Spatial trajectories are ubiquitous and complex signals. Their analysis is crucial in many research fields, from urban planning to neuroscience. Several approaches have been proposed to cluster trajectories. They rely on hand-crafted features, which struggle to capture the spatio-temporal complexity of the signal, or on Artificial Neural Networks (ANNs) which can be more efficient but less interpretable. In this paper we present a novel ANN architecture designed to capture the spatio-temporal patterns characteristic of a set of trajectories, while taking into account the demographics of the navigators. Hence, our model extracts markers linked to both behaviour and demographics. We propose a composite signal analyser (CompSNN) combining three simple ANN modules. Each of these modules uses different signal representations of the trajectory while remaining interpretable. Our CompSNN performs significantly better than its modules taken in isolation and allows to visualise which parts of the signal were most useful to discriminate the trajectories.

In recent years, multi-access edge computing (MEC) is a key enabler for handling the massive expansion of Internet of Things (IoT) applications and services. However, energy consumption of a MEC network depends on volatile tasks that induces risk for energy demand estimations. As an energy supplier, a microgrid can facilitate seamless energy supply. However, the risk associated with energy supply is also increased due to unpredictable energy generation from renewable and non-renewable sources. Especially, the risk of energy shortfall is involved with uncertainties in both energy consumption and generation. In this paper, we study a risk-aware energy scheduling problem for a microgrid-powered MEC network. First, we formulate an optimization problem considering the conditional value-at-risk (CVaR) measurement for both energy consumption and generation, where the objective is to minimize the loss of energy shortfall of the MEC networks and we show this problem is an NP-hard problem. Second, we analyze our formulated problem using a multi-agent stochastic game that ensures the joint policy Nash equilibrium, and show the convergence of the proposed model. Third, we derive the solution by applying a multi-agent deep reinforcement learning (MADRL)-based asynchronous advantage actor-critic (A3C) algorithm with shared neural networks. This method mitigates the curse of dimensionality of the state space and chooses the best policy among the agents for the proposed problem. Finally, the experimental results establish a significant performance gain by considering CVaR for high accuracy energy scheduling of the proposed model than both the single and random agent models.

Multi-Class Incremental Learning (MCIL) aims to learn new concepts by incrementally updating a model trained on previous concepts. However, there is an inherent trade-off to effectively learning new concepts without catastrophic forgetting of previous ones. To alleviate this issue, it has been proposed to keep around a few examples of the previous concepts but the effectiveness of this approach heavily depends on the representativeness of these examples. This paper proposes a novel and automatic framework we call mnemonics, where we parameterize exemplars and make them optimizable in an end-to-end manner. We train the framework through bilevel optimizations, i.e., model-level and exemplar-level. We conduct extensive experiments on three MCIL benchmarks, CIFAR-100, ImageNet-Subset and ImageNet, and show that using mnemonics exemplars can surpass the state-of-the-art by a large margin. Interestingly and quite intriguingly, the mnemonics exemplars tend to be on the boundaries between different classes.

Area under ROC curve (AUC) is a widely used performance measure for classification models. We propose two new distributionally robust AUC maximization models (DR-AUC) that rely on the Kantorovich metric and approximate the AUC with the hinge loss function. We consider the two cases with respectively fixed and variable support for the worst-case distribution. We use duality theory to reformulate the DR-AUC models and derive tractable convex optimization problems. The numerical experiments show that the proposed DR-AUC models -- benchmarked with the standard deterministic AUC and the support vector machine models - perform better in general and in particular improve the worst-case out-of-sample performance over the majority of the considered datasets, thereby showing their robustness. The results are particularly encouraging since our numerical experiments are conducted with training sets of small size which have been known to be conducive to low out-of-sample performance.

We study the information content of nuclear masses from the perspective of global models of nuclear binding energies. To this end, we employ a number of statistical methods and diagnostic tools, including Bayesian calibration, Bayesian model averaging, chi-square correlation analysis, principal component analysis, and empirical coverage probability. Using a Bayesian framework, we investigate the structure of the 4-parameter Liquid Drop Model by considering discrepant mass domains for calibration. We then use the chi-square correlation framework to analyze the 14-parameter Skyrme energy density functional calibrated using homogeneous and heterogeneous datasets. We show that a quite dramatic parameter reduction can be achieved in both cases. The advantage of Bayesian model averaging for improving uncertainty quantification is demonstrated. The statistical approaches used are pedagogically described; in this context this work can serve as a guide for future applications.

Supervised machine learning algorithms have seen spectacular advances and surpassed human level performance in a wide range of specific applications. However, using complex ensemble or deep learning algorithms typically results in black box models, where the path leading to individual predictions cannot be followed in detail. In order to address this issue, we propose the novel "Cyclic Boosting" machine learning algorithm, which allows to efficiently perform accurate regression and classification tasks while at the same time allowing a detailed understanding of how each individual prediction was made.

Beginning from a basic neural-network architecture, we test the potential benefits offered by a range of advanced techniques for machine learning, in particular deep learning, in the context of a typical classification problem encountered in the domain of high-energy physics, using a well-studied dataset: the 2014 Higgs ML Kaggle dataset. The advantages are evaluated in terms of both performance metrics and the time required to train and apply the resulting models. Techniques examined include domain-specific data-augmentation, learning rate and momentum scheduling, (advanced) ensembling in both model-space and weight-space, and alternative architectures and connection methods.

Following the investigation, we arrive at a model which achieves equal performance to the winning solution of the original Kaggle challenge, whilst being significantly quicker to train and apply, and being suitable for use with both GPU and CPU hardware setups. These reductions in timing and hardware requirements potentially allow the use of more powerful algorithms in HEP analyses, where models must be retrained frequently, sometimes at short notice, by small groups of researchers with limited hardware resources. Additionally, a new wrapper library for PyTorch called LUMINis presented, which incorporates all of the techniques studied.

Attribution methods provide insights into the decision-making of machine learning models like artificial neural networks. For a given input sample, they assign a relevance score to each individual input variable, such as the pixels of an image. In this work we adapt the information bottleneck concept for attribution. By adding noise to intermediate feature maps we restrict the flow of information and can quantify (in bits) how much information image regions provide. We compare our method against ten baselines using three different metrics on VGG-16 and ResNet-50, and find that our methods outperform all baselines in five out of six settings. The method's information-theoretic foundation provides an absolute frame of reference for attribution values (bits) and a guarantee that regions scored close to zero are not necessary for the network's decision. For reviews: https://openreview.net/forum?id=S1xWh1rYwB For code: https://github.com/BioroboticsLab/IBA

We focus on estimating emph{a priori} generalization error of two-layer ReLU neural networks (NNs) trained by mean squared error, which only depends on initial parameters and the target function, through the following research line. We first estimate emph{a priori} generalization error of finite-width two-layer ReLU NN with constraint of minimal norm solution, which is proved by cite{zhang2019type} to be an equivalent solution of a linearized (w.r.t. parameter) finite-width two-layer NN. As the width goes to infinity, the linearized NN converges to the NN in Neural Tangent Kernel (NTK) regime citep{jacot2018neural}. Thus, we can derive the emph{a priori} generalization error of two-layer ReLU NN in NTK regime. The distance between NN in a NTK regime and a finite-width NN with gradient training is estimated by cite{arora2019exact}. Based on the results in cite{arora2019exact}, our work proves an emph{a priori} generalization error bound of two-layer ReLU NNs. This estimate uses the intrinsic implicit bias of the minimum norm solution without requiring extra regularity in the loss function. This emph{a priori} estimate also implies that NN does not suffer from curse of dimensionality, and a small generalization error can be achieved without requiring exponentially large number of neurons. In addition the research line proposed in this paper can also be used to study other properties of the finite-width network, such as the posterior generalization error.

We focus on the challenge of finding a diverse collection of quality solutions on complex continuous domains. While quality diver-sity (QD) algorithms like Novelty Search with Local Competition (NSLC) and MAP-Elites are designed to generate a diverse range of solutions, these algorithms require a large number of evaluations for exploration of continuous spaces. Meanwhile, variants of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) are among the best-performing derivative-free optimizers in single-objective continuous domains. This paper proposes a new QD algorithm called Covariance Matrix Adaptation MAP-Elites (CMA-ME). Our new algorithm combines the self-adaptation techniques of CMA-ES with archiving and mapping techniques for maintaining diversity in QD. Results from experiments based on standard continuous optimization benchmarks show that CMA-ME finds better-quality solutions than MAP-Elites; similarly, results on the strategic game Hearthstone show that CMA-ME finds both a higher overall quality and broader diversity of strategies than both CMA-ES and MAP-Elites. Overall, CMA-ME more than doubles the performance of MAP-Elites using standard QD performance metrics. These results suggest that QD algorithms augmented by operators from state-of-the-art optimization algorithms can yield high-performing methods for simultaneously exploring and optimizing continuous search spaces, with significant applications to design, testing, and reinforcement learning among other domains.

This paper develops a general framework for analyzing asymptotics of $V$-statistics. Previous literature on limiting distribution mainly focuses on the cases when $n o infty$ with fixed kernel size $k$. Under some regularity conditions, we demonstrate asymptotic normality when $k$ grows with $n$ by utilizing existing results for $U$-statistics. The key in our approach lies in a mathematical reduction to $U$-statistics by designing an equivalent kernel for $V$-statistics. We also provide a unified treatment on variance estimation for both $U$- and $V$-statistics by observing connections to existing methods and proposing an empirically more accurate estimator. Ensemble methods such as random forests, where multiple base learners are trained and aggregated for prediction purposes, serve as a running example throughout the paper because they are a natural and flexible application of $V$-statistics.

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph $F$ into a large network $mathcal{G}$. We propose two complementary MCMC algorithms for sampling a random graph homomorphisms and establish bounds on their mixing times and concentration of their time averages. Based on our sampling algorithms, we propose a novel framework for network data analysis that circumvents some of the drawbacks in methods based on independent and neigborhood sampling. Various time averages of the MCMC trajectory give us various computable observables, including well-known ones such as homomorphism density and average clustering coefficient and their generalizations. Furthermore, we show that these network observables are stable with respect to a suitably renormalized cut distance between networks. We provide various examples and simulations demonstrating our framework through synthetic networks. We also apply our framework for network clustering and classification problems using the Facebook100 dataset and Word Adjacency Networks of a set of classic novels.

Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often have an interesting theoretical interpretation in real problems. However, standard factor analysis is only applicable when the variables are scaled, which is often inappropriate, for example, in data obtained from questionnaires in the field of psychology,where the variables are often categorical. In this framework, we propose a factor model for the analysis of multivariate ordered and non-ordered polychotomous data. The inference procedure is done under the Bayesian approach via Markov chain Monte Carlo methods. Two Monte-Carlo simulation studies are presented to investigate the performance of this approach in terms of estimation bias, precision and assessment of the number of factors. We also illustrate the proposed method to analyze participants' responses to the Motivational State Questionnaire dataset, developed to study emotions in laboratory and field settings.

A deep neural network has relieved the burden of feature engineering by human experts, but comparable efforts are instead required to determine an effective architecture. On the other hands, as the size of a network has over-grown, a lot of resources are also invested to reduce its size. These problems can be addressed by sparsification of an over-complete model, which removes redundant parameters or connections by pruning them away after training or encouraging them to become zero during training. In general, however, these approaches are not fully differentiable and interrupt an end-to-end training process with the stochastic gradient descent in that they require either a parameter selection or a soft-thresholding step. In this paper, we propose a fully differentiable sparsification method for deep neural networks, which allows parameters to be exactly zero during training, and thus can learn the sparsified structure and the weights of networks simultaneously using the stochastic gradient descent. We apply the proposed method to various popular models in order to show its effectiveness.

A major difficulty of solving continuous POMDPs is to infer the multi-modal distribution of the unobserved true states and to make the planning algorithm dependent on the perceived uncertainty. We cast POMDP filtering and planning problems as two closely related Sequential Monte Carlo (SMC) processes, one over the real states and the other over the future optimal trajectories, and combine the merits of these two parts in a new model named the DualSMC network. In particular, we first introduce an adversarial particle filter that leverages the adversarial relationship between its internal components. Based on the filtering results, we then propose a planning algorithm that extends the previous SMC planning approach [Piche et al., 2018] to continuous POMDPs with an uncertainty-dependent policy. Crucially, not only can DualSMC handle complex observations such as image input but also it remains highly interpretable. It is shown to be effective in three continuous POMDP domains: the floor positioning domain, the 3D light-dark navigation domain, and a modified Reacher domain.

Boosting is one of the most successful ideas in machine learning. The most well-accepted explanations for the low generalization error of boosting algorithms such as AdaBoost stem from margin theory. The study of margins in the context of boosting algorithms was initiated by Schapire, Freund, Bartlett and Lee (1998) and has inspired numerous boosting algorithms and generalization bounds. To date, the strongest known generalization (upper bound) is the $k$th margin bound of Gao and Zhou (2013). Despite the numerous generalization upper bounds that have been proved over the last two decades, nothing is known about the tightness of these bounds. In this paper, we give the first margin-based lower bounds on the generalization error of boosted classifiers. Our lower bounds nearly match the $k$th margin bound and thus almost settle the generalization performance of boosted classifiers in terms of margins.

We study the problem of parameter estimation for a non-ergodic Gaussian Vasicek-type model defined as $dX_t=(mu+ heta X_t)dt+dG_t, tgeq0$ with unknown parameters $ heta>0$ and $muinR$, where $G$ is a Gaussian process. We provide least square-type estimators $widetilde{ heta}_T$ and $widetilde{mu}_T$ respectively for the drift parameters $ heta$ and $mu$ based on continuous-time observations ${X_t, tin[0,T]}$ as $T ightarrowinfty$.

Our aim is to derive some sufficient conditions on the driving Gaussian process $G$ in order to ensure that $widetilde{ heta}_T$ and $widetilde{mu}_T$ are strongly consistent, the limit distribution of $widetilde{ heta}_T$ is a Cauchy-type distribution and $widetilde{mu}_T$ is asymptotically normal. We apply our result to fractional Vasicek, subfractional Vasicek and bifractional Vasicek processes. In addition, this work extends the result of cite{EEO} studied in the case where $mu=0$.

We study the interplay of two important issues on Bayesian model selection (BMS): censoring and model misspecification. We consider additive accelerated failure time (AAFT), Cox proportional hazards and probit models, and a more general concave log-likelihood structure. A fundamental question is what solution can one hope BMS to provide, when (inevitably) models are misspecified. We show that asymptotically BMS keeps any covariate with predictive power for either the outcome or censoring times, and discards other covariates. Misspecification refers to assuming the wrong model or functional effect on the response, including using a finite basis for a truly non-parametric effect, or omitting truly relevant covariates. We argue for using simple models that are computationally practical yet attain good power to detect potentially complex effects, despite misspecification. Misspecification and censoring both have an asymptotically negligible effect on (suitably-defined) false positives, but their impact on power is exponential. We portray these issues via simple descriptions of early/late censoring and the drop in predictive accuracy due to misspecification. From a methods point of view, we consider local priors and a novel structure that combines local and non-local priors to enforce sparsity. We develop algorithms to capitalize on the AAFT tractability, approximations to AAFT and probit likelihoods giving significant computational gains, a simple augmented Gibbs sampler to hierarchically explore linear and non-linear effects, and an implementation in the R package mombf. We illustrate the proposed methods and others based on likelihood penalties via extensive simulations under misspecification and censoring. We present two applications concerning the effect of gene expression on colon and breast cancer.

Adaptive importance samplers are adaptive Monte Carlo algorithms to estimate expectations with respect to some target distribution which extit{adapt} themselves to obtain better estimators over a sequence of iterations. Although it is straightforward to show that they have the same $mathcal{O}(1/sqrt{N})$ convergence rate as standard importance samplers, where $N$ is the number of Monte Carlo samples, the behaviour of adaptive importance samplers over the number of iterations has been left relatively unexplored. In this work, we investigate an adaptation strategy based on convex optimisation which leads to a class of adaptive importance samplers termed extit{optimised adaptive importance samplers} (OAIS). These samplers rely on the iterative minimisation of the $chi^2$-divergence between an exponential-family proposal and the target. The analysed algorithms are closely related to the class of adaptive importance samplers which minimise the variance of the weight function. We first prove non-asymptotic error bounds for the mean squared errors (MSEs) of these algorithms, which explicitly depend on the number of iterations and the number of samples together. The non-asymptotic bounds derived in this paper imply that when the target belongs to the exponential family, the $L_2$ errors of the optimised samplers converge to the optimal rate of $mathcal{O}(1/sqrt{N})$ and the rate of convergence in the number of iterations are explicitly provided. When the target does not belong to the exponential family, the rate of convergence is the same but the asymptotic $L_2$ error increases by a factor $sqrt{ ho^star} > 1$, where $ ho^star - 1$ is the minimum $chi^2$-divergence between the target and an exponential-family proposal.

The Rosenbrock function is an ubiquitous benchmark problem for numerical optimisation, and variants have been proposed to test the performance of Markov Chain Monte Carlo algorithms. In this work we discuss the two-dimensional Rosenbrock density, its current $n$-dimensional extensions, and their advantages and limitations. We then propose a new extension to arbitrary dimensions called the Hybrid Rosenbrock distribution, which is composed of conditional normal kernels arranged in such a way that preserves the key features of the original kernel. Moreover, due to its structure, the Hybrid Rosenbrock distribution is analytically tractable and possesses several desirable properties, which make it an excellent test model for computational algorithms.

Deep networks run with low precision operations at inference time offer power and space advantages over high precision alternatives, but need to overcome the challenge of maintaining high accuracy as precision decreases. Here, we present a method for training such networks, Learned Step Size Quantization, that achieves the highest accuracy to date on the ImageNet dataset when using models, from a variety of architectures, with weights and activations quantized to 2-, 3- or 4-bits of precision, and that can train 3-bit models that reach full precision baseline accuracy. Our approach builds upon existing methods for learning weights in quantized networks by improving how the quantizer itself is configured. Specifically, we introduce a novel means to estimate and scale the task loss gradient at each weight and activation layer's quantizer step size, such that it can be learned in conjunction with other network parameters. This approach works using different levels of precision as needed for a given system and requires only a simple modification of existing training code.

In classification models fairness can be ensured by solving a constrained optimization problem. We focus on fairness constraints like Disparate Impact, Demographic Parity, and Equalized Odds, which are non-decomposable and non-convex. Researchers define convex surrogates of the constraints and then apply convex optimization frameworks to obtain fair classifiers. Surrogates serve only as an upper bound to the actual constraints, and convexifying fairness constraints might be challenging.

We propose a neural network-based framework, emph{FNNC}, to achieve fairness while maintaining high accuracy in classification. The above fairness constraints are included in the loss using Lagrangian multipliers. We prove bounds on generalization errors for the constrained losses which asymptotically go to zero. The network is optimized using two-step mini-batch stochastic gradient descent. Our experiments show that FNNC performs as good as the state of the art, if not better. The experimental evidence supplements our theoretical guarantees. In summary, we have an automated solution to achieve fairness in classification, which is easily extendable to many fairness constraints.

We propose a novel estimation procedure for scale-by-scale lead-lag relationships of financial assets observed at high-frequency in a non-synchronous manner. The proposed estimation procedure does not require any interpolation processing of original datasets and is applicable to those with highest time resolution available. Consistency of the proposed estimators is shown under the continuous-time framework that has been developed in our previous work Hayashi and Koike (2018). An empirical application to a quote dataset of the NASDAQ-100 assets identifies two types of lead-lag relationships at different time scales.

When the response mechanism is believed to be not missing at random (NMAR), a valid analysis requires stronger assumptions on the response mechanism than standard statistical methods would otherwise require. Semiparametric estimators have been developed under the model assumptions on the response mechanism. In this paper, a new statistical test is proposed to guarantee model identifiability without using any instrumental variable. Furthermore, we develop optimal semiparametric estimation for parameters such as the population mean. Specifically, we propose two semiparametric optimal estimators that do not require any model assumptions other than the response mechanism. Asymptotic properties of the proposed estimators are discussed. An extensive simulation study is presented to compare with some existing methods. We present an application of our method using Korean Labor and Income Panel Survey data.

Given a multivariate data set, sparse principal component analysis (SPCA) aims to extract several linear combinations of the variables that together explain the variance in the data as much as possible, while controlling the number of nonzero loadings in these combinations. In this paper we consider 8 different optimization formulations for computing a single sparse loading vector; these are obtained by combining the following factors: we employ two norms for measuring variance (L2, L1) and two sparsity-inducing norms (L0, L1), which are used in two different ways (constraint, penalty). Three of our formulations, notably the one with L0 constraint and L1 variance, have not been considered in the literature. We give a unifying reformulation which we propose to solve via a natural alternating maximization (AM) method. We show the the AM method is nontrivially equivalent to GPower (Journ'{e}e et al; JMLR 11:517--553, 2010) for all our formulations. Besides this, we provide 24 efficient parallel SPCA implementations: 3 codes (multi-core, GPU and cluster) for each of the 8 problems. Parallelism in the methods is aimed at i) speeding up computations (our GPU code can be 100 times faster than an efficient serial code written in C++), ii) obtaining solutions explaining more variance and iii) dealing with big data problems (our cluster code is able to solve a 357 GB problem in about a minute).

Nicolas Garcia Trillos, Daniel Sanz-Alonso.

Source: Bayesian Analysis, Volume 15, Number 1, 29--56.

Abstract:
The Bayesian update can be viewed as a variational problem by characterizing the posterior as the minimizer of a functional. The variational viewpoint is far from new and is at the heart of popular methods for posterior approximation. However, some of its consequences seem largely unexplored. We focus on the following one: defining the posterior as the minimizer of a functional gives a natural path towards the posterior by moving in the direction of steepest descent of the functional. This idea is made precise through the theory of gradient flows, allowing to bring new tools to the study of Bayesian models and algorithms. Since the posterior may be characterized as the minimizer of different functionals, several variational formulations may be considered. We study three of them and their three associated gradient flows. We show that, in all cases, the rate of convergence of the flows to the posterior can be bounded by the geodesic convexity of the functional to be minimized. Each gradient flow naturally suggests a nonlinear diffusion with the posterior as invariant distribution. These diffusions may be discretized to build proposals for Markov chain Monte Carlo (MCMC) algorithms. By construction, the diffusions are guaranteed to satisfy a certain optimality condition, and rates of convergence are given by the convexity of the functionals. We use this observation to propose a criterion for the choice of metric in Riemannian MCMC methods.

Christophe Leterrier
Feb 28, 2018; 38:2135-2145
Viewpoints

To view more press releases, please visit http://www.snl.com/irweblinkx/news.aspx?iid=1024452.

The latest edition of The State of Food Security and Nutrition in the World will be launched on Monday 15 July 2019 during a special event on the [...]

The Farmers’ Market has been postponed for Friday 6 March and until further notice.

Researchers compared tree rings from around the world to determine that a volcano on Santorini probably erupted in 1560 B.C.

These dairy products are no longer edible, but they're still valuable to researchers

The rendering builds on decades of data that dates back to the Apollo missions, which happened some fifty years ago

Press release about the Basel Committee launching the consolidated Basel Framework, 16 December 2019.

Quebecers, like the rest of the world, are growing accustomed to the uncertainty that's accompanied the pandemic. But they may not appreciate their government adding to that already hefty burden.

The consolidated banking statistics provide quarterly data on the worldwide consolidated positions of banks headquartered in reporting countries. They are designed to analyse the exposure of internationally active banks of different nationalities to individual countries and sectors.

See what’s happening in the CME Group Agricultural markets, including the latest in the options market and opportunities from seasonality, cheese market updates, Black Sea grain news and more.

See volume, open interest, and other trading highlights for Fertilizer swaps and futures markets offered by CME Group.

Address by Mr Philip Lowe, Governor of the Reserve Bank of Australia, at the Reserve Bank of Australia, Sydney, 21 April 2020.

The National Capital Commission has reversed its decision and will now allow passersby to take photos at this year's Canadian Tulip Festival.

1. Coronavirus Outbreak Updates: Maharashtra reports 1,089 new COVID-19 cases across state, 748 in Mumbai; total infections at 19,063  Firstpost
2. Migrant workers | Maharashtra train accident victims were battling hunger  The Hindu
3. Maharashtra: They thought no trains were running, loco driver spotted them too late to stop  The Indian Express
4. ‘Stay where you are’: Shivraj Chouhan appeals to migrants after train tragedy  Hindustan Times
5. MP Ministers Ask Shivraj to Probe Tenure of Kamal Nath to ‘Expose Massive Corruption’  News18
6. View Full coverage on Google News

The NDP wants the Saskatchewan government to delay Phase 2 of its reopening plan, currently scheduled for May 19.

Here's a look at what's happening in our area on Thursday, May 7.

Here's a look at what's happening in our area on Friday, May 8.

See what’s happening in the CME Group Agricultural markets, including the latest in the options market and opportunities from seasonality, cheese market updates, Black Sea grain news and more.

See volume, open interest, and other trading highlights for Fertilizer swaps and futures markets offered by CME Group.

A number of popular iOS apps, including TikTok, Pinterest and Spotify, began to crash on Wednesday after an update to Facebook's SDK rolled out, software that many developers rely on to streamline the user login process.

Brydge on Wednesday launched a new update to improve its Brydge Pro+ keyboard with trackpad that recently starting shipping for iPad Pro. AppleInsider goes hands-on with the latest firmware to see how Brydge's improvements have strengthened the user experience of its flagship product.