Evolutionary Model of the Personal Income Distribution

The aim of this work is to establish the personal income distribution from the elementary constituents of a free market; products of a representative good and agents forming the economic network. The economy is treated as a self-organized system. Based on the idea that the dynamics of an economy is governed by slow modes, the model suggests that for short time intervals a fixed ratio of total labour income (capital income) to net income exists (Cobb-Douglas relation). Explicitly derived is Gibrat's law from an evolutionary market dynamics of short term fluctuations. The total private income distribution is shown to consist of four main parts. From capital income of private firms the income distribution contains a lognormal distribution for small and a Pareto tail for large incomes. Labour income contributes an exponential distribution. Also included is the income from a social insurance system, approximated by a Gaussian peak. The evolutionary model is able to reproduce the stylized facts of the income distribution, shown by a comparison with empirical data of a high resolution income distribution. The theory suggests that in a free market competition between products is ultimately the origin of the uneven income distribution

Self-Organization in Communication Networks

We develop a dynamic model to study the formation of communication networks. In this model, individuals periodically make decisions concerning the continuation of existing information links and the formation of new information links, with their cohorts. These decisions trade off the costs of forming and maintaining links against the potential rewards from doing so. We analyze the long run behavior of this process of link formation and dissolution. Our results establish that this process always self-organizes, i.e., irrespective of the number of agents, and the initial network, the dynamic process converges to a limit social communication network with probability one. Furthermore, we prove that the limiting network is invariably either a wheel network or the empty network. We show in the (corresponding) static network formation game that, while a variety of architectures can be sustained in equilibrium, the wheel is the unique efficient architecture for the interesting class of parameters. Thus, our results imply that the dynamics have strong equilibrium selection properties

Connecting Irreversible to Reversible Aggregation: Time and Temperature

We report molecular dynamics simulations of a gel-forming mixture of ellipsoidal patchy particles with different functionality. We show that in this model, which disfavors the formation of bond-loops, elapsed time during irreversible aggregation -- leading to the formation of an extended network -- can be formally correlated with equilibrium temperature in reversible aggregation. We also show that it is possible to develop a parameter-free description of the self-assembly kinetics, bringing reversible and irreversible aggregation of loopless branched systems to the same level of understanding as equilibrium polymerization.Comment: 5 pages, 4 figure

Self-Organization in Communication Networks

We develop a dynamic model to study the formation of communication networks. In this model, individuals periodically make decisions concerning the continuation of existing information links and the formation of new information links, with their cohorts. These decisions trade off the costs of forming and maintaining links against the potential rewards from doing so. We analyze the long run behavior of this process of link formation and dissolution. Our results establish that this process always self-organizes, i.e., irrespective of the number of agents, and the initial network, the dynamic process converges to a limit social communication network with probability one. Furthermore, we prove that the limiting network is invariably either a wheel network or the empty network. We show in the (corresponding) static network formation game that, while a variety of architectures can be sustained in equilibrium, the wheel is the unique efficient architecture for the interesting class of parameters. Thus, our results imply that the dynamics have strong equilibrium selection properties.networks;learning;coordination;self-organization;path-dependence

GRINN: A Physics-Informed Neural Network for solving hydrodynamic systems in the presence of self-gravity

Modeling self-gravitating gas flows is essential to answering many fundamental questions in astrophysics. This spans many topics including planet-forming disks, star-forming clouds, galaxy formation, and the development of large-scale structures in the Universe. However, the nonlinear interaction between gravity and fluid dynamics offers a formidable challenge to solving the resulting time-dependent partial differential equations (PDEs) in three dimensions (3D). By leveraging the universal approximation capabilities of a neural network within a mesh-free framework, physics informed neural networks (PINNs) offer a new way of addressing this challenge. We introduce the gravity-informed neural network (GRINN), a PINN-based code, to simulate 3D self-gravitating hydrodynamic systems. Here, we specifically study gravitational instability and wave propagation in an isothermal gas. Our results match a linear analytic solution to within 1\% in the linear regime and a conventional grid code solution to within 5\% as the disturbance grows into the nonlinear regime. We find that the computation time of the GRINN does not scale with the number of dimensions. This is in contrast to the scaling of the grid-based code for the hydrodynamic and self-gravity calculations as the number of dimensions is increased. Our results show that the GRINN computation time is longer than the grid code in one- and two- dimensional calculations but is an order of magnitude lesser than the grid code in 3D with similar accuracy. Physics-informed neural networks like GRINN thus show promise for advancing our ability to model 3D astrophysical flows

Avenues for emergent ecologies

In this work, we present some fascinating behaviour emerging from a simple synthetic chemistry model. The results of Ono and Ikegami (2001) demonstrated the spontaneous formation of primitive, self-reproducing cells from a random homogeneous mixture of chemical components. Their model made use of a simple, artificial reaction network. Discrete particles were placed on a triangular lattice and the dynamics consisted of the following particle transitions: translation over one lattice spacing and chemical transformation. The primary particle types were membrane-forming particles, catalysts and water. The membrane particles formed structures akin to lipid bilayers. Their synthesis was stimulated by the catalyst particles, which were also capable of template self-replication using precursors. The system readily exhibits protocell formation from a random initial condition. These protocells form, grow, divide and eventually decay in a continuous cycle. Such emergent dynamics were an illuminating result given that the simulation itself only defines local interactions between particles and a set of physical transition rules. The protocell structures are not explicitly represented or built into the model. Hence it demonstrated a basic physical logic wherein the concepts of self-maintenance and self-reproduction could arise spontaneously from a set of simpler, lower level rules. In essence, it was an in silico realisation of the principle of autopoiesis.We decided to extend this work by augmenting the particle species repertoire. An additional catalyst was added, which did not stimulate the synthesis of membrane particles, but rather stimulated their decay. It was expected that this would reduce the rate of protocell formation. However a surprising dynamic was uncovered with this new system. As one might expect the protocells did not arise in abundance as in the original model. Instead they formed in small, isolated colonies since this was the only means by which they could avoid the destructive effects of the new catalyst. However because this toxic particle was also autocatalytic (like the other, constructive catalyst), its concentration rose sharply in regions confined by membrane particles since the membranes slowed their outward diffusion. Thus membranes actually created a niche for the toxic catalyst. This in turn produced a predator-prey dynamic with clouds of the toxic particle growing near protocells and protocells being forced to grow in the opposite direction to avoid the destructive effects of the new particle. These results reveal that high level, ecological phenomena can manifest themselves even in simple physico-chemical systems. They demonstrate that ideas of natural selection and fitness are intimately bound with the basic principle of free energy minimisation. We have also now enhanced the model further by adding a second reaction network. It is similar, but independent to the first and allows for two "species" of protocell. It is also possible for hybrids to form, comprised of mixtures of the membrane particles from the two reaction networks. Results from this new version are currently being gathered and analyse

Universal dynamics of biological pattern formation in spatio-temporal morphogen variations

In biological systems, chemical signals termed morphogens self-organize into patterns that are vital for many physiological processes. As observed by Turing in 1952, these patterns are in a state of continual development, and are usually transitioning from one pattern into another. How do cells robustly decode these spatio-temporal patterns into signals in the presence of confounding effects caused by unpredictable or heterogeneous environments? Here, we answer this question by developing a general theory of pattern formation in spatio-temporal variations of ‘pre-pattern’ morphogens, which determine gene-regulatory network parameters. Through mathematical analysis, we identify universal dynamical regimes that apply to wide classes of biological systems. We apply our theory to two paradigmatic pattern-forming systems, and predict that they are robust with respect to non-physiological morphogen variations. More broadly, our theoretical framework provides a general approach to classify the emergent dynamics of pattern-forming systems based on how the bifurcations in their governing equations are traversed

Synthesis and application of ionic molecular and polymeric materials

Materials are built from atoms and molecules through different interactions. Few artificial material is built primarily with ionic interaction despite its ubiquitous existence in living systems. My research has focused on filling this void by developing novel ionic molecular and polymeric materials for both fundamental understandings of the systems and various applications such as self-healing. With one theme of ionic functional materials, my research has broadly evolved into three areas: Chapters 2-3 focus on the development of structure-property relationship of network-forming ionic glasses and liquids; Chapter 4 focus on the application of network-forming ionic liquids for the cause of shockwave absorption; Chapter 5 extends the exploration into the realm of polymeric ionic rubber and its application as self-healing materials. The network-forming ionic glass is a stable glassy organic network that is primarily connected by ionic interaction. It was found that the glass transition temperature of ionic glass series with increasing alkyl backbone length showed an intriguing odd-even effect. The mechanism was revealed by inelastic neutron scattering as different dynamics of odd- and even-numbered cations in liquid state. Structurally, thanks to the nano-segregation, the network-forming ionic liquid proved to be an excellent shockwave absorption material. Further investigation indicated that a shock-induced ordering in network-forming ionic liquids contributed to its overall shockwave absorption performance. Similar to the small molecule ionic glass and liquids, an oligomeric anion, a carboxylate-terminated copolymer of polybutadiene(PBD) and polyacrylonitrile(PAN), was chosen as the counterion for multivalent cations to build a polymeric amorphous ionic network. An ionic rubber that combines competitive mechanical properties and full reprocessibiltiy was successfully prepared where ionic interaction plays the key role of the dynamic crosslink. The reversible ionic crosslink renders excellent properties including high plateau modulus, rate-dependent stress releasing and super-fast self-healing at room temperature. These studies on the ionic glass and ionic rubber have advanced the development of artificial ionic materials in the aspect of both fundamental knowledges on structure-property relationship and practical application including shockwave absorption and self-healing