17 problems

Colimit analogy conjecture. The notion of a colimit may give useful analogies to the way complex biological systems operate.

Information rates quantify time-directed information flows in stochastic processes; here, Gaussian processes are the processes for which the proposed estimators would be developed.…

The Agentic Hive is a formal framework for self-organizing multi-agent systems in which the population of agents undergoes demographic dynamics governed by multi-sector growth theo…

Let $W(N)$ denote the number of available states of a system with $N$ components, and let the brain be considered as a system whose components are brain regions. A growth rate is f…

Let $f$ be a function on a set $\textbf{X}$. If $f(\textbf{X})$ is an expected value, require that $f$ is also defined on every local instance $\textbf{X}=\textbf{x}$. Localizabili…

Let $J$ be the Jacobian of a multiscale, coupled random dynamical system, with state components $\boldsymbol{\eta}$ and $\boldsymbol{\mu}$, and let $H$ denote its Hessian form. A w…

Let $\tilde{\mathcal{H}}(\mathcal{X}^T)$ denote the normalised Shannon entropy of the frequencies with which player archetypes are used during time period $T$, defined by … For any…

Subleading large-deviation conjecture. The probability of the event $x_{max}<x$ has the asymptotic form

N^{1/4}-scaling conjecture. The number of unstable directions of typical equilibria in the entire transition region is proportional to

In an open-parametric driven system $g$ with scalar parameter $\alpha$ and input $\cev{u}$, let $X_n(\alpha,\bar{u})$ denote the set describing the collective states of the system…

Memory-loss conjecture. The memory is predominantly lost during the abrupt transitions caused by localized buckling of the interaction networks.

Let $\sigma_\mu^{\ell}$ denote the elusive information conditioned on a present of length $\ell$, and let $\sigma_\mu^{\infty}$ be its limiting value as $\ell$ tends to infinity. V…

Consider a protein energy landscape decomposed into hierarchically organized basins of local minima. Let the equilibration time within a basin be compared with the time required to…

Ultrametricity is a property of a metric space in which the strong triangle inequality holds. The paper considers complex systems with extremal sparse statistics and rare-event sta…

A cellular automaton (CA) is a discrete dynamical system whose cells synchronously update according to a fixed local rule. A blinker is a stationary glider, while a particle is a d…

A cellular automaton (CA) is a dynamical system whose sites update according to a local rule, and its evolving configurations can contain coherent localized structures called parti…

A cellular automaton (CA) is a dynamical system formed by updating configurations according to a local rule; Wolfram's classification calls CAs exhibiting complex behavior, includi…