Continuity Assumption Research Articles

MGDA: Model-based Goal Data Augmentation for Offline Goal-conditioned Weighted Supervised Learning

Recently, a state-of-the-art series of algorithms—Goal-Conditioned Weighted Supervised Learning (GCWSL) methods—has been introduced to address the challenges inherent in offline goal-conditioned reinforcement learning (RL). GCWSL optimizes a lower bound on the goal-conditioned RL objective and has demonstrated exceptional performance across a range of goal-reaching tasks, offering a simple, effective, and stable solution. Nonetheless, researches has revealed a critical limitation in GCWSL: the absence of trajectory stitching capabilities. In response, goal data augmentation strategies have been proposed to enhance these methods. However, existing techniques often fail to effectively sample appropriate augmented goals for GCWSL. In this paper, we establish unified principles for goal data augmentation, emphasizing goal diversity, action optimality, and goal reachability. Building on these principles, we propose a Model-based Goal Data Augmentation (MGDA) approach, which leverages a dynamics model to sample more appropriate augmented goals. MGDA uniquely incorporates the local Lipschitz continuity assumption within the learned model to mitigate the effects of compounding errors. Empirical results demonstrate that MGDA significantly improves the performance of GCWSL methods on both state-based and vision-based maze datasets, outperforming previous goal data augmentation techniques in their ability to enhancing stitching capabilities.

Non-Fourier heat transport in graphene nanoribbons: Regulation of temperature oscillations and cooling effects

Existing research indicates that phonon heat transport in low-dimensional materials exhibits significant non-Fourier heat transport behavior, particularly under ultrafast and nanoscale conditions. This study develops a non-Fourier heat conduction model based on the continuous medium assumption, incorporating both temperature gradient and heat flux hysteresis effects. Using a first-principles finite element numerical simulation framework, we investigate phonon heat transport in graphene nanoribbons under Gaussian transient thermal pulse excitation. Numerical results show that at a low temperature of 80 K, N scattering mechanisms dominate, leading to a temperature oscillation phenomenon characterized by a transition from ballistic to hydrodynamic transport. As the initial temperature increases to 150 and 300 K, R scattering effects become predominant, resulting in a gradual transition of heat transport toward a diffusion mechanism, which significantly diminishes or even eliminates the temperature oscillations. Furthermore, by adjusting the discrete parameters of the Gaussian thermal pulse, localized temperature fluctuations and cooling effects can be induced at 100 K. This research not only provides theoretical support for the quantitative analysis of the microscopic mechanisms of phonon heat transport in low-dimensional materials but also offers potential theoretical foundations for efficient thermal management design in transient thermal grating experiments and graphene-based semiconductor devices.

Augury and Forerunner: Real‐Time Feedback Via Predictive Numerical Optimization and Input Prediction

AbstractIn many interactive systems, user input initializes and launches an iterative optimization procedure. The goal is to provide assistive feedback to some creation/editing process. Examples include constraint‐based GUI layout and complex snapping scenarios. Many geometric problems, such as fitting a shape to data, involve optimizations which may take seconds to complete (or even longer), yet require human guidance. In order to make these optimization routines practical in interactive sessions, simplifications or sacrifices must be made. Canonically, non‐convex optimization problems are solved iteratively by taking a series of steps towards a solution. By their nature, there are many locally optimal solutions; which solution is found is highly dependent on an initial guess. There is a fundamental conflict between optimization and interactivity. Interrupting and restarting the optimization every time the user, e.g. moves the mouse prevents any solution from being computed until the user ceases interaction. Continuing to run the optimization procedure computes a perpetually outdated solution. This presents a particular unsolved challenge with respect to direct manipulation. Every time the user, e.g. moves the mouse, the entire optimization must be re‐started with the new user input, since returning a stale result associated with the previous user state is undesirable. We propose predictive short‐circuiting to reduce this fundamental tension. Our approach memoizes paths in the optimization's configuration space and predicts the trajectory of future optimization in real time, leveraging common continuity assumptions. This enables direct manipulation of formerly sluggish interactions. We demonstrate our approach on geometric fitting tasks. Additionally, we evaluate complementary mouse motion prediction algorithms as a means to discard or skip optimization problems that are irrelevant to the user's intended initial configuration for a targeted optimization procedure. Predicting where the mouse cursor will be located at the end of an operation, such as dragging a model of an engine component into scanned point cloud data to perform geometric alignment, allows us to pre‐emptively begin solving the targeted problem before the user finishes their movement. We take advantage of the fact that the prediction indicates the approximate energy basin the optimization procedure will need to explore.

Excess demand approach with non-convexity and discontinuity: a generalization of the Gale–Nikaido–Kuhn–Debreu lemma

Abstract This paper provides a three-fold generalization of the Gale–Nikaido–Kuhn–Debreu lemma, a fundamental result for classical Walrasian general equilibrium theory. It weakens the (i) convexity assumption on the given (excess demand) correspondence, and (ii) the continuity assumption by synthesizing both the majorization and inclusion approaches, and uses these results to derive a (iii) theorem on the existence of a Walrasian equilibrium in an exchange economy with externalities, and non-ordered, non-convex, price-dependent preferences under a weaker continuity assumption that is assumed in the literature. It also highlights a trade-off between the weakened continuity and convexity assumptions.

Определение давления газа в полостях расслоения горного массива в зонах, опасных по прорывам метана из почвы

Methane outbreaks from mine excavation soils occurring in coalmines cause serious damage to enterprises and threaten the life and health of miners. The normative forecasting method of the phenomenon was studied at the end of the 20th century. It assumes high error rates of the second kind and therefore requires improvement. The mechanism of hazardous area formation assumes the occurrence of stratification cavities in the rocks of mine excavation soils filled with methane under high pressure, followed by the loss of containment of the cavity and a gas explosion. The acceptance of gas pressure in the cavity at the level of methane geostatic pressure for the calculation is considered one of the possible causes of the insufficient accuracy of the method mentioned above. The study is dedicated to the determination of the balanced pressure of methane in the stratification cavity in conditions of a leak-tight system «methane source — stratification cavity». Due to accepting the assumption of continuity of cavity volume and leak-tightness of the system «methane source — stratification cavity», determining the balanced pressure of methane in this system has been reduced to a static problem. In the course of problem-solving, a quadratic equation based on the Boyle — Mariotte law and a formula for the phase balance of methane in coal has been developed. The values of the balanced pressure of methane in the stratification cavity have been calculated for various mining and geological indices. Actual indices of the rock mass have been adopted as the initial data. The obtained values of balanced pressure are approximately three times lower than the formation pressures existing in natural conditions. Therefore, the assumptions regarding the invidious comparison of methane pressure in the stratification cavity with the geostatic pressure when determining the probability of soil rock destruction and the following methane outbreak have been fully confirmed.

Dual‐Inertial Viscosity‐Based Subgradient Extragradient Methods for Equilibrium Problems Over Fixed Point Sets

ABSTRACTThis paper introduces a new algorithmic framework for solving pseudomonotone equilibrium problems and demicontractive fixed‐point problems. Unlike conventional methods that incorporate a single inertial step, our approach employs dual inertia to accelerate convergence while preserving stability. The proposed method combines the viscosity approximation technique with the extragradient method to guarantee strong convergence. Initially, the extragradient method is applied under a Lipschitz continuity assumption on the equilibrium bifunction. Subsequently, this condition is relaxed by adopting a self‐adaptive step size strategy, allowing variable step sizes to be updated iteratively based on the current iterates information. Notably, the algorithm operates without requiring prior knowledge of the Lipschitz constants or any line search procedures. Strong convergence is established under mild condition, and its applicability to variational inequality problems is demonstrated. Numerical experiments validate the effectiveness of the proposed approach, showcasing its capability to handle large‐scale and complex problems efficiently while outperforming traditional single‐inertia methods.

A neurodynamic approach with fixed-time convergence for complex-variable pseudo-monotone variational inequalities

A neurodynamic approach with fixed-time convergence for complex-variable pseudo-monotone variational inequalities

Existence of solutions and well-posedness for set optimization problems with an application in the robust optimization

In this paper, first a generalization of the Weierstrass theorem for set-valued mappings in the absence of usual continuity and compactness assumptions is derived. Then, new notions of well-posedness for set-valued optimization problems are presented and some necessary and sufficient conditions for well-posedness of these problems are obtained. Finally, as an application, we provide some results for a robust set-valued optimization problem.

Adverse Weather Optical Flow: Cumulative Homogeneous-Heterogeneous Adaptation.

Optical flow has made great progress in clean scenes, while suffers degradation under adverse weather due to the violation of the brightness constancy and gradient continuity assumptions of optical flow. Typically, existing methods mainly adopt domain adaptation to transfer motion knowledge from clean to degraded domain through one-stage adaptation. However, this direct adaptation is ineffective, since there exists a large gap due to adverse weather and scene style between clean and real degraded domains. Moreover, even within the degraded domain itself, static weather (e.g., fog) and dynamic weather (e.g., rain) have different impacts on optical flow. To address above issues, we explore synthetic degraded domain as an intermediate bridge between clean and real degraded domains, and propose a cumulative homogeneous-heterogeneous adaptation framework for real adverse weather optical flow. Specifically, for clean-degraded transfer, our key insight is that static weather possesses the depth-association homogeneous feature which does not change the intrinsic motion of the scene, while dynamic weather additionally introduces the heterogeneous feature which results in a significant boundary discrepancy in warp errors between clean and degraded domains. For synthetic-real transfer, we figure out that cost volume correlation shares a similar statistical histogram between synthetic and real degraded domains, benefiting to holistically aligning the homogeneous correlation distribution for synthetic-real knowledge distillation. Under this unified framework, the proposed method can progressively and explicitly transfer knowledge from clean scenes to real adverse weather. In addition, we further collect a real adverse weather dataset with manually annotated optical flow labels and perform extensive experiments to verify the superiority of the proposed method.

Hybrid Chebyshev-Type Methods for Solving Nonlinear Equations

Chebyshev-type methods have replaced the Chebyshev method in practice for solving nonlinear equations in abstract spaces. These methods are of the same R-order of three. However, they are easier to deal with, since the computationally expensive second derivative of the operator involved does not appear on these methods. However, the invertibility of the first derivative is still required at each step of the iteration. In this article, the inverse is replaced by a finite sum of linear operators. The convergence of the new Hybrid Chebyshev-Type Method (HCTM) is established under relaxed generalized continuity assumptions on the derivative and majorizing sequences. The iterates of the new methods converge to the original ones, but they are easier to find. Moreover, the numerical examples demonstrate that the new iterates converge essentially as fast to the solution. The methodology of this article can be used on other methods with inverses along the same lines due to its generality.

A Nonparametric Model for High-Frequency Energy Prices

Abstract This paper proposes an efficient approach for modelling a high frequency continuous time diffusion process for the dynamics of crude oil. While various applications of continuous time models are considered in the literature, the results on choosing the right model are mixed. We employ a very general non-parametric approach to capture the dynamics of the crude oil market proxied by United States Oil (USO) exchange traded fund. This approach is purely data driven and does not require specification of the drift or the diffusion coefficient function. The proposed nonparametric kernel-based estimation procedure relies on the local polynomial kernel regression, where the choice of a bandwidth parameter plays a significant role. We demonstrate that besides offering a convenient way of estimating the continuous-time models for energy prices, our estimation procedure performs well when dealing with predicting USO prices out-of-sample. The analysis is extended by incorporating possible jump diffusion, where the assumption of continuity of the stochastic process is relaxed and a jump component is added to the diffusion process. In addition, we extend our model by adding possible seasonalities in the underlying dynamics, which requires decomposing the price by means of the Maximum Overlap Discrete Wavelet Transform (MODWT) algorithm and applying nonparametric kernel-based estimation procedure to modelling of the deseasonalized prices.

The Relations Between Hölder Continuity Assumptions on the Direction of Vorticity and Energy Equality

The Relations Between Hölder Continuity Assumptions on the Direction of Vorticity and Energy Equality

On the Implementation of Iterative Methods Without Inverse Updating for Solving Equations in Banach Spaces

The implementation of iterative methods using inverses to solve equations is a computationally expensive or impossible task in general. This is the case, since the analytical form of the inverse is difficult to find in practice. That is why, we replace the inverse by a sum of linear operators which is well defined. The convergence of the resulting hybrid methods is studied based on majorizing sequences under generalized continuity assumptions on the operators involved and in the setting of a Banach space. It is demonstrated by numerical experimentations that the convergence order as well as the number of iterations required to obtain a predetermined error tolerance when comparing the original to the hybrid method is essentially the same.

Water compression induced ionic negative differential resistance in nanopores.

The mass transport behavior through nanoscale channels, greatly influenced by the structures and dynamics of nanoconfined water, plays an essential role in many biophysical processes. However, the dynamics of nanoconfined water under an external field and its effects are still not fully understood. Here, on the basis of molecular dynamics simulations, we theoretically show that the ionic current of [Bmim][PF6] through narrow pores in graphene membrane exhibits an ionic negative differential resistance effect-the ionic current decreases as the voltage increases over a certain threshold. This effect arises from the violation of traditional fluid dynamics as the assumption of continuity and homogeneity of fluids is no longer effective in ultrathin nanopores. The gradient of electric field around the atomic-thin layer produces a strong gradient force on the polarized water inside the nanopore. This dielectrophoretically compressed water leads to a hydrostatic force that repels ions from entering the nanopore. Our findings may advance the understanding of hydrostatic mechanism, which governs ion transport through nanopores.

The generalized Łojasiewicz inequality for definable and subanalytic multifunctions

The generalized Łojasiewicz inequality for definable and subanalytic multifunctions

Delayed Interval-Valued Symmetric Stochastic Integral Equations

In this paper, delayed stochastic integral equations with an initial condition and a drift coefficient given as interval-valued mappings are considered. These equations have a certain symmetric form that distinguishes them from classical single-valued stochastic integral equations and has implications for the properties of the diameter of the values of the solutions of the equations. The main result of the paper is the theorem that there is a unique solution to the equation considered. It was obtained under the assumptions of continuity of the kernels and Lipschitz continuity of the drift and diffusion coefficients. The proof of the existence of the solution is carried out by the method of iterating successive approximations. The paper ends with theorems about the continuous dependence of the solution on the initial function, kernels and nonlinearities.

A geometric view of seismic wavefields: implications for imaging dense clusters of events

SUMMARY Imaging dense clusters of seismicity is crucial to many problems in seismology: to delineate complex systems of faults, provide constraints on the causes of volcanic and cryogenic swarms, and to shed light on possible means to prevent damaging induced seismicity in mining, geothermal, and oil and gas extraction activities. Current imaging methods rely upon high-resolution relative location techniques, commonly requiring arrival-time picks for seismic phases. This paper examines an alternative approach, based upon concepts drawn from differential geometry, that images directly from waveform data. It relies upon the common assumption of spatial continuity of seismic wavefield observations, which implies that a differentiable map exists between the source region to be imaged and waveform observations considered as elements of a vector space. The map creates an image of event clusters on a Riemannian manifold embedded in that vector space. The image can be visualized by projecting the observations into a tangent space of the manifold and is a distorted rendering of cluster geometry. However, the distortion can be predicted and removed if a model for wavefield propagation is available. This visualization approach is applicable to clusters of uniform events with highly similar waveforms, such as are commonly acquired with correlation detectors or other pattern matching techniques. To assess its performance, it is applied to the closely related reciprocal problem of imaging the (known) geometry of an array from observations by the array of several regional events. Differences between the original problem and its reciprocal analogue are noted and controlled for in the analysis. Chief among the differences is the necessity for aligning the waveforms in the original problem, which, to maintain consistency with the original problem, is solved in the reciprocal problem by a generalization of the VanDecar–Crosson algorithm. The VanDecar–Crosson algorithm exhibits a bias, shown through an analysis of the situation when the observed wavefields are adequately modelled as plane waves. In that circumstance, the bias can be predicted and removed. In a test using a portion of a large-N array, this imaging approach is shown to successfully reconstruct the array geometry. The method is applicable directly to infinitesimal array apertures, but is extended to a larger aperture by partitioning the image into local, effectively infinitesimal overlapping subsets. These are inverted, then assembled into a global picture of the array geometry using constraints provided by the overlapped regions. Although demonstrated in a reciprocal array context, the method appears viable for imaging clusters of events with highly similar source mechanisms and time histories.

Unwrap Intractable C‐Band Coseismic Interferograms: An Improved SNAPHU Method With Range Offset Gradients as Prior Information

AbstractC‐band Interferometric Synthetic Aperture Radar (InSAR) data are widely used to map coseismic deformation. However, phase unwrapping errors are commonly distributed near faults owing to decorrelation and steep phase gradients from short radar wavelengths. Here, we propose an improved SNAPHU phase‐unwrapping algorithm that considers the prior information of the range offset gradients (P‐SNAPHU) to overcome the constraints imposed by the phase continuity assumption. P‐SNAPHU exploits median filtering of homogeneous pixels for initial denoising of range offset and then refines range offset gradients divisionally through saliency extraction. The derived gradients are used to estimate the expected values of the cost functions for the low‐coherence fringes. The synthetic experiments show significant improvements in the phase‐unwrapping accuracy of the P‐SNAPHU method compared with classical unwrapping methods. We apply the P‐SNAPHU method to unwrap Sentinel‐1 coseismic interferograms of three large (Mw > 6.5) strike‐slip earthquake events that the existing classical methods could not successfully unwrap. In the comparison of the unwrapped interferograms with the external global navigation satellite system (GNSS) displacements and those from the classical methods, we find that P‐SNAPHU significantly reduces the phase unwrapping errors with the mean absolute error of 7.2, 2.3, and 1.8 cm for the 2023 Kahramanmaraş earthquake doublet, the 2016 Kumamoto earthquake, and the 2019 Ridgecrest earthquakes, respectively. Based on the unwrapped results derived from P‐SNAPHU, an estimate is made regarding the shallow slip deficit of the 2023 Kahramanmaraş earthquake doublet, which is approximately 7%. Therefore, P‐SNAPHU is useful for developing and applying C‐band InSAR data for large earthquakes and volcanic activity.

A Modified Three-terms CG Method with the MWWP Line Search and its Application to Image Restoration

Abstract In this article, an innovative method, which integrates the optimized three-term Polak–Ribière–Polyak (PRP) conjugate gradient (CG) method with the improved WWP line search rule, is presented and applied in the field of image restoration. The proposed search direction exhibits sufficient descent and trust region characteristics, maintaining its effectiveness regardless of the specific line search rule employed. We established the global convergence of the presented algorithm and eliminated the dependence on the Lipschitz continuity assumption. The numerical comparisons with the PRP CG method revealed the superior performance of the designed algorithm in the field of image restoration. This research outcome provides strong support for further advancements in the field of image recovery.

Penerapan Standar Akuntansi Keuangan EMKM Pada Laporan Laba Rugi di Kedai Hobi Kopi Kecamatan Ambulu Kabupaten Jember

SAK EMKM is used by entities that do not or have not been able to fulfill the accounting requirements regulated in SAK ETAP. In SAK EMKM, the entity's financial statements are prepared using basic accrual and business continuity assumptions, as used by micro, small and medium entities and using the business entity concept. This research aims to determine the application of SAK EMKM to the profit and loss report at the "Hobi Kopi" Shop, Ambulu District, Jember Regency. This research uses a qualitative descriptive approach and analyzes the data using a profit and loss report form based on SAK EMKM. The results of this research show that Kedai Hobi Kopi's profit and loss recording is not in accordance with SAK EMKM. The SAK EMKM explains that there are items in the Profit and Loss Report, namely income, operating expenses, other expenses and tax expenses. Meanwhile, Kedai Hobi Kopi's profit and loss report presents COGS where the COGS contains operating expenses which should be separated for each type of expense. There are still expense accounts that have not been included in the income statement, such as asset depreciation expenses and asset repair expenses. After implementing SAK EMKM in the profit and loss report, there is no difference in the nominal profit achieved because basically the expenses presented by Kedai Hobi Kopi are in accordance with the expense rules based on SAK EMKM.