Statistical Field Theory and Neural Structures Dynamics III: Effective Action for Connectivities, Interactions and Emerging Collective States

This paper elaborates on the effective field theory for the connectivity field previously introduced in ([7]). We demonstrate that dynamic interactions among connectivities induce modifications in the background state. These modifications can be understood as the emergence of interacting collective states above the background state. The emergence of such states is contingent on both interactions and the shape of the static or quasi-static background, which acts as a conditioning factor for potential emerging states

Statistical Field Theory and Neural Structures Dynamics IV: Field-Theoretic Formalism for Interacting Collective States

Building upon the findings presented in the first three papers of this series, we formulate an effective field theory for interacting collective states. These states consist of a large number of interconnected neurons and are distinguished by their intrinsic activity. The field theory encompasses an infinite set of fields, each of which characterizes the dynamics of a specific type of collective state. Interaction terms within the theory drive transitions between various collective states, allowing us to describe processes such as activation, association, and deactivation of these states

A Statistical Field Perspective on Capital Allocation and Accumulation: Individual dynamics

We have shown, in a series of articles, that a classical description of a large number of economic agents can be replaced by a statistical fields formalism. To better understand the accumulation and allocation of capital among different sectors, the present paper applies this statistical fields description to a large number of heterogeneous agents divided into two groups. The first group is composed of a large number of firms in different sectors that collectively own the entire physical capital. The second group, investors, holds the entire financial capital and allocates it between firms across sectors according to investment preferences, expected returns, and stock prices variations on financial markets. In return, firms pay dividends to their investors. Financial capital is thus a function of dividends and stock valuations, whereas physical capital is a function of the total capital allocated by the financial sector. Whereas our previous work focused on the background fields that describe potential long-term equilibria, here we compute the transition functions of individual agents and study their probabilistic dynamics in the background field, as a function of their initial state. We show that capital accumulation depends on various factors. The probability associated with each firm's trajectories is the result of several contradictory effects: the firm tends to shift towards sectors with the greatest long-term return, but must take into account the impact of its shift on its attractiveness for investors throughout its trajectory. Since this trajectory depends largely on the average capital of transition sectors, a firm's attractiveness during its relocation depends on the relative level of capital in those sectors. Thus, an under-capitalized firm reaching a high-capital sector will experience a loss of attractiveness, and subsequently, in investors. Moreover, the firm must also consider the effects of competition in the intermediate sectors. An under-capitalized firm will tend to be ousted out towards sectors with lower average capital, while an over-capitalized firm will tend to shift towards higher averagecapital sectors. For investors, capital allocation depends on their short and long-term returns. These returns are not independent: in the short-term, returns are composed of both the firm's dividends and the increase in its stock prices. In the long-term, returns are based on the firm's growth expectations, but also, indirectly, on expectations of higher stock prices. Investors' capital allocation directly depends on the volatility of stock prices and {\ldots}rms'dividends. Investors will tend to reallocate their capital to maximize their short and long-term returns. The higher their level of capital, the stronger the reallocation will be.Comment: arXiv admin note: substantial text overlap with arXiv:2312.16173, arXiv:2205.0308

Statistical Field Theory and Neural Structures Dynamics II: Signals Propagation, Interferences, Bound States

We continue our study of a field formalism for large sets of interacting neurons, together with their connectivity functions. Expanding upon the foundation laid in ([9]), we formulate an effective formalism for the connectivity field in the presence of external sources. We proceed to deduce the propagation of external signals within the system. This enables us to investigate the activation and association of groups of bound cells

An Economic Approach to the Self : the Dual Agent

This paper extends the notion of the rational agent in economics by acknowledging the role of the unconscious in the agent�s decision-making process. It argues that the unconscious can be modelled by a rational agent with his own objective function and set of information. The combination of both the conscious and unconscious agents is called the "dual agent". This dual agent presents rationally biased behaviors that may not disappear through aggregation, and could be potentially measured. It also provides a theoretical approach to the emotionally-driven actions. On the social sciences side, the paper pleads for a wider use of substantive rationality in the understanding of human behavior

Statistical Field Theory and Neural Structures Dynamics I: Action Functionals, Background States and External Perturbations

This series of papers models the dynamics of a large set of interacting neurons within the framework of statistical field theory. The system is described using a two-field model. The first field represents the neuronal activity, while the second field accounts for the interconnections between cells. This model is derived by translating a probabilistic model involving a large number of interacting cells into a field formalism. The current paper focuses on deriving the background fields of the system, which describe the potential equilibria in terms of interconnected groups. Dynamically, we explore the perturbation of these background fields, leading to processes such as activation, association, and reactivation of groups of cells

Statistical Field Theory and Networks of Spiking Neurons

This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems in interaction [45][46]. Our model keeps track of individual interacting neurons dynamics but also preserves some of the features and goals of neural field dynamics, such as indexing a large number of neurons by a space variable. Thus, this paper bridges the scale of individual interacting neurons and the macro-scale modelling of neural field theory

An Economic Approach to the Self : the Dual Agent

This paper extends the notion of the rational agent in economics by acknowledging the role of the unconscious in the agents decision-making process. It argues that the unconscious can be modelled by a rational agent with his own objective function and set of information. The combination of both the conscious and unconscious agents is called the "dual agent". This dual agent presents rationally biased behaviors that may not disappear through aggregation, and could be potentially measured. It also provides a theoretical approach to the emotionally-driven actions. On the social sciences side, the paper pleads for a wider use of substantive rationality in the understanding of human behavior.rational agent; decision-making; conscious; unconscious; asymmetry of information; imperfect information; dual agent; theory of emotion; substantive and procedural rationality; psychology; bias