A technique for adding range restrictions to generalized searching problems

In a generalized searching problem, a set $S$ of $n$ colored geometric objects has to be stored in a data structure, such that for any given query object $q$, the distinct colors of the objects of $S$ intersected by $q$ can be reported efficiently. In this paper, a general technique is presented for adding a range restriction to such a problem. The technique is applied to the problem of querying a set of colored points (resp.\ fat triangles) with a fat triangle (resp.\ point). For both problems, a data structure is obtained having size $O(n^{1+\epsilon})$ and query time $O((\log n)^2 + C)$. Here, $C$ denotes the number of colors reported by the query, and $\epsilon$ is an arbitrarily small positive constant

Further results on generalized intersection searching problems: counting, reporting, and dynamization

In a generalized intersection searching problem, a set, $S$, of colored geometric objects is to be preprocessed so that given some query object, $q$, the distinct colors of the objects intersected by $q$ can be reported efficiently or the number of such colors can be counted efficiently. In the dynamic setting, colored objects can be inserted into or deleted from $S$. These problems generalize the well-studied standard intersection searching problems and are rich in applications. Unfortunately, the techniques known for the standard problems do not yield efficient solutions for the generalized problems. Moreover, previous work on generalized problems applies only to the static reporting problems. In this paper, a uniform framework is presented to solve efficiently the counting/reporting/dynamic versions of a variety of generalized intersection searching problems, including: 1-, 2-, and 3-dimensional range searching, quadrant searching, interval intersection searching, 1- and 2-dimensional point enclosure searching, and orthogonal segment intersection searching

Automated Modeling of Microwave Structures by Enhanced Neural Networks

The paper describes the methodology of the automated creation of neural models of microwave structures. During the creation process, artificial neural networks are trained using the combination of the particle swarm optimization and the quasi-Newton method to avoid critical training problems of the conventional neural nets. In the paper, neural networks are used to approximate the behavior of a planar microwave filter (moment method, Zeland IE3D). In order to evaluate the efficiency of neural modeling, global optimizations are performed using numerical models and neural ones. Both approaches are compared from the viewpoint of CPU-time demands and the accuracy. Considering conclusions, methodological recommendations for including neural networks to the microwave design are formulated

Fast algorithms for collision and proximity problems involving moving geometric objects

Consider a set of geometric objects, such as points, line segments, or axes-parallel hyperrectangles in \IR^d, that move with constant but possibly different velocities along linear trajectories. Efficient algorithms are presented for several problems defined on such objects, such as determining whether any two objects ever collide and computing the minimum inter-point separation or minimum diameter that ever occurs. The strategy used involves reducing the given problem on moving objects to a different problem on a set of static objects, and then solving the latter problem using techniques based on sweeping, orthogonal range searching, simplex composition, and parametric search

Effizient algorithms for generalized intersection searching on non-iso-oriented objects

In a generalized intersection searching problem, a set $S$ of colored geometric objects is to be preprocessed so that, given a query object $q$, the distinct colors of the objects of $S$ that are intersected by $q$ can be reported or counted efficiently. These problems generalize the well-studied standard intersection searching problems and are rich in applications. Unfortunately, the solutions known for the standard problems do not yield efficient solutions to the generalized problems. Recently, efficient solutions have been given for generalized problems where the input and query objects are iso-oriented, i.e., axes-parallel, or where the color classes satisfy additional properties, e.g., connectedness. In this paper, efficient algorithms are given for several generalized problems involving non-iso-oriented objects. These problems include: generalized halfspace range searching in ${\cal R}^d$, for any fixed $d \geq 2$, segment intersection searching, triangle stabbing, and triangle range searching in ${\cal R}^2$. The techniques used include: computing suitable sparse representations of the input, persistent data structures, and filtering search

Responding to the new International Classification of Diseases-11 prolonged grief disorder during the COVID-19 pandemic: a new bereavement network and three-tiered model of care

The field of bereavement research and care is at a tipping point. The introduction of prolonged grief disorder (PGD) in the International Classification of Diseases (ICD-11) has ignited clinical interest in this new disorder, along with debate over challenges in validating and implementing these new criteria. At the same time, the global COVID-19 pandemic has launched several local and international efforts to provide urgent support and comfort for individuals and communities suffering from grief. Recently, grief experts have called for a collective response to these complicated bereavements and possible increase in PGD due to COVID-19. Here we outline a new European network that aims to unite a community of grief researchers and clinicians to provide accessible, evidence-based support particularly during times of unprecedent crisis. The Bereavement Network Europe (BNE) has been developed with two main aims. Firstly, to develop expert agreed, internationally acceptable guidelines for bereavement care through a three-tiered approach. Secondly, to provide a platform for researchers and clinicians to share knowledge, collaborate, and develop consensus protocols to facilitate the introduction of PGD to diverse stakeholders. This article outlines the current status and aims of the BNE along with the plans for upcoming network initiatives and the three-tiered bereavement care guidelines in response to the COVID-19 pandemic. Keywords: Bereavement network Europe; COVID-19; ICD-11; Prolonged grief disorder; Three-tiered bereavement care

Linear and nonlinear trending and prediction for AVHRR time series data

The variability of AVHRR calibration coefficient in time was analyzed using algorithms of linear and non-linear time series analysis. Specifically we have used the spline trend modeling, autoregressive process analysis, incremental neural network learning algorithm and redundancy functional testing. The analysis performed on available AVHRR data sets revealed that (1) the calibration data have nonlinear dependencies, (2) the calibration data depend strongly on the target temperature, (3) both calibration coefficients and the temperature time series can be modeled, in the first approximation, as autonomous dynamical systems, (4) the high frequency residuals of the analyzed data sets can be best modeled as an autoregressive process of the 10th degree. We have dealt with a nonlinear identification problem and the problem of noise filtering (data smoothing). The system identification and filtering are significant problems for AVHRR data sets. The algorithms outlined in this study can be used for the future EOS missions. Prediction and smoothing algorithms for time series of calibration data provide a functional characterization of the data. Those algorithms can be particularly useful when calibration data are incomplete or sparse

Development of Stresses in Cohesionless Poured Sand

The pressure distribution beneath a conical sandpile, created by pouring sand from a point source onto a rough rigid support, shows a pronounced minimum below the apex (`the dip'). Recent work of the authors has attempted to explain this phenomenon by invoking local rules for stress propagation that depend on the local geometry, and hence on the construction history, of the medium. We discuss the fundamental difference between such approaches, which lead to hyperbolic differential equations, and elastoplastic models, for which the equations are elliptic within any elastic zones present .... This displacement field appears to be either ill-defined, or defined relative to a reference state whose physical existence is in doubt. Insofar as their predictions depend on physical factors unknown and outside experimental control, such elastoplastic models predict that the observations should be intrinsically irreproducible .... Our hyperbolic models are based instead on a physical picture of the material, in which (a) the load is supported by a skeletal network of force chains ("stress paths") whose geometry depends on construction history; (b) this network is `fragile' or marginally stable, in a sense that we define. .... We point out that our hyperbolic models can nonetheless be reconciled with elastoplastic ideas by taking the limit of an extremely anisotropic yield condition.Comment: 25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps. Philosophical Transactions A, Royal Society, submitted 02/9