Related papers: Component systems: do null models explain everythi…
Compositionality has traditionally been understood as a major factor in productivity of language and, more broadly, human cognition. Yet, recently, some research started to question its status, showing that artificial neural networks are…
Complex systems' modeling and simulation are powerful ways to investigate a multitude of natural phenomena providing extended knowledge on their structure and behavior. However, enhanced modeling and simulation require integration of…
For a multi-component system, general formulas are derived for the dimension of a coexisting region in the phase diagram in various state spaces.
Biological systems exhibit two structural features on many levels of organization: sparseness, in which only a small fraction of possible interactions between components actually occur; and modularity - the near decomposability of the…
We show that modularity, a quantity introduced in the study of networked systems, can be generalized and used in the clustering problem as an indicator for the quality of the solution. The introduction of this measure arises very naturally…
In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…
The fast changing reality in technical and natural domains perceived by always more accurate observations has drawn attention on new and very broad class of systems with specific behaviour represented under the common wording complexity.…
We investigate the most general phase space of configurations, consisting of all possible ways of assigning elementary attributes, ``energies'', to elementary positions, ``cells''. We discuss how this space possesses structures that can be…
General regression and classification models are constructed as linear combinations of simple rules derived from the data. Each rule consists of a conjunction of a small number of simple statements concerning the values of individual input…
The complexity of a system, in general, makes it difficult to determine some or almost all matrix elements of its operators. The lack of accuracy acts as a source of randomness for the matrix elements which are also subjected to an external…
Liquid mixtures of many interacting components often exhibit numerous coexisting types of droplets. An exciting example is the cytosol of biological cells, where diverse droplets, called condensates, are essential for cellular function.…
Structural-equations models (SEMs) are perhaps the most commonly used framework for modeling causality. However, as we show, naively extending this framework to infinitely many variables, which is necessary, for example, to model dynamical…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
Generalized Additive Models (GAMs) are commonly considered *interpretable* within the ML community, as their structure makes the relationship between inputs and outputs relatively understandable. Therefore, it may seem natural to…
The aim of this manuscript is to contain the arguments and define the theoretical objects for building a general framework to model population dynamics from the ground up, relying mainly on the probabilistic landscapes defining the dynamics…
All biological systems are subject to perturbations: due to thermal fluctuations, external environments, or mutations. Yet, while biological systems are composed of thousands of interacting components, recent high-throughput experiments…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
Many of life's most fascinating phenomena emerge from interactions among many elements--many amino acids determine the structure of a single protein, many genes determine the fate of a cell, many neurons are involved in shaping our thoughts…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
Compositionality supports the manipulation of large systems by working on their components. For model-based testing, this means that large systems can be tested by modelling and testing their components: passing tests for all components…