Cluster Representation Research Articles

A Cluster-Based Deep Learning Model Perceiving Series Correlation for Accurate Prediction of Phonon Spectrum.

The spectral properties are the most prevalent continuous representation for characterizing transport phenomena and excitation responses, yet their accurate predictions remain a challenge due to the inability to perceive series correlations by existing machine learning (ML) models. Herein, a ML model named cluster-based series graph networks (CSGN) is developed based on the dynamical theory of crystal lattices to predict phonon density of states (PDOS) spectrum for crystal materials. The multiple atomic cluster representation is constructed to capture the diverse vibration modes, while the mixture Gaussian process and dynamic time warping mechanism are compiled to project from clusters to PDOS spectrum. Accurate predictions of complicated spectra with multiple or overlapping peaks are achieved. The high performance of CSGN model can be attributed to the pertinent feature extraction and the appropriate similarity evaluation, which enable the natural perception of structure-property relation and intrinsic series correlations as confirmed in the predictive results. The transferable and interpretable CSGN model advances ML predictions of spectral properties and reveals the potential of designing ML methods based on physical mechanisms.

A Dual-Masked Deep Structural Clustering Network With Adaptive Bidirectional Information Delivery.

Structured clustering networks, which alleviate the oversmoothing issue by delivering hidden features from autoencoder (AE) to graph convolutional networks (GCNs), involve two shortcomings for the clustering task. For one thing, they used vanilla structure to learn clustering representations without considering feature and structure corruption; for another thing, they exhibit network degradation and vanishing gradient issues after stacking multilayer GCNs. In this article, we propose a clustering method called dual-masked deep structural clustering network (DMDSC) with adaptive bidirectional information delivery (ABID). Specifically, DMDSC enables generative self-supervised learning to mine deeper interstructure and interfeature correlations by simultaneously reconstructing corrupted structures and features. Furthermore, DMDSC develops an ABID module to establish an information transfer channel between each pairwise layer of AE and GCNs to alleviate the oversmoothing and vanishing gradient problems. Numerous experiments on six benchmark datasets have shown that the proposed DMDSC outperforms the most advanced deep clustering algorithms.

Clinical outcome-guided deep temporal clustering for disease progression subtyping

ObjectiveComplex diseases exhibit heterogeneous progression patterns, necessitating effective capture and clustering of longitudinal changes to identify disease subtypes for personalized treatments. However, existing studies often fail to design clustering-specific representations or neglect clinical outcomes, thereby limiting the interpretability and clinical utility. MethodWe design a unified framework for subtyping longitudinal progressive diseases. We focus on effectively integrating all data from disease progressions and improving patient representation for downstream clustering. Specifically, we propose a clinical Outcome-Guided Deep Temporal Clustering (OG-DTC) that generates representations informed by clustering and clinical outcomes. A GRU-based seq2seq architecture captures the temporal dynamics, and the model integrates k-means clustering and outcome regression to facilitate the formation of clustering structures and the integration of clinical outcomes. The learned representations are clustered using a Gaussian mixture model to identify distinct subtypes. The clustering results are extensively validated through reproducibility, stability, and significance tests. ResultsWe demonstrated the efficacy of our framework by applying it to three Alzheimer’s Disease (AD) clinical trials. Through the AD case study, we identified three distinct subtypes with unique patterns associated with differentiated clinical declines across multiple measures. The ablation study revealed the contributions of each component in the model and showed that jointly optimizing the full model improved patient representations for clustering. Extensive validations showed that the derived clustering is reproducible, stable, and significant. ConclusionOur temporal clustering framework can derive robust clustering applicable for subtyping longitudinal progressive diseases and has the potential to account for subtype variability in clinical outcomes.

A framework for spatial-temporal cluster evolution representation and analysis based on graphs

Analysis on spatial-temporal data has several benefits that range from an improved traffic network in a city to increased earnings for drivers and ridesharing companies. A common analysis technique is clustering. However, most clustering techniques consider a constrained representation of clusters that is limited to a single timestamp. Evolving clusters exist through several timestamps and interact with other spatial-temporal objects or clusters, having cluster relationships. When many evolving clusters exist for analysis, a graph can be used to represent cluster evolution. In this article, we propose a framework for graph-based cluster evolution representation and analysis. The framework represents cluster structure and relationships as well as provides a graph representation of cluster evolution for analysis. Evaluation is done in three case studies with spatial-temporal data about taxis that can identify important phenomena or trends in movements in a city for traffic improvement.

Joint local smoothness and low-rank tensor representation for robust multi-view clustering

Low-rank tensor representation (LRTR) has become a significant method for achieving improved multi-view clustering (MVC) performance. Generally, most LRTR methods impose a tensor low-rank constraint (TLRC) on a tensor, which is spliced by the representation matrix of each view, to explore the low-rank prior hidden in these representation matrices. However, two problems remain unsolved. On the one hand, these representation matrices still contain noise since the raw data usually possess noise; on the other hand, and more importantly, is there any other prior information that can be explored among these representation matrices? Since samples located in the same cluster are similar, the coefficients of their representation matrices should exhibit similar. That is, these representation matrices should be local smoothness (LS), which is also verified by our numerical tests. In addition, the use of the LS prior helps to denoise the noise contain in the data. Then, in this paper, we propose a joint LS and LRTR for robust MVC method (LS-LRTR), which can simultaneously exploit the low-rank and LS priors. Specifically, we utilize a TLRC to explore the low-rank prior in the representation matrices. Subsequently, to mine the LS prior and further reduce the influence of noise, we introduce the Total Variation (TV) norm to the constraint representation matrices. Then, we fuse the TLRC and TV norm into a unified framework. Additionally, we apply an Augmented Lagrange Multiplier to solve the optimization problem of LS-LRTR. Experiments conducted on several datasets indicate that LS-LRTR outperforms the state-of-the-art clustering methods.

FedCCL: Federated dual-clustered feature contrast under domain heterogeneity

Federated learning (FL) facilitates a privacy-preserving neural network training paradigm through collaboration between edge clients and a central server. One significant challenge is that the distributed data is not independently and identically distributed (non-IID), typically including both intra-domain and inter-domain heterogeneity. However, recent research is limited to simply using averaged signals as a form of regularization and only focusing on one aspect of these non-IID challenges. Given these limitations, this paper clarifies these two non-IID challenges and attempts to introduce cluster representation to address them from both local and global perspectives. Specifically, we propose a dual-clustered feature contrast-based FL framework with dual focuses. First, we employ clustering on the local representations of each client, aiming to capture intra-class information based on these local clusters at a high level of granularity. Then, we facilitate cross-client knowledge sharing by pulling the local representation closer to clusters shared by clients with similar semantics while pushing them away from clusters with dissimilar semantics. Second, since the sizes of local clusters belonging to the same class may differ for each client, we further utilize clustering on the global side and conduct averaging to create a consistent global signal for guiding each local training in a contrastive manner. Experimental results on multiple datasets demonstrate that our proposal achieves comparable or superior performance gain under intra-domain and inter-domain heterogeneity.

Enhancing clustering representations with positive proximity and cluster dispersion learning

Contemporary deep clustering approaches often rely on contrastive or non-contrastive techniques to acquire effective representations for clustering tasks. Contrastive methods apply negative pairs to achieve homogenous representations but can introduce class collision problems, potentially compromising clustering performance. In contrast, non-contrastive techniques prevent class collisions but may produce non-uniform representations that lead to clustering collapse. In this work, we propose a novel end-to-end deep clustering approach named PIPCDR, designed to harness the strengths of both approaches while mitigating their limitations. PIPCDR incorporates a positive instance proximity loss and a cluster dispersion regularizer. The positive instance proximity loss ensures alignment between augmented views of instances and their sampled neighbors, enhancing within-cluster compactness by selecting genuinely positive pairs within the embedding space. Meanwhile, the cluster dispersion regularizer maximizes inter-cluster distances while minimizing within-cluster compactness, promoting uniformity in the learned representations. PIPCDR excels in producing well-separated clusters, generating uniform representations, avoiding class collision issues, and enhancing within-cluster compactness. We extensively validate the effectiveness of PIPCDR within an end-to-end Majorize-Minimization framework, demonstrating its competitive performance on moderate-scale clustering benchmark datasets and establishing new state-of-the-art results on large-scale datasets.

Topologically guided exfoliation of 3D metal-organic frameworks into nanosheets

Herein a general concept for screening 3D metal-organic frameworks (MOFs) for 2D nanosheets design is presented. Active coordination centers and terminal ligands of 3D-to-2D MOF nanosheets can result in self-assembly of multilayer structures. In comparison to 2D MOFs, 3D frameworks can provide nanosheets with better adhesion, strength, adsorptive capacity and catalytic activity. They are also promising in semiconductors, sensorics, and drug delivery systems. However, less than a dozen of 3D-to-2D MOF nanosheets have been produced to date. Therefore, we applied topological tools of ToposPro and Cambridge Structural Database for screening 3D MOFs as sources of new 2D nanosheets. Cluster representation uncovered the potential existence of 2D nanosheets as subnets of 3D networks in 3032 structures. Furthermore, parameters of building units, net topologies, and accessible channels were analyzed. The concept was proved by synthesis and successful exfoliation of new compound [Zn4(THIP)(HCO2)3(H2O)4]∙DMF (1), which was assembled from 4,5,6-trihydroxyisophtalic acid (H5THIP) as intralayer linker, formate anions as both intralayer linker and interlayer pillar, and Zn(II) as coordination center. In the compound, H5THIP shows complete deprotonation that is unique for hydroxyisophthalate ligands. The crystalline phase of the compound was studied by SCXRD, PXRD, FTIR, and TGA measurements. Nanosheets of height 0.1–90 nm and lateral sizes above 400 nm were produced by sonication of crystals in ethanol. The exfoliation was proved by SEM with EDS, PXRD, AFM, TEM, and BET surface measurements.

Structured Deep Graph Clustering Network Based on Consistency Constraint

Graph clustering is an essential task in data analysis. Recently, there has been a notable trend in the application of deep learning in graph clustering. However, it is worth noting that existing deep graph clustering methods primarily focus on the topological information of nodes while overlooking the use of attribute information in the learned feature representations. In addition, they do not address the consistency of the space distribution in attribute and structure clustering results. To tackle these critical issues, a novel structured deep graph clustering network with consistency constraint (CC-DGC) is proposed. The network first constructs an autoencoder to learn and transmit hierarchical attribute information to the graph autoencoder (GAE). Subsequently, the GAE integrates the received hierarchical attribute information with extracted topological information to generate enhanced clustering representations. Moreover, this paper designs a consistency constraint module to promote consistency between the autoencoder and the GAE by optimizing the cluster space distributions they produce. Finally, the feature extraction and clustering classification processes are synchronized and optimized in a self-supervised manner within a unified framework. Extensive experiments illustrate that the proposed CC-DGC demonstrates superiority over the state-of-the-art deep graph clustering methods on five benchmark datasets.

Lost in syllabification. Special cases of geminatio consonantium and syllabarum diuisio through the fringes of the Latin-Greek writing koine

AbstractThe present paper deals with a marginal divergent spelling consisting in the geminatio of a consonant littera in pre- or post-consonantal position. The phenomenon is found in both Latin and Greek non-literary texts. The analysis is conducted on two levels, one grapho-phonological and one historical. In fact, the phenomenon results to be particularly relevant as for the relation between spelling and syllabic representation of heterosyllabic clusters and as for the dimension of contact between Latin and Greek scripts. First, a synchronic cut of Latin non-literary texts is examined to evaluate the occurrence of this geminatio and its ratio of distribution along the different types of clusters. It can be stated that the geminatio at hand represents a metagraphic signal of syllab(ific)ation indeterminacy, as is further corroborated by the examination of metalinguistic sources. Secondly, the historical perspective is then addressed. This spelling can be interpreted as a feature, albeit marginal and stemming from ephemeral slips, of writing koine, as is further evidenced by the examination of two sample clusters of texts.

Mapping of Government’s Communication Strategies in the COVID-19 Era on Social Media

This study explores the changing government communication methods throughout the unusual COVID-19 epidemic, with a focus on using social media as the main instrument for engaging with the public. We utilize a bibliometric methodology, examining an extensive dataset of articles obtained from journals indexed in Scopus. Using VOSviewer software, we provide a visual representation of the main theme clusters in this research. NVivo 12 Plus also supports word cloud analysis, which allows for the discovery of commonly used phrases and patterns within the analyzed material. The results of study reveals a range of communication strategies adopted by governments globally in response to the pandemic. These measures involve promoting communication in both directions, utilizing social media platforms to spread information, and using efficient strategies to communicate risks. The data demonstrates a predominance of research that specifically examines risk communication driven by the government, emphasizing its vital role in crisis management. In addition, the VOSviewer mapping reveals the presence of four unique theme clusters. The "government communication" cluster focuses on subjects such as communication strategy, the ongoing epidemic, the challenge of fake news, and the influence on public anxiety. These areas are key to the research and investigation within this cluster. This comprehensive analysis illuminates the complex correlation between social media communication techniques and successful public health actions amidst a worldwide crisis.

Multi-scale graph clustering network

Deep graph clustering, a fundamental yet formidable task in data analysis, aims to partition samples belonging to the same category into their respective clusters. Recently, significant advancements in graph self-supervised learning have been made through generative and contrastive learning methods. However, existing methods focus on directly aggregating neighboring node information during the feature extraction stage, thereby neglecting the crucial long-range correlations between nodes. Consequently, non-neighbor node information within the same category remains unexplored, leading to subpar performance in the clustering task. To address this issue, we propose a generative method named Multi-scale Graph Clustering Network (MGCN) to learn comprehensive and rich graph representations for deep graph clustering in the feature encoding stage. Specifically, we design a Multi-hop Adaptive Convolutional Module (MACM) integrated into MGCN, which effectively aggregates high-order neighbor node features in each layer of the network. Additionally, we develop an autoencoder to assist MACM in enhancing attribute information, which prevents the node's own features from being overshadowed in the multi-scale feature learning process. Experimental results demonstrate that our proposed MGCN method achieves significantly better clustering performance than existing methods on multiple public datasets.

Multi-model approach for wind resource assessment

This study presents a multi-model approach for wind resource assessment of a wind farm affected by external wakes. The Weather Research and Forecasting model (WRF), a mesoscale model, is employed to simulate external wind farm wakes, while the Farm Optimization and eXtended yield Evaluation Software (FOXES), an engineering model, is used to simulate the wind farm of interest. This hybrid approach addresses the limitation of both models, mainly the lack of layout effects in mesoscale models and the poor representation of cluster wakes in engineering models. A case study, focusing on the Kaskasi wind farm in the Heligoland cluster, shows that the WRF model predicts larger wake losses compared to FOXES, with the multi-model approach yielding intermediate results. Systematic differences are found as a function of wind speed and seasonality, while the models behave differently as a function of turbulence intensity. The external wake effect was clearly identified for one wind direction sector in WRF and the multi-model approach, while FOXES failed to represent this. The proposed methodology does not only enhance classic resource assessment, but also facilitates efficient layout optimization using cluster waked inflow and allows for wind farm control studies, contributing to both planning and operational phases of wind farm management.

Sampling clustering based on multi-view attribute structural relations.

In light of the exponential growth in information volume, the significance of graph data has intensified. Graph clustering plays a pivotal role in graph data processing by jointly modeling the graph structure and node attributes. Notably, the practical significance of multi-view graph clustering is heightened due to the presence of diverse relationships within real-world graph data. Nonetheless, prevailing graph clustering techniques, predominantly grounded in deep learning neural networks, face challenges in effectively handling multi-view graph data. These challenges include the incapability to concurrently explore the relationships between multiple view structures and node attributes, as well as difficulties in processing multi-view graph data with varying features. To tackle these issues, this research proposes a straightforward yet effective multi-view graph clustering approach known as SLMGC. This approach uses graph filtering to filter noise, reduces computational complexity by extracting samples based on node importance, enhances clustering representations through graph contrastive regularization, and achieves the final clustering outcomes using a self-training clustering algorithm. Notably, unlike neural network algorithms, this approach avoids the need for intricate parameter settings. Comprehensive experiments validate the supremacy of the SLMGC approach in multi-view graph clustering endeavors when contrasted with prevailing deep neural network techniques.

Percolation transition for random forests in d⩾3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$d\\geqslant 3$\\end{document}

The arboreal gas is the probability measure on (unrooted spanning) forests of a graph in which each forest is weighted by a factor β>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\beta >0$\\end{document} per edge. It arises as the q→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$q\ o 0$\\end{document} limit of the q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$q$\\end{document}-state random cluster model with p=βq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$p=\\beta q$\\end{document}. We prove that in dimensions d⩾3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$d\\geqslant 3$\\end{document} the arboreal gas undergoes a percolation phase transition. This contrasts with the case of d=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$d=2$\\end{document} where no percolation transition occurs.The starting point for our analysis is an exact relationship between the arboreal gas and a non-linear sigma model with target space the fermionic hyperbolic plane H0|2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbb{H}^{0|2}$\\end{document}. This latter model can be thought of as the 0-state Potts model, with the arboreal gas being its random cluster representation. Unlike the standard Potts models, the H0|2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbb{H}^{0|2}$\\end{document} model has continuous symmetries. By combining a renormalisation group analysis with Ward identities we prove that this symmetry is spontaneously broken at low temperatures. In terms of the arboreal gas, this symmetry breaking translates into the existence of infinite trees in the thermodynamic limit. Our analysis also establishes massless free field correlations at low temperatures and the existence of a macroscopic tree on finite tori.

AI-Enhanced evaluation of YouTube content on post-surgical incontinence following pelvic cancer treatment

BackgroundSeveral pelvic area cancers exhibit high incidence rates, and their surgical treatment can result in adverse effects such as urinary and fecal incontinence, significantly impacting patients' quality of life. Post-surgery incontinence is a significant concern, with prevalence rates ranging from 25 to 45% for urinary incontinence and 9–68% for fecal incontinence. Cancer survivors are increasingly turning to YouTube as a platform to connect with others, yet caution is warranted as misinformation is prevalent. ObjectiveThis study aims to evaluate the information quality in YouTube videos about post-surgical incontinence after pelvic area cancer surgery. MethodsA YouTube search for "Incontinence after cancer surgery" yielded 108 videos, which were subsequently analyzed. To evaluate these videos, several quality assessment tools were utilized, including DISCERN, GQS, JAMA, PEMAT, and MQ-VET. Statistical analyses, such as descriptive statistics and intercorrelation tests, were employed to assess various video attributes, including characteristics, popularity, educational value, quality, and reliability. Also, artificial intelligence techniques like PCA, t-SNE, and UMAP were used for data analysis. HeatMap and Hierarchical Clustering Dendrogram techniques validated the Machine Learning results. ResultsThe quality scales presented a high level of correlation one with each other (p < 0.01) and the Artificial Intelligence-based techniques presented clear clustering representations of the dataset samples, which were reinforced by the Heat Map and Hierarchical Clustering Dendrogram. ConclusionsYouTube videos on "Incontinence after Cancer Surgery" present a "High" quality across multiple scales. The use of AI tools, like PCA, t-SNE, and UMAP, is highlighted for clustering large health datasets, improving data visualization, pattern recognition, and complex healthcare analysis.

Comparative Study on Automated Reference Summary Generation using BERT Models and ROUGE Score Assessment

Automatic text summarization is a sub-area in text mining in which a computer system determines the most informative information in the original text to produce a summary for certain jobs and users. In the development of the systems, one of the most important tasks is to evaluate the quality of summaries produced by the systems. Generally, the evaluation task becomes laborious, time-consuming, and expensive because it requires significant efforts on annotation tasks for humans to manually create reference summaries. Being able to generate automatic reference summaries would promote the development of summarization systems in term of speed and evaluation. In this paper, we proposed an Auto-Ref Summary Generation framework for automatically generating reference summaries used in the generic text summarization evaluation task, the Sliced Summary. Given a set of clusters from a cluster ground-truth label dataset, variants of BERT models were utilized for creating cluster representations. The automatic reference summaries were later generated through a centroid-based summarization approach. Overall, DistilBERT, ROBERTa, and SBERT have played crucial roles in automatic summary generation, achieving the highest ROUGE-1 score of 0.47060. However, this does not meet our expectation on text coherence and readability aspects. Although the summaries generated through our proposed framework could not be used as the replacement of the manual summaries, this study has shed new light on the acquisition of automatic reference summaries from a ground-truth label dataset.

Clustering index analysis on EMG-Torque relation-based representation of complex neuromuscular changes after spinal cord injury

Spinal cord injury (SCI) resulting in complex neuromuscular pathology is not sufficiently well understood. To better quantify neuromuscular changes after SCI, this study uses a clustering index (CI) method for surface electromyography (sEMG) clustering representation to investigate the relation between sEMG and torque in SCI survivors. The sEMG signals were recorded from 13 subjects with SCI and 13 gender-age matched able-bodied subjects during isometric contraction of the biceps brachii muscle at different torque levels using a linear electrode array. Two torque representations, maximum voluntary contraction (MVC%) and absolute torque, were used. CI values were calculated for sEMG. Regression analyses were performed on CI values and torque levels of elbow flexion, revealing a strong linear relationship. The slopes of regressions between SCI survivors and control subjects were compared. The findings indicated that the range of distribution of CI values and slopes was greater in subjects with SCI than in control subjects (p < 0.05). The increase or decrease in slope was also observed at the individual level. This suggests that the CI and its sEMG clustering-torque relation may serve as valuable quantitative indicators for determining neuromuscular lesions after SCI, contributing to the development of effective rehabilitation strategies for improving motor performance.

The Cluster Complex for Cluster Poisson Varieties and Representations of Acyclic Quivers

Abstract Let $\mathcal{X}$ be a skew-symmetrizable cluster Poisson variety. The cluster complex $\Delta ^{+}(\mathcal{X})$ was introduced in [ 12]. It codifies the theta functions on $\mathcal{X}$ that restrict to a character of a seed torus. Every seed $\textbf{s}$ for $\mathcal{X}$ determines a fan realization $\underline{\Delta ^{+}_{\textbf{s}}(\mathcal{X})}$ of $\Delta ^{+}(\mathcal{X})$. For every $\textbf{s}$ we provide a simple and explicit description of the cones of $\underline{\Delta ^{+}_{\textbf{s}}(\mathcal{X})}$ and their facets using c-vectors. Moreover, we give formulas for the theta functions parametrized by the integral points of $\underline{\Delta ^{+}_{\textbf{s}}(\mathcal{X})}$ in terms of $F$-polynomials. In case $\mathcal{X}$ is skew-symmetric and the quiver $Q$ associated to $\textbf{s}$ is acyclic, we describe the normal vectors of the supporting hyperplanes of the cones of $\underline{\Delta ^{+}_{\textbf{s}}(\mathcal{X})}$ using g-vectors of (non-necessarily rigid) objects in $\textsf{K}^{\textrm{b}}(\textrm{proj} \; kQ)$.

Study of Raman Scattering of Light in Liquid Arenes and Their Halogen-Substituted ones in the Low-Frequency Region of the Spectrum

Purpose. Investigation of Raman scattering of light in liquid arenas and their halogenated ones in the low-frequency range of the spectrum, taking into account the clustering processes in their structure.Methods. Raman spectroscopy methods were used, as well as a modeling method using cluster representations of the structure of liquids. Raman spectra of light in the low-frequency range from 17 to 500 cm–1 were obtained using a LabRAM HR Evolution spectrometer at room temperature (23°C).Results. The analysis of theoretical and experimental work on the properties of dimeric configurations of benzene and on the effect of clustering processes in substances on their IR and Raman spectra is carried out. Low-frequency Raman spectra of liquid benzene, o-xylene, ethylbenzene, fluorobenzene, chlorobenzene, brombenzene, toluene, o-fluorotoluene, m-fluorotoluene, p-fluorotoluene, o-chlorotoluene, m-chlorotoluene, p-chlorotoluene, 2,4-dichlorotoluene, 2,6-dichlorotoluene were obtained. The model of formation and disintegration of cluster formations has been tested. Formulas have been obtained for estimating the minimum frequency of libration oscillations of the ωmin dimer formation in the cluster structure and the position of the maxima of spectral bands in the low-frequency region of the Raman spectrum, depending on the number of particles included in the cluster formations. The theoretical results obtained by ωmin are in satisfactory agreement with the experimental data within the total error.The proposed model makes it possible to predict the position of some spectral bands of the Raman spectrum. The presence of other spectral bands is obviously related to the multiparticle interaction in the cluster structure and requires additional research.Conclusion. The proposed model of formation and decay of cluster formations and the relations following from it allow us to estimate the value of the minimum frequency in the low-frequency range of the Raman spectrum of liquid arenes and their halogenated ones from the known values of the enthalpy of formation and the moment of inertia of the dimer. Conversely, using known values of the minimum frequency, the values of the enthalpy of formation and the moment of inertia of the dimer can be estimated without resorting to complex quantum mechanical calculations.