Related papers: Reducing Frustration in Spin Systems: Social Balan…
The set of solutions of random constraint satisfaction problems (zero energy groundstates of mean-field diluted spin glasses) undergoes several structural phase transitions as the amount of constraints is increased. This set first breaks…
We theoretically study the magnetic excitations in a frustrated two-leg spin-ladder system, in which antiferromagnetic exchange interactions act on the nearest-neighbor and next-nearestneighbor bonds in the leg direction, and on the…
This paper presents a novel approach to the problem of almost global attitude stabilization. The reduced attitude is steered along a geodesic path on the n-sphere. Meanwhile, the full attitude is stabilized on SO(n). This action,…
Many difficult computational problems involve the simultaneous satisfaction of multiple constraints which are individually easy to satisfy. Such problems occur in diffractive imaging, protein folding, constrained optimization (e.g., spin…
Evolutionary optimisation algorithm is employed to design networks of phase-repulsive oscillators that achieve an anti-phase synchronised state. By introducing the link frustration, the evolutionary process is implemented by rewiring the…
In a broad class of sparse random constraint satisfaction problems(CSP), deep heuristics from statistical physics predict that there is a condensation phase transition before the satisfiability threshold, governed by one-step replica…
We study maximum entropy mechanisms of information exchange between agents modeled by neural networks and the macroscopic states of a society of such agents in a few situations. Mathematical quantification of surprise, distrust of other…
We consider Achlioptas processes for k-SAT formulas. We create a semi-random formula with n variables and m clauses, where each clause is a choice, made on-line, between two or more uniformly random clauses. Our goal is to delay the…
Certain classical statistical systems with strong local constraints are known to exhibit Coulomb phases, where long-range correlation functions have power-law forms. Continuous transitions from these into ordered phases cannot be described…
We consider the random regular $k$-NAE-SAT problem with $n$ variables each appearing in exactly $d$ clauses. For all $k$ exceeding an absolute constant $k_0$, we establish explicitly the satisfiability threshold $d_*=d_*(k)$. We prove that…
Here we study the NP-complete $K$-SAT problem. Although the worst-case complexity of NP-complete problems is conjectured to be exponential, there exist parametrized random ensembles of problems where solutions can typically be found in…
We introduce a highly structured family of hard satisfiable 3-SAT formulas corresponding to an ordered spin-glass model from statistical physics. This model has provably "glassy" behavior; that is, it has many local optima with large energy…
The Fredkin model describes a spin-half chain segment subject to three-body, correlated-exchange interactions and twisted boundary conditions. The model is frustration-free, and its ground state wave function is known exactly. Its…
We study the collective dynamics of oscillator networks with phase-repulsive coupling, considering various network sizes and topologies. The notion of link frustration is introduced to characterize and quantify the network dynamical states.…
To describe the slow dynamics of a system out of equilibrium, but close to a dynamical arrest, we generalize the ideas of previous work to the case where time-translational invariance is broken. We introduce a model of the dynamics that is…
A one dimensional classically chaotic spin chain with asymmetric coupling and two different inter-spin interactions, nearest neighbors and all-to-all, has been considered. Depending on the interaction range, dynamical properties, as…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
Spontaneous symmetry breaking (SSB) is a property of Hamiltonian equilibrium states which, in the thermodynamic limit, retain a finite average value of an order parameter even after a field coupled to it is adiabatically turned off. In the…
We establish the satisfiability threshold for random $k$-SAT for all $k\ge k_0$, with $k_0$ an absolute constant. That is, there exists a limiting density $\alpha_*(k)$ such that a random $k$-SAT formula of clause density $\alpha$ is with…
The dynamics of the kicked-rotor, that is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular is studied statistically. The evolution (Frobenius-Perron) operator of phase…