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National responses should be improved and accelerated to meet the target of ending the Acquired ImmunoDeficiency Syndrome (AIDS) epidemic by 2030. In the Republic of Cyprus, Men who have Sex with Men (MSM) are disproportionately affected by Human Immunodeficiency Virus (HIV), accounting approximately for half of all annual HIV diagnoses. This study assesses the evolution of HIV incidence in MSM in Cyprus until 2030 using a model calibrated to Cypriot epidemiological data. Four scenarios were examined: status quo, two scenarios focusing on introducing Pre-Exposure Prophylaxis (PrEP), and a 90% HIV incidence reduction scenario. Reaching only the 95-95-95 HIV cascade of care targets among MSM would reduce HIV incidence by 48.6% by 2030 compared to 2015. Initiating a PrEP intervention only for high risk MSM would cause a modest further reduction in HIV incidence. To meet the 90% reduction target, PrEP should be expanded to both high and medium risk MSM and, after 2025, behavioral interventions should be implemented so as high-risk MSM gradually move to the medium-risk category. Cyprus will not reach the HIV incidence reduction target by 2030 unless PrEP is gradually promoted and delivered to all high and medium risk MSM along with awareness and behavioral interventions. [ABSTRACT FROM AUTHOR]

This article proposes two new classes of nonparametric tests for the correct specification of linear spatial autoregressive models based on the "integrated conditional moment" approach. Our test statistics are constructed as continuous functionals of a residual marked empirical process as well as its projected version. We derive asymptotic properties of the test statistics under the null hypothesis, the alternative hypothesis, and a sequence of local alternatives. The proposed tests do not involve the selection of tuning parameters such as bandwidths and are able to detect a broad class of local alternatives converging to the null at the parametric rate n − 1 / 2 , with n being the sample size. We also propose a multiplier bootstrap procedure that is computationally simple to approximate the critical values. Monte Carlo simulations illustrate that our tests have a reasonable size and satisfactory power for different types of data-generating processes. Finally, an empirical analysis of growth convergence is carried out to demonstrate the usefulness of the tests. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a large class of (so-called) conditional indicators, on a complete probability space with respect to a sub σ-algebra. A conditional indicator is a positive mapping, which is not necessary linear, but may share common features with the conditional expectation, such as the tower property or the projection property. Several characterizations are formulated. Beyond the definitions, we provide some non trivial examples that are used in finance and may inspire new developments in the theory of operators on Riesz spaces. [ABSTRACT FROM AUTHOR]

In Savinien Cyrano de Bergerac's (1619–55) tale of a voyage to the sun, Les États et Empires du Soleil, a cosmic traveller's physical body, as well as his light-propelled spacecraft, undergo eerie transformations. After the vehicle shines like enamel and gold in blazing sun rays, it fades to transparency. Meanwhile, the narrator's body becomes diaphanous, revealing inner organs that gleam in hues of scarlet, vermillion, and garnet. This article develops a close reading of this passage. The authors analyse the passage's narrative descriptions, first alongside Neoplatonic metaphors of saintly bodies as prisms for divine light, then in relation to early modern discourse about optics, magnetism, and anatomy, and finally as burlesque allusions to an infant's conception and birth. At length, the authors suggest that these descriptions can inspire feelings of ecstasy, insolence, and yearning in readers, and that this array of sentiments can facilitate an experience of freeing the imagination. [ABSTRACT FROM AUTHOR]

AbstractFunctional data analysis (FDA) is an important modern paradigm for handling infinite-dimensional data. An important task in FDA is clustering, which identifies subgroups based on the shapes of measured curves. Considering that derivatives can provide additional useful information about the shapes of functionals, we propose a novel L2 distance between two random functions by incorporating the functions and their derivative information to determine the dissimilarity of curves under a unified scheme for dense observations. The Karhunen–Loève expansion is used to approximate the curves and their derivatives. Cluster membership prediction for each curve intends to minimize the new distances between the observed and predicted curves through subspace projection among all possible clusters. We provide consistent estimators for the curves, curve derivatives, and the proposed distance. Identifiability issues of the clustering procedure are also discussed. The utility of the proposed method is illustrated via simulation studies and applications to two real datasets. The proposed method can considerably improve cluster performance compared with existing functional clustering methods. Supplementary materials for the article are available online. [ABSTRACT FROM AUTHOR]

We study the existence and uniqueness of solutions to the inverse quasi-variational inequality problem. Motivated by the dynamical approach to solving optimization problems such as variational inequality, monotone inclusion, and inverse variational problems, we consider a dynamical system associated with the inverse quasi-variational inequality problem, and establish the existence and uniqueness of a solution to the proposed system. We prove that every trajectory of the proposed dynamical system converges to the unique solution of the inverse quasi-variational inequality problem and that the system is globally asymptotically stable at its equilibrium point. We also prove that if the function which governs the inverse quasi-variational inequality problem is strongly monotone and Lipschitz continuous, then the dynamical system is globally exponentially stable at its equilibrium point. We discretize the dynamical system and show that the sequence generated by the discretization of the system converges strongly to the unique solution of the inverse quasi-variational inequality problem under certain assumptions on the parameters involved. Finally, we provide numerical examples to support and illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In a personal paper about the author's animus, Watsky explores his fascination with Louise Glück, after attempting to solicit first her poetry for Jung Journal and then an interview about her voice in her poetry shortly after her death. He realized he had projected his anima onto a complete stranger known only through her writing. Suspicious of his motives, he proceeds to read her entire oeuvre during a two-week period, exploring their intersections and their divergences. Watsky then narrates a previous projection onto the writer Joanna Field who turned out to be the Freudian analyst Marion Milner. After reading all of her work and convinced that she had been influenced by Jung, he sought her out in Hamstead, England. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new relaxed method for solving the split feasibility problem in Hilbert spaces. In our method, the projection to the halfspace is replaced by the one to the intersection of two halfspaces. We give convergence of the sequence generated by our method under some suitable assumptions. Finally, we give a numerical example for illustrating the efficiency and implementation of our algorithms in comparison with existing algorithms in the literature. [ABSTRACT FROM AUTHOR]

The establishment of refugee settlements has caused profound segmented impacts on the coverage of land use/cover types. Few studies have computed the spatial drivers of land use/cover changes in Refugee prone areas. This study explored how refugee settlements induced geo-changes in land use/cover in Bidi-Bidi refugee settlement in Uganda. Sentinel-2B images (2015, 2017 and 2020) were used to assess and predict (2030 and 2040) the spatial areal extent of land use/cover changes. The images were classified using Supervised algorithm (Maximum-likelihood) and used CA-Markov model to generate transitions into the future. A Binary Logistic regression was used to compute the spatial drivers of geo-changes. Our results reveal that the settlements triggered more geo-changes in built-up (0.6%), refugee settlements (4.1%), and subsistence farmlands (7.0%) at the expense of woodlands (−0.3%), wetlands (−2.9%), and grasslands (−8.3%). The same trajectory will also be expected between 2030 and 2040. The most critical spatial drivers of these changes are as follows: population growth, increased temperatures, precipitation variation, distance to water sources, distance to roads, distance to police posts, and distance to trading centres. To reduce the acceleration of changes in land use/cover types, this study agitates for equal spatial establishment of woodlots, promotion of alternative sources of energy and livelihoods, and settlement construction materials. [ABSTRACT FROM AUTHOR]

I show that a broad class of constrained nonparametric instrumental variable estimators are projections of the corresponding unconstrained estimators on the constrained set with respect to some norm. In addition, for estimators based on Tikhonov regularization, constrained estimation can be viewed as two-step projection: first project the data on the unconstrained set, and then project this projection on the constrained set. As an application, I use the projection property to establish sufficient conditions for the consistency of a sieve-based and a kernel-based constrained estimator. [ABSTRACT FROM AUTHOR]

To assess the trends in non-melanoma skin cancer (NMSC) incidence in Hong Kong from 1990 to 2019 and the associations of age, calendar period, and birth cohort, to make projections to 2030, and to examine the drivers of NMSC incidence. We assessed the age, calendar period, and birth cohort effects of NMSC incidence in Hong Kong between 1990 and 2019 using an age-period-cohort model. Using Bayesian age-period-cohort analysis with integrated nested Laplace approximations, we projected the incidence of NMSC in Hong Kong to 2030. From 1990 to 2019, the age-standardized incidence rate of NMSC increased from 6.7 per 100,000 population to 8.6 per 100,000 population in men and from 5.4 per 100,000 to 5.9 per 100,000 population in women, among the 19,568 patients in the study (9812 male patients [50.14%]). The annual net drift was 2.00% (95% confidence interval [CI]: 1.50–2.50%) for men and 1.53% (95% CI: 0.95–2.11%) for women. Local drifts increased for both sexes above the 35–39-year age group. The period and cohort risk of developing NMSC tended to rise but slowed gradually in the most recent period and post-1975 birth cohort. From 2019 to 2030, it is projected that the number of newly diagnosed NMSC cases in Hong Kong will increase from 564 to 829 in men and from 517 to 863 in women. Population aging, population growth, and epidemiologic changes contributed to the increase in incident NMSCs, with population aging being the most significant contributor. The slowing of the period and cohort effects suggests that the rising incidence of NMSC is partly attributable to increased awareness and diagnosis. The increasing prevalence of NMSC among the elderly and an aging population will significantly impact the clinical workload associated with NMSC for the foreseeable future. [ABSTRACT FROM AUTHOR]

Cet article étudie les propriétés sémantiques et distributionnelles du nom objectif, tout en mettant au jour les difficultés rencontrées dans l'élaboration de typologies nominales et dans la manipulation des tests dédiés à leur justification. Objectif est un nom capsule, largement reconnu comme tel dans les recherches qui lui sont consacrées. Cette classe de noms relevant d'un mode de fonctionnement particulier, il n'en demeure pas moins que l'on peut attribuer une catégorie sémantique à objectif. Les tests distributionnels proposés dans la littérature peinent cependant à circonscrire l'ensemble de ses caractéristiques, dans la mesure où il présente des propriétés des noms d'objets mentaux et des noms de lieux. [ABSTRACT FROM AUTHOR]

Projection operators are fundamental algorithmic operators in Analysis and Optimization. It is well known that these operators are firmly nonexpansive; however, their composition is generally only averaged and no longer firmly nonexpansive. In this note, we introduce the modulus of averagedness and provide an exact result for the composition of two linear projection operators. As a consequence, we deduce that the Ogura–Yamada bound for the modulus of the composition is sharp. [ABSTRACT FROM AUTHOR]

Artificial Intelligence systems cannot yet match human abilities to apply knowledge to situations that vary from what they have been programmed for, or trained for. In visual object recognition, methods of inference exploiting top-down information (from a model) have been shown to be effective for recognising entities in difficult conditions. Here a component of this type of inference, called 'projection', is shown to be a key mechanism to solve the problem of applying knowledge to varied or challenging situations, across a range of AI domains, such as vision, robotics, or language. Finally, the relevance of projection to tackling the commonsense knowledge problem is discussed. [ABSTRACT FROM AUTHOR]

This article explores the use of technology in congregational worship, specifically focusing on electronic projection systems and streaming/recording services. It notes that the adoption of these technologies is more common in predominantly white Protestant congregations and varies based on factors such as size, financial resources, technological experience, and cultural factors. While larger congregations with more resources are more likely to incorporate technologies like streaming and smartphone apps, Catholic congregations are less likely to do so. The use of smartphones during worship is encouraged by about one-third of all congregations, primarily for accessing scripture. Ultimately, the decision to incorporate technology in worship services is made by congregational leaders based on their mission and community traditions. [Extracted from the article]

This work contributes to study the particle projection mechanism during gas injection on a molten steel bath surface. The studied element is called "dome". It results from a cluster of particles which is propelled and molded onto the vault of the VOD installation. A bibliographical analysis of previous projection studies leads toward two main topics: an analytic model to characterize the collected projections and a chemical analysis to trace the emission droplets. The main result leads to observe that the predicted droplet size and dome quantity go hand in hand with results obtained experimentally for the studied casting. Indeed, based on semi-empirical equations in literature, an analytical model predicts an average propelled particle size of about 500 μm with a dome mass of one-Ton. Furthermore, the metallographic analysis of some samples highlight a crystallization of seeds linked each other and, the presence of spherical droplets size between 100 and 800 µm. [ABSTRACT FROM AUTHOR]

The Oblique Mercator (OM) has been the runt in the family of conformal coordinate projection where its particular attribute of arbitrary orientation has been largely ignored. It is proposed that the Oblique Mercator, as a conformal projection, is well-suited to bridge the gap between a conventional north-oriented projection and the family of engineering grids that are unit-scaled and arbitrarily oriented improve the management of coordinate reference systems (CRS) between GIS and CAD/BIM software that has been, and remains, a significant cause of inefficiency for engineering design and construction, and for plane surveying. Issues relating to the selection of an optimal set of HOM projection parameters are discussed, including a new method to transform an existing engineering grid into an optimised HOM grid. [ABSTRACT FROM AUTHOR]

The intrinsic infinite-dimensional nature of functional data creates a bottleneck in the application of traditional classifiers to functional settings. These classifiers are generally either unable to generalize to infinite dimensions or have poor performance due to the curse of dimensionality. To address this concern, we propose building a distance-weighted discrimination (DWD) classifier on scores obtained by projecting data onto one specific direction. We choose this direction by minimizing, over a reproducing kernel Hilbert space, an empirical risk function containing the DWD classifier loss function. Our proposed classifier avoids overfitting and enjoys the appealing properties of DWD classifiers. We further extend this framework to accommodate functional data classification problems where scalar covariates are involved. In contrast to previous work, we establish a nonasymptotic estimation error bound on the relative misclassification rate. Through simulation studies and a real-world application, we demonstrate that the proposed classifier performs favorably relative to other commonly used functional classifiers in terms of prediction accuracy in finite-sample settings. for this article are available online. [ABSTRACT FROM AUTHOR]

Here we deal with the stabilisation problem of non-diagonal systems by boundary control. In the studied setting, the boundary control input is subject to a constant delay. We use the spectral decomposition method and split the system into two components: an unstable and a stable one. To stabilise the unstable part of the system, we connect, for the first time in the literature, the famous backstepping control design technique with the direct-proportional control design. More precisely, we construct a proportional open-loop stabiliser, then, by means of the Artstein transformation we close the loop. At the end of the paper, an example is provided in order to illustrate the acquired results. [ABSTRACT FROM AUTHOR]

Projection does not reliably serve cognition; it all too often contributes to failures of knowledge. Our projecting not only imaginatively misrepresents the world by attributing a feature of ourself to it. In doing so it can misrepresent us as lacking that feature. It is an act of the imagination which re-locates unwanted attributes into a motivated misrepresentation which distorts our grasp of reality and of ourselves. The imaginative act itself is not consciously intended so that we take the resulting picture at face value, despite the distortion. Without a strong reason to question this misperception the projection remains undetected and the misrepresentation affects our relations to others. Projection serving motivated self-deception thus evades correction. Realistic self-knowledge becomes possible through psychoanalysis when the patient's projections are received by the analyst as communications impinging on her capacity for sympathy. I show how the psychology of sympathy we find in Hume and Smith provides a philosophical frame of reference for understanding this interaction between sympathy and projection. I bring sympathy together with contemporary Kleinian psychoanalytic theory to explain how psychoanalytic interpretation engages with this interaction to reduce the effects of projection and enable a self-knowledge grounded in the subject's own experience of herself. [ABSTRACT FROM AUTHOR]

The exponential function and its logarithmic counterpart are essential corner stones of nonlinear mathematical modelling. In this paper, we treat their conic extensions, the exponential cone and the relative entropy cone, in primal, dual and polar form, and show that finding the nearest mapping of a point onto these convex sets all reduce to a single univariate root-finding problem. This leads to a fast projection algorithm shown numerically robust over a wide range of inputs. [ABSTRACT FROM AUTHOR]

We present a new approach known as greedy segmentation (GS) to identify multiple changepoints for a functional data sequence. The proposed multiple changepoint detection criterion links detectability with the projection onto a suitably chosen subspace and the changepoint locations. The changepoint estimator identifies the true changepoints for any predetermined number of changepoint candidates, either over-reporting or under-reporting. This theoretical finding supports the proposed GS estimator, which can be efficiently obtained in a greedy manner. The GS estimator's consistency holds without being restricted to the conventional at most one changepoint condition, and it is robust to the relative positions of the changepoints. Based on the GS estimator, the test statistic's asymptotic distribution leads to the novel GS algorithm, which identifies the number and locations of changepoints. Using intensive simulation studies, we compare the finite sample performance of the GS approach with other competing methods. We also apply our method to temporal changepoint detection in weather datasets. [ABSTRACT FROM AUTHOR]

The burden of stomach cancer remains high in Hong Kong. We sought to evaluate the associations of age, period, and birth cohort with the changing trend in the incidence of stomach cancer and to provide projections through 2030. We performed an age-period-cohort analysis and projections up to 2030 using data from the Hong Kong Cancer Registry. Additionally, we used a population decomposition algorithm to assess the drivers in the number of incident cases of stomach cancer in Hong Kong. Among the 26,813 stomach cancer patients, from 1994 to 2018, the age-standardized incidence rate of stomach cancer decreased for both sexes. The incidence increased with age and was highest for those aged 85 years or older. Period relative risk (RR) showed a monotonic decreasing pattern throughout the study period for both sexes before 2010. Cohort RR for males was monotonically decreasing but changed little after the 1967–1971 birth cohort. In contrast, cohort RR for females declined in the pre-1927–1931 birth cohort but slowed down since. It is projected that there will be 906 male patients and 954 female patients in 2030. Decomposition analysis suggested that population growth and aging were associated with substantial changes in the number of incident cases of stomach cancer in Hong Kong. Both period and cohort risk of developing stomach cancer in Hong Kong have slowed down or plateaued. Our study demonstrates that population aging and growth are the main drivers of the increased number of incident cases of stomach cancer in Hong Kong. [ABSTRACT FROM AUTHOR]

This paper documents a computational implementation of a projection and rescaling algorithm for solving one of the alternative feasibility problems find x ∈ L ∩ Ω or find x ^ ∈ L ⊥ ∩ Ω , where L is a linear subspace in R n , L ⊥ is its orthogonal complement, and Ω ⊆ R n is the interior of a direct product of second order cones. The gist of the projection and rescaling algorithm is to enhance a low-cost first-order method (a basic procedure) with an adaptive reconditioning transformation (a rescaling step). We give a full description of a Python implementation of this algorithm and present multiple sets of numerical experiments on synthetic problem instances with varied levels of conditioning. Our computational experiments provide promising evidence of the effectiveness of the projection and rescaling algorithm. Our Python code is publicly available. Furthermore, the simplicity of the algorithm makes a computational implementation in other environments completely straightforward. [ABSTRACT FROM AUTHOR]

The Programme of International Student Assessment (PISA) has instigated domestic policy debate aimed at improving education systems' quality and efficiency. Its high performers are often described as knowledge-based legitimation tools that have become reference societies. This article analyses if and the extent to which PISA affects the choice of reference societies used in education policy. We conducted a systematic literature review of scholarly peer-reviewed journal articles. We identify two ways in which PISA affects the reference societies chosen: it builds but also triggers the collapse of the reference societies used in domestic education policy. However, there are also cases in which PISA has little influence on which countries or regions are used as references. The domestic processes of choosing the reference societies used in education policy emerge as more nuanced than first expected. This article provides a firm basis for a much-needed understanding of the topic. [ABSTRACT FROM AUTHOR]

When the rapid moving interference exists, especially in the presence of look direction mismatch, coherent local scattering and so on, the output performance of beamformer will degrade dramatically. To solve this problem, a novel robust adaptive null broadening beamforming method based on subspace projection is proposed. First, the proposed beamformer requires a priori information, that is, the spatial sector where the desired signal and interference may locate, so as to construct the signal-plus-noise covariance matrix (SPNCM) and interference-plus-noise covariance matrix (IPNCM). Then, the desired signal steering vector (SV) is calibrated twice. The desired signal SV is estimated from the SPNCM and subsequently calibrated by using the uncertainty set optimisation method. Next, we construct the null broadening projection matrix by tapering the interference subspace got from IPNCM. Finally, the sample covariance matrix is processed by projection technology and diagonal loading technology. The optimal weight vector is obtained by the new covariance matrix and calibrated desired signal SV. Simulation results show that the proposed method can form wide null in the incident direction of interference and prevent interference from moving out of the null when the rapid moving interference exists. The proposed method outperforms other existing methods. [ABSTRACT FROM AUTHOR]

We propose a projection-based test to check logistic regression models when the dimension of the covariate vector may be divergent. The proposed test achieves a reduction in dimension, and the proposed method behaves as if only a single covariate is present. The test is shown to be consistent and can detect root-n local alternatives. We derive the asymptotic distribution of the proposed test under the null hypothesis and establish the test's asymptotic behavior under the local and global alternatives. The numerical performance is remarkably attractive comparing to the existing methods. Real examples are presented for illustration. for this article are available online. [ABSTRACT FROM AUTHOR]

Many patients resist engagement in the therapeutic relationship because they fear the traumatic consequences of the mobilization of thwarted selfobject needs in what they fear will be a faulty, nonempathic environment. At times this resistance is manifest in "narcissistic rage" as described by Heinz Kohut. Providing opportunities for selfobject experience in work with these patients can be challenging. In his 1971 paper The Use of the Object, D.W. Winnicott described a developmental process in which the state of omnipotent merger with important objects undergoes a transformation in which the other is increasingly recognized as not only outside the self, but also in possession of a subjectivity of its own and thus can be made use of. In work with some seriously and persistently mentally ill, the client's capacity to make use of the clinician is poorly developed or highly conflicted. Given this the clinical process in which the client achieves the recognition of the worker and trust in their intentions—and hence can make use of them as a selfobject, is often prolonged and stormy. A case is discussed at length that illustrates this. The report documents the importance of holding, containment, management of the countertransference, and survival strategies for the clinician. It also shows the patient's growing ability to make use of the clinician as a selfobject as she struggles to understand and cope with changes in her life world and self-experience. [ABSTRACT FROM AUTHOR]

This work aims to provide a deep learning framework to segment woods from tree point clouds. We develop a novel preprocessing layer before the classical sampling and convolution structure called the projection layer to organize 3D point clouds into 2D points. Input data are transformed into projection data along axis and planes for the subsequent convolution process, which helps decrease the complexity of networks. In order to obtain optimal and effective projection data for capturing local features, we formulate the 2D transformation in the learning process using two learnable angle parameters. The projection map is updated in the learning process for capturing geometric structure information, which plays an important role in wood point segmentation. Experiments show that we have achieved the loss and misclassification error of 0.41% and 8%, respectively, on wood points extraction from handheld laser scanning data. Besides, we also achieve the correctness, completeness and F -score of 90.4%, 91.5% and 0.91, respectively, in a public vehicle laser scanning dataset. [ABSTRACT FROM AUTHOR]

Let P and Q be projections on a Hilbert C * -module. This paper deals with the orthogonal complementarity of certain range closures associated with P and Q. Some necessary and sufficient conditions are derived under which (P, Q) is harmonious. [ABSTRACT FROM AUTHOR]

In this paper, as an extension of the isotone projection cone, we consider the isotonicity of the metric projection operator with respect to the mutually dual orders induced by the cone and its dual cone in Hilbert spaces. We first discuss the relation between the isotonicity of the projection onto the cone and its dual cone. Some sufficient conditions for the isotonicity of the projection with respect to the mutually dual orders onto general cones are then proved. By using the self-dual cone in the hyperplane, we establish some specific isotone projection cones. Some properties and representations of the projection onto these cones are studied. We also prove some heredity and expansivity for the isotonicity of the projection onto these cones. By using the isotonicity characterizations of the projection with respect to the mutually dual orders, some solvability and approximation theorems for the complementarity and conic optimization problems are obtained. In Theorems 5.1–5.4, if the order relation does not satisfy the regularity, to guarantee convergence of isotone Picard iterations, three different order methods are used, respectively. Our results generalize those about the isotone projection cone and methods to establish isotone iterations for complementarity problems. [ABSTRACT FROM AUTHOR]

In this paper, we extend the operations of parallel addition A:B and parallel subtraction A ÷ B from the cone of bounded nonnegative self-adjoint operators to the linear bounded operators on a Hilbert space. Some conditions for the relations A † : B † = (A + B) † , B = (A : B) ÷ A , (A C) ÷ (B C) = (A ÷ B) C , A ÷ B = (P (A † − B †) P) † , B = A : (B ÷ A) , (C A) : (C B) = C (A : B) to be true are studied and the solution of the equation A:X = B is investigated. Moreover, some relationships between the parallel addition and subtraction of projections are obtained. [ABSTRACT FROM AUTHOR]

Art Therapists have long been aware of the intersubjective complexities that are evoked in art therapy in relation to images, art-making and their attendant processes. These have often been understood with reference to the psychodynamic concepts of transference and countertransference. In this paper we ask, what happens to these processes when art therapy moves online and becomes digitally-mediated? How do the dynamics of 'the Virtual' affect the image and art-making, and the therapeutic relationship? Drawing on Schaverien and Jung's ideas about transference and countertransference, we propose a new model or 'map' of Art Therapy which helps to think about these questions, which we call a 'Hexagonal Relationship'. To date, published literature has tended to foreground the logistics and practicalities of moving art therapy online, with consideration of complex interpersonal dynamics occupying less of a central space in emerging narratives about digitally-mediated art therapy. We suggest that applying our model to practice could potentially support art therapists to access deeper, less conscious and perhaps more symbolic levels of material in online work, in service of the client's process. We invite art therapists and clients to consider our model with reference to their own experiences of digitally-mediated art therapy, and to test out our questions and hypotheses in their own contexts. Art Therapists work with the idea that the images made in art therapy are affected by the relationship between the person making the image (often known as 'the client'), the art therapist, and the environment in which the art therapy session takes place. Making and reflecting on images is a way of understanding and working with whatever is going on for the client, both in their 'external' life and also in their 'internal world' (for example, their thoughts, feelings, imaginings and beliefs). A lot of art therapy now happens online, particularly since the start of the COVID-19 pandemic, and we are all part of the digital world in terms of how we communicate and relate with others. We think it is helpful to consider how art therapy (including the therapeutic relationship, art-making processes and the images made) might be affected by the digital environment and so we have written this paper to explore these ideas. We show readers a diagram of what we call the 'Hexagonal Relationship' to help explain what we mean. We think this will help us to understand more of what happens in art therapy in the digital world, making this kind of therapeutic help more effective and meaningful for clients and their art therapists. We hope that clients and art therapists will test out these ideas for themselves and come into a conversation with us (perhaps through papers like this one, published in art therapy journals) about how well our ideas stand up to actual experience. [ABSTRACT FROM AUTHOR]

In order to generate the three-dimensional (3D) mesh of draped fabric based on a two-dimensional (2D) fabric projection, the 3D point cloud of draped fabric was scanned via a self-built 3D scanning device followed by triangulation. The 3D boundary of fabric drape model and the two-dimensional contour of the projection of the fabric drape model were extracted respectively. Two neural networks were constructed to bridge the 2D fabric drape projection and the 3D boundary of draped fabric. With the trained neural networks, the 3D boundary of draped fabric could be inferred by merely referring a 2D projection of draped fabric. Six reference triangular meshes with different triangle density were generated. Driven by two mesh deformation methods, Laplacian deformation and Poisson deformation, the reference mesh was deformed into 3D mesh similar to scanned fabric drape models (meshes). The result shows that the generated models have a high agreement with the scanned meshes. In addition, the Laplacian deformation outperforms Poisson deformation in generating 3D fabric drape models. [ABSTRACT FROM AUTHOR]

This article focuses on ‘therefore’ constructions such as ‘The switch is on, and therefore the lights are on’. We submit that the contribution of ‘therefore’ is to express a dependence as part of the core content of these constructions, rather than being conveyed by conventional implicature or a triggered presupposition. We argue that the standard objections to this view can be answered by relying on a general hypothesis about projection, leaving our view on solid ground. [ABSTRACT FROM AUTHOR]

It is well-known that the lattice of all submodules of a module is modular. However, this is not the case for the lattice of subsemimodules of a semimodule. We show examples and describe these lattices for a given semimodule. We study closed and splitting subsemimodules and submodules of a given semimodule or module M , respectively. We derive a sufficient condition under which the lattice L c (M) of closed subsemimodules is a homomorphic image of the lattice L (M) of all subsemimodules. We describe the ordered set of splitting submodules of a module and show a natural bijective correspondence between this poset and the poset of all projections of this module. We show that this poset is orthomodular. This result extends the case known for the poset of closed subspaces of a Hilbert space which is used in the logic of quantum mechanics. [ABSTRACT FROM AUTHOR]

This paper focuses on efficient projection onto the intersection of a half-space and a box-like set and its generalized Jacobian. Based on the Lagrangian duality theory, we deal with the projection problem via a semismooth Newton algorithm with line search safeguard, which admits global and locally quadratic convergence, to solve a univariate semismooth equation. Numerical experiments show that our proposed algorithm outperforms favourably the existing state-of-the-art standard solvers and is able to reliably solve very large-scale projection problems. Besides, we derive an explicit expression of a generalized Jacobian of the studied projection, which is an essential component of second-order nonsmooth methods. [ABSTRACT FROM AUTHOR]

We consider the distributionally robust optimization and show that computing the distributional worst-case is equivalent to computing the projection onto the canonical simplex with additional linear inequality. We consider several distance functions to measure the distance of distributions. We write the projections as optimization problems and show that they are equivalent to finding a zero of real-valued functions. We prove that these functions possess nice properties such as monotonicity or convexity. We design optimization methods with guaranteed convergence and derive their theoretical complexity. We demonstrate that our methods have (almost) linear observed complexity. [ABSTRACT FROM AUTHOR]

We present a variation on the Chamberlin trimetric map projection. This new projection, which we call the matrix trimetric projection, consists of a linear transformation of the squares of the distances between a given point and three control points. The formula of the forward projection is simpler than the Chamberlin projection, and admits an inverse formula which requires numerical iteration of only one parameter. We make comparisons between the two projections using a representative list of control points. The Chamberlin trimetric projection outperforms the matrix trimetric projection on measures of angle deformation and area deformation, but the opposite is true for a measure of distance deformation, and the difference between the results of the projections is small over all measures. The forward Matrix trimetric projection can be calculated in half the time of the Chamberlin trimetric projection. We conclude that the matrix trimetric projection is a viable alternative to the Chamberlin trimetric projection, especially if an inverse is required or speed is important. [ABSTRACT FROM AUTHOR]

In projection-based model order reduction, a reduced-order approximation of the original full-order system is obtained by projecting it onto a reduced subspace that contains its dominant characteristics. The problem of frequency-weighted H 2 -optimal model order reduction is to construct a local optimum in terms of the H 2 -norm of the weighted error transfer function. In this paper, a projection-based model order reduction algorithm is proposed that constructs a reduced-order model, which nearly satisfies the first-order optimality conditions for the frequency-weighted H 2 -optimal model order reduction problem. It is shown that as the order of the reduced model is increased, the deviation in the satisfaction of the optimality conditions reduces further. Numerical methods are also discussed that improve the computational efficiency of the proposed algorithm. Four numerical examples are presented to demonstrate the efficacy of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The aim of this study is to predict the Turkish Lira's exchange rate against the US Dollar by combining models. As a result, the authors include three univariate forecasting models: ARIMA, Naive, and Exponential smoothing, and one multivariate model: NARDL for the first time with Artificial Neural Network model. To the best of our knowledge, it is a unique study to integrate univariate models, ANN with NARDL. The researchers utilize two combination criteria to forecast the Turkish Lira, namely, equal weightage and var-cor. The findings conclude that the combination of NARDL and Naive outperforms all standalone and combined time series techniques. The results indicate that the Turkish Lira's currency rate against the USD is strongly reliant on recent time-series observations with symmetric and asymmetric behavior of macro-economic fundamentals. [ABSTRACT FROM AUTHOR]

We investigate a class of finite dimensional iteratively regularized Gauss–Newton methods for solving nonlinear irregular operator equations in a Hilbert space. The developed technique allows to investigate in a uniform style various discretization methods such as projection, quadrature and collocation schemes and to take into account available restrictions on the solution. We propose an a posteriori stopping rule for the iterative process and establish an accuracy estimate for obtained approximation. The regularized Gauss–Newton method combined with the quadrature discretization and the a posteriori iteration stopping is applied to a model ionospheric radiotomography problem. The problem is reduced to a nonlinear integral equation describing the phase shift of a sounding radio signal in dependence of the free electron concentration in the ionospheric plasma. We establish the unique solvability of the inverse problem in the class of analytic functions. [ABSTRACT FROM AUTHOR]

The authors of this article explore the relationship between the cultural, unconscious and conscious dynamics in setting up infant observations in Delhi. The specific focus of the paper is the concept of 'Nazar', Evil eye, in India. The paper presents the experiences of a young woman observer in India, going in to observe an infant as a requirement of her psychotherapy training. The paper is an attempt to make sense of what happened five years ago in setting up the observation. It sheds light on how a cultural artefact such as 'Nazar' becomes a barrier to being able to undertake baby observation. The article also extends its understanding of what 'Nazar' can symbolise, both in the internal and the external world of both observer and observed. It goes on to explore the link between mother's ambivalence both towards her child and towards the young female observer. [ABSTRACT FROM AUTHOR]

Halpern's iteration method, discovered by Halpern in 1967, is an iterative algorithm for finding fixed points of a nonexpansive mapping in Hilbert and Banach spaces. Since many optimization problems can be cast into fixed point problems of nonexpansive mappings, Halpern's method plays an important role in optimization methods. This paper discusses recent advances in convergence and rate of convergence results of Halpern's method, and applications in optimization problems, including variational inequalities, monotone inclusions, Douglas-Rachford splitting method, and minimax problems. [ABSTRACT FROM AUTHOR]

Okehurst – the stately home in Vernon Lee's "Oke of Okehurst; Or, The Phantom Lover" – is the epitome of English architecture, dating back to "Norman or Saxon" times. Yet inside, the house is populated with far-flung objects and traces of the exotic: Persian rugs, majolica ornaments, and "rose-leaves and spices put into china bowls." The house and its contents are intoxicating, and nothing is more exotic, perfumed, or exquisite than Alice, who with her husband (and cousin) William Oke are the last members of the family's line. Okehurst also reverberates with the presences of its previous inhabitants which drive the current Okes to repeat the family's history of madness and murder. The haunting of Okehurst is particularly interesting when considered alongside material from Lee's archive. This paper will consider the traces of Lee's own complex ancestry and the problems of empire and matrilineal ancestral wealth and inheritance, whilst utilising correspondence from Lee to her mother, and her partner, Mary Robinson to suggest the possible inspiration for Cotes Common and Okehurst Manor. Throughout this consideration of haunted spaces – both inside and outside – this paper will also make reference to the 1886 manuscript of "Oke of Okehurst," which has never previously been studied. [ABSTRACT FROM AUTHOR]

An element a in a *-ring R has *-DMP inverse if there exists m ∈ N such that a m ∈ R # ∩ R † and (a m) # = (a m) †. If m = 1, then a is said to have *-gMP inverse. In this paper, we present several new characterizations of *-DMP inverses in a *-ring. We prove that a has *-DMP inverse if and only if there exists a projection e ∈ comm (a) such that a + e ∈ R − 1 and ae is nilpotent if and only if there exist m ∈ N and x ∈ R such that x a m + 1 = a m and a x = x a = (a x) *. Moreover, we prove that a ∈ R has *-gMP inverse if and only if a a * = u a , a * a = a v for some u , v ∈ R − 1. The corresponding new characterization of *-DMP inverse is thereby obtained. [ABSTRACT FROM AUTHOR]

This paper documents a computational implementation of a projection and rescaling algorithm for finding most interior solutions to the pair of feasibility problems f i n d x ∈ L ∩ R + n a n d f i n d x ˆ ∈ L ⊥ ∩ R + n , where L denotes a linear subspace in R n and L ⊥ denotes its orthogonal complement. The projection and rescaling algorithm is a recently developed method that combines a basic procedure involving only low-cost operations with a periodic rescaling step. We give a full description of a MATLAB implementation of this algorithm and present multiple sets of numerical experiments on synthetic problem instances with varied levels of conditioning. Our computational experiments provide promising evidence of the effectiveness of the projection and rescaling algorithm. Our MATLAB code is publicly available. Furthermore, the simplicity of the algorithm makes a computational implementation in other environments completely straightforward. [ABSTRACT FROM AUTHOR]

Existing projection designs (e.g. maximum projection designs) attempt to achieve good space-filling properties in all projections. However, when using a Gaussian process (GP), model-based design criteria such as the entropy criterion is more appropriate. We employ the entropy criterion averaged over a set of projections, called expected entropy criterion (EEC), to generate projection designs. We show that maximum EEC designs are invariant to monotonic transformations of the response, i.e. they are optimal for a wide class of stochastic process models. We also demonstrate that transformation of each column of a Latin hypercube design (LHD) based on a monotonic function can substantially improve the EEC. Two types of input transformations are considered: a quantile function of a symmetric Beta distribution chosen to optimize the EEC, and a nonparametric transformation corresponding to the quantile function of a symmetric density chosen to optimize the EEC. Numerical studies show that the proposed transformations of the LHD are efficient and effective for building robust maximum EEC designs. These designs give projections with markedly higher entropies and lower maximum prediction variances (MPV's) at the cost of small increases in average prediction variances (APV's) compared to state-of-the-art space-filling designs over wide ranges of covariance parameter values. [ABSTRACT FROM AUTHOR]

This paper investigates how the choice of progress variable in tabulated chemistry affects the mass burning rates of premixed laminar flames. Simulations are carried out using finite rate, detailed chemistry (DC) and Flamelet Generated Manifolds (FGM). Through comparison of detailed chemistry and FGM (using different progress variable definitions), it is found that for FGM the mass burning rate depends on the choice of progress variable and thus results in a different mass burning rate than detailed chemistry. Since the mass burning rate is influenced by stretch and transport phenomena, the effects of these on mass burning rates are analysed. While FGM qualitatively predicts the effect of stretch on the mass burning rate compared to detailed chemistry, there are quantitative differences. It is shown that this is mainly caused by a lack of projection in usual FGM applications. When the projection of the source term and the diffusion term are included in the table, FGM becomes independent of the choice of progress variable and the effects of stretch are better represented by FGM similar to detailed chemistry. [ABSTRACT FROM AUTHOR]

We consider a neural network approach to an inverse variational inequality which is assumed to have a non-empty set of solutions. In the case of gradient mappings, we prove that every trajectory of the network converges to the solution set in the case of convex potentials and if the solution set is singleton, the network is globally asymptotically stable at the equilibrium point. We also prove that if the network has a strongly convex potential, then the network is globally exponentially stable at the equilibrium point. Another purpose of this paper is to point out certain fatal mistakes in the paper by Zou et al. [A novel method to solve inverse variational inequality problems based on neural networks. Neurocomputing. 2016;173:1163–1168]. [ABSTRACT FROM AUTHOR]