In the literature, frames generated by unitary representations of groups (known as group-frames) are studied only for Hilbert spaces. We make first study of frames for Banach spaces generated by isometric invertible representations of discrete groups on Banach spaces. These frames are characterized using left regular, right regular, Gram-matrices and group-matrices on classical sequence spaces. A sufficiently large collection of functional-vector pairs using the double commutant of the representation is identified which generate group-frames for Banach spaces. Subsequently, we study Schauder frames generated by time-frequency shift operators on finite dimensional Banach spaces. We derive Moyal formula, fundamental identity of Gabor analysis, Wexler-Raz criterion and Ron-Shen duality in functional form.

A contrasting empirical evaluation will be provided with the aim of suggesting that the reductionist approach results in experiments that are not reproducible.

Scene classification plays an important role in the intelligent processing of high-resolution satellite (HRS) remotely sensed image. In HRS image classification, multiple features, e.g. shape, color, and texture features, are employed to represent scenes from different perspectives. Accordingly, effective integration of multiple features always results in better performance compared to methods based on a single feature in the interpretation of HRS image. In this paper, we introduce a multi-task joint sparse and low-rank representation model to combine the strength of multiple features for HRS image interpretation. Specifically, a multi-task learning formulation is applied to simultaneously consider sparse and low-rank structure across multiple tasks. The proposed model is optimized as a non-smooth convex optimization problem using an accelerated proximal gradient method. Experiments on two public scene classification datasets demonstrate that the proposed method achieves remarkable performance and improves upon the state-of-art methods in respective applications.

In this paper, we propose a novel network representation learning model TransPath to encode heterogeneous information networks (HINs). Traditional network representation learning models aim to learn the embeddings of a homogeneous network. TransPath is able to capture the rich semantic and structure information of a HIN via meta-paths. We take advantage of the concept of translation mechanism in knowledge graph which regards a meta-path, instead of an edge, as a translating operation from the first node to the last node. Moreover, we propose a user-guided meta-path sampling strategy which takes users' preference as a guidance, which could explore the semantics of a path more precisely, and meanwhile improve model efficiency via the avoidance of other noisy and meaningless meta-paths. We evaluate our model on two large-scale real-world datasets DBLP and YELP, and two benchmark tasks similarity search and node classification. We observe that TransPath outperforms other state-of-the-art baselines consistently and significantly.

In the paper, the authors survey integral representations (including the Lévy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the (weighted) geometric means and their reciprocals, and the Toader--Qi mean) and the multivariate (weighted) geometric means and their reciprocals, derive integral representations of bivariate complex geometric mean and its reciprocal, and apply these newly-derived integral representations to establish integral representations of Heronian mean of power 2 and its reciprocal.

This paper analyzes the representation behaviors of a comparison measure between two compared fuzzy sets. Three types of restrictions on two fuzzy sets are considered in this paper: the two disjoint union fuzzy sets, the two disjoint fuzzy sets and the two general fuzzy sets. Differences exist among the numbers of possible representations of a comparison measure for the three types of fuzzy sets restrictions. The value of comparison measure is constant for the two disjoint union fuzzy sets. There are 42 candidate representations of a comparison measure for the two disjoint fuzzy sets. Of which 13 candidate representations with one or two terms can be used to easily calculate and compare a comparison measure.

In this paper, it is shown that the bivariate beta statistical manifold of the first kind with three parameters has a gradient system Hamiltonian and is completely integrable. It is shown that this system admits a Lax pair representation. The question here is how to construct a gradient system and show that it is completely integrable while determining the integrable curves on the three-parameter bivariate beta manifold of the first kind admitting a potential function?To do this, we prove the existence of the potential on the manifold using ovidiu in Ovidiu, then using Amari's theorems in Amari, we show that this coordinate system admits a dual coordinate system. This will allow us to determine the Riemannian metric on the variety and to construct the gradient system. We linearise this system using Nakamura's method. We prove that it is Hamiltonian and completely integrable using the theorem in \cite{mama-proceeding}. It is shown that the Bivariate Beta of the first kind with three parameters, is an exponential function. The gradient system is linearizable. It is proven that the associate gradient system is Hamiltonian with $ \mathcal{H} $ which is in involution and satisfying $d\mathcal{H}=0.$ Therefore, the gradient system obtained is a sub-dynamical system of a $4$-dimensional system and is a completely integrable system. We show that the gradient system on the statistical model has the following Lax pair representation: $ \dot{L}= \left[L, N\right] $ where $L$ is a symmetric matrix and $N$ is the diagonal matrix. The gradient system defined by the Bivariate Beta family of the first kind with three parameters odd-dimensional manifold is a completely integrable Hamiltonian system.

The aim of this paper is to bring together quaternions and generalized complex numbers. Generalized quaternions with generalized complex number components are expressed and their algebraic structures are examined. Several matrix representations and computational results are introduced. As a crucial part, alternative approach for generalized quaternion matrix with elliptic number entries are developed.

This study aims to identify modern bureaucratic government phenomenon expressed in W.H. Auden’s poem “The Unknown Citizen” (UC). This phenomenon will be revealed through the use of figures of speech, symbols and imagery in the poem. This poem is chosen as the object of the study since phenomenon happened in the poem represents people’s life and government practice in the modern era. Government, in the poem, seems to be very dominant. Its bureaucratic apparatus is powerful. Through its sophisticated technology, the bureau of statistics is able to detect the citizen’s identity. But, ironically, it could have not identified UC’s name as he lived in the world. He, then, was honored by the state by being erected the marble monument. The poem is analyzed by applying phenomenological criticism. The analysis finds that the representation of modern government is expressed through symbols emphasized by dramatic irony and supported by the use of internal sensation imagery. UC is the allegory of the average person with his bravery he sacrifices for the country. The state ought to give him an honor. In this poem Auden, actually, wants to write a parody for establishing monuments in some countries to honor the struggles of their soldiers who died in the World War I. Those monuments are really tombs since the function of a monument is a state’s thanksgiving for their sacrifice.

The QBIT theory is an attempt toward solving the problem of consciousness based on empirical evidence provided by various scientific disciplines including quantum mechanics, biology, information theory, and thermodynamics. This theory formulates the problem of consciousness in the following four questions: (1) What is the nature of qualia? (2) How are qualia generated? (3) Why are qualia subjective? (4) Why does a quale have a particular quality or meaning?In sum, the QBIT theory proposes that (1) when a pack of quantum information is compressed beyond a certain threshold, a quale is generated; (2) a quale is a superdense pack of maximally entangled qubits in a pure state; (3) when information-theoretic certainty of a system about an external stimulus exceeds a particular level, the system becomes conscious of that stimulus; (4) subjectivity of consciousness is due to the fact that maximally entangled pure states are private and unshareable.

Knowledge graphs (KGs) play a crucial role in many applications, such as question answering, but incompleteness is an urgent issue for their broad application. Much research in knowledge graph completion (KGC) has been performed to resolve this issue. The methods of KGC can be classified into two major categories: rule-based reasoning and embedding-based reasoning. The former has high accuracy and good interpretability, but a major challenge is to obtain effective rules on large-scale KGs. The latter has good efficiency and scalability, but it relies heavily on data richness and cannot fully use domain knowledge in the form of logical rules. We propose a novel method that injects rules and learns representations iteratively to take full advantage of rules and embeddings. Specifically, we model the conclusions of rule groundings as 0-1 variables and use a rule confidence regularizer to remove the uncertainty of the conclusions. The proposed approach has the following advantages: 1) It combines the benefits of both rules and knowledge graph embeddings (KGEs) and achieves a good balance between efficiency and scalability. 2) It uses an iterative method to continuously improve KGEs and remove incorrect rule conclusions. Evaluations on two public datasets show that our method outperforms the current state-of-the-art methods, improving performance by 2.7% and 4.3% in mean reciprocal rank (MRR).

Rural environment has experienced changes as a result of Covid-19, which encourage the introduction of sustainability in education. However, the representation of rurality in school geography and in the 2030 Agenda are factors that continue to present rurality as a concept opposed to urban spaces. The objective was to investigate the perception that the student has about the rural environment from an instrument and his drawings to understand if the explanation of it allows to introduce elements related to sustainability in educational projects. The quantitative research approach allows analyzing the psychometric properties of an instrument to measure the perception of the rural environment of a sample of 300 fifteen-year-old students from Brazil, Colombia and Spain. Those school knowledges that idealize rurality warn of the pedagogical difficulties to promote the teaching of rurality from sustainability criteria and condition the formation of students from a citizenship committed to social problems. This study is important because it diagnoses the elements that intervene in the teaching of rurality from school geography and provides some suggestions to include sustainability in educational projects.

The ecosystem is an essential biological concept linking the living and the inanimate and represents the main structural and functional unit of nature. The biodiversity that exists on our planet can be organized into closely interconnected living worlds: acellular (viruses and capsidless genetic elements), prokaryotic (bacteria and archaea), and eukaryotic (all nucleated organisms). I want to highlight the presence of viruses as components of biodiversity because they are often overlooked in many studies despite their essential ecological and evolutionary role. Furthermore, I propose seven distinctive hallmarks that are inherent to any ecosystem: biodiversity, physical environment, hierarchy, interactivity, openness, “homecostasis”, and evolutionary. From the interaction and coupling of these living worlds with the environment (the environmental world), I define the ecosystem as a specific and dynamic ensemble of living and non-living worlds that functions as an open, hierarchical, and evolving system. This complex web of interactions that we call ecosystem can be graphically represented as a triangle reflecting the dynamic equilibrium between all the worlds. Finally, I propose a new way of graphically relating the ecosystem to biodiversity by taking the ecosystem as the nucleus from which all living worlds emerge.

The paper describes problems with the current additive manufacturing chain before considering additive manufacturing as part of a modern manufacturing chain. Additive manufacturing can be used for near net-shape for finishing, for repair or for adding special features which cannot be made with traditional manufacturing. This paper describes how STEP-NC deals with these different scenarios in terms of accuracy, multi-material and variation of slice direction. The possibilities of multi-material objects also raises questions about the design of such objects and how these need to be handled by an advanced controller. The paper also describes non-planar slicing. Curved direction and cylindrical direction are shown to improve the accuracy of curved structure additive manufacturing. STEP-NC using boundary representation has better capability of depicting complex internal structures for additive processes. By using exact model of the final product represented by STEP-NC, the paper demonstrates improvements in data size reduction, slicing accuracy, and precise manipulation of internal structure.

In this note we construct explicit complex and real matrix representations for the generators of real Clifford algebra $C\ell_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal geometry. We find two classes of representation, the normal representation and exceptional one. The normal representation is a large class of representation which can only be expanded into $4m+1$ dimension, but the exceptional representation can be expanded as generators of the next period. In the cases $p+q=4m$, the representation is unique in equivalent sense. These results are helpful for both theoretical analysis and practical calculation. The generators of Clifford algebra are the faithful basis of $p+q$ dimensional Minkowski space-time or Riemann space, and Clifford algebra converts the complicated relations in geometry into simple and concise algebraic operations, so the Riemann geometry expressed in Clifford algebra will be much simple and clear.

This paper undertakes a critical analysis and evaluates the recent developments in the study of Islam and how it has gone beyond Orientalism; as Martin and Ernst remark in the preface and acknowledgements of Rethinking Islamic Studies: from Orientalism to Cosmopolitanism that the last three decades—after the publication of Orientalism in 1978—“has been a liberating experience for us as scholars initially trained in narrowly textual ‘Orientalist’ approaches, as we have been forced by circumstance to address many issues of contemporary political and social relevance.” However, I will also acknowledge the alternate perspective that these developments may not have gone beyond Said’s Orientalism, but have rather reinforced and maintained - and have “decidedly worsened”—the very ideas Said introduced in Orientalism because of issues such as: Islamic fundamentalism and the aftermath of 9/11, and how the study of Islam has been influenced by these issues in modern times thus returning to the Orientalist approach. I will look at the history of Orientalism in the study of Islam, then the emergence of space for self-representation, and then I will look at the current study of Islam. Esposito argues that Orientalism has taken a new form, and no longer romanticizes the Middle East as having sandy deserts where genies, thieves and evil sorcerers vied after scantily clad princesses amid a backdrop of white palaces and peasant-ridden streets, as presented in the film ‘Aladdin’.

A cursory look at Indian prime time news tells us much about the tone and tenor of the people associated with it. Exaggerations, hyperbole, and tempers run wild and news anchors flail in theatrical rage. News channels and news editors display their ideological affiliations subliminally. These affiliations — a factor of personal political stance, funding bodies, and investors — lead to partisan bias in the framing of news and, in some cases, can easily translate into racial prejudice. In this paper, I examine news coverage related to Muslims in India. I study the coverage of two issues specifically– love jihad and triple talaq –in prime time English news of two channels – Times Now and Republic TV. My analysis of the content, tone, and tenor of their coverage shows that these channels propagate associations between Islam and backwardness, ignorance and violence through consistent employment of the following tropes – ‘Muslim women need to be saved from Muslim men’, ‘Hindu women need to be saved from Muslim men’, and ‘Muslims are not fully Indian – they are anti-national’. I place this study of news media within the current political climate in India and briefly touch on the conversations it guides and provokes. This is also a call for further analysis on this subject to examine and evaluate how discourse manipulates public conversations and policy decisions.

Aging is a major risk factor for the higher incidence and prevalence of chronic conditions, such as cancer, cardiovascular and metabolic diseases, and neurodegenerative diseases. Closely linked with the onset of all these age-related diseases is immunosenescence, a condition defined as progressive reconfiguration of the immune functions leading to an increased susceptibility to infectious diseases, poorer response to vaccination, increased prevalence of cancer, rheumatoid arthritis, and other chronic diseases characterized by a pro-inflammatory state named inflammaging. Given that immunosenescence frames age-related diseases, it is natural to ask how these illnesses are related under the context of innate and adaptative components of the immune system. Knowledge processing by Formal Concept Analysis (FCA) of age-related diseases framed in an immunosenescence multivalued context shows that a hierarchy among these diseases emerges with a subconcept-superconcept nested structure, with two clusters, first made of metabolic diseases, cancer, and cardiovascular diseases. Second metabolic and neurodegenerative diseases and rheumatoid arthritis. Metabolic diseases seem to be a pivot illness and they must be a primary target given their global incidence and prevalence and their cost-effective treatments like regular physical activity, weight loss, healthy diet, stopping smoking, and reducing or managing stress. Another implication of the ontological analysis of age-related diseases is about the nature of immunosenescence, suggesting that initial symptoms of age-related diseases are mainly related to innate immune mechanisms, and developing of severe symptoms of age-related diseases like cancer, cardiovascular or neurodegenerative diseases depends on the activation of acquired immunity processes.

Reducing office buildings’ energy consumption can contribute significantly towards carbon reduction commitments since it represents 10% of total energy consumption. Major components are lighting (40% of consumption), electrical equipment (35%), and heating and central cooling systems (25\%). Occupants’ behaviours impact these energy consumption components, with solid evidence on the role of individual behaviours. In this work, we propose a methodology that uses virtual choreographies to identify and prioritize behaviour-change interventions towards office users based on the potential impact on energy consumption. The data shows that some behaviours with significant consumption have little potential for behavioural change impact, while other behaviours hold substantial potential for lowering energy consumption via behavioural change.

In this paper, we propose an unsupervised blind restoration model for images in hybrid degradation scenes. The proposed model encodes the content information and degradation information of images and then uses the attention module to disentangle the two kinds of information. It can improve the ability of disentangled presentation learning for a generative adversarial network (GAN) to restore the images in hybrid degradation scenes, enhance the detailed features of restored image and remove the artifact combining the adversarial loss, cycle-consistency loss, and perception loss. The experimental results on the DIV2K dataset and medical images show that the proposed method outperforms existing unsupervised image restoration algorithms in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and subjective visual evaluation.

The level of ambiguity in describing glycan structure has significantly increased with the upsurge of large scale glycomics and glycoproteomics experiments. Consequently, an ontology-based model appears as an appropriate solution for navigating this data. However, navigation is not sufficient and the model should also enable advanced search and comparison. A new ontology with a tree logical structure is introduced to represent glycan structures irrespective of the precision of molecular details. The model heavily relies on the GlycoCT encoding of glycan structures. Its implementation in the GlySTreeM knowledge base was validated with GlyConnect data and benchmarked with the Glycowork library. GlySTreeM is shown to be fast, consistent, reliable and more flexible than existing solutions for matching parts of or whole glycan structures. The model is also well suited to painless future expansion. Availability:https://glyconnect.expasy.org/glystreem/wiki

Machine learning has become an increasingly ubiquitous technology, as big data continues to inform and influence everyday life and decision-making. Currently in healthcare, as well as in most other industries, the two most prevalent machine learning paradigms are supervised learning and transfer learning. Both practices rely on large-scale, manually annotated datasets to train increasingly complex models. However, the requirement of data to be manually labeled leaves an excess of unused, unlabeled data available in both public and private data repositories. Self-supervised learning (SSL) is a growing area of machine learning that has the ability to take advantage of unlabeled data. Contrary to other machine learning paradigms, SSL algorithms create artificial supervisory signals from unlabeled data and pretrain algorithms on these signals. The aim of this review is two-fold: firstly, we provide a formal definition of SSL, divide SSL algorithms into their four unique subsets, and review the state-of-the-art published in each of those subsets between the years of 2014-2020. Second, this work surveys recent SSL algorithms published in healthcare, in order to provide medical experts with a clearer picture of how they can integrate SSL into their research, with the objective of leveraging unlabeled data.

How a species is represented by marketers of animal-based products both reflects and shapes how consumers think about that animal. By examining the explicit statements, and implicit messages encoded in the imagery on supermarket egg boxes, this paper explores how hens are represented by whole egg retailers. Content analysis reveals two prominent messages purveyed through eggbox graphics, namely those pertaining to hen welfare and human health. The later disenfranchises hens from their products by focusing on the nutritional value of eggs, whereas the former reflects a public concern for the welfare of egg-laying hens. Although claims of improvements in welfare practices are undoubtedly exploited as marketing tools, they serve to raise awareness and drive competitors to adopt similar practices. Welfare claims are a direct response to public concerns about the plight of hens, and may positively influence industry welfare standards. However, idyllic depictions displayed on eggboxes also lull consumers into the belief that those eggs are an ethically sound food choice, regardless of the actual standard of living experienced by the hens.

In tele-monitoring, wireless body area networks (WBANs), sleep analysis and other applications involving electroencephalogram (EEG) signal, due to the high number of EEG recording channels, long recording time and several repetition of recordings to reach the highest signal-to-noise ratio, the amount of acquired data by the sensors is too large, demanding use of some compression procedure. Compressed sensing can be considered as one of the most effective compression methods in terms of compression ratio, which needs the underlying signal be sparse or have sparse representation in an appropriate domain. EEG signal is not sparse in time domain, therefore, in this paper correlation based weighted recursive least squares dictionary learning algorithm (CBW-RLS) is proposed that uses between-channel correlations to sparsify EEG signals. Due to the low-rank structure of EEG signals, exploiting between-channel correlations increase the sparsity level of the model while reducing the computational cost of dictionary learning procedure. This is done by merely updating the dictionary atoms which are involved in the sparse model of the previous data, reducing the total number of data used at each iteration and speeding up the dictionary learning algorithm. The simulation results show that the proposed method has better performance in terms of both quality of the EEG reconstruction and the computational cost compared to the other methods.

This paper explores ballot split by type and introduces universal measures of democratic power flow and accountable local representation. These measures allow definitive comparison of electoral systems between countries, and choice of a new electoral system within a country based on existing data and with minimum assumptions.

The two main strategies used in this study are the binary representation and the decomposition of a natural number into many compound functions of odd function and even function. The Collatz conjecture regarding odd even numbers in number theory can be examined and discussed using them in this way: The sequence created by the finite iterations of the Collatz function becomes the ultimately periodic sequence if any natural number is the beginning value, proving the conjecture that has been held for 85 years.

Taste determination in small molecules is critical in food chemistry, but traditional experimental methods can be time-consuming. Consequently, computational techniques have emerged as val-uable tools for this task. In this study, we explore taste prediction using various molecular feature representations and assess the performance of different machine learning algorithms on a dataset comprising 2,601 molecules. The results reveal that GNN-based models outperform other ap-proaches in taste prediction. Moreover, consensus models that combine diverse molecular repre-sentations demonstrate improved performance. Among these, molecular fingerprints + GNN con-sensus model emerges as the top performer, highlighting the complementary strengths of GNNs and molecular fingerprints. These findings have significant implications for food chemistry research and related fields. By leveraging these computational approaches, taste prediction can be expedited, leading to advancements in understanding the relationship between molecular structure and taste perception in various food components and related compounds.

This paper proposes a Grouped Contrastive Learning of self-supervised Sentence Representation (GCLSR), which can learn an effective and meaningful representation of sentences. Previous works maximize the similarity between two vectors to be the objective of contrastive learning, suffering from the high-dimensionality of the vectors. In addition, most previous works have adopted discrete data augmentation to obtain positive samples and directly employed contrastive framework of computer vision to perform contrastive training, which could hamper contrastive training because text data is discrete and sparse compared with image data. To address those issues, we propose a grouped contrastive learning framework, i.e., GCLSR, which divides the high-dimensional feature vector into several groups and respectively computes the groups’ contrastive losses to make use of more local information, eventually obtaining a more fine-grained sentence representation. In addition, in GCLSR, we design a new self-attention mechanism and a continuous as well as partial word vector augmentation (PWVA). For the discrete and sparse text data, the usage of self-attention could help model focus the informative words by measuring the importance of every word in a sentence. By using the PWVA, GCLSR can obtain high-quality positive samples used for contrastive learning. Experimental results demonstrate that our proposed GCLSR achieves an encouraging result on the challenging datasets of the standard semantic textual similarity (STS) task and transfer task.

The deployment of Artificial Intelligence (AI) systems in decentralized environments is on the rise, yet representation of shared conceptualization in such scenarios remains a challenging issue. The absence of a shared understanding can lead to suboptimal performance of AI systems and hinders the ability to comprehend the knowledge and beliefs of agents in the domain. This paper proposes a formal model for modeling conceptualization in AI systems that integrates ontology, epistemology, and epistemic logic. The model aims to address the gap in representing shared conceptualization in decentralized environments and enhance the performance of AI systems operating in such environments. The proposed model is a hybrid structure that blends extensional and intensional structures and leverages logic-based languages for modeling purposes. A case study in the healthcare sector is presented to illustrate the application of the proposed model. The study contributes to the existing literature by providing a formal model for representing shared conceptualization in decentralized environments, which can be utilized to optimize the performance of AI systems in these environments.

The continuous nature of space and time is a fundamental tenet of many scientific endeavours. That digital representation imposes granularity is well recognized but whether it is possible to address space completely remains unanswered. Part 1 argues that Hales’ proof of Keppler’s conjecture on the packing of hard spheres suggests the answer to be ‘no’, providing examples of why this matters in GIS generally and spatio-temporal GIS in particular. Part 2 seeks to resolve the dichotomy between continuous and granular space, showing how a continuous space may be emergent over a random graph. However, its projection into 3D/4D imposes granularity. Perhaps surprisingly, representing space and time as locally conjugate may be key to addressing a ‘smooth’ spatial continuum. This insight leads to the suggestion of Face Centered Cubic Packing as a space-time topology but also raises further questions for spatio-temporal representation.

Many studies in the field of robot navigation have focused on environment representation and localization. The goal of map representation is to summarize spatial information in topological and geometrical abstracts. By providing strong priors, maps improve the performance and reliability of automated robots. Due to the transition to fully automated driving in recent years, there has been a constant effort to design methods and technologies to improve the precision of road participants and the environment's information. Among these efforts is the High Definition (HD) Map concept. Making HD maps requires accuracy, completeness, verifiability, and extensibility. Because of the complexity of HD mapping, it is currently expensive and difficult to implement, particularly in an urban environment. In an urban traffic system, the road model is at least a map with sets of roads, lanes, and lane markers. While more research is being dedicated to mapping and localization, a comprehensive review of the various types of map representation is still required. This paper presents a brief overview of map representation, followed by a detailed literature review of HD Map for automated vehicles. The current state of AV mapping is encouraging, the field has matured to a point where detailed maps of complex environments are built in real-time and have been proved useful. Many existing techniques are robust to noise and can cope with a large range of environments. Nevertheless, there are still open problems for future research. AV mapping will continue to be a highly active research area essential to the goal of achieving full autonomy.

Capacity Expansion Models (CEMs) are optimization models used for long-term energy planning on national to continental scale. They are typically computationally demanding, thus in need of simplification, where one such simplification is to reduce the temporal representation. This paper investigates how using representative periods to reduce the temporal representation in CEMs distorts results compared to a benchmark model of a full chronological year. The test model is a generic CEM applied to Europe, equipped with a novel formulation for storage in model versions with reduced temporal representation. We test the performance of reduced models at penetration levels of wind and solar of 90%. Three measures for accuracy are used: (i) system cost, (ii) total capacity mix and (iii) regional capacity. We find that: (i) the system cost is well represented (~5% deviation from benchmark) with as few as ten representative days, (ii) the capacity mix is in general fairly well (~20% deviation) represented with 50 or more representative days, and (iii) the regional capacity mix displays large deviations (>50%) from benchmark for as many as 250 representative days. We conclude that modelers should be aware of the error margins when presenting results on these three aspects.

Ancient numismatics, that is, the study of ancient currencies (predominantly coins), is an interesting domain for the application of computer vision and machine learning, and has been receiving an increasing amount of attention in recent years. Notwithstanding the number of articles published on the topic, the variety of different methodological approaches described, and the mounting realisation that the relevant problems in the field are most challenging indeed, all research to date has entirely ignored one specific, readily accessible modality: colour. Invariably, colour is discarded and images of coins treated as being greyscale. The present article is the first one to question this decision (and indeed, it is a decision). We discuss the reasons behind the said choice, present a case why it ought to be reexamined, and in turn investigate the issue for the first time in the published literature. Specifically, we propose two new colour-based representations specifically designed with the aim of being applied to ancient coin analysis, and argue why it is sensible to employ them in the first stages of the classification process as a means of drastically reducing the initially enormous number of classes involved in type matching ancient coins (tens of thousands, just for Ancient Roman Imperial coins). Furthermore, we introduce a new data set collected with the specific aim of denomination-based categorisation of ancient coins, where we hypothesised colour could be of potential use, and evaluate the proposed representations. Lastly, we report surprisingly successful performances which goes further than confirming our hypothesis—rather, they convincingly demonstrate a much higher relevant information content carried by colour than even we expected. Thus we trust that our findings will be noted by others in the field and that more attention and further research will be devoted to the use of colour in automatic ancient coin analysis.

The QBIT theory is an attempt toward solving the problem of consciousness in the light of Quantum mechanics, Biology, Information theory, and Thermodynamics. “Internal representation” is a key concept in the QBIT theory of consciousness. An internal representation is defined as a pack of information (within a cognitive system) that represents an external stimulus.The QBIT theory suggests that when robustness of an internal representation exceeds a certain threshold, a conscious experience (or a quale) is generated. In this paper, the concept of internal representation and its relation with consciousness is explored.

Indoor scene recognition has great significance for intelligent applications such as mobile robots, location-based services (LBS) and so on. Wherever we are or whatever we do, we are under a specific scene. The human brain can easily discern a scene with a quick glance. However, for a machine to achieve this purpose, on one hand, it often requires plenty of well-annotated data which is time-consuming and labor-intensive. On the other hand, it is hard to learn effective visual representations due to large intra-category variation and inter-categories similarity of indoor scenes. To solve these problems, in this paper, we adopted an unsupervised visual representation learning method which can learn from unlabeled data with a Siamese Convolutional Neural Network (Siamese ConvNet) and graph-based constraints. Specifically, we first mined relationships between unlabeled samples with a graph structure. And then, these relationships can be used as supervision for representation learning with a Siamese network. In this method, firstly, a k-NN graph would be constructed by taking each image as a node in the graph and its k nearest neighbors are linked to form the edges. Then, with this graph, cycle consistency and geodesic distance would be considered as criteria for positive and negative pairs mining respectively. In other words, by detecting cycles in the graph, images with large differences but in the same cycle can be considered as same category (positive pairs). By computing geodesic distance instead of Euclidean distance from one node to another, two nodes with large geodesic distance can be regarded as in different categories (negative pairs). After that, visual representations of indoor scenes can be learned by a Siamese network in an unsupervised manner with the mined pairs as inputs. In order to evaluate the proposed method, we tested it on two scene-centric datasets, MIT67 and Places365. Experiments with different number of categories have been conducted to excavate the potential of proposed method. The results demonstrated that semantic visual representations for indoor scenes can be learned in this unsupervised manner. In addition, with the learned visual representations, indoor scene recognition models trained with the learned representations and a few of labeled samples can achieve competitive performance compared to the state-of-the-art approaches.

Aiming at the problems that large amount of video monitoring image data in underground coal mines leads to difficulties in transmission and storage, compressed sensing theory is introduced to encode and decode video images, and a new distributed video coding scheme is proposed. In order to obtain more sparse representation and more general applicability, a block-based adaptive sparse base scheme is proposed. For the acquisition of side information, fixed weight is usually used to synthesize side information and the correlation between different image blocks is neglected, a block-based classification weighted side information generation scheme is proposed. Experimental results show that the block-based classification codec scheme can make full use of inter-frame correlation. Under the appropriate sampling rate, the PSNR value of video reconstruction increases, which effectively improves the quality of video frame reconstruction.

This work presents datasets that can be used for getting a good understanding of an essential geoscience content knowledge that describe earth’s coordinate systems. This include coordinate system used for spherical/spheroidal earth with latitudes and longitudes and their subsequent transformations to 2d maps on a variety of media (paper as well as digital) using the process of map projections. The datasets include PDF documents that are embedded with 3d models, animations and mathematical equations. The dataset has separate PDF documents for geographic (for spherical earth) and projected (2d) coordinate systems. Additionally, the data set include individual 3d models that can be used in various digital systems (including apps) and the animations in mp4 format that can be watched on most of the modern digital devices.

In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a Bernstein function and a completely monotonic function respectively, establishes a Lévy-Khintchine representation for the generating function of multivariate logarithmic polynomials, deduces an integral representation for multivariate logarithmic polynomials, presents an integral representation for the reciprocal of the generating function of multivariate logarithmic polynomials, computes real and imaginary parts for the generating function of multivariate logarithmic polynomials, derives two integral formulas, and denies the uniform convergence of a known integral representation for Bernstein functions.

A symbolic analysis of Archimedes’ periodical number system is developed, from which a natural link emerges with the modern positional number systems with zero. After the publication of Fibonacci’s Liber Abaci, the decimal Indo-Arabic positional system was the basis of the algorithmic and algebraic trend of modern mathematics, but even if zero plays a crucial role in algebra and mathematical analysis, zeroless positional systems show the same capability of producing efficient arithmetical algorithms based on operation tables over digits. The crucial role of digits is assessed, by considering a representation of numbers based on strings in lexicographic order. A new algorithm for the determination of decimal periods is presented,, by remarking the cruciality of this topic in number theory. Periods of ordinal numbers, and enumerations of recursive enumerability are shortly recalled. Concluding remarks are formulated about the deep relationship among numbers and information, which shed new light on a red line passing through the whole history of mathematics

Cyberspace map, as one of the important tools to describe cyberspace, gives an image to the unpredictable and illusory cyberspace, and has become a research hotspot in the fields of cartography, cyberspace security. Clarifying the concept of cyberspace map and constructing the conceptual model of cyberspace map can promote people's unified cognition of cyberspace. Based on the view of cartography, this paper compares and analyzes some related concepts of cyberspace map, discusses the characteristics of cyberspace map，and gives its concept. After that, it analyzes people's cognition of cyberspace composition. On this basis, it caters to this cognition mode and proposes the conceptual model of cyberspace map. Then, the connotation of the model is elaborated from three aspects: element-space association dimension, element mapping dimension and the map representation dimension. Finally, the specific composition and symbolization of various elements are analyzed. The model provides the top-level framework and theoretical guidance for the research of cyberspace map. This paper aims to adapt to the development trend of Cartography in ternary space, clarify the basic concept of cyberspace map, promote the development of cyberspace mapping theory, and lay the foundation for subsequent research.

We present an ontology log-OLOG- representation of the classical Miller-Urey experiment, usually considered as a paradigm for spontaneous generation of biomolecules on the prebiotic Earth and also, as a key in understanding the chemical evolution phenomena linked to the origins of life. Ologging The Miler-Urey experiment enables us, through the categorical notion of fibre product or pullback, to define the concept of Biogenic Space, as a space containing low complexity biogenic units subjected to appropriate physical and chemical conditions, facilitating the synthesis of highly complex organic molecules. Also, we characterize the Biogenic Space as a concrete universal object that could be associated with the preconditions for life inside various structures in the universe such as exoplanets and exomoons located in habitable zones, but also in interstellar and intergalactic organic clouds.

Scientific progress is increasingly dependent on knowledge in computation-ready forms. In the life sciences, among others, many scientists therefore extract and structure knowledge from the literature. In a process called manual curation, they enter knowledge into spreadsheets, or into databases where it serves their and many others' research. Valuable as these curation efforts are, the range and detail of what can practically be captured and shared remains limited, because of the constraints of current curation tools. Many important contextual aspects of observations described in literature simply do not fit in the form defined by these tools, and thus cannot be captured. Here we present the design of an easy-to-use, general-purpose method and interface, that enables the precise semantic capture of virtually unlimited types of information and details, using only a minimal set of building blocks. Scientists from any discipline can use this to convert any complex knowledge into a form that is easily readable and meaningful for both humans and computers. The method VSM forms a universal and high-level language for encoding ideas, and for interacting with digital knowledge.

VSM is a recently introduced method for entering and displaying any type of knowledge, in a form that is both semantically precise for computation and intuitive for human understanding. VSM is the combination of a new semantic model, and the design for a dedicated user interface to support it. Here we present the implementation of this user interface, as a sophisticated HTML-element, <vsm-box>, that can be embedded in any web-based curation app. We show how developers can use it for biocuration projects, customize it to particular end-user needs, and contribute to its growth. Vsm-box is open-source at https://github.com/vsmjs/vsm-box under the AGPL license, as a JavaScript (ES6) Vue.js web-component that runs in all modern web browsers. It is the capstone of the Vsmjs organization at https://github.com/vsmjs that groups its supporting modules. Extensive supplementary material on VSM and vsm-box is available at https://vsmjs.github.io.

While the knowledge about the development of understanding positive integers is rapidly growing, the development of understanding zero is not well-known. Here we tested several components of preschoolers’ understanding zero: whether they can use empty sets in numerical tasks, whether they can use empty sets soon after they understand the cardinality principle, whether they know what the word “zero” refers to, and whether they categorize zero as a number. The results show that preschoolers can handle empty sets in numerical tasks as soon as they understand the cardinality principle or even earlier, and some of them know that these sets are labeled as “zero.” However, they are unsure whether zero is a number. These results identify three components of knowledge about zero: operational knowledge, linguistic knowledge, and meta knowledge. To account for these results we propose that preschoolers might understand numbers as the properties of items or objects in a set. In this view, zero cannot be a number, because an empty set does not include any items, and the missing items cannot have any property, excluding also the number property. This model might explain why zero is handled correctly in numerical tasks, while it is not regarded to be a number.

This paper presents a novel method to extract local features, which instead of calculating local extrema computes global maxima in a discretized scale-space representation. To avoid obtaining precise scales by interpolation and to achieve perfect rotation invariance, two essential techniques, increasing the width of kernels in pixel and utilizing disk-shaped convolution template are adopted in this method. Since the size of a convolution template is finite and finite templates can introduce computational error into convolution, we sufficiently discuss this problem and work out an upper bound of the computational error. The upper bound is utilized in the method to ensure that all features obtained are computed under a given tolerance. Besides, the technique of relative threshold to determine features is adopted to reinforce the robustness for the scene of changing illumination. Simulations show that this new method attains high performance of repeatability in various situations including scale change, rotation, blur, JPEG compression, illumination change and even viewpoint change.

Using an algebraic method for solving the wave equation in quantum mechanics, we encountered a new class of orthogonal polynomials on the real line. One of these is a four-parameter polynomial with a discrete spectrum. Another that appeared while solving a Heun-type equation has a mix of continuous and discrete spectra. Based on these results and on our recent study of the solution space of an ordinary differential equation of the second kind with four singular points, we introduce a modification of the hypergeometric polynomials in the Askey scheme. Up to now, all of these polynomials are defined only by their three-term recursion relations and initial values. However, their other properties like the weight function, generating function, orthogonality, Rodrigues-type formula, etc. are yet to be derived analytically. This is an open problem in orthogonal polynomials.

This paper considers target characterization and recognition in radar images with keypoint-based local descriptor. Most of the preceding works rely on the global features or raw intensity values, and hence produce the limited recognition performance. Moreover, the global features are sensitive to the real-world sources of variability, such as aspect view, configu-ration, and incidence angle changes, clutter, articulation, and occlusion. Keypoint-based local descriptor was developed as a powerful strategy to address invariance to contrast change and geometric distortion. This property inspires us to investigate whether the family of local features are relevant for radar target recognition. Most of the preceding works typically devote to finding the correspondences between a collected image and a reference one. The representative applications include image register and change detection. Little work was pursued to target recognition in SAR images. This is because the huge number of local descriptors resulting from radar images make the computational cost and memory consumption unacceptable. To handle the problems, this paper develops two families of methods. The proposed methods are used to achieve target recognition by means of local descriptors. Our first solver refers to building multiple linear regression models, and addresses the problem by the theory of sparse representation. The second scheme rebuilds a new feature by the feature quantization skill, from which the inference can be drawn. Multiple comparative studies are pursued to verify the performance of detectors and descriptors popularly used. The source code was publicly released on https://ganggangdong.github.io/homepage/.

Dictionary Learning (DL) and Sparse Representation (SR) based Classifier have impacted greatly on the classification performance and has had good recognition rate on image data. In Video Semantic Analysis (VSA), the local structure of video data contains more vital discriminative information needed for classification. However, this has not been fully exploited by the current DL based approaches. Besides, similar coding findings are not being realized from video features with the same video category. Based on the issues stated afore, a novel learning algorithm, called Sparsity based Locality-Sensitive Discriminative Dictionary Learning(SLSDDL) for VSA is proposed in this paper. In the proposed algorithm, a discriminant loss function for the category based on sparse coding of the sparse coefficients is introduced into structure of Locality-Sensitive Dictionary Learning (LSDL) algorithm. Finally, the sparse coefficients for the testing video feature sample are solved by the optimized method of SLSDDL and the classification result for video semantic is obtained by minimizing the error between the original and reconstructed samples. The experiment results show that, the proposed SLSDDL significantly improves the performance of video semantic detection compared with the comparative state-of-the-art approaches. Moreover, the robustness to various diverse environments in video is also demonstrated, which proves the universality of the novel approach.

There has been considerable progress in implicit neural representation to upscale an image to any arbitrary resolution. However, existing methods are based on defining a function to predict the RGB value from just four specific loci. Relying on just four loci is insufficient as it leads to losing fine details from the neighboring region(s). We show that by taking into account the semi-local region leads to an improvement in performance. In this paper, we propose applying a new technique called Overlapping Windows on Semi-Local Region (OW-SLR) to an image to obtain any arbitrary resolution by taking the coordinates of the semi-local region around a point in the latent space. This extracted detail is used to predict the RGB value of a point. We illustrate the technique by applying the algorithm to the Optical Coherence Tomography-Angiography (OCT-A) images and show that it can upscale them to random resolution. This technique outperforms the existing state-of-the-art methods when applied to the OCT500 dataset. OW-SLR provides better results for classifying healthy and diseased retinal images such as diabetic retinopathy and normals from the given set of OCT-A images. The project page is available at https://rishavbb.github.io/ow-slr/index.html

In bioinformatics research, traditional machine learning methods have demonstrated efficacy in addressing Euclidean data. However, real-world data often encompasses non-Euclidean forms, such as graph data, which contain intricate structural patterns or high-order relationships that elude conventional machine-learning approaches. Representation learning seeks to derive valuable data representations from enhancing predictive or analytic tasks, capturing vital patterns and structures. This method has proven particularly beneficial in bioinformatics and biomedicine, as it effectively handles high-dimensional, sparse data, detects complex biological patterns, and optimizes predictive performance. In recent years, graph representation learning has become a popular research direction. It embeds graphs into a low-dimensional space while preserving the structural and attribute information of the graph, enabling better feature extraction for downstream tasks. This study extensively reviews representation learning advancements, particularly in the research of representation methods since the emergence of COVID-19. We begin with an analysis and classification of neural network-based language model representation learning techniques as well as graph representation learning methods. Subsequently, we explore their methodological innovations in the context of COVID-19, with a focus on the domains of drugs, public health, and healthcare. Furthermore, we discuss the challenges and opportunities associated with graph representation learning. This comprehensive review presents invaluable insights for researchers as it documents the development of COVID-19 and offers experiential lessons to preempt future infectious diseases. Moreover, this study guides future bioinformatics and biomedicine research methodologies.

We say that a system {zmF(z)}m=0∞ is a Beurling system if F is an outer function. Beurling’s approximation theorem asserts that if F is an outer function from H2(D) then the system {zmF(z)}m=0∞ is complete in the space H2(D). We prove that a Beurling system with F∈Hp(D),1≤p&lt;∞ is an M−bases in Hp(D) with an explicit dual system. Any function f∈Hp(D),1≤p&lt;∞ can be expanded as a series by the system {zmF(z)}m=0∞. For different methods of summation we characterize outer functions F for which the expansion converges to f. Related results for weighted Hardy spaces in the unit disc are studied. Particularly we prove Rosenblum’s hypothesis.

Medical records contain many terms which are difficult to process. Our aim in this study is to allow the visual exploration of the information in medical databases where the texts presents a large number of syntactic variations and abbreviations, through an interface which facilitates content identification, navigation and information retrieval. We propose the use of multi-term tag clouds as content representation tools and as assistants for the browsing and querying tasks. The tag cloud generation is achieved through a novelty mathematical method that allows related terms to remain grouped together within the tags To evaluate this proposal, we have used a database with 24,481 records. 23 expert users in the medical field were tasked to complete a survey to evaluate the generated tag clouds properties and we obtained a precision of 0.990, a recall of 0.870 and a F1score of 0.904 in the evaluation of the tag cloud as an information retrieval tool. The main contribution of this approach is that we automatically generate a visual interface over the text capable of capturing the semantics of the information and facilitating access to medical records.

Shells, probably like no other product of nature, have played an important role in the history of mankind. The pre-Hispanic civilizations of Ibero-America also used certain type of shells profusely in their religious ceremonies, in particular, in Ecuador there were two species of main importance, the Spondylus princeps and the Spondylus calcifer broadly employed to manufacture ornaments that possess a strong symbolic, religious and social meaning and that were almost exclusively used by ruling classes. Among these ornaments, the faces carved on the Spondylus shells are little known. In the present study, we chose a total of fifteen (15) pieces from the Pastor Restrepo Lince´s archaeomalacology collection to understand the possible uses of these objects, through the interpretation of the gestures represented on the faces, their dimensions, and their geographical distribution in pre-Hispanic Ecuador. To achieve the proposed objective, we approach the present investigation from the perspective of the formal analysis of concepts, which is a mathematical theory of representation of knowledge, finding that these faces carved in Spondylus, were used daily or in special ceremonial occasions and that its use was common in all the regional cultures of ancient Ecuador, from the oldest such as Valdivia, and for more than 2000 years, indicating a long tradition of the use of Spondylus as an object of great symbolic and economic value until the arrival of the Spanish

With the evolution of computing technology in many application like human robot interaction, human computer interaction and health-care system, 3D human body models and their dynamic motions has gained popularity. Human performance accompanies human body shapes and their relative motions. Research on human activity recognition is structured around how the complex movement of a human body is identified and analyzed. Vision based action recognition from video is such kind of tasks where actions are inferred by observing the complete set of action sequence performed by human. Many techniques have been revised over the recent decades in order to develop a robust as well as effective framework for action recognition. In this survey, we summarize recent advances in human action recognition, namely the machine learning approach, deep learning approach and evaluation of these approaches.

The electrocardiogram (ECG) was the first biomedical signal where digital signal processing techniques were extensively applied. By its own nature, the ECG is typically a sparse signal, composed of regular activations (the QRS complexes and other waveforms, like the P and T waves) and periods of inactivity (corresponding to isoelectric intervals, like the PQ or ST segments), plus noise and interferences. In this work, we describe an efficient method to construct an overcomplete and multi-scale dictionary for sparse ECG representation using waveforms recorded from real-world patients. Unlike most existing methods (which require multiple alternative iterations of the dictionary learning and sparse representation stages), the proposed approach learns the dictionary first, and then applies an efficient sparse inference algorithm to model the signal using the learnt dictionary. As a result, our method is much more efficient from a computational point of view than other existing methods, thus becoming amenable to deal with long recordings from multiple patients. Regarding the dictionary construction, we locate first all the QRS complexes in the training database, then we compute a single average waveform per patient, and finally we select the most representative waveforms (using a correlation-based approach) as the basic atoms that will be resampled to construct the multi-scale dictionary. Simulations on real-world records from Physionet's PTB database show the good performance of the proposed approach.

This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.

In the paper, by virtue of a Lévy–Khintchine representation and an alternative integral representation for the weighted geometric mean, the authors establish a Lévy–Khintchine representation and an alternative integral representation for the Toader–Qi mean. Moreover, the authors also collect an probabilistic interpretation and applications in engineering of the Toader–Qi mean.

Self-supervised learning is a method that learns general representation from unlabeled data. Masked image modeling (MIM), one of the generative self-supervised learning methods, has drawn attention showing state-of-the-art performance on various downstream tasks, though showing poor linear separability resulting from the token-level approach. In this paper, we propose a contrastive learning-based multi-view masked autoencoder for MIM, exploiting an image-level approach by learning common features from two different augmented views. We strengthen MIM by learning long-range global patterns from contrastive loss. Our framework adopts simple encoder-decoder architecture, learning rich and general representation by following a simple process: 1) two different views are generated from an input image with random masking and by contrastive loss, we can learn semantic distance of the representations generated by an encoder. By applying a high mask ratio, 80%, it works as strong augmentation and alleviates the representation collapse problem. 2) With reconstruction loss, decoder learns to reconstruct an original image from the masked image. We assess our framework by several experiments on benchmark datasets of image classification, object detection, and semantic segmentation. We achieve 84.3% fine-tuning accuracy on ImageNet-1K classification and 76.7% in linear probing, exceeding previous studies and show promising results on other downstream tasks. Experimental results demonstrate that our work can learn rich and general image representation by applying contrastive loss to masked image modeling.

In recent years, there has been a growing interest in remote sensing image-text cross-modal retrieval due to the rapid development of space information technology and the significant increase in remote sensing image data volume. One approach that has shown promising results in cross-modal retrieval of natural images is the multimodal fusion encoding method. However, remote sensing images have unique characteristics that make the retrieval task challenging. Firstly, the semantic features of remote sensing images are fine-grained, meaning they can be divided into multiple basic units of semantic expression. Additionally, these images exhibit variations in resolution, color, and perspective. Different combinations of basic units of semantic expression can generate diverse text descriptions. These characteristics pose considerable challenges for cross-modal retrieval. To address these challenges, this paper proposes a multi-task guided fusion encoder (MTGFE) based on the multimodal fusion encoding method. The model incorporates three tasks: image-text matching (ITM), masked language modeling (MLM), and the newly introduced multi-view joint representations contrast (MVJRC) task. By jointly training the model with these tasks, we aim to enhance its capability to capture fine-grained correlations between remote sensing images and texts. Specifically, the MVJRC task is designed to improve the model’s consistency in feature expression and fine-grained correlation, particularly for remote sensing images with significant differences in resolution, color, and angle. Furthermore, to address the computational complexity associated with large-scale fusion models and improve retrieval efficiency, this paper proposes a retrieval filtering method. This method achieves higher retrieval efficiency while minimizing accuracy loss. Extensive experiments were conducted on four public datasets to evaluate the proposed method, and the results validate its effectiveness. Overall, this study focuses on remote sensing image-text cross-modal retrieval and introduces the MTGFE model, which combines multimodal fusion encoding with multiple tasks to enhance the model’s ability to capture fine-grained correlations. Additionally, a retrieval filtering method is proposed to improve retrieval efficiency. Experimental results demonstrate the effectiveness of the proposed method.

Multimodal medical image fusion is a fundamental but challenging problem in the fields of brain science research and brain disease diagnosis, and it is challenging for sparse representation (SR)-based fusion to characterize activity level with single measurement and no loss of effective information. In this paper, the Kronecker-criterion-based SR framework is applied for medical image fusion with a patch-based activity level integrating salient features of multiple domains. Inspired by the formation process of vision system, the spatial saliency is characterized by textural contrast (TC), which is composed of luminance and orientation contrasts to promote more highlighted texture information to participate in the fusion process. As substitution of the conventional l1-norm-based sparse saliency, a metric of sum of sparse salient features (SSSF) is used for promoting more significant coefficients to participate in the composition of activity level measure. The designed activity level measure is verified to be more conducive to maintain the integrity and sharpness of detailed information. Various experiments on multiple groups of clinical medical images verify the effectiveness of the proposed fusion method on both visual quality and objective assessment. Furthermore, the research work of this paper is helpful for further detection and segmentation of medical images.

Drug repositioning (also called drug repurposing) is a strategy for identifying new therapeutic targets for existing drugs. This approach is of great importance in pharmacology as it is a faster and cheaper way to develop new medical treatments. In this paper, we present, to our knowledge, the first application of multiplex-heterogeneous network embedding to drug repositioning. Network embedding learns the vector representations of nodes, opening the whole machine learning toolbox for a wide variety of applications including link prediction, node labelling or clustering. So far, the application of network embedding for drug repositioning focused on heterogeneous networks. Our approach for drug repositioning is based on multiplex-heterogeneous network embedding. Such method allows the richness and complexity of multiplex and heterogeneous networks to be projected in the same vector space. In other words, multiplex-heterogeneous networks aggregate different multi-omics data in the same network representation. We validate the approach on a task of link prediction and on a case study for SARS-CoV2 drug repositioning. Experimental results show that our approach is highly robust and effective for finding new drug-target associations.

Only by understanding the ability to take third-person perspective can we begin to elucidate the neural processes responsible for one’s inimitable conscious experience. The current study examined differences in hemispheric laterality during a first-person perspective (1PP) and third-person perspective (3PP) taking task, when using Transcranial Magnetic Stimulation (TMS). Participants were asked to take either the 1PP or 3PP when identifying the number of spheres in a virtual scene. During this task, single-pulse TMS was delivered to the motor cortex of both the left and right hemispheres of 10 healthy volunteers. Measures of TMS-induced motor-evoked potentials (MEPs) of the contralateral abductor pollicis brevis (APB) were employed as an indicator of lateralized cortical activation. The data suggest that the right hemisphere is more important in discriminating between 1PP and 3PP. These data add a novel method for determining perspective taking and add to the literature supporting the role of the right hemisphere in meta representation.

The paper describes an algorithm for semantic representation of behavioral contexts relative to a dichotomic decision alternative. The contexts are represented as quantum qubit states in two-dimensional Hilbert space visualized as points on the Bloch sphere. The azimuthal coordinate of this sphere functions as a one-dimensional semantic space in which the contexts are accommodated according to their subjective relevance to the considered uncertainty. The contexts are processed in triples defined by knowledge of a subject about a binary situational factor. The obtained triads of context representations function as stable cognitive structure at the same time allowing a subject to model probabilistically-variative behavior. The developed algorithm illustrates an approach for quantitative subjectively-semantic modeling of behavior based on conceptual and mathematical apparatus of quantum theory.

A precise understanding of the genes and associated genomes of SARS-CoV2 is important for various reasons such as discovering origin of the virus and virulence and so on. A thorough descriptive understanding of the SARS-CoV2 genomes and other coronavirus of the beta-coronavirus genus is primarily important. In this article, a set of ten genomes of four CoVs and their associated genes are considered for this present study. A spatial representations of nucleotide bases including purine-pyrimidine representations of the different genes of the corresponding genomes are quantified using Hurst exponent, Shannon entropy and density estimation of different nucleotides including GC content, in order to draw a comparison and contrast among the ten genomes of different types of CoVs which include MERS, SARS-CoV, HKU1 (Human Coronavirus) and associated their genes.

When phenomena in quantum mechanics are interpreted from the perspective of bio-psychology, wave function collapse from several to a single eigenstate must be plausibly explained. Quantum mechanics requires a context, yet the context of an observer is rarely considered. On the other hand, in bio-psychology, the observer context is examined to explain superposition and collapse by different mental functions used in everyday life. Three mental functions are described, one of which is responsible for observation, and the others for conservation and treatment of information in mental representation. Whereas observation produces information with certainty, the subsequent processes result in uncertain potentiality. In order to encompass uncertainty, multiple possibilities are simultaneously considered in mental superposition, one of which should represent the unknown future outcome. During observation, all suggested potentialities necessarily collapse to one real outcome. The collapse of superposition does not occur in observable physical reality, but in its mental representation. Some physical principles—such as superposition, infinity and nothingness before the Big Bang—are pure phenomena of mental representation, which will always remain unverifiable by observation. This argument proves that mental representation brought about by the observer context participates in the production of mental models for the best approximation of physical reality.

The purpose of this paper is to build a new bridge between category theory and a generalized probability theory known as noncommutative probability or quantum probability, which was originated as a mathematical framework for quantum theory, in terms of states as linear functional defined on category algebras. We clarify that category algebras can be considered as generalized matrix algebras and that the notions of state on category as linear functional defined on category algebra turns out to be a conceptual generalization of probability measures on sets as discrete categories. Moreover, by establishing a generalization of famous GNS (Gelfand-Naimark-Segal) construction, we obtain a representation of category algebras of †-categories on certain generalized Hilbert spaces which we call semi-Hilbert modules over rigs.

Designing motion representations for the problem of 3D human action recognition from skeleton sequences is an important yet challenging task. An effective representation should be robust to noise, invariant to viewpoint changes and result in a good performance with low-computational demand. Two main challenges in this task include how to efficiently represent spatio-temporal patterns of skeletal movements and how to learn their discriminative features for classification task. This paper presents a novel skeleton-based representation and a deep learning framework for 3D action recognition using RGB-D sensors. We propose to build an action map called SPMF (Skeleton Posture-Motion Feature), which is a compact image representation built from skeleton poses and their motions. An Adaptive Histogram Equalization (AHE) algorithm is then applied on the SPMF to enhance their local patterns and form an enhanced action map, namely Enhanced-SPMF. For learning and classification tasks, we exploit Deep Convolutional Neural Networks based on the DenseNet architecture to learn directly an end-to-end mapping between input skeleton sequences and their action labels via the Enhanced-SPMFs. The proposed method is evaluated on four challenging benchmark datasets, including both individual actions, interactions, multiview and large-scale datasets. The experimental results demonstrate that the proposed method outperforms previous state-of-the-art approaches on all benchmark tasks, whilst requiring low computational time for training and inference.

Containing hundreds of spectral bands (features), hyperspectral images (HSIs) have high ability in discrimination of land cover classes. Traditional HSIs data processing methods consider the same importance for all bands in the original feature space (OFS), while different spectral bands play different roles in identification of samples of different classes. In order to explore the relative importance of each feature, we learn a weighting matrix and obtain the relative weighted feature space (RWFS) as an enriched feature space for HSIs data analysis in this paper. To overcome the difficulty of limited labeled samples which is common case in HSIs data analysis, we extend our method to semisupervised framework. To transfer available knowledge to unlabeled samples, we employ graph based clustering where low rank representation (LRR) is used to define the similarity function for graph. After construction the RWFS, any arbitrary dimension reduction method and classification algorithm can be employed in RWFS. The experimental results on two well-known HSIs data set show that some dimension reduction algorithms have better performance in the new weighted feature space.

In the paper, the author presents explicit and unified expressions for a sequence of improper integrals in terms of the beta functions and the Wallis ratios. Hereafter, the author derives integral representations for the Catalan numbers originating from combinatorics.

This work considers the task of representation learning on the attributed relational graph (ARG). Both the nodes and edges in an ARG are associated with attributes/features allowing ARGs to encode rich structural information widely observed in real applications. Existing graph neural networks offer limited ability to capture complex interactions within local structural contexts, which hinders them from taking advantage of the expression power of ARGs. We propose Motif Convolution Module (MCM), a new motif-based graph representation learning technique to better utilize local structural information. The ability to handle continuous edge and node features is one of MCM’s advantages over existing motif-based models. MCM builds a motif vocabulary in an unsupervised way and deploys a novel motif convolution operation to extract the local structural context of individual nodes, which is then used to learn higher-level node representations via multilayer perceptron and/or message passing in graph neural networks. When compared with other graph learning approaches to classifying synthetic graphs, our approach is substantially better in capturing structural context. We also demonstrate the performance and explainability advantages of our approach by applying it to several molecular benchmarks.

Incorporating source-side linguistic knowledge into the neural machine translation (NMT) model has recently achieved impressive performance on machine translation tasks. One popular method is to generalize the word embedding layer of the encoder to encode each word and its linguistic features. The other method is to change the architecture of the encoder to encode syntactic information. However, the former cannot explicitly balance the contribution from the word and its linguistic features. The latter cannot flexibly utilize various types of linguistic information. Focusing on the above issues, this paper proposes a novel NMT approach that models the words in parallel to the linguistic knowledge by using two separate encoders. Compared with the single encoder based NMT model, the proposed approach additionally employs the knowledge-based encoder to specially encode linguistic features. Moreover, it shares parameters across encoders to enhance the model representation ability of the source-side language. Extensive experiments show that the approach achieves significant improvements of up to 2.4 and 1.1 BLEU points on Turkish→English and English→Turkish machine translation tasks, respectively, which indicates that it is capable of better utilizing the external linguistic knowledge and effective improving the machine translation quality.

We show that, as in the case of the principle of minimum action in classical and quantum mechanics, there exists an even more general principle in the very fundamental structure of quantum space-time: This is the principle of minimal group that allows to consistently and simultaneously obtain a natural description of the spacetime dynamics and the physical states admissible in it. The theoretical construction is based on the physical states that are average values of the generators of the Metaplectic group Mp(n) , the double covering of SL(2C) in a vector representation, with respect to the coherent states carrying the spin weight. Our main results here are: (i) There exists a connection between the dynamics given by the Metaplectic group symmetry generators and the physical states (mappings of the generators through bilinear combinations of the basic states). (ii) The ground states are coherent states of the Perelomov-Klauder type defined by the action of the Metaplectic group which divide the Hilbert space into even and odd states mutually orthogonal. They carry a spin weight 1/4 and 3/4 respectively from which, two other basic states can be formed. (iii) The physical states, mapped bilinearly with the basic 1/4 and 3/4 spin weight states, plus their symmetric and antisymmetric combinations, have spin contents s = 0, 1/2, 1, 3/2 and 2. (iv) The generators realized with the bosonic variables of the harmonic oscillator introduce a natural supersymmetry and a superspace whose line element is the geometrical Lagrangian of our model. (v) From the line element as operator level, a coherent physical state of spin 2 can be obtained and naturally related to the metric tensor. (vi) The metric tensor is naturally discretized by taking the discrete series given by the basic states (coherent states) in the n number representation, reaching the classical (continuous) space-time for n going to infinity. (vii) There emerges a relation between the eigenvalue of our coherent state metric solution and the black hole area (entropy) as A_{bh}/4 l_{p}^{2} = I alpha I relating the phase space of the metric found g_{ab} and the black hole area A_{bh} through the Planck length l_{p}^{2} and the eigenvalue I alpha I of the coherent states. As a consequence of the lowest level of the quantum discrete space-time spectrum, eg the ground state associated to n = 0 and its characteristic length, there exists a minimum entropy related to the black hole history.

Accurate climate data at fine spatial resolution are essential for scientific research and the development and planning of crucial social systems, such as energy and agriculture. Among them, sea surface temperature plays a critical role as the associated El Niño-Southern Oscillation (ENSO) is considered a significant signal of global interannual climate system. In this paper, we propose an implicit neural representation-based interpolation method with temporal information (T_INRI) to reconstruct climate data of high spatial resolution, with sea surface temperature as the research object. Traditional deep learning models for generating high-resolution climate data are only applicable to fixed resolution enhancement scales. In contrast, the proposed T_INRI method is not limited to the enhancement scale provided during the training process and its results indicate that it can enhance low-resolution input by arbitrary scale. Additionally, we discuss the impact of temporal information on the generation of high-resolution climate data, specifically, which month the low-resolution sea surface temperature data is from. Our experimental results indicate that T_INRI is advantageous over traditional interpolation methods under different enhancement scales, and the temporal information can improve T_INRI performance for a different calendar month. We also examined the potential capability of T_INRI in recovering missing grid value. These results demonstrate that the proposed T_INRI is a promising method for generating high-resolution climate data and has significant implications for climate research and related applications.

The term Concept has been a prominent part of investigations in psychology and neurobiology where, mostly, it is mathematically or theoretically represented. The Concepts are also studied computationally through their symbolic, distributed and hybrid representations. The majority of these approaches focused on addressing concrete concepts notion, but the view of the abstract concept is rarely explored. Moreover, most computational approaches have a predefined structure or configurations. The proposed method, Regulated Activation Network (RAN), has an evolving topology and learns representations of Abstract Concepts by exploiting the geometrical view of Concepts, without supervision. In the article, the IRIS data was used to demonstrate: the RAN's modeling; flexibility in concept identifier choice; and deep hierarchy generation. Data from IoT's Human Activity Recognition problem is used to show automatic identification of alike classes as abstract concepts. The evaluation of RAN with 8 UCI benchmarks and the comparisons with 5 Machine Learning models establishes the RANs credibility as a classifier. The classification operation also proved the RAN's hypothesis of abstract concept representation. The experiments demonstrate the RANs ability to simulate psychological processes (like concept creation and learning) and carry out effective classification irrespective of training data size.

The relationship between Climate Change and Water is an obvious and key issue within the Sustainable Development Goals. This study aims to investigate the social representation created around this relationship in three different territorial contexts in order to evaluate the influence of the territory on the perception of the risk of Climate Change and its relationship with water. By means of a questionnaire completed by 1709 university students, the climatic literacy of the individual was evaluated in order to relate it to other dimensions on the relationship between Climate Change and Water (information, training previous on climate change and pro-environmental attitudes) in their different dimensions in three different territorial contexts. The results show that the socio-cultural context influences the social representation of Climate Change, but not from the climatological condition, so that it is reasonable to think that the social representation of this relationship is favoured by a common culture around this relationship.

Recently we started the development of Holographic Dendrogramic Theory (DH-theory). It is based on the novel mathematical representation of the relational event universe (in the spirit of (Smolin, Barbour, Rovelli). Elementary events are represented by branches of dendrograms, finite trees, which are generated from data with clustering algorithms. In this note we study the dynamics of the event-universe generated by the appearance of a new event. Generally, each new event can generate the complete reconstruction of the whole dendrogramic universe. However, we found (via numerical simulation) unexpected stability of this universe. Its events are coupled via the hierarchic relational structure which is relatively stable with respect even random generation of new events. We also observe the regularity patterns in location of new events on dendrograms. In the curse of evolution, the dendrogram’s complexity increases and determine the arrow of time the event universe. We use the complexity measure from particle shape dynamics which was shown to be increase in both direction away from a Janus point and thus determine the arrow of time in symmetrical manner away from a Janus point. The particle shape dynamics theory is a relational theory with close ideological resemblance to DH-theory as both relays on Mach’s principle and Leibniz’s relationalism and his principles. By using the complexity measure on dendrograms and its p-adic string representation, we demonstrate the emergence of time arrow from the p-adic zero-dimensional field, where space and time are absent.

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence A287326 in OEIS. The main property of A287326 that it returns a perfect cube n as sum of n-th row terms over k; 0 ≤ k ≤ n−1 or 1 ≤ k ≤ n, by means of its symmetry. In this paper we have derived a similar triangles in order to receive powers m = 5; 7 as row items sum and generalized obtained results in order to receive every odd-powered monomial n^2m+1; m ≥ 0 as sum of row terms of corresponding triangle. In other words, in this manuscript are found and discussed the polynomials D_m(n,k) and U_m(n,k), such that, when being summed up over k in some range with respect to m and n returns the monomial n^2m+1.

An explanation of the origin of dark matter is suggested in this work. The argument is based on symmetry considerations about the concept of mass. In the Wigner's view, the rest mass and the spin of a free elementary particle in flat space-time are the two invariants that characterize the associated unitary irreducible representation of the Poincar\'e group. The Poincar\'e group has two and only two deformations with maximal symmetry. They describe respectively the de Sitter (dS) and Anti de Sitter (AdS) kinematic symmetries. Analogously to their shared flat space-time limit, two invariants, spin and energy scale for de Sitter and rest energy for Anti de Sitter, characterize the unitary irreducible representation associated with dS and AdS elementary systems. While the dS energy scale is a simple deformation of the Poincaré rest energy and so has a purely mass nature, AdS rest energy is the sum of a purely mass component and a kind of zero-point energy derived from the curvature. An analysis based on recent estimates on the chemical freeze-out temperature marking in Early Universe the phase transition quark-gluon plasma epoch to the hadron epoch supports the guess that dark matter energy might originate from an effective AdS curvature energy.

In this paper we provide some bounds for the error in approximating the Riemann-Stieltjes integral $\int_{a}^{b}f (t) du (t)$ by the generalized trapezoidal rule \begin{equation*} \left[ u\left( b\right) -u\left( x\right) \right] f\left( b\right) +\left[ u\left( x\right) -u\left( a\right) \right] f\left( a\right) \end{equation*} under various assumptions for the integrand $f$ and the integrator $u$ for which the above integral exists. Applications for continuous functions of selfadjoint operators and unitary operators in Hilbert spaces are provided as well.

For evaluating probabilities of arbitrary random events with respect to a given multivariate probability distribution, specific techniques are of great interest. An important two-dimensional high risk limit law is the Gauss-exponential distribution whose probabilities can be dealt with based upon the Gauss-Laplace law. The latter will be considered here as an element of the newly introduced family of (p,q)-spherical distributions. Based upon a suitably defined non-Euclidean arc-length measure on (p,q)-circles we prove geometric and stochastic representations of these distributions and correspondingly distributed random vectors, respectively. These representations allow dealing with the new probability measures similarly like with elliptically contoured distributions and more general homogeneous star-shaped ones. This is demonstrated at hand of a generalization of the Box-Muller simulation method. En passant, we prove an extension of the sector and circle number functions.

Despite the importance of few-shot learning, the lack of labeled training data in the real world, makes it extremely challenging for existing machine learning methods as this limited data set does not represent the data variance well. In this research, we suggest employing a generative approach using variational autoencoders (VAEs), which can be used specifically to optimize few-shot learning tasks by generating new samples with more intra-class variations. The purpose of our research is to increase the size of the training data set using various methods to improve the accuracy and robustness of the few-shot face recognition. Specifically, we employ the VAE generator to increase the size of the training data set, including the basic and the novel sets while utilizing transfer learning as the backend. Based on extensive experimental research, we analyze various data augmentation methods to observe how each method affects the accuracy of face recognition. We conclude that the face generation method we proposed can effectively improve the recognition accuracy rate to 96.47% using both the base and the novel sets.

A relationship between the functional Schr\"odinger representation and the precanonical quantization of a nonlinear scalar field theory is extended to arbitrary curved space-times. The canonical functional derivative Schr\"odinger equation is derived from the manifestly covariant precanonical Schr\"odinger equation in a singular limiting case when the ultraviolet parameter $\varkappa$ introduced by precanonical quantization is identified with the invariant delta-function at equal spatial points. In the same limiting case, the Schr\"odinger wave functional is expressed as the trace of the multidimensional product integral of Clifford-algebra-valued precanonical wave functions restricted to a certain field configuration. Thus the standard QFT in curved space-time in functional Schr\"odinger representation emerges from the precanonical formulation of quantum fields as a singular limiting case.

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

Machine learning (ML) has found increasing use in research on energy conversion and storage technologies, in particular, so-called sustainable technologies. While often ML is used to directly optimize the parameters or phenomena of interest in the space of features, in this perspective, we focus on using ML to construct objects and methods that help in or enable the modeling of the underlying phenomena. We highlight the need for machine learning from very sparse and unevenly distributed numeric data in multidimensional spaces in these applications. After a brief introduction of some common regression-type machine learning techniques, we will focus on more advanced ML techniques which use these known methods as building blocks of more complex schemes and thereby allow working with extremely sparse data and also allow generating insight. Specifically, we will highlight the utility of using representations with sub-dimensional functions by combining the high-dimensional model representation ansatz with machine learning methods like neural networks or Gaussian process regressions in applications ranging from heterogeneous catalysis to nuclear energy.

What is the function of cognition? On one influential account, cognition evolved to co-ordinate behaviour with environmental change or complexity (Godfrey-Smith 1996). Liberal interpretations of this view ascribe cognition to an extraordinarily broad set of biological systems – even bacteria, which modulate their activity in response to salient external cues, would seem to qualify as cognitive agents. However, equating cognition with adaptive flexibility per se glosses over important distinctions in the way biological organisms deal with environmental complexity. Drawing on contemporary advances in theoretical biology and computational neuroscience, we cash these distinctions out in terms of different kinds of generative models, and the representational and uncertainty-resolving capacities they afford. This analysis leads us to propose a formal criterion for delineating cognition from other, more pervasive forms of adaptive plasticity. On this view, biological cognition is rooted in a particular kind of functional organisation; namely, that which enables the agent to detach from the present and engage in counterfactual (active) inference.

One of creators of quantum mechanics P. Jordan in his work on quantum biology claimed that life's missing laws were the rules of chance and probability of the quantum world. The article presents author’s results of studying frequencies (or probabilities) of nucleotides on so-called epi-chains of long DNA sequences of various eukaryotic and prokaryotic genomes. DNA epi-chains are algorithmically constructed subsequencies of DNA nucleotide sequences. According to the algorithm of construction of any epi-chain of the order n, the epi-chain is such nucleotide subsequence, in which the numerations of adjacent nucleotides differ by natural number n (n = 1, 2, 3, 4,…). Correspondingly each epi-chain of order n ≥ 2 contains n times less nucleotides than the original DNA sequence. The presented results unexpectedly discover that in long single-stranded and double-stranded DNA of any tested genome its DNA epi-chains of different orders n (values n are not too large) have practically identical frequencies (or probabilities) of each kind of nucleotides. These data allow considering DNA as a regular rich set of epi-chains, which can play a certain role in genetic and epigenetic phenomena as the author belives. Appropriate rules of nucleotide frequencies on epi-chains of long DNA sequences are formulated for further their tests on a wider set of genomes. These results testify on existence of long-range coherence in long DNA and remind the Fröhlich's theory of long-range coherence in biological systems. The phenomenological data are discussed from different standpoints: the DNA double helices and helical antennas with circular polarizations of electromagnetic waves; relations with the Fröhlich's theory; numerical analysis of DNA epi-chains under binary representations of nucleotides. Results are useful for developing quantum and algebraic biology.

We propose a non-invasive approach to control the quality of spheroids and their fusion into a complex bioconstruct. The proposed method is based on the union of the nutrient concentration change calculated using Fick's law and the "reaction-diffusion" equations, taking into account absorption coefficient with specifying the exact fusion geometry using implicit Function Repre-sentation (FRep) functions. The proposed approach allows us to analyze the viability of cells within the spheroid, predict the fusion of spheroids, and accurately model complex heteroge-neous biostructures as a future task for our research. These results will significantly accelerate the development of such a promising field of additive biotechnologies as 3D bioprinting.

In this perspective article, we ponder topographical enhancements of artificial neural networks. In our recent paper in JMLR, we proved a quasi-equivalence between the network width and depth and also discussed the power of intra-links, which can be viewed as network height. In 1982, Hopfield published a network to model human associative memory, which contains many loops for dynamic evolution toward fixed points. Based on noising-denoising loops, diffusion models are recently developed to enable Bayesian modeling and inference with big data. Furthermore, we envision development of multi-AI-agent systems through “netware” engineering as a quantum leap of software engineering for emergent behaviors and autonomous AI at individual and population levels. We believe that the novel use of links and loops in space and time via multi-scale coupling would catalyze the next-generation neural networks.

Examining the similarity of event environments or surroundings, more precisely settings, provides additional insight in analyzing event sequences as it provides information about the context and potential common factors that may have influenced them. This article proposes a new similarity measure for event setting sequences, which involve the space and time in which events occur. While similarity measures for spatiotemporal event sequences have been studied, the settings and setting sequences have not yet been studied. While modeling event setting sequences we consider spatial and temporal scales to define the bounds of the setting and incorporates dynamic variables alongside static variables. Using a matrix-based representation and an extended Jaccard index we developed new similarity measures that allow for the use of all variable data types. We successfully used these similarity measures coupled with other multivariate statistical analysis approaches in a case study involving setting sequences and pollution event sequences associated with the same monitoring stations, which validate the hypothesis that more similar spatial-temporal settings or setting sequences may generate more similar events or event sequences. In conclusion, these similarity measures have many potential real-world applications, and offer researchers a powerful tool for understanding different factors and their dynamics corresponding to occurrences of spatiotemporal event sequences.

In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to get two new representations of the fundamental solution in form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed form formulas for particular cases of the fundamental solution are derived. In particular, we solve an open problem of representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

In the paper, the authors establish two identities to express the generating function of the Chebyshev polynomials of the second kind and its higher order derivatives in terms of the generating function and its derivatives each other, deduce an explicit formula and an identities for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials, the central Delannoy numbers, and the Fibonacci polynomials.

Motivated by a common Mathematical Finance topic, this paper surveys several results concerning windings of 2-dimensional processes, including planar Brownian motion, complex-valued Ornstein-Uhlenbeck processes and planar stable processes. In particular, we present Spitzer's asymptotic Theorem for each case. We also relate this study to the pricing of Asian options.

Variational Auto-Encoders (VAEs) are deep generative models used for unsupervised learning, however their standard version is not topology-aware in practice since the data topology may not be taken into consideration. In this paper, we propose two different approaches with the aim to preserve the topological structure between the input space and the latent representation of a VAE. Firstly, we introduce InvMap-VAE as a way to turn any dimensionality reduction technique, given an embedding it produces, into a generative model within a VAE framework providing an inverse mapping into original space. Secondly, we propose the Witness Simplicial VAE as an extension of the Simplicial Auto-Encoder to the variational setup using a witness complex for computing the simplicial regularization, and we motivate this method theoretically using tools from algebraic topology. The Witness Simplicial VAE is independent of any dimensionality reduction technique and together with its extension, Isolandmarks Witness Simplicial VAE, preserves the persistent Betti numbers of a data set better than a standard VAE.

In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their "space of evolution" associated to a homogeneous symplectic manifold by a Lagrange 2-form, and defines in case of non null cohomology (non equivariance of the coadjoint action on the moment map with appearance of an additional cocyle) a Gibbs density (of maximum entropy) that is covariant under the action of dynamic groups of physics (eg, Galileo's group in classical physics). Souriau Lie Group Thermodynamics was also addressed 30 years after Souriau by R. F. Streater in the framework of Quantum Physics by Information Geometry for some Lie algebras, but only in the case of null cohomology. Souriau method could then be applied on Lie Groups to define a covariant maximum entropy density by Kirillov representation theory. We will illustrate this method for homogeneous Siegel domains and more especially for Poincaré unit disk by considering SU(1,1) group coadjoint orbit and by using its Souriau’s moment map. For this case, the coadjoint action on moment map is equivariant. For non-null cohomology, we give the case of Lie group SE(2). Finally, we will propose a new geometric definition of Entropy that could be built as a generalized Casimir invariant function in coadjoint representation, and Massieu characteristic function, dual of Entropy by Legendre transform, as a generalized Casimir invariant function in adjoint representation, where Souriau cocycle is a measure of the lack of equivariance of the moment mapping.

Perhaps the greatest challenge in the graft copolymerization of acrylic acid onto starch initiated by Fenton’s is the selectivity of the grafting reaction. Low selectivity means that too much of unwanted homopolymer polyacrylic acid is produced. In this paper, it has been analyzed why with this reaction system, involving a water soluble monomer and indirect initiation, the graft selectivity is such a challenge. Several other grafting reactions, especially with monomers of low water solubility or when direct initiation is applied, show a better grafting performance. A scheme is presented based on reaction engineering principles, that supports an explanation of the observed differences. A more selective activation of starch is a factor, but perhaps even more important is a low monomer to starch ratio at the starting sites of graft reactions. Based on these insights, several methods to improve the graft selectivity are evaluated, with the help of literature data but mostly by experimental explorations in our laboratory. Most promising appears to be a dedicated dosage method, to add monomer in portions over time, tested in a batch reactor with gelatinized cassava starch. This way, both grafting percentage and graft selectivity could be improved. Such could not be realized with the more conventional dosage, which is to add all monomer before the start of the reaction. This can be considered a principal breaktrough. Still, more research and development would be needed to refine the method and to implement the idea also in a continuous reactor at larger scale.

Let $f\left(1\right)=1$ , and let $f(n+1)=2^{2^{f\left(n\right)}}$ for every positive integer n. We consider the following hypothesis: if a system S ⊆ {x_i · x_j = x_k : i, j, k ∈ {1, . . . , n}} ∪ {x_i + 1 = x_k : i, k ∈{1, . . . , n}} has only finitely many solutions in non-negative integers x₁, . . . , x_n, then each such solution (x₁, . . . , x_n) satisfies x₁, . . . , x_n ≤ f (2n). We prove: (1) the hypothesisimplies that there exists an algorithm which takes as input a Diophantine equation, returns an integer, and this integer is greater than the heights of integer (non-negative integer, positive integer, rational) solutions, if the solution set is finite; (2) the hypothesis implies that there exists an algorithm for listing the Diophantine equations with infinitely many solutions in non-negative integers; (3) the hypothesis implies that the question whether or not a given Diophantine equation has only finitely many rational solutions is decidable by a single query to an oracle that decides whether or not a given Diophantine equation has a rational solution; (4) the hypothesis implies that the question whether or not a given Diophantine equation has only finitely many integer solutions is decidable by a single query to an oracle that decides whether or not a given Diophantine equation has an integer solution; (5) the hypothesis implies that if a set $\mathfrak{M}$ ⊆ has a finite-fold Diophantine representation, then $\mathfrak{M}$ is computable.