Exact Maps Research Articles

Differences in Advanced Therapeutic Modalities for Overactive Bladder in the United States by Race

ObjectiveTo investigate the impact of race on prescription patterns of therapies for OAB. MethodsThe TriNetX Diamond network was queried to identify adult females with a diagnosis of urinary urgency incontinence (UUI) or OAB, excluding those with stress incontinence or mixed incontinence. Treatments were defined as behavioral, medical, or minimally invasive in accordance with American Urological Association (AUA) guidelines. Propensity score matching for multiple covariates was performed using the greedy nearest-neighbor algorithm. Cox proportional hazards regression analysis was employed to compare the matched cohorts. Rates of treatment by three-digit zip codes were compared through chi-square tests or Fisher’s exact tests and geographic distribution maps were generated via STATA 17.0. ResultsWe identified 2,687,316 adult females diagnosed with OAB; 767,159 identified as White and 108,464 as Black. Within these cohorts, 16.6% of Black patients and 20.4% of White patients received OAB treatment. Twenty-six-point three percent of US zip-codes contained data for both White and Black patients, and in all these zip codes, White patients received significantly higher rates of prescriptions compared to Black patients. After propensity-score matching, significant differences in prescriptions persisted between the two groups with White patients exhibiting higher rates of any prescription. ConclusionsOur results demonstrate a significantly lower rate of prescriptions of medical and minimally invasive therapies for Black women. These racial differences in prescription of advanced therapeutic modalities for OAB may not be secondary to diagnosis but are likely secondary to prescribing disparities. Further research is needed to understand these differences.

An exploration of circumbinary systems using gravitational microlensing

Gravitational microlensing is one of the methods to detect exoplanets–planets outside our solar system. Here, we focus on the theoretical modeling of systems with three lensing objects and in particular circumbinary systems. Circumbinary systems include two stars and at least one planet and are estimated to represent a sizeable portion of all exoplanets. Extending a method developed for binary lenses to the three lens case, we explore the parameter space of circumbinary systems, producing exact magnification maps and light curves.

Maps unlock the full dynamics of targeted energy transfer via a vibro-impact nonlinear energy sink

We consider a model of a vibro-impact nonlinear energy sink (VI-NES), where a ball moves within a cavity of an externally forced mass, impacting either end of the cavity. These impacts result in energy transfer from the mass to the ball, thus limiting the oscillations of the larger system. We develop a semi-analytical map-based approach, recently used for an inclined impact pair model, in the setting where there is energy transfer between the mass and the ball. With this approach we analytically derive exact expressions for the full dynamics of the VI-NES system without restricting the range of parameters, in contrast to other recent work in which an approximate reduced model is valid only for small mass of the ball, small amplitude, and a limited frequency range. We develop the bifurcation analysis for the full VI-NES system, based on exact maps between the states at successive impacts. This analysis yields parameter ranges for complex periodic responses and stability analyses for O(1) mass of the ball, forcing frequencies that are not the same as the natural frequency, and large amplitude forcing. The approach affords the flexibility to analytically study the dynamics of different periodic solutions and their stability, including a variety of impact sequences in the full two degree-of-freedom model of VI-NES. Comparisons of quantities that characterize the energy transfer point to the significance of different types of periodic behavior, which may occur for different parameter combinations. Our semi-analytical results also provide the impact phase, which plays an important role in the efficiency of the energy transfer.

Review on Tomato Ripe Detection and Segmentation Using Deep learning Models for Sustainable Agricultural Development

Using natural resources to maximize yields is possible when .precision agriculture is used in a diversified environment. Automating agriculture can reduce resource consumption and enhance food quality. Sowing, monitoring, controlling weeds, managing pests, and harvesting crops are all possible with agricultural robots. To estimate crop production, it is necessary to physically count fruits, flowers, or fruits at various stages of growth. Precision and dependability are provided by remote sensing technologies for agricultural production forecasting and estimation. Automated image analysis using deep learning and computer vision (CV) produces exact field maps. In this review, deep learning (DL) techniques were found to improve the accuracy of smart farming, so we present different methodologies to automate the detection of agricultural yields using virtual analysis and classifiers. The smart farming will generate a sustainable agricultural development.

Image Processing: Convert a Sketch into Coloures Image using cGAN

Synthesizing realistic images from human drawn sketches is a challenging problem in computer graphics and vision. Existing approaches either need exact edge maps, or rely on retrieval of existing photographs. In this work, we propose a novGenerative Adversarial Network(GAN) approach that synthesizes plausible images from 50 categories including motorcycles, horses and couches. We demonstrate a data augmentation technique for sketches which is fully automatic, and we show that the augmented data is helpful to our task. We introduce a new network building block suitable for both the generator and discriminator which improves the information flow by injecting the input image at multiple scales. Compared to state-of-the-art image translation methods, our approach generates more realistic images and achieves significantly higher Inception Scores.

On simultaneous linearization of certain commuting nearly integrable diffeomorphisms of the cylinder

AbstractLet $$\mathcal {F}$$ F and $$\mathcal {K}$$ K be commuting $$C^\infty $$ C ∞ diffeomorphisms of the cylinder $$\mathbb {T}\times \mathbb {R}$$ T × R that are, respectively, close to $$\mathcal {F}_0 (x, y)=(x+\omega (y), y)$$ F 0 ( x , y ) = ( x + ω ( y ) , y ) and $$T_\alpha (x, y)=(x+\alpha , y)$$ T α ( x , y ) = ( x + α , y ) , where $$\omega (y)$$ ω ( y ) is non-degenerate and $$\alpha $$ α is Diophantine. Using the KAM iterative scheme for the group action we show that $$\mathcal {F}$$ F and $$\mathcal {K}$$ K are simultaneously $$C^\infty $$ C ∞ -linearizable if $$\mathcal {F}$$ F has the intersection property (including the exact symplectic maps) and $$\mathcal {K}$$ K satisfies a semi-conjugacy condition. We also provide examples showing necessity of these conditions. As a consequence, we get local rigidity of certain class of $$\mathbb {Z}^2$$ Z 2 -actions on the cylinder, generated by commuting twist maps.

A multiple instance solver framework based on dynamic overset grid method for flow field simulation of array configuration with moving components

This paper presents a novel computational fluid dynamics (CFD) framework for flow simulation of complex configurations containing relatively moving components. The framework is based on the dynamic overset grid method and is intrinsically parallel. The user only needs to decompose complex configurations into topologically simple components according to the geometric features and generate high-quality computational meshes around these components. The framework can then automatically instantiate multiple fully functional CFD solvers to solve the flow fields on the meshes of all components simultaneously in a one-to-one correspondence. Thus, the geometric relationships of the components are transformed into concurrent states of the instance solvers, and accordingly, their flow fields are coupled through the intercommunication among instance solvers. The framework is implemented in a parallel environment based on the Message Passing Interface (MPI). An instantiation space is formed by splitting the world communicator into desired number of fully functional sub-communicators. Within this space, the same number of independent solvers with complete input and output interfaces can be instantiated from the same template solver. The data coupling between instance solvers is realised using the dynamic overset grid method, and the whole process is achieved automation by approaches of collision detection, Exact Inverse Maps (EIM)-based donor cell search, and robust Implicit Hole Cutting (IHC). Numerical results show that the framework is effective for configurations with complex topologies, and it is particularly suitable for numerical simulations of array configurations with relatively moving components.

NaturaSat—A Software Tool for Identification, Monitoring and Evaluation of Habitats by Remote Sensing Techniques

The NaturaSat software integrates various image processing techniques together with vegetation data, into one multipurpose tool that is designed for performing facilities for all requirements of habitat exploration, all in one place. It provides direct access to multispectral Sentinel-2 data provided by the European Space Agency. It supports using these data with various vegetation databases, in a user-friendly environment, for, e.g., vegetation scientists, fieldwork experts, and nature conservationists. The presented study introduces the NaturaSat software, describes new powerful tools, such as the semi-automatic and automatic segmentation methods, and natural numerical networks, together with validated examples comparing field surveys and software outputs. The software is robust enough for field work researchers and stakeholders to accurately extract target units’ borders, even on the habitat level. The deep learning algorithm, developed for habitat classification within the NaturaSat software, can also be used in various research tasks or in nature conservation practices, such as identifying ecosystem services and conservation value. The exact maps of the habitats obtained within the project can improve many further vegetation and landscape ecology studies.

Predator‐prey models with memory and kicks: Exact solution and discrete maps with memory

In this paper, we proposed new predator‐prey models that take into account memory and kicks. Memory is understood as the dependence of current behavior on the history of past behavior. The equations of these proposed models are generalizations of the Lotka‐Volterra and Kolmogorov equations by using the Caputo fractional derivative of non‐integer order and periodic kicks. This fractional derivative allows us to take into account memory with power‐law fading. The periodic kicks, which are described by Dirac delta‐functions, take into account short duration of interaction between predators and prey. For the proposed equations, which are fractional differential equations with kicks, we obtain exact solutions that describe behaviors of predator and prey with power‐law fading memory. Using these exact solutions, we derive, without using any approximations, new discrete maps with memory that represent the proposed predator‐prey models with memory.

Marea/Northern Hawwariya in northern Egypt: Integrated results of non‐invasive and excavation works

AbstractMarea/Northern Hawwariya is one of the largest and most important archaeological sites dating between the 3rd century BC and the 8th century AD located at Lake Mareotis in northern Egypt. Even though excavations have been carried out since the end of the 1970s, the settlement is still largely unexplored. To rectify this situation, non‐invasive research has been carried out on 21.5 ha of the site using a precise positioning system and magnetometer measurements. Exact topographic and magnetic maps were prepared based on the data that were obtained. Simultaneously, verification research were carried out, including archaeological excavations, registering surface findings and satellite image analysis. In the south‐eastern part of the site, electrical resistivity measurements were taken as well. This approach allowed for the identification of the densely built areas of the Byzantine and Early Islamic town. On the south‐western side, some magnetic anomalies were registered, following regular patterns with clear linear borders and surrounded by wetlands without clear signs of habitation. On the northern side, the settlement was limited by an artificial coastline, forming straight waterfronts made of stone blocks. As for the town itself, a 260‐m street with adjacent regular built‐up areas was discovered. This regularity points to an order of planning, at least for the Byzantine part of the settlement. Recording of large amplitude magnetic anomalies proves the presence of heavily burnt objects. They may be interpreted as remains of kilns, perhaps used to manufacture amphorae, glass vessels and lime. Electrical resistivity measurements in the south‐eastern part of the site localized cavities in the natural limestone rock uplift. These may have been rock‐cut tombs. Multidisciplinary, non‐invasive research in Marea/Northern Hawwariya allowed for the quick generation of new knowledge on the topography of the site, significantly enriching information on its form and the functions of its various parts.

Staged Sketch-to-Image Synthesis via Semi-supervised Generative Adversarial Networks

Sketch-based image synthesis is a challenging problem in computer graphics and vision. Existing approaches either require exact edge maps or rely on the retrieval of existing photographs, which limits their applications in real-world scenarios. Accordingly in this work, we propose a staged semi-supervised generative adversarial networks based method for sketch-to-image synthesis, which can directly generate realistic images from novice sketches. More specifically, we first adopt a conditional generative adversarial network (CGAN) to extract class-wise representations from unpaired images. These class-wise representations are then exploited and incorporated with another CGAN, which are used to generate realistic images from sketches. By incorporating the class-wise representations, our method can leverage both the general class information from unpaired images and the targeted object information from input sketches. Additionally, this network architecture also enables us to take full advantage of widely available unpaired images and learn more accurate class representations. Extensive experiments demonstrate, compared with state-of-the-art image translation methods, our approach can achieve more promising results and synthesize images with significantly better Inception Scores and Frechet Inception Distance.

Global behaviors of weak KAM solutions for exact symplectic twist maps

We investigated several global behaviors of the weak KAM solutions uc(x,t) parametrized by c∈H1(T,R). For the suspended Hamiltonian H(x,p,t) of the exact symplectic twist map, we could find a family of weak KAM solutions uc(x,t) parametrized by c(σ)∈H1(T,R) with c(σ) continuous and monotonic and∂tuc+H(x,∂xuc+c,t)=α(c),a.e.(x,t)∈T2, such that sequence of weak KAM solutions {uc}c∈H1(T,R) is 1/2-Hölder continuity of parameter σ∈R. Moreover, for each generalized characteristic (no matter regular or singular) solving{x˙(s)∈co[∂pH(x(s),c+D+uc(x(s),s+t),s+t)],x(0)=x0,(x0,t)∈T2, we evaluate it by a uniquely identified rotational number ω(c)∈H1(T,R). This property leads to a certain topological obstruction in the phase space and causes local transitive phenomenon of trajectories. Besides, we discussed this applies to high-dimensional cases.

Measure and Capacity of Wandering Domains in Gevrey Near-integrable Exact Symplectic Systems

A wandering domain for a diffeomorphism is an open connected set whose iterates are pairwise disjoint. We endow A^n = T^n x R^n with its usual exact symplectic structure. An integrable diffeomorphism Φ^h, i.e. the time-one map of a Hamiltonian h which depends only on the action variables, has no nonempty wandering domains. The aim of this paper is to estimate the size (measure and Gromov capacity) of wandering domains in the case of an exact symplectic perturbation of Φ^h , in the analytic or Gevrey category. Upper estimates are related to Nekhoroshev theory, lower estimates are related to examples of Arnold diffusion. This is a contribution to the quantitative Hamiltonian perturbation initiated in previous works on the optimality of long term stability estimates and diffusion times; our emphasis here is on discrete systems because this is the natural setting to study wandering domains. We first prove that the measure (or the capacity) of these wandering domains is exponentially small, with an upper bound of the form exp(-c e^(-1/2nα)), where e is the size of the perturbation, α is the Gevrey exponent (α is at least 1, α=1 for analytic systems) and c is some positive constant depending mildly on h. This is obtained as a consequence of an exponential stability theorem for near-integrable exact symplectic maps, in the analytic or Gevrey category, for which we give a complete proof based on the most recent improvements of Nekhoroshev theory for Hamiltonian flows, and which requires the development of specific Gevrey suspension techniques. The second part of the paper is devoted to the construction of near-integrable Gevrey systems possessing wandering domains, for which the capacity (and thus the measure) can be estimated from below. We suppose that n is at least 2, essentially because KAM theory precludes Arnold diffusion in too low a dimension. For any α>1, we produce examples with lower bounds of the form exp(-c e^(-1/2(n-1)(α-1))). This is done by means of a coupling technique, involving rescaled standard maps possessing wandering discs in A and near-integrable systems possessing periodic domains of arbitrarily large periods in A^(n-1). The most difficult part of the construction consists in obtaining a perturbed pendulum-like system on A with periodic islands of arbitrarily large periods, whose areas are explicitly estimated from below. Our proof is based on a version due to Herman of the translated curve theorem.

A Parameterization Method for Lagrangian Tori of Exact Symplectic Maps of $R^2r$

We are concerned with analytic exact symplectic maps of ${\mathbb R}^{2r}$ endowed with the standard symplectic form. We study the existence of a real analytic torus of dimension $r$, invariant by the map and carrying quasi-periodic motion with a prefixed Diophantine rotation vector. Therefore, this torus is a Lagrangian manifold. We address the problem by the parameterization method in KAM theory. The main aspect of our approach is that we do not look for the parameterization of the torus as a solution of the corresponding invariance equation. Instead, we consider a set of three equations that, all together, are equivalent to the invariance equation. These equations arise from the geometric and dynamical properties of the map and the torus. Suppose that an approximate solution of these equations is known and that a suitable nondegeneracy (twist) condition is satisfied. Then, this system of equations is solved by a quasi-Newton-like method, provided that the initial error is sufficiently small. By “quasi-Newton-like” we mean that the convergence is almost quadratic but that at each iteration we have to solve a nonlinear equation. Although it is straightforward to build a quasi-Newton method for the selected set of equations, proceeding in this way we improve the convergence condition. The selected definition of error reflects the level at which the error associated with each of these three equations contributes to the total error. The map is not required to be close to integrable or expressed in action-angle variables. Suppose the map is $\varepsilon$-close to an integrable one, and consider the portion of the phase space not filled up by Lagrangian invariant tori of the map. Then, the upper bound for the Lebesgue measure of this set that we may predict from the result is of ${\mathcal O}(\varepsilon^{1/2})$. In light of the classical KAM theory for exact symplectic maps, an upper bound of ${\mathcal O}(\varepsilon^{1/2})$ for this measure is the expected estimate. The result also has some implications for finitely differentiable maps.

Topology mapping algorithm for 2D and 3D Wireless Sensor Networks based on maximum likelihood estimation

Automation of many sensor network protocols requires maps indicating sensor locations. Physical coordinate based maps capture the physical layout including voids and shapes, but obtaining the required distance values is often not feasible or economical. Alternative is to use topological maps based only on connectivity Information. Due to lack of physical distances, they are not faithful representatives of the physical layout. Here we present Maximum Likelihood-Topology Maps (ML-TM) that provide a more accurate physical representation, by using the probability of signal reception, an easily measurable parameter that is sensitive to the distance. Approach is illustrated using a mobile robot that listens to signals transmitted by sensor nodes and maps the packet reception probability to a coordinate system using a signal receiving probability function. ML-TM is an intermediate map between exact physical maps and hop- based topology coordinates. Results show that ML-TM algorithm generates maps for various network shapes with voids/obstacles in different environmental conditions with an error less than 7%. Performance of the algorithm in 3D sensor networks is also illustrated.

Exact maps in density functional theory for lattice models

In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and graphically illustrate the complete exact density-to-wavefunction map that underly the Hohenberg–Kohn theorem in density functional theory. Having the explicit wavefunction-to-density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragments decreases and the correlation grows. We denominate this feature as intra-system steepening and discuss how it relates to the well-known inter-system derivative discontinuity. The inter-system derivative discontinuity is an exact concept for coupled subsystems with degenerate ground state. However, the coupling between subsystems as in charge transfer processes can lift the degeneracy. An important conclusion is that for such systems with a near-degenerate ground state, the corresponding cut along the particle number N of the exact density functionals is differentiable with a well-defined gradient near integer particle number.

Photon self-interaction on deformed spacetime

A novel nonlocal four-photon interaction on the deformed spacetime is derived and studied in the three selected models (I, II, III). The first two models (I, II) are obtained via two distinct second-order $\theta$-exact Seiberg-Witten maps of the noncommutative U(1) gauge field strength on Moyal space. The third one (III), inspired by the manifestly gauge invariant structures emerging in the first two, due to the model generality has been constructed with a different set of freedom parameters. The physical relevancy of all models is analyzed by evaluating the four-photon-tadpole diagram, which, when combined with the bubble graph, enables us to fully consider all contributions to the one-loop photon polarization tensor. For an arbitrary noncommutative matrix theta^\mu\nu, the full quadratic IR divergence cancellation in the one-loop photon two-point function is obtained with particular combinations of Seiberg-Witten map/gauge-symmetry freedom parameters in models I and II. Finally, our model III enables complete elimination of all pathological terms in the photon polarization tensor at one-loop order if a special value for the theta matrix is chosen.

Invariant curves for exact symplectic twist maps of the cylinder with Bryuno rotation numbers

Since Moser's seminal work it is well known that the invariant curves of smooth nearly integrable twist maps of the cylinder with Diophantine rotation number are preserved under perturbation. In this paper we show that, in the analytic class, the result extends to Bryuno rotation numbers. First, we will show that the series expansion for the invariant curves in powers of the perturbation parameter can be formally defined, then we shall prove that the series converges absolutely in a neighbourhood of the origin. This will be achieved using multiscale analysis and renormalisation group techniques to express the coefficients of the series as sums of values which are represented graphically as tree diagrams and then exploit cancellations between terms contributing to the same perturbation order. As a byproduct we shall see that, when perturbing linear maps, the series expansion for an analytic invariant curve converges for all perturbations if and only if the corresponding rotation number satisfies the Bryuno condition.

Exact circle maps and KMS states

We describe the KMS states and the ground states for the gauge action on the C*-algebra of the oriented transformation groupoid of a continuous piecewise monotone and exact map of the circle.

Chaotic Dynamics in an Impact Problem

We consider the model describing the vertical motion of a ball falling with constant acceleration on a wall and elastically reflected. The wall is supposed to move in the vertical direction according to a given periodic function $f$. We show that a modification of a method of Angenent based on sub and super solutions can be applied in order to detect chaotic dynamics. Using the theory of exact symplectic twist maps of the cylinder one can prove the result under "natural" conditions on the function $f$.