Cover Mapping Research Articles

A Study on Usage of Treated Wastewater as Resource Management for the Sustainable Development of Al Amerat

Abstract Sustaining life on Earth is dependent upon water as an invaluable resource. Oman is in a semi-arid region where the majority of the water demand is satisfied by the desalination process. The government allocates a substantial budget for both desalination and wastewater treatment processes to develop an advanced infrastructure for water and wastewater treatment projects. One of the cutting-edge technologies that has been developed to treat water is SBR, for the removal of toxic elements, coarse particles, pollutants, etc before the treated wastewater eventually gets discharged into the sea. In the present study, Al-Amerat (Muscat Governorate) has been selected to assess the usage of treated wastewater for various purposes to evaluate the sustainability of the current water resources management. This research focuses on assessing the volume of wastewater produced in the study area to navigate the most sustainable approaches for the management of the treated wastewater such as gardening, agriculture, industrial activities, and groundwater recharge. Future generated wastewater has been quantified considering the forecasted population in 2040 in the study area. Various maps such as geomorphology, land use/land cover maps, and groundwater potential maps were generated using GIS in this study. The water demand for various sectors has been assessed with an estimation of 7%, 20%, and 63% of the total wastewater produced (per day) that can be utilized for groundwater recharge, gardening, and agriculture respectively. This study eases the burden on the desalination process by adopting alternative approaches to enhance the sustainability of the current measures.

An encoding generative modeling approach to dimension reduction and covariate adjustment in causal inference with observational studies

In this article, we develop CausalEGM, a deep learning framework for nonlinear dimension reduction and generative modeling of the dependency among covariate features affecting treatment and response. CausalEGM can be used for estimating causal effects in both binary and continuous treatment settings. By learning a bidirectional transformation between the high-dimensional covariate space and a low-dimensional latent space and then modeling the dependencies of different subsets of the latent variables on the treatment and response, CausalEGM can extract the latent covariate features that affect both treatment and response. By conditioning on these features, one can mitigate the confounding effect of the high dimensional covariate on the estimation of the causal relation between treatment and response. In a series of experiments, the proposed method is shown to achieve superior performance over existing methods in both binary and continuous treatment settings. The improvement is substantial when the sample size is large and the covariate is of high dimension. Finally, we established excess risk bounds and consistency results for our method, and discuss how our approach is related to and improves upon other dimension reduction approaches in causal inference.

Pigeonhole Design: Balancing Sequential Experiments from an Online Matching Perspective

Practitioners and academics have long appreciated the benefits of covariate balancing when they conduct randomized experiments. For web-facing firms running online A/B tests, however, it still remains challenging in balancing covariate information when experimental subjects arrive sequentially. In this paper, we study an online experimental design problem, which we refer to as the online blocking problem. In this problem, experimental subjects with heterogeneous covariate information arrive sequentially and must be immediately assigned into either the control or the treated group. The objective is to minimize the total discrepancy, which is defined as the minimum weight perfect matching between the two groups. To solve this problem, we propose a randomized design of experiment, which we refer to as the pigeonhole design. The pigeonhole design first partitions the covariate space into smaller spaces, which we refer to as pigeonholes, and then, when the experimental subjects arrive at each pigeonhole, balances the number of control and treated subjects for each pigeonhole. We analyze the theoretical performance of the pigeonhole design and show its effectiveness by comparing against two well-known benchmark designs: the matched-pair design and the completely randomized design. We identify scenarios when the pigeonhole design demonstrates more benefits over the benchmark design. To conclude, we conduct extensive simulations using Yahoo! data to show a 10.2% reduction in variance if we use the pigeonhole design to estimate the average treatment effect. This paper was accepted by George Shanthikumar, data science. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.02184 .

On multiplicative spectral sequences for nerves and the free loop spaces

We construct a multiplicative spectral sequence converging to the cohomology algebra of the diagonal complex of a bisimplicial set with coefficients in a field. The construction provides a spectral sequence converging to the cohomology algebra of the classifying space of a category internal to the category of topological spaces. By applying the machinery to a Borel construction, we explicitly determine the mod p cohomology algebra of the free loop space of the real projective space for each odd prime p. This example is emphasized as an important computational case. Moreover, we represent generators in the singular de Rham cohomology algebra of the diffeological free loop space of a non-simply connected manifold M with differential forms on the universal cover of M via Chen's iterated integral map.

The classifying element for quotients of Fermat curves

Suppose C is a cyclic Galois cover of the projective line branched at the three points 0, 1, and ∞ . Under a mild condition on the ramification, we determine the structure of the graded Lie algebra of the lower central series of the fundamental group of C in terms of a basis which is well-suited to studying the action of the absolute Galois group of Q .

P010 To establish compliance with British Society for paediatric and adolescent rheumatology (BSPAR) and the Royal College of Ophthalmology (RCOphth) guidelines for screening for uveitis in juvenile idiopathic arthritis (JIA) at a District General Hospital: a retrospective audit

Abstract Background/Aims JIA associated Uveitis (JIA-U) is most common extra-articular manifestation of JIA. The prevalence of uveitis in JIA is approximately 8-30%, but may be as high as 45-57% in young patients with oligoarticular disease. Uveitis is predominantly asymptomatic and requires slit-lamp examination for diagnosis. Up to 67% of JIA-U cases develop ocular complications such as cataracts (20%), glaucoma (19%), band keratopathy (16%), macular oedema and irreversible permanent visual impairment. The primary objective of our audit was to establish compliance of our service with BSPAR/RCOphth 2006 uveitis screening guidelines and therefore reduce the risk of visual complications in children with JIA. Methods A retrospective review of clinical records of children with rheumatological conditions attending our clinic was performed over five-year period. A total of 42 patients with JIA were identified. Data was collated using excel sheet audit tool. Results Results were analysed in accordance with the four major guideline domains as below. 1. Initial Screening exam within 6 weeks of referral: 40 out of 42 children screened within six weeks with 95% compliance rate. 2. Symptomatic patients seen within one week of referral: 4 out of 13 children seen in time with 30% compliance. 70% non-compliance was due to non-availability of ophthalmology appointment. 3. Uveitis may flare on stopping Methotrexate/DMARD’s. Patients should get screened two monthly for six months: 9 out of 13 children were screened with 70% compliance. 15% non-compliance was due to non-availability of ophthalmology appointment. 4. Ongoing screening at two-monthly intervals from onset of arthritis for six months, then 3-4 monthly: 15 out of 20 children screened with 75% compliance. 20% non-compliance was due to non-availability of ophthalmology appointment. Conclusion Practice at our centre as judged against the BSPAR/RCOphth guidelines was suboptimal. The main cause of non-compliance was due to staffing issue, rather than lack of healthcare professional training, delay in onward referral or non-attendance of patients. Non-availability of regular ophthalmology cover with cross-site commitment stretched the uveitis screening service at our centre. We presented this audit in our trust paediatric governance meeting. As a result of this audit, the frequency of paediatric ophthalmology clinics was increased to one a week. The paediatric nurse specialist facilitated liaison with the ophthalmology department and improved compliance with attendance. Patient database on shared drive was regularly updated with separate column for ophthalmology follow-up. The ophthalmologists were granted access to this database detailing clinic attendance and diagnosis. Parent education, reinforced with appropriate literature and a child friendly clinic environment improved awareness and reduces non-attendance. Combined clinics with ophthalmology are being explored. We plan to re-audit the service in near future to assess the impact after above remedial measures. A similar multi-site nation-wide audit may help identify and address local and national concerns. Disclosure K.K. Garg: None. T. Walton: None. A. Holliday: None.

Enumerating regular graph coverings whose covering transformation groups are $$\mathbb {Z}_p$$-extensions of a cyclic group

Enumerating regular graph coverings whose covering transformation groups are $$\mathbb {Z}_p$$-extensions of a cyclic group

Mixed Hodge Structures on Alexander Modules

Motivated by the limit mixed Hodge structure on the Milnor fiber of a hypersurface singularity germ, we construct a natural mixed Hodge structure on the torsion part of the Alexander modules of a smooth connected complex algebraic variety. More precisely, let U U be a smooth connected complex algebraic variety and let f : U → C ∗ f\colon U\to \mathbb {C}^* be an algebraic map inducing an epimorphism in fundamental groups. The pullback of the universal cover of C ∗ \mathbb {C}^* by f f gives rise to an infinite cyclic cover U f U^f of U U . The action of the deck group Z \mathbb {Z} on U f U^f induces a Q [ t ± 1 ] \mathbb {Q}[t^{\pm 1}] -module structure on H ∗ ( U f ; Q ) H_*(U^f;\mathbb {Q}) . We show that the torsion parts A ∗ ( U f ; Q ) A_*(U^f;\mathbb {Q}) of the Alexander modules H ∗ ( U f ; Q ) H_*(U^f;\mathbb {Q}) carry canonical Q \mathbb {Q} -mixed Hodge structures. We also prove that the covering map U f → U U^f \to U induces a mixed Hodge structure morphism on the torsion parts of the Alexander modules. As applications, we investigate the semisimplicity of A ∗ ( U f ; Q ) A_*(U^f;\mathbb {Q}) , as well as possible weights of the constructed mixed Hodge structures. Finally, in the case when f : U → C ∗ f\colon U\to \mathbb {C}^* is proper, we prove the semisimplicity and purity of A ∗ ( U f ; Q ) A_*(U^f;\mathbb {Q}) , and we compare our mixed Hodge structure on A ∗ ( U f ; Q ) A_*(U^f;\mathbb {Q}) with the limit mixed Hodge structure on the generic fiber of f f .

The universal vector extension of an abeloid variety

Let $A$ be an abelian variety over a complete non-Archimedean field $K$. The universal cover of the Berkovich space attached to $A$ reflects the reduction behaviour of $A$. In this paper the universal cover of the universal vector extension $E(A)$ of $A$ is described. In a forthcoming paper ( arXiv:2007.04659), this will be one of the crucial tools to show that rigid analytic functions on $E(A)$ are all constant.

Coverings of Graphoids: Existence Theorem and Decomposition Theorems

A graphoid is a mixed multigraph with multiple directed and/or undirected edges, loops, and semiedges. A covering projection of graphoids is an onto mapping between two graphoids such that at each vertex, the mapping restricts to a local bijection on incoming edges and outgoing edges. Naturally, as it appears, this definition displays unusual behaviour since the projection of the corresponding underlying graphs is not necessarily a graph covering. Yet, it is still possible to grasp such coverings algebraically in terms of the action of the fundamental monoid and combinatorially in terms of voltage assignments on arcs. In the present paper, the existence theorem is formulated and proved in terms of the action of the fundamental monoid. A more conventional formulation in terms of the weak fundamental group is possible because the action of the fundamental monoid is permutational. The standard formulation in terms of the fundamental group holds for a restricted class of coverings, called homogeneous. Further, the existence of the universal covering and the problems related to decomposing regular coverings via regular coverings are studied in detail. It is shown that with mild adjustments in the formulation, all the analogous theorems that hold in the context of graphs are still valid in this wider setting.

Periodic partitions with minimal perimeter

We show existence of fundamental domains which minimize a general perimeter functional in a homogeneous metric measure space. In some cases, which include the usual perimeter in the universal cover of a closed Riemannian manifold, and the fractional perimeter in Rn, we can prove regularity of the minimal domains. As a byproduct of our analysis we obtain that a countable partition which is minimal for the fractional perimeter is locally finite and regular, extending a result previously known for the local perimeter. Finally, in the planar case we provide a detailed description of the fundamental domains which are minimal for a general anisotropic perimeter.

Locally conformally product structures

A locally conformally product (LCP) structure on compact manifold [Formula: see text] is a conformal structure [Formula: see text] together with a closed, non-exact and non-flat Weyl connection [Formula: see text] with reducible holonomy. Equivalently, an LCP structure on [Formula: see text] is defined by a reducible, non-flat, incomplete Riemannian metric [Formula: see text] on the universal cover [Formula: see text] of [Formula: see text], with respect to which the fundamental group [Formula: see text] acts by similarities. It was recently proved by Kourganoff that in this case [Formula: see text] is isometric to the Riemannian product of the flat space [Formula: see text] and an incomplete irreducible Riemannian manifold [Formula: see text]. In this paper, we show that for every LCP manifold [Formula: see text], there exists a metric [Formula: see text] such that the Lee form of [Formula: see text] with respect to [Formula: see text] vanishes on vectors tangent to the distribution on [Formula: see text] defined by the flat factor [Formula: see text], and use this fact in order to construct new LCP structures from a given one by taking products. We also establish links between LCP manifolds and number field theory, and use them in order to construct large classes of examples, containing all previously known examples of LCP manifolds constructed by Matveev–Nikolayevsky, Kourganoff and Oeljeklaus–Toma (OT-manifolds).

An interpretable neural network-based non-proportional odds model for ordinal regression

This study proposes an interpretable neural network-based non-proportional odds model (N3POM) for ordinal regression. N3POM is different from conventional approaches to ordinal regression with non-proportional models in several ways: (1) N3POM is defined for both continuous and discrete responses, whereas standard methods typically treat the continuous variables as if they were discrete, (2) instead of estimating response-dependent finite-dimensional coefficients of linear models from discrete responses as is done in conventional approaches, we train a non-linear neural network to serve as a coefficient function. Thanks to the neural network, N3POM offers flexibility while preserving the interpretability of conventional ordinal regression. We establish a sufficient condition under which the predicted conditional cumulative probability locally satisfies the monotonicity constraint over a user-specified region in the covariate space. Additionally, we provide a monotonicity-preserving stochastic (MPS) algorithm for effectively training the neural network. We apply N3POM to several real-world datasets.

Alon–Boppana-Type Bounds for Weighted Graphs

The unraveled ball of radius $r$ centered at a vertex $v$ in a weighted graph $G$ is the ball of radius $r$ centered at $v$ in the universal cover of $G$. We present a general bound on the maximum spectral radius of unraveled balls of fixed radius in a weighted graph.
 The weighted degree of a vertex in a weighted graph is the sum of weights of edges incident to the vertex. A weighted graph is called regular if the weighted degrees of its vertices are the same. Using the result on unraveled balls, we prove a variation of the Alon–Boppana theorem for regular weighted graphs.

Inferring HIV transmission patterns from viral deep-sequence data via latent typed point processes.

Viral deep-sequencing data play a crucial role toward understanding disease transmission network flows, providing higher resolution compared to standard Sanger sequencing. To more fully utilize these rich data and account for the uncertainties in outcomes from phylogenetic analyses, we propose a spatial Poisson process model to uncover human immunodeficiency virus (HIV) transmission flow patterns at the population level. We represent pairings of individuals with viral sequence data as typed points, with coordinates representing covariates such as gender and age and point types representing the unobserved transmission statuses (linkage and direction). Points are associated with observed scores on the strength of evidence for each transmission status that are obtained through standard deep-sequence phylogenetic analysis. Our method is able to jointly infer the latent transmission statuses for all pairings and the transmission flow surface on the source-recipient covariate space. In contrast to existing methods, our framework does not require preclassification of the transmission statuses of data points, and instead learns them probabilistically through a fully Bayesian inference scheme. By directly modeling continuous spatial processes with smooth densities, our method enjoys significant computational advantages compared to previous methods that rely on discretization of the covariate space. We demonstrate that our framework can capture age structures in HIV transmission at high resolution, bringing valuable insights in a case study on viral deep-sequencing data from Southern Uganda.

Quantile set-regression with application in precision medicine

Quantile regression is commonly used in statistical analysis. It is more general than the ordinary regression. However in some practical investigations, the interest is the conditional quantile of the response given the covariates belonging to some set. For example in subgroup analysis, the goal is to classify the patients into two subgroups, one with whom benefit the most from the treatment and the other not so beneficial. This is equivalent to finding an optimal set in the covariate space, such that a patient is favored for the treatment if his/her covariates fall in this set, and otherwise not. Motivated by this practical problem we extend our recent work on set-regression to quantile set regression, defined as the conditional quantile of the response given the covariates belonging to a given set. This extends the notion of the classical quantile regression and is particularly suitable for precision medicine and other applications. The method is easy to use and in principle it works for sets of any shapes, but our current codes only work for certain particular shaped sets, the balls and rectangles. Simulation studies are conducted to evaluate the performance of the proposed method, which show superior promising results of the proposed method. Then the method is applied to analyze an AIDS Clinical Trials Group data.

Interactive Design and Optics-Based Visualization of Arbitrary Non-Euclidean Kaleidoscopic Orbifolds.

Orbifolds are a modern mathematical concept that arises in the research of hyperbolic geometry with applications in computer graphics and visualization. In this paper, we make use of rooms with mirrors as the visual metaphor for orbifolds. Given any arbitrary two-dimensional kaleidoscopic orbifold, we provide an algorithm to construct a Euclidean, spherical, or hyperbolic polygon to match the orbifold. This polygon is then used to create a room for which the polygon serves as the floor and the ceiling. With our system that implements Möbius transformations, the user can interactively edit the scene and see the reflections of the edited objects. To correctly visualize non-Euclidean orbifolds, we adapt the rendering algorithms to account for the geodesics in these spaces, which light rays follow. Our interactive orbifold design system allows the user to create arbitrary two-dimensional kaleidoscopic orbifolds. In addition, our mirror-based orbifold visualization approach has the potential of helping our users gain insight on the orbifold, including its orbifold notation as well as its universal cover, which can also be the spherical space and the hyperbolic space.

INDUCED REGULAR PERFECT GRAPHS

A graph G is said to be R-perfect if, for all induced subgraphs H of G, the induced regular independence number of each induced subgraph H is equal to its corresponding induced regular cover. Here, the induced regular independence number is the maximum number of vertices in H such that no two belong to the same induced regular subgraph in H, and the induced regular cover of H is the minimum number of induced regular subgraphs in H required to cover the vertex set of H. This article introduces the notion of induced regular perfect graphs or R-perfect graphs through which we study the structural properties of R-perfect graphs and identify a forbidden class of graphs for the same. This further leads to the characterization of R-perfect biconnected graphs. With these results, we derive and prove a general characterization for R-perfect graphs.

Kähler manifolds and cross quadratic bisectional curvature

We continue the study of the two curvature notions for Kähler manifolds introduced by the first named author earlier: the so-called cross quadratic bisectional curvature (CQB) and its dual ( ^{d} CQB) (which is a Hermitian form on maps between T'M and T''M ). We first show that compact Kähler manifolds with CQB _{1}>0 (CQB _{1} is the restriction to rank 1 maps) or ^{d} CQB _{1}>0 are Fano, while nonnegative CQB _{1} or ^{d} CQB _{1} leads to a Fano manifold as well, provided that the universal cover does not contain a flat de Rham factor. For the latter statement we employ the Kähler–Ricci flow to deform the metric. We conjecture that all Kähler C-spaces have nonnegative CQB and positive ^{d} CQB. By giving irreducible such examples with arbitrarily large second Betti numbers we show that the positivity of these two curvatures puts no restriction on the Betti number. A strengthened conjecture is that any Kähler C-space actually has positive CQB unless it is a {\mathbb{P}}^{1} bundle. Finally, we give an example of a nonsymmetric, irreducible Kähler C-space with b_{2}>1 and positive CQB, as well as of compact non-locally-symmetric Kähler manifolds with \textup{CQB}<0 and ^{d}\textup{CQB}<0 .

Chiral polytopes whose smallest regular cover is a polytope

We give a criterion for when the smallest regular cover of a chiral polytope P is itself a polytope, using only information about the facets and vertex-figures of P.