Related papers: Growth Functions, Rates and Classes of String-Base…
We develop a semi-analytical model to describe the cosmological evolution of networks of cosmic strings with small-scale structure, by extending the velocity-dependent one-scale model to include an additional lengthscale describing the…
A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton…
This review summarizes the recent developments in topological string theory from the author's perspective, mostly focused on aspects of research in which the author is involved. After a brief overview of the theory, we discuss two aspects…
A new model for biological growth is introduced that couples the geometry of an organism (or part of the organism) to the flow and deposition of material. The model has three dynamical variables (a) a Riemann metric tensor for the geometry,…
Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates.…
The study of the dynamic behavior of cross-sectional ranks over time for functional data and the ranks of the observed curves at each time point and their temporal evolution can yield valuable insights into the time dynamics of functional…
The cosmological fluid equations describe the early gravitational dynamics of cold dark matter (CDM), exposed to a uniform component of dark energy, the cosmological constant $\Lambda$. Perturbative predictions for the fluid equations…
In an evolutionary system in which the rules of mutation are local in nature, the number of possible outcomes after $m$ mutations is an exponential function of $m$ but with a rate that depends only on the set of rules and not the size of…
This paper proposes an attributed network growth model. Despite the knowledge that individuals use limited resources to form connections to similar others, we lack an understanding of how local and resource-constrained mechanisms explain…
For years the model performance in machine learning obeyed a power-law relationship with the model size. For the consideration of parameter efficiency, recent studies focus on increasing model depth rather than width to achieve better…
Understanding the geometry of learned distributions is fundamental to improving and interpreting diffusion models, yet systematic tools for exploring their landscape remain limited. Standard latent-space interpolations fail to respect the…
The applicability of computational and dynamical systems models to organisms is scrutinized, using examples from developmental biology and cognition. Developmental morphogenesis is dependent on the inherent material properties of developing…
It was recently shown that velocity-dependent forces between parallel fundamental strings moving apart in a $D-$dimensional spacetime implied an accelerating expanding universe in $D-1$-dimensional space-time. Exact solutions were obtained…
We study the space-time correlation and response functions in nonequilibrium growth processes described by linear stochastic Langevin equations. Exploiting exclusively the existence of space and time dependent symmetries of the noiseless…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
We analyze all individual cosmic strings of various lengths in a large ensemble of the global cosmic string networks in the post-inflationary scenario, obtained from numerical simulations on a discrete lattice with $N^3 = 4096^3$. A strong…
Network growth models that embody principles such as preferential attachment and local attachment rules have received much attention over the last decade. Among various approaches, random walks have been leveraged to capture such…
Efficient state space models (SSMs), such as linear recurrent neural networks and linear attention variants, offer computational advantages over Transformers but struggle with tasks requiring long-range in-context retrieval-like text…
We investigate a class of Young diagrams growing via the addition of unit cells and satisfying the constraint that the height difference between adjacent columns $\geq r$. In the long time limit, appropriately re-scaled Young diagrams…
Motion planning problems can be simplified by admissible projections of the configuration space to sequences of lower-dimensional quotient-spaces, called sequential simplifications. To exploit sequential simplifications, we present the…