Deterministic Relations Research Articles

Abstract Cyclic Functional Relation and Taxonomies of Cyclic Signals Mathematical Models: Construction, Definitions and Properties

This work is devoted to the procedure of the construction of an abstract cyclic functional relation, which summarizes and extends the known results for a cyclically correlated random process and a cyclic (cyclically distributed) random process to the case of arbitrary cyclic functional relations. Two alternative definitions of the abstract cyclic functional relation are given, and the fundamental properties of its cyclic and phase structures are presented. The theorem on the invariance of cyclicity attributes of an abstract cyclic functional relation to shifts of its argument, and which are determined by the rhythm function of this functional relation, is formulated and proved. This theorem gives the sufficient and necessary conditions that the rhythm function of an abstract cyclic functional relation must satisfy. By specifying the range of values and attributes of the cyclicity of an abstract cyclic functional relation, the definitions of important classes of cyclic functional relations are formulated. A deductive approach to building a wide system of taxonomies of classes of deterministic, stochastic, fuzzy and interval cyclic functional relations as potential mathematical models of cyclic signals is demonstrated. A comparative analysis of an abstract cyclic functional relation with the known mathematical models of cyclic signals was carried out. The results obtained in the article significantly expand and systematize the mathematical tools of the description of cyclic signals and are the basis for the development of effective model-based technologies for processing and computer simulation of signals with a cyclic space-time structure.

The Semantics of Stative Locative Events in Vietnamese: A Spatial Exploration

This study utilizes mathematical formalism and Figure-Ground argument mapping to categorize stative locative events in Vietnamese as surjective or bijective. Bijective events exhibit a one-to-one mapping of Figures and Grounds, while surjectives allow a single Figure to map onto multiple Grounds. Through analysis of Vietnamese sentences, the paper demonstrates how bijective and surjective locatives encode deterministic and ambiguous spatial relations between Figures and Grounds, respectively. This novel distinction aids in enhancing the understanding of locative event typologies and provides an explanatory model for cross-linguistic analysis. The proposed integrated formal framework combines predicate logic, set theory, and lexical semantics to account for complex locative meanings, with significant applications in computational and theoretical linguistics, as well as cognitive science.

Nonlinear Causal Discovery for High-Dimensional Deterministic Data.

Nonlinear causal discovery with high-dimensional data where each variable is multidimensional plays a significant role in many scientific disciplines, such as social network analysis. Previous work majorly focuses on exploiting asymmetry in the causal and anticausal directions between two high-dimensional variables (a cause-effect pair). Although there exist some works that concentrate on the causal order identification between multiple variables, i.e., more than two high-dimensional variables, they do not validate the consistency of methods through theoretical analysis on multiple-variable data. In particular, based on the asymmetry for the cause-effect pair, if model assumptions for any pair of the data are violated, the asymmetry condition will not hold, resulting in the deduction of incorrect order identification. Thus, in this article, we propose a causal functional model, namely high-dimensional deterministic model (HDDM), to identify the causal orderings among multiple high-dimensional variables. We derive two candidates' selection rules to alleviate the inconvenient effects resulted from the violated-assumption pairs. The corresponding theoretical justification is provided as well. With these theoretical results, we develop a method to infer causal orderings for nonlinear multiple-variable data. Simulations on synthetic data and real-world data are conducted to verify the efficacy of our proposed method. Since we focus on deterministic relations in our method, we also verify the robustness of the noises in simulations.

Modeling User Reviews through Bayesian Graph Attention Networks for Recommendation

Recommender systems relieve users from cognitive overloading by predicting preferred items for users. Due to the complexity of interactions between users and items, graph neural networks (GNN) use graph structures to effectively model user–item interactions. However, existing GNN approaches have the following limitations: (1) User reviews are not adequately modeled in graphs. Therefore, user preferences and item properties that are described in user reviews are lost for modeling users and items; and (2) GNNs assume deterministic relations between users and items, which lack the stochastic modeling to estimate the uncertainties in neighbor relations. To mitigate the limitations, we build tripartite graphs to model user reviews as nodes that connect with users and items. We estimate neighbor relations with stochastic variables and propose a Bayesian graph attention network (i.e., ContGraph) to accurately predict user ratings. ContGraph incorporates the prior knowledge of user preferences to regularize the posterior inference of attention weights. Our experimental results show that ContGraph significantly outperforms 13 state-of-the-art models and improves the best performing baseline (i.e., ANR) by 5.23% on 25 datasets in the five-core version. Moreover, we show that correctly modeling the semantics of user reviews in graphs can help express the semantics of users and items.

Reionization with Simba: How Much Does Astrophysics Matter in Modeling Cosmic Reionization?

Traditional large-scale models of reionization usually employ simple deterministic relations between halo mass and luminosity to predict how reionization proceeds. We here examine the impact on modeling reionization of using more detailed models for the ionizing sources as identified within the 100 h −1 Mpc cosmological hydrodynamic simulation Simba, coupled with postprocessed radiative transfer. Comparing with simple (one-to-one) models, the main difference with using Simba sources is the scatter in the relation between dark matter halos and star formation, and hence ionizing emissivity. We find that, at the power spectrum level, the ionization morphology remains mostly unchanged, regardless of the variability in the number of sources or escape fraction. In particular, the power spectrum shape remains unaffected and its amplitude changes slightly by less than 5%–10%, throughout reionization, depending on the scale and neutral fraction. Our results show that simplified models of ionizing sources remain viable to efficiently model the structure of reionization on cosmological scales, although the precise progress of reionization requires accounting for the scatter induced by astrophysical effects.

Rapid Tsunami Potential Assessment Using GNSS Ionospheric Disturbance: Implications from Three Megathrusts

The current tsunami early warning systems always issue alarms once large undersea earthquakes are detected, inevitably resulting in false warnings since there are no deterministic scaling relations between earthquake size and tsunami potential. In this paper, we assess tsunami potential by analyzing co-seismic ionospheric disturbances (CIDs). We examined CIDs of three megathrusts (the 2014 Mw 8.2 Iquique, the 2015 Mw 8.3 Illapel, and the recent 2021 Mw 8.2 Alaska events) as detected by Global Navigation Satellite System (GNSS) observations. We found that CIDs near the epicenter generated by the 2021 Mw 8.2 Alaska event were significantly weaker than those of the two Chilean events, despite having similar earthquake magnitudes. The propagation direction of CIDs from the Mw 8.2 Alaska earthquake further revealed ruptures toward the deeper seismogenic zone, implying less seafloor uplift and hazardous flooding. Our work sheds light on incorporating GNSS-based CIDs for more trustworthy tsunami warning systems.

Application and discussion of various crack closure models to predict fatigue crack growth in 6061-T651 aluminium alloy

Fatigue is one of the main causes of failures as well as mechanical fractures in structural details made of aluminium alloys under cyclic loading, where the materials (during the crack growth process) are subject to the stress R-ratio effects and crack closure phenomenon.In this research work, a comparison of the effect of various crack closure/opening models on the fatigue crack growth behaviour of 6061-T651 aluminium alloy is presented. The crack closure models under consideration are the following: Elber; Katcher and Kaplan; Clerivet and Bathias; Schijve; Zhang; Newman; Savaidis; Codrington-Kotousov; and, Correia. A comparison between these models and experimental data is also done. Deterministic quadratic relations based on experimental results between U vs R and Reff vs. R are suggested and compared with various crack closure models under consideration, where U is a quantitative parameter function of crack opening and closing concept. This investigation into the crack closure/opening effects is made using experimental results from the first cycle and stabilised measurements (U1 and Us). Correia’s and Newman’s models presented a better agreement with the experimental results (Ud,s or Reff,s). In this study, the crack closure quantitative parameters based on the first cycle and stabilised measurements reveal to be different, where Uand Reff vary with the crack growth process, which suggests the assumptions listed by Hudak and Davidson, Ellyin, and Correia seem to be correct. Therefore, it can be concluded that the simultaneous monitoring of CTOD-based experimental measurements of the crack closure effects and getting the crack tip stress–strain field based on digital image correlation (DIC) measurements, supported by analytical/numerical solutions, seems to be a good way to describe the fatigue crack growth.

Children’s developing capacity to calibrate the verbal testimony of others with observed evidence when inferring causal relations

Across two studies (N = 120), we investigated the development of children’s ability to calibrate the certainty of verbal testimony with observable data that varied in the degree of predictive causal accuracy. In Study 1, 4- and 5-year-olds heard a certain explanation or an uncertain explanation about deterministic causal relations. The 5-year-olds made more accurate causal inferences when the informant provided a certain and more calibrated explanation. In Study 2, children heard similar explanations about probabilistic relations, making the uncertain informant more calibrated. The 5-year-olds were more likely to infer the correct causal relations when the informant was uncertain, but only when the explanation was attuned to the stochasticity of the individual causal events (or outcomes that sometimes occur). These findings imply that the capacity to integrate, and make efficient inferences, from distinct sources of knowledge emerges during the preschool years.

Development of a technique for computer simulation of the stress state of the drive drum shell of a belt conveyor to optimize its design parameters

The paper considers the method of computer simulation of the stress-strain state of the drive drum shell in the NASTRAN integrated environment. Due to the complexity of determining stresses and deformations in the drum sections by the analytical method, it is proposed to solve this important problem using the numerical finite-element method. At the preliminary stage of computer modeling, a mechanical design scheme was developed, including a variable pressure that changes depending on the angle of rotation of the drum, the deterministic relations describing the variable force factors are based on the Euler ratio. It is also proposed to take into account the pressure from the variable friction force, which depends on the changing coefficient of adhesion of the belt to the drum. As a result of the computer calculation, the equivalent Mises stresses of 65 MPa were determined, the safety factor was 4.2 and the components of the tangential stresses were determined using the stress tensor marker, the shear stress reached the level τ=16 MPa for fabric tape and τ=3.14 MPa for rubber tape. According to the results of the calculation, the dependence of the tangential stresses on the angle of rotation of the drum was constructed. A diagram of the change in the component of tangential stresses along the forming shell of the drum was constructed. Analysis of stress-strain state allowed us to determine the factor of safety of the drum shell. Based on the analysis of equivalent stresses, it is proposed to further calculate the durability of the drum using the method of long-term fatigue. The computer calculation of shear stresses in the component allows choosing the rational parameters of the lining, based on such indicators as peel strength and break, as well as determining the angle 61° of the slab lining required to improve the reliability and traction ability of the pipeline

On the Resilience of Even-Mansour to Invariant Permutations

Symmetric cryptographic primitives are often exposed to invariances: deterministic relations between plaintexts and ciphertexts that propagate through the primitive. Recent invariant subspace attacks have shown that these can be a serious issue. One way to mitigate invariant subspace attacks is at the primitive level, namely by proper use of round constants (Beierle et al., CRYPTO 2017). In this work, we investigate how to thwart invariance exploitation at the mode level, namely by assuring that a mode never evaluates its underlying primitive under any invariance. We first formalize the use of invariant cryptographic permutations from a security perspective, and analyze the Even-Mansour block cipher construction. We further demonstrate how the model composes, and apply it to the keyed sponge construction. The security analyses exactly pinpoint how the presence of linear invariances affects the bounds compared with analyses in the random permutation model. As such, they give an exact indication how invariances can be exploited. From a practical side, we apply the derived security bounds to the case where the Even-Mansour construction is instantiated with the 512-bit ChaCha permutation, and derive a distinguishing attack against Even-Mansour-ChaCha in 2^{128} queries, faster than the birthday bound. Comparable results are derived for instantiation using the 200-bit Keccak permutation without round constants (attack in 2^{50} queries), the 1024-bit CubeHash permutation (attack in 2^{256} queries), and the 384-bit Gimli permutation without round constants (attack in 2^{96} queries). The attacks do not invalidate the security of the permutations themselves, but rather they demonstrate the tightness of our bounds and confirm that care should be taken when employing a cryptographic primitive that has nontrivial linear invariances.

ВОПРОСЫ МЕТОДОЛОГИИ ГЕОЛОГО-ГЕОМОРФОЛОГИЧЕСКИХ ИССЛЕДОВАНИЙ ДЛЯ ЦЕЛЕЙ МЕТАЛЛОГЕНИИ

The basic questions of the methodology of geological and geomorphological study (ore geomorphology, morphostructural analysis, morphotectonics, neotectonics) of ore-bearing territories are considered. The concepts of "geomorphologic systems organization element" as the smallest particle of matter preserving the structure and properties of a mineral, as well as "objectives", "objects" and "subjects" of morphostructural and morphotectonic studies for solving problems of metallogeny have been formulated. In areas with complex geological structure, it is recommended to carry out complex of morphostructural and morphotectonic works with repeated solution of direct and inverse problems: relief and geological environment, geological environment relief. This will make it possible to establish the totality of available deterministic and chronological relations between landforms and structural elements of the lithosphere. Along with the solution of traditional problems of ore geomorphology, it is proposed to use the developed original complex of morphostructural and morphotectonic studies.

Analysis of Runoff-Sediment Cointegration and Uncertainty Relations at Different Temporal Scales in the Middle Reaches of the Yellow River, China

To understand the intricate runoff-sediment relationship in the middle Yellow River basin (MYRB), the Toudaoguai, Longmen, Tongguan and Huayuankou sites in the MYRB were selected to analyze the deterministic equilibrium and uncertainty relations of runoff-sediment based on 55-year hydrological data at multi-time scales. The Johansen test and wavelet neural network were used to verify the cointegration relationship among hydrological series. Runoff-sediment uncertain statistical relations and dynamics in the MYRB were also analyzed based on rating curves and hysteresis loops. The results showed that the logarithmic sequences of sediment load (SL), runoff and suspended sediment concentration (SSC) conformed to a linear cointegration relationship at the Toudaoguai station or in spring, winter or under small flow at other stations, but a nonlinear cointegration relationship was observed in other cases at other stations. Regarding runoff-sediment uncertain relationships, the rating curves, and hysteresis loops differed in stations (Toudaoguai and the other stations), as well as discharge (threshold: 1000 m3/s), season (ice-flood and rainy season) and saturation of flow at flood and monthly scales. At the annual scale, phased and unsynchronized characteristics of runoff and sediment load were evident with a decreasing trend. This study on the runoff-sediment relationship can rationally provide a theoretical basis for the management and development of the Yellow River and other similar rivers with sufficient sediment, especially for areas with serious soil erosion.

What Does the Operator Algebra of Quantum Statistics Tell Us about the Objective Causes of Observable Effects?

Quantum physics can only make statistical predictions about possible measurement outcomes, and these predictions originate from an operator algebra that is fundamentally different from the conventional definition of probability as a subjective lack of information regarding the physical reality of the system. In the present paper, I explore how the operator formalism accommodates the vast number of possible states and measurements by characterizing its essential function as a description of causality relations between initial conditions and subsequent observations. It is shown that any complete description of causality must involve non-positive statistical elements that cannot be associated with any directly observable effects. The necessity of non-positive elements is demonstrated by the uniquely defined mathematical description of ideal correlations which explains the physics of maximally entangled states, quantum teleportation and quantum cloning. The operator formalism thus modifies the concept of causality by providing a universally valid description of deterministic relations between initial states and subsequent observations that cannot be expressed in terms of directly observable measurement outcomes. Instead, the identifiable elements of causality are necessarily non-positive and hence unobservable. The validity of the operator algebra therefore indicates that a consistent explanation of the various uncertainty limited phenomena associated with physical objects is only possible if we learn to accept the fact that the elements of causality cannot be reconciled with a continuation of observable reality in the physical object.

Cinematographic coloring of open space in Volodymyr Drozd’s short prose from 1960s

The paper considers the style manner of V. Drozd’s prose from his early writing period with a focus on cinematographic aesthetics of color and possibilities of the screen design of plein air as the most free spatial environment for visual development of the image. The writer’s literary means have their analogues in the well-known contemporary films (“October”, “Poem about Sea”, “Red Desert”).
 
 The dynamic plein air compositions have certain screen potential. The images of open-space are related to freedom in dynamic and successive change of a scene, and alternation of verbal pictures. They are rather close to the specifc cinematographic representation of action, as their color markers may be associated with an imaginary film. The first V. Drozd’s attempts of designing the color and light of plein air are marked with an accent on the hues of the represented objects, the dynamism of objects in the imaginary shots, and expressive motion, increased with spectral indicators. A growth of the writer’s mastery is related to development of successive color ‘melody’, based on nuances of the visual impressions, and harmonized with internal action progress. Plastic imaginal markers with limited color range also remind the technique of cinematographic rush, adding emotional and psychological mood connotations to the narration and stimulating positive (nostalgic, elegiac) associations. Although they may seem random, the light and color signals acquire cinematographic expressiveness due to integration into the plot and its internal action, and to the dynamics of the character’s point of view. Abandoning a picturesque fixed nature, the author acquires possibility to decode wider associative meanings with color and light markers, search for deeper semantics of visual image complexes, and construct deterministic relations of a character and environment. Even minimal visual signals contribute to the color structure of a verbal shot. Such terseness and obscurity of objects in the prospect of a narrative camera, and a rapid change of plein air sections are similar to the features of cinematographic aesthetics and poetics.

Stochastic evolution of hydraulic geometry relations in the lower Yellow River of China under environmental uncertainties

Hydraulic geometry relations comprise a classic way to understand characteristics of a river. However, environmental changes pose large uncertainties for the reliability of such relations. In the current study, on the basis of the ordinary differential equations (ODEs) formed through linear treatment of the deterministic power-law hydraulic geometry relations, a set of stochastic differential equations (SDEs) driven by Fractional white noise and Poisson noise are developed to simulate the historical dynamic probability distributions of typical hydraulic geometry variables such as slope, width, depth, and velocity with bankfull discharge variation over time in the lower Yellow River of China. One group of possible stochastic average behaviors within the next 50 years are calculated under three different design incoming water-sediment conditions (including 300, 600, and 800 million t of annual average sediment discharge). In each part of the lower reaches, after estimation of the SDE parameters using a nonparametric maximum likelihood estimation (MLE) method, the model is carefully examined using Monte Carlo simulation as compared with the deterministic control models. The results of this comparison reveal the potential responses of hydraulic geometry characteristics to environmental disturbances, and the average trends mainly agree with the measurements. Comparisons among the three different prediction results reveal the stochastic average solution generally is greater than the deterministic solution. The results also confirm the severe negative impacts that result from the condition of 300 million t of incoming sediment, thus, pointing out the need to raise the level of river evolution alert for the lower Yellow River of China in the future. Moreover, with the help of the stochastic computation, the stream power and hydraulic width/depth ratio could be representative of an effective systematic measure for river dynamics. The proposed stochastic approach is not only important to development in the field of fluvial relations, but also beneficial to the practical design and monitoring of a river system according to specified accuracy requirements.

Learning Intransitivity: From Intransitive Geometrical Objects to ‘Rhizomatic’ Intransitivity

A new class of intransitive objects — geometrical and mathematical constructions forming intransitive cycles A > B > C > A — are presented. In contrast to the famous intransitive dice, lotteries, etc., they show deterministic (not probabilistic) intransitive relations. The simplest ones visualize intransitivity that can be understood at a qualitative level and does not require quantitative reasoning. They can be used as manipulatives for learning intransitivity. Classification of the types of situations in which the transitivity axiom does and does not work is presented. Four levels of complexity of intransitivity are introduced, from simple combinatorial intransitivity to a “rhizomatic” one. A possible version of the main educational message for students in teaching and learning transitivity-intransitivity is presented.

Probabilistic S-N fields based on statistical distributions applied to metallic and composite materials: State of the art

Fatigue life prediction of materials can be modeled by deterministic relations, via mean or median S-N curve approximation. However, in engineering design, it is essential to consider the influence of fatigue life scatter using deterministic-stochastic methods to construct reliable S-N curves and determine safe operation regions. However, there are differences between metals and composites that must be considered when proposing reliable S-N curves, such as distinct fracture mechanisms, distinct ultimate strengths under tension and compression loading, and different cumulative fatigue damage mechanisms including low-cycle fatigue. This study aims at conducting a review of the models used to construct probabilistic S-N fields ( P-S-N fields) and demonstrate the methodologies applied to fit the P-S-N fields that are best suited to estimate fatigue life of the selected materials. Results indicate that the probabilistic Stüssi and Sendeckyj models were the most suitable for composite materials, while, for metals, only the probabilistic Stüssi model presented a good fitting of the experimental data, for all fatigue regimes.7

A deterministic rewrite system for the probabilistic λ-calculus

AbstractIn this paper we present an operational semantics for the ‘call-by-name’ probabilistic λ-calculus, whose main feature is to use only deterministic relations and to have no constraint on the reduction strategy. The calculus enjoys similar properties to the usual λ-calculus. In particular we prove it to be confluent, and we prove a standardisation theorem.

ДЕТЕРМИНИЗМ В АНАЛИТИЧЕСКОЙ ФИЛОСОФИИ ЯЗЫКА: УСЛОВИЕ ВОЗНИКНОВЕНИЯ СВЯЗЕЙ

The article aims to analyse determinism and systemic relations in epistemology of analytical philosophy of language, to clarify determinism features. Epistemology of analytical philosophy of language is a promising research area, and determinism conception is a relevant object of scientific research. The author proposes a methodology to differentiate deterministic relations, identifies the levels of an epistemological system and parameters of influence, which are formed according to the determinism principle. The paper focuses on developing epistemology of theories as a separate discipline.

Data fusion detects consistent relations between non-lesional white matter myelin, executive function, and clinical characteristics in multiple sclerosis.

We examined the influence of dysfunctional, non-lesional white matter on cognitive performance in multiple sclerosis (MS). Forty-six MS subjects were assessed using MRI-based myelin water imaging (MWI), and average myelin water fraction (MWF) values across 20 white matter regions of interest (ROIs) were determined. A data-fusion method, multiset canonical correlation analysis (MCCA), was used to investigate the multivariate, deterministic joint relations between MWF, executive function, and demographic and clinical characteristics. MCCA revealed one significant component (p = 0.009) which consisted of three linked profiles, with a pairwise correlation between the MWF and cognitive profiles of r = 0.37, a correlation between MWF and demographics profiles of r = 0.31, and between cognitive and demographics profiles r = 0.64. White matter ROIs representing long-range intra-hemispheric tracts and ROIs connecting the two hemispheres were positively related through their individual profiles to overall cognitive performance, education and female gender, while age, EDSS, and disease duration were related negatively. Surprisingly, lesions within the ROIs had a negligible effect on overall relations between imaging, cognitive, and demographic variables. These findings indicate that there is a strong association between a pattern of MWF values and cognitive performance in MS, which is modulated by age, education, and disease severity. Moreover, this consistent relation involves multiple white matter regions and is separate from the influence of lesions.