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International audience; Sparsity-based methods, such as wavelets, have been the state of the art for more than 20 years for inverse problems before being overtaken by neural networks. In particular, U-nets have proven to be extremely effective. Their main ingredients are a highly nonlinear processing, a massive learning made possible by the flourishing of optimization algorithms with the power of computers (GPU) and the use of large available datasets for training. It is far from obvious to say which of these three ingredients has the biggest impact on the performance. While the many stages of nonlinearity are intrinsic to deep learning, the usage of learning with training data could also be exploited by sparsity-based approaches. The aim of our study is to push the limits of sparsity to use, similarly to U-nets, massive learning and large datasets, and then to compare the results with U-nets. We present a new network architecture, called learnlets, which conserves the properties of sparsity-based methods such as exact reconstruction and good generalization properties, while fostering the power of neural networks for learning and fast calculation. We evaluate the model on image denoising tasks. Our conclusion is that U-nets perform better than learnlets on image quality metrics in distribution, while learnlets have better generalization properties.

This paper studies a setting in which multiple suppliers compete for a buyer's procurement business. The buyer faces uncertain demand and there is a requirement to reserve capacity in advance of knowing the demand. Each supplier has costs that are two dimensional, with some costs incurred before demand is realized in order to reserve capacity and some costs incurred after demand is realized at the time of delivery. A distinctive feature of our model is that the marginal costs may not be constants, and this naturally leads us to a supply function competition framework in which each supplier offers a schedule of prices and quantities. We treat this problem as an example of a general class of capacity games and show that, when the optimal supply chain profit is submodular, in equilibrium the buyer makes a reservation choice that maximizes the overall supply chain profit, each supplier makes a profit equal to their marginal contribution to the supply chain, and the buyer takes the remaining profit. We further prove that this submodularity property holds under two commonly studied settings: (1) there are only two suppliers; and (2) in the case of more than two suppliers, the marginal two-dimension costs of each supplier are non-decreasing and constant, respectively., Comment: 35 pages

The topology of isosurfaces changes at isovalues of critical points, making such points an important feature when building contour trees or Morse-Smale complexes. Hexahedral elements with linear interpolants can contain additional off-vertex critical points in element bodies and on element faces. Moreover, a point on the face of a hexahedron which is critical in the element-local context is not necessarily critical in the global context. In ‘`Exploring Scalar Fields Using Critical Isovalues’' Weber et al. introduce a method to determine whether critical points on faces are also critical in the global context, based on the gradient of the asymptotic decider in each element that shares the face. However, as defined, the method of Weber et al. contains an error, and can lead to incorrect results. In this work we correct the error.

Efficient anomaly detection and diagnosis in multivariate time-series data is of great importance for modern industrial applications. However, building a system that is able to quickly and accurately pinpoint anomalous observations is a challenging problem. This is due to the lack of anomaly labels, high data volatility and the demands of ultra-low inference times in modern applications. Despite the recent developments of deep learning approaches for anomaly detection, only a few of them can address all of these challenges. In this paper, we propose TranAD, a deep transformer network based anomaly detection and diagnosis model which uses attention-based sequence encoders to swiftly perform inference with the knowledge of the broader temporal trends in the data. TranAD uses focus score-based self-conditioning to enable robust multi-modal feature extraction and adversarial training to gain stability. Additionally, model-agnostic meta learning (MAML) allows us to train the model using limited data. Extensive empirical studies on six publicly available datasets demonstrate that TranAD can outperform state-of-the-art baseline methods in detection and diagnosis performance with data and time-efficient training. Specifically, TranAD increases F1 scores by up to 17%, reducing training times by up to 99% compared to the baselines., Comment: Accepted in VLDB 2022

We present a novel distributed memory Tridiagonal solver library, targeting large-scale systems based on modern multi-core and many-core processor architectures. The library uses methods based on both approximate and exact algorithms. Performance comparisons with the state-of-the-art, using both a large Cray EX system and a GPU cluster show the algorithmic trade-offs required at increasing machine scale to achieve good performance, particularly considering the advent of exascale systems.

Graphical abstract, Highlights • Novel cell-free protein synthesis reaction buffer improves performance by 400%. • Enhanced performance is maintained across the synthesis of different proteins. • Protein synthesis performance is robust across different cell lysate batches and E. coli strains. • Buffer components affect aspects of reaction kinetics in differing ways., Cell-free protein synthesis (CFPS) reactions have grown in popularity with particular interest in applications such as gene construct prototyping, biosensor technologies and the production of proteins with novel chemistry. Work has frequently focussed on optimising CFPS protocols for improving protein yield, reducing cost, or developing streamlined production protocols. Here we describe a statistical Design of Experiments analysis of 20 components of a popular CFPS reaction buffer. We simultaneously identify factors and factor interactions that impact on protein yield, rate of reaction, lag time and reaction longevity. This systematic experimental approach enables the creation of a statistical model capturing multiple behaviours of CFPS reactions in response to components and their interactions. We show that a novel reaction buffer outperforms the reference reaction by 400% and importantly reduces failures in CFPS across batches of cell lysates, strains of E. coli, and in the synthesis of different proteins. Detailed and quantitative understanding of how reaction components affect kinetic responses and robustness is imperative for future deployment of cell-free technologies.

Changepoint models typically assume the data within each segment are independent and identically distributed conditional on some parameters that change across segments. This construction may be inadequate when data are subject to local correlation patterns, often resulting in many more changepoints fitted than preferable. This article proposes a Bayesian changepoint model that relaxes the assumption of exchangeability within segments. The proposed model supposes data within a segment are m-dependent for some unknown $$m \geqslant 0$$ m ⩾ 0 that may vary between segments, resulting in a model suitable for detecting clear discontinuities in data that are subject to different local temporal correlations. The approach is suited to both continuous and discrete data. A novel reversible jump Markov chain Monte Carlo algorithm is proposed to sample from the model; in particular, a detailed analysis of the parameter space is exploited to build proposals for the orders of dependence. Two applications demonstrate the benefits of the proposed model: computer network monitoring via change detection in count data, and segmentation of financial time series.

Creating scalable, high performance PDE-based simulations requires a suitable combination of discretizations, differential operators, preconditioners and solvers. The required combination changes with the application and with the available hardware, yet software development time is a severely limited resource for most scientists and engineers. Here we demonstrate that generating simulation code from a high-level Python interface provides an effective mechanism for creating high performance simulations from very few lines of user code. We demonstrate that moving from one supercomputer to another can require significant algorithmic changes to achieve scalable performance, but that the code generation approach enables these algorithmic changes to be achieved with minimal development effort.

The purpose of this paper is to initiate a theory concerning the dynamics of asymptotically holomorphic polynomial-like maps. Our maps arise naturally as deep renormalizations of asymptotically holomorphic extensions of C r (r > 3) unimodal maps that are infinitely renormalizable of bounded type. Here we prove a version of the Fatou-Julia-Sullivan theorem and a topological straightening theorem in this setting. In particular, these maps do not have wandering domains and their Julia sets are locally connected.

Motivation Single-cell/nuclei RNA-sequencing (scRNA-seq) technologies can simultaneously quantify gene expression in thousands of cells across the genome. However, the majority of the noncoding RNAs, such as microRNAs (miRNAs), cannot currently be profiled at the same scale. MiRNAs are a class of small noncoding RNAs and play an important role in gene regulation. MiRNAs originate from the processing of primary transcripts, known as primary-microRNAs (pri-miRNAs). The pri-miRNA transcripts, independent of their cognate miRNAs, can also function as long noncoding RNAs, code for micropeptides or even interact with DNA, acting like enhancers. Therefore, it is apparent that the significance of scRNA-seq pri-miRNA profiling expands beyond using pri-miRNA as proxies of mature miRNAs. However, there are no computational methods that allow profiling and quantification of pri-miRNAs at the single-cell-type resolution. Results We have developed a simple yet effective computational framework to profile pri-MiRNAs from single-cell RNA-sequencing datasets (PPMS). Based on user input, PPMS can profile pri-miRNAs at cell-type resolution. PPMS can be applied to both newly produced and publicly available datasets obtained via single cell or single-nuclei RNA-seq. It allows users to (i) investigate the distribution of pri-miRNAs across cell types and cell states and (ii) establish a relationship between the number of cells/reads sequenced and the detection of pri-miRNAs. Here, to demonstrate its efficacy, we have applied PPMS to publicly available scRNA-seq data generated from (i) individual chambers (ventricles and atria) of the human heart, (ii) human pluripotent stem cells during their differentiation into cardiomyocytes (the heart beating cells) and (iii) hiPSCs-derived cardiomyocytes infected with severe acute respiratory syndrome coronavirus 2.

Wasserstein balls, which contain all probability measures within a pre-specified Wasserstein distance to a reference measure, have recently enjoyed wide popularity in the distributionally robust optimization and machine learning communities to formulate and solve data-driven optimization problems with rigorous statistical guarantees. In this technical note we prove that the Wasserstein ball is weakly compact under mild conditions, and we offer necessary and sufficient conditions for the existence of optimal solutions. We also characterize the sparsity of solutions if the Wasserstein ball is centred at a discrete reference measure. In comparison with the existing literature, which has proved similar results under different conditions, our proofs are self-contained and shorter, yet mathematically rigorous, and our necessary and sufficient conditions for the existence of optimal solutions are easily verifiable in practice.

We give asymptotically converging semidefinite programming hierarchies of outer bounds on bilinear programs of the form $\mathrm{Tr}\big[M(X\otimes Y)\big]$, maximized with respect to semidefinite constraints on $X$ and $Y$. Applied to the problem of quantum error correction this gives hierarchies of efficiently computable outer bounds on the optimal fidelity for any message dimension and error model. The first level of our hierarchies corresponds to the non-signalling assisted fidelity previously studied by [Leung & Matthews, IEEE Trans.~Inf.~Theory 2015], and positive partial transpose constraints can be added and used to give a sufficient criterion for the exact convergence at a given level of the hierarchy. To quantify the worst case convergence speed of our hierarchies, we derive novel quantum de Finetti theorems that allow imposing linear constraints on the approximating state. In particular, we give finite de Finetti theorems for quantum channels, quantifying closeness to the convex hull of product channels as well as closeness to local operations and classical forward communication assisted channels. As a special case this constitutes a finite version of Fuchs-Schack-Scudo's asymptotic de Finetti theorem for quantum channels. Finally, our proof methods also allow us to answer an open question from [Brand��o & Harrow, STOC 2013] by improving the approximation factor of de Finetti theorems with no symmetry from $O(d^{k/2})$ to $\mathrm{poly}(d,k)$, where $d$ denotes local dimension and $k$ the number of copies., 33 pages, New Title, v3

Professional service firms (PSFs) such as management consulting, law, accounting, investment banking, architecture, advertising and home-repair companies provide services for complicated turnkey projects. The firm bids for a project and, if successful in the bid, assigns employees to work on the project. We formulate this as a revenue management problem under two assumptions: a quality-revelation setup where the employees that would be assigned to the project are committed ex ante, as part of the bid, and a quality-reputation setup where the bid’s win probability depends on past performance, say an average of the quality of past jobs. We first model a stylized Markov-Chain model of the problem amenable to analysis and show that upfront revelation of the assigned employees has subtle advantages. Subsequent to this analysis, we develop an operational stochastic dynamic programming framework under the revelation model to aid the firm in this bidding and assignment process. We show that the problem is computationally challenging and provide a series of bounds and solution methods to approximate the stochastic dynamic program. Based on our model and computational methods we are able to address a number of interesting business questions for a PSF, such as the optimal utilization levels and the value of each employee type. Our methodology provides management a toolkit for bidding on projects as well as to perform workforce analytics and to make staffing decisions.

It is often assumed that events cannot occur simultaneously when modelling data with point processes. This raises a problem as real-world data often contains synchronous observations due to aggregation or rounding, resulting from limitations on recording capabilities and the expense of storing high volumes of precise data. In order to gain a better understanding of the relationships between processes, we consider modelling the aggregated event data using multivariate Hawkes processes, which offer a description of mutually-exciting behaviour and have found wide applications in areas including seismology and finance. Here we generalise existing methodology on parameter estimation of univariate aggregated Hawkes processes to the multivariate case using a Monte Carlo Expectation Maximization (MC-EM) algorithm and through a simulation study illustrate that alternative approaches to this problem can be severely biased, with the multivariate MC-EM method outperforming them in terms of MSE in all considered cases., Comment: 14 pages, 5 figures

This paper studies an optimal investment and consumption problem with heterogeneous consumption of basic and luxury goods, together with the choice of time for retirement. The utility for luxury goods is not necessarily a concave function. The optimal heterogeneous consumption strategies for a class of non-homothetic utility maximizer are shown to consume only basic goods when the wealth is small, to consume basic goods and make savings when the wealth is intermediate, and to consume almost all in luxury goods when the wealth is large. The optimal retirement policy is shown to be both universal, in the sense that all individuals should retire at the same level of marginal utility that is determined only by income, labor cost, discount factor as well as market parameters, and not universal, in the sense that all individuals can achieve the same marginal utility with different utility and wealth. It is also shown that individuals prefer to retire as time goes by if the marginal labor cost increases faster than that of income. The main tools used in analyzing the problem are from PDE and stochastic control theory including variational inequality and dual transformation. We finally conduct the simulation analysis for the featured model parameters to investigate practical and economic implications by providing their figures.

Funder: Cambridge Trust, Funder: Islamic Development Bank, Funder: AstraZeneca, Lipoteichoic acid synthase (LtaS) is a key enzyme for the cell wall biosynthesis of Gram-positive bacteria. Gram-positive bacteria that lack lipoteichoic acid (LTA) exhibit impaired cell division and growth defects. Thus, LtaS appears to be an attractive antimicrobial target. The pharmacology around LtaS remains largely unexplored with only two small-molecule LtaS inhibitors reported, namely "compound 1771" and the Congo red dye. Structure-based drug discovery efforts against LtaS remain unattempted due to the lack of an inhibitor-bound structure of LtaS. To address this, we combined the use of a molecular docking technique with molecular dynamics (MD) simulations to model a plausible binding mode of compound 1771 to the extracellular catalytic domain of LtaS (eLtaS). The model was validated using alanine mutagenesis studies combined with isothermal titration calorimetry. Additionally, lead optimization driven by our computational model resulted in an improved version of compound 1771, namely, compound 4 which showed greater affinity for binding to eLtaS than compound 1771 in biophysical assays. Compound 4 reduced LTA production in S. aureus dose-dependently, induced aberrant morphology as seen for LTA-deficient bacteria, and significantly reduced bacteria titers in the lung of mice infected with S. aureus. Analysis of our MD simulation trajectories revealed the possible formation of a transient cryptic pocket in eLtaS. Virtual screening (VS) against the cryptic pocket led to the identification of a new class of inhibitors that could potentiate β-lactams against methicillin-resistant S. aureus. Our overall workflow and data should encourage further drug design campaign against LtaS. Finally, our work reinforces the importance of considering protein conformational flexibility to a successful VS endeavor.

As a tractable approach, regularization is frequently adopted in sparse optimization. This gives rise to regularized optimization, which aims to minimize the ℓ0 norm or its continuous surrogates that characterize the sparsity. From the continuity of surrogates to the discreteness of the ℓ0 norm, the most challenging model is the ℓ0-regularized optimization. There is an impressive body of work on the development of numerical algorithms to overcome this challenge. However, most of the developed methods only ensure that either the (sub)sequence converges to a stationary point from the deterministic optimization perspective or that the distance between each iteration and any given sparse reference point is bounded by an error bound in the sense of probability. In this paper, we develop a Newton-type method for the ℓ0-regularized optimization and prove that the generated sequence converges to a stationary point globally and quadratically under the standard assumptions, theoretically explaining that our method can perform surprisingly well.

A domain-theoretic method for solving initial value problems (IVPs) is presented, together with proofs of soundness, completeness, and some results on the algebraic complexity of the method. While the common fixed-precision interval arithmetic methods are restricted by the precision of the underlying machine architecture, domain-theoretic methods may be complete, i.e., the result may be obtained to any degree of accuracy. Furthermore, unlike methods based on interval arithmetic which require access to the syntactic representation of the vector field, domain-theoretic methods only deal with the semantics of the field, in the sense that the field is assumed to be given via finitely-representable approximations, to within any required accuracy. In contrast to the domain-theoretic first-order Euler method, the second-order method uses the local Lipschitz properties of the field. This is achieved by using a domain for Lipschitz functions, whose elements are consistent pairs that provide approximations of the field and its local Lipschitz properties. In the special case where the field is differentiable, the local Lipschitz properties are exactly the local differential properties of the field. In solving IVPs, Lipschitz continuity of the field is a common assumption, as a sufficient condition for uniqueness of the solution. While the validated methods for solving IVPs commonly impose further restrictions on the vector field, the second-order Euler method requires no further condition. In this sense, the method may be seen as the most general of its kind. To avoid complicated notations and lengthy arguments, the results of the paper are stated for the second-order Euler method. Nonetheless, the framework, and the results, may be extended to any higher-order Euler method, in a straightforward way.

Stochastic processes provide a mathematically elegant way to model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. However, in practice efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($$\pi $$ π VAE). $$\pi $$ π VAE is a new continuous stochastic process. We use $$\pi $$ π VAE to learn low dimensional embeddings of function classes by combining a trainable feature mapping with generative model using a VAE. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions such as their integrals. For popular tasks, such as spatial interpolation, $$\pi $$ π VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate an elegant and scalable means of performing fully Bayesian inference for stochastic processes within probabilistic programming languages such as Stan.

We present explicit constructions of orthogonal polynomials inside quadratic bodies of revolution, including cones, hyperboloids, and paraboloids. We also construct orthogonal polynomials on the surface of quadratic surfaces of revolution, generalizing spherical harmonics to the surface of a cone, hyperboloid, and paraboloid. We use this construction to develop cubature and fast approximation methods.

Graphical abstract, The brain is a highly complex organ consisting of numerous types of cells with ample diversity at the epigenetic level to achieve distinct gene expression profiles. During neuronal cell specification, transcription factors (TFs) form regulatory modules with chromatin remodeling proteins to initiate the cascade of epigenetic changes. Currently, little is known about brain epigenetic regulatory modules and how they regulate gene expression in a cell-type specific manner. To infer TFs involved in neuronal specification, we applied a recursive motif search approach on the differentially methylated regions identified from single-cell methylomes. The epigenetic transcription regulatory modules (ETRM), including EGR1 and MEF2C, were predicted and the co-expression of TFs in ETRMs were examined with RNA-seq data from single or sorted brain cells using a conditional probability matrix. Lastly, computational predications were validated with EGR1 ChIP-seq data. In addition, methylome and RNA-seq data generated from Egr1 knockout mice supported the essential role of EGR1 in brain epigenome programming, in particular for excitatory neurons. In summary, we demonstrated that brain single cell methylome and RNA-seq data can be integrated to gain a better understanding of how ETRMs control cell specification. The analytical pipeline implemented in this study is freely accessible in the Github repository (https://github.com/Gavin-Yinld/brain_TF).

Graphical abstract, With omics data being generated at an unprecedented rate, genome-scale modelling has become pivotal in its organisation and analysis. However, machine learning methods have been gaining ground in cases where knowledge is insufficient to represent the mechanisms underlying such data or as a means for data curation prior to attempting mechanistic modelling. We discuss the latest advances in genome-scale modelling and the development of optimisation algorithms for network and error reduction, intracellular constraining and applications to strain design. We further review applications of supervised and unsupervised machine learning methods to omics datasets from microbial and mammalian cell systems and present efforts to harness the potential of both modelling approaches through hybrid modelling.

Two-stage robust optimization problems, in which decisions are taken both in anticipation ofand in response to the observation of an unknown parameter vector from within an uncertaintyset, are notoriously challenging. In this paper, we develop convergent hierarchies of primal (con-servative) and dual (progressive) bounds for these problems that trade off the competing goalsof tractability and optimality: While the coarsest bounds recover a tractable but suboptimalaffine decision rule approximation of the two-stage robust optimization problem, the refinedbounds lift extreme points of the uncertainty set until an exact but intractable extreme pointreformulation of the problem is obtained. Based on these bounds, we propose a primal-duallifting scheme for the solution of two-stage robust optimization problems that accommodatesfor discrete here-and-now decisions, infeasible problem instances as well as the absence of a rela-tively complete recourse. The incumbent solutions in each step of our algorithm afford rigorouserror bounds, and they can be interpreted as piecewise affine decision rules. We illustrate theperformance of our algorithm on illustrative examples and on an inventory management problem.

We give upper and lower bounds on the power of subsystems of the Ideal Proof System (IPS), the algebraic proof system recently proposed by Grochow and Pitassi (J. ACM, 2018), where the circuits comprising the proof come from various restricted algebraic circuit classes. This mimics an established research direction in the Boolean setting for subsystems of Extended Frege proofs, where proof-lines are circuits from restricted Boolean circuit classes. Except one, all of the subsystems considered in this paper can simulate the well-studied Nullstellensatz proof system, and prior to this work there were no known lower bounds when measuring proof size by the algebraic complexity of the polynomials (except with respect to degree, or to sparsity). We give two general methods of converting certain algebraic circuit lower bounds into proof complexity ones. However, we need to strengthen existing lower bounds to hold for either the functional model or for multiplicities (see below). Our techniques are reminiscent of existing methods for converting Boolean circuit lower bounds into related proof complexity results, such as feasible interpolation. We obtain the relevant types of lower bounds for a variety of classes (sparse polynomials, depth-3 powering formulas, read-once oblivious algebraic branching programs, and multilinear formulas), and infer the relevant proof complexity results. We complement our lower bounds by giving short refutations of the previously studied subset-sum axiom using IPS subsystems, allowing us to conclude strict separations between some of these subsystems. Our first method is a functional lower bound, a notion due to Grigoriev and Razborov (Appl. Algebra Eng. Commun. Comput., 2000), which says that not only does a polynomial f require large algebraic circuits, but that any polynomial g agreeing with f on the Boolean cube also requires large algebraic circuits. For our classes of interest, we develop functional lower bounds where g(x¯¯¯) equals 1/p(x¯¯¯) where p is a constant-degree polynomial, which in turn yield corresponding IPS lower bounds for proving that p is nonzero over the Boolean cube. In particular, we show superpolynomial lower bounds for refuting variants of the subset-sum axiom in various IPS subsystems. Our second method is to give lower bounds for multiples, that is, to give explicit polynomials whose all (nonzero) multiples require large algebraic circuit complexity. By extending known techniques, we are able to obtain such lower bounds for our classes of interest, which we then use to derive corresponding IPS lower bounds. Such lower bounds for multiples are of independent interest, as they have tight connections with the algebraic hardness versus randomness paradigm.

We prove decomposition theorems for sparse positive (semi)definite polynomial matrices that can be viewed as sparsity-exploiting versions of the Hilbert--Artin, Reznick, Putinar, and Putinar--Vasilescu Positivstellensätze. First, we establish that a polynomial matrix $P(x)$ with chordal sparsity is positive semidefinite for all $x\in \mathbb{R}^n$ if and only if there exists a sum-of-squares (SOS) polynomial $\sigma(x)$ such that $\sigma P$ is a sum of sparse SOS matrices. Second, we show that setting $\sigma(x)=(x_1^2 + \cdots + x_n^2)^\nu$ for some integer $\nu$ suffices if $P$ is homogeneous and positive definite globally. Third, we prove that if $P$ is positive definite on a compact semialgebraic set $\mathcal{K}=\{x:g_1(x)\geq 0,\ldots,g_m(x)\geq 0\}$ satisfying the Archimedean condition, then $P(x) = S_0(x) + g_1(x)S_1(x) + \cdots + g_m(x)S_m(x)$ for matrices $S_i(x)$ that are sums of sparse SOS matrices. Finally, if $\mathcal{K}$ is not compact or does not satisfy the Archimedean condition, we obtain a similar decomposition for $(x_1^2 + \cdots + x_n^2)^\nu P(x)$ with some integer $\nu\geq 0$ when $P$ and $g_1,\ldots,g_m$ are homogeneous of even degree. Using these results, we find sparse SOS representation theorems for polynomials that are quadratic and correlatively sparse in a subset of variables, and we construct new convergent hierarchies of sparsity-exploiting SOS reformulations for convex optimization problems with large and sparse polynomial matrix inequalities. Numerical examples demonstrate that these hierarchies can have a significantly lower computational complexity than traditional ones.

This paper presents an impedance type ankle haptic interface for providing users with an immersive navigation experience in virtual reality (VR). The ankle platform actuated by an electric motor with feedback control enables the use of foot-tapping gestures to create a walking experience similar to a real one and to haptically render different types of walking terrains. Experimental studies demonstrated that the interface can be easily used to generate virtual walking and it is capable to render terrains such as hard and soft surfaces, and multi-layer complex dynamic terrains. The designed system is a seated-type VR locomotion interface, therefore allowing its user to maintain a stable seated posture to comfortably navigate a virtual scene.

Computation is increasingly being used to try to accelerate the discovery of new materials. One specific example of this is porous molecular materials, specifically porous organic cages, where the porosity of the materials predominantly comes from the internal cavities of the molecules themselves. The computational discovery of novel structures with useful properties is currently hindered by the difficulty in transitioning from a computational prediction to synthetic realisation. Attempts at experimental validation are often time-consuming, expensive and, frequently, the key bottleneck of material discovery. In this work, we developed a computational screening workflow for porous molecules that includes consideration of the synthetic difficulty of material precursors, aimed at easing the transition between computational prediction and experimental realisation. We trained a machine learning model by first collecting data on 12,553 molecules categorised either as `easy-to-synthesise' or `difficult-to-synthesise' by expert chemists with years of experience in organic synthesis. We used an approach to address the class imbalance present in our dataset, producing a binary classifier able to categorise easy-to-synthesise molecules with few false positives. We then used our model during computational screening for porous organic molecules to bias towards precursors whose easier synthesis requirements would make them promising candidates for experimental realisation and material development. We found that even by limiting precursors to those that are easier-to-synthesise, we are still able to identify cages with favourable, and even some rare, properties.

The main objective of this paper is to define a logic for reasoning about distributed time-stamped claims. Such a logic is interesting for theoretical reasons, i.e., as a logic per se, but also because it has a number of practical applications, in particular when one needs to reason about a huge amount of pieces of evidence collected from different sources, where some of the pieces of evidence may be contradictory and some sources are considered to be more trustworthy than others. We introduce the Time-Stamped Claim Logic including a sound and complete sequent calculus that allows one to reduce the size of the collected set of evidence and removes inconsistencies, i.e., the logic ensures that the result is consistent with respect to the trust relations considered. In order to show how Time-Stamped Claim Logic can be used in practice, we consider a concrete cyber-attribution case study.

We propose a novel method for drift estimation of multiscale diffusion processes when a sequence of discrete observations is given. For the Langevin dynamics in a two-scale potential, our approach relies on the eigenvalues and the eigenfunctions of the homogenized dynamics. Our first estimator is derived from a martingale estimating function of the generator of the homogenized diffusion process. However, the unbiasedness of the estimator depends on the rate with which the observations are sampled. We therefore introduce a second estimator which relies also on filtering the data, and we prove that it is asymptotically unbiased independently of the sampling rate. A series of numerical experiments illustrate the reliability and efficiency of our different estimators.

A significant challenge for recommender systems (RSs), and in fact for AI systems in general, is the systematic definition of explanations for outputs in such a way that both the explanations and the systems themselves are able to adapt to their human users' needs. In this paper we propose an RS hosting a vast repertoire of explanations, which are customisable to users in their content and format, and thus able to adapt to users' explanatory requirements, while being reasonably effective (proven empirically). Our RS is built on a graphical chassis, allowing the extraction of argumentation scaffolding, from which diverse and varied argumentative explanations for recommendations can be obtained. These recommendations are interactive because they can be questioned by users and they support adaptive feedback mechanisms designed to allow the RS to self-improve (proven theoretically). Finally, we undertake user studies in which we vary the characteristics of the argumentative explanations, showing users' general preferences for more information, but also that their tastes are diverse, thus highlighting the need for our adaptable RS.

We present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator's banded sparsity structure when acting on specific Jacobi polynomial bases. The method is not restricted to convolution-type kernels of the form $K(x,y)=K(x-y)$ but instead works for general kernels at competitive speeds and with exponential convergence. We provide various numerical experiments on problems with or without known analytic solutions and comparisons with other methods., Comment: 24 pages, 8 figures

Multistage robust optimization problems, where the decision maker can dynamically react to consecutively observed realizations of the uncertain problem parameters, pose formidable theoretical and computational challenges. As a result, the existing solution approaches for this problem class typically determine suboptimal solutions under restrictive assumptions. In this paper, we propose a robust dual dynamic programming (RDDP) scheme for multistage robust optimization problems. The RDDP scheme takes advantage of the decomposable nature of these problems by bounding the costs arising in the future stages through lower and upper cost-to-go functions. For problems with uncertain technology matrices and/or constraint right-hand sides, our RDDP scheme determines an optimal solution in finite time. Also, if the objective function and/or the recourse matrices are uncertain, our method converges asymptotically (but deterministically) to an optimal solution. Our RDDP scheme does not require a relatively complete recourse, and it offers deterministic upper and lower bounds throughout the execution of the algorithm. We show the promising performance of our algorithm in a stylized inventory management problem.Supplemental material is available at https://doi.org/10.1287/opre.2018.1835. 67 3 813 830

Programming environments have evolved from purely text based to using graphical user interfaces, and now we see a move toward web-based interfaces, such as Jupyter. Web-based interfaces allow for the creation of interactive documents that consist of text and programs, as well as their output. The output can be rendered using web technology as, for example, text, tables, charts, or graphs. This approach is particularly suitable for capturing data analysis workflows and creating interactive educational material. This article describes SWISH, a web front-end for Prolog that consists of a web server implemented in SWI-Prolog and a client web application written in JavaScript. SWISH provides a web server where multiple users can manipulate and run the same material, and it can be adapted to support Prolog extensions. In this article we describe the architecture of SWISH, and describe two case studies of extensions of Prolog, namely Probabilistic Logic Programming and Logic Production System, which have used SWISH to provide tutorial sites.

The need for efficient tools is pressing in the era of big data, particularly in streaming data applications. As data streams are ubiquitous, the ability to accurately detect multiple changepoints, without affecting the continuous flow of data, is an important issue. Change detection for categorical data streams is understudied, and existing work commonly introduces fixed control parameters while providing little insight into how they may be chosen. This is ill-suited to the streaming paradigm, motivating the need for an approach that introduces few parameters which may be set without requiring any prior knowledge of the stream. This paper introduces such a method, which can accurately detect changepoints in categorical data streams with fixed storage and computational requirements. The detector relies on the ability to adaptively monitor the category probabilities of a multinomial distribution, where temporal adaptivity is introduced using forgetting factors. A novel adaptive threshold is also developed which can be computed given a desired false positive rate. This method is then compared to sequential and nonsequential change detectors in a large simulation study which verifies the usefulness of our approach. A real data set consisting of nearly 40 million events from a computer network is also investigated.

Of central importance to the $$\alpha $$ BB algorithm is the calculation of the $$\alpha $$ values that guarantee the convexity of the underestimator. Improvement (reduction) of these values can result in tighter underestimators and thus increase the performance of the algorithm. For instance, it was shown by Wechsung et al. (J Glob Optim 58(3):429–438, 2014) that the emergence of the cluster effect can depend on the magnitude of the $$\alpha $$ values. Motivated by this, we present a refinement method that can improve (reduce) the magnitude of $$\alpha $$ values given by the scaled Gerschgorin method and thus create tighter convex underestimators for the $$\alpha $$ BB algorithm. We apply the new method and compare it with the scaled Gerschgorin on randomly generated interval symmetric matrices as well as interval Hessians taken from test functions. As a measure of comparison, we use the maximal separation distance between the original function and the underestimator. Based on the results obtained, we conclude that the proposed refinement method can significantly reduce the maximal separation distance when compared to the scaled Gerschgorin method. This approach therefore has the potential to improve the performance of the $$\alpha $$ BB algorithm.