Projective Dimension Research Articles

Bounds on cohomological support varieties

Over a local ring R R , the theory of cohomological support varieties attaches to any bounded complex M M of finitely generated R R -modules an algebraic variety V R ( M ) {\mathrm {V}}_R(M) that encodes homological properties of M M . We give lower bounds for the dimension of V R ( M ) {\mathrm {V}}_R(M) in terms of classical invariants of R R . In particular, when R R is Cohen–Macaulay and not complete intersection we find that there are always varieties that cannot be realized as the cohomological support of any complex. When M M has finite projective dimension, we also give an upper bound for dim ⁡ V R ( M ) \dim {\mathrm {V}}_R(M) in terms of the dimension of the radical of the homotopy Lie algebra of R R . This leads to an improvement of a bound due to Avramov, Buchweitz, Iyengar, and Miller on the Loewy lengths of finite free complexes, and it recovers a result of Avramov and Halperin on the homotopy Lie algebra of R R . Finally, we completely classify the varieties that can occur as the cohomological support of a complex over a Golod ring.

Analysis of the chemical diffusion master equation for creation and mutual annihilation reactions

We propose an infinite dimensional generating function method for finding the analytical solution of the so-called chemical diffusion master equation (CDME) for creation and mutual annihilation chemical reactions. CDMEs model by means of an infinite system of coupled Fokker–Planck equations the probabilistic evolution of chemical reaction kinetics associated with spatial diffusion of individual particles; here, we focus an creation and mutual annihilation chemical reactions combined with Brownian diffusion of the single particles. Using our method we are able to link certain finite dimensional projections of the solution of the CDME to the solution of a single linear fourth order partial differential equation containing as many variables as the dimension of the aforementioned projection space. Our technique extends the one presented in Lanconelli [J. Math. Anal. Appl. 526, 127352 (2023)] and Lanconelli et al. [arXiv:2302.10700 [math.PR] (2023)] which allowed for an explicit representation for the solution of birth-death type CDMEs.

Ext modules related to syzygies of the residue field

Let R be a commutative noetherian ring. In this paper, we find out close relationships between the module M being embedded in a module of projective dimension at most n and the (n+1)-torsionfreeness of the nth syzygy of M. As an application, when R is local with residue field k, we compute the dimensions as k-vector spaces of Ext modules related to syzygies of k.

Seeing Santurbán through ISDS: A sociolegal case study of Eco Oro v. Colombia

AbstractThis article aims to enrich the emerging, multi-coloured tapestry of ‘international law in context’ through a study of how international economic law operates in complex investment-related disputes. Focusing on the Eco Oro v. Colombia investor-state arbitration, and drawing on both doctrinal analysis and sociolegal research, the study investigates how different actors make sense of the issues, of the dispute, and of the law. Besides shedding light on the neglected multi-actor, multi-layered dimensions of investment disputes, and on tensions between often incommensurable values, juxtaposing arbitral proceedings and underlying social realities highlights how investor-state arbitration involves a socio-political process of re-presenting actors, territory, the environment, and livelihoods through the prism of international arrangements that are primarily designed to protect foreign investment. The findings provide policy pointers on the need for systemic reform of international investment law, moving away from the predominant emphasis on investment protection and investor-state dispute settlement, towards a governance model that effectively considers the social, political, and environmental dimensions of foreign investment projects.

Barile–Macchia resolutions

We construct cellular resolutions for monomial ideals via discrete Morse theory. In particular, we develop an algorithm to create homogeneous acyclic matchings and we call the cellular resolutions induced from these matchings Barile–Macchia resolutions. These resolutions are minimal for edge ideals of weighted oriented forests and (most) cycles. As a result, we provide recursive formulas for graded Betti numbers and projective dimension. Furthermore, we compare Barile–Macchia resolutions to those created by Batzies and Welker and some well-known simplicial resolutions. Under certain assumptions, whenever the above resolutions are minimal, so are Barile–Macchia resolutions.

Journey of medical device development from the bench to the bedside—four real-life examples of commercial biomaterials development

Translating biomaterials research into clinical products is a multidisciplinary yet rewarding journey. It should primarily aim to improve patient treatment and clinical outcomes by addressing unmet clinical needs. Four examples of commercial development of biomaterial implants illustrate the diversity of paths, starting from academic research work (AlchiMedics, TISSIUM, Cousin Surgery) or corporate initiatives to develop new products (Medtronic-Sofradim Production). They have been selected from the Translational Research session of the 2022 Conference of the European Society for Biomaterials (ESB) in Bordeaux (France). Commitment, agility, and perseverance were among the key common skills to successfully meet challenges, especially the most unexpected ones. All dimensions of translation projects must be integrated from the start, including the regulatory strategy.

Dilemmas of recognition and redistribution: Constituting intersectional subjects of inclusion in migrant support work

AbstractIn this study, I explore how the subject of inclusion is constituted as intersectional in the organizational discursive practices of a civil society organization promoting migrant and refugee inclusion. Drawing on Crenshaw's notion of political intersectionality and Fraser's politics of recognition and redistribution, I analyze the political dimension of an inclusion project by showing how intersectional categories are connected to differentiated struggles and strategies of inclusion. The ethnographic study illustrates how two subject positions are constituted as being underpinned by either the logic of recognition or redistribution. Moreover, the findings show how the two strategies interact, revealing the dynamics of privilege and disadvantage at play in the inclusion project. The paper contributes to critical studies on inclusion and intersectionality in organizational contexts by extending our understanding of power dynamics and tensions as integral parts of the intersectional approach.

ВЕЛИКИЕ СТРОЙКИ КОММУНИЗМА В ЗЕРКАЛЕ СОВЕТСКОЙ НОСТАЛЬГИИ

The article examines the evolution of the mythology of the great construction projects of communism in the context of nostalgia for the Soviet. The author shows the specifics of the formation of the mythology of great construction projects in the Soviet media sphere through connection with the basic constructs of the official communist ideology. This mythologem was never able to move into the discourses of historical memory, since the exposure of the cult of personality and mass repressions launched the process of undermining trust in the Soviet mythological pathos of the great construction projects of communism until its complete ideological corrosion during the period of perestroika. However, the specifics of the accumulation of primary scientific data on the history of the economy of forced labor in the USSR pushed into the shadows the real participation in great construction projects not only of the civilian population, but also of Komsomol activists who went en masse to these sites at the call of the Communist Party. The initial conditions of many construction projects were very harsh, and the objects themselves were distinguished not only by their scale, but also by their knowledge intensity, which implied their high technological efficiency. Currently, great Soviet construction projects penetrate into the space of media memory through the digital content of tourists, whomthey attract as a source of unprecedented impressions of exotic sights. The author concludes that in the case of great construction projects, Soviet nostalgia as a cultural movement works with the material, rather than symbolic, dimension of great construction projects, drawing positive connotations to elevate their image within the experience industry.

On Regularity and Projective Dimension of Invariant Chains of Monomial Ideals

On Regularity and Projective Dimension of Invariant Chains of Monomial Ideals

Development of the Cost and Time Estimation Factors of the Project Dimension in the Agile Software

Development of the Cost and Time Estimation Factors of the Project Dimension in the Agile Software

Sincere silting modules and vanishing conditions

We study characterizations of sincere modules, sincere silting modules and tilting modules in terms of various vanishing conditions. Let R be a perfect ring and T be an R-module. It is proved that T is sincere silting if and only if T is presilting satisfing the vanishing condition KerExt R 0 ≤ i ≤ 1 ( T , − ) = 0 , and that T is tilting if and only if KerExt R 0 ⩽ i ⩽ 1 ( T , − ) = 0 and Gen T ⊆ KerExt R 1 ⩽ i ⩽ 2 ( T , − ) . As an application, we prove that a sincere silting R-module T of finite projective dimension is tilting if and only if Ext R i ( T , T ( J ) ) = 0 for all sets J and all integer i ≥ 1 . This not only extends a main result of Zhang’s paper [Self-orthogonal τ-tilting modules and tilting modules, J Pure Appl Algebra, 2022, 226: 106860] from finitely generated modules over Artin algebras to infinitely generated modules over more general rings, but also gives it a different proof without using Auslander-Reiten translations.

Die Bauaussteckung als landestypische Eigenheit

The use of construction scopes in building permit procedures is a Swiss peculiarity and serves both as a means of publicity and to illustrate the dimensions of a construction project. However, whether or not construction scopes can also be useful in other countries depends on the legal system and a cost-benefit analysis.

On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane

On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane

Dual Discriminative Low-Rank Projection Learning for Robust Image Classification

Numerous methods have exploited projection learning to extract low-dimensional features for image classification. Some projection learning methods integrate low-rank matrix recovery into classification models to equip the projection subspace with discrimination and robustness against corruption. However, these methods cannot directly recover “clean” components from the new datum in a low-dimensional subspace. Additionally, they are sensitive to the selection of projection dimensions. To overcome these shortcomings, we propose a dual discriminative low-rank projection learning framework for robust image classification. Specifically, the proposed method learns a low-rank projection and a semi-orthogonal projection to recover “clean” components from the original data and simultaneously obtain a low-dimensional subspace. Thereafter, to preserve discriminative information in the low-dimensional subspace, an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> -norm term is constructed by concentrating the projected intra-class samples around their adaptive class centroids. Regression-based terms are appended using the low-dimensional features extracted from the recovered clean data and the class centroids for more accurate classification. Experiments on five public databases with various corruptions demonstrate that the proposed method can robustly classify image data despite a small training sample sizes and gross corruption. The superiority of the proposed method is further verified on the large-scale PubFig83 database, on which it achieves an 87.58% classification accuracy.

Depth and Stanley Depth of the Edge Ideals of r-Fold Bristled Graphs of Some Graphs

In this paper, we find values of depth, Stanley depth, and projective dimension of the quotient rings of the edge ideals associated with r-fold bristled graphs of ladder graphs, circular ladder graphs, some king’s graphs, and circular king’s graphs.

On the reducing projective dimension over local rings

Abstract In this paper, we are concerned with certain invariants of modules, called reducing invariants, which have been recently introduced and studied by Araya–Celikbas and Araya–Takahashi. We raise the question whether the residue field of each commutative Noetherian local ring has finite reducing projective dimension and obtain an affirmative answer for the question for a large class of local rings. Furthermore, we construct new examples of modules of infinite projective dimension that have finite reducing projective dimension and study several fundamental properties of reducing dimensions, especially properties under local homomorphisms of local rings.

A case study of quality control application with BIM-laser scanning collaboration in building construction process

Housing accounts for the largest share of the volume of the construction sector. Housing is the living space that people use on a permanent or temporary basis. Living space is also expected to have the desired quality. Quality requires construction in accordance with specified conditions and rules. In order to minimize possible errors in the design and construction process and to achieve the desired level of quality, continuous, scientific and instrumental controls are required. In recent years, with the rapid development of technology, methods have been developed that have achieved good results using integrated technology, which has begun to replace the quality controls performed by traditional methods. This new technology partnership called Building Information Modelling and Laser Scanning is described in this study. The aim of the study is to show that human error in building inspection can be minimized with the help of technology. In the study, a building was selected from a sample public housing project. Two dimensional projects of the building were converted into three dimensions using Building Information Modelling. In the current state of construction, point clouds were captured using laser scanning. The point clouds were converted to three dimensions. The construction defects were calculated by overlaying the BIM model with the real point cloud data. After checking, it was found that 2.2 % of the productions were defective productions. It was found that 97.8 % of the productions were within acceptable tolerance limits. The results obtained on a sample residential building demonstrate the importance of these new solutions for quality control and error-free production

Systematic review of various 3D volume construction algorithms adopted in isocentric C-arm devices

C-arm systems are well established in clinical routines which produces two- dimensional (2D) projection images, which are not sufficient to provide the depth information required by surgeons during interventional procedures. Due to this, the procedural time and radiation dosage are significantly higher which leads to increased procedural cost. In order to extract depth information from 2D projection images acquired with stepwise rotation between 0 to 180 degrees, various 3D volume construction algorithms are developed. The purpose of this paper is to systematically review the various 3D volume construction algorithms in order to develop a cost-effective solution to be incorporated in the iso-centric C-arm machines without 3D volume construction algorithms. The proposed review process is done in the following aspects: i. State-of-the-art 3D volume construction algorithms ii. Comparing the different aspects of commercially available iso- centric C-arm machines incorporated with 3D volume construction algorithms. The impact of various 3D construction algorithms in improving different aspects such as image quality, resolution, procedure time, radiation dose, and accuracy of the final 3D model is discussed. Based on the findings we recommend a procedure to develop and validate a 3D volume construction algorithm. 3D volume construction from C-arm images helps to construct Multi Planar Reconstruction (MPR) views during interventional procedures which will provide in-depth information and minimize the procedure time, cost, and dosage to the patient.

Relevansi Nilai-Nilai Multikultural Dalam Buku Pendidikan Agama Islam dan Budi Pekerti dengan Dimensi Projek Penguatan Profil Pelajar Pancasila

Multicultural values ​​are very important for students to understand because this will build a noble personality, love of the homeland, love of culture. This research will analyze the suitability of multicultural values ​​contained in PAI student textbooks for class VII SMP with the Project Dimensions of Strengthening the Pancasila Student Profile. This research uses a qualitative approach with a library research type. Data collection was carried out by reviewing documents, namely textbooks for students of Islamic Religious Education and Characteristics at Grade VII Middle School. Data analysis techniques include content analysis and critical analysis. Checking the validity of the findings was carried out using triangulation techniques. The value of tolerance contains 4 dimensions P5, these dimensions are the dimensions of faith and devotion to God Almighty, independence, mutual cooperation and global diversity. The democratic values ​​contain 3 P5 dimensions, namely the dimensions of independence, mutual cooperation and global diversity. The value of humanism contains 4 dimensions, namely the dimensions of independence, mutual cooperation, global diversity and creativity. Meanwhile, the value of equality contains 4 P5 dimensions, namely the dimensions of faith and devotion to God Almighty, independence, mutual cooperation and global diversity.

Particle-Picking in Cryo-Electron Microscopy Images with Online Resources

Aims: Use deep learning online resources to identify and pick single particle views in micrographs to enable high quality three-dimensional reconstruction for macromolecular structure determination. Study Design: Using the keyhole limpet hemocyanin dataset, a public cryo electron microscopy (cryo-EM) dataset containing two dimensional projections of the particles in two views (top and side) in several orientations, and a recent deep learning algorithm made available in a GitHub repository, we design the procedure to pick both views with high degree of confidence, using only online resources and running in a standard laptop. Methodology: The defocus images are subject to a pre-processing stage to increase its contrast and ameliorate its radiometric range. This is followed by a training stage, that needs a few images annotated with examples of both views of interest – top and side view – identified using user-friendly tools available online. The annotated subset of images is divided for train and validation purposes, and the algorithm runs to produce a set of weights, that can be used for inference in any other similar image, locating all the instances of the particles in both views in seconds. Results: From the 57 images used to evaluate the performance of the algorithm, 63% had both precision and recall better than 90%. The global precision on the test dataset was 91.6% and recall 98.1%. Considering each view separately, top views detections attain a precision of 91.7%, with 100% for recall; side views recall remains on 96.7%, while precision attain 91.5%. Conclusion: Deep learning methods are a promising tool for extracting large amounts of single particle views as needed for quality 3D structure reconstruction, as they can be implemented with minimal computer skills and trained to achieve state-of-the-art automatic discrimination, as described in this study.