We give a common mathematical characterization of relevant stochastic evolution schemes built up in the literatute to attack the quantum measurement problem. This characterization is based on two hypotheses, namely, (i) the trace conservation with probability one and (ii) the existence of a complex phase determining a linear support for the stochastic process driving the random evolution.

Access to urban green space is associated with the enhancement of health and disparities in access generate issues of spatial equity and socioenvironmental justice. The aim of this study is to measure spatial accessibility and investigate access disparities to UGSs in urban areas of Harbin, China. A Gaussian-based two-step floating catchment area method and spatial autocorrelation analysis were used to measure the accessibility and evaluate its distribution patterns in residential tracts. Bivariate correlation was employed to examine the statistical relations (...) between demographic characteristics of residential tracts and green space access. The results show that most residential tracts have minimal green space access within walking distance, while a few have limited access within cycling distance. Additionally, spatial disparities were found with low-accessibility tracts clustering in the center of the city, while high-accessibility tracts were located in northern and southern suburbs. Demographic disparities were also identified in the study: females have less access to UGS than males, areas with a high birth rate generally have more access, and population density is negatively associated with UGS access. The findings not only indicate that Harbin has an uneven distribution and disproportionate provision of UGS for urban residents but also identify which areas and population groups within the city are disadvantaged in access to UGS and thus provide suggestions for future construction and provision of UGS. (shrink)

Similarity profiled association mining from time stamped transaction databases is an important topic of research relatively less addressed in the field of temporal data mining. Mining temporal patterns from these time series databases requires choosing and applying similarity measure for similarity computations and subsequently pruning temporal patterns. This research proposes a novel z-space based interest measure named as Krishna Sudarsana for time-stamped transaction databases by extending interest measure Srihass proposed in previous research. Krishna Sudarsana is designed by using the product (...) based fuzzy Gaussian membership function and performs similarity computations in z-space to determine the similarity degree between any two temporal patterns. The interest measure is designed by considering z-values between z = 0 and z = 3.09. Applying the Krishna Sudarsana requires moving the threshold value given by user to a different transformation space which is a defined as a function of standard deviation. In addition to proposing interest measure, new expressions for standard deviation and equivalent z-space threshold are derived for similarity computations. For experimental evaluation, we considered Naïve, Sequential and Spamine algorithms that applies Euclidean distance function and compared performance of these three approaches to Z-Spamine algorithm that uses Krishna Sudarsana by choosing various test cases. Experiment results proved the performance of the proposed approach is better to Sequential approach that uses snapshot database scan strategy and Spamine approach that uses lattice based database scan strategy. (shrink)

We study operator equations within the Turing machine based framework for computability in analysis. Is there an algorithm that maps pairs to solutions of Tx = u ? Here we consider the case when T is a bounded linear mapping between Hilbert spaces. We are in particular interested in computing the generalized inverse T†u, which is the standard concept of solution in the theory of inverse problems. Typically, T† is discontinuous and hence no computable mapping. However, we will use effective (...) versions of theorems from the theory of regularization to show that the mapping ↦ T†u is computable. We then go on to study the computability of average-case solutions with respect to Gaussian measures which have been considered in information based complexity. Here, T† is considered as an element of an L2-space. We define suitable representations for such spaces and use the results from the first part of the paper to show that ↦ T† is computable. (shrink)

The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many (...) authors dismiss the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails problem) and second (structured tails problem) exist in the literature. I argue that while the first is a pseudo-problem, the second has not been adequately addressed. The third (multiverse tails problem) reformulates the second to account for recently discovered dynamical consequences of collapse. Finally the fourth (tails problem dilemma) shows that solving the third by replacing the Gaussian with a non-Gaussian collapse function introduces new conflict with relativity theory. (shrink)

In this chapter, one considers finance at its very foundations, namely, at the place where assumptions are being made about the ways to measure the two key ingredients of finance: risk and return. It is well known that returns for a large class of assets display a number of stylized facts that cannot be squared with the traditional views of 1960s financial economics (normality and continuity assumptions, i.e. Brownian representation of market dynamics). Despite the empirical counterevidence, normality and continuity assumptions (...) were part and parcel of financial theory and practice, embedded in all financial practices and beliefs. Our aim is to build on this puzzle for extracting some clues revealing the use of one research strategy in academic community, model tinkering defined as a particular research habit. We choose to focus on one specific moment of the scientific controversies in academic finance: the ‘leptokurtic crisis’ opened by Mandelbrot in 1962. The profoundness of the crisis came from the angle of the Mandelbrot’s attack: not only he emphasized an empirical inadequacy of the Brownian representation, but also he argued for an inadequate grounding of this representation. We give some insights in this crisis and display the model tinkering strategies of the financial academic community in the 1970s and the 1980s. (shrink)

In 1907 Borel published a remarkable essay on the paradox of the Heap (“Un paradoxe économique: le sophisme du tas de blé et les vérités statistiques”), in which Borel proposes what is likely the first statistical account of vagueness ever written, and where he discusses the practical implications of the sorites paradox, including in economics. Borel’s paper was integrated in his book Le Hasard, published 1914, but has gone mostly unnoticed since its publication. One of the originalities of Borel’s essay (...) is that it puts forward a model of vagueness as imprecision, making particular use of the Gaussian law of measurement errors to model categorization. The aim of our paper is to give a presentation of the historical context of Borel’s essay, to spell out the mathematical details of his model, and to provide a critical assessment of his theory. Three aspects of Borel’s account are particularly discussed: the first concerns the comparison between Borel’s statistical account and posterior degree-theoretic accounts of vagueness. The second concerns the anti-epistemicist flavor of Borel’s approach, whereby the idea of statistical fluctuation is used to undermine the notion of sharp boundary for vague predicates. The third concerns the problematic link between Borel’s model of vagueness as imprecision and the notion of semantic indeterminacy. An English translation of Borel’s original essay is appended to this paper (Erkenntnis, this issue). (shrink)

The social and cognitive science replication crisis is partly due to the limitations of commonly used statistical tools. Inferential statistics require that unsystematic measurement variation is independent of system history, and weak relative to systematic or causal sources of variation. However, contemporary systems research underscores the dynamic, adaptive nature of social, cognitive, and behavioral systems. Variation in human activity includes the influences of intrinsic dynamics intertwined with changing contextual circumstances. Conventional inferential techniques presume milder forms of variability, such as unsystematic (...) measurement error, as in a Gaussian distribution. Inferential statistics indicate an elementary Newtonian cause-effect metaphor for change that is inconsistent with known principles of change in complex systems. Pattern formation in self-organizing systems and quantum probability are used to illustrate theoretical metaphors that instantiate alternative notions of change in complex systems. Inferential statistics and related techniques are crucial scientific resources. However, in the social and behavioral sciences, they must be practiced in conjunction with an appropriate general systems framework that accommodates intrinsic fluctuations and contextual adaptation. (shrink)

By the relational realist interpretation of wave function collapse, the quantum mechanical actualization of potentia is defined as a decoherence-driven process by which each actualization (in “orthodox” terms, each measurement outcome) is conditioned both by physical and logical relations with the actualities conventionally demarked as “environmental” or external to that particular outcome. But by the relational realist interpretation, the actualization-in-process is understood as internally related to these “enironmental” data per the formalism of quantum decoherence. The concept of “actualization via wave (...) function collapse” is accounted for solely by virtue of these presupposed logical relations—the same logical relations otherwise presupposed by the scientific method itself—and thus requires no “external” physical-dynamical trigger: e.g., the Gaussian hits of GRW, acts of conscious observation, etc. By the relational realist interpretation, it is the physical and logical relations among quantum actualities (quantum “final real things”) that drives the process of decoherence and, via the latter, the logically conditioned actualization of potentia. In this regard, the relational realist interpretation of quantum mechanics is a praxiological interpretation; that is, these physical and logical relations are ontologically active relations, contributing not just to the epistemic coordination of quantum actualizations, but to the process of actualization itself. (shrink)

Image denoising is one of the important problems in the research field of computer vision, artificial intelligence, 3D vision, and image processing, where the fundamental aim is to recover the original image features from a noisy contaminated image. The camera sensor additive noise present in the holographic recording process reduces the quality of the retrieved image. Even though various techniques have been developed to minimize the noise in digital holography, the noise reduction still remains a challenging task. This article presents (...) a compressive sensing technique to minimize the additive noise in the digital holographic reconstruction process. We demonstrate the reduction of additive noise using complex wave retrieval method as a sensing matrix in the CS model. The proposed CS method to suppress the noise during the reconstruction process is illustrated using numerical simulations. Only 50% of the pixel measurements are considered in the noisy hologram, which is far less than the original complex object pixels. The impact of additive gaussian noise in the recording plane on the reconstruction accuracy of both intensity and phase distribution is analysed. The CS method denoises and estimates the complex object information accurately. The numerical simulation results have shown that the proposed CS method has effectively minimized the noise in the reconstructed image and has greatly improved the quality of both intensity and phase information. (shrink)

Let A 1 , A 2 , A 3 A 4 be four observables, the compatible observables among them being (A 1 , A 3 ), (A 1 , A 4 ), (A 2 , A 3 ), (A 2 , A 4 ). In order that the empirical data be reproducible by a quantum or a classical theory, the two-point correlation functions $$\{ C_{ij} = \left\langle {A_i A_j } \right\rangle :i,j a compatible pair\} $$ must necessarily satisfy $$|X_{13} X_{14} (...) - X_{23} X_{24} | \leqslant \left( {1 - X_{13} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {1 - X_{14} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + \left( {1 - X_{23} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {1 - X_{24} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} (*)$$ where Xij=CijC ii −1/2 C jj −1/2 . In the case ofGaussian data, this inequality is alsosufficient; If (*) holds, there is a Gaussian joint distribution for A 1 , A 2 , A 3 , A 4 which reproduces the Gaussian data for compatible pairs. It follows that Bell's inequality is satisfied by all true-false propositions about the Gaussian data. A further consequence of the analysis is thatquantum Gaussian fields satisfy Bell's inequality for all true-false propositions aboutfield measurements.The maximum violation of (*) corresponds to Rastall's example in the case of two-valued observables. (shrink)

In this paper, we propose a person verification scheme using a novel combination of palmprint and speech. The crucial aspect of biometric based verification lies in its use of features in verification. Thus, in this paper, we propose two novel feature extraction methods for palmprint verification. The proposed methods are based on the Gaussian mixture model followed by subspace based approaches such as ICA I and ICA II, called independent component analysis I mixture model and independent component analysis II (...) mixture model for palmprint verification. The speech verification system uses sphericity based measurement for person verification. The proposed multimodal biometric system uses a fairly large database of 150 users. The robustness of the proposed methods is validated by introducing six different types of noises on palmprint images and Gaussian white noise with two different signal-to-noise ratios on speech samples. Then, fusion of palmprint and speech are carried out at match score level using the weighted SUM rule for both clean and noisy conditions. Finally, we compare the results of combined biometric with the results of individual biometric and also the results of the proposed methods against conventional subspace methods. (shrink)

The definition of mass as a random variable is applied to the study of the decay rates. A decay is assumed possible when the fluctuation of the Gaussian variables involved makes a definite relation satisfied. Computing the probability of this process leads to the determination of the decay amplitude. This calculation, unified for baryons and mesons, is worked out in the lower and medium spectrum (up to2000 MeV for baryons and mesons), and fits to≈20 MeV the accurate measurements of (...) width and branching ratios. (shrink)

A longstanding paradox was first reported by David Miller in 1975 and highlighted by Karl Popper in 1979. Miller showed that the ranking of predictions from two theories, in terms of closeness to observation, appears to be reversed when the problem is transformed into a different mathematical space. He concluded that “… no false theory can … be closer to the truth than is another theory”. This flies in the face of normal scientific practice and is thus paradoxical; it is (...) named here the “Miller-Popper paradox”. This paper proposes a resolution of the paradox, through consideration of the inevitable errors and uncertainties in both observations and predictions. It is proved that, for linear transformations and Gaussian error distributions, the transformation between spaces creates no change in quantitative measures of “closeness-to-observation” when these measures are based in probability theory. The extension of this result to nonlinear transformations and to non-Gaussian error distributions is also discussed. These results demonstrate that concepts used in comparison of predictions with observations—concepts of “closeness”, “consistency”, “agreement”, “falsification”, etc.—all imply some knowledge of the uncertainty characteristics of both predictions and observations. (shrink)

Abnormal behavior detection of social security funds is a method to analyze large-scale data and find abnormal behavior. Although many methods based on spectral clustering have achieved many good results in the practical application of clustering, the research on the spectral clustering algorithm is still in the early stage of development. Many existing algorithms are very sensitive to clustering parameters, especially scale parameters, and need to manually input the number of clustering. Therefore, a density-sensitive similarity measure is introduced in this (...) paper, which is obtained by introducing new parameters to transform the Gaussian function. Under this metric, the distance between data points belonging to different classes will be effectively amplified, while the distance between data points belonging to the same class will be reduced, and finally, the distribution of data will be effectively clustered. At the same time, the idea of Eigen gap is introduced into the spectral clustering algorithm, and the verified gap sequence is constructed on the basis of Laplace matrix, so as to solve the problem of the number of initial clustering. The strong global search ability of artificial bee colony algorithm is used to make up for the shortcoming of spectral clustering algorithm that is easy to fall into local optimal. The experimental results show that the adaptive spectral clustering algorithm can better identify the initial clustering center, perform more effective clustering, and detect abnormal behavior more accurately. (shrink)

We review studies of an evolution operator ℒ for a discrete Langevin equation with a strongly hyperbolic classical dynamics and a Gaussian noise. The leading eigenvalue of ℒ yields a physically measurable property of the dynamical system, the escape rate from the repeller. The spectrum of the evolution operator ℒ in the weak noise limit can be computed in several ways. A method using a local matrix representation of the operator allows to push the corrections to the escape rate (...) up to order eight in the noise expansion parameter. These corrections then appear to form a divergent series. Actually, via a cumulant expansion, they relate to analogous divergent series for other quantities, the traces of the evolution operators ℒn. Using an integral representation of the evolution operator ℒ, we then investigate the high order corrections to the latter traces. Their asymptotic behavior is found to be controlled by sub-dominant saddle points previously neglected in the perturbative expansion, and to be ultimately described by a kind of trace formula. (shrink)

Determining the nature of binding in grapheme-color synaesthesia has consequences for understanding the neural basis of synaesthesia and visual awareness in general. We evaluated type- and token-based letter-color binding using a synaesthetic version of the object-reviewing paradigm. Although mean response times failed to reveal any significant differences between synaesthetes and control participants, RT analyses with ex-Gaussian distributions revealed that the response facilitation in the synaesthesia group reflected type representations exclusively, while response facilitation in the control group, who learned letter-color (...) associations, was dominated by token representations. Thus, letter-color associations in associator synaesthetes are type-based, and do not involve binding to object tokens, consistent with their subjective reports. Contrary to recent studies that failed to find differences between synaesthetes and non-synaesthetes with behavioral measures, response time distribution analyses indicate that color sensations in synaesthetes are not simply the extreme form of normal letter-color associations, and cannot be attributed to demand characteristics. (shrink)

As traditional methods such as questionnaires for measuring risk propensity are not applicable in some scenarios, a nonintrusive method that could automatically identify individuals' risk propensity could be valuable. This study utilized Defense of the Ancients 2 single match data and historical statistics to train predictive models to identify risk propensity by machine learning methods. Self-reported risk propensity scores from 218 DOTA 2 players were paired with their behavioral metrics. The best-performing model occurred with Gaussian process regression. The root (...) mean square error of this model was 1.10, the correlation between predicted scores and self-reported questionnaire scores was 0.44, the R-squared was 0.17, and the test–retest reliability was 0.67. We discussed how selected behavioral features could contribute to predicting risk propensity and how the approach could be of potential value in the application of perceiving individuals' risk propensities. Moreover, the limitations of our study were discussed, and recommendations were made for future studies in this field. (shrink)

The recovery after the unprecedented pandemic crisis that Europe has currently been facing is strengthening the strong dependence between social, economic, and environmental fields, maintaining green investments and innovation at the core of the European strategies. Shifting to clean industries is a challenging mission that a complex network of stakeholders and their different interests must take into account. Within this network, the interplay between environmental and financial performance of a company represents a common point with a growing emphasis on the (...) transparency and the materiality capacity of the disclosed information. This paper uses the Structural Equation Modeling and the Gaussian Graphical Models as graphical analysis approaches and offers a first insight about the interaction between environmental materiality measures and financial performance. A preliminary step of the scientific research consisted of a hand-mapping investigation about materiality conditions. Starting from the Materiality Map developed by the Sustainability Accounting Standards Board, this paper extends the main concept about materiality and investigates it on three different content ranges, which focus on the general environmental policy of the company, the targets set, and its concrete footprint. The methodology approaches were grounded on a newly compiled dataset provided by the Thomson Reuters database for 194 Economic European Area oil and gas companies. The results provide significant evidences for the manifestation of materiality and emphasize the informational content of the individual environmental measures as an important condition for its financial impact. Adding to the environmental-financial performance relationship, our findings have both practical and academic relevance for the economic field and sustainable growth goals. (shrink)

Data hiding and watermarking are considered one of the most important topics in cyber security. This article proposes an optimized method for embedding a watermark image in a cover medium (color image). First, the color of the image is separated into three components (RGB). Consequently, the discrete wavelet transform is applied to each component to obtain four bands (high–high, high–low, low–high, and low–low), resulting in 12 bands in total. By omitting the low–low band from each component, a new square matrix (...) is formed from the rest bands to be used for the hiding process after adding keys to it. These keys are generated using a hybrid approach, combining two chaotic functions, namely Gaussian and exponential maps. The embedding matrix is divided into square blocks with a specific length, each of which is converted using Hessenberg transform into two matrices, P and H. For each block, a certain location within the H-matrix is used for embedding a secret value; the updated blocks are assembled, and the reverse process is performed. An optimization method is applied, through the application of the firework algorithm, on the set of the initial values that generate keys. Using an optimization procedure to obtain keys requires performing lowest possible change rate in an image and maintain the quality of the image. To analyze and test the efficiency of the proposed method, mean-square error (MSE) and peak signal-to-noise ratio (PSNR) measurements are calculated. Furthermore, the robustness of the watermark is computed by applying several attacks. The experimental results show that the value of the MSE is reduced by about 0.01 while the value of the PSNR is increased by about 1.25 on average. Moreover, the proposed method achieved a high-retrieval rate in comparison with the non-optimization approach. (shrink)

In a previous paper, a statistical method of constructing quantum models of classical properties has been described. The present paper concludes the description by turning to classical mechanics. The quantum states that maximize entropy for given averages and variances of coordinates and momenta are called ME packets. They generalize the Gaussian wave packets. A non-trivial extension of the partition-function method of probability calculus to quantum mechanics is given. Non-commutativity of quantum variables limits its usefulness. Still, the general form of (...) the state operators of ME packets is obtained with its help. The diagonal representation of the operators is found. A general way of calculating averages that can replace the partition function method is described. Classical mechanics is reinterpreted as a statistical theory. Classical trajectories are replaced by classical ME packets. Quantum states approximate classical ones if the product of the coordinate and momentum variances is much larger than Planck constant. Thus, ME packets with large variances follow their classical counterparts better than Gaussian wave packets. (shrink)

Nonlinear time series denoising is the prerequisite for extracting effective information from observation sequence. An effective chaotic signal denoising method not only has a good signal-to-noise ratio enhancement performance, but also can remain as a good unpredictable denoised signal. However, the inherent characteristics of chaos, such as extreme sensitivity to initial values and broadband spectrum, pose challenges for noise reduction of polluted chaotic signals. To address these issues, an adaptive smoothing multiscale morphological filtering is proposed to reconstruct chaotic signals. In (...) the process of noise reduction for contaminated chaotic signals, firstly, a multiscale morphological filter is constructed adaptively according to the multiscale permutation entropy of morphological filter residuals, and the contaminated signals are filtered. Secondly, the weight coefficients of scale structural element are calculated by the residual sum of squares operation, and the chaotic signals are reconstructed. Finally, the resampled filter signals are smoothed by cubic B-spline interpolation operation. In the experiment, the Lorenz signal with white Gaussian noise, the measured sunspot, and the chaotic vibration signal are reconstructed by four comparison methods. The test results show that the proposed ASMMF method has obvious advantages in noise suppression and topological trajectory restoration. (shrink)

Heart rate variability (HRV) is an indicator of the regulation of the heart, see Task Force (Circulation 93(5):1043–1065, 1996). This study compares the regulation of the heart in two cases of healthy subjects within real life situations: Marathon runners and shift workers. After an update on the state of the art on HRV processing, we specify our probabilistic model: We choose modeling heartbeat series by locally stationary Gaussian process (Dahlhaus in Ann Stat 25, 1997). HRV is then processed by (...) the combination of two statistical methods: (1) Continuous wavelet transform for calculating the spectral density energy in the high frequency (HF) and low frequency (LF) bands and (2) Change point analysis to detect changes of heart regulation. Next, we plot the variations of the HF and LF energy in extreme conditions for both populations. This puts in light, that physical activities (rest, moderate sport, marathon race) can be ordered in a logical continuum. This allows to define a new index based on HF and LF energy that is log HF + log LF which appears relevant to measure HR regulation. The results obtained are pertinent but have to be completed by further studies. (shrink)

Philosophers have disagreed on the composition of force for decades. The main divergence concerns the fundamental question: given a certain motion that is observable, which force or forces are present in it, component or resultant forces? The present paper focuses on the conditions for dealing with this problem. I will argue that we are not able to infer force from the observation of a motion, as required by the problem. I will further argue that the validity of the Newtonian algorithm (...) is not a sufficient condition for that inference because the Gaussian algorithm, which is equally valid, differs from the former with regard to the forces present in motions. Under these circumstances, I will make recourse to an experiment available in physics in which the force present in a motion is measured. Thus, we obtain a numerical value for this force. This result, playing the role of a counterexample, clarifies the composition of force issue significantly. (shrink)

Color coding is used to guide attention in computer displays for such critical tasks as baggage screening or air traffic control. It has been shown that a display object attracts more attention if its color is more similar to the color for which one is searching. However, what does similar precisely mean? Can we predict the amount of attention that a display color will receive during a search for a given target color? To tackle this question, two color‐search experiments measuring (...) the selectivity of saccadic eye movements and mapping out its underlying color space were conducted. A variety of mathematical models, predicting saccadic selectivity for given target and display colors, were devised and evaluated. The results suggest that applying a Gaussian function to a weighted Euclidean distance in a slightly modified HSI color space is the best predictor of saccadic selectivity in the chosen paradigm. Hue and intensity information by itself provides a basis for useful predictors, spanning a possibly spherical color space of saccadic selectivity. Although the current models cannot predict saccadic selectivity values for a wide variety of visual search tasks, they reveal some characteristics of color search that are of both theoretical and applied interest, such as for the design of human–computer interfaces. (shrink)

We present the Dirac and Laplacian operators on Clifford bundles over space–time, associated to metric compatible linear connections of Cartan–Weyl, with trace-torsion, Q. In the case of nondegenerate metrics, we obtain a theory of generalized Brownian motions whose drift is the metric conjugate of Q. We give the constitutive equations for Q. We find that it contains Maxwell’s equations, characterized by two potentials, an harmonic one which has a zero field (Bohm-Aharonov potential) and a coexact term that generalizes the Hertz (...) potential of Maxwell’s equations in Minkowski space.We develop the theory of the Hertz potential for a general Riemannian manifold. We study the invariant state for the theory, and determine the decomposition of Q in this state which has an invariant Born measure. In addition to the logarithmic potential derivative term, we have the previous Maxwellian potentials normalized by the invariant density. We characterize the time-evolution irreversibility of the Brownian motions generated by the Cartan–Weyl laplacians, in terms of these normalized Maxwell’s potentials. We prove the equivalence of the sourceless Maxwell equation on Minkowski space, and the Dirac-Hestenes equation for a Dirac-Hestenes spinor field written on Minkowski space provided with a Cartan–Weyl connection. If Q is characterized by the invariant state of the diffusion process generated on Euclidean space, then the Maxwell’s potentials appearing in Q can be seen alternatively as derived from the internal rotational degrees of freedom of the Dirac-Hestenes spinor field, yet the equivalence between Maxwell’s equation and Dirac-Hestenes equations is valid if we have that these potentials have only two components corresponding to the spin-plane. We present Lorentz-invariant diffusion representations for the Cartan–Weyl connections that sustain the equivalence of these equations, and furthermore, the diffusion of differential forms along these Brownian motions. We prove that the construction of the relativistic Brownian motion theory for the flat Minkowski metric, follows from the choices of the degenerate Clifford structure and the Oron and Horwitz relativistic Gaussian, instead of the Euclidean structure and the orthogonal invariant Gaussian. We further indicate the random Poincaré–Cartan invariants of phase-space provided with the canonical symplectic structure. We introduce the energy-form of the exact terms of Q and derive the relativistic quantum potential from the groundstate representation. We derive the field equations corresponding to these exact terms from an average on the invariant state Cartan scalar curvature, and find that the quantum potential can be identified with 1 / 12R(g), where R(g) is the metric scalar curvature. We establish a link between an anisotropic noise tensor and the genesis of a gravitational field in terms of the generalized Brownian motions. Thus, when we have a nontrivial curvature, we can identify the quantum nonlocal correlations with the gravitational field. We discuss the relations of this work with the heat kernel approach in quantum gravity. We finally present for the case of Q restricted to this exact term a supersymmetric system, in the classical sense due to E.Witten, and discuss the possible extensions to include the electromagnetic potential terms of Q. (shrink)

In this paper, we propose an adaptive Gaussian incremental expectation stadium parameter estimation algorithm for sports video analysis and prediction through the study and analysis of sports videos. The features with more discriminative power are selected from the set of positive and negative templates using a feature selection mechanism, and a sparse discriminative model is constructed by combining a confidence value metric strategy. The sparse generative model is constructed by combining L1 regularization and subspace representation, which retains sufficient representational (...) power while dealing with outliers. To overcome the shortcomings of the traditional multiplicative fusion mechanism, this paper proposes an adaptive selection mechanism based on Euclidean distance, which aims to detect deteriorating models in time during the dynamic tracking process and adopt corresponding strategies to construct more reasonable likelihood functions. Based on the Bayesian citation framework, the adaptive selection mechanism is used to combine the sparse discriminative model and the sparse generative model. Also, different online updating strategies are adopted for the template set and Principal Component Analysis subspace to alleviate the drift problem while ensuring that the algorithm can adapt to the changes of target appearance in the dynamic tracking environment. Through quantitative and qualitative evaluation of the experimental results, it is verified that the algorithm proposed in this paper has stronger robustness compared with other classical algorithms. Our proposed visual object tracking algorithm not only outperforms existing visual object tracking algorithms in terms of accuracy, success rate, accuracy, and robustness but also achieve the performance required for real-time tracking in terms of execution speed on the central processing unit. This paper provides an in-depth analysis and discussion of the adaptive Gaussian incremental expectation stadium parameter estimation algorithm for sports video analysis. Using a variety of county-level algorithms for analysis and multiple solutions to improve the accuracy of the results, we obtain a more efficient and accurate algorithm. (shrink)

An intervention may have an effect on units other than those to which it was administered. This phenomenon is called interference and it usually goes unmodeled. In this paper, we propose to combine Lauritzen-Wermuth-Frydenberg and Andersson-Madigan-Perlman chain graphs to create a new class of causal models that can represent both interference and non-interference relationships for Gaussian distributions. Specifically, we define the new class of models, introduce global and local and pairwise Markov properties for them, and prove their equivalence. We (...) also propose an algorithm for maximum likelihood parameter estimation for the new models, and report experimental results. Finally, we show how to compute the effects of interventions in the new models. (shrink)

In the data collection phase, the digital images are captured using sensors that often contaminated by noise (undesired random signal). In digital image processing task, enhancing the image quality and reducing the noise is a central process. Image denoising effectively preserves the image edges to a higher extend in the flat regions. Several adaptive filters (median filter, Gaussian filter, fuzzy filter, etc.) have been utilized to improve the smoothness of digital image, but these filters failed to preserve the image (...) edges while removing noise. In this paper, a modified fuzzy set filter has been proposed to eliminate noise for restoring the digital image. Usually in fuzzy set filter, sixteen fuzzy rules are generated to find the noisy pixels in the digital image. In modified fuzzy set filter, a set of twenty-four fuzzy rules are generated with additional four pixel locations for determining the noisy pixels in the digital image. The additional eight fuzzy rules ease the process of finding the image pixels,whether it required averaging or not. In this scenario, the input digital images were collected from the underwater photography fish dataset. The efficiency of the modified fuzzy set filter was evaluated by varying degrees of Gaussian noise (0.01, 0.03, and 0.1 levels of Gaussian noise). For performance evaluation, Structural Similarity (SSIM), Mean Structural Similarity (MSSIM), Mean Square Error (MSE), Normalized Mean Square Error (NMSE), Universal Image Quality Index (UIQI), Peak Signal to Noise Ratio (PSNR), and Visual Information Fidelity (VIF) were used. The experimental results showed that the modified fuzzy set filter improved PSNR value up to 2-3 dB, MSSIM up to 0.12-0.03, and NMSE value up to 0.38-0.1 compared to the traditional filtering techniques. (shrink)

Concern about air-quality in urban areas has led to the implementation of Low Emission Zones as one of many other initiatives to control it. Recently in Spain, the enactment of a law made this mandatory for cities with a population larger than 50k inhabitants. The delimitation of these areas is not without controversy because of possible negative economic and social impacts. Therefore, clear assessments of how these initiatives decrease pollutant concentrations are to be provided. Madrid Central is a major initiative (...) of Madrid city council for reducing motor traffic and the associated air pollution in the city centre. This Low Emission Zone starts at the end of 2018, but the first fully-operational period corresponds to the second quarter of 2019. In this work, a methodology based on the Gaussian Process to analyse the evolution of Nitrogen Dioxide inside Madrid Central is undertaken. A Gaussian Process is a stochastic process suitable for interpretable model selection and predictions. Due to its probabilistic nature it provides error estimation at predictions. After the activation of Madrid Central, a relevant reduction of Nitrogen Dioxide has been observed. However, the role of the meteorology during this period must be ascertained to correctly evaluate the role of the activation of the Low Emission Zone against a prone weather. In this work, a model based on the Gaussian Process is trained with meteorological information to predict the concentration of Nitrogen Dioxide at Madrid Central, $[NO_{2}]$. This probabilistic description allows extracting statistical information on the reduction affected by the meteorological scenario and separately by the Madrid Central activation. (shrink)

In this article, we extend the Bayesian nonparametric regression method Gaussian Process Regression to the analysis of longitudinal panel data. We call this new approach Gaussian Process Panel Modeling (GPPM). GPPM provides great flexibility because of the large number of models it can represent. It allows classical statistical inference as well as machine learning inspired predictive modeling. GPPM offers frequentist and Bayesian inference without the need to resort to Markov chain Monte Carlo-based approximations, which makes the approach exact (...) and fast. GPPMs are defined using the kernel-language, which can express many traditional modeling approaches for longitudinal data, such as linear structural equation models, multilevel models, or state-space models but also various commonly used machine learning approaches. As a result, GPPM is uniquely able to represent hybrid models combining traditional parametric longitudinal models and nonparametric machine learning models. In the present paper, we introduce GPPM and illustrate its utility through theoretical arguments as well as simulated and empirical data. (shrink)

David Cooper explores and defends the view that a reality independent of human perspectives is necessarily indescribable, a "mystery." Other views are shown to be hubristic. Humanists, for whom "man is the measure" of reality, exaggerate our capacity to live without the sense of an independent measure. Absolutists, who proclaim our capacity to know an independent reality, exaggerate our cognitive powers. In this highly original book Cooper restores to philosophy a proper appreciation of mystery-that is what provides a measure of (...) our beliefs and conduct. (shrink)

Effective feature representation is the key to success of machine learning applications. Recently, many feature learning models have been proposed. Among these models, the Gaussian process latent variable model for nonlinear feature learning has received much attention because of its superior performance. However, most of the existing GPLVMs are mainly designed for classification and regression tasks, thus cannot be used in data clustering task. To address this issue and extend the application scope, this paper proposes a novel GPLVM for (...) clustering. Specifically, by combining GPLVM with the subspace clustering method, our C-GPLVM can obtain more representative latent variable for clustering. Moreover, it can directly predict the new samples by introducing a back constraint in the model, thus being more suitable for big data learning tasks such as analysis of chaotic time series and so on. In the experiment, we compare it with the related GPLVMs and clustering algorithms. The experimental results show that the proposed model not only inherits the feature learning ability of GPLVM but also has superior clustering accuracy. (shrink)

This study aims to identify the necessary strategies for the development of a sustainable financial system. For this purpose, a novel approach could be provided for soft computing with Gaussian-based fuzzy DEMATEL approach to understand the significant levels and impact-relation degrees of these criteria. For robustness check, this evaluation has also been performed for triangular and trapezoidal fuzzy sets. There are many novelties of this study. Firstly, computer science has a significant role in the decision-making process. Another specificity is (...) that the use of Gaussian numbers with fuzzy numbers is a new area. In addition, interval type-2 fuzzy sets also provide a significant advantage in decision-making under uncertainty. The results demonstrate that the size of the alternative financing, investment in efficient projects, and effective advertisement/promotions are the most important items to affect the performance of alternative banking system of emerging economies. Hence, it is recommended that the new banking applications should be applied by the state or the state can provide some incentives for foreign banks to invest in emerging economies, such as tax reduction. Another important point is that the financial intermediations should generate a component financial analysis team to examine the financial reports of the companies in detail so that the financial credibility of these companies can be evaluated more effectively. (shrink)

The sense of agency is typically defined as the experience of controlling one’s own actions, and through them, changes in the external environment. It is often assumed that this experience is a single, unified construct that can be experimentally manipulated and measured in a variety of ways. In this article, we challenge this assumption. We argue that we should acknowledge four possible agency-related psychological constructs. Having a clear grasp of the possible constructs is important since experimental procedures are only able (...) to target some but not all the possible constructs. The unacknowledged misalignment of the possible constructs of a sense of agency and the experimental procedures is a major theoretical and methodological obstacle to studying the sense of agency. Only if we recognize the nature of this obstacle will we be able to design the experimental paradigms that would enable us to study the responsible computational mechanisms. (shrink)

Within the context of psychological measurement, realist commitments pervade methodology. Further, there are instances where particular scientific practices and decisions are explicable most plausibly against a background assumption of epistemic realism. That psychometrics is a realist enterprise provides a possible toehold for Stephen Jay Gould’s objections to psychometrics in The Mismeasure of Man and Joel Michell’s charges that psychometrics is a “pathological science.” These objections do not withstand scrutiny. There are no fewer than three activities in ongoing psychometric research which (...) presuppose a commitment to a minimal epistemic realism. Those activities include selecting between different models for representing data, estimating ability in the context of item response theory, and the move to make the individual the fundamental unit of analysis in psychometrics thereby calling for a shift in what sorts of data are evidentially relevant. In none of these activities are the commitments and disregard for evidence that Gould and Michell find objectionable or “pathological.”. (shrink)

We propose a reformulation of the ideal $\mathcal {N}$ of Lebesgue measure zero sets of reals modulo an ideal J on $\omega $, which we denote by $\mathcal {N}_J$. In the same way, we reformulate the ideal $\mathcal {E}$ generated by $F_\sigma $ measure zero sets of reals modulo J, which we denote by $\mathcal {N}^*_J$. We show that these are $\sigma $ -ideals and that $\mathcal {N}_J=\mathcal {N}$ iff J has the Baire property, which in turn is equivalent to (...) $\mathcal {N}^*_J=\mathcal {E}$. Moreover, we prove that $\mathcal {N}_J$ does not contain co-meager sets and $\mathcal {N}^*_J$ contains non-meager sets when J does not have the Baire property. We also prove a deep connection between these ideals modulo J and the notion of nearly coherence of filters (or ideals). We also study the cardinal characteristics associated with $\mathcal {N}_J$ and $\mathcal {N}^*_J$. We show their position with respect to Cichoń’s diagram and prove consistency results in connection with other very classical cardinal characteristics of the continuum, leaving just very few open questions. To achieve this, we discovered a new characterization of $\mathrm {add}(\mathcal {N})$ and $\mathrm {cof}(\mathcal {N})$. We also show that, in Cohen model, we can obtain many different values to the cardinal characteristics associated with our new ideals. (shrink)