Miracle-dz/UniFAR-FTUs huggingface dataset:
FRIEZE PATTERNS WITH COEFFICIENTS

Frieze patterns, as introduced by Coxeter in the 1970s, are closely related to cluster algebras without coefficients. A suitable generalization of frieze patterns, linked to cluster algebras with coefficients, has only briefly appeared in an unpublished manuscript by Propp. In this paper, we study these frieze patterns with coefficients systematically and prove various fundamental results, generalizing classic results for frieze patterns. As a consequence, we see how frieze patterns with coefficients can be obtained from classic frieze patterns by cutting out subpolygons from the triangulated polygons associated with classic Conway–Coxeter frieze patterns. We address the question of which frieze patterns with coefficients can be obtained in this way and solve this problem completely for triangles. Finally, we prove a finiteness result for frieze patterns with coefficients by showing that for a given boundary sequence there are only finitely many (nonzero) frieze patterns with coefficients with entries in a subset of the complex numbers without an accumulation point.
Extracting physical power plant parameters from historical behaviour

The information needed for fundamental modelling of the power markets-the efficiency, start-up, fixed, and variable operating costs of each power plant—is not publicly available. These parameters are usually estimated by considering the type of technology and the age of a power plant.We present a method to extract these parameters for thermal power plants on the British electricity market using only the publicly available data. For each power plant, we solve a bilevel optimisation problem, where the inner level solves the Unit Commitment (UC) problem and outputs the optimal schedule given the prices of fuel, emissions, electricity, and the unknown plant parameters. The outer level then optimises over the plant parameters matching the historical production of each plant as closely as possible.
Ensayo clínico aleatorizado de un programa de atención farmacéutica al alta frente a seguimiento habitual en pacientes con insuficiencia cardiaca

Objetivo: Valorar la eficacia de una intervencion educativa multifactorial realizada por un farmaceutico en pacientes con insuficiencia cardiaca (IC). Metodo: Ensayo clinico aleatorizado, prospectivo, abierto, en pacientes ingresados por IC. Los pacientes asignados al grupo intervencion recibieron informacion sobre la enfermedad, el tratamiento farmacologico, educacion dietetica y seguimiento telefonico activo. Se realizaron visitas a los 2, 6 y 12 meses. Se evaluaron los reingresos hospitalarios, dias de hospitalizacion, cumplimiento terapeutico, satisfaccion con la atencion recibida y calidad de vida (EuroQol); se realizo un estudio economico para valorar el posible impacto del programa. La intervencion la efectuo el servicio de farmacia en coordinacion con la unidad de cardiologia. Resultados: Se han incluido 134 pacientes, de edad media 75 anos, nivel de estudios bajo. Los pacientes del grupo intervencion presentaron un mayor nivel de adherencia al tratamiento que los pacientes del grupo control. A los 12 meses de seguimiento, los pacientes del grupo intervencion reingresaron un 32,9% menos que los del grupo control. El promedio de dias de hospitalizacion por paciente en el grupo control fue de 9,6 (DE = 18,5) frente a 5,9 (DE = 14,1) del grupo intervencion. No se registraron diferencias en la calidad de vida, pero el grupo intervencion presento mayor puntuacion en la escala de satisfaccion a los dos meses [9,0 (DE = 1,3) vs. 8,2 (DE = 1,8) p = 0,026]. Al ajustar un modelo de supervivencia de Cox con la fraccion de eyeccion, los pacientes del grupo intervencion presentaron un menor riesgo de reingreso (Hazard ratio 0,56; IC95%: 0,32-0,97). El analisis economico evidencio un ahorro en gastos hospitalarios de 578 ? por paciente favorable al grupo intervencion. Conclusiones: La atencion farmaceutica al alta hospitalaria permite reducir el numero de reingresos en pacientes con insuficiencia cardiaca, los dias totales de hospitalizacion y mejora la adherencia al tratamiento sin aumentar los costes de la atencion.
Complexity-based approach for El Niño magnitude forecasting before the spring predictability barrier

Significance Although El Niño events characterized by anomalous episodic warmings of the eastern equatorial Pacific can trigger disasters in various parts of the globe, reliable forecasts of their magnitude are still limited to about 6 mo ahead. A significant extension of this prewarning time would be instrumental for mitigating some of the worst damages. Here we introduce an approach relying on information entropy, which achieves some doubling of the prewarning time. The approach is based on our finding that the entropy in one calendar year exhibits a strong correlation with the magnitude of an El Niño that starts in the following year and thus allows us to forecast the onset and the magnitude of an El Niño event 1 y in advance. The El Niño Southern Oscillation (ENSO) is one of the most prominent interannual climate phenomena. Early and reliable ENSO forecasting remains a crucial goal, due to its serious implications for economy, society, and ecosystem. Despite the development of various dynamical and statistical prediction models in the recent decades, the “spring predictability barrier” remains a great challenge for long-lead-time (over 6 mo) forecasting. To overcome this barrier, here we develop an analysis tool, System Sample Entropy (SysSampEn), to measure the complexity (disorder) of the system composed of temperature anomaly time series in the Niño 3.4 region. When applying this tool to several near-surface air temperature and sea surface temperature datasets, we find that in all datasets a strong positive correlation exists between the magnitude of El Niño and the previous calendar year’s SysSampEn (complexity). We show that this correlation allows us to forecast the magnitude of an El Niño with a prediction horizon of 1 y and high accuracy (i.e., root-mean-square error = 0.23° C for the average of the individual datasets forecasts). For the 2018 El Niño event, our method forecasted a weak El Niño with a magnitude of 1.11±0.23° C. Our framework presented here not only facilitates long-term forecasting of the El Niño magnitude but can potentially also be used as a measure for the complexity of other natural or engineering complex systems.
Transfer Reward Learning for Policy Gradient-Based Text Generation

Task-specific scores are often used to optimize for and evaluate the performance of conditional text generation systems. However, such scores are non-differentiable and cannot be used in the standard supervised learning paradigm. Hence, policy gradient methods are used since the gradient can be computed without requiring a differentiable objective. However, we argue that current n-gram overlap based measures that are used as rewards can be improved by using model-based rewards transferred from tasks that directly compare the similarity of sentence pairs. These reward models either output a score of sentence-level syntactic and semantic similarity between entire predicted and target sentences as the expected return, or for intermediate phrases as segmented accumulative rewards. We demonstrate that using a \textit{Transferable Reward Learner} leads to improved results on semantical evaluation measures in policy-gradient models for image captioning tasks. Our InferSent actor-critic model improves over a BLEU trained actor-critic model on MSCOCO when evaluated on a Word Mover's Distance similarity measure by 6.97 points, also improving on a Sliding Window Cosine Similarity measure by 10.48 points. Similar performance improvements are also obtained on the smaller Flickr-30k dataset, demonstrating the general applicability of the proposed transfer learning method.
Thermodynamics and phase transition of a Gauss-Bonnet black hole in a cavity

Considering a canonical ensemble, in which the temperature and the charge on a wall of the cavity are fixed, we investigate the thermodynamics of a D-dimensional Gauss-Bonnet black hole in a finite spherical cavity. Moreover, it shows that the first law of thermodynamics is still satisfied. We then discuss the phase structure and transition in both five and six dimensions. Specifically, we show that there always exist two regions in the parameter space. In one region, the system possesses one single phase. However in the other region, there could coexist three phases and a van der Waals-like phase transition occurs. Finally, we find that there is a fairly close resemblance in thermodynamic properties and phase structure of a Gauss-Bonnet-Maxwell black hole, either in a cavity or in anti-de Sitter space.
Multi-epoch X-ray spectral analysis of the narrow-line Seyfert 1 galaxy Mrk 478

A multi-epoch X-ray spectral and variability analysis is conducted for the narrow-line Seyfert 1 (NLS1) active galactic nucleus (AGN) Mrk 478. All available X-ray data from XMM–Newton and Suzaku satellites, spanning from 2001 to 2017, are modelled with a variety of physical models, including partial covering, soft Comptonization, and blurred reflection, to explain the observed spectral shape and variability over the 16 yr. All models are a similar statistical fit to the data sets, though the analysis of the variability between data sets favours the blurred reflection model. In particular, the variability can be attributed to changes in flux of the primary coronal emission. Different reflection models fit the data equally well, but differ in interpretation. The use of reflionx predicts a low disc ionization and power law dominated spectrum, while relxill predicts a highly ionized and blurred reflection dominated spectrum. A power law dominated spectrum might be more consistent with the normal X-ray-to-UV spectral shape (αox). Both blurred reflection models suggest a rapidly spinning black hole seen at a low inclination angle, and both require a sub-solar (∼0.5) abundance of iron. All physical models require a narrow emission feature at $6.7{\rm \, keV}$ likely attributable to Fe xxv emission, while no evidence for a narrow $6.4{\rm \, keV}$ line from neutral iron is detected.
Deep Graph Library: Towards Efficient and Scalable Deep Learning on Graphs

Accelerating research in the emerging field of deep graph learning requires new tools. Such systems should support graph as the core abstraction and take care to maintain both forward (i.e. supporting new research ideas) and backward (i.e. integration with existing components) compatibility. In this paper, we present Deep Graph Library (DGL). DGL enables arbitrary message handling and mutation operators, flexible propagation rules, and is framework agnostic so as to leverage high-performance tensor, autograd operations, and other feature extraction modules already available in existing frameworks. DGL carefully handles the sparse and irregular graph structure, deals with graphs big and small which may change dynamically, fuses operations, and performs auto-batching, all to take advantages of modern hardware. DGL has been tested on a variety of models, including but not limited to the popular Graph Neural Networks (GNN) and its variants, with promising speed, memory footprint and scalability.
Análisis de la marcha y evaluación de la calidad de vida después del entrenamiento de la marcha en pacientes con lesión medular

Introduccion. Durante los ultimos anos ha sido posible rehabilitar la actividad motora en los pacientes con lesion medular parcial, especialmente para poder caminar. Objetivo. Evaluar el impacto del entrenamiento de la marcha en una cinta sin fin con soporte del peso corporal con respecto a los parametros temporoespaciales y la calidad de vida. Pacientes y metodos. Se estudio a 12 pacientes de ambos sexos. Se les habia diagnosticado una lesion medular parcial de origen traumatico al menos 12 meses antes. Podian caminar, y su funcion motora por debajo del nivel de la lesion estaba parcialmente preservada y clasificada como nivel C o D. Despues de la evaluacion inicial, los participantes se entrenaron en una cinta sin fin con soporte del peso corporal, con dos sesiones por semana de 30 minutos de duracion cada una, durante un periodo de cuatro meses, lo que supuso un total de 30 sesiones. Los parametros temporoespaciales de la marcha y la calidad de vida de los pacientes se analizaron antes y despues del entrenamiento. Resultados. Hubo mejoras importantes en todos los parametros temporoespaciales evaluados (p 0,05). Conclusion. El entrenamiento en una cinta sin fin con soporte del peso corporal en pacientes con lesion medular fue eficaz a la hora de mejorar los parametros temporoespaciales de la marcha, pero no se produjeron cambios en su calidad de vida.
Dissociation energy of molecular hydrogen isotopologues

The nonrelativistic energy together with relativistic and quantum electrodynamic corrections for all the molecular hydrogen isotopologues (D$_2$, T$_2$, HD, HT, DT) were evaluated without expansion in the electron-nucleus mass ratio. The obtained results significantly improve the uncertainty of theoretical predictions, reaching a value below 1 MHz for the total dissociation energy. We observe good agreement with the experimental value for D$_2$ and $3\,\sigma$ discrepancy for the HD molecule, while no experimental values for the dissociation energy of molecules involving tritium have yet been obtained.
Can we trust deep learning models diagnosis? The impact of domain shift in chest radiograph classification

While deep learning models become more widespread, their ability to handle unseen data and generalize for any scenario is yet to be challenged. In medical imaging, there is a high heterogeneity of distributions among images based on the equipment that generates them and their parametrization. This heterogeneity triggers a common issue in machine learning called domain shift, which represents the difference between the training data distribution and the distribution of where a model is employed. A high domain shift tends to implicate in a poor generalization performance from the models. In this work, we evaluate the extent of domain shift on four of the largest datasets of chest radiographs. We show how training and testing with different datasets (e.g., training in ChestX-ray14 and testing in CheXpert) drastically affects model performance, posing a big question over the reliability of deep learning models trained on public datasets. We also show that models trained on CheXpert and MIMIC-CXR generalize better to other datasets.
General framework for verifying pure quantum states in the adversarial scenario

Bipartite and multipartite entangled states are of central interest in quantum information processing and foundational studies. Efficient verification of these states, especially in the adversarial scenario, is a key to various applications, including quantum computation, quantum simulation, and quantum networks. However, little is know about this topic in the adversarial scenario. Here we initiate a systematic study of pure-state verification in the adversarial scenario. In particular, we introduce a general method for determining the minimal number of tests required by a given strategy to achieve a given precision. In the case of homogeneous strategies, we can even derive an analytical formula. Furthermore, we propose a general recipe to verifying pure quantum states in the adversarial scenario by virtue of protocols for the nonadversarial scenario. Thanks to this recipe, the resource cost for verifying an arbitrary pure state in the adversarial scenario is comparable to the counterpart for the nonadversarial scenario, and the overhead is at most three times for high-precision verification. Our recipe can readily be applied to efficiently verify bipartite pure states, stabilizer states, hypergraph states, weighted graph states, and Dicke states in the adversarial scenario.
The Duality Between Color and Kinematics and its Applications

This review describes the duality between color and kinematics and its applications, with the aim of gaining a deeper understanding of the perturbative structure of gauge and gravity theories. We emphasize, in particular, applications to loop-level calculations, the broad web of theories linked by the duality and the associated double-copy structure, and the issue of extending the duality and double copy beyond scattering amplitudes. The review is aimed at doctoral students and junior researchers both inside and outside the field of amplitudes and is accompanied by various exercises.
Species subsets and embedded networks of S-systems

Magombedze and Mulder (2013) studied the gene regulatory system of \textit{Mycobacterium Tuberculosis} (\textit{Mtb}) by partitioning this into three subsystems based on putative gene function and role in dormancy/latency development. Each subsystem, in the form of $S$-system, is represented by an embedded chemical reaction network (CRN), defined by a species subset and a reaction subset induced by the set of digraph vertices of the subsystem. Based on the network decomposition theory initiated by Feinberg in 1987, we have introduced the concept of incidence-independent and developed the theory of $\mathscr{C}$- and $\mathscr{C}^*$-decompositions including their structure theorems in terms of linkage classes. With the $S$-system CRN $\mathscr{N}$ of Magombedze and Mulder's \textit{Mtb} model, its reaction set partition induced decomposition of subnetworks that are not CRNs of $S$-system but constitute independent decomposition of $\mathscr{N}$. We have also constructed a new $S$-system CRN $\mathscr{N}^*$ for which the embedded networks are $\mathscr{C}^*$-decomposition. We have shown that subnetworks of $\mathscr{N}$ and the embedded networks (subnetworks of $\mathscr{N}^*$) are digraph homomorphisms. Lastly, we attempted to explore modularity in the context of CRN.
Elliptic solutions of Boussinesq type lattice equations and the elliptic Nth root of unity

We establish an infinite family of solutions in terms of elliptic functions of the lattice Boussinesq systems by setting up a direct linearisation scheme, which provides the solution structure for those equations in the elliptic case. The latter, which contains as main structural element a Cauchy kernel on the torus, is obtained from a dimensional reduction of the elliptic direct linearisation scheme of the lattice Kadomtsev-Petviashvili equation, which requires the introduction of a novel technical concept, namely the "elliptic cube root of unity". Thus, in order to implement the reduction we define, more generally, the notion of {\em elliptic $N^{\rm th}$ root of unity}, and discuss some of its properties in connection with a special class of elliptic addition formulae. As a particular concrete application we present the class of elliptic $N$-soliton solutions of the lattice Boussinesq systems.
DLGNet: A Transformer-based Model for Dialogue Response Generation

Neural dialogue models, despite their successes, still suffer from lack of relevance, diversity, and in many cases coherence in their generated responses. On the other hand, transformer-based models such as GPT-2 have demonstrated an excellent ability to capture long-range structures in language modeling tasks. In this paper, we present DLGNet, a transformer-based model for dialogue modeling. We specifically examine the use of DLGNet for multi-turn dialogue response generation. In our experiments, we evaluate DLGNet on the open-domain Movie Triples dataset and the closed-domain Ubuntu Dialogue dataset. DLGNet models, although trained with only the maximum likelihood objective, achieve significant improvements over state-of-the-art multi-turn dialogue models. They also produce best performance to date on the two datasets based on several metrics, including BLEU, ROUGE, and distinct n-gram. Our analysis shows that the performance improvement is mostly due to the combination of (1) the long-range transformer architecture with (2) the injection of random informative paddings. Other contributing factors include the joint modeling of dialogue context and response, and the 100% tokenization coverage from the byte pair encoding (BPE).
On the regularity of the total variation minimizers

We prove regularity results for the unique minimizer of the total variation functional, currently used in image processing analysis since the work by Rudin, Osher and Fatemi. In particular, we show that if the source term [Formula: see text] is locally (respectively, globally) Lipschitz, then the solution has the same regularity with local (respectively, global) Lipschitz norm estimated accordingly. The result is proved in any dimension and for any (regular) domain. So far we extend a similar result proved earlier by Caselles, Chambolle and Novaga for dimension [Formula: see text] and (in case of the global regularity) for convex domains.
Mogriﬁer LSTM

Many advances in Natural Language Processing have been based upon more expressive models for how inputs interact with the context in which they occur. Recurrent networks, which have enjoyed a modicum of success, still lack the generalization and systematicity ultimately required for modelling language. In this work, we propose an extension to the venerable Long Short-Term Memory in the form of mutual gating of the current input and the previous output. This mechanism affords the modelling of a richer space of interactions between inputs and their context. Equivalently, our model can be viewed as making the transition function given by the LSTM context-dependent. Experiments demonstrate markedly improved generalization on language modelling in the range of 3–4 perplexity points on Penn Treebank and Wikitext-2, and 0.01–0.05 bpc on four character-based datasets. We establish a new state of the art on all datasets with the exception of Enwik8, where we close a large gap between the LSTM and Transformer models.
McDiarmid-Type Inequalities for Graph-Dependent Variables and Stability Bounds

A crucial assumption in most statistical learning theory is that samples are independently and identically distributed (i.i.d.). However, for many real applications, the i.i. d. assumption does not hold. We consider learning problems in which examples are dependent and their dependency relation is characterized by a graph. To establish algorithm-dependent generalization theory for learning with non-i.i. d. data, we first prove novel McDiarmid-type concentration inequalities for Lipschitz functions of graph-dependent random variables. We show that concentration relies on the forest complexity of the graph, which characterizes the strength of the dependency. We demonstrate that for many types of dependent data, the forest complexity is small and thus implies good concentration. Based on our new inequalities we are able to build stability bounds for learning from graph-dependent data.
Towards Understanding Neural Machine Translation with Word Importance

Although neural machine translation (NMT) has advanced the state-of-the-art on various language pairs, the interpretability of NMT remains unsatisfactory. In this work, we propose to address this gap by focusing on understanding the input-output behavior of NMT models. Specifically, we measure the word importance by attributing the NMT output to every input word through a gradient-based method. We validate the approach on a couple of perturbation operations, language pairs, and model architectures, demonstrating its superiority on identifying input words with higher influence on translation performance. Encouragingly, the calculated importance can serve as indicators of input words that are under-translated by NMT models. Furthermore, our analysis reveals that words of certain syntactic categories have higher importance while the categories vary across language pairs, which can inspire better design principles of NMT architectures for multi-lingual translation.