The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance.

This paper addresses the broader topic of using game theoretical learning mechanisms to efficiently and effectively identify relevant (e.g., optimal and non-mixed) solutions to large scale optimization problems. The longer-term goal is for the proposed MCFP-variants to become established methods for finding pure Nash equilibria and global optima of large-scale problems.

We discuss finding minimum spanning trees (MSTs) on connected graphs with countably many nodes of finite degree. When edge costs are summable and an MST exists (which is not guaranteed in general), we show that an algorithm that finds MSTs on finite subgraphs (called layers) converges in objective value to the cost of an MST of the whole graph as the sizes of the layers grow to infinity. We call this the layered greedy algorithm since a greedy algorithm is used to find MSTs on each finite layer. We stress that the overall algorithm is not greedy since edges can enter and leave iterate spanning trees as larger layers are considered. However, in the setting where the underlying graph has the finite cycle (FC) property (meaning that every edge is contained in at most finitely many cycles) and distinct edge costs, we show that a unique MST T\ast exists and the layered greedy algorithm produces iterates that converge to T\ast by eventually ``locking in"" edges after finitely many iterations. Applications to network deployment are discussed.

The power spectrum of the nonlinearly evolved large-scale mass distribution recovers only a minority of the information available on the mass fluctuation amplitude. We investigate the recovery of this information in 2D "slabs" of the mass distribution averaged over $\approx100$~$h^{-1}$Mpc along the line of sight, as might be obtained from photometric redshift surveys. We demonstrate a Hamiltonian Monte Carlo (HMC) method to reconstruct the non-Gaussian mass distribution in slabs, under the assumption that the projected field is a point-transformed Gaussian random field, Poisson-sampled by galaxies. When applied to the \textit{Quijote} $N$-body suite at $z=0.5$ and at a transverse resolution of 2~$h^{-1}$Mpc, the method recovers $\sim 30$ times more information than the 2D power spectrum in the well-sampled limit, recovering the Gaussian limit on information. At a more realistic galaxy sampling density of $0.01$~$h^3$Mpc$^{-3}$, shot noise reduces the information gain to a factor of 5 improvement over the power spectrum at resolutions of 4~$h^{-1}$Mpc or smaller.

Reinforcement learning (RL) requires an agent to interact with an environment to maximize the cumulative rather than the immediate reward. Recently, there as been a significant growth in the availability of scalable RL tasks, e.g. OpenAI gym. However, most benchmarking studies concentrate on RL solutions based on some form of deep learning. In this work, we benchmark a family of linear genetic programming based approaches to the 2-d biped walker problem. The biped walker is an example of a RL environment described in terms of a multi-dimensional, real-valued 24-d input and 4-d action space. Specific recommendations are made regarding mechanisms to adopt that are able to consistently produce solutions, in this case using transfer from periodic restarts.

In finite graphs, greedy algorithms are used to find minimum spanning trees (MinST) and maximum spanning trees (MaxST). In infinite graphs, we illustrate a general class of problems where a greedy approach discovers a MaxST while a MinST may be unreachable. Our algorithm is a natural extension of Prim's to infinite graphs with summable and strictly positive edge weights, producing a sequence of finite trees that converge to a MaxST.

We introduce a simplex method for general countably infinite linear programs. Previous literature has focused on special cases, such as infinite network flow problems or Markov decision processes. A novel aspect of our approach is the placing of data and decision variables in a Hilbert space that elegantly encodes a ``discounted"" weighting to ensure the continuity of infinite sums. Under some assumptions, including that all basic feasible solutions are nondegenerate with strictly positive support and the set of bases is closed in an appropriate topology, we show convergence to the optimal value for our proposed simplex algorithm. We show that existing applications naturally fit this more general framework.

We introduce the algorithm Bayesian Optimization (BO) with Fictitious Play (BOFiP) for the optimization of high dimensional black box functions. BOFiP decomposes the original, high dimensional, space into several sub-spaces defined by non-overlapping sets of dimensions. These sets are randomly generated at the start of the algorithm, and they form a partition of the dimensions of the original space. BOFiP searches the original space with alternating BO, within sub-spaces, and information exchange among sub-spaces, to update the sub-space function evaluation. The basic idea is to distribute the high dimensional optimization across low dimensional sub-spaces, where each sub-space is a player in an equal interest game. At each iteration, BO produces approximate best replies that update the players belief distribution. The belief update and BO alternate until a stopping condition is met. High dimensional problems are common in real applications, and several contributions in the BO literature have highlighted the difficulty in scaling to high dimensions due to the computational complexity associated to the estimation of the model hyperparameters. Such complexity is exponential in the problem dimension, resulting in substantial loss of performance for most techniques with the increase of the input dimensionality. We compare BOFiP to several state-of-the-art approaches in the field of high dimensional black box optimization. The numerical experiments show the performance over three benchmark objective functions from 20 up to 1000 dimensions. A neural network architecture design problem is tested with 42 up to 911 nodes in 6 up to 92 layers, respectively, resulting into networks with 500 up to 10,000 weights. These sets of experiments empirically show that BOFiP outperforms its competitors, showing consistent performance across different problems and increasing problem dimensionality.

We develop novel dual-ascent and primal-dual methods to solve infinite-horizon nonstationary deterministic dynamic programs. These methods are finitely implementable and converge in value to optimality. Moreover, the dual-ascent method produces a sequence of improving dual solutions that pointwise converge to an optimal dual solution, while the primal-dual algorithm provides a sequence of primal basic feasible solutions with value error bounds from optimality that converge to zero. Our dual-based methods work on a more general class of infinite network flow problems that include the shortest-path formulation of dynamic programs as a special case. To our knowledge, these are the first dual-based methods proposed in the literature to solve infinite-horizon nonstationary deterministic dynamic programs.

Solving a stochastic optimization problem often involves performing repeated noisy function evaluations at points encountered during the algorithm. Recently, a continuous optimization framework for executing a single observation per search point was shown to exhibit a martingale property so that associated estimation errors are guaranteed to converge to zero. We generalize this martingale single observation approach to problems with mixed discrete–continuous variables. We establish mild regularity conditions for this class of algorithms to converge to a global optimum.

We explore an alternative method to the usual shear correlation function approach for the estimation of aperture mass statistics in weak lensing survey data. Our approach builds on the direct estimator method of Schneider (1998). In this paper, to test and validate the methodology, we focus on the aperture mass dispersion. After computing the signal and noise for a weighted set of measured ellipticites we show how the direct estimator can be made into a linear order algorithm that enables a fast and efficient computation. We then investigate the applicability of the direct estimator approach in the presence of a real survey mask with holes and chip gaps. For this we use a large ensemble of full ray-tracing mock simulations. By using various weighting schemes for combining information from different apertures we find that inverse variance weighting the individual aperture estimates with an aperture completeness greater than 70 per cent coverage yields an answer that is in close agreement with the standard correlation function approach. We then apply this approach to the CFHTLenS as pilot scheme and find that our method recovers to high accuracy the Kilbinger (2013) result for the variance of both the E and B mode signal, after we correct the catalogue for the shear bias in the lensfit algorithm for pairs closer than 9". We then explore the cosmological information content of the direct estimator using the Fisher information approach. We show that there is a only modest loss in cosmological information from the rejection of apertures that are of low completeness. This method unlocks the door to fast and efficient methods for recovering higher order aperture mass statistics in linear order operations.

We consider an infinite quadratic programming problem with positive semi-definite quadratic costs, equality constraints and unbounded variables. Sufficient conditions are given for there to exist an optimal solution. Specifically, we require that (1) the cost operator be strictly positive definite when restricted to the orthogonal complement of its kernel, and (2) the constraint operator have closed range when restricted to the kernel of the cost operator. Condition (1) is shown to be equivalent to the spectrum of the restricted cost operator being bounded away from zero. Similarly, condition (2) is equivalent to the minimum modulus of the restricted constraint operator being positive. In the presence of separability, we give a sufficient condition for (2) to hold in terms of finite dimensional truncations of the restricted constraint operator. We apply our results to a broad class of infinite horizon optimization problems. In this setting, the finite dimensional truncations can be considered to be finite dimensional approximations to our problem whose limit, in a somewhat formal sense, is our infinite dimensional problem. Each of these approximations has properties (1) and (2) by virtue of their finite-dimensionality, i.e., each admits an optimal solution. However, our infinite dimensional problem may not. Thus, we give sufficient conditions for our problem to also admit an optimal solution. Finally, we illustrate this application in the case of an infinite horizon LQ regulator problem (a production planning problem).

Visual reinforcement learning implies that, decision making policies are identified under delayed rewards from an environment. Moreover, state information takes the form of high-dimensional data, such as video. In addition, although the video might characterize a 3D world in high resolution, partial observability will place significant limits on what the agent can actually perceive of the world. This means that the agent also has to: (1) provide efficient encodings of state, (2) store the encodings of state efficiently in some form of memory, (3) recall such memories after arbitrary delays for decision making. In this work, we demonstrate how an external memory model facilitates decision making in the complex world of multi-agent 'deathmatches' in the ViZDoom first person shooter environment. The ViZDoom environment provides a complex environment of multiple rooms and resources in which agents are spawned from multiple different locations. A unique approach is adopted to defining external memory for genetic programming agents in which: (1) the state of memory is shared across all programs. (2) Writing is formulated as a probabilistic process, resulting in different regions of memory having short- versus long-term memory. (3) Read operations are indexed, enabling programs to identify regions of external memory with specific temporal properties. We demonstrate that agents purposefully navigate the world when external memory is provided, whereas those without external memory are limited to merely 'flight or fight' behaviour.

Researchers explored the perspectives of third-grade students attending a 6-week science, technology, engineering, and mathematics (STEM) achievement motivation pilot program at a university’s early childhood development center serving a Hispanic population. Researchers obtained data from interviews, observations, and a focus group. Four major themes emerged from this phenomenological qualitative investigation. Findings support the implementation by school counselors of STEM achievement motivation programs with young students, who in this study reported an understanding of concepts presented and their application to math and science projects. The findings have implications for counselors employed in school settings.

Finding optimal policies when the objective function can only be observed with a noisy error has traditionally required repeated observations to average out the noise. In this paper, we prove for a very large class of continuous stochastic optimization problems and search algorithms that a single observation for each candidate solution suffices to completely eliminate the error. This surprising result can best be understood through the metaphor of facing a continuum of slot machines and observing the reward for a single pull of the arm for each machine as we search for a machine delivering the best return. By the impossibility of systems, the average winnings must approach the expected winnings regardless of how we select the sequence of machines to test. This same martingale property is inherited for simulation optimization so that a single observation also suffices for convergence to the global optimum. The resulting savings in simulation time can be quite significant.

We provide a simplex algorithm for a structured class of uncapacitated countably infinite network flow problems. Previous efforts required explicit capacities on arcs with uniformity properties that facilitate duality arguments. By contrast, this paper takes a "primal" approach by devising a simplex method that provably converges to the optimal value using arguments based on convergence of spanning trees and nonnegativity of reduced costs. This allows for removal of explicit capacity bounds. The method also converges, on a subsequence, to an extremal optimal solution. Our method is tailored to our problem setting-acyclic networks with nodes of only nonnegative supplies (or, alternatively, only demands). The necessary structure can be found in a variety of applied settings not amenable to existing methods, including nonstationary infinite-horizon dynamic programming. A finite implementation of our simplex algorithm is provided for the infinite horizon dynamic lot-sizing problem under linear costs.

A tangled program graph framework (TPG) was recently proposed as an emergent process for decomposing tasks and simultaneously composing solutions by organizing code into graphs of teams of programs. The initial evaluation assessed the ability of TPG to discover agents capable of playing Atari game titles under the Arcade Learning Environment. This is an example of ‘visual’ reinforcement learning, i.e. agents are evolved directly from the frame buffer without recourse to hand designed features. TPG was able to evolve solutions competitive with state-of-the-art deep reinforcement learning solutions, but at a fraction of the complexity. One simplification assumed was that the visual input could be down sampled from a 210 × 160 resolution to 42 × 32 . In this work, we consider the challenging 3D first person shooter environment of ViZDoom and require that agents be evolved at the original visual resolution of 320 × 240 pixels. In addition, we address issues for developing agents capable of operating in multi-task ViZDoom environments simultaneously. The resulting TPG solutions retain all the emergent properties of the original work as well as the computational efficiency. Moreover, solutions appear to generalize across multiple task scenarios, whereas equivalent solutions from deep reinforcement learning have focused on single task scenarios alone.

The safety assessment of a flavour substance examines several factors, including metabolic and physiological disposition data. The present article provides an overview of the metabolism and disposition of flavour substances by identifying general applicable principles of metabolism to illustrate how information on metabolic fate is taken into account in their safety evaluation. The metabolism of the majority of flavour substances involves a series both of enzymatic and non-enzymatic biotransformation that often results in products that are more hydrophilic and more readily excretable than their precursors. Flavours can undergo metabolic reactions, such as oxidation, reduction, or hydrolysis that alter a functional group relative to the parent compound. The altered functional group may serve as a reaction site for a subsequent metabolic transformation. Metabolic intermediates undergo conjugation with an endogenous agent such as glucuronic acid, sulphate, glutathione, amino acids, or acetate. Such conjugates are typically readily excreted through the kidneys and liver. This paper summarizes the types of metabolic reactions that have been documented for flavour substances that are added to the human food chain, the methodologies available for metabolic studies, and the factors that affect the metabolic fate of a flavour substance.

Summary StatementThis work raises the potential of utilizing stem cells to catalyze cartilage regeneration by a minimal number of neonatal chondrocytes via controlling cell distribution in 3D matri...