Related papers: Phase Transitions in Decision Problems Over Odd-Si…
The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. The term ``Anderson transition'' is understood in a broad sense, including both metal-insulator transitions and quantum-Hall-type…
An important task in network analysis is the detection of anomalous events in a network time series. These events could merely be times of interest in the network timeline or they could be examples of malicious activity or network…
We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…
In this paper we examine decision problems associated with various classes of convex languages, studied by Ang and Brzozowski (under the name "continuous languages"). We show that we can decide whether a given language L is prefix-,…
Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…
Barber and Erde asked the following question: if $B$ generates $\mathbb Z^d$ as an additive group, then must the extremal sets for the vertex/edge-isoperimetric inequality on the Cayley graph $\operatorname{Cay}(\mathbb Z^d,B)$ form a…
The `random intersection graph with communities' models networks with communities, assuming an underlying bipartite structure of groups and individuals. Each group has its own internal structure described by a (small) graph, while groups…
Almost all normal-incommensurate phase transitions observed experimentally are continuous. We show that there is not any theoretical reason for this general behaviour in perfect crystals. A normal-incommensurate phase transition that is not…
For three natural classes of dynamic decision problems; 1. additively separable problems, 2. discounted problems, and 3. discounted problems for a fixed discount factor; we provide necessary and sufficient conditions for one sequential…
We re-examine a population model which exhibits a continuous absorbing phase transition which belongs to directed percolation in 1+1 dimensions and a first order transition in 2+1 dimensions and above. Studying the model on fractal…
We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive graphs and trees.
According to conventional wisdom, ambiguity accelerates optimal timing by decreasing the value of waiting in comparison with the unambiguous benchmark case. We study this mechanism in a multidimensional setting and show that in a…
Quantum phase transitions in a system of N bosons with angular momentum L=0,2 (s,d) and a single fermion with angular momentum j are investigated both classically and quantum mechanically. It is shown that the presence of the odd fermion…
Phase distortion refers to the alteration of the phase relationships between frequencies in a signal, which can be perceptible. In this paper, we discuss a special case of phase distortion known as phase-intercept distortion, which is…
Random constraint satisfaction problems can display a very rich structure in the space of solutions, with often an ergodicity breaking -- also known as clustering or dynamical -- transition preceding the satisfiability threshold when the…
We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a…
The order from quantum disorder (OFQD) phenomenon was first discovered in quantum spin systems in geometric frustrated lattice. Similar phenomenon was also discovered in interacting bosonic systems or quantum spin systems with spin-orbit…
In this review we consider the performance of the quantum adiabatic algorithm for the solution of decision problems. We divide the possible failure mechanisms into two sets: small gaps due to quantum phase transitions and small gaps due to…
The nonequilibrium phase transition in a system of diffusing, coagulating particles in the presence of a steady input and evaporation of particles is studied. The system undergoes a transition from a phase in which the average number of…
Number partitioning is an NP-complete problem of combinatorial optimization. A statistical mechanics analysis reveals the existence of a phase transition that separates the easy from the hard to solve instances and that reflects the…