Set Of Discrete Locations Research Articles

Convolutional conditional neural processes for local climate downscaling

Abstract. A new model is presented for multisite statistical downscaling of temperature and precipitation using convolutional conditional neural processes (convCNPs). ConvCNPs are a recently developed class of models that allow deep-learning techniques to be applied to off-the-grid spatio-temporal data. In contrast to existing methods that map from low-resolution model output to high-resolution predictions at a discrete set of locations, this model outputs a stochastic process that can be queried at an arbitrary latitude–longitude coordinate. The convCNP model is shown to outperform an ensemble of existing downscaling techniques over Europe for both temperature and precipitation taken from the VALUE intercomparison project. The model also outperforms an approach that uses Gaussian processes to interpolate single-site downscaling models at unseen locations. Importantly, substantial improvement is seen in the representation of extreme precipitation events. These results indicate that the convCNP is a robust downscaling model suitable for generating localised projections for use in climate impact studies.

Adaptive Discrete Mapping of Dynamic Nanomechanical Property of Soft Materials on Atomic Force Microscope

In this paper, an adaptive discrete nanomechanical mapping (A-DNM) technique is proposed for mapping time-varying nanomechanical properties of soft sample using atomic force microscope (AFM). Mapping time-varying nanomechanical properties is needed to investigate samples undergoing dynamic evolutions. However, current continuously-scanning-based approach is too slow to capture the time-elapsing variations over the entire sampled area, or is limited to small-area mapping only. Contrarily, we propose to extend a discrete nanomechanical mapping scheme where only a set of discrete locations (points of interests, POIs) are visited, by adaptively adjust the distribution of the measurement time between the POIs through a batch process. The proposed approach is demonstrated by implementing it to map the nanomechanical evolution of a poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) polymer during the crystallization process.

Gossip algorithm for multi-agent systems via random walk

This paper proposes an asynchronous gossip framework where agents move according to independent random walks over a location graph and interactions may occur only when two agents share the same location. Our goal is to investigate how average consensus may be achieved when agents’ motion occurs over a set of discrete locations with topological constraints. This could be used to model the spreading of information across moving crowds or the coordination of agents monitoring a discrete set of points of interest.

Sensor Placement for Optimal Control of Infinite-Dimensional Systems

An important challenge in controlling distributed parameter systems is implementing feedback control laws over an infinite-dimensional space. One widely studied approach is to place sensors at a set of discrete locations and then approximate the state feedback using the sensor outputs. This approach naturally raises the question of where the sensors should be located. In this paper, we investigate the problem of placing a set of sensors on the unit interval in order to minimize the mean-square deviation between a desired infinite-dimensional control law, and an approximate finite-dimensional controller obtained by applying state feedback at the chosen sensor positions. We propose a greedy algorithm and derive optimality bounds on the selected set of sensors. We also present a simplified greedy algorithm in which the incremental improvements from adding each sensor are not updated at each step. We analyze the performance of the approaches under two scenarios. In the case where the sensor placements are constrained such that each of the detection radii of each pair of sensors do not overlap, we show that the two algorithms are equivalent and achieve a 1/2 + ε optimality guarantee, where ε can be made arbitrarily small at the cost of increased computational overhead. When overlaps exist between sensor detection areas, we derive an optimality bound for the simplified algorithm. The value of the optimality bound is determined by the sensor model, cardinality of sensor set, and the allowed minimum sensor distance. Our approach is illustrated through numerical study, in which we compare our proposed greedy algorithm, the current state-of-the-art approach, and the true optimum obtained from exhaustive search.

Bend-it

Elastically deforming wire structures are lightweight, durable, and can be bent within minutes using CNC bending machines. We present a computational technique for the design of kinetic wire characters, tailored for fabrication on consumer-grade hardware. Our technique takes as input a network of curves or a skeletal animation, then estimates a cable-driven, compliant wire structure which matches user-selected targets or keyframes as closely as possible. To enable large localized deformations, we shape wire into functional spring-like entities at a discrete set of locations. We first detect regions where changes to local stiffness properties are needed, then insert bendable entities of varying shape and size. To avoid a discrete optimization, we first optimize stiffness properties of generic, non-fabricable entities which capture well the behavior of our bendable designs. To co-optimize stiffness properties and cable forces, we formulate an equilibrium-constrained minimization problem, safeguarding against inelastic deformations. We demonstrate our method on six fabricated examples, showcasing rich behavior including large deformations and complex, spatial motion.

Joint Optimization of Fluence Field Modulation and Regularization for Multi-Task Objectives.

This work investigates task-driven optimization of fluence field modulation (FFM) and regularization for model-based iterative reconstruction (MBIR) when different imaging tasks are presented by different organs. Example applications of the design framework were demonstrated in an abdomen phantom where the task of interest in the liver is a low-contrast, low-frequency detection task while that in the kidney is a high-contrast, high-frequency discrimination task. The global performance objective is based on maximizing local detectability index (d') at a discrete set of locations. Two objective functions were formulated based on different imaging needs: 1) a maxi-min objective where all tasks are equally important, and 2) a region-of-interest (ROI) objective to maximize imaging performance in an ROI while maintaining a minimum level of performance elsewhere. The FFM pattern for the maxi-min objective is determined by the most challenging task in the liver where both angular and spatial modulation resulted in a ~35% improvement in d' compared to an unmodulated case. The FFM for the ROI objective prescribes the most fluence to the organs of interest, boosting d' by ~59%, but manages to achieve the minimum d' target elsewhere. A spatially varying regularization was found to be important when tasks of different frequency content are present in different parts of the image - the optimal regularization strength for the two studied tasks differed by two orders of magnitude. Initial investigations in this work demonstrated that a multi-task objective is potentially important in shaping the optimal FFM and MBIR regularization, and that these tools may help to generalize task-based acquisition and reconstruction design for more complex diagnostic scenarios.

Optimizing source and receiver placement in multistatic sonar networks to monitor fixed targets

Multistatic sonar networks consisting of non-collocated sources and receivers are a promising development in sonar systems, but they present distinct mathematical challenges compared to the monostatic case in which each source is collocated with a receiver. This paper is the first to consider the optimal placement of both sources and receivers to monitor a given set of target locations. Prior publications have only considered optimal placement of one type of sensor, given a fixed placement of the other type. We first develop two integer linear programs capable of optimally placing both sources and receivers within a discrete set of locations. Although these models are capable of placing both sources and receivers to any degree of optimality desired by the user, their computation times may be unacceptably long for some applications. To address this issue, we then develop a two-step heuristic process, Adapt-LOC, that quickly selects positions for both sources and receivers, but with no guarantee of optimality. Based on this, we also create an iterative approach, Iter-LOC, which leads to a locally optimal placement of both sources and receivers, at the cost of larger computation times relative to Adapt-LOC. Finally, we perform computational experiments demonstrating that the newly developed algorithms constitute a powerful portfolio of tools, enabling the user to slect an appropriate level of solution quality, given the available time to perform computations. Our experiments include three real-world case studies.

SU-F-T-350: Continuous Leaf Optimization (CLO) for IMRT Leaf Sequencing

Purpose: To study a new step-and-shoot IMRT leaf sequencing model that avoids the two main pitfalls of conventional leaf sequencing: (1) target fluence being stratified into a fixed number of discrete levels and/or (2) aperture leaf positions being restricted to a discrete set of locations. These assumptions induce error into the sequence or reduce the feasible region of potential plans, respectively. Methods: We develop a one-dimensional (single leaf pair) methodology that does not make assumptions (1) or (2) that can be easily extended to a multi-row model. The proposed continuous leaf optimization (CLO) methodology takes in an existing set of apertures and associated intensities, or solution “seed,” and improves the plan without the restrictiveness of 1or (2). It then uses a first-order descent algorithm to converge onto a locally optimal solution. A seed solution can come from models that assume (1) and (2), thus allowing the CLO model to improve upon existing leaf sequencing methodologies. Results: The CLO model was applied to 208 generated target fluence maps in one dimension. In all cases for all tested sequencing strategies, the CLO model made improvements on the starting seed objective function. The CLO model also was able to keep MUs low. Conclusion: The CLO model can improve upon existing leaf sequencing methods by avoiding the restrictions of (1) and (2). By allowing for more flexible leaf positioning, error can be reduced when matching some target fluence. This study lays the foundation for future models and solution methodologies that can incorporate continuous leaf positions explicitly into the IMRT treatment planning model. Supported by Cancer Prevention & Research Institute of Texas (CPRIT) - ID RP150485

Construction of the minimal dominating set in the design of Wi-Fi-network

Currently, wireless technology is becoming the preferred, and in some cases the only possible for the information communication devices. If you need coverage of a large space with a complex configuration arises the need to efficiently host multiple Wi-Fi emitters, providing a stable connection with each possible location of the receiver signals. Suppose we have a model that allows to determine the coverage of a stable connection Wi-Fi emitter at a given spatial point. Then the problem of locating Wi-Fi emitters can be formulated as determining a discrete set of locations of transducers satisfying the condition. Otherwise, it is necessary to determine the positions of all the emitters that completely cover a given area, and the number of emitters should be minimal. In this formulation it is the task of the lowest coverage – the problem of finding the smallest set of columns of the matrix, "covering" all of her lines. To develop methods for solving a problem of the smallest covering usually resort to its matrix interpretation, which reduces to the problem of the smallest dominating set of a graph. From the point of view of the formulation of the problem of the smallest covering two cases are possible configuration of the coverage area of the surrounding space Wi-Fi emitters: 1. without variable. Its peculiarity is that the coverage area is completely defined by the location of the emitter. It is possible in the case where the coverage area of the symmetric or the orientation of the directivity diagram of the radiation is fixed. In this case it is possible to build a graph associated with the set of locations of emitters in which each point of placement are associated with adjacent vertices. In this formulation we arrive at the problem of the smallest dominating set of a graph. 2. Variable. It takes place in the case when the diagram of radiation is directed, and the coverage area may vary depending on the orientation of the emitter. That is, the actual emitter can be deployed in an infinite number of different provisions, but the limb covered points significantly limits the number of different orientations. In this case, each point position of the transmitter can be put into correspondence with several matrix rows and cover each point will correspond to exactly one column.

Opportunistic Sampling for Joint Population Size and Density Estimation

Consider a set of probes, called “agents”, who sample, based on opportunistic contacts, a population moving between a set of discrete locations. An example of such agents are Bluetooth probes that sample the visible Bluetooth devices in a population. Based on the obtained measurements, we construct a parametric statistical model to jointly estimate the total population size (e.g., the number of visible Bluetooth devices) and their spatial density. We evaluate the performance of our estimators by using Bluetooth traces obtained during an open-air event and Wi-Fi traces obtained on a university campus.

The properties of cosmic velocity fields

Understanding the velocity field is very important for modern cosmology: it gives insights to structure formation in general, and also its properties are crucial ingredients in modelling redshift-space distortions and in interpreting measurements of the kinetic Sunyaev-Zeldovich effect. Unfortunately, characterising the velocity field in cosmological N-body simulations is inherently complicated by two facts: i) The velocity field becomes manifestly multi-valued after shell-crossing and has discontinuities at caustics. This is due to the collisionless nature of dark matter. ii) N-body simulations sample the velocity field only at a set of discrete locations, with poor resolution in low-density regions. In this paper, we discuss how the associated problems can be circumvented by using a phase-space interpolation technique. This method provides extremely accurate estimates of the cosmic velocity fields and its derivatives, which can be properly defined without the need of the arbitrary "coarse-graining" procedure commonly used. We explore in detail the configuration-space properties of the cosmic velocity field on very large scales and in the highly nonlinear regime. In particular, we characterise the divergence and curl of the velocity field, present their one-point statistics, analyse the Fourier-space properties and provide fitting formulae for the velocity divergence bias relative to the non-linear matter power spectrum. We furthermore contrast some of the interesting differences in the velocity fields of warm and cold dark matter models. We anticipate that the high-precision measurements carried out here will help to understand in detail the dynamics of dark matter and the structures it forms.

Position and Movement Detection of Wireless Sensor Network Devices Relative to a Landmark Graph

We present a novel probabilistic framework for reliable indoor positioning of mobile sensor network devices. Compared to existing approaches, ours adopts complex computations in exchange for high localization accuracy while needing low hardware investment and moderate set-up cost. To that end, we use full distributional information on signal measurements at a set of discrete locations, termed landmarks. Positioning of a mobile device is done relative to the resulting landmark graph and the device can be found near a landmark or in the area between two landmarks. Key elements of our approach include profiling the signal measurement distributions over the coverage area using a special interpolation technique; a two-tier statistical positioning scheme that improves efficiency by adding movement detection; and joint clusterhead placement optimization for both localization and movement detection. The proposed system is practical and has been implemented using standard wireless sensor network hardware. Experimentally, our system achieved an accuracy equivalent to less than 5 meters with 95 percent success probability and less than 3 meters with an 87 percent success probability. This performance is superior to well-known contemporary systems that use similar low-cost hardware.

(Approximate) Uncertain Skylines

Given a set of points with uncertain locations, we consider the problem of computing the probability of each point lying on the skyline, that is, the probability that it is not dominated by any other input point. If each point's uncertainty is described as a probability distribution over a discrete set of locations, we improve the best known exact solution. We also suggest why we believe our solution might be optimal. Next, we describe simple, near-linear time approximation algorithms for computing the probability of each point lying on the skyline. In addition, some of our methods can be adapted to construct data structures that can efficiently determine the probability of a query point lying on the skyline.

Boundary element modeling with variable nodal and collocation point locations

In both the real variable and Complex Variable Boundary Element Methods (CVBEM), nodal points are typically located on the problem boundary and then various techniques are used to fit boundary condition values at the nodal point locations such as collocation (equating approximation function to boundary condition values at a discrete set of locations on the boundary) or least squares minimization on the boundary, among others. In this paper, the CVBEM is used to examine the significant improvement in approximation accuracy achieved by using as additional approximation variables the actual nodal point locations (both on the problem boundary as well as exterior of the problem domain union boundary), and to also use as additional approximation variables the locations where boundary conditions are fitted (i.e. collocation points). The developed concepts also apply directly to the more commonly used real variable boundary element technique. Our results show that significant improvement in modeling accuracy is achieved by including the nodal point coordinates and also the collocation point coordinates as additional variables to be optimized.

Providing and finding k‐road‐coverage efficiently in wireless sensor networks

ABSTRACTIn this paper, we study k‐road‐coverage problems in wireless sensor networks (WSNs). Assume there is a 2‐dimensional area Ω with a given road map = (V,E) where E contains all road segments and V consists of all intersection points on Ω. The first question we study is about ‘sensor deployment’, i.e., how to deploy a minimum number of sensor nodes on Ω such that each path (each road segment) on is k‐covered when all sensor nodes have the same sensing range. When sensors can only be deployed in a set of discrete locations, we propose an efficient method with the approximation ratio 6 + ϵ for the special case where k = 1 and O(k) generally. If sensors can be deployed in arbitrary locations, we propose an efficient method with the approximation ratio 24 + ϵ when k = 1 and O(k) generally. The second question we study is about ‘path query’, i.e., how to find the k‐covered path or k‐support path connecting any given source/destination pair of points on the road map . Basically, given any source/destination pair of points S and D, we present two algorithms which can efficiently find a k‐covered path connecting S and D and a k‐supported path connecting S and D, respectively. Copyright © 2010 John Wiley & Sons, Ltd.

Existence for a Diffusing Population with Discrete Returns to the Interior

We examine a one-dimensional steady-state diffusion model for a biological population in which individuals collected either throughout the domain or from one endpoint of the domain are returned to the population at a discrete set of locations. Specifically, the modeling equations are u″(x)+f(x,u(x))+(∑ni=1κiδβi(x))g(∫10α(s)u(s)ds)=0 in the former case and u″(x)+f(x,u(x))+(∑ni=1κiδβi(x))g(u′(0)) in the latter case, where the function g specifies the rate of return and f is the usual net population growth term. With Dirichlet boundary conditions imposed at both ends of the domain, the topological transversality theorem is used to show that a positive solution exists provided g does not increase too rapidly.

An optimum design for 3-D fixture synthesis in a point set domain

Addresses the problem of fixture synthesis for 3-D workpieces with a set of discrete locations on the workpiece surface as a point set of candidates for locator and clamp placement. A sequential optimization approach is presented in order to reduce the complexity associated with an exhaustive search. The approach is based on a concept of optimum experimental design, while the optimization focuses on the fixture performance of workpiece localization accuracy. In using the D-optimality criterion to minimize the workpiece positioning errors, two different greedy algorithms are developed for force-closure fixturing in the point set domain. Both 2-D and 3-D examples are presented to illustrate the effectiveness of the synthesis approach.

Quiet Geomagnetic Field Representation for All Days and Latitudes.

This paper describes a technique for obtaining the quiet-time geomagnetic field variation expected for all days of the year and distribution of latitudes from a limited set of selected quiet days within a year at a discrete set of locations. We used a data set of observatories operated by Indian and USSR scientists in 1976 and 1977 near 75°E longitude as illustration. Our method relies upon spatial smoothing of the decomposed spectral components. An evaluation of the fidelity of the resulting model shows correlation coefficients usually above 0.9 at the lower latitudes and near 0.7 at the higher latitudes with variations identified as dependent upon season and field element

Interpolation methods for shaped reflector analysis

The diffraction analysis of reflector surfaces which are described only at a discrete set of locations usually leads to the requirement of an interpolation to determine the surface characteristics over a continuum of locations. Two methods of interpolation, the global and the local methods, are presented. The global interpolation representation is a closed-form or series expression valid over the entire surface. The coefficients of a series expression are found by an integration of all of the raw data. Since the number of coefficients used to describe the surface is much smaller than the number of raw data points, the integration effectively provides a smoothing of the raw data. The local interpolation provides a closed-form expression for only a small area of the reflector surface. The subreflector is divided into sectors each of which has constant discretized data. Each area segment is then locally described by a two-dimensional quadratic surface. The second derivative data give the desired smoothed values.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>