Previously a new scheme of quantum information processing based on spin coherent states of two component Bose-Einstein condensates was proposed (Byrnes et al. Phys. Rev. A 85, 40306(R)). In this paper we give a more detailed exposition of the scheme, expanding on several aspects that were not discussed in full previously. The basic concept of the scheme is that spin coherent states are used instead of qubits to encode qubit information, and manipulated using collective spin operators. The scheme goes beyond the continuous variable regime such that the full space of the Bloch sphere is used. We construct a general framework for quantum algorithms to be executed using multiple spin coherent states, which are individually controlled. We illustrate the scheme by applications to quantum information protocols, and discuss possible experimental implementations. Decoherence effects are analyzed under both general conditions and for the experimental implementation proposed.

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A -uniform hypergraph = ( , ) is called ℓ-orientable, if there is an assignment of each edge ∈ to one of its vertices ∈ such that no vertex is assigned more than ℓ edges. Let , , be a hypergraph, drawn uniformly at random from the set of all -uniform hypergraphs with vertices and edges. In this paper we establish the threshold for the ℓ-orientability of , , for all ≥ 3 and ℓ ≥ 1, i.e., we determine a critical quantity * ,ℓ such that with probability 1 − (1) the graph , , has an ℓorientation if < * ,ℓ , but fails doing so if > * ,ℓ . Our result has various applications including sharp load thresholds for cuckoo hashing, load balancing with guaranteed maximum load, and massive parallel access to hard disk arrays.

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There has been significant progress in unsupervised network representation learning (UNRL) approaches over graphs recently with flexible random-walk approaches, new optimization objectives and deep architectures. However, there is no common ground for systematic comparison of embeddings to understand their behavior for different graphs and tasks. We argue that most of the UNRL approaches either model and exploit neighborhood or what we call context information of a node. These methods largely differ in their definitions and exploitation of context. Consequently, we propose a framework that casts a variety of approaches -random walk based, matrix factorization and deep learning based -into a unified context-based optimization function. We systematically group the methods based on their similarities and differences. We study their differences which we later use to explain their performance differences (on downstream tasks).We conduct a large-scale empirical study considering 9 popular and recent UNRL techniques and 11 real-world datasets with varying structural properties and two common tasks -node classification and link prediction. We find that for non-attributed graphs there is no single method that is a clear winner and that the choice of a suitable method is dictated by certain properties of the embedding methods, task and structural properties of the underlying graph. In addition we also report the common pitfalls in evaluation of UNRL methods and come up with suggestions for experimental design and interpretation of results. Comprehensive Experimental Evaluation.In our evaluation of UNRL methods we investigate the conceptual differences between the embedding approaches that result in performance differences on downstream tasks. First, using graphs with diverse structural characteristics we argue about the utility of several approaches. We carefully chose 11 large arXiv:1903.07902v5 [cs.LG]

Abstract. Balls-into-bins games describe in an abstract setting several multiple-choice scenarios, and allow for a systematic and unified theoretical treatment. In the process that we consider, there are n bins, initially empty, and m = cn balls. Each ball chooses independently and uniformly at random k ≥ 3 bins. We are looking for an allocation such that each ball is placed into one of its chosen bins and no bin has load greater than 1. How quickly can we find such an allocation? We present a simple and novel algorithm that finds such an allocation (if it exists) and runs in linear time with high probability. Our algorithm finds applications in finding perfect matchings in a special class of sparse random bipartite graphs, orientation of random hypergraphs, load balancing and hashing.

Recent works in recommendation systems have focused on diversity in recommendations as an important aspect of recommendation quality. In this work we argue that the post-processing algorithms aimed at only improving diversity among recommendations lead to discrimination among the users. We introduce the notion of user fairness which has been overlooked in literature so far and propose measures to quantify it. Our experiments on two diversification algorithms show that an increase in aggregate diversity results in increased disparity among the users.

A k-uniform hypergraph H = (V, E) is called ℓ-orientable, if there is an assignment of each edge e ∈ E to one of its vertices v ∈ e such that no vertex is assigned more than ℓ edges. Let H n,m,k be a hypergraph, drawn uniformly at random from the set of all k-uniform hypergraphs with n vertices and m edges. In this paper we establish the threshold for the ℓ-orientability of H n,m,k for all k ≥ 3 and ℓ ≥ 2, i.e., we determine a critical quantity c * k,ℓ such that with probability 1 − o(1) the graph H n,cn,k has an ℓ-orientation if c < c * k,ℓ , but fails doing so if c > c * k,ℓ . Our result has various applications including sharp load thresholds for cuckoo hashing, load balancing with guaranteed maximum load, and massive parallel access to hard disk arrays.