Arbitrary Measure Research Articles

On the discrepancy of low-dimensional probability measures

Calculating the star-discrepancy of a point set in the d d -dimensional unit cube with respect to the Lebesgue measure is an NP-hard problem. Still explicit formulas, which allow for an easy implementation, have been derived. These formulas are particularly compact in the case of dimensions d = 1 , 2 d=1,2 by the work of Niederreiter, and Bundschuh and Zhu. In this paper, we generalize their formulas to arbitrary measures in the dimension d = 1 d=1 and to a wide class of measures in the dimension d = 2 d=2 . In order to give a potential application of such formulas, we reprove from it the fact that the Lebesgue measure is the hardest measure to approximate in the dimension d = 1 d=1 .

Protection Against Arbitrary or Discriminatory Measures in International Investment Law

Protection against arbitrary or discriminatory measures is a clause for the protection of foreign investments that is included in international investment agreements. The clause imposes an obligation on the state where the investment is made not to harm foreign investments by arbitrary or discriminatory measures. Although it is sometimes overshadowed by other investment protection standards in international investment arbitration, it is actually an independent standard that is frequently regulated in investment agreements. In this article, firstly, the drafting of the protection against arbitrary or discriminatory measures in international investment agreements, its elements and its historical development are discussed. After that, the meaning and scope of the concepts of "arbitrariness" and "discrimination", which are two elements, were examined.

Quantum dot based Kitaev chains: Majorana quality measures and scaling with increasing chain length

Realizing Majorana bound states (MBSs) in short, well-controllable chains of coupled quantum dots sidesteps the problem of disorder but requires finetuning and does not give the true topological protection inherent to long chains. Here, we introduce a quality measure that is also applicable in the presence of strong electron-electron interactions and that quantifies the closeness to topological protection of finetuned MBSs in short quantum dot chains. We call this measure local distinguishability (LD) because it puts a bound to the degree an arbitrary local measurement can distinguish between two states. We study the LD for quantum dot chains of different length. The three-dot chain is studied in detail, and we find that it may not always be an improvement over the two-dot case, a fact that can be understood within an effective model derived from perturbation theory. For longer chains, the LD vanishes exponentially, signaling a transition to a topological phase with two ground states that cannot be distinguished by any local measurement. Published by the American Physical Society 2024

Quantum Fluctuation Theorem for Arbitrary Measurement and Feedback Schemes.

Fluctuation theorems and the second law of thermodynamics are powerful relations constraining the behavior of out-of-equilibrium systems. While there exist generalizations of these relations to feedback controlled quantum systems, their applicability is limited, in particular when considering strong and continuous measurements. In this Letter, we overcome this shortcoming by deriving a novel fluctuation theorem, and the associated second law of information thermodynamics, which remain applicable in arbitrary feedback control scenarios. In our second law, the entropy production is bounded by the coarse-grained entropy production that is inferrable from the measurement outcomes, an experimentally accessible quantity that does not diverge even under strong continuous measurements. We illustrate our results by a qubit undergoing discrete and continuous measurement, where our approach provides a useful bound on the entropy production for all measurement strengths.

DeepSketch: A Query Sketching Interface for Deep Time Series Similarity Search

By empowering domain experts to perform interactive exploration of large time series datasets, sketch-based query interfaces have revitalized interest in the well-studied problem of time series similarity search. In this new interaction paradigm, recent similarity algorithms (e.g., Qetch, Peax, LineNet) that attempt to capture perceptually relevant features have supplanted older, more straightforward distance measures (e.g., Euclidean, DTW). However, the downside of these algorithms is the resulting difficulty in designing corresponding index structures to support efficient similarity search over large datasets, thus necessitating brute-force search. This demo will showcase Deep Time Series Similarity Search (DTS3), our pluggable indexing pipeline for arbitrary distance measures. DTS3 can automatically train a foundation model for any custom, user-supplied distance measure with no strict constraints (e.g., differentiability), thus enabling fast retrieval via an off-the-shelf vector DBMS. Using our DeepSketch web interface, participants can compare DTS3 to the baseline brute-force versions of several similarity algorithms to see that our approach can achieve much lower latency without sacrificing accuracy when searching over large, real-world time series datasets.

Non-Sliced Optical Arbitrary Waveform Measurement (OAWM) Using a Silicon Photonic Receiver Chip

Non-Sliced Optical Arbitrary Waveform Measurement (OAWM) Using a Silicon Photonic Receiver Chip

Spatiotemporal Filter Velocimetry With Arbitrary-Shaped Measurement Region For Accurate Measurement In The Vicinity Of A Boundary

Viscous stress at a boundary or an interface is a source of drag acting on a body or a fluid particle and therefore its measurement is of great importance for understanding the motion of the body or the fluid particle. In this study, spatiotemporal filter velocimetry (SFV: Hosokawa & Tomiyama, 2012) is extended to arbitrary quadrilateral measurement areas fitted to an interface shape for accurate measurement of flow about a deformed drop, and it is applied to flows about single drops of glycerol-water solution falling in stagnant silicon oil under clean and contaminated conditions. Figure 1 shows the trajectories of tracer particles and the measured velocity distributions. No separation is observed for the spherical and ellipsoidal drops. On the other hand, the stagnant region is observed in the dimple region of the tail of the cap drop. These results clearly indicate that the flow about the deformed drop is successfully measured by SFV with arbitrary quadrilateral measurement areas. Figure 2 shows the trajectories of tracer particles and the measured velocity distributions of single ellipsoidal drops in clean and contaminated systems. Triton X-100 was used as the surfactant and its concentration C in the drop ranges from 0.0 to 0.1 mol/m3 . The drop tail becomes flat and then slightly dimpled shape, and the internal circulation becomes weak as C increases. The internal circulation remains even at the high surfactant concentration condition under which the internal circulation in single spherical drop is fully damped (Hosokawa et al., 2017). We also evaluate interfacial velocity, interfacial shear stresses, the Marangoni stress and surfactant concentration at the interface from measured velocity distributions in the vicinity of the interface. As a result, we confirmed that SFV enables us to measure velocity distribution about a single deformed drop and enables us to evaluate interfacial velocity, interfacial shear stresses, the Marangoni stress and surfactant concentration at the interface.

Domination of nonlinear semigroups generated by regular, local Dirichlet forms

AbstractIn this article we study perturbations of local, nonlinear Dirichlet forms on arbitrary topological measure spaces. As a main result, we show that the semigroup generated by a local, regular, nonlinear Dirichlet form $${\mathcal {E}}$$ E dominates the semigroup generated by another local functional $${\mathcal {F}}$$ F if, and only if, $${\mathcal {F}}$$ F is a specific zero order perturbation of $${\mathcal {E}}$$ E . On the way, we prove a nonlinear version of the Riesz–Markov representation theorem, we define an abstract boundary of a topological measure space, and apply the notion of nonlinear capacity. The main result helps to classify the perturbations that lie between Neumann and Dirichlet boundary conditions.

Optimal Sensor Placement with Minimal Predicted Posterior Variance

The performance of each monitoring system critically depends on the sensor layout and typical optimization criteria are based on the accessibility to the structure on site, experience with similar structures, and an optimal signal-to-noise ratio. More advanced criteria aim to optimize the feature extraction process, and this paper aims to develop a sensor placement strategy for optimal damage diagnosis. The approach is based on Bayesian updating and the optimization goal is to find a sensor layout that is the most sensitive to small changes in the examined system parameters. It is shown that such layouts manifest themselves through a minimum variance in the posterior distribution. Using Kalman filters, the posterior variance can be “predicted” based on the measurement error and numerical models, so no data from and no simulations in the damaged state are required. By employing a polynomial chaos expansion (PCE)-based Kalman filter, the method becomes applicable for structures with many measurement channels, multiple examined system parameters, and for a large number of sensor combinations. Gaussian distributions are assumed for both system inputs and outputs. For proof of concept, the sensor placement is optimized on a numerical cantilever beam, demonstrating that the method can efficiently find the optimal sensor layout. Moreover, arbitrary measurement quantities (inclinations, vibrations, etc.) or damage-sensitive features (statistical values, modal parameters, etc.) can be used as observations, and multiple system parameters can be considered at the same time. Among other factors, an optimal sensor layout leads to large measurement responses, a small measurement error, and more advanced statistical quantities that will be elaborated on in detail.

Improving the Legal System in Accordance With the Requirements for Building a Socialist Rule-Of-Law State in Vietnam

Objective: This study aims to contribute further discussions on solutions to enhance the quality of the legal system in the context of Vietnam advancing to stage 2 (stage 1 being the quantitative aspect) of the process of perfecting its legal system. Theoretical Framework: This research adopts the ROCCIPI model theory to identify several solutions for improving the Vietnamese legal system within the context of the requirements for building a rule-of-law state in Vietnam, as embodied in Resolution No. 27. Research Methods: This paper employs methods such as the analysis of written laws, document analysis, and comparative analysis. Results and Conclusion: The research results indicate that after prolonged efforts to build a legal system almost from scratch, Vietnam now has a legal framework and procedural system that covers most social relations, gradually replacing arbitrary measures previously imposed by public entities. However, the Vietnamese legal documents system exhibits numerous inadequacies and lacks stability. One of the causes is the involvement of multiple intermediaries in the law-making process, leading to a multi-layered legal system with various procedures (often referred to as "sub-licenses") that interfere with the effectiveness of regulations. Despite modernization efforts, Vietnam's legislative techniques have not significantly improved the quality of legal documents. Therefore, this study proposes solutions focusing on addressing these issues based on the ROCCIPI model approach, which the author believes is suitable for Vietnam's political and legislative realities. Research Implications: This study is set against the backdrop of the Communist Party's continued emphasis on legal formalization, reflecting a consistent policy direction towards building a state that upholds the rule of law. The author agrees that building and perfecting the legal system in any country must begin with an awareness of the law's position and role in social life, from the perspective of the entity controlling and regulating society. Therefore, this research, premised on the consistent guiding capacity of the Communist Party and the State of Vietnam in the legislative process, will discuss ways to progressively perfect the legislative process with strong leadership and constructive roles from these two entities. Originality/Value: Since the promulgation of the Law on Promulgation of Legal Documents in 2008 , issues regarding efficiency, rationality, inflation, and overlap of legal documents have not been resolved. Numerous studies have identified causes, consequences, and proposed legislative solutions to optimize the legislative process and establish a legal life for the documents. The contribution of this study, beginning with a hypothesis about the strong regulatory role of political and social management entities, with an awareness of the law's role in this process, will provide solutions focusing on three aspects of the legislative process: reducing intermediary layers between rules and social life; continuing to emphasize the stability of rules with the central regulatory role of the state; and finally, the techniques of drafting documents, which can be frequently adjusted to meet the two aforementioned objectives.

Necessary condition for information transfer under simulated parity-time-symmetric evolution

Parity-time (PT) symmetric quantum theory can broaden the scope of quantum dynamics beyond unitary evolution which may lead to numerous counter-intuitive phenomena, including single-shot discrimination of non-orthogonal states, faster evolution of state than the standard quantum speed limit, and violation of no-signaling principle. On the other hand, PT -symmetric evolution can be realized as reduced dynamics of a subsystem in real experiments within the scope of standard QT. In this experimental setup, if one side of a composite system is evolved according to a PT -symmetric way, a non-trivial information transfer can happen, i.e. the operation performed at one side can be gathered by the other side. By considering an arbitrary shared state between two parties situated in two distant locations and arbitrary measurements, we show that the PT -symmetric evolution of the reduced subsystem at one side is not sufficient for this information transfer to occur. Specifically, we prove that the information transfer can only happen when the density matrix and the corresponding measurements contain complex numbers. Moreover, we connect the entanglement content of the shared state with the efficacy of information transfer. We find evidence that the task becomes more efficient with the increase of dimension.

Prediction of dynamical systems from time-delayed measurements with self-intersections

In the context of predicting the behaviour of chaotic systems, Schroer, Sauer, Ott and Yorke conjectured in 1998 that if a dynamical system defined by a smooth diffeomorphism T of a Riemannian manifold X admits an attractor with a natural measure μ of information dimension smaller than k, then k time-delayed measurements of a one-dimensional observable h are generically sufficient for μ-almost sure prediction of future measurements of h. In a previous paper we established this conjecture in the setup of injective Lipschitz transformations T of a compact set X in Euclidean space with an ergodic T-invariant Borel probability measure μ. In this paper we prove the conjecture for all (also non-invertible) Lipschitz systems on compact sets with an arbitrary Borel probability measure, and establish an upper bound for the decay rate of the measure of the set of points where the prediction is subpar. This partially confirms a second conjecture by Schroer, Sauer, Ott and Yorke related to empirical prediction algorithms as well as algorithms estimating the dimension and number of required delayed measurements (the so-called embedding dimension) of an observed system. We also prove general time-delay prediction theorems for locally Lipschitz or Hölder systems on Borel sets in Euclidean space.

Monge-Ampère equations on compact Hessian manifolds

We consider degenerate Monge-Ampere equations on compact Hessian manifolds. We establish compactness properties of the set of normalized quasi-convex functions and show local and global comparison principles for twisted Monge-Ampere operators. We then use the Perron method to solve Monge-Ampere equations whose RHS involves an arbitrary probability measure, generalizing works of Cheng-Yau, Delanoe, Caffarelli-Viaclovsky and Hultgren-Onnheim. The intrinsic approach we develop should be useful in deriving similar results on mildly singular Hessian varieties, in line with the Strominger-Yau-Zaslow conjecture.

Pointwise convergence of multiple ergodic averages – PCMEA

Pointwise convergence of multiple ergodic averages – PCMEA Given an arbitrary measure preserving system we show that the multilinear ergodic averages sampled along an arbitrary number of sequences coming from a Hardy field converge pointwise almost everywhere. We aim to prove this for as wide a class of Hardy field functions as possible. To do so, we establish a long variational inequality along lacunary sequences which implies a maximal inequality, norm convergence, and pointwise convergence. By a transference argument it suffices prove this long variational inequality in the case that the measure preserving system is the integers. This reduction allows us to use tools from discrete harmonic analysis, additive combinatorics, and analytic number theory. We then give applications in areas such as upcrossings, equidistribution, and combinatorics.

Stitching interferometry for long X-ray mirrors with lateral multi-shift-based absolute calibration.

To eliminate the reference mirror (REF) error of the Fizeau interferometer for measuring X-ray mirrors, the reference calibration method of lateral multi-shift measurements at the hundreds-micrometer pixel level is presented. Because of the high aspect ratio of long X-ray mirrors, by shifting the surface under test (SUT) along the tangential direction with integer multiple pixels, we extend the calibration method by using the difference between multiple shifted measurements to build an augmented multi-matrix for extracting the two-dimensional (2D) absolute surface. The method can be applied to arbitrary measurement regions of the test optics, and the measurement for both the benchmark sub-aperture and calibration of the REF is accomplished in a single measuring process. Furthermore, by adjusting the shift to the millimeter scale, reference-subtracted sub-apertures can be stitched to obtain the absolute 2D map of the X-ray mirror. Experimental results show that all the 2D discrepancies reach sub-nanometer repeatability, and comparison results between the long trace profiler (LTP) and the proposed method have been performed. Therefore, the results demonstrated that the proposed method meets the requirements of X-ray mirror measurements.

Busemann--Petty-type problem for μ-intersection bodies

Abstract The Busemann–Petty problem of arbitrary measure for symmetric star bodies is proposed and studied by Zvavitch, which is a generalization of the classical Busemann–Petty problem. In this paper, we study the Busemann–Petty-type problem for homogeneous measure for general star bodies.

Deep learning and data augmentation for partial discharge detection in electrical machines

Fault testing in the production line of automotive traction machines is essential to ensure the desired lifetime. Since repetitive partial discharges (PDs) caused by anomalies in the insulation system lead to premature breakdowns of electrical machines, a reliable PD detection is of great importance. This paper proposes deep learning (DL) methods to improve the discrimination of PD from background noise in comparison with the state-of-the-art amplitude based PD detection in the production line. First, a systematic data extraction and labeling procedure is introduced to obtain correctly labeled datasets from arbitrary PD measurements. In addition, datasets are enhanced with low signal-to-noise ratio PD pulses by applying a special data augmentation approach. 13 different convolutional, recurrent and fully connected neural networks are compared for various time-frequency representations of the input signals. Hyperparameters for input transform, network topology and solver are optimized for all 13 combinations to ensure a fair case study. As a result, the two-dimensional convolutional neural network with continuous wavelet transform achieves the best accuracy of around 99.76% on a test dataset of PD signals originating from previously not utilized test objects. All DL models considered in this comparison outperform the state-of-the-art threshold-based PD classification. Even for PD events with an amplitude close to the noise level, the detection rate is still around 95% for the best network. Furthermore, without applying the proposed data augmentation procedure, the DL models investigated are not able to distinguish small PD pulses from noise.

Dynamic currency hedging with non-Gaussianity and ambiguity

This paper introduces a non-Gaussian dynamic currency hedging strategy for globally diversified investors with ambiguity. It provides theoretical and empirical evidence that, under the stylized fact of non-Gaussianity of financial returns and for a given optimal portfolio, the investor-specific ambiguity can be estimated from historical asset returns without the need for additional exogenous information. Acknowledging non-Gaussianity, we compute an optimal ambiguity-adjusted mean-variance (dynamic) currency allocation. Next, we propose an extended filtered historical simulation that combines Monte Carlo simulation based on volatility clustering patterns with the semi-parametric non-normal return distribution from historical data. This simulation allows us to incorporate investor's ambiguity into a dynamic currency hedging strategy algorithm that can numerically optimize an arbitrary risk measure, such as the expected shortfall. The out-of-sample backtest demonstrates that, for globally diversified investors, the derived non-Gaussian dynamic currency hedging strategy is stable, robust, and highly risk reductive. It outperforms the benchmarks of constant hedging as well as static/dynamic hedging approaches with Gaussianity in terms of lower maximum drawdown and higher Sharpe and Sortino ratios, net of transaction costs.

The Mismatch Thesis. Fiction and Reality in the Accumulation of Capital

Political economists, both mainstream and Marxist, find it difficult to reconcile the «real» and «financial» appearances of capital. The conventional view is that «real» capital is an objective productive entity; that «finance» merely reflects this reality; and that, unfortunately, the reflection is often inaccurate, causing the two to «mismatch». This convention, we argue, is baseless if not fraudulent. First, although economists know full well that «real» capital, comprising different capital goods, cannot have a unique objective quantity – they measure this pseudo quantity anyway, arbitrarily. Second, when they realize that their arbitrary measure of «real» capital differs greatly from the corresponding magnitude of finance, they blame the deviation on invisible fluctuations in intangible capital, investor irrationality and market imperfections. And third, they insist that «real» accumulation drives «financial» accumulation, even though their own measures show that the two processes move in opposite directions! Political economists, both mainstream and Marxist, find it difficult to reconcile the «real» and «financial» appearances of capital. The conventional view is that «real» capital is an objective productive entity; that «finance» merely reflects this reality; and that, unfortunately, the reflection is often inaccurate, causing the two to «mismatch». This convention, we argue, is baseless if not fraudulent. First, although economists know full well that «real» capital, comprising different capital goods, cannot have a unique objective quantity – they measure this pseudo quantity anyway, arbitrarily. Second, when they realize that their arbitrary measure of «real» capital differs greatly from the corresponding magnitude of finance, they blame the deviation on invisible fluctuations in intangible capital, investor irrationality and market imperfections. And third, they insist that «real» accumulation drives «financial» accumulation, even though their own measures show that the two processes move in opposite directions!

Taking Into Care - In The Child's Best Interest? The German Youth Welfare Office is under criticism from the European Parliament

Introduction: The number of children taken into care by German youth welfare offices has been increasing for years as a result of changes in the law according to publicly known endangerments to child welfare. Due to an increase in petitions from non-German parents to the European Parliament's Petitions Committee against administrative acts that they felt to be arbitrary (e.g. taking into care), the European Parliament repeatedly (2007, 2018, 2022, 2023) dealt with the processes in the German Youth Welfare Office. Material and Methods: Compilation of the documents of the Petitions Committee of the European Parliament in 2007, 2018, 2022, and 2023 on the German Youth Welfare Office. Additional searches in Pubmed, google scholar, and google under the keywords child welfare, the best interest of the child, damage to health through taking into care, harm to children through taking into care, the impact of financial threats to parents to youth welfare, psychological trauma through taking into care by the youth welfare office. Reproduction of the essential questions of the member European Parliament (MEPs) and answers of German authorities and family courts. Structure in: The principle “In the best children’s interest” and “child wellbeing (welfare)”, legal duties of the youth office, taking into care by youth office, the power of youth office, relationship court youth office, control of the German youth office, costs of the proceedings, guardian ad litem, duties and functions of the court. The answers of the German authorities are summarized in the respective sections, supplemented by relevant literature and personal communications. Results: For years, the German youth welfare office has been criticized for either failing to protect the welfare of the child or protecting it too late. Over the past 20 years or so, changes in the law have led to increasing numbers of childcare takings based on undefined norms of the child's best interests and child welfare. In short: the guardian state is increasingly intervening in the family, which is protected by Article 6 of the Basic Law, with the unclear justification that the parents are overburdened or lacking (proof of) the ability to bring up children, precisely regarding Article 6 invoking the guardian state, and is separating parents from their children without having sufficient scientific knowledge about the consequences of taking the children into care. The families receive high bills for this, disregarding proportionality and exclusion criteria. The possibility of changing something by complaining is small. The responsible community decides on the complaint itself. Transparency is reduced with the exclusion of the public and the rejection of requests to inspect files. This led to the expressed suspicion of arbitrary measures and an increase in petitions to the European Petitions Committee, which has been dealing with the youth welfare office since 2007 and even came to Germany for a "fact-finding visit" in 2022. The questions from the MEPs on the above areas were partly answered incompletely or not at all or contradicted the literature and the evidence. The answers of the German community of responsibility prompted the MEPs to ask further questions (Amendments 2023). Conclusion: It cannot be denied that the answers of the youth welfare office were not very convincing for the MEPs of the petition committee, taking into account the scientific literature and known documents. The lack of transparency (e.g., refusal to inspect files) and agreements reinforced the MEPs' negative impression of the youth welfare office (shadow body, where there is smoke, there is fire), and led to the announcement of further controls by the MEPs.