Set Of Points Research Articles

Learning Spatio-Temporal Radon Footprints for Assessment of Parkinson’s Dyskinesia

Parkinson’s disease is a severe neurodegenerative disorder that leads to loss of control over various motor and mental functions. Its progression can be limited with medication, particularly through the use of levodopa. However, prolonged administration of levodopa often results in disorders independent of those caused by the disease. The detection of these disorders is based on the clinical examination of patients, through different type of activities and tasks, using the Unified Dyskinesia Rating Scale (UDysRS). In the present work, our aim is to develop a state-of-the-art assessment system for levodopa-induced dyskinesia (LID) using the joint coordinate data of a human skeleton body depicted on videotaped activities related to UDysRS. For this reason, we combine a robust mathematical method for encoding action sequences known as Spatio-temporal Radon Footprints (SRF) with a Convolutional Neural Network (CNN), in order to estimate dyskinesia’s ratings for six body parts. We introduce two different methodological approaches: Global SRF-CNN and Local SRF-CNN, based on the set of skeletal points used in the encoding scheme. A comparison between these approaches reveals that Local SRF-CNN demonstrates better performance than the Global one. Finally, Local SRF-CNN outperforms the state-of-the-art technique, on both tasks, for UDysRS dyskinesia assessment, using joint coordinate data of the human body, achieving an overall performance in mean RMSE value of 0.6198 for Drinking task and 0.4885 for Communication, compared to 0.6575 and 0.5175, respectively. This illustrates the ability of the proposed machine learning system to successfully assess LID.

Filtration evolution of hypergraphs: A novel approach to studying multidimensional datasets.

The rapid growth of large datasets has led to a demand for novel approaches to extract valuable insights from intricate information. Graph theory provides a natural framework to model these relationships, but standard graphs may not capture the complex interdependence between components. Hypergraphs are a powerful extension of graphs that can represent higher-order relationships in the data. In this paper, we propose a novel approach to studying the structure of a dataset using hypergraph theory and a filtration method. Our method involves building a set of hypergraphs based on a variable distance parameter, enabling us to infer qualitative and quantitative information about the data structure. We apply our method to various sets of points, dynamical systems, signal models, and real electrophysiological data. Our results show that the proposed method can effectively differentiate between varying datasets, demonstrating its potential utility in a range of scientific applications.

NRTR: Neuron Reconstruction With Transformer From 3D Optical Microscopy Images.

The neuron reconstruction from raw Optical Microscopy (OM) image stacks is the basis of neuroscience. Manual annotation and semi-automatic neuron tracing algorithms are time-consuming and inefficient. Existing deep learning neuron reconstruction methods, although demonstrating exemplary performance, greatly demand complex rule-based components. Therefore, a crucial challenge is designing an end-to-end neuron reconstruction method that makes the overall framework simpler and model training easier. We propose a Neuron Reconstruction Transformer (NRTR) that, discarding the complex rule-based components, views neuron reconstruction as a direct set-prediction problem. To the best of our knowledge, NRTR is the first image-to-set deep learning model for end-to-end neuron reconstruction. The overall pipeline consists of the CNN backbone, Transformer encoder-decoder, and connectivity construction module. NRTR generates a point set representing neuron morphological characteristics for raw neuron images. The relationships among the points are established through connectivity construction. The point set is saved as a standard SWC file. In experiments using the BigNeuron and VISoR-40 datasets, NRTR achieves excellent neuron reconstruction results for comprehensive benchmarks and outperforms competitive baselines. Results of extensive experiments indicate that NRTR is effective at showing that neuron reconstruction is viewed as a set-prediction problem, which makes end-to-end model training available.

Active design of diffuse acoustic fields in enclosures.

This paper presents a numerical framework for designing diffuse fields in rooms of any shape and size, driven at arbitrary frequencies. That is, we aim at overcoming the Schroeder frequency limit for generating diffuse fields in an enclosed space. We formulate the problem as a Tikhonov regularized inverse problem and propose a low-rank approximation of the spatial correlation that results in significant computational gains. Our approximation is applicable to arbitrary sets of target points and allows us to produce an optimal design at a computational cost that grows only linearly with the (potentially large) number of target points. We demonstrate the feasibility of our approach through numerical examples where we approximate diffuse fields at frequencies well below the Schroeder limit.

AI-Enhanced Healthcare: Not a new Paradigm for Informed Consent.

With the increasing prevalence of artificial intelligence (AI) and other digital technologies in healthcare, the ethical debate surrounding their adoption is becoming more prominent. Here I consider the issue of gaining informed patient consent to AI-enhanced care from the vantage point of the United Kingdom's National Health Service setting. I build my discussion around two claims from the World Health Organization: that healthcare services should not be denied to individuals who refuse AI-enhanced care and that there is no precedence to seeking patient consent to AI-enhanced care. I discus U.K. law relating to patient consent and the General Data Protection Regulation to show that current standards relating to patient consent are adequate for AI-enhanced care. I then suggest that in the future it may not be possible to guarantee patient access to non-AI-enhanced healthcare, in a similar way to how we do not offer patients manual alternatives to automated healthcare processes. Throughout my discussion I focus on the issues of patient choice and veracity in the patient-clinician relationship. Finally, I suggest that the best way to protect patients from potential harms associated with the introduction of AI to patient care is not via an overly burdensome patient consent process but via evaluation and regulation of AI technologies.

Gravitational Waves and gravitino mass in No-Scale Supergravity inflation with Polonyi term

We study a No-Scale supergravity inflation model which has a non-minimal deformation of the Kähler potential and a Wess-Zumino superpotential extended by the inclusion of a Polonyi mass term. The non-minimal structure of the Kähler potential is responsible for an inflexion point that can lead to the production of gravitational waves at late stages of inflation, while the Polonyi term breaks supersymmetry at the end of inflation, generating a non-vanishing gravitino mass. After a thorough parameter space scan, we identify promising points for gravitational wave production. We then study the resulting gravitational wave energy density for this set of points, and we observe that the gravitational waves should be observable in the next generation of both space-based and ground-based interferometers. Finally, we show how the presence of the Polonyi term can be used to further boost the gravitational wave energy density, which is correlated with the gravitino mass. The code used for the scan and the numerical analysis is provided at https://gitlab.com/miguel.romao/gw-and-m32-no-scale-inflation-polonyi.

Weyl Sums over Integers with Digital Restrictions

We estimate Weyl sums over the integers with sum of binary digits either fixed or restricted by some congruence condition. In our proofs, we use ideas that go back to a paper by Banks, Conflitti, and the first author (2002). Moreover, we apply the “main conjecture” on the Vinogradov mean value theorem established by Bourgain, Demeter, and Guth (2016) and Wooley (2016, 2019). We use our result to give an estimate of the discrepancy of point sets defined by the values of polynomials at arguments having the sum of binary digits restricted in different ways.

Pancreatic δ-cells influence the glycaemic set point.

Pancreatic δ-cells influence the glycaemic set point.

SHIV-C109p5 NHP induces rapid disease progression in elderly macaques with extensive GI viral replication.

CCR5-tropic simian/human immunodeficiency viruses (SHIV) with clade C transmitted/founder envelopes represent a critical tool for the investigation of HIV experimental vaccines and microbicides in nonhuman primates, although many such isolates lead to spontaneous viral control post infection. Here, we generated a high-titer stock of pathogenic SHIV-C109p5 by serial passage in two rhesus macaques (RM) and tested its virulence in aged monkeys. The co-receptor usage was confirmed before infecting five geriatric rhesus macaques (four female and one male). Plasma viral loads were monitored by reverse transcriptase-quantitative PCR (RT-qPCR), cytokines by multiplex analysis, and biomarkers of gastrointestinal damage by enzyme-linked immunosorbent assay. Antibodies and cell-mediated responses were also measured. Viral dissemination into tissues was determined by RNAscope. Intravenous SHIV-C109p5 infection of aged RMs leads to high plasma viremia and rapid disease progression; rapid decrease in CD4+ T cells, CD4+CD8+ T cells, and plasmacytoid dendritic cells; and wasting necessitating euthanasia between 3 and 12 weeks post infection. Virus-specific cellular immune responses were detected only in the two monkeys that survived 4 weeks post infection. These were Gag-specific TNFα+CD8+, MIP1β+CD4+, Env-specific IFN-γ+CD4+, and CD107a+ T cell responses. Four out of five monkeys had elevated intestinal fatty acid binding protein levels at the viral peak, while regenerating islet-derived protein 3α showed marked increases at later time points in the three animals surviving the longest, suggesting gut antimicrobial peptide production in response to microbial translocation post infection. Plasma levels of monocyte chemoattractant protein-1, interleukin-15, and interleukin-12/23 were also elevated. Viral replication in gut and secondary lymphoid tissues was extensive.IMPORTANCESimian/human immunodeficiency viruses (SHIV) are important reagents to study prevention of virus acquisition in nonhuman primate models of HIV infection, especially those representing transmitted/founder (T/F) viruses. However, many R5-tropic SHIV have limited fitness in vivo leading to many monkeys spontaneously controlling the virus post acute infection. Here, we report the generation of a pathogenic SHIV clade C T/F stock by in vivo passage leading to sustained viral load set points, a necessity to study pathogenicity. Unexpectedly, administration of this SHIV to elderly rhesus macaques led to extensive viral replication and fast disease progression, despite maintenance of a strict R5 tropism. Such age-dependent rapid disease progression had previously been reported for simian immunodeficiency virus but not for R5-tropic SHIV infections.

A study of new labor market entrants' job satisfaction trajectories during a series of consecutive job changes.

Previous research on the psychological effect of job change has revealed a honeymoon-hangover pattern during the turnover process. However, there is a dearth of evidence on how individuals react and adapt to multiple job changes over their working lives. This study distinguishes adaptation to a single job change in the short term from adaptation to the process of job change in the long term. Drawing on two large-scale, long-running panel data sets from Britain and Australia, it examined how job satisfaction trajectory evolved as individuals made a series of consecutive job changes since they first entered the labor market. Our fixed effect analyses show that in both countries, individuals experienced a stronger honeymoon effect with each successive job change, before gradually reverting to their baseline job satisfaction. In short, the amplitude of the honeymoon-hangover effect increased across multiple job changes. By distinguishing "adaptation to change" from "change in adaptation," this study generates original insights into the role of job mobility in facilitating career development and extends set point theory from understanding the impact of single life events to recurring life events. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Time-resolved ion energy measurements using a retarding potential analyzer for electric propulsion applications.

To completely characterize the evolving state of a plasma, diagnostic tools that enable measurements of the time-resolved behavior are required. In this study, a gridded ion source with superimposed oscillations was utilized to verify the functionality of a high-speed retarding potential analyzer (HSRPA), at frequencies equivalent to the low frequency oscillations occurring in Hall effect thrusters (HETs). The verification of this device provides an effective alternative to existing diagnostics for measuring time-resolved ion energies. Retarding potential analyzers (RPAs) have established themselves as a fundamental diagnostic in the field of electric propulsion (EP), enabling the measurement of ion energy distributions within the plumes of EP thrusters. The work presented here has demonstrated the capability of a standard RPA in conjunction with high-speed circuitry and data fusion techniques to produce time-resolved ion energy distribution functions (IEDFs) at higher frequencies and beam potentials than have previously been investigated. Tested frequencies ranged between 20 and 80kHz with 10V peak-to peak oscillations at a mean beam potential of 570V. In addition, measurements were conducted with several waveforms, functioning as the superimposed oscillation, including a sine wave, triangle wave, and noisy sine wave. Data from the HSRPA were successfully reconstructed into time series utilizing two data fusion techniques: the empirical transfer function method and shadow manifold interpolation. Time-resolved IEDFs were produced at all frequency set points and waveforms. This investigation has demonstrated the HSRPA effectiveness at producing time-resolved measurements under conditions similar to those occurring in HETs.

Mustard ‘Amara’ Benefits from Superelevated CO2 While Adapting to Far-red Light Over Time

Compared with the ambient Earth carbon dioxide concentration (≈415 μmol⋅mol–1), the International Space Station has superelevated carbon dioxide (≈2800 μmol⋅mol–1), which can be a stressor to certain crops. Far-red light can drive plant photosynthesis and increase extension growth and biomass. However, the effects of far-red light under superelevated carbon dioxide are unclear. We grew hydroponic mustard (Brassica carinata) ‘Amara’ seedlings in four growth chambers using a randomized complete block design with two carbon dioxide concentrations (415 and 2800 μmol⋅mol–1), two lighting treatments, and two blocks at temperature and relative humidity set points of 22 °C and 40%, respectively. Each growth chamber had two lighting treatments at the same total photon flux density of 200 μmol⋅m–2⋅s–1. Under the same blue and green light at 50 μmol⋅m–2⋅s–1 each, plants received either red light at 100 μmol⋅m–2⋅s–1 or red + far-red light at 50 μmol⋅m–2⋅s–1 each. At day 15 after planting, far-red light did not influence shoot fresh or dry mass at 415 μmol⋅mol–1 carbon dioxide, but decreased both parameters by 22% to 23% at 2800 μmol⋅mol–1 carbon dioxide. Increasing the carbon dioxide concentration increased shoot fresh and dry mass 27% to 49%, regardless of the lighting treatment. Far-red light decreased leaf area by 16% at 2800 μmol⋅mol–1 carbon dioxide, but had no effect at 415 μmol⋅mol–1 carbon dioxide. Increasing the carbon dioxide concentration increased leaf area by 21% to 33%, regardless of far-red light. Regardless of the carbon dioxide concentration, far-red light promoted stem elongation and decreased chlorophyll concentrations by 39% to 42%. These responses indicate far-red light elicited a crop-specific shade avoidance response in mustard ‘Amara’, increasing extension growth but decreasing leaf area, thereby reducing light interception and biomass. In addition, carbon dioxide enrichment up to 2800 μmol⋅mol–1 increased the biomass of mustard ‘Amara’ but decreased the biomass of other crops, indicating crop-specific tolerance to superelevated carbon dioxide. In conclusion, mustard ‘Amara’ seedlings benefit from superelevated carbon dioxide, but exhibit growth reduction under far-red light under superelevated carbon dioxide.

Fixed Point Set and Equivariant Map of a S-Topological Transformation Group

The fixed point set and equivariant map of a S-topological transformation group is explored in this work. For any subset K of G, it is established that the fixed point set XK is clopen in X and for a free S-topological transformation group, it is proved that the fixed point set of K is equal to the fixed point set of closure and interior of the subgroup of G generated by K. Subsequently, it is proved that the map between STCG(X) and STCG’(X’) is a homomorphism under a Φ’- equivariant map. Also, it is proved that there is an isomorphism between the quotient topological groups and some basic properties of fixed point set of a S-topological transformation group are studied.

Seismic 3D full-horizon tracking based on a knowledge graph to represent the stratigraphic sequence relationship

Seismic 3D full-horizon tracking is a fundamental and crucial step in sequence analysis and reservoir modeling. Existing automatic full-horizon tracking approaches lack effective methods for representing the stratigraphic sequence relationships in seismic data. However, the inability to represent the stratigraphic sequence relationships fully and accurately makes it challenging to address discontinuous areas affected by faults and unconformities. To address this issue, we develop a knowledge graph representing the stratigraphic sequence relationship, which enables the simultaneous extraction of all horizon surfaces once the stratigraphic distribution of the seismic data is obtained. This method first generates horizon patches and calculates the fault attributes, followed by the construction of an initial knowledge graph that characterizes the overall distribution of horizon patches and faults. The initial knowledge graph comprises nodes and edges. The nodes represent horizon patches, and their attributes cover the geographical location information of the patches and faults. Simultaneously, the edges represent the relationship between the horizon patches, including the stratigraphic sequence relationship, and their attributes illustrate the potential for connecting these patches. Furthermore, we introduce a multilayer knowledge graph based on the point-set topology to fuse the nodes. This allows for the continuous merging of the horizon patches to obtain horizon surfaces across discontinuities with the constraints of fault attributes and stratigraphic sequence relationships in 3D space. Synthetic and field examples demonstrate that our approach can effectively represent stratigraphic sequence relationships and accurately track horizons located in discontinuous areas with faults and unconformities.

Rough Convergence of Double Sequences in $n-$Normed Spaces

In this study, we introduced the concepts of rough convergence, rough Cauchy double sequence, and the set of rough limit points of a double sequence, as well as the rough convergence criteria associated with this set in $n$-normed spaces. Later, we proved that this set is both closed and convex. Finally, we presented the relationships between rough convergence and rough Cauchy double sequence in $n$-normed spaces.

An Upper Bound for the Number of Rectangulations of a Planar Point Set

We prove that every set of n points in the plane has at most $(16+\frac{5}{6})^n$ rectangulations. This improves upon a long-standing bound of Ackerman. Our proof is based on the cross-graph charging-scheme technique.

Discrete cooperative coverage location models with alternative facility types in a probabilistic setting

AbstractIn this paper, we discuss discrete location problems where the objective is to locate a given number of facilities of different types in order to appropriately cover a given set of demand points. The coverage provided to each demand point is the result of the cooperation among the located facilities. The different types of facility refer to the coverage radius or quality of coverage that each type may provide. We present a non‐linear formulation of the problem where the objective is to maximize the percentage of demand points that are appropriately covered. We then show how the model can be linearized based on a representation of probabilities through a network structure. To address large instances of the problem, we introduce a genetic algorithm (GA) that is based on the representation of the solution by two chromosomes. Computational experiments over a wide range of randomly generated problems indicate the GA clearly outperforms CPLEX, especially in larger instances.

$\mathbb{T}-$Relative Fuzzy Linear Programming for $\mathbb{T}-$Relative Fuzzy Target Coverage Problems

Optimal set covering problems are commonplace in communication, remote sensing, logistics, image processing, and network fields [3]. Thus, studies on determining optimal covering sets (sensors) of points (targets) in a region have emerged recently. One characteristic of these studies is the consideration of cases where a target is considered fully covered when it falls within a coverage area ("Boolean" coverage). Consequently, optimality solutions/methods/algorithms founded on this coverage scheme are usually too restrictive and (or) precise and so are not suitable for many complex and real life situations, which are most times plagued with ambiguity, vagueness, imprecision and approximate membership of points and (or) covering sets. Fuzzy structures have proven to be suitable for the representation and analysis of such complex systems with many successful applications. Although fuzzy sets generalizes a set, a more recent generalization for both and its related concepts is the Relative fuzzy set [1] which gives a dynamic fuzzy representation to sets. $\mathbb{T}-$Relative Fuzzy fixed points results of $\mathbb{T}-$Relative fuzzy maps were studied in [5] and recently, the concept of $\mathbb{T}-$Relative fuzzy linear programming [6] was introduced as a generalization of fuzzy linear programming. The results were applied to generalize the Boolean set based covering problems in literature to a $\mathbb{T}-$Relative fuzzy Boolean coverage one. Although, Shan et al. in [15] and others [16] - [21] have given a probabilistic coverage consideration but this lacks subjectivity in representing vagueness and imprecision inherent in most systems. In this present article the Linear Programming (LP) formulation of “A Computational Physics-based Algorithm for Target Coverage Problems" by Jordan Barry and Christopher Thron is generalized by considering a fuzzy and relative fuzzy target coverage instead of the crisp set Boolean coverage. Also we introduce the Fuzzy Linear Programming (FLP) and the $\mathbb{T}-$Relative Fuzzy Linear Programming (RFLP) for the set coverage problem which allows for ascertaining dynamic optimality with aspiration levels.

Optimal mass of structure with motion described by Sturm-Liouville operator: design and predesign

We find an optimal design of a structure described by a Sturm-Liouville (S-L) problem with a spectral parameter in the boundary conditions. Using an approach from calculus of variations, we determine a set of critical points of a corresponding mass functional. However, these critical points - which we call predesigns - do not necessarily themselves represent meaningful solutions: it is of course natural to expect a mass to be real and positive. This represents a generalization of previous work on the topic in several ways. First, previous work considered only boundary conditions and S-L coefficients under certain simplifying assumptions. Principally, we do not assume that one of the coefficients vanishes as in the previous work. Finally, we introduce a set of solvability conditions on the S-L problem data, confirming that the corresponding critical points represent meaningful solutions we refer to as designs. Additionally, we present a natural schematic for testing these conditions, as well as suggesting a code and several numerical examples.
 For more information see https://ejde.math.txstate.edu/Volumes/2024/08/abstr.html

How fast can we play Tetris greedily with rectangular pieces?

Consider a variant of Tetris played on a board of width w and infinite height, where the pieces are axis-aligned rectangles of arbitrary integer dimensions, the pieces can only be moved before letting them drop, and a row does not disappear once it is full. Suppose we want to follow a greedy strategy: let each rectangle fall where it will end up the lowest given the current state of the board. To do so, we want a data structure which can always suggest a greedy move. In other words, we want a data structure which maintains a set of O(n) rectangles, supports queries which return where to drop the rectangle, and updates which insert a rectangle dropped at a certain position and return the height of the highest point in the updated set of rectangles. We show via a reduction from the Multiphase problem [Pătraşcu, 2010] that on a board of width w=Θ(n), if the OMv conjecture [Henzinger et al., 2015] is true, then both operations cannot be supported in time O(n1/2−ϵ) simultaneously. The reduction also implies polynomial bounds from the 3-SUM conjecture and the APSP conjecture. On the other hand, we show that there is a data structure supporting both operations in O(n1/2log3/2⁡n) time on boards of width nO(1), matching the lower bound up to an no(1) factor.