In a dependently typed language, we can guarantee correctness of our programmes by providing formal proofs. To check them, the typechecker elaborates these programs and proofs into a low-level core language. However, this core language is by nature hard to understand by mere humans, so how can we know we proved the right thing? This question occurs in particular for dependent copattern matching, a powerful language construct for writing programmes and proofs by dependent case analysis and mixed induction/coinduction. A definition by copattern matching consists of a list of clauses that are elaborated to a case tree, which can be further translated to primitive eliminators. In previous work this second step has received a lot of attention, but the first step has been mostly ignored so far. We present an algorithm elaborating definitions by dependent copattern matching to a core language with inductive data types, coinductive record types, an identity type, and constants defined by well-typed case trees. To ensure correctness, we prove that elaboration preserves the first-match semantics of the user clauses. Based on this theoretical work, we reimplement the algorithm used by Agda to check left-hand sides of definitions by pattern matching. The new implementation is at the same time more general and less complex, and fixes a number of bugs and usability issues with the old version. Thus, we take another step towards the formally verified implementation of a practical dependently typed language.

Ruitenburg’s Theorem says that every endomorphism f of a finitely generated free Heyting algebra is ultimately periodic if f fixes all the generators but one. More precisely, there is N ≥ 0 such that fN+2 = fN, thus the period equals 2. We give a semantic proof of this theorem, using duality techniques and bounded bisimulation ranks. By the same techniques, we tackle investigation of arbitrary endomorphisms of free algebras. We show that they are not, in general, ultimately periodic. Yet, when they are (e.g. in the case of locally finite subvarieties), the period can be explicitly bounded as function of the cardinality of the set of generators.

Recurrence can be used as a function definition schema for any nontrivial free algebra, yielding the same computational complexity in all cases. We show that primitive-recursive computing is in fact independent of free algebras altogether, and can be characterized by a generic programming principle, namely the control of iteration by the depletion of finite components of the underlying structure.

The Garsia–Wachs algorithm is an algorithm for building a binary leaf tree whose cost is as small as possible. The problem and the algorithm are described in more detail below, but the task is essentially the same as that of building a Huffman coding tree with the added constraint that the fringe of the tree has to be exactly the given list of inputs (in Huffman coding, the fringe of the tree can be any permutation of the input). As we will show below, the Garsia–Wachs algorithm can be implemented with a linearithmic running time—a running time of O (n log n) steps for an input of length n, the same time bound as for Huffman coding.

The link prediction task has found numerous applications in real-world scenarios. However, in most of the cases like interactions, purchases, mobility, etc., links can re-occur again and again across time. As a result, the data being generated is excessively large to handle, associated with the complexity and sparsity of networks. Therefore, we propose a very fast, memory-less, and dynamic sampling-based method for predicting recurring links for a successive future point in time. This method works by biasing the links exponentially based on their time of occurrence, frequency, and stability. To evaluate the efficiency of our method, we carried out rigorous experiments with massive real-world graph streams. Our empirical results show that the proposed method outperforms the state-of-the-art method for recurring links prediction. Additionally, we also empirically analyzed the evolution of links with the perspective of multi-graph topology and their recurrence probability over time.

Ontology matching aims at discovering mappings between the entities of two ontologies. It plays an important role in the integration of heterogeneous data sources that are described by ontologies. Interactive ontology matching involves domain experts in the matching process. In some approaches, the expert provides feedback about mappings between ontology entities, that is, these approaches select mappings to present to the expert who replies which of them should be accepted or rejected, so taking advantage of the knowledge of domain experts towards finding an alignment. In this paper, we present Alin, an interactive ontology matching approach which uses expert feedback not only to approve or reject selected mappings but also to dynamically improve the set of selected mappings, that is, to interactively include and to exclude mappings from it. This additional use for expert answers aims at increasing in the benefit brought by each expert answer. For this purpose, Alin uses four techniques. Two techniques were used in the previous versions of Alin to dynamically select concept and attribute mappings. Two new techniques are introduced in this paper: one to dynamically select relationship mappings and another one to dynamically reject inconsistent selected mappings using anti-patterns. We compared Alin with state-of-the-art tools, showing that it generates alignment of comparable quality.

In this paper, we study the equilibrium valuation for currency options in a setting of the two-country Lucas-type economy. Different from the continuous model in Bakshi and Chen [1], we propose a discontinuous model with jump processes. Empirical findings reveal that the jump components in each country's money supply can be decomposed into the simultaneous co-jump component and the country-specific jump component. Each of the jump components is modeled with a Poisson process whose jump intensity follows a mean reversion stochastic process. By solving a partial integro-differential equation (PIDE), we get a closed-form solution to the PIDE for a European call currency option. The numerical results show that the derived option pricing formula is efficient for practical use. Importantly, we find that the co-jump has a significant impact on option price and implied volatility.

Measures of bipartite network structure have recently gained attention from network scholars. However, there is currently no measure for identifying key players in two-mode networks. This article proposes measures for identifying key players in bipartite networks. It focuses on two measures: fragmentation and cohesion centrality. It extends the centrality measures to bipartite networks by considering (1) cohesion and fragmentation centrality within a one-mode projection, (2) cross-modal cohesion and fragmentation centrality, where a node in one mode is influential in the one-mode projection of the other mode, and (3) cohesion and fragmentation centrality across the entire bipartite structure. Empirical examples are provided for the Southern Women’s data and on the Ndrangheta mafia data.

Nowadays, modern Earth Observation systems continuously generate huge amounts of data. A notable example is the Sentinel-2 Earth Observation mission, developed by the European Space Agency as part of the Copernicus Programme, which supplies images from the whole planet at high spatial resolution (up to 10 m) with unprecedented revisit time (every 5 days at the equator). In this data-rich scenario, the remote sensing community is showing a growing interest toward modern supervised machine learning techniques (e.g., deep learning) to perform information extraction, often underestimating the need for reference data that this framework implies. Conversely, few attention is being devoted to the use of network analysis techniques, which can provide a set of powerful tools for unsupervised information discovery, subject to the definition of a suitable strategy to build a network-like representation of image data. The aim of this work is to provide clues on how Satellite Image Time Series can be profitably represented using complex network models, by proposing a methodology to build a multilayer network from such data. This is the first work to explore the possibility to exploit this model in the remote sensing domain. An example of community detection over the provided network in a real-case scenario for the mapping of complex land use systems is also presented, to assess the potential of this approach.

A principled approach to understand networks is to formulate generative models and infer their parameters from given network data. Due to the scarcity of data in the form of multiple networks that have evolved from the same process, generative models are typically formulated to learn parameters from a single network observation, hence ignoring the natural variability of the “true” process. In this paper, we highlight the importance of variability in evaluating generative models and present two ways of quantifying the variability for a finite set of networks. The first evaluation scheme compares the statistical properties of networks in a dissimilarity space, while the other relies on data-driven entropy measures to compute variability in network populations. Using these measures, we evaluate the ability of four generative models to synthesize networks that capture the variability of the “true” process. Our empirical analysis suggests that generative models fitted for a single network observation fail to capture the variability in the network population. Our work highlights the need for rethinking the way we evaluate the goodness-of-fit of new and existing network models and devising models that are capable of matching the variability of network populations when available.

In this paper, two strategies are proposed to optimize the energy consumption of a new screw in-pipe inspection robot which is steerable. In the first method, optimization is performed using the optimal path planning and implementing the Hamilton–Jacobi–Bellman (HJB) method. Since the number of actuators is more than the number of degrees of freedom of the system for the proposed steerable case, it is possible to minimize the energy consumption by the aid of the dynamics of the system. In the second method, the mechanics of the robot is modified by installing some turbine blades through which the drag force of the pipeline fluid can be employed to decrease the required propulsion force of the robot. It is shown that using both of the mentioned improvements, that is, using HJB formulation for the steerable robot and installing the turbine blades can significantly save power and energy. However, it will be shown that for the latter case this improvement is extremely dependent on the alignment of the fluid stream direction with respect to the direction of the robot velocity, while this optimization is independent of this case for the former strategy. On the other hand, the path planning dictates a special pattern of speed functionality while for the robot equipped by blades, saving the energy is possible for any desired input path. The correctness of the modeling is verified by comparing the results of MATLAB and ADAMS, while the efficiency of the proposed optimization algorithms is checked by the aid of some analytic and comparative simulations.

The present investigation analyses the potential of a pedagogical dynamic assessment (DA) approach to foster second language (L2) development through the use of a mobile instant messaging application. Students’ zone of actual and proximal development is observed through the use of a grammar and vocabulary level test and the use of the WhatsApp application respectively. Sixty students taking a B1 English course at the language centre of a Spanish university were studied. A mixed methods methodology was used to analyse the differences between two pre-existing groups (control and experimental), each consisting of 30 participants. Both groups received the same tuition and content, and students in the experimental group participated in a daily conversation in the application during a five-month period where negative feedback was provided by the teacher through the use of an inventory of prompts, from most implicit to most explicit. Throughout the research, pedagogical mobile-mediated DA became a central part of the students’ learning process, extending learning beyond the in-class time and becoming a constant source of L2 input and feedback. Moreover, results indicated that DA and dialogic mediation helped students reflect on their language performance, gradually requiring less explicit feedback and metalinguistic explanations.

A dual-arm space robot has large potentials in on-orbit servicing. However, there exist multiple dynamic coupling effects between the two arms, each arm, and the base, bringing great challenges to the trajectory planning and dynamic control of the dual-arm space robotic system. In this paper, we propose a dynamic coupling modeling and analysis method for a dual-arm space robot. Firstly, according to the conservation principle of the linear and angular momentum, the dynamic coupling between the base and each manipulator is deduced. The dynamic coupling factor is then defined to evaluate the dynamic coupling degree. Secondly, the dynamic coupling equations between the two arms, each arm, and the base are deduced, respectively. The dynamic coupling factor is suitable not only for single-arm space robots but also for multi-arm space robot systems. Finally, the multiple coupling effects of the dual-arm space robotic system are analyzed in detail through typical cases. Simulation results verified the proposed method.