Number Of Complexes Research Articles

Towards effective, robust and utility-preserving watermarking of GPS trajectories

Personal GPS trajectory is essential for businesses and emerging data markets due to its relevance in various data-driven methods, including traffic forecasting, accident prediction, and profiling driving behavior. Watermarking is a method that facilitates verification of data ownership and authenticity by embedding provenance information into the data. Whereas watermarking is commonly adopted in the image and audio domains, only a few initial watermarking methods exist for GPS trajectory data. GPS trajectory watermarking is particularly challenging due to the spatio-temporal data properties and easiness of data modification. As a result, existing watermarking methods often embed only minimal provenance information, lack robustness, and can fail to preserve data utility for downstream applications. In this work, we propose W-Trace - a novel, effective, robust, and utility-preserving GPS trajectory watermarking method. W-Trace transforms a GPS trajectory into a complex domain and applies the Fourier transformation to decompose the trajectory into the frequency representation. W-Trace embeds watermarks in the frequency representation and verifies them in a spatiotemporally-aware procedure. We demonstrate the effectiveness, robustness, and utility of the proposed W-Trace approach in realistic settings using real-world GPS trajectory datasets. In contrast to the baselines, the proposed W-Trace approach is robust to a wide range of trajectory modifications while preserving the GPS trajectory characteristics required for the downstream applications.

Genetically engineered bacteria can do complex math

Genetically engineered bacteria can do complex math

Statistical Distribution Theory and Fractional Calculus

This is an overview paper. This paper is an attempt to show that fractional calculus can be reached through statistical distribution theory. This paper brings together results on fractional integrals and fractional derivatives of the first and second kinds in the real and complex domains in the scalar, vector, and matrix-variate cases, and shows that all these results can be reached through statistical distribution theory. It is shown that the whole area of fractional integrals can be reached through distributions of products and ratios in the scalar variable case and distributions of symmetric products and symmetric ratios in the matrix-variate cases. While summarizing the materials, the real domain results are also listed side by side with the complex domain results so that a comparative study is possible. Fractional integrals and derivatives in the real domain mean that the parameters involved could be real or complex with appropriate conditions, the arbitrary function is real-valued, and the variables involved are all real. These in the complex domain mean that the parameters could be real or complex and the arbitrary function is still real-valued but the variables involved are in the complex domain. Fully complex domain means the variables as well as the arbitrary function are in the complex domain. Most of the materials on fractional integrals and fractional derivatives involving a single matrix or a number of matrices in the real or complex domain are of this author. Slight modifications of the results, compared with the published works in various papers, are there in various sections. In the paragraph on notations, the lemmas that are taken from this author’s own book on Jacobians are common with published works and hence the similarity index with this author’s works will be high. Section Matrix-Variate Joint Distributions and Fractional Integrals in Many Matrix-Variate Cases material on a statistical approach to Kiryakova’s multi-index fractional integral and its extension to the real scalar case of second kind integrals as well as extensions of first and second kind integrals to real and complex matrix-variate cases are believed to be new. Matrix differential operators are introduced in Section Fractional Derivatives and, with the help of these operators, fractional derivatives are constructed from the corresponding fractional integrals. These operators are applicable in a large variety of functions. Applicability is shown through identities created from scale transformed gamma random variables. Some concluding remarks are given and some open problems are pointed out in Section Concluding Remarks.

Structural and functional insights from the sequences and complex domain architecture of adhesin-like proteins from Methanobrevibacter smithii and Methanosphaera stadtmanae

Methanogenic archaea, or methanogens, are crucial in guts and rumens, consuming hydrogen, carbon dioxide, and other fermentation products. While their molecular interactions with other microorganisms are not fully understood, genomic sequences provide information. The first genome sequences of human gut methanogens, Methanosphaera stadtmanae and Methanobrevibacter smithii, revealed genes encoding adhesin-like proteins (ALPs). These proteins were also found in other gut and rumen methanogens, but their characteristics and functions remain largely unknown. This study analyzes the ALP repertoire of M. stadtmanae and M. smithii using AI-guided protein structure predictions of unique ALP domains. Both genomes encode more than 40 ALPs each, comprising over 10% of their genomes. ALPs contain repetitive sequences, many of which are unmatched in protein domain databases. We present unique sequence signatures of conserved ABD repeats in ALPs and propose a classification based on domain architecture. Our study offers insights into ALP features and how methanogens may interact with other microorganisms.

A dynamic mid-crustal magma domain revealed by the 2023 to 2024 Sundhnúksgígar eruptions in Iceland.

Mid-crustal magma domains are the source of many basaltic eruptions. Lavas from individual eruptions are often chemically homogeneous, suggesting that they derive from single, well-mixed magma reservoirs. The 2023 to 2024 eruptions at Sundhnúksgígar in the Svartsengi volcanic system in Iceland provide an opportunity to observe the behavior of a mid-crustal magma domain at high spatial and temporal resolution by detailed sampling and geochemical characterization. We observed substantial mantle-derived geochemical variability in the products erupted in the first hours of the December 2023 and January, February, and March to May 2024 eruptions, indicating that the eruptions derived from multiple magma reservoirs, which mineral-melt equilibration pressures place in the mid crust. The unusual presence of geochemical heterogeneity in the mid-crustal magma domain provides insights into how dynamic and complex mid-crustal magma domains can be.

Spectral Galerkin Approximation and Error Analysis Based on a Mixed Scheme for Fourth‐Order Problems in Complex Regions

ABSTRACTIn this article, an efficient spectral Galerkin method, which is based on a mixed scheme, is proposed and studied for solving fourth‐order problems in complex regions. The fundamental idea behind this approach is to transform the initial problem into an equivalent form in cylindrical coordinates and to reshape the computational domain into a product‐type rectangular one, which facilitates the utilization of spectral methods. However, when considering the equivalent fourth‐order form directly in cylindrical coordinates, it introduces intricate pole conditions and variable coefficients, posing challenges to both theoretical analysis and algorithm implementation. To address this, we employ the orthogonality of Fourier series to further decompose it into a sequence of decoupled two‐dimensional fourth‐order eigenvalue problems. For each such problem, we introduce an auxiliary function to transform it into an equivalent second‐order coupled system. Building on this, we formulate a mixed variational formulation and discrete scheme, and prove the error estimates for eigenvalue and eigenfunction approximations. Furthermore, we extend this algorithm to the two‐dimensional complex domains. Finally, a series of numerical examples are presented, and the numerical results validate the effectiveness of the algorithm and the correctness of the theoretical results.

Functions of a Complex Variable with a Large Parameter and Construction of Regions

The study of the asymptotic behavior of solutions of singularly perturbed equations in complex domains comes down to the study of integrals of exponential functions containing a large parameter. Such integrals differ significantly from the integrals to which the saddle point method is applicable. The saddle point method is not applicable to study such integrals. Thus, the problem arises of constructing domains and choosing integration paths for studying such integrals. In this work, specific examples of integrals show the construction of regions in the complex plane and the choice of integration paths. The chosen integration paths ensure that the integrals are bounded over a large parameter as this parameter tends to infinity. When constructing the domain and choosing integration paths, level lines of some harmonic functions that have zeros and singular points were used. The principle of symmetry is also used. In early works, cases were considered when the eigenvalues ​​of the first approximation matrix of a singularly perturbed equation had only zeros or only poles. Cases where the eigenvalues ​​have zeros and poles were not considered.

Discovery of Novel Thiazole-Based SIRT2 Inhibitors as Anticancer Agents: Molecular Modeling, Chemical Synthesis and Biological Assays.

The search and development of effective sirtuin small molecule inhibitors (SIRTIs) continues to draw great attention due to their wide range of pharmacological applications. Based on SIRTs' involvement in different biological pathways, their ligands were investigated for many diseases, such as cancer, neurodegenerative disorders, diabetes, cardiovascular diseases and autoimmune diseases. The elucidation of a substantial number of SIRT2-ligand complexes is steering the identification of novel and more selective modulators. Among them, SIRT2 in the presence of the SirReal2 analog series was the most studied. On this basis, we recently reported structure-based analyses leading to the discovery of thiazole-based compounds acting as SIRT2 inhibitors (T1, SIRT2 IC50 = 17.3 µM). Herein, ligand-based approaches followed by molecular docking simulations allowed us to evaluate in silico a novel small series of thiazoles (3a-3d and 5a, 5d) as putative SIRT2 inhibitors. Results from the computational studies revealed comparable molecular interaction fields (MIFs) and docking positionings of most of these compounds with respect to reference SIRT2Is. Biochemical and biological assays validated this study and pointed to compound 5a (SIRT2 IC50 = 9.0 µM) as the most interesting SIRT2I that was worthy of further development as an anticancer agent.

Domain knowledge-powered attention for air traffic management hazardous events classification

The automated classification of hazardous events in Air Traffic Management (ATM) involves concise texts with specialized terminology. The problem is currently addressed by machine learning text classification methods; however, some methods overlook domain knowledge, while others require it excessively. This research aims to identify a process for integrating low-cost, text-based domain knowledge into classification to address the issue of domain shift. To achieve this, the Wide and Deep Bidirectional Encoder Representations from Transformers (WD-BERT) model is proposed, featuring a unique knowledge-powered attention mechanism. WD-BERT's Wide Attention module assesses the compatibility between input text and domain knowledge to determine class probabilities, while its Deep Attention module extracts contextual features guided by domain knowledge. Additionally, a text mining method is employed to extract domain knowledge from ATM regulation texts. The model is trained and evaluated using a dataset derived from the China ATM Hazard Source Database. It achieves a multi-label classification accuracy of 80.24% and an F1-micro score of 0.88, outperforming comparative models with state-of-the-art performance. Breakdown analyses of the model indicate that the carefully designed attention mechanism endows WD-BERT with the ability to integrate domain knowledge, allowing it to excel in contexts involving complex sentences, multiple terms, and domain shifts. The innovation of this study lies in the proposed domain knowledge-powered attention mechanism, which allows simply organized domain knowledge to effectively guide ATM hazardous events classification, alleviating the impact of domain shift. This method can also be applied to other vertical domains without knowledge graphs.

Clinical characteristics and genetics functional analysis of two children with Spinal muscular atrophy

To explore the characteristics of SMN1 gene variants and carry out functional verification for two children with Spinal muscular atrophy (SMA). Two male children with complicated SMA diagnosed at the Children's Hospital Affiliated to Capital Institute of Pediatrics respectively in July 2021 and April 2022 due to delayed or retrograde motor development were selected as the study subjects. Clinical data of the children were collected. Primary culture of skin fibroblasts was carried out, and peripheral blood samples were collected from both children and their parents. Multiplex ligation-dependent probe amplification, combined long-range PCR and nested PCR, and Sanger sequencing were carried out to detect the copy number and variants of the SMN1 gene. Absolute quantitative real-time PCR, Western blotting and immunofluorescence were used to determine the transcriptional level of the SMN gene, expression of the SMN protein, and the number of functional SMN protein complexes (gems body), respectively. This study was approved by the Children's Hospital Affiliated to Capital Institute of Pediatrics (Ethics No. SHERLLM2021009). Child 1, a 1-year-old boy, was clinically diagnosed with type 1 SMA. Child 2, a 2-and-a-half-year-old boy, was clinically diagnosed with type 3 SMA. Both children were found to harbor a paternally derived SMN1 deletion and a maternally derived SMN1 gene variant, namely c.824G>T (p.Gly275Val) and c.884A>T (p.*295Leu). Compared with the normal controls and carriers, the levels of full-length SMN1 transcripts in their peripheral blood and skin fibroblast cell lines were significantly decreased (P < 0.05), and the levels of SMN protein normalized to that of β-actin, and the numbers of gems bodies in the primary fibroblast cells were also significantly lower (P < 0.05). Based on the guidelines from the American College of Medical Genetics and Genomics, both variants were classified as likely pathogenic (PS3+PM3+PM5+PP3; PS3+PM3+PM4+PP3). Following the diagnosis, both children had received nusinersen treatment. Although their motor function was improved, child 1 still died at the age of 2 due to severe pulmonary infection. The walking ability of child 2 was significantly improved, and his prognosis appeared to be good. Two cases of clinically complicated SMA have been confirmed by genetic testing and experimental studies, which has provided a reference for their accurate treatment.

A scalable convolutional neural network approach to fluid flow prediction in complex environments

We evaluate the capability of convolutional neural networks (CNNs) to predict a velocity field as it relates to fluid flow around various arrangements of obstacles within a two-dimensional, rectangular channel. We base our network architecture on a gated residual U-Net template and train it on velocity fields generated from computational fluid dynamics (CFD) simulations. We then assess the extent to which our model can accurately and efficiently predict steady flows in terms of velocity fields associated with inlet speeds and obstacle configurations not included in our training set. Real-world applications often require fluid-flow predictions in larger and more complex domains that contain more obstacles than used in model training. To address this problem, we propose a method that decomposes a domain into subdomains for which our model can individually and accurately predict the fluid flow, after which we apply smoothness and continuity constraints to reconstruct velocity fields across the whole of the original domain. This piecewise, semicontinuous approach is computationally more efficient than the alternative, which involves generation of CFD datasets required to retrain the model on larger and more spatially complex domains. We introduce a local orientational vector field entropy (LOVE) metric, which quantifies a decorrelation scale for velocity fields in geometric domains with one or more obstacles, and use it to devise a strategy for decomposing complex domains into weakly interacting subsets suitable for application of our modeling approach. We end with an assessment of error propagation across modeled domains of increasing size.

Properties and Applications of Complex Fractal–Fractional Operators in the Open Unit Disk

A fractal–fractional calculus is presented in term of a generalized gamma function (ℓ−gamma function: Γℓ(.)). The suggested operators are given in the symmetric complex domain (the open unit disk). A novel arrangement of the operators shows the normalization associated with every operator. We investigate a number of significant geometric features thanks to this. Additionally, some integrals, such the Alexander and Libra integral operators, are associated with these operators. Simple power functions are among the illustrations that are provided. Additionally, the formulation of the discrete ℓ−fractal–fractional operators is conducted. We demonstrate that well-known examples are involved in the extended operators.

Pernambuco-Alagoas, Riacho do Pontal, and Sergipano domains of the Borborema Province, Northeastern Brazil: a geological and geochronological synthesis

Abstract In recent years, the number of works seeking to advance the geological and geotectonic knowledge of the Borborema Province has been increasing. However, in the context of the Southern Borborema Province there are few studies aimed at understanding its tectonic evolution in an integrated way. This work presents a review of the lithostratigraphic and geochronological data available for the Pernambuco-Alagoas, Riacho do Pontal and Faixa Sergipana Domains, located in the southern portion of the Borborema Province (Northeast Brazil), in addition to a discussion on the tectonic evolution model. The Southern Borborema Province fully encompasses the state of Alagoas and partially the states of Pernambuco, Sergipe, Bahia and Piauí, and is delimited to the north by the Pernambuco Lineament and to the south by the São Francisco Craton. The methodology involved bibliographical survey, geological cartography, geochronological compilation, creation of detrital zircon histograms for metasedimentary rocks (with unconformity below 10%) and magmatic “barcodes” for ortho-derived rocks and preparation of regional geological profiles. The tectonic evolution of the Southern Borborema Province began with the breakup of the Rodínia Supercontinent (1000 Ma) during the Cariris Velhos Cycle. The processes involved in the interaction of fragments descending from Rodinia are diachronic, in a broad scenario of accretions and collisions that resulted in the merger of Gondwana. The Pernambuco-Alagoas Block is considered a complex tectonic domain, which was affected by the Cariris Velhos (1000 – 950 Ma) and Brasiliana (740 - 570 Ma) orogenies (Caxito &amp; Alkmim 2023), preserving remnants of Archean rocks (Riacho Seco Fragment) and proterozoic. The Riacho do Pontal Domain and the Faixa Sergipana Domain are part of a large folding system formed from the collision of the Pernambuco-Alagoas Domain with the São Francisco Craton, in a tangential deformation, vergent towards the craton, during the Brasiliana Orogeny. From the ages of the syncollisional granites we can infer that the orogenic event that gave rise to the aforementioned folded bands occurred at very close time intervals, presenting a slight diachronism. The article presents an integrated approach to tectonic evolution, however, the need for new studies is quite evident, with an emphasis on isotopic geology, geochronology, geochemistry and geological mapping that can contribute to the understanding of the processes involved in the formation of tectonic domains, their space-time relationships and their implications for the evolution of the Gondwana Continent.

Synthesis of Halogen-Substituted [12]Mercuracarborands-4. Crystal Structure of {[(9,12-I&lt;sub&gt;2&lt;/sub&gt;-C&lt;sub&gt;2&lt;/sub&gt;B&lt;sub&gt;10&lt;/sub&gt;H&lt;sub&gt;8&lt;/sub&gt;-1,2-Hg)&lt;sub&gt;4&lt;/sub&gt;]Cl}Na(H&lt;sub&gt;2&lt;/sub&gt;O)&lt;sub&gt;n&lt;/sub&gt;

The reactions of the dilithium derivatives of 9,12-dihalogen-ortho-carboranes 1,2-Li2-C2B10H8-9,12-X2 (X = Cl, Br, I) with mercury chloride HgCl2 afford a number of complexes of the chloride ion with the halogen derivatives of [12] mercuracarborand-4: {[(9,12-X2-C2B10H8-1,2ʹ-Hg)4]Cl}Na · nH2O. The molecular crystal structure of the complex of the[12]mercuracarborand-4 octaiodine derivative with the chloride ion is determined by X-ray diffraction. The substituents at the periphery of the mercury-containing macrocycle are found to exert a substantial effect on the macrocycle geometry leading to the transition from the planar to butterfly conformation, whose geometry is predetermined by a set of intermolecular interactions in the crystal.

On the adaption of biological transport networks affected by complex domains

On the adaption of biological transport networks affected by complex domains

ANALYSIS OF THE CROWD MANAGEMENT AND PEDESTRIAN MOVEMENT DURING HAJJ PILGRIMAGE ON MAKKAH

The Hajj pilgrimage, the world's largest annual mass gathering, poses significant challenges in crowd management and pedestrian movement due to the sheer number of participants and logistical complexities. This study emphasizes the need for effective strategies to ensure the safety of millions of pilgrims in Mecca, Saudi Arabia. By reviewing literature and analysing pedestrian movement systems, it identifies key bottlenecks and safety risks, especially during high-density periods like Nafra day. Field observations from 2019 to 2024, including the post-COVID-19 era, offer insights into crowd behaviour and the effectiveness of management strategies. The study highlights the importance of integrating advanced simulation tools with urban design to optimize pedestrian pathways and prevent overcrowding, contributing to Saudi Vision 2030's goals of enhancing the pilgrimage experience and ensuring participant safety.

Effect of charge inversion on the electrokinetic transport of nanoconfined multivalent ionic solutions

Understanding the effects of phenomena occurring at electrically charged interfaces, such as charge inversion (CI), is crucial for enabling electroosmosis as an efficient transport mechanism in nanodevices. Here, we employ molecular dynamics (MD) simulations to systematically analyze the effect of CI on the electrokinetic transport of multivalent ionic solutions confined in amorphous silica nanochannels. We employ mixtures of monovalent and multivalent counterions while fixing the total ionic concentration to establish correlations between observed phenomena and the amount of multivalent ionic species in the electrolyte solution. The results show that the development of CI is related to a decrease in the mobility of the fluid layers adjacent to the charged surface. In addition, we observe that interfacial overcharging disrupts the water molecular orientation in the fluid layers adjacent to the channel walls. From the non-equilibrium MD simulations of electro-osmotic flow, we disclose the influence of phenomena related to the presence of CI. In particular, flow reversal occurs in scenarios involving CI due to increased local viscosity and a higher concentration of coions within the hydrodynamically mobile and electrokinetically active region of the charged interface. We also find that the magnitude of the wall zeta (ζ) potential displays a monotonic increase with the development of CI in the system. Moreover, we explain why positioning the wall ζ potential at an imaginary (slip) plane, which separates the hydrodynamically mobile and immobile fluid, is misleading.

Mixed volumes of networks with binomial steady-states

The steady-state degree of a chemical reaction network is the number of complex steady-states for generic rate constants and initial conditions. One way to bound the steady-state degree is through the mixed volume of an associated steady-state system. In this work, we show that for partitionable binomial chemical reaction systems, whose resulting steady-state systems are given by a set of binomials and a set of linear (not necessarily binomial) conservation equations, computing the mixed volume is equivalent to finding the volume of a single mixed cell that is the translate of a parallelotope. Additionally, we give a coloring condition on cycle networks to identify reaction systems with binomial steady-state ideals. We highlight both of these theorems using a class of networks referred to as species-overlapping networks and give a formula for the mixed volume of these networks.

A Robust and Optimal Iterative Algorithm Employing a Weight Function for Solving Nonlinear Equations with Dynamics and Applications

This study introduces a novel, iterative algorithm that achieves fourth-order convergence for solving nonlinear equations. Satisfying the Kung–Traub conjecture, the proposed technique achieves an optimal order of four with an efficiency index (I) of 1.587, requiring three function evaluations. An analysis of convergence is presented to show the optimal fourth-order convergence. To verify the theoretical results, in-depth numerical comparisons are presented for both real and complex domains. The proposed algorithm is specifically examined on a variety of polynomial functions, and it is shown by the efficient and accurate results that it outperforms many existing algorithms in terms of speed and accuracy. The study not only explores the proposed method’s convergence properties, computational efficiency, and stability but also introduces a novel perspective by considering the count of black points as an indicator of a method’s divergence. By analyzing the mean number of iterations necessary for methods to converge within a cycle and measuring CPU time in seconds, this research provides a holistic assessment of both the efficiency and speed of iterative methods. Notably, the analysis of basins of attraction illustrates that our proposed method has larger sets of initial points that yield convergence.

Galicia and Donbass as Ideal models of regional identity: sociocultural roots of the confrontation between Western and Eastern Ukraine

The article examines ideal models of regional identity in Ukraine – Galicia and Donbass. It is emphasised that Ukraine, having become a sovereign state and appeared on the political map of the world in 1991, faced the problem of a pronounced mosaic of regions. Individual regions were included in Ukraine already formed as distinctive entities with stable features of culture and way of life of the population. The authors emphasise that on the territory of Ukraine there coexisted a number of territorial complexes that were rather weakly connected with each other, and their subordination to various states due to frequent changes in borders determined their complex interaction. The processes of changing the political affiliation of regions actualise the identification issue, and identity in such conditions turns into a kind of demiurge of reality and can act as the main, and sometimes the only source of meanings. The declaration of independence by Ukraine actualised historically formed contradictions, previously existing mainly latently. The article proves the existence of socio-cultural regions, unique ethno-territorial communities, creating a continuum with a clearly expressed dichotomy - Donbass and Galicia. Beginning from the first years of Ukraine's independence, the image of the new independent country as a great European power, the formation of which has always been hindered and continues to be hindered by Russia, was actively introduced into the consciousness of citizens. That is, a project was promoted based on Galician nationalism (with an emphatically Russophobic basis) and the concept of the &amp;amp;quot;titular Ukrainian nation&amp;amp;quot;. In turn, regionalist sentiments in the Eastern Ukraine showed that regional identity can have great potential for the social integration of citizens. Since the 1990s, Donbass has often acted as an object of deliberate &amp;amp;quot;otherness&amp;amp;quot; on the part of the Ukrainian political and cultural elite, which was a contrasting background in the context of the practices of national construction in Ukraine. The authors conclude that the formation of Ukrainian national identity was carried out in a very contradictory manner and was characterised by a clear dominance of regional identity in the Eastern Ukraine against the background of the total promotion of the Galician project, and since 2014, its promotion has been carried out by armed means. However, the violent desire to level the regional identity of the inhabitants of the Eastern Ukraine launched the process of secession of the region - the self-proclamation of the DPR and LPR and their subsequent inclusion in the Russian Federation in 2022.