Hesitant fuzzy sets are widely used in the instances of uncertainty and hesitation. The inclusion relationship is an important and foundational definition for sets. Hesitant fuzzy set, as a kind of set, needs explicit definition of inclusion relationship. Base on the hesitant fuzzy membership degree of discrete form, several kinds of inclusion relationships for hesitant fuzzy sets are proposed. And then some foundational propositions of hesitant fuzzy sets and the families of hesitant fuzzy sets are presented. Finally, some foundational propositions of hesitant fuzzy information systems with respect to parameter reductions are put forward, and an example and an algorithm are given to illustrate the processes of parameter reductions.
Tracking ripening tomatoes is time consuming and labor intensive. Artificial intelligence technologies combined with those of computer vision can help users optimize the process of monitoring the ripening status of plants. To this end, we have proposed a tomato ripening monitoring approach based on deep learning in complex scenes. The objective is to detect mature tomatoes and harvest them in a timely manner. The proposed approach is declined in two parts. Firstly, the images of the scene are transmitted to the pre-processing layer. This process allows the detection of areas of interest (area of the image containing tomatoes). Then, these images are used as input to the maturity detection layer. This layer, based on a deep neural network learning algorithm, classifies the tomato thumbnails provided to it in one of the following five categories: green, brittle, pink, pale red, mature red. The experiments are based on images collected from the internet gathered through searches using tomato state across diverse languages including English, German, French, and Spanish. The experimental results of the maturity detection layer on a dataset composed of images of tomatoes taken under the extreme conditions, gave a good classification rate.
The notion of an e-value has been recently proposed as a possible alternative to critical regions and p-values in statistical hypothesis testing. In this paper we consider testing the nonparametric hypothesis of symmetry, introduce analogues for e-values of three popular nonparametric tests, define an analogue for e-values of Pitman's asymptotic relative efficiency, and apply it to the three nonparametric tests. We discuss limitations of our simple definition of asymptotic relative efficiency and list directions of further research.
There has recently been an explosion of interest in how "higher-order" structures emerge in complex systems. This "emergent" organization has been found in a variety of natural and artificial systems, although at present the field lacks a unified understanding of what the consequences of higher-order synergies and redundancies are for systems. Typical research treat the presence (or absence) of synergistic information as a dependent variable and report changes in the level of synergy in response to some change in the system. Here, we attempt to flip the script: rather than treating higher-order information as a dependent variable, we use evolutionary optimization to evolve boolean networks with significant higher-order redundancies, synergies, or statistical complexity. We then analyse these evolved populations of networks using established tools for characterizing discrete dynamics: the number of attractors, average transient length, and Derrida coefficient. We also assess the capacity of the systems to integrate information. We find that high-synergy systems are unstable and chaotic, but with a high capacity to integrate information. In contrast, evolved redundant systems are extremely stable, but have negligible capacity to integrate information. Finally, the complex systems that balance integration and segregation (known as Tononi-Sporns-Edelman complexity) show features of both chaosticity and stability, with a greater capacity to integrate information than the redundant systems while being more stable than the random and synergistic systems. We conclude that there may be a fundamental trade-off between the robustness of a systems dynamics and its capacity to integrate information (which inherently requires flexibility and sensitivity), and that certain kinds of complexity naturally balance this trade-off.
Self-testing is a method to certify quantum states and measurements in a device-independent way. The device-independent certification of quantum properties is purely based on input-output measurement statistics of the involved devices with minimal knowledge about their internal workings. Bipartite pure entangled states can be self-tested, but, in the case of multipartite pure entangled states, the answer is not so straightforward. Nevertheless, \v{S}upi\'{c} et al. recently introduced a novel self-testing method for any pure entangled quantum state, which leverages network assistance and relies on bipartite entangled measurements. Hence, their scheme loses the true device-independent flavor of self-testing. In this regard, we provide a self-testing scheme for genuine multipartite pure entangle states in the true sense by employing a generalized Hardy-type non-local argument. Our scheme involves only local operations and classical communications and does not depend on bipartite entangled measurements and is free from any network assistance. In addition, we provide the device-independent bound of the maximum probability of success for generalized Hardy-type nonlocality argument.
Open sets are central to mathematics, especially analysis and topology, in ways few notions are. In most, if not all, computational approaches to mathematics, open sets are only studied indirectly via their 'codes' or 'representations'. In this paper, we study how hard it is to compute, given an arbitrary open set of reals, the most common representation, i.e. a countable set of open intervals. We work in Kleene's higher-order computability theory, which was historically based on the S1-S9 schemes and which now has an intuitive lambda calculus formulation due to the authors. We establish many computational equivalences between on one hand the 'structure' functional that converts open sets to the aforementioned representation, and on the other hand functionals arising from mainstream mathematics, like basic properties of semi-continuous functions, the Urysohn lemma, and the Tietze extension theorem. We also compare these functionals to known operations on regulated and bounded variation functions, and the Lebesgue measure restricted to closed sets. We obtain a number of natural computational equivalences for the latter involving theorems from mainstream mathematics.
A generalization of Passing-Bablok regression is proposed for comparing multiple measurement methods simultaneously. Possible applications include assay migration studies or interlaboratory trials. When comparing only two methods, the method reduces to the usual Passing-Bablok estimator. It is close in spirit to reduced major axis regression, which is, however, not robust. To obtain a robust estimator, the major axis is replaced by the (hyper-)spherical median axis. The method is shown to reduce to the usual Passing-Bablok estimator if only two methods are compared. This technique has been applied to compare SARS-CoV-2 serological tests, bilirubin in neonates, and an in vitro diagnostic test using different instruments, sample preparations, and reagent lots. In addition, plots similar to the well-known Bland-Altman plots have been developed to represent the variance structure.
Serial, or sequential, fusion of multiple biometric matchers has been not thoroughly investigated so far. However, this approach exhibits some advantages with respect to the widely adopted parallel approaches. In this paper, we propose a novel theoretical framework for the assessment of performance of such systems, based on a previous work of the authors. Benefits in terms of performance are theoretically evaluated, as well as estimation errors in the model parameters computation. Model is analyzed from the viewpoint of its pros and cons, by mean of preliminary experiments performed on NIST Biometric Score Set 1.
Remotely sensed data are dominated by mixed Land Use and Land Cover (LULC) types. Spectral unmixing (SU) is a key technique that disentangles mixed pixels into constituent LULC types and their abundance fractions. While existing studies on Deep Learning (DL) for SU typically focus on single time-step hyperspectral (HS) or multispectral (MS) data, our work pioneers SU using MODIS MS time series, addressing missing data with end-to-end DL models. Our approach enhances a Long-Short Term Memory (LSTM)-based model by incorporating geographic, topographic (geo-topographic), and climatic ancillary information. Notably, our method eliminates the need for explicit endmember extraction, instead learning the input-output relationship between mixed spectra and LULC abundances through supervised learning. Experimental results demonstrate that integrating spectral-temporal input data with geo-topographic and climatic information significantly improves the estimation of LULC abundances in mixed pixels. To facilitate this study, we curated a novel labeled dataset for Andalusia (Spain) with monthly MODIS multispectral time series at 460m resolution for 2013. Named Andalusia MultiSpectral MultiTemporal Unmixing (Andalusia-MSMTU), this dataset provides pixel-level annotations of LULC abundances along with ancillary information. The dataset (//zenodo.org/records/7752348) and code (//github.com/jrodriguezortega/MSMTU) are available to the public.
Ordinal pattern dependence has been introduced in order to capture co-monotonic behavior between two time series. This concept has several features one would intuitively demand from a dependence measure. It was believed that ordinal pattern dependence satisfies the axioms which Grothe et al. [8] proclaimed for a multivariate measure of dependence. In the present article we show that this is not true and that there is a mistake in the article Betken et al. [5]. Furthermore we show that ordinal pattern dependence satisfies a slightly modified set of axioms.
Languages have long been described according to their perceived rhythmic attributes. The associated typologies are of interest in psycholinguistics as they partly predict newborns' abilities to discriminate between languages and provide insights into how adult listeners process non-native languages. Despite the relative success of rhythm metrics in supporting the existence of linguistic rhythmic classes, quantitative studies have yet to capture the full complexity of temporal regularities associated with speech rhythm. We argue that deep learning offers a powerful pattern-recognition approach to advance the characterization of the acoustic bases of speech rhythm. To explore this hypothesis, we trained a medium-sized recurrent neural network on a language identification task over a large database of speech recordings in 21 languages. The network had access to the amplitude envelopes and a variable identifying the voiced segments, assuming that this signal would poorly convey phonetic information but preserve prosodic features. The network was able to identify the language of 10-second recordings in 40% of the cases, and the language was in the top-3 guesses in two-thirds of the cases. Visualization methods show that representations built from the network activations are consistent with speech rhythm typologies, although the resulting maps are more complex than two separated clusters between stress and syllable-timed languages. We further analyzed the model by identifying correlations between network activations and known speech rhythm metrics. The findings illustrate the potential of deep learning tools to advance our understanding of speech rhythm through the identification and exploration of linguistically relevant acoustic feature spaces.