The article obtains large deviation asymptotic for sub-critical communication networks modelled as signal-interference-noise-ratio(SINR) random networks. To achieve this, we define the empirical power measure and the empirical connectivity measure, as well as prove joint large deviation principles(LDPs) for the two empirical measures on two different scales. Using the joint LDPs, we prove an Asymptotic equipartition property(AEP) for wireless telecommunication Networks modelled as the subcritical SINR random networks. Further, we prove a Local Large deviation principle(LLDP) for the sub-critical SINR random network. From the LLDPs, we prove the large deviation principle, and a classical McMillan Theorem for the stochastic SINR model processes. Note that, the LDPs for the empirical measures of this stochastic SINR random network model were derived on spaces of measures equipped with the $\tau-$ topology, and the LLDPs were deduced in the space of SINR model process without any topological limitations. We motivate the study by describing a possible anomaly detection test for SINR random networks.

Gauss quadrature integral approximation is extended to include integrals with a measure consisting of a continuous as well as a discrete component. That is, we give an approximation for the integral of a function plus its sum over a discrete weighted set.

The notion of the informational measure of symmetry is introduced according to: HsymG=-i=1kPGilnPGi, where PGi is the probability of appearance of the symmetry operation Gi within the given 2D pattern. HsymG is interpreted as an averaged uncertainty in the presence of symmetry elements from the group G in the given pattern. The informational measure of symmetry of the “ideal” pattern built of identical equilateral triangles is established as HsymD3=1.792. The informational measure of symmetry of the random, completely disordered pattern is zero, Hsym=0. Informational measure of symmetry is calculated for the patterns generated by the P3 Penrose tessellation. Informational measure of symmetry does not correlate neither with the Voronoi entropy of the studied patterns nor with the continuous measure of symmetry of the patterns.

In this paper we use Toeplitz quantization to extend in a very natural way Kostant's theorem for the group $SU(m)$ to the group of symplectomorphisms of the unit sphere and we also give another proof of the infinite dimensional version of Schur and Horn theorem for the sphere based on Schur and Horn theorem for Hermitian matrices.

Animal-based measures are the measure of choice in animal welfare assessment protocols as they can often be applied completely independently to the housing or production system employed. Although there has been a small body of work on potential animal-based measures for farmed crocodilians [1-3], they have not been studied in the context of an animal welfare assessment protocol. Potential animal-based measures, that could be used to reflect the welfare state of farmed crocodilians, were identified and aligned with the Welfare Quality® principles of good housing, good health, good feeding and appropriate behaviour. A consultation process with a panel of experts was used to evaluate and score the potential measures in terms of validity and feasibility. This resulted in a toolbox of measures being identified for further development and integration into animal welfare assessment on the farm. Animal-based measures related to ‘good feeding’ and ‘good health’ received the highest scores for validity and feasibility by the experts. There was less agreement on the animal-based measures that could be used to reflect ‘appropriate behaviour’. Where no animal-based measures were deemed to reliably reflect a welfare criterion nor be useful as a measure on the farm, additional measures of resources or management were suggested as alternatives. Future work in this area should focus on the reliability of the proposed measures and involve further evaluation of their validity and feasibility as they relate to different species of crocodilian and farming system.

In this work we present a new unsupervised and language-independent methodology to detect relations of textual generality, for this, we introduce a particular case of textual entailment (TE), namely Textual Entailment by Generality (TEG). TE aims to capture primary semantic inference needs across applications in Natural Language Processing (NLP). Since 2005, in the TE recognition (RTE) task, systems are asked to automatically judge whether the meaning of a portion of the text, the Text - T, entails the meaning of another text, the Hypothesis - H. Several novel approaches and improvements in TE technologies demonstrated in RTE Challenges are signalling of renewed interest towards a more in-depth and better understanding of the core phenomena involved in TE. In line with this direction, in this work, we focus on a particular case of entailment, entailment by generality, to detect relations of textual generality. In-text, there are different kinds of entailment, yielded from different types of implicative reasoning (lexical, syntactical, common sense based), but here we focus just on TEG, which can be defined as an entailment from a specific statement towards a relatively more general one. Therefore, we have T→GH whenever the premise T entails the hypothesis H, being it also more general than the premise. We propose an unsupervised and language-independent method to recognize TEGs, from a pair ⟨T,H⟩ having an entailment relation. To this end, we introduce an Informative Asymmetric Measure (IAM) called Simplified Asymmetric InfoSimba (AISs), which we combine with different Asymmetric Association Measures (AAM). In this work, we hypothesize the existence of a particular mode of TE, namely TEG. Thus, the main contribution of our study is to highlight the importance of this inference mechanism. Consequently, the new annotation data seems to be a valuable resource for the community.

We communicate the theoretical results in the study of utilizing the quantum phenomena in optical current for quantum computation in the context of high precision voltage measurements. These results can be used around computation by quantum sampling and quantum communication as the basis for further research and physical implementations. We propose a Main Optical Setup (MOS) for such computation which allows to make a superstructure to implement specific computations and algorithms. To create MOS we used the nonlinear units (e.g., beta- barium borate crystal), arranged in series, powered with pulsed laser pump, and ended with the beam splitter to generate the output state of a number of entangled photon pairs. The computation is made by propagation of entanglement with beam splitters applied crossword and adjustable phase shifters that are tools for parameter steering. We show how to implement the series of cosine-based components on the example of two-component case. The results opens a broad area for future research in the area of building quantum optimizer using the quantum sampling methods and in the area of high precision temporal measurement of voltage, which is the important process for building high-fidelity devices.

Studies have shown the unconditional danger of biological attacks on underground hydroelectric pumped-storage power stations. A hypothetical list of biological damage to water conduits and dams is determined. Relevant predictions are given, as well as accident events of hydraulic structures are described. A universal scheme for the application of hazard protection measures, which can be comprehensive, has been developed. Praemonitus praemunitus – precautions should be taken.

Academic conferences offer scientists the opportunity to share their findings and knowledge with other researchers. However, the number of conferences is rapidly increasing worldwide. Unlike journals that possess accreditation indices, there is no appropriate accreditation for international conferences. Here, a bibliometric measure is proposed that enables scholars to evaluate conference quality before attending.

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, we will extend the expected value of the function w.r.t the uniform probability measure on sets measurable in the Caratheodory sense to be finite for a larger class of functions, since the set of all measurable functions with infinite or undefined expected values forms a prevalent subset of the set of all measurable functions, which means "almost all" measurable functions have infinite or undefined expected values. Before we define the specific problem in section 2, we will outline some preliminary definitions. We'll then define the specific problem (along with a partial solution in section 3) to visualize the complete solution. Along the way, we will ask a series of questions to clarify our understanding of the paper.

Introduction: This study aimed to validate the psychometric properties of the German eHealth Impact Questionnaire (eHIQ-G), which is divided into two independently administered and scored parts. Methods: 162 people with MS browsed one of two possible websites containing information on MS and completed an online survey. Internal consistency was assessed by Cronbach’s alpha and structural validity by Confirmatory Factor Analysis. Construct validity was examined by assessing correlations with the eHealth Literacy Questionnaire and the General Self-Efficacy Scale. Moreover, the mean difference of the eHIQ-G score between the two websites was investigated. Results: Cronbach’s alpha for the eHIQ-G subscales ranged from .833 to .885. The eHIQ-G part 1 achieved acceptable levels of goodness-of-fit indices, whereas the fit for the eHIQ-G part 2 was poor and likewise for the alternative modified models. The correlations with the reference instruments were 0.08 – 0.62 and as expected. Older age was related with lower eHIQ-G part 1 score, whereas no significant effect was found for education. Although not significant, the website ‘AMSEL’ reached higher mean scores on eHIQ part 2. Conclusion: The eHIQ-G has good internal consistency, and sufficient structural and construct validity. It will facilitate the measurement of the impact of websites providing health information.

Bonchev and Trinajstic defined two distance based entropy measures to measure the molecular branching of molecular graphs in 1977 [Information theory, distance matrix, and molecular branching, J. Chem. Phys., 38 (1977), 4517–4533]. In this paper we use these entropy measures which are based on distance matrices of graphs. The first one is based on distribution of distances in distance matrix and the second one is based on distribution of distances in upper triangular submatrix. We obtain the two entropy measures of paths, stars, complete graphs, cycles and complete bipartite graphs. Finally we obtain the minimal trees with respect to these entropy measures with fixed diameter.

Quantum coherence is an important physical resource in quantum information science, and also as one of the most fundamental and striking features in quantum physics. In this paper, we obtain a symmetry-like relation of relative entropy measure $C_r(\rho)$ of coherence for $n$-partite quantum states $\rho$, which gives lower and upper bounds for $C_r(\rho)$. Meanwhile, we discuss the conjecture about the validity of the inequality $C_r(\rho)\leq C_{\ell_1}(\rho)$ for any state $\rho$. We observe that every mixture $\eta$ of a state $\rho$ satisfying $C_r(\rho)\leq C_{\ell_1}(\rho)$ and any incoherent state $\sigma$ also satisfies the conjecture. We also note that if the von Neumann entropy is defined by the natural logarithm $\ln$ instead of $\log_2$, then the reduced relative entropy measure of coherence $\bar{C}_r(\rho)=-\rho_{\rm{diag}}\ln \rho_{\rm{diag}}+\rho\ln \rho$ satisfies the inequality ${\bar{C}}_r(\rho)\leq C_{\ell_1}(\rho)$ for any mixed state $\rho$.

Physical roots, exemplifications and consequences of periodic and aperiodic ordering (represented by Fibonacci series) in biological systems are discussed. The role and physical and biological roots of symmetry and asymmetry appearing in biological patterns is addressed. Generalization of the Curie-Neumann Principle as applied to biological objects is presented, briefly summarized as: “asymmetry is what creates a biological phenomenon”. The “up-bottom approach” and “bottom up” approaches to the explanation of symmetry in organisms are presented in detail. The “up-bottom approach”, implies that the symmetry of the biological structure follows the symmetry of media in which this structure is functioning; the “bottom-up” approach, in turn, adopt that the symmetry of biological structures emerges from the symmetry of molecules constituting the structure. A diversity of mathematical measures applicable for quantification of ordering in biological patterns is introduced. The continuous, Shannon and Voronoi measures of symmetry/ordering and their application to biology objects are addressed. The fine structure of the notion of “ordering” is discussed. Informational/algorithmic roots of ordering inherent for the biological systems are considered. Ordered/symmetrical patterns provide economy of biological information, necessary for algorithmic description of a biological entity. Application of the Landauer principle bridging physics and theory of information to the biological systems is discussed.

I want to find an extension of the Hausdorff Measure and Fractal Measure which allows me to compute a unique, satisfying average for functions defined on non-fractal, measurable sets in the sense of Carathedory which has no gauge function.

In this study, we used the natural and anthropogenic characteristics of a coastal region to generate risk maps showing vulnerability and potential hazards, and proposed design criteria for coastal defense and land use for the various kinds of risks faced. The Yunlin coast: a first-level protection area in mid-west Taiwan, was then used as an example to illustrate the proposed design criteria. The safety of the present coastal defenses and land use of the Yunlin coastal area was assessed, and coastal protection measures for hazard prevention were proposed based on the generated risk map. The results can be informative for future coastal management and the promotion of sustainable development of coastal zones.

We examined a series of real-world, pictorial photographs with varying characteristics, along with their modification by noise addition and unsharp masking. As response metrics we used three different versions of the aesthetic measure originally proposed by Birkhoff. The first aesthetic measure, which has been used in other studies, and which we used in our previous work as well, showed a preference for the least complex of the images. It provided no justification for noise addition, but did reveal enhancement on unsharp masking. Optimum level of unsharp masking varied with the image, but was predictable from the individual image’s GIF compressibility. We expect this result to be useful for guiding the processing of pictorial photographic imagery. The second aesthetic measure, that of informational aesthetics based on entropy alone failed to provide useful discrimination among the images or the conditions of their modification. A third measure, derived from the concepts of entropy maximization, as well as the hypothesized preference of observers for “simpler”, i.e., more compressible, images, yielded qualitatively the same results as the more traditional version of the measure. Differences among the photographs and the conditions of their modification were more clearly defined with this metric, however.

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.

Online digital mental health communities can contribute to users’ mental health positively and negatively. Yet the measurement of outcomes and impact relating to digital mental health communities is difficult to capture. In this paper we demonstrate the development of an online experience measure for a specific children and young people’s community inside a digital mental health service. The development is informed by three phases: (i) item reduction through Estimate-Talk-Estimate modified Delphi methods, (ii) user testing with participatory action research and (iii) a pilot within the digital service community to explore its use. Rounds of experts talks help to reduce the items. User experience workshops helped to inform the usability and appearance, wording, and purpose of the measure. Finally, the pilot results highlight completion rates, difference in scores for age and community roles and a preference to ‘relate to others’; as a mechanism of support. Outcomes frequently selected in the measure show the importance of certain aspects of the community, such as safety, connection, and non-judgment previously highlighted in the literature. Self-reported helpfulness scales like this one could be used as indicators of meaningful engagement within the community and its content but further research is required to ascertain its acceptability and validity. Phased approaches involving stakeholders and participatory action research enhances the development of digitally enabled measurement tools.

In this article, rst we are going to review the concept of ordinary frames , in more general case in measure spaces, namely, gc-frames. We try to develop the use of measure space in describing frames. Then by means of the gc-frames, we shall introduce gn-operators, which we shall show that each trace class operator has a vector-valued integral representation and vice-versa.

Voronoi entropy for the random patterns and patterns demonstrating various elements of symmetry are calculated. The symmetric patterns are characterized by the values of the Voronoi entropy very close to those inherent to random ones. This contradicts the idea that the Voronoi entropy quantifies the ordering of the seed points, constituting the pattern. The extension of the Shannon-like formula embracing symmetric patterns is suggested. Analysis of Voronoi diagrams enables revealing of the elements of symmetry of the pattern.

With the rapid spread of built-in GPS handheld smart devices, the trajectory data from GPS sensors has grown explosively. Trajectory data has spatio-temporal characteristics and rich information. Using trajectory data processing techniques can mine the patterns of human activities and the moving patterns of vehicles in the intelligent transportation systems. A trajectory similarity measure is one of the most important issues in trajectory data mining (clustering, classification, frequent pattern mining, etc.). Unfortunately, the main similarity measure algorithms with the trajectory data have been found to be inaccurate, highly sensitive of sampling methods, and have low robustness for the noise data. To solve the above problems, three distances and their corresponding computation methods are proposed in this paper. The point-segment distance can decrease the sensitivity of the point sampling methods. The prediction distance optimizes the temporal distance with the features of trajectory data. The segment-segment distance introduces the trajectory shape factor into the similarity measurement to improve the accuracy. The three kinds of distance are integrated with the traditional dynamic time warping algorithm (DTW) algorithm to propose a new segment–based dynamic time warping algorithm (SDTW). The experimental results show that the SDTW algorithm can exhibit about 57%, 86%, and 31% better accuracy than the longest common subsequence algorithm (LCSS), and edit distance on real sequence algorithm (EDR) , and DTW, respectively, and that the sensitivity to the noise data is lower than that those algorithms.

As paradigm of complex behavior, multifractals describe the underlying geometry of self-similar objects or processes. Building on the connection between entropy and multifractals, we show here that the generalized dimension of geodesic trajectories in General Relativity coincides with the four-dimensionality of classical spacetime.

Cultivated land plays an important role in water and soil loss in the earth-rocky mountainous region, northern China, however, its responses to soil control measures and rainfall characteristics are still not fully understood. In this study, 85 erosive rainfall events in 2011-2019 were grouped into three types, and the responses of runoff and soil loss on five cultivated plots with different slopes in the upstream catchment of the Miyun Reservoir to soil conservation measures and rainfall regimes were evaluated. Results found that event-averaged runoff depths and soil loss rates on the five plots ranged from 7.05 mm to 0.03 mm and from 300.51 t km-2 to 0.37 t km-2 respectively, depending on rainfall regimes, soil conservation measures, and slope gradients. The high occurring frequency (i.e., 72.94%) rainfall regime A with short rainfall duration (RD), low rainfall amount (P), and high mean rainfall intensity (Im) yielded lower runoff depth and higher soil loss rate. Rainfall regime B with longer RD, and higher P and Im, however, produced higher rainfall depth and lower soil loss rate. Terraced plot had the highest runoff and soil loss reduction efficiencies of over 96.03%. Contour tillage had comparable sediment reduction efficiency to that of the terraced plot on gentle slopes (gradient less than 11.0%), while its runoff reduction efficiency was less than 13.11%. This study implies that in the Miyun Reservoir catchment and similar regions in the world, contour tillage should be promoted on gentle slopes, and terrace construction should be given enough attention since it can greatly reduce water quantity and cause water shortage in downstream catchments.

An idea expressed in the paper [Entropy 2017, 19, 345] about the deductive formulation of a physical theory resting on explicitly- and universally-introduced basic concepts is developed. An entropic measure of time with a number of properties leading to an analog of the Galilei–Einstein relativity principle is considered. Using the introduced measure and a simple model, a kinematic law relating the size, time, and number of particles of a system is obtained. Corollaries of this law are examined. In particular, accelerated increase of the system size and, if the system size remains unchanged, decrease of the number of particles are found. An interesting corollary is the emergence of repulsive and attractive forces inversely proportional to the square of the system size for relatively dense systems and constant for sufficiently rarefied systems.

Nowadays, we live in a world in which people are facing with a lot of data that should be stored or displayed. One of the key methods to control and manage this data refers to grouping and classifying them in clusters. Today, clustering has a critical role in information retrieval methods for organizing large collections inside a few significant clusters. One of the main motivations for the use of clustering is to determine and reveal the hidden and inherent structure of a set of data. Ensemble clustering algorithms combine multiple clustering algorithms to finally reach an overall clustering system. Ensemble clustering methods by lack of information fusing utilize several primary partitions of data to find better ways. Since various clustering algorithms look at the different data points, they can produce various partitions from such data. It is possible to create a partition with high performance by combining the partitions obtained from different algorithms, even if the clusters to be very dense from each other. Most studies in this area have examined all the initial clusters. In this study, a new method is used in which the most sustainable clusters are utilized instead of all primary produced clusters. Consensus function based on co-association matrixes used to select more stable clusters. The most stable clusters selection method is done by cluster stability criterion based on F-measure. Optimization functions are used to optimize the obtained final clusters. The genetic algorithm is the optimizer used in this article to find the ultimate clusters participated in a consensus. Experimental results on several datasets show that the output of proposed method is various clusters with high stability.

Precipitation and human activities are two essential forcing dynamics that influence hydrological processes. To investigate those impacts, the Zuli River Basin (ZRB, a typical tributary basin of the Yellow River in China) was chosen to identify the impact of precipitation and human activities on runoff and sediment discharge. A double mass curve (DMC) analysis and the test methods, including accumulated variance analysis, sequential cluster, Lee-Heghnian, and moving t-test methods was utilized to determine the abrupt change point based on data from 1956 to 2015. Correlation formulas and multiple regression methods were used to calculate the runoff and sediment discharge reduction effects of soil conservation measures and to estimate the contribution rate of precipitation and soil conservation measures to runoff and sediment discharge. Our results show that the runoff reduction effect of soil conservation measures (45%) is greater than the sediment discharge reduction effect (32%). Soil conservation measures were the main factor controlling the 74.5% and 75.0% decrease in runoff and sediment discharge, respectively. Additionally, the contribution rate of vegetation measures was higher than that of engineering measures. This study provides scientific strategies for water resource management and soil conservation planning at catchment scale to face future hydrological variability.

Microbial biofilms cause several environmental and industrial issues, even on the human health. Although they have represented a threaten due to their resistance to antibiotics, there are currently no approved antibiofilm agents for clinical treatments. The multi-functionality of antimicrobial peptides (AMPs) including the antibiofilm activity and their potentialities to target multiple mi-crobes motivated the synthesis of AMP relatives for developing antibiofilm agents for clinical purposes. Antibiofilm peptides (ABFPs) have been organized in databases that allowed the building of prediction tools which have assisted in the discovery/design of new antibiofilm agents. However, the complex network approach has been explored yet as an assistant tool for this aim. Herein, a kind of similarity networks, called the Half-Space Proximal Network (HSPN) is applied to represent/analyse the chemical space of the ABFPs aimed to identify promising scaf-folds for the development of next generation antimicrobials, able to target both planktonic and biofilm microbial forms. Such analyses also considered the metadata associated to the ABFPs such as origin, other activities, targets, etc. in which the relationships were projected by multilayer networks called metadata networks (METNs). From the complex networks mining, a reduced but informative set of 66 ABFPs representing the original antibiofilm space was extracted. This subset retained from the most central to atypical ABFPs, having some of them, desired properties for developing next generation antimicrobials. So, this subset is advisable for assisting the search/design both new antibiofilm/antimicrobial agents. The provided ABFP motifs list, dis-covered within the HSPN communities, is also useful for the same purpose.

The alteration of natural land cover to impervious surfaces during development increases stormwater runoff. Stormwater Control Measures (SCMs) are used to manage water quantity and enhance water quality by restoring the hydrologic cycle altered by development. Often, SCMs have an outflow pipe to handle overflows or to manage the release of water detained when infiltration is not possible. Traditionally, these are static controls (e.g. a small orifice is used to restrict the volume of outflow), however, these systems can be improved by instituting real-time controls (RTC). RTC improve the functionality of SCMs by dynamically controlling outflows to adjust to environmental conditions. A major impediment to the widespread implementation of RTC is the high cost of installation and operation. This study utilized machine learning methods to develop a forecasting approach for the implementation of low-cost RTC that were implemented on a programmable gate of the outlet structure of a multi-stage basin in southeastern Pennsylvania. The goals were to decrease the peak flow exiting the basin during rain events, increase the volume of water detained, decrease the number of overtopping events, maintain healthy vegetation in the basin, and protect the downstream vegetation from erosion. Multiple popular data science algorithms were evaluated including multiple linear regression and long short-term memory. These algorithms were used with a dataset, which consisted of four years of historical sensor data, collected in 5-minute intervals, to train models to predict water levels to optimize operations. The accuracy of 30 models with three different methods of handling missing values were compared. A long short-term memory model configured with a 30-minute lead time produced the best results. Having an approximate same lag time of 30 minutes for the contributing drainage area of the SCM provided a sufficient RTC functioning period to improve the performance of the outlet structure.

Chirality depends on particular symmetries. For crystal structures it describes the absence of mirror planes and inversion centers, and in addition to translations, only rotations are allowed as symmetry elements. However, chiral space groups have additional restrictions on the allowed screw rotations as a symmetry element, because they always appear in enantiomorphous pairs. This study classifies and distinguishes the chiral structures and space groups. The chirality is quantified using Hausdorff distances and continuous chirality measures and selected crystal structures are reported. The chirality is discussed for bulk solids and their surfaces. Moreover, the band structure, and thus, the density of states, is found to be affected by the same crystal parameters as the chirality. However, it is independent of handedness. The Berry curvature, as a topological measure of the electronic structure, depends on the handedness, but is not a proof for the chirality because it responds on the inversion of a structure. For molecules, optical circular dichroism is one of the most important measures for the chirality. Thus, it is proposed in this study that the circular dichroism in the angular distribution of photoelectrons in high symmetry configurations can be used to distinguish the handedness of chiral solids and their surfaces.

As shown earlier, the algorithmic complexity, like Shannon information and Boltzmann entropy, tends to increase in accordance with the general law of complification. However, the algorithmic complexity of most material systems does not reach its maximum, i.e. chaotic state, due to the various laws of nature that create certain structures. The complexity of such structures is very different from the algorithmic complexity, and we intuitively feel that its maximal value should be somewhere between order and chaos. I propose a formula for calculation such structural complexity, which can be called - structuredness. The structuredness of any material system is determined by structures of three main types: stable, dissipative, and post-dissipative. The latter are defined as stable structures created by dissipative ones, directly or indirectly. Post-dissipative structures, as well as stable, can exist for an unlimited time, but at the micro level only, without energy influx. The appearance of such structures leads to the “ratchet” process, which determines the structuregenesis in non-living and, especially, in living systems. This process allows systems with post-dissipative structures to develop in the direction of maximum structuring due to the gradual accumulation of these structures, even when such structuring contradicts the general law of complification.

The operations of digitization, transmission and storage of medical data, particularly images require increasingly effective encoding methods not only in terms of compression ratio and flow of information but also in terms of visual quality. At first, there was DCT (discrete cosine transform) then DWT (discrete wavelet transform) and their associated standards in terms of coding and image compression. After that, the 2nd generation wavelets seeks to be positioned and confronted to the image and video coding methods currently used. It is in this context that we suggested a method combining bandelets and SPIHT (set partitioning in hierarchical trees) algorithm. There are two main reasons for our approach: the first lies in the nature of the bandelet transform to take advantage by capturing the geometrical complexity of the image structure. The second reason stems in the suitability of encoding the bandelet coefficients by the SPIHT encoder. Quality measurements shows that in some cases (for low bit rates) the performances of the proposed coding compete with the well-established ones and opens up new application prospects in the field of medical imaging.

Recently emerging data-driven citizen sciences need to harness increasing amount of massive data with varying quality. This paper develops essential theoretical frameworks and example models and examine its computational complexity for interactive data-driven citizen science within the context of guided self-organization. We first define a conceptual model that incorporates quality of observation in terms of accuracy and reproducibility, ranging between subjectivity, inter-subjectivity, and objectivity. Next, we examine the database's algebraic and topological structure in relation to informational complexity measures, and evaluate its computational complexities with respect to exhaustive optimization. Conjectures of criticality are obtained on self-organizing processes of observation and dynamical model development. Example analysis is demonstrated with the use of biodiversity assessment database, the process that inevitably involves human subjectivity for the management in open complex systems.

In this article, we introduce the concept of soft intervals, soft ordering and sequences of soft real numbers, and some of their structural properties are studied. The notion of soft Lebesgue measure on the soft real numbers has been introduced. Also, a correspondence relationship has been established between the soft Lebesgue measure and the classical Lebesgue measure. Furthermore, we have studied some exciting results and relations between the soft Lebesgue measure and the Lebesgue measure of soft real sets.

Informational (Shannon) measures of symmetry are introduced and analyzed for the patterns built of 1D and 2D shapes. The informational measure of symmetry Hsym (G) characterizes the an averaged uncertainty in the presence of symmetry elements from the group G in a given pattern; whereas the Shannon-like measure of symmetry Ωsym (G) quantifies averaged uncertainty of appearance of shapes possessing in total n elements of symmetry belonging to group G in a given pattern. Hsym(G1)=Ωsym(G1)=0 for the patterns built of irregular, non-symmetric shapes. Both of informational measures of symmetry are intensive parameters of the pattern and do not depend on the number of shapes, their size and area of the pattern. They are also insensitive to the long-range order inherent for the pattern. Informational measures of symmetry of fractal patterns are addressed. The mixed patterns including curves and shapes are considered. Time evolution of the Shannon measures of symmetry is treated. The close-packed and dispersed 2D patterns are analyzed.

This paper presents an unsupervised feature selection method for multi-dimensional histogram-valued data. We define a multi-role measure, called the compactness, based on the concept size of given objects and/or clusters described by a fixed number of equal probability bin-rectangles. In each step of clustering, we agglomerate objects and/or clusters so as to minimize the compactness for the generated cluster. This means that the compactness plays the role of a similarity measure between objects and/or clusters to be merged. To minimize the compactness is equivalent to maximize the dis-similarity of the generated cluster, i.e., concept, against the whole concept in each step. In this sense, the compactness plays the role of cluster quality. We also show that the average compactness of each feature with respect to objects and/or clusters in several clustering steps is useful as feature effectiveness criterion. Features having small average compactness are mutually covariate, and are able to detect geometrically thin structure embedded in the given multi-dimensional histogram-valued data. We obtain thorough understandings of the given data by the visualization using dendrograms and scatter diagrams with respect to the selected informative features. We illustrate the effectiveness of the proposed method by using an artificial data set and real histogram-valued data sets.

We propose an iterative scheme for feature-based positioning using a new weighted dissimilarity measure with the goal of reducing the impact of large errors among the measured or modeled features. The weights are computed from the location-dependent standard deviations of the features and stored as part of the reference fingerprint map (RFM). Spatial filtering and kernel smoothing of the kinematically collected raw data allow efficiently estimating the standard deviations during RFM generation. In the positioning stage, the weights control the contribution of each feature to the dissimilarity measure, which in turn quantifies the difference between the set of online measured features and the fingerprints stored in the RFM. Features with little variability contribute more to the estimated position than features with high variability. Iterations are necessary because the variability depends on the location, and the location is initially unknown when estimating the position. Using real WiFi signal strength data from extended test measurements with ground truth in an office building, we show that the standard deviations of these features vary considerably within the region of interest and are neither simple functions of the signal strength nor of the distances from the corresponding access points. This is the motivation to include the empirical standard deviations in the RFM. We then analyze the deviations of the estimated positions with and without the location-dependent weighting. In the present example the maximum radial positioning error from ground truth are reduced by 40% comparing to kNN without the weighted dissimilarity measure.

The use of risk measures such as the Value at Risk (VaR) or Tail Conditional Expectation (TCE) is required by the Basel Committee on Banking Supervision in determining a bank’s risk profile. However, both measures can be shown to have shortcomings in the information that they provide to regulators and investors. In this paper we present an introduction to risk measure calculations before demonstrating the weaknesses of these measures. Through the exploration of specific cases we show how familiar yet differing risk profiles have identical values for combinations of these measures. From this evidence we recommend that a sequence of several risk measures should be used to give a more accurate representation of the risk contained on banking balance sheet.

We proposed in this work the introduction of a new vision of stochastic processes through geometry induced by dilation. The dilation matrices of a given process are obtained by a composition of rotation matrices built in with respect to partial correlation coefficients. Particularly interesting is the fact that the obtention of dilation matrices is regardless of the stationarity of the underlying process. When the process is stationary, only one dilation matrix is obtained and it corresponds therefore to Naimark dilation. When the process is nonstationary, a set of dilation matrices is obtained. They correspond to Kolmogorov decomposition. In this work, the nonstationary class of periodically correlated processes was of interest. The underlying periodicity of correlation coefficients is then transmitted to the set of dilation matrices. Because this set lives on the Lie group of rotation matrices, we can see them as points of a closed curve on the Lie group. Geometrical aspects can then be investigated through the shape of the obtained curves, and to give a complete insight into the space of curves, a metric and the derived geodesic equations are provided. The general results are adapted to the more specific case where the base manifold is the Lie group of rotation matrices, and because the metric in the space of curve naturally extends to the space of shapes, this enables a comparison between curves’ shapes and allows then the classification of processes’ measure.

This article introduces ten similarity measures that utilize cosine and cotangent functions to compare (m,n)-rung orthopair fuzzy sets, this a super class of q-rung orthopair fuzzy sets. Further, we applied our established weighted similarity measures to medical diagnosis, pattern recognition,and building material problems and also presented the comparison between established measures with the existing cosine and cotangent measures of q-rung orthopair, pythagorean and intuitionistic fuzzy sets. Lastly, we considered a numerical example that demonstrates the effective and scientific application of these similarity measures in plant leaf disease classification. Furthermore, we present graphical interpretations to demonstrate the effectiveness of our established measures.

Anomaly Detection in real time data is accepted as a vital research area. Clustering has effectively been tried for this purpose. As the datasets are real time, the time of generating of the data is also important. In this article, we introduce a mixture of partitioning and agglomerative hierarchical approach to detect anomalies from such datasets. It is a two-phase method which follows partitioning approach first and then agglomerative hierarchical approach. The dataset can have mixed attributes. In phase-1, a unified metric defined on mixed attributes is used. The same is also used for merging of similar clusters in phase-2. Also, we have kept the track of time attribute of each data instance which produces the clusters with their lifetimes in phase-1. Then in phase-2, we merge the similar clusters. While merging, the similar clusters, the lifetimes of the corresponding clusters with overlapping cores are to be superimposed producing fuzzy time intervals. This way, each cluster will have an associated fuzzy lifetime. The data instances either belonging sparse clusters or not belonging to any of the clusters can be treated as anomalies. The efficacy of the algorithms can be established using both complexity analysis as well as experimental studies.

Properties of the Voronoi tessellations arising from the random 2D distribution points are reported. We applied the procedure of dividing the sides of Voronoi cells into equal or random parts to Voronoi diagrams generated by a set of randomly placed on the plane points. The dividing points were then used to construct the following Voronoi diagram. Repeating this procedure led to a surprising effect of positional ordering of Voronoi cells, reminiscent of the formation of lamellae and spherulites in linear semi-crystalline polymers and metallic glasses. Thus, we can conclude, that by applying even a simple set of rules to a random set of seeds we introduce order into an initially disordered system. At the same time, the Voronoi entropy showed a tendency to values typical for completely random patterns and did not distinguish the short-range ordering. The Voronoi entropy and the continuous measure of symmetry of the patterns demonstrated the distinct asymptotic behavior, while approaching the close saturation values with the increase of the number of the iteration steps. Voronoi entropy grew, with the number of iterations, whereas the continuous measure of symmetry of the same patterns demonstrated the opposite asymptotic behavior. The Voronoi entropy is not an unambiguous measure of order in the 2D patterns. The more symmetrical patterns may demonstrate the higher values of the Voronoi entropy.

In this paper, we found a new model for compact star with charged anisotropic matter distribution considering an extended version of the Chaplygin equation of state. We specify a particular form of the metric potential Z(x) that allows us to solve the Einstein-Maxwell field equations. The obtained model satisfies all physical properties expected in a realistic star such that the expressions for the radial pressure, energy density, metric coefficients, measure of anisotropy and the mass are fully well defined and are regular in the interior of star. The solution obtained in this work can have multiple applications in astrophysics and cosmology.

The core of risk aggregation in the Solvency II Standard Formula is the so-called square root formula. We argue that it should be seen as a means for the aggregation of different risks to an overall risk rather than being associated with variance-covariance based risk analysis. Considering the Solvency II Standard Formula from the viewpoint of linear geometry, we immediately find that it defines a norm and therefore provides a homogeneous and sub-additive tool for risk aggregation. Hence Euler's Principle for the reallocation of risk capital applies and yields explicit formulas for capital allocation in the framework given by the Solvency II Standard Formula. This gives rise to the definition of diversification functions, which we define as monotone, subadditive, and homogeneous functions on a convex cone. Diversification functions constitute a class of models for the study of the aggregation of risk, and diversification. The aggregation of risk measures using a diversification function preserves the respective properties of these risk measures. Examples of diversification functions are given by seminorms, which are monotone on the convex cone of non-negative vectors. Each L^p norm has this property, and any scalar product given by a non-negative positive semidefinite matrix does as well. In particular, the Standard Formula is a diversification function and hence a risk measure that preserves homogeneity, subadditivity, and convexity.

Clustering algorithms for multi-database mining (MDM) rely on computing $(n^2-n)/2$ pairwise similarities between $n$ multiple databases to generate and evaluate $m\in[1, (n^2-n)/2]$ candidate clusterings in order to select the ideal partitioning which optimizes a predefined goodness measure. However, when these pairwise similarities are distributed around the mean value, the clustering algorithm becomes indecisive when choosing what database pairs are considered eligible to be grouped together. Consequently, a trivial result is produced by putting all the $n$ databases in one cluster or by returning $n$ singleton clusters. To tackle the latter problem, we propose a learning algorithm to reduce the fuzziness in the similarity matrix by minimizing a weighted binary entropy loss function via gradient descent and back-propagation. As a result, the learned model will improve the certainty of the clustering algorithm by correctly identifying the optimal database clusters. Additionally, in contrast to gradient-based clustering algorithms which are sensitive to the choice of the learning rate and require more iterations to converge, we propose a learning-rate-free algorithm to assess the candidate clusterings generated on the fly in a fewer upper-bounded iterations. Through a series of experiments on multiple database samples, we show that our algorithm outperforms the existing clustering algorithms for MDM.

This research is aimed at determining the characteristics of the current level of entrepreneurial potential of the Three Seas Initiative (3SI) countries, the ability to overcome the consequences of extraordinary events, such as COVID-19 and prospects for the return to an accelerated development once the destabiliser of the economic system, the coronavirus pandemic, has ceased. Eurostat, World Bank and the World Economic Forum data for 2015-2019 were used for the purpose of the research. The research was divided into three stages, i.e. assessment of economic development on the basis of a synthetic ratio of economic anchor development, for which a relative benchmark method based on spatial median (so-called L1 median or Weber point) was used, identification of conditions for the development of entrepreneurial capacity and statistical analysis showing the correlation between economic anchor measures and selected factors of the 3SI countries economic development. Our study found that the entrepreneurial capacity of the 3SI countries in 2015-2019 was determined by nine characteristics, belonging to six areas, i.e. local economy, demographic situation, social situation, trade exchange, innovation and tourism economy. The entrepreneurial potential of the 3SI countries was spatially diversified, and its development was determined, among others, by the entrepreneurial activity of residents (entrepreneurship index) and the conditions for running a business.

Feature selection is a crucial step to overcome the curse of dimensionality problem in data mining. This work proposes Recursive k-means Silhouette Elimination (RkSE) as a new unsupervised feature selection algorithm to reduce dimensionality in univariate and multivariate time-series datasets. Where k-means clustering is applied recursively to select the cluster representative features, following a unique application of silhouette measure for each cluster and a user-defined threshold as the feature selection or elimination criteria. The proposed method is evaluated on a hydraulic test rig, multi sensor readings in two different fashions: (1) Reduce the dimensionality in a multivariate classification problem using various classifiers of different functionalities. (2) Classification of univariate data in a sliding window scenario, where RkSE is used as a window compression method, to reduce the window dimensionality by selecting the best time points in a sliding window. Moreover, the results are validated using 10-fold cross validation technique. As well as, compared to the results when the classification is pulled directly with no feature selection applied. Additionally, a new taxonomy for k-means based feature selection methods is proposed. The experimental results and observations in the two comprehensive experiments demonstrated in this work reveal the capabilities and accuracy of the proposed method.

Bipolar neutrosophic set is an important extension of bipolar fuzzy set. This set is a hybridization of bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions. In this paper, we develop cross entropy measures of bipolar neutrosophic sets and prove its properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove its properties. Thereafter, we develop two novel multi-attribute decision making methods based on the proposed cross entropy measures. In the decision making framework, we calculate the weighted cross entropy measures between each alternative and the ideal alternative to rank the alternatives and choose the best one. We solve two illustrative examples of multi-attribute decision making problems and compare the obtained result with the results of other existing methods to show the applicability and effectiveness of the developed method. In the end, the main conclusion and future scope of research are summarized.

The objective of the paper is to introduce new similarity measure for single valued neutrosophic sets based on logarithm function. We define logarithm similarity measure and their weighted similarity measure for single valued neutrosophic sets. Then we define hybrid logarithm similarity measure and weighted hybrid logarithm similarity measure for single valued neutrosophic sets. We prove the basic properties of the proposed measures. We then define an entropy function using logarithm function to determine unknown attribute weights. We develop a novel multi attribute group decision making strategy for single valued neutrosophic sets based on the weighted hybrid logarithm similarity measure. We address an illustrative example to demonstrate the effectiveness and aptness of the proposed strategies. We conduct a sensitivity analysis of the developed strategy. We also make a comparison between the obtained results from proposed strategies and different existing strategies in the literature.

Green infrastructure systems are often overdesigned. This may be a byproduct of static sizing (e.g., accounting for a design storm’s runoff volume but not exfiltration rates) or may be deliberate (e.g., buffering against performance loss through time). Regardless, overdesign may compromise plants’ access to water in systems where soil pits are embedded in infiltration beds. It could raise the storm size required for water to reach soil pits, reducing water availability between storms, which could ultimately induce plant physiological stress. This study investigated the hydrological dynamics and water relations of a tree trench system suspected to have been overbuilt and identified factors contributing to, compounding, and mitigating the risk of plant stress. Results provided strong evidence that the abovementioned processes played out. Water in the infiltration bed reached soil pits only once in three years, with that event occurring during a hydrant release. Moreover, minimal water was retained in the soil pit during the event due to the hydraulic properties of the soil media. Through a growing season, one of the two tree types frequently experienced water stress, while the other did so only rarely. These contrasting responses can likely be attributed to roots either being largely confined to the soil pits or reaching a deeper water source. Implications of these results for green infrastructure design are considered.

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.

Peptide-based drugs are promising anticancer candidates due to their biocompatibility, and low toxicity. Particularly, tumor homing peptides (THPs) have the ability to bind specifically to can-cer cells receptors and tumor vasculature. Despite their potential to develop antitumor drugs, there are few available prediction tools to assist the discovery of new THPs. Two webservers based on machine learning models are currently active, the TumorHPD (https://webs.iiitd.edu.in/raghava/tumorhpd) and the THPep (http://codes.bio/thpep), and more recently the SCMTHP (SCMTHP (pmlabstack.pythonanywhere.com), based on scoring card method. Herein, a novel method based on network science and similarity searching implemented in the starPep toolbox (http://mobiosd-hub.com/starpep/) is presented for THPs discovery. The approach leverages from exploring the structural space of THPs with Chemical Space Networks (CSNs) and from applying centrality measures to identify the most relevant and non-redundant THPs sequences within the CSN. Such THPs were considered as queries (Qs) for multi-query similarity searches that applies a group fusion (MAX-SIM rule) model. The resulting multi-query similarity searching models (SSMs) were validated with three benchmarking datasets of THPs/non-THPs. Predictions achieved accuracies ranged from 92.64 to 99.18% and Matthews Correlation Coefficients between 0.894-0.98, outperforming state-of-the-art predictors. The best model was applied to repurpose AMPs from the starPep database as THPs, which were subse-quently optimized for the TH activity. Finally, 54 promising THP leads were discovered, and their sequences were analyzed to encounter novel motifs. These results demonstrate the potential of CSNs and multi-query similarity searching for a rapid and accurate identification of THPs.

Evidence-based medicine (EBM) is in crisis, in part due to bad methods, which are understood as misuse of statistics that is considered correct in itself. This article exposes two related common misconceptions in statistics, the effect size (ES) based on correlation (CBES) and a misconception of contingency tables (MCT). CBES is a fallacy based on misunderstanding of correlation and ES and confusion with 2 × 2 tables, which makes no distinction between gross crosstabs (GCTs) and contingency tables (CTs). This leads to misapplication of Pearson’s Phi, designed for CTs, to GCTs and confusion of the resulting gross Pearson Phi, or mean-square effect half-size, with the implied Pearson mean square contingency coefficient. Generalizing this binary fallacy to continuous data and the correlation in general (Pearson’s r) resulted in flawed equations directly expressing ES in terms of the correlation coefficient, which is impossible without including covariance, so these equations and the whole CBES concept are fundamentally wrong. MCT is a series of related misconceptions due to confusion with 2 × 2 tables and misapplication of related statistics. The misconceptions are threatening because most of the findings from contingency tables, including CBES-based meta-analyses, can be misleading. Problems arising from these fallacies are discussed and the necessary changes to the corpus of statistics are proposed resolving the problem of correlation and ES in paired binary data. Since exposing these fallacies casts doubt on the reliability of the statistical foundations of EBM in general, we urgently need to revise them.

There is a skin allergy epidemic in the western world, and the rate of deterioration has increased significantly in the past 5-10 years. It is probable that there are many environmental contributing factors, yet some studies have linked it primarily to the rise in the use of synthetic chemical ingredients in modern cosmetics. Our challenge, therefore, was to find a mechanism to determine the effect these substances have on skin health, and whether they really are a primary cause of long term damage to the skin. The first problem is the lack of any definitive way to measure skin health. Motivated by the overwhelming evidence for a link between deficient gut flora and ill health, we decided to look at whether our skin microbiota could similarly be used as an indicator of skin health. Our research illustrates how it is microbiota diversity alone that can predict whether skin is healthy or not, after we revealed a complete lack of conclusive findings linking the presence or abundance of particular species of microbe to skin problems. This phenomenon is replicated throughout nature, where high biodiversity always leads to healthy ecosystems. ‘Caveman’ skin, untouched by modern civilisation, was far different to ‘western’ skin and displayed unprecedented levels of bacterial diversity. The less exposed communities were to western practices, the higher the skin diversity, which is clear evidence of an environmental factor in the developed world damaging skin. For the first time we propose benchmark values of diversity against which we can measure skin to determine how healthy it is. This gives us the ability to be able to predict which people are more likely to be prone to skin ailments, and start to test whether cosmetic ingredients and products are a main cause of the skin allergy epidemic.

A catastrophic loss of microbial biodiversity on the skin has led to alarming increase in the prevalence of allergies and long-term damage to the skin, which could also have damaging knock on effects to overall health. This study uses 50 human participants, to obtain an average (benchmark) value for the biodiversity of ‘healthy’ western skin, which is crucial in updating our 2017 skin health measuring mechanism to use standardised methodology. Previous work with a larger sample size was unsatisfactory for use as a benchmark due to its use of different and outdated diversity indices. We also investigated the effect of age and sex, two known skin microbiome affecting factors. Although no statistical significance is seen for age- and sex- related changes in diversity, there appear to be changes related to age which elaborates on previous work which used larger, more general age ranges. Our study indicates adults age 28-37 have highest diversity, and age 48-57 the lowest. Crucially, because of this study we are now able to update the skin health measuring mechanism from our 2017 work. This will aid diagnostic assessment of susceptibility to cutaneous conditions or diseases, and treatment. Testing any human subject will be rapidly improved by obtaining future benchmark diversity values for any age, sex, body site and area of residence, to which they can be compared. This improvement means we can also more accurately investigate the ultimate question: What factors in the western world are a main cause of the skin allergy epidemic? This could lead to future restriction of certain synthetic chemicals or products found to be particularly harmful to the skin.

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.