Somoclu is a massively parallel tool for training self-organizing maps on large data sets written in C++. It builds on OpenMP for multicore execution, and on MPI for distributing the workload across the nodes in a cluster. It is also able to boost training by using CUDA if graphics processing units are available. A sparse kernel is included, which is useful for high-dimensional but sparse data, such as the vector spaces common in text mining workflows. Python, R and MATLAB interfaces facilitate interactive use. Apart from fast execution, memory use is highly optimized, enabling training large emergent maps even on a single computer.

In classical hydrodynamics with uniform density, vortices move with the local fluid velocity. This description is rewritten in terms of forces arising from the interaction with other vortices. Two such positive straight vortices experience a repulsive interaction and precess in a positive (anticlockwise) sense around their common centroid. A similar picture applies to vortices in a two-component two-dimensional uniform Bose-Einstein condensate (BEC) coherently coupled through rf Rabi fields. Unlike the classical case, however, the rf Rabi coupling induces an attractive interaction and two such vortices with positive signs now rotate in the negative (clockwise) sense. Pairs of counter-rotating vortices are instead found to translate with uniform velocity perpendicular to the line joining their cores. This picture is extended to a single vortex in a two-component trapped BEC. Although two uniform vortex-free components experience familiar Rabi oscillations of particle-number difference, such behavior is absent for a vortex in one component because of the nonuniform vortex phase. Instead the coherent Rabi coupling induces a periodic vorticity transfer between the two components.

In accessibility tests for digital preservation, over time we experience drifts of localized and labelled content in statistical models of evolving semantics represented as a vector field. This articulates the need to detect, measure, interpret and model outcomes of knowledge dynamics. To this end we employ a high-performance machine learning algorithm for the training of extremely large emergent self-organizing maps for exploratory data analysis. The working hypothesis we present here is that the dynamics of semantic drifts can be modeled on a relaxed version of Newtonian mechanics called social mechanics. By using term distances as a measure of semantic relatedness vs. their PageRank values indicating social importance and applied as variable ‘term mass’, gravitation as a metaphor to express changes in the semantic content of a vector field lends a new perspective for experimentation. From ‘term gravitation’ over time, one can compute its generating potential whose fluctuations manifest modifications in pairwise term similarity vs. social importance, thereby updating Osgood’s semantic differential. The dataset examined is the public catalog metadata of Tate Galleries, London.

Bell inequalities have traditionally been used to demonstrate that quantum theory is nonlocal, in the sense that there exist correlations generated from composite quantum states that cannot be explained by means of local hidden variables. With the advent of device-independent quantum information processing, Bell inequalities have gained an additional role as certificates of relevant quantum properties. In this work we consider the problem of designing Bell inequalities that are tailored to detect the presence of maximally entangled states. We introduce a class of Bell inequalities valid for an arbitrary number of measurements and results, derive analytically their maximal violation and prove that it is attained by maximally entangled states. Our inequalities can therefore find an application in device-independent protocols requiring maximally entangled states.

We develop a reinforcement-learning algorithm to construct a feedback policy that delivers quantum-enhanced interferometric-phase estimation up to 100 photons in a noisy environment. We ensure scalability of the calculations by distributing the workload in a cluster and by vectorizing time-critical operations. We also improve running time by introducing accept-reject criteria to terminate calculation when a successful result is reached. Furthermore, we make the learning algorithm robust to noise by fine-tuning how the objective function is evaluated. The results show the importance and relevance of well-designed classical machine learning algorithms in quantum physics problems.

Noninvasive measurement of blood pressure by optical methods receives considerable interest, but the complexity of the measurement and the difficulty of adjusting parameters restrict applications. We develop a method for estimating the systolic and diastolic blood pressure using a single-point optical recording of a photoplethysmographic (PPG) signal. The estimation is data-driven, we use automated machine learning algorithms instead of mathematical models. Combining supervised learning with a discrete wavelet transform, the method is insensitive to minor irregularities in the PPG waveform, hence both pulse oximeters and smartphone cameras can record the signal. We evaluate the accuracy of the estimation on 78 samples from 65 subjects (40 male, 25 female, age 29±7) with no history of cardiovascular disease. The estimate for systolic blood pressure has a mean error 4.9±4.9 mm Hg, and 4.3±3.7 mm Hg for diastolic blood pressure when using the oximeter-obtained PPG. The same values are 5.1±4.3 mm Hg and 4.6±4.3 mm Hg when using the phone-obtained PPG, comparing with A&D UA-767PBT result as gold standard. The simplicity of the method encourages ambulatory measurement, and given the ease of sharing the measured data, we expect a shift to data-oriented approaches deriving insight from ubiquitous mobile devices that will yield more accurate machine learning models in monitoring blood pressure.

The current deliverable summarises the work conducted within task T4.5 of WP4, presenting our proposed approaches for contextualised content interpretation, aimed at gaining insightful contextualised views on content semantics. This is achieved through the adoption of appropriate context-aware semantic models developed within the project, and via enriching the semantic descriptions with background knowledge, deriving thus higher level contextualised content interpretations that are closer to human perception and appraisal needs. More specifically, the main contributions of the deliverable are the following: A theoretical framework using physics as a metaphor to develop different models of evolving semantic content. A set of proof-of-concept models for semantic drifts due to field dynamics, introducing two methods to identify quantum-like (QL) patterns in evolving information searching behaviour, and a QL model akin to particle-wave duality for semantic content classification. Integration of two specific tools, Somoclu for drift detection and Ncpol2spda for entanglement detection. An “energetic” hypothesis accounting for contextualized evolving semantic structures over time. A proposed semantic interpretation framework, integrating (a) an ontological inference scheme based on Description Logics (DL), (b) a rule-based reasoning layer built on SPARQL Inference Notation (SPIN), (c) an uncertainty management framework based on non-monotonic logics. A novel scheme for contextualized reasoning on semantic drift, based on LRM dependencies and OWL’s punning mechanism. An implementation of SPIN rules for policy and ecosystem change management, with the adoption of LRM preconditions and impacts. Specific use case scenarios demonstrate the context under development and the efficiency of the approach. Respective open-source implementations and experimental results that validate all the above.All these contributions are tightly interlinked with the other PERICLES work packages: WP2 supplies the use cases and sample datasets for validating our proposed approaches, WP3 provides the models (LRM and Digital Ecosystem models) that form the basis for our semantic representations of content and context, WP5 provides the practical application of the technologies developed to preservation processes, while the tools and algorithms presented in this deliverable can be deployed in combination with test scenarios, which will be part of the WP6 test beds.

Entanglement is one of the most studied properties of quantum mechanics for its application in quantum information protocols. Nevertheless, detecting the presence of entanglement in large multipartite sates keeps being a great challenge both from the theoretical and the experimental point of view. Most of the known methods either have computational costs that scale inefficiently with the number of parties or require more information on the state than what is attainable in every-day experiments. We introduce a new technique for entanglement detection that provides several important advantages in these respects. First, its scales efficiently with the number of parties, thus allowing for application to systems composed by up to few tens of parties. Second, it needs only the knowledge of a subset of all possible measurements on the state, therefore being apt for experimental implementation. Moreover, since it is based on the detection of nonlocality, our method is device-independent. We report several examples of its implementation for well-known multipartite states, showing that the introduced technique has a promising range of applications.

In supervised learning, an inductive learning algorithm extracts general rules from observed training instances, then the rules are applied to test instances. We show that this splitting of training and application arises naturally, in the classical setting, from a simple independence requirement with a physical interpretation of being non-signalling. Thus, two seemingly different definitions of inductive learning happen to coincide. This follows from very specific properties of classical information, which break down in the quantum setup. We prove a quantum de Finetti theorem for quantum channels, which shows that in the quantum case, the equivalence holds in the asymptotic setting (for large number of test instances). This reveals a natural analogy between classical learning protocols and their quantum counterparts, thus allowing to naturally enquire about standard elements in computational learning theory, such as structural risk minimization, model and sample complexity.

Quantum control is valuable for various quantum technologies such as high-fidelity gates for universal quantum computing, adaptive quantum-enhanced metrology, and ultra-cold atom manipulation. Although supervised machine learning and reinforcement learning are widely used for optimizing control parameters in classical systems, quantum control for parameter optimization is mainly pursued via gradient-based greedy algorithms. Although the quantum fitness landscape is often compatible for greedy algorithms, sometimes greedy algorithms yield poor results, especially for large-dimensional quantum systems. We employ differential evolution algorithms to circumvent the stagnation problem of non-convex optimization, and we average over the objective function to improve quantum control fidelity for noisy systems. To reduce computational cost, we introduce heuristics for early termination of runs and for adaptive selection of search subspaces. Our implementation is massively parallel and vectorized to reduce run time even further. We demonstrate our methods with two examples, namely quantum phase estimation and quantum gate design, for which we achieve superior fidelity and scalability than obtained using greedy algorithms.