$ and $p$. Several experimental data are fitted by tuning the two parameters. In particular, the significance of the value of $\alpha$ that corresponds to an experimental data is discussed and is justified according to behavioral context. Recommendations for possible extensions of the model are also enumerated.

Abstract:
A mathematical model of coastal forest growth is proposed to describe and test the effects of salinity and inundation in the long-term growth performance and carbon sequestration of monospecific mangrove ($Rhizophora\; mucronata$) plantation in the Philippines. We used allometry in expressing the mangrove growth equation, and stochasticity in scheduling population-level events that drive the development of the mangrove forest. Analysis of the model unveils an index, $\xi$, that could be used in assessing a strategy which could promote optimum carbon-stock accumulation in the long run. If initial plot is configured such that $\xi > 1$, the $R.\; mucronata$ plantations could achieve an above-ground biomass per hectare (AGB) of $1000\mbox{ t/ha}$, or about $500\mbox{ tC/ha}$, in approximately $200$ to $250$ years post planting. In contrast, the current restoration strategy implemented in the Philippines corresponds to the case that $\xi <1$. Consequently, the restored mangroves could not achieve stable growth without the support of costly human assistance such as frequent replanting. Rather, through that typical strategy and in the absence of assistance, the AGB decreases with time until all trees die. Mangrove restoration could therefore be planned strategically to mitigate costly and wasteful implementation. The proposed index $\xi$ thus serves as an early indicator for the progress or demise of restored mangroves.

Abstract:
Animal and human clusters are complex adaptive systems and many are organized in cluster sizes $s$ that obey the frequency-distribution $D(s)\propto s^{-\tau}$. Exponent $\tau$ describes the relative abundance of the cluster sizes in a given system. Data analyses have revealed that real-world clusters exhibit a broad spectrum of $\tau$-values, $0.7\textrm{(tuna fish schools)}\leq\tau\leq 2.95\textrm{(galaxies)}$. We show that allelomimesis is a fundamental mechanism for adaptation that accurately explains why a broad spectrum of $\tau$-values is observed in animate, human and inanimate cluster systems. Previous mathematical models could not account for the phenomenon. They are hampered by details and apply only to specific systems such as cities, business firms or gene family sizes. Allelomimesis is the tendency of an individual to imitate the actions of its neighbors and two cluster systems yield different $\tau$ values if their component agents display different allelomimetic tendencies. We demonstrate that allelomimetic adaptation are of three general types: blind copying, information-use copying, and non-copying. Allelomimetic adaptation also points to the existence of a stable cluster size consisting of three interacting individuals.