We have studied a model of a complex fluid consisting of particles interacting through a hard core and a short range attractive potential of both Yukawa and square-well form. Using a hybrid method, including a self-consistent and quite accurate approximation for the liquid integral equation in the case of the Yukawa fluid, perturbation theory to evaluate the crystal free energies, and modecoupling theory of the glass transition, we determine both the equilibrium phase diagram of the system and the lines of equilibrium between the supercooled fluid and the glass phases. For these potentials, we study the phase diagrams for different values of the potential range, the ratio of the range of the interaction to the diameter of the repulsive core being the main control parameter. Our arguments are relevant to a variety of systems, from dense colloidal systems with depletion forces, through particle gels, nano-particle aggregation, and globular protein crystallization.

k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understanding the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous k-cores, where each vertex is assigned a local threshold k(i). In this Letter we identify a binary mixture of heterogeneous k-cores which exhibits a tricritical point. We investigate the new scaling scenario and calculate the relevant critical exponents, by analytical and computational methods, for Erdős-Rényi networks and 2D square lattices.

Federated learning (FL) is quickly becoming the de facto standard for the distributed training of deep recommendation models, using on-device user data and reducing server costs. In a typical FL process, a central server tasks end-users to train a shared recommendation model using their local data. The local models are trained over several rounds on the users' devices and the server combines them into a global model, which is sent to the devices for the purpose of providing recommendations. Standard FL approaches use randomly selected users for training at each round, and simply average their local models to compute the global model. The resulting federated recommendation models require significant client effort to train and many communication rounds before they converge to a satisfactory accuracy. Users are left with poor quality recommendations until the late stages of training. We present a novel technique, FedFast, to accelerate distributed learning which achieves good accuracy for all users very early in the training process. We achieve this by sampling from a diverse set of participating clients in each training round and applying an active aggregation method that propagates the updated model to the other clients. Consequently, with FedFast the users benefit from far lower communication costs and more accurate models that can be consumed anytime during the training process even at the very early stages. We demonstrate the efficacy of our approach across a variety of benchmark datasets and in comparison to state-of-the-art recommendation techniques. CCS CONCEPTS• Information systems → Recommender systems; • Computing methodologies → Neural networks.

We introduce an order parameter for dynamical arrest. Dynamically available volume (unoccupied space that is available to the motion of particles) is expressed as holes for the simple lattice models we study. Near the arrest transition the system is dilute in holes, so we expand dynamical quantities in a series of hole density. Unlike the situation when presented in particle density, all cases of simple models that we examine have a quadratic dependence of the diffusion constant on hole density. This observation implies that in certain regimes ideal dynamical arrest transitions may possess a hitherto unnoticed degree of universality.

We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. Our results apply to two dimensions, but there is no significant barrier to extending them to higher dimensionality. We develop a new importance-sampling procedure in simulation, based on rare events around "holes", that enables us to access bootstrap lengths beyond those previously studied. By framing a new theory in terms of paths or processes that lead to emptying of the lattice we are able to develop systematic corrections to the existing theory and compare them to simulations. Thereby, for the first time in the literature, it is possible to obtain credible comparisons between theory and simulation in the accessible density range.

k-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analyzing the resilience of a network under random damage, an extension of this model is introduced, allowing different vertices to have their own degree of resilience. This extension is named heterogeneous k-core percolation and it is characterized by several interesting critical phenomena. Here we analytically investigate binary mixtures in a wide class of configuration model networks and categorize the different critical phenomena which may occur. We observe the presence of critical and tricritical points and give a general criterion for the occurrence of a tricritical point. The calculated critical exponents show cases in which the model belongs to the same universality class of facilitated spin models studied in the context of the glass transition.

Jamming, or dynamical arrest, is a transition at which many particles stop moving in a collective manner. In nature it is brought about by, for example, increasing the packing density, changing the interactions between particles, or otherwise restricting the local motion of the elements of the system. The onset of collectivity occurs because, when one particle is blocked, it may lead to the blocking of a neighbor. That particle may then block one of its neighbors, these effects propagating across some typical domain of size named the dynamical correlation length. When this length diverges, the system becomes immobile. Even where it is finite but large the dynamics is dramatically slowed. Such phenomena lead to glasses, gels, and other very long-lived nonequilibrium solids. The bootstrap percolation models are the simplest examples describing these spatio-temporal correlations. We have been able to solve one such model in two dimensions exactly, exhibiting the precise evolution of the jamming correlations on approach to arrest. We believe that the nature of these correlations and the method we devise to solve the problem are quite general. Both should be of considerable help in further developing this field.T here exists within nature a whole class of systems that exhibit a geometrical percolation transition at which they become spanned by a single infinite cluster extending across the whole system (1-3). Such transitions may be observed, for example, by randomly occupying lattice sites at some prescribed density. Spatio-temporal particle correlations implied by simple dynamical models may also be studied by using percolation ideas. Indeed, since its introduction (4, 5), the potential of the bootstrap percolation problem (6, 7) to analyze the dynamics of a system of highly coupled and locally interacting units has been recognized. The range of applications has continued to grow (8)(9)(10)(11)(12).This problem is of particular interest because of a growing focus on, and appreciation of, the unifying role of dynamical arrest (13-17) or jamming (18) in the formation of complex condensed states of matter. Despite many advances, there is as yet no complete and fundamental conceptual framework to describe the phenomena. In comparable situations it has been an important lesson of critical phenomena (19,20) that an exact solution, even of a 2D model system, can be of great assistance in broader efforts to understand the issues. Thus, an exact closed solution of one bootstrap problem (with all of the implications of strong packing-induced coupling and divergent correlated domains) would represent, even without direct access to transport coefficients, a solution of a nontrivial (and non-mean field) jamming or arrest scenario. We will present such a solution in this article.That such a treatment is possible must be considered surprising, for there have been no prior indications of such simplification, to our knowledge.The connection of the bootstrap percolation problem to jamming phenomena is clear. Thus, particles, process...

An important task for recommender system is to generate explanations according to a user's preferences. Most of the current methods for explainable recommendations use structured sentences to provide descriptions along with the recommendations they produce. However, those methods have neglected the review-oriented way of writing a text, even though it is known that these reviews have a strong influence over user's decision.In this paper, we propose a method for the automatic generation of natural language explanations, for predicting how a user would write about an item, based on user ratings from different items' features. We design a character-level recurrent neural network (RNN) model, which generates an item's review explanations using longshort term memories (LSTM). The model generates text reviews given a combination of the review and ratings score that express opinions about different factors or aspects of an item. Our network is trained on a sub-sample from the large real-world dataset BeerAdvocate. Our empirical evaluation using natural language processing metrics shows the generated text's quality is close to a real user written review, identifying negation, misspellings, and domain specific vocabulary.