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In the random assignment problem, objects are randomly assigned to agents keeping in view the agents' preferences over objects. A random assignment specifies the probability of an agent getting an object. We examine the structural and…
Approximate simulation, an extension of simulation relations from formal methods to continuous systems, is a powerful tool for hierarchical control of complex systems. Finding an approximate simulation relation between the full "concrete"…
Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex…
We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility,…
Odd elasticity describes the unusual elastic response of solids whose stress-strain relationship is not compatible with an elastic potential. Here, we present a study of odd elasticity in a driven granular matter system composed of grains…
Passive elastic elements can contribute to stability, energetic efficiency, and impact absorption in both biological and robotic systems. They also add dynamical complexity which makes them more challenging to model and control. The impact…
Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing -- in studying the…
This paper considers the motion of an object subjected to dry friction and an external random force. The objective is to characterize the role of the correlation time of the external random force. We develop efficient stochastic simulation…
This paper studies a stylized model of local interaction where agents choose from an ever increasing set of vertically ranked actions, e.g. technologies. The driving forces of the model are infrequent upward shifts (``updates''), followed…
Training materials through periodic drive allows to endow materials and structures with complex elastic functions. As a result of the driving, the system explores the high dimensional space of structures, ultimately converging to a…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
Robustness, the ability of a system to maintain performance under significant and unanticipated environmental changes, is a critical property for robotic systems. While biological systems naturally exhibit robustness, there is no…
Elastoplastic lattice models for the response of solids to deformation typically incorporate structure only implicitly via a local yield strain that is assigned to each site. However, the local yield strain can change in response to a…
We show numerically that the response of simple amorphous solids (elastic networks and particle packings) to a local force dipole is characterized by a lengthscale $\ell_c$ that diverges as unjamming is approached as $\ell_c \sim (z -…
In an experimental study of single enzyme reactions, it has been proposed that the rate constants of the enzymatic reactions fluctuate randomly, according to a given distribution. To quantify the uncertainty arising from random rate…
In many sliding systems consisting of solid object on a solid substrate under dry condition, the friction force does not depend on the apparent contact area and is proportional to the loading force. This behaviour is called Amontons' law…
In this paper we introduce and study a new concept of parametrised topological complexity, a topological invariant motivated by the motion planning problem of robotics. In the parametrised setting, a motion planning algorithm has high…
In swarm robotics, just as for an animal swarm in Nature, one of the aims is to reach and maintain a desired configuration. One of the possibilities for the team, to reach this aim, is to see what its neighbours are doing. This approach…
By means of linear theory of elastoplasticity, solutions are given for screw and edge dislocations situated in an isotropic solid. The force stresses, strain fields, displacements, distortions, dislocation densities and moment stresses are…
Computer systems can be found everywhere: in space, in our homes, in our cars, in our pockets, and sometimes even in our own bodies. For concerns of safety, economy, and convenience, it is important that such systems work correctly.…