Journal articles on the topic 'Dirichlet environments'
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Man, Jun Feng, Hai Yu Lin, Qian Qian Li, and Xiang Bing Wen. "Segmentation and Tracking of Human in Crowded Environments." Advanced Materials Research 255-260 (May 2011): 2281–85. http://dx.doi.org/10.4028/www.scientific.net/amr.255-260.2281.
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The occlusion problem in crowded people environment makes human segmentation and tracking more difficult in video surveillance. Thus, a human segmentation method combing human model with body edge curve is presented. Because segmentation may result in serious defect and distortion, robust BP neural network model is adopted as tracking mode. For improving autonomous learning ability of BP network, Hierarchical Dirichlet Process (HDP) is used to decide whether new types of human body characteristic data is generated, which provides decision basis for BP network learning. The simulation experiments confirm that the method presented in this paper can effectively solve the problem of partial human body occlusion. Meanwhile, this method has unique advantage of simplicity and real-time over others.
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Petitgirard, Julien, Tony Piguet, Philippe Baucour, Didier Chamagne, Eric Fouillien, and Jean-Christophe Delmare. "Steady State and 2D Thermal Equivalence Circuit for Winding Heads—A New Modelling Approach." Mathematical and Computational Applications 25, no. 4 (October 18, 2020): 70. http://dx.doi.org/10.3390/mca25040070.
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The study concerns the winding head thermal design of electrical machines in difficult thermal environments. The new approach is adapted for all basic shapes and solves the thermal behaviour of a random wire layout. The model uses the nodal method but does not use the common homogenization method for the winding slot. The layout impact can be precisely studied to find different hotspots. To achieve this a Delaunay triangulation provides the thermal links between adjoining wires in the slot. Voronoï tessellation gives a cutting to estimate thermal conductance between adjoining wires. This thermal behaviour is simulated in cell cutting and it is simplified with the thermal bridge notion to obtain a simple solving of these thermal conductances. The boundaries are imposed on the slot borders with Dirichlet condition. Then solving with many Dirichlet conditions is described. Some results show different possible applications with rectangular and round shapes, one ore many boundaries, different limit condition values and different layouts. The model can be integrated into a larger model that represents the stator to have best results.
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Ahmad, Bashir, and Juan J. Nieto. "Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions." International Journal of Differential Equations 2010 (2010): 1–10. http://dx.doi.org/10.1155/2010/649486.
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We study a Dirichlet boundary value problem for Langevin equation involving two fractional orders. Langevin equation has been widely used to describe the evolution of physical phenomena in fluctuating environments. However, ordinary Langevin equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractal medium, numerous generalizations of Langevin equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Langevin equation. This gives rise to the fractional Langevin equation with a single index. Recently, a new type of Langevin equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space.
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Zhang, Kai, Ming Li, and Jingzhi Li. "Estimation of Impacts of Removing Arbitrarily Constrained Domain Details to the Analysis of Incompressible Fluid Flows." Communications in Computational Physics 20, no. 4 (October 2016): 944–68. http://dx.doi.org/10.4208/cicp.071015.050216a.
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AbstractRemoving geometric details from the computational domain can significantly reduce the complexity of downstream task of meshing and simulation computation, and increase their stability. Proper estimation of the sensitivity analysis error induced by removing such domain details, called defeaturing errors, can ensure that the sensitivity analysis fidelity can still be met after simplification. In this paper, estimation of impacts of removing arbitrarily constrained domain details to the analysis of incompressible fluid flows is studied with applications to fast analysis of incompressible fluid flows in complex environments. The derived error estimator is applicable to geometric details constrained by either Dirichlet or Neumann boundary conditions, and has no special requirements on the outer boundary conditions. Extensive numerical examples were presented to demonstrate the effectiveness and efficiency of the proposed error estimator.
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Gurcan, Fatih, Ozcan Ozyurt, and Nergiz Ercil Cagitay. "Investigation of Emerging Trends in the E-Learning Field Using Latent Dirichlet Allocation." International Review of Research in Open and Distributed Learning 22, no. 2 (January 14, 2021): 1–18. http://dx.doi.org/10.19173/irrodl.v22i2.5358.
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E-learning studies are becoming very important today as they provide alternatives and support to all types of teaching and learning programs. The effect of the COVID-19 pandemic on educational systems has further increased the significance of e-learning. Accordingly, gaining a full understanding of the general topics and trends in e-learning studies is critical for a deeper comprehension of the field. There are many studies that provide such a picture of the e-learning field, but the limitation is that they do not examine the field as a whole. This study aimed to investigate the emerging trends in the e-learning field by implementing a topic modeling analysis based on latent Dirichlet allocation (LDA) on 41,925 peer-reviewed journal articles published between 2000 and 2019. The analysis revealed 16 topics reflecting emerging trends and developments in the e-learning field. Among these, the topics “MOOC,” “learning assessment,” and “e-learning systems” were found to be key topics in the field, with a consistently high volume. In addition, the topics of “learning algorithms,” “learning factors,” and “adaptive learning” were observed to have the highest overall acceleration, with the first two identified as having a higher acceleration in recent years. Going by these results, it is concluded that the next decade of e-learning studies will focus on learning factors and algorithms, which will possibly create a baseline for more individualized and adaptive mobile platforms. In other words, after a certain maturity level is reached by better understanding the learning process through these identified learning factors and algorithms, the next generation of e-learning systems will be built on individualized and adaptive learning environments. These insights could be useful for e-learning communities to improve their research efforts and their applications in the field accordingly.
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Abrashina-Zhadaeva, N., and N. Romanova. "Vector Additive Decomposition for 2D Fractional Diffusion Equation." Nonlinear Analysis: Modelling and Control 13, no. 2 (April 25, 2008): 137–43. http://dx.doi.org/10.15388/na.2008.13.2.14574.
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Such physical processes as the diffusion in the environments with fractal geometry and the particles’ subdiffusion lead to the initial value problems for the nonlocal fractional order partial differential equations. These equations are the generalization of the classical integer order differential equations.
An analytical solution for fractional order differential equation with the constant coefficients is obtained in [1] by using Laplace-Fourier transform. However, nowadays many of the practical problems are described by the models with variable coefficients.
In this paper we discuss the numerical vector decomposition model which is based on a shifted version of usual Gr¨unwald finite-difference approximation [2] for the non-local fractional order operators. We prove the unconditional stability of the method for the fractional diffusion equation with Dirichlet boundary conditions. Moreover, a numerical example using a finite difference algorithm for 2D fractional order partial differential equations is also presented and compared with the exact analytical solution.
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Anedda, Claudia, and Fabrizio Cuccu. "Optimal location of resources and Steiner symmetry in a population dynamics model in heterogeneous environments." Annales Fennici Mathematici 47, no. 1 (January 13, 2022): 305–24. http://dx.doi.org/10.54330/afm.113547.
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The subject of this paper is inspired by Cantrell and Cosner (1989) and Cosner, Cuccu and Porru (2013). Cantrell and Cosner (1989) investigate the dynamics of a population in heterogeneous environments by means of diffusive logistic equations. An important part of their study consists in finding sufficient conditions which guarantee the survival of the species. Mathematically, this task leads to the weighted eigenvalue problem \(-\Delta u =\lambda m u \) in a bounded smooth domain \(\Omega\subset \mathbb{R}^N\), \(N\geq 1\), under homogeneous Dirichlet boundary conditions, where \(\lambda \in \mathbb{R}\) and \(m\in L^\infty(\Omega)\). The domain \(\Omega\) represents the environment and \(m(x)\), called the local growth rate, says where the favourable and unfavourable habitats are located. Then, Cantrell and Cosner (1989) consider a class of weights \(m(x)\) corresponding to environments where the total sizes of favourable and unfavourable habitats are fixed, but their spatial arrangement is allowed to change; they determine the best choice among them for the population to survive.
In our work we consider a sort of refinement of the result above. We write the weight \(m(x)\) as sum of two (or more) terms, i.e. \(m(x)=f_1(x)+f_2(x)\), where \(f_1(x)\) and \(f_2(x)\) represent the spatial densities of the two resources which contribute to form the local growth rate \(m(x)\). Then, we fix the total size of each resource allowing its spatial location to vary. As our first main result, we show that there exists an optimal choice of \(f_1(x)\) and \(f_2(x)\) and find the form of the optimizers. Our proof relies on some results in Cosner, Cuccu and Porru (2013) and on a new property (to our knowledge) about the classes of rearrangements of functions. Moreover, we show that if \(\Omega\) is Steiner symmetric, then the best arrangement of the resources inherits the same kind of symmetry. (Actually, this is proved in the more general context of the classes of rearrangements of measurable functions.
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Lindgren, Charlie, Asif M. Huq, and Kenneth Carling. "Who Are the Intended Users of CSR Reports? Insights from a Data-Driven Approach." Sustainability 13, no. 3 (January 21, 2021): 1070. http://dx.doi.org/10.3390/su13031070.
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There is extant research on theorization, conceptualization, determinants, and consequences of corporate social responsibility (CSR). However, what firms include in their CSR or sustainability reports are much less covered and are predominantly covered in case studies of individual firms. In this paper, we instead take a holistic view and simultaneously explore what firms around the globe currently disclose in these reports, more specifically we investigate if firms are shareholder or stakeholder focused. In this investigation, we check the alignment of the reports to the materiality framework of Sustainability Accounting Standards Board (SASB) which was developed having shareholders as the intended user. To estimate what firms disclose in CSR reports we used the unsupervised Bayesian machine learning approach latent Dirichlet allocation (LDA) developed by Blei et al. We conclude that firms target shareholders as the intended users of these reports, even in environments where stakeholder approach of management is argued to be more dominant. Methodologically, we contribute by demonstrating that topic modeling can enhance the objectivity in reviewing CSR-reports.
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Alahmari, Nala, Sarah Alswedani, Ahmed Alzahrani, Iyad Katib, Aiiad Albeshri, and Rashid Mehmood. "Musawah: A Data-Driven AI Approach and Tool to Co-Create Healthcare Services with a Case Study on Cancer Disease in Saudi Arabia." Sustainability 14, no. 6 (March 11, 2022): 3313. http://dx.doi.org/10.3390/su14063313.
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The sustainability of human existence is in dire danger and this threat applies to our environment, societies, and economies. Smartization of cities and societies has the potential to unite individuals and nations towards sustainability as it requires engaging with our environments, analyzing them, and making sustainable decisions regulated by triple bottom line (TBL). Poor healthcare systems affect individuals, societies, the planet, and economies. This paper proposes a data-driven artificial intelligence (AI) based approach called Musawah to automatically discover healthcare services that can be developed or co-created by various stakeholders using social media analysis. The case study focuses on cancer disease in Saudi Arabia using Twitter data in the Arabic language. Specifically, we discover 17 services using machine learning from Twitter data using the Latent Dirichlet Allocation algorithm (LDA) and group them into five macro-services, namely, Prevention, Treatment, Psychological Support, Socioeconomic Sustainability, and Information Availability. Subsequently, we show the possibility of finding additional services by employing a topical search over the dataset and have discovered 42 additional services. We developed a software tool from scratch for this work that implements a complete machine learning pipeline using a dataset containing over 1.35 million tweets we curated during September–November 2021. Open service and value healthcare systems based on freely available information can revolutionize healthcare in manners similar to the open-source revolution by using information made available by the public, the government, third and fourth sectors, or others, allowing new forms of preventions, cures, treatments, and support structures.
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Sabot, Christophe, and Laurent Tournier. "Reversed Dirichlet environment and directional transience of random walks in Dirichlet environment." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 47, no. 1 (February 2011): 1–8. http://dx.doi.org/10.1214/09-aihp344.
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Kim, Cho-Myong, A.-Ram Jo, and Yang-Kyun Kim. "Reviews Analysis of Korean Clinics Using LDA Topic Modeling." Journal of Korean Medicine 43, no. 1 (March 1, 2022): 73–86. http://dx.doi.org/10.13048/jkm.22007.
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Objectives: In the health care industry, the influence of online reviews is growing. As medical services are provided mainly by providers, those services have been managed by hospitals and clinics. However, direct promotions of medical services by providers are legally forbidden. Due to this reason, consumers, like patients and clients, search a lot of reviews on the Internet to get any information about hospitals, treatments, prices, etc. It can be determined that online reviews indicate the quality of hospitals, and that analysis should be done for sustainable hospital marketing.Method: Using a Python-based crawler, we collected reviews, written by real patients, who had experienced Korean medicine, about more than 14,000 reviews. To extract the most representative words, reviews were divided by positive and negative; after that reviews were pre-processed to get only nouns and adjectives to get TF(Term Frequency), DF(Document Frequency), and TF-IDF(Term Frequency – Inverse Document Frequency). Finally, to get some topics about reviews, aggregations of extracted words were analyzed by using LDA(Latent Dirichlet Allocation) methods. To avoid overlap, the number of topics is set by Davis visualization.Results and Conclusions: 6 and 3 topics extracted in each positive/negative review, analyzed by LDA Topic Model. The main factors, consisting of topics were 1) Response to patients and customers. 2) Customized treatment (consultation) and management. 3) Hospital/Clinic’s environments.
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Saura and Bennett. "A Three-Stage method for Data Text Mining: Using UGC in Business Intelligence Analysis." Symmetry 11, no. 4 (April 10, 2019): 519. http://dx.doi.org/10.3390/sym11040519.
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The global development of the Internet, which has enabled the analysis of large amounts of data and the services linked to their use, has led companies to modify their business strategies in search of new ways to increase marketing productivity and profitability. Many strategies are based on business intelligence (BI) and marketing intelligence (MI) that make it possible to extract profitable knowledge and insights from large amounts of data generated by company customers in digital environments. In this context, the present study proposes a three-step research methodology based on data text mining (DTM). In further research, this methodology can be used for business intelligence analysis (BIA) strategies to analyze user generated content (UGC) in social networks and on digital platforms. The proposed methodology unfolds in the following three stages. First, a Latent Dirichlet Allocation (LDA) model that determines the database topic is used. Second, a sentiment analysis (SA) is proposed. This SA is applied to the LDA results to divide the topics identified in the sample into three sentiments. Thirdly, textual analysis (TA) with data text mining techniques is applied on the topics in each sentiment. The proposed methodology offers important advances in data text mining in terms of accuracy, reliability and insight generation for both researchers and practitioners seeking to improve the BIA processes in business and other sectors.
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Sabot, Christophe, and Nathanaël Enriquez. "Random Walks in a Dirichlet Environment." Electronic Journal of Probability 11 (2006): 802–16. http://dx.doi.org/10.1214/ejp.v11-350.
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Sabot, Christophe, and Laurent Tournier. "Random walks in Dirichlet environment: an overview." Annales de la faculté des sciences de Toulouse Mathématiques 26, no. 2 (2017): 463–509. http://dx.doi.org/10.5802/afst.1542.
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Park, Yumin, and Yong-Wook Shin. "Trend Analysis of Pet Plants Before and After COVID-19 Outbreak Using Topic Modeling: Focusing on Big Data of News Articles from 2018 to 2021." Journal of People, Plants, and Environment 24, no. 6 (December 31, 2021): 563–72. http://dx.doi.org/10.11628/ksppe.2021.24.6.563.
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Background and objective The ongoing COVID-19 pandemic restricted daily life, forcing people to spend time indoors. With the growing interest in mental health issues and residential environments, ‘pet plants’ have been receiving attention during the unprecedented social distancing measures. This study aims to analyze the change in trends of pet plants before and during the COVID-19 pandemic and provide basic data for studies related to pet plants and directions of future development. Methods A total of 2,016 news articles using the keyword ‘pet plants’ were collected on Naver News from January 1, 2018 to August 15, 2019 (609 articles) and January 1, 2020 to August 15, 2021 (1,407 articles). The texts were tokenized into words using KoNLPy package, ultimately coming up with 63,597 words. The analyses included frequency of keywords and topic modeling based on Latent Dirichlet Allocation (LDA) to identify the inherent meanings of related words and each topic. Results Topic modeling generated three topics in each period (before and during the COVID-19), and the results showed that pet plants in daily life have become the object of ‘emotional support’ and ‘healing’ during social distancing. In particular, pet plants, which had been distributed as a solution to prevent solitary deaths and depression among seniors living alone, are now expanded to help resolve the social isolation of the general public suffering from COVID-19. The new term ‘plant butler’ became a new trend, and there was a change in the trend in which people shared their hobbies and information about pet plants and communicated with others in online. Conclusion Based on these findings, the trend data of pet plants before and after the outbreak of COVID-19 can provide the basis for activating research on pet plants and setting the direction for development of related industries considering the continuous popularity and trend of indoor gardening and green hobby.
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Zimbelman, Eloise G., and Robert F. Keefe. "Lost in the woods: Forest vegetation, and not topography, most affects the connectivity of mesh radio networks for public safety." PLOS ONE 17, no. 12 (December 7, 2022): e0278645. http://dx.doi.org/10.1371/journal.pone.0278645.
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Real-time data- and location-sharing using mesh networking radios paired with smartphones may improve situational awareness and safety in remote environments lacking communications infrastructure. Despite being increasingly used for wildland fire and public safety applications, there has been little formal evaluation of the network connectivity of these devices. The objectives of this study were to 1) characterize the connectivity of mesh networks in variable forest and topographic conditions; 2) evaluate the abilities of lidar and satellite remote sensing data to predict connectivity; and 3) assess the relative importance of the predictive metrics. A large field experiment was conducted to test the connectivity of a network of one mobile and five stationary goTenna Pro mesh radios on 24 Public Land Survey System sections approximately 260 ha in area in northern Idaho. Dirichlet regression was used to predict connectivity using 1) both lidar- and satellite-derived metrics (LIDSAT); 2) lidar-derived metrics only (LID); and 3) satellite-derived metrics only (SAT). On average the full network was connected only 32.6% of the time (range: 0% to 90.5%) and the mobile goTenna was disconnected from all other devices 18.2% of the time (range: 0% to 44.5%). RMSE for the six connectivity levels ranged from 0.101 to 0.314 for the LIDSAT model, from 0.103 to 0.310 for the LID model, and from 0.121 to 0.313 for the SAT model. Vegetation-related metrics affected connectivity more than topography. Developed models may be used to predict the connectivity of real-time mesh networks over large spatial extents using remote sensing data in order to forecast how well similar networks are expected to perform for wildland firefighting, forestry, and public safety applications. However, safety professionals should be aware of the impacts of vegetation on connectivity.
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Tournier, Laurent. "Asymptotic direction of random walks in Dirichlet environment." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 51, no. 2 (May 2015): 716–26. http://dx.doi.org/10.1214/13-aihp582.
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Skeen, Simone J., Stephen Scott Jones, Carolyn Marie Cruse, and Keith J. Horvath. "Integrating Natural Language Processing and Interpretive Thematic Analyses to Gain Human-Centered Design Insights on HIV Mobile Health: Proof-of-Concept Analysis." JMIR Human Factors 9, no. 3 (July 21, 2022): e37350. http://dx.doi.org/10.2196/37350.
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Background HIV mobile health (mHealth) interventions often incorporate interactive peer-to-peer features. The user-generated content (UGC) created by these features can offer valuable design insights by revealing what topics and life events are most salient for participants, which can serve as targets for subsequent interventions. However, unstructured, textual UGC can be difficult to analyze. Interpretive thematic analyses can preserve rich narratives and latent themes but are labor-intensive and therefore scale poorly. Natural language processing (NLP) methods scale more readily but often produce only coarse descriptive results. Recent calls to advance the field have emphasized the untapped potential of combined NLP and qualitative analyses toward advancing user attunement in next-generation mHealth. Objective In this proof-of-concept analysis, we gain human-centered design insights by applying hybrid consecutive NLP-qualitative methods to UGC from an HIV mHealth forum. Methods UGC was extracted from Thrive With Me, a web app intervention for men living with HIV that includes an unstructured peer-to-peer support forum. In Python, topics were modeled by latent Dirichlet allocation. Rule-based sentiment analysis scored interactions by emotional valence. Using a novel ranking standard, the experientially richest and most emotionally polarized segments of UGC were condensed and then analyzed thematically in Dedoose. Design insights were then distilled from these themes. Results The refined topic model detected K=3 topics: A: disease coping; B: social adversities; C: salutations and check-ins. Strong intratopic themes included HIV medication adherence, survivorship, and relationship challenges. Negative UGC often involved strong negative reactions to external media events. Positive UGC often focused on gratitude for survival, well-being, and fellow users’ support. Conclusions With routinization, hybrid NLP-qualitative methods may be viable to rapidly characterize UGC in mHealth environments. Design principles point toward opportunities to align mHealth intervention features with the organically occurring uses captured in these analyses, for example, by foregrounding inspiring personal narratives and expressions of gratitude, or de-emphasizing anger-inducing media.
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Sabot, Christophe. "Markov chains in a Dirichlet environment and hypergeometric integrals." Comptes Rendus Mathematique 342, no. 1 (January 2006): 57–62. http://dx.doi.org/10.1016/j.crma.2005.10.028.
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Li, Chenchen, Xiang Yan, Xiaotie Deng, Yuan Qi, Wei Chu, Le Song, Junlong Qiao, Jianshan He, and Junwu Xiong. "Latent Dirichlet Allocation for Internet Price War." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 639–46. http://dx.doi.org/10.1609/aaai.v33i01.3301639.
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Current Internet market makers are facing an intense competitive environment, where personalized price reductions or discounted coupons are provided by their peers to attract more customers. Much investment is spent to catch up with each other’s competitors but participants in such a price cut war are often incapable of winning due to their lack of information about others’ strategies or customers’ preference. We formalize the problem as a stochastic game with imperfect and incomplete information and develop a variant of Latent Dirichlet Allocation (LDA) to infer latent variables under the current market environment, which represents preferences of customers and strategies of competitors. Tests on simulated experiments and an open dataset for real data show that, by subsuming all available market information of the market maker’s competitors, our model exhibits a significant improvement for understanding the market environment and finding the best response strategies in the Internet price war. Our work marks the first successful learning method to infer latent information in the environment of price war by the LDA modeling, and sets an example for related competitive applications to follow.
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Winkler, Michael. "Reaction-Driven Relaxation in Three-Dimensional Keller–Segel–Navier–Stokes Interaction." Communications in Mathematical Physics 389, no. 1 (November 29, 2021): 439–89. http://dx.doi.org/10.1007/s00220-021-04272-y.
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AbstractThe Keller–Segel–Navier–Stokes system $$\begin{aligned} \left\{ \begin{array}{rcll} n_t + u\cdot \nabla n &{}=&{} \Delta n - \chi \nabla \cdot (n\nabla c) + \rho n-\mu n^2,\\ c_t + u\cdot \nabla c &{}=&{} \Delta c-c+n, \\ u_t + (u\cdot \nabla )u &{}=&{} \Delta u + \nabla P + n \nabla \phi + f(x,t), \qquad \nabla \cdot u=0, \end{array} \right. \qquad \qquad (\star ) \end{aligned}$$ n t + u · ∇ n = Δ n - χ ∇ · ( n ∇ c ) + ρ n - μ n 2 , c t + u · ∇ c = Δ c - c + n , u t + ( u · ∇ ) u = Δ u + ∇ P + n ∇ ϕ + f ( x , t ) , ∇ · u = 0 , ( ⋆ ) is considered in a smoothly bounded convex domain $$\Omega \subset \mathbb {R}^3$$ Ω ⊂ R 3 , with $$\phi \in W^{2,\infty }(\Omega )$$ ϕ ∈ W 2 , ∞ ( Ω ) and $$f\in C^1(\bar{\Omega }\times [0,\infty );\mathbb {R}^3)$$ f ∈ C 1 ( Ω ¯ × [ 0 , ∞ ) ; R 3 ) , and with $$\chi >0, \rho \in \mathbb {R}$$ χ > 0 , ρ ∈ R and $$\mu >0$$ μ > 0 . As recent literature has shown, for all reasonably mild initial data a corresponding no-flux/no-flux/Dirichlet initial-boundary value problem possesses a global generalized solution, but the knowledge on its regularity properties has not yet exceeded some information on fairly basic integrability features. The present study reveals that whenever $$\omega >0$$ ω > 0 , requiring that $$\begin{aligned} \frac{\rho }{\min \{\mu ,\mu ^{\frac{3}{2}+\omega }\}} < \eta \end{aligned}$$ ρ min { μ , μ 3 2 + ω } < η with some $$\eta =\eta (\omega )>0$$ η = η ( ω ) > 0 , and that f satisfies a suitable assumption on ultimate smallness, is sufficient to ensure that each of these generalized solutions becomes eventually smooth and classical. Furthermore, under these hypotheses ($$\star $$ ⋆ ) is seen to admit an absorbing set with respect to the topology in $$L^\infty (\Omega )$$ L ∞ ( Ω ) . By trivially applying to the case when $$\mu >0$$ μ > 0 is arbitrary and $$\rho \le 0$$ ρ ≤ 0 , these results especially assert essentially unconditional statements on eventual regularity in taxis-reaction systems interacting with liquid environments, such as arising in contexts of models for broadcast spawning discussed in recent literature.
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VIOLARD, ERIC. "A MATHEMATICAL THEORY AND ITS ENVIRONMENT FOR PARALLEL PROGRAMMING." Parallel Processing Letters 04, no. 03 (September 1994): 313–28. http://dx.doi.org/10.1142/s0129626494000296.
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This paper presents the main concepts of the mathematical theory PEI for parallel programming and emphasizes its derivation power. The mathematical basis of this theory leads to a nice implementation in CENTAUR7 of an environment whose purpose is to transform parallel programs. It is illustrated by two similar examples: the convolution sum and the Dirichlet product. The second one uses non-affine dependencies that can be easily taken into account using PEI.
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van Draanen, Jenna, HaoDong Tao, Saksham Gupta, and Sam Liu. "Geographic Differences in Cannabis Conversations on Twitter: Infodemiology Study." JMIR Public Health and Surveillance 6, no. 4 (October 5, 2020): e18540. http://dx.doi.org/10.2196/18540.
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Background Infodemiology is an emerging field of research that utilizes user-generated health-related content, such as that found in social media, to help improve public health. Twitter has become an important venue for studying emerging patterns in health issues such as substance use because it can reflect trends in real-time and display messages generated directly by users, giving a uniquely personal voice to analyses. Over the past year, several states in the United States have passed legislation to legalize adult recreational use of cannabis and the federal government in Canada has done the same. There are few studies that examine the sentiment and content of tweets about cannabis since the recent legislative changes regarding cannabis have occurred in North America. Objective To examine differences in the sentiment and content of cannabis-related tweets by state cannabis laws, and to examine differences in sentiment between the United States and Canada between 2017 and 2019. Methods In total, 1,200,127 cannabis-related tweets were collected from January 1, 2017, to June 17, 2019, using the Twitter application programming interface. Tweets then were grouped geographically based on cannabis legal status (legal for adult recreational use, legal for medical use, and no legal use) in the locations from which the tweets came. Sentiment scoring for the tweets was done with VADER (Valence Aware Dictionary and sEntiment Reasoner), and differences in sentiment for states with different cannabis laws were tested using Tukey adjusted two-sided pairwise comparisons. Topic analysis to determine the content of tweets was done using latent Dirichlet allocation in Python, using a Java implementation, LdaMallet, with Gensim wrapper. Results Significant differences were seen in tweet sentiment between US states with different cannabis laws (P=.001 for negative sentiment tweets in fully illegal compared to legal for adult recreational use states), as well as between the United States and Canada (P=.003 for positive sentiment and P=.001 for negative sentiment). In both cases, restrictive state policy environments (eg, those where cannabis use is fully illegal, or legal for medical use only) were associated with more negative tweet sentiment than less restrictive policy environments (eg, where cannabis is legal for adult recreational use). Six key topics were found in recent US tweet contents: fun and recreation (keywords, eg, love, life, high); daily life (today, start, live); transactions (buy, sell, money); places of use (room, car, house); medical use and cannabis industry (business, industry, company); and legalization (legalize, police, tax). The keywords representing content of tweets also differed between the United States and Canada. Conclusions Knowledge about how cannabis is being discussed online, and geographic differences that exist in these conversations may help to inform public health planning and prevention efforts. Public health education about how to use cannabis in ways that promote safety and minimize harms may be especially important in places where cannabis is legal for adult recreational and medical use.
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Sabot, Christophe. "Random Dirichlet environment viewed from the particle in dimension $d\ge3$." Annals of Probability 41, no. 2 (March 2013): 722–43. http://dx.doi.org/10.1214/11-aop699.
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Moussa, Rafed. "Discrete Dirichlet forms as traces of Feller’s one-dimensional diffusions." Open Journal of Mathematical Sciences 6, no. 1 (June 21, 2022): 168–76. http://dx.doi.org/10.30538/oms2022.0185.
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Our primary purpose is to compute explicitly traces of the Dirichlet forms related to Feller's one-dimensional diffusions on countable sets via Fukushima's method. For discrete measures, the obtained trace form can be described as a Dirichlet form on the graph.
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Algazin, O. D., and A. V. Kopaev. "A Mixed Boundary Value Problem for the Laplace Equation in a semi-infinite Layer." Mathematics and Mathematical Modeling, no. 5 (February 6, 2021): 1–12. http://dx.doi.org/10.24108/mathm.0520.0000229.
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The paper offers a solution of the mixed Dirichlet-Neumann and Dirichlet-Neumann-Robin boundary value problems for the Laplace equation in the semi-infinite layer, using the previously obtained solution of the mixed Dirichlet-Neumann boundary value problem for a layer.The functions on the right-hand sides of the boundary conditions are considered to be functions of slow growth, in particular, polynomials. The solution to boundary value problems is also sought in the class of functions of slow growth. Continuing the functions on the right-hand sides of the boundary conditions on the upper and lower sides of the semi-infinite layer from the semi-hyperplane to the entire hyperplane, we obtain the Dirichlet-Neumann problem for the layer, the solution of which is known and written in the form of a convolution. If the right-hand sides of the boundary conditions are polynomials, then the solution is also a polynomial. To the solution obtained it is necessary to add the solution of the problem for a semi-infinite layer with homogeneous boundary conditions on the upper and lower sides and with an inhomogeneous boundary condition of Dirichlet, Neumann or Robin on the lateral side. This solution is written as a series. If we take a finite segment of the series, then we obtain a solution that exactly satisfies the Laplace equation and the boundary conditions on the upper and lower sides of the semi-infinite layer and approximately satisfies the boundary condition on the lateral side.An example of solving the Dirichlet-Neumann and Dirichlet-Neumann-Robin problems is considered, describing the temperature field of a semi-infinite plate the upper side of which is heat-isolated, on the lower side the temperature is set in the form of a polynomial, and the lateral side is either heat-isolated, or holds a zero temperature, or has heat exchange with a zero-temperature environment. For the first two Dirichlet-Neumann problems, the solution is obtained in the form of polynomials. For the third Dirichlet-Neumann-Robin problem, the solution is obtained as a sum of a polynomial and a series. If in this solution the series is replaced by a finite segment, then an approximate solution of the problem will be obtained, which approximately satisfies the Robin condition on the lateral side of the semi-infinite layer.
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Ferreira, Johannes T., Tanita Botha, and Andriette Bekker. "Tsallis and Other Generalised Entropy Forms Subject to Dirichlet Mixture Priors." Symmetry 14, no. 6 (May 28, 2022): 1110. http://dx.doi.org/10.3390/sym14061110.
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Entropy indicates a measure of information contained in a complex system, and its estimation continues to receive ongoing focus in the case of multivariate data, particularly that on the unit simplex. Oftentimes the Dirichlet distribution is employed as choice of prior in a Bayesian framework conjugate to the popular multinomial likelihood with K distinct classes, where consideration of Shannon- and Tsallis entropy is of interest for insight detection within the data on the simplex. However, this prior choice only accounts for negatively correlated data, therefore this paper incorporates previously unconsidered mixtures of Dirichlet distributions as potential priors for the multinomial likelihood which addresses the drawback of negative correlation. The power sum functional, as the product moment of the mixture of Dirichlet distributions, is of direct interest in the multivariate case to conveniently access the Tsallis- and other generalized entropies that is incorporated within an estimation perspective of the posterior distribution using real economic data. A prior selection method is implemented to suggest a suitable prior for the consideration of the practitioner; empowering the user in future for consideration of suitable priors incorporating entropy within the estimation environment as well as having the option of certain mixture of Dirichlet distributions that may require positive correlation.
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Taira, Kazuaki. "A Class of Semilinear Parabolic Problems and Analytic Semigroups." Mathematics 10, no. 22 (November 21, 2022): 4381. http://dx.doi.org/10.3390/math10224381.
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(1) Background: This paper is devoted to the study of a class of semilinear initial boundary value problems of parabolic type. (2) Methods: We make use of fractional powers of analytic semigroups and the interpolation theory of compact linear operators due to Lions–Peetre. (3) Results: We give a functional analytic proof of the C2 compactness of a bounded regular solution orbit for semilinear parabolic problems with Dirichlet, Neumann and Robin boundary conditions. (4) Conclusions: As an application, we study the dynamics of a population inhabiting a strongly heterogeneous environment that is modeled by a class of diffusive logistic equations with Dirichlet and Neumann boundary conditions.
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Chauhan, Uttam, and Apurva Shah. "Topic Modeling Using Latent Dirichlet allocation." ACM Computing Surveys 54, no. 7 (September 30, 2022): 1–35. http://dx.doi.org/10.1145/3462478.
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We are not able to deal with a mammoth text corpus without summarizing them into a relatively small subset. A computational tool is extremely needed to understand such a gigantic pool of text. Probabilistic Topic Modeling discovers and explains the enormous collection of documents by reducing them in a topical subspace. In this work, we study the background and advancement of topic modeling techniques. We first introduce the preliminaries of the topic modeling techniques and review its extensions and variations, such as topic modeling over various domains, hierarchical topic modeling, word embedded topic models, and topic models in multilingual perspectives. Besides, the research work for topic modeling in a distributed environment, topic visualization approaches also have been explored. We also covered the implementation and evaluation techniques for topic models in brief. Comparison matrices have been shown over the experimental results of the various categories of topic modeling. Diverse technical challenges and future directions have been discussed.
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Sabot, Christophe. "Random walks in random Dirichlet environment are transient in dimension d ≥ 3." Probability Theory and Related Fields 151, no. 1-2 (May 22, 2010): 297–317. http://dx.doi.org/10.1007/s00440-010-0300-0.
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Tournier, Laurent. "Integrability of exit times and ballisticity for random walks in Dirichlet environment." Electronic Journal of Probability 14 (2009): 431–51. http://dx.doi.org/10.1214/ejp.v14-609.
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Ghoreishi, Afshin, and Roger Logan. "Positive solutions of a class of biological models in a heterogeneous environment." Bulletin of the Australian Mathematical Society 44, no. 1 (August 1991): 79–94. http://dx.doi.org/10.1017/s0004972700029488.
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In this paper we discuss existence of positive solutions to a general nonlinear elliptic system of reaction-diffusion equations representing a predator-prey or competition model of interaction between two species, in a heterogeneous environment. We also consider homogeneous Dirichlet and/or Robin boundary conditions. In the predator-prey case we give necessary and sufficient conditions for the existence of positive solutions, while in the competition case we give sufficient conditions. We use index theory in a positive cone to attack our problem and characterise our results by the sign of the first eigenvalues of certain Schrodinger type operators.
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Van Order, Jeanine. "Dirichlet twists of GL n -automorphic L-functions and hyper-Kloosterman Dirichlet series." Annales de la Faculté des sciences de Toulouse : Mathématiques 30, no. 3 (October 26, 2021): 633–703. http://dx.doi.org/10.5802/afst.1687.
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LÓPEZ, RAFAEL. "WETTING PHENOMENA AND CONSTANT MEAN CURVATURE SURFACES WITH BOUNDARY." Reviews in Mathematical Physics 17, no. 07 (August 2005): 769–92. http://dx.doi.org/10.1142/s0129055x05002443.
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In a microscopic scale or microgravity environment, interfaces in wetting phenomena are usually modeled by surfaces with constant mean curvature (CMC surfaces). Usually, the condition regarding the constancy of the contact angle along the line of separation between different phases is assumed. Although the classical capillary boundary condition is the angle made at the contact line, configurations also occur in which a Dirichlet condition is appropriate. In this article, we discuss those with vanishing boundary conditions, such as those that occur on a thin flat portion of a plate of general shape covered with water. In this paper, we review recent works on the existence of CMC surfaces with non-empty boundary, with a special focus on the Dirichlet problem for the constant mean curvature equation.
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Khalil, Carine, Welmoed van Deen, Taylor Dupuy, Gaurav Syal, Corey Arnold, Susan Cazzetta, Pradeep Nazarey, and Brennan Spiegel. "PATIENTS’ PERSPECTIVES, EXPERIENCES, AND CONCERNS WITH CROHN’S PERIANAL FISTULAE: INSIGHTS FROM SOCIAL MEDIA PLATFORMS." Inflammatory Bowel Diseases 28, Supplement_1 (January 22, 2022): S92—S93. http://dx.doi.org/10.1093/ibd/izac015.149.
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Abstract INTRODUCTION Crohn’s perianal fistulae (CPF) impact the physical, emotional, and social wellbeing of patients. Despite the high biopsychosocial burden of CPF, limited data exist regarding how patients navigate challenges associated with this complication of CD and how they perceive treatments. Social media offers a rich opportunity to gain an in-depth understanding of the impact of CPF on patients’ daily lives outside of controlled environments. In this study, we used social media to examine patients’ experiences and concerns with CPF and assess its impact on their behavior and overall wellbeing. METHODS We used a mixed-method approach to examine 119,986 publicly available posts related to CPF from 10 US CD forums between 1/1/10-1/1/20. We randomly selected 700 posts for qualitative analysis using an inductive thematic approach. A latent Dirichlet allocation probabilistic topic model was applied to explore themes in an unsupervised manner within the collection of the 119,986 posts. Fifty topics were generated and manually reviewed to identify themes, which were compared to the themes identified in the qualitative data analysis. RESULTS We distinguished 4 main themes and several subthemes that were also identified in the qualitative thematic analysis. In 38% of the posts, patients used social media to seek peer-support and information about CPF symptoms, treatments, diet, experimental therapies, natural remedies, and patients’ apprehension regarding treatments. Moreover, 30% of the posts focused on discussions surrounding the biopsychosocial burden of CPF. Patients reported pain and constant discomfort, psychological effects including stress symptoms, distress, and fear, as well as social impact on work and intimate relationships. In 21% of the posts users discussed challenges associated with CPF treatments including financial challenges, unsuccessful procedures/treatments, recurrence of CPF post-treatment, and lack of information on CPF treatments. Lastly, 15% of the posts involved patients’ experiences with medications and surgeries such as efficacy of treatments, side effects experienced and complications. While the quantitative analysis revealed an additional subtheme related to financial challenges and local and topical care, the qualitative analysis revealed an additional subtheme related to patients’ apprehension to undergo treatments (Figure 1). DISCUSSION Social media analysis reveals a dynamic range of themes governing patients’ perspectives and experiences with CPF. The use of a mixed-methods approach generated complementary insights regarding patients’ need for information about CPF, the biopsychosocial burden of CPF, the different encountered challenges with treatment and the difficulty to navigate among available management options. These results highlight a gap in patient educational needs for CPF.
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Kumar, S., and R. C. Tiwari. "Bayes estimation of reliability under a random environment governed by a Dirichlet prior." IEEE Transactions on Reliability 38, no. 2 (June 1989): 218–23. http://dx.doi.org/10.1109/24.31110.
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Zhang, Xiaohong, and Yan Gao. "Multimedia text classification algorithm using potential Dirichlet distribution in mobile cloud computing environment." Multimedia Tools and Applications 79, no. 13-14 (December 6, 2019): 9615–27. http://dx.doi.org/10.1007/s11042-019-08253-1.
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CONRAD, FLORIAN, TORBEN FATTLER, and MARTIN GROTHAUS. "AN INVARIANCE PRINCIPLE FOR THE TAGGED PARTICLE PROCESS IN CONTINUUM WITH SINGULAR INTERACTION POTENTIAL." Infinite Dimensional Analysis, Quantum Probability and Related Topics 16, no. 04 (December 2013): 1350032. http://dx.doi.org/10.1142/s021902571350032x.
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We consider the dynamics of a tagged particle in an infinite particle environment moving according to a stochastic gradient dynamics. For singular interaction potentials this tagged particle dynamics was constructed first in Ref. 7, using closures of pre-Dirichlet forms which were already proposed in Refs. 13 and 24. The environment dynamics and the coupled dynamics of the tagged particle and the environment were constructed separately. Here we continue the analysis of these processes: Proving an essential m-dissipativity result for the generator of the coupled dynamics from Ref. 7, we show that this dynamics does not only contain the environment dynamics (as one component), but is, given the latter, the only possible choice for being the coupled process. Moreover, we identify the uniform motion of the environment as the reversed motion of the tagged particle. (Since the dynamics are constructed as martingale solutions on configuration space, this is not immediate.) Furthermore, we prove ergodicity of the environment dynamics, whenever the underlying reference measure is a pure phase of the system. Finally, we show that these considerations are sufficient to apply Ref. 4 for proving an invariance principle for the tagged particle process. We remark that such an invariance principle was studied before in Ref. 13 for smooth potentials, and shown by abstract Dirichlet form methods in Ref. 24 for singular potentials. Our results apply for a general class of Ruelle measures corresponding to potentials possibly having infinite range, a non-integrable singularity at 0 and a nontrivial negative part, and fulfill merely a weak differentiability condition on ℝd\{0}.
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Kannitha, Diandra Zakeshia Tiara, Mustafid Mustafid, and Puspita Kartikasari. "PEMODELAN TOPIK PADA KELUHAN PELANGGAN MENGGUNAKAN ALGORITMA LATENT DIRICHLET ALLOCATION DALAM MEDIA SOSIAL TWITTER." Jurnal Gaussian 11, no. 2 (August 28, 2022): 266–77. http://dx.doi.org/10.14710/j.gauss.v11i2.35474.
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Large scale social restrictions (PSBB) is a policy issued by the Government of Indonesia as one of the efforts to reduce the spread of the Covid-19 virus. The impact of the policy is that it requires people to conduct activities online . This makes the internet users in Indonesia in the year 2020 up to 73.7%. Each provider must be able to determine strategies in order to maintain the quality of service and customer loyalty. Good reputation for the company is also important, so customers want to use internet services through their company. One of them is by listening to the complaints of the customers towards the company. In this research, modeling the topic of customer complaints carried out using the Latent Dirichlet Allocation Algorithm. The Latent Dirichlet Allocation Algorithm was chosen because the method has good performance. The topic modelling process is carried out using the gibbs sampling estimation. The topic that is often complained to First Media is that internet was turns off while working, while for IndiHome is that the internet often turns off and disconnect. Based on the results of the interpretation, 70% for First Media and 81,81% for IndiHome that these topics had been in accordance with what is complained by customers through their tweets. From the topic that have been known, it can be used as an evaluation for their company in order to maintain service quality and customer loyalty
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Teh, Phoey Lee, Scott Piao, Mansour Almansour, Huey Fang Ong, and Abdul Ahad. "Analysis of Popular Social Media Topics Regarding Plastic Pollution." Sustainability 14, no. 3 (February 1, 2022): 1709. http://dx.doi.org/10.3390/su14031709.
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Plastic pollution is one of the most significant environmental issues in the world. The rapid increase of the cumulative amount of plastic waste has caused alarm, and the public have called for actions to mitigate its impacts on the environment. Numerous governments and social activists from various non-profit organisations have set up policies and actively promoted awareness and have engaged the public in discussions on this issue. Nevertheless, social responsibility is the key to a sustainable environment, and individuals are accountable for performing their civic duty and commit to behavioural changes that can reduce the use of plastics. This paper explores a set of topic modelling techniques to assist policymakers and environment communities in understanding public opinions about the issues related to plastic pollution by analysing social media data. We report on an experiment in which a total of 274,404 tweets were collected from Twitter that are related to plastic pollution, and five topic modelling techniques, including (a) Latent Dirichlet Allocation (LDA), (b) Hierarchical Dirichlet Process (HDP), (c) Latent Semantic Indexing (LSI), (d) Non-Negative Matrix Factorisation (NMF), and (e) extension of LDA—Structural Topic Model (STM), were applied to the data to identify popular topics of online conversations, considering topic coherence, topic prevalence, and topic correlation. Our experimental results show that some of these topic modelling techniques are effective in detecting and identifying important topics surrounding plastic pollution, and potentially different techniques can be combined to develop an efficient system for mining important environment-related topics from social media data on a large scale.
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Oh, Hye-Ra, and Yunjae Cheong. "An Exploratory Study on the Characteristics of Short-Form Advertising Using LDA(Latent Dirichlet Allocation) Topic Modeling." Advertising Research 135 (December 31, 2022): 51–86. http://dx.doi.org/10.16914/ar.2022.135.51.
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null, Conghui Shen, and Jingshi Xu. "Multipliers of Dirichlet-Type Subspaces of Weighted Bloch Spaces." Journal of Mathematical Study 55, no. 3 (June 2022): 229–41. http://dx.doi.org/10.4208/jms.v55n3.22.01.
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Peresypkina, E. V., and V. A. Blatov. "Molecular coordination numbers in crystal structures of organic compounds." Acta Crystallographica Section B Structural Science 56, no. 3 (June 1, 2000): 501–11. http://dx.doi.org/10.1107/s0108768199016675.
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The calculation of molecular coordination numbers (MCNs), and topological and geometrical analysis of the environment of molecules in the crystal structures of 23 067 organic compounds, shows that Kitaigorodskii's close-packing model, assuming the predominance of MCN = 12, works correctly in only a few cases, whereas MCN = 14 is the most frequent. To explain this fact the close-packing model is extended with the model of the thinnest covering of space by deformable molecules. It is shown that the packing of molecules of arbitrary shape and composition can be better described with geometrical, but not topological, parameters of their short-range environment, which is conveniently characterized by molecular Voronoi–Dirichlet polyhedra.
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Mittou, Brahim. "Explicit formulas for sums related to Dirichlet L-functions." Notes on Number Theory and Discrete Mathematics 28, no. 4 (November 11, 2022): 744–48. http://dx.doi.org/10.7546/nntdm.2022.28.4.744-748.
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Let $p\geq3$ be a prime number and let $m, n$ and $l$ be integers with $\gcd(l,p)=1$. Let $\chi$ be a Dirichlet character modulo $p$ and $L(s,\chi)$ be the Dirichlet L-function corresponding to $\chi$. Explicit formulas for: $$\dfrac{2}{p-1} \sum \limits\sb{\underset{\chi(-1)=+1}{\chi\hspace{-0.2cm} \mod p}} \chi(l) L(m,\chi)L(n,\overline{\chi}) \text{ and }\dfrac{2}{p-1} \sum \limits\sb{\underset{\chi(-1)=-1}{\chi\hspace{-0.2cm} \mod p}} \chi(l) L(m,\chi)L(n,\overline{\chi})$$ are given in this paper by using the properties of character sums and Bernoulli polynomials.
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Liu, Yuanyuan, Jingying Chen, Cunjie Shan, Zhiming Su, and Pei Cai. "A Hierarchical Regression Approach for Unconstrained Face Analysis." International Journal of Pattern Recognition and Artificial Intelligence 29, no. 08 (November 22, 2015): 1556011. http://dx.doi.org/10.1142/s021800141556011x.
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Head pose and facial feature detection are important for face analysis. However, many studies reported good results in constrained environment, the performance could be decreased due to the high variations in facial appearance, poses, illumination, occlusion, expression and make-up. In this paper, we propose a hierarchical regression approach, Dirichlet-tree enhanced random forests (D-RF) for face analysis in unconstrained environment. D-RF introduces Dirichlet-tree probabilistic model into regression RF framework in the hierarchical way to achieve the efficiency and robustness. To eliminate noise influence of unconstrained environment, facial patches extracted from face area are classified as positive or negative facial patches, only positive facial patches are used for face analysis. The proposed hierarchical D-RF works in two iterative procedures. First, coarse head pose is estimated to constrain the facial features detection, then the head pose is updated based on the estimated facial features. Second, the facial feature localization is refined based on the updated head pose. In order to further improve the efficiency and robustness, multiple probabilitic models are learned in leaves of the D-RF, i.e. the patch’s classification, the head pose probabilities, the locations of facial points and face deformation models (FDM). Moreover, our algorithm takes a composite weight voting method, where each patch extracted from the image can directly cast a vote for the head pose or each of the facial features. Extensive experiments have been done with different publicly available databases. The experimental results demonstrate that the proposed approach is robust and efficient for head pose and facial feature detection.
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Moss, Fabian C., and Martin Rohrmeier. "Discovering Tonal Profiles with Latent Dirichlet Allocation." Music & Science 4 (January 2021): 205920432110488. http://dx.doi.org/10.1177/20592043211048827.
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Music analysis, in particular harmonic analysis, is concerned with the way pitches are organized in pieces of music, and a range of empirical applications have been developed, for example, for chord recognition or key finding. Naturally, these approaches rely on some operationalization of the concepts they aim to investigate. In this study, we take a complementary approach and discover latent tonal structures in an unsupervised manner. We use the topic model Latent Dirichlet Allocation and apply it to a large historical corpus of musical pieces from the Western classical tradition. This method conceives topics as distributions of pitch classes without assuming a priori that they correspond to either chords, keys, or other harmonic phenomena. To illustrate the generative process assumed by the model, we create an artificial corpus with arbitrary parameter settings and compare the sampled pieces to real compositions. The results we obtain by applying the topic model to the musical corpus show that the inferred topics have music-theoretically meaningful interpretations. In particular, topics cover contiguous segments on the line of fifths and mostly correspond to diatonic sets. Moreover, tracing the prominence of topics over the course of music history over [Formula: see text]600 years reflects changes in the ways pitch classes are employed in musical compositions and reveals particularly strong changes at the transition from common-practice to extended tonality in the 19th century.
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Gutlyanskii, V., V. Ryazanov, E. Sevost'yanov, and E. Yakubov. "BMO and Dirichlet problem for degenerate Beltrami equation." Ukrainian Mathematical Bulletin 19, no. 3 (2022): 327–54. http://dx.doi.org/10.32782/1810-3200-2022-19-3-3.
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Blatov, V. A., L. V. Pogildyakova, and V. N. Serezhkin. "Analysis of the environment of beryllium, magnesium and alkaline earth atoms in oxygen-containing compounds." Acta Crystallographica Section B Structural Science 55, no. 2 (April 1, 1999): 139–46. http://dx.doi.org/10.1107/s0108768198010805.
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About 2100 inorganic and organometallic compounds containing beryllium, magnesium and alkaline earth atoms (M) were investigated with Voronoi–Dirichlet polyhedra (VDPs). It is shown that the coordination numbers (CNs) of the M atoms in MO n coordination polyhedra can be determined by means of VDPs without crystal-chemical radii. The distributions of the M—O distances in the coordination spheres of the M atoms are bimodal for M = Be or Mg and monomodal for the other alkaline earth metals. Beryllium and magnesium coordination polyhedra containing weak M—O contacts were classified by variants of their distortions. It is found that the volume of the domains of the Mg, Ca, Sr and Ba atoms is independent of their CNs at CN \ge 6 (up to 16 for barium). The possibility of using the model of deformable spheres to describe the crystal structure of the compounds investigated is suggested.
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Cao, Buqing, Bing Li, Jianxun Liu, Mingdong Tang, Yizhi Liu, and Yanxinwen Li. "Mobile Service Recommendation via Combining Enhanced Hierarchical Dirichlet Process and Factorization Machines." Mobile Information Systems 2019 (March 25, 2019): 1–11. http://dx.doi.org/10.1155/2019/6423805.
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Recently, Mashup is becoming a promising software development method in the mobile service computing environment, which enables software developers to compose existing mobile services to create new or value-added composite RESTful web application. Due to the rapid increment of mobile services on the Internet, it is difficult to find the most suitable services for building user-desired Mashup application. In this paper, we integrate word embeddings enhanced hierarchical Dirichlet process and factorization machines to recommend mobile services to build high-quality Mashup application. This method, first of all, extends the description documents of Mashup applications and mobile services by using Word2vec tool and derives latent topics from the extended description documents of Mashup and mobile services by exploiting the hierarchical Dirichlet process. Secondly, the factorization machine is applied to train these latent topics to predict the probability of mobile services invoked by Mashup and recommend mobile services with high-quality for Mashup development. Finally, the performance of the proposed method is comprehensively evaluated. The experimental results indicate that compared with the existing recommendation methods, the proposed method has significant improvements in MAE and RMSE.
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Zhang, Zhengdi, and Abdelrazig K. Tarboush. "The diffusive model for West Nile virus with advection and expanding fronts in a heterogeneous environment." International Journal of Biomathematics 13, no. 07 (August 17, 2020): 2050057. http://dx.doi.org/10.1142/s1793524520500576.
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In this paper, we investigate a reaction–diffusion–advection model with expanding fronts, which models the spatial transmission of West Nile virus (WNv) in a heterogeneous environment. A free boundary problem is formulated and the global existence and uniqueness of the solution is presented. In addition to a classical basic reproduction number, the spatial-temporal basic reproduction number for the model with null Dirichlet boundary condition is introduced and the risk index associated with the virus in spatial setting is defined, and their properties are discussed. Sufficient conditions for the WNv to vanish or spread are given, and the asymptotic behavior of the solution to the free boundary problem when the spreading occurs is established. Our results show that the initial number of infected populations and the expanding capability of the expanding fronts exhibit important impacts on the extinction or persistence of the virus.