Exponential Connection Research Articles

Information geometry of the Otto metric

AbstractWe introduce the dual of the mixture connection with respect to the Otto metric which represents a new kind of exponential connection. This provides a dual structure consisting of the mixture connection, the Otto metric as a Riemannian metric, and the new exponential connection. We derive the geodesic equation of this exponential connection, which coincides with the Kolmogorov forward equation of a gradient flow. We then derive the canonical contrast function of the introduced dual structure.

An Improved TCN Considering Data Augmentation in Enabling Load Classification

In modern power system, along with the developments of the data collecting technologies, the intensive and high-dimensional load data collection can be achieved. Therefore, to deeply reveal the patterns and behaviors hidden in the load dataset using load classification is of great significance for improving the service quality and the user experience of the power system. However, inevitable issues, for example the data missing and class imbalance are frequently reported in the present load dataset, which deteriorates the performance of the classification algorithms. Also, due to the special features, for example the time series, periodicity, and fluctuation of the load data, the traditional data classification algorithms also encounter performance defects. Therefore, this paper presents a data augmentation based enhanced temporal convolutional network (TCN) algorithm in enabling load classification. In the data augmentation phase, first an LRTC-TSVD algorithm is presented to implement the missing data completion. Second, a WGAN based class balancing approach is further presented to solve the class imbalance issue. Then, in the enhanced TCN phase, a WeightNorm, exponential linear unit (ELU) activation function, residual connection, and bidirectional feature fusion techniques based improved TCN (ITCN) algorithm is presented to carry out the accurate load data classification. Combining the data augmentation and the enhanced TCN phases, the ITCN algorithm is finally conducted. Based on the benchmark load datasets, the performances of the presented ITCN are evaluated. The experimental results report that the presented data augmentations can improve the quality of the dataset, moreover the classification algorithm is able to achieve the satisfied classification accuracy.

Influence of Soil Moisture and Crust Formation on Soil Evaporation Rate: A Wind Tunnel Experiment in Hungary

In both arid and semiarid regions, erosion by wind is a significant threat against sustainability of natural resources. The objective of this work was to investigate the direct impact of various soil moisture levels with soil texture and organic matter on soil crust formation and evaporation. Eighty soil samples with different texture (sand: 19, loamy sand: 21, sandy loam: 26, loam: 8, and silty loam: 6 samples) were collected from the Nyírség region (Eastern Hungary). A wind tunnel experiment was conducted on four simulated irrigation rates (0.5, l.0, 2.0, and 5.0 mm) and four levels of wind speeds (4.5, 7.8, 9.2, and 15.5 m s−1). Results showed that watering with a quantity equal to 5 mm rainfall, with the exception of sandy soils, provided about 5–6 h protection against wind erosion, even in case of a wind velocity as high as 15.5 m s−1. An exponential connection was revealed between wind velocities and the times of evaporation (R2 = 0.88–0.99). Notably, a two-way ANOVA test revealed that both wind velocity (p < 0.001) and soil texture (p < 0.01) had a significant effect on the rate of evaporation, but their interaction was not significant (p = 0.26). In terms of surface crusts, silty loamy soils resulted in harder and more solid crusts in comparison with other textures. In contrast, crust formation in sandy soils was almost negligible, increasing their susceptibility to wind erosion risk. These results can support local municipalities in the development of a local plan against wind erosion phenomena in agricultural areas.

Quantum Statistical Manifolds.

Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose, the emphasis is shifted from a manifold of strictly positive density matrices to a manifold of faithful quantum states on the C*-algebra of bounded linear operators. In addition, ideas from the parameter-free approach to information geometry are adopted. The underlying Hilbert space is assumed to be finite-dimensional. In this way, technicalities are avoided so that strong results are obtained, which one can hope to prove later on in a more general context. Two different atlases are introduced, one in which it is straightforward to show that the quantum states form a Banach manifold, the other which is compatible with the inner product of Bogoliubov and which yields affine coordinates for the exponential connection.

A Direct Link between the Fragile-to-Strong Transition and Relaxation in Supercooled Liquids.

It is known that both the fragile-to-strong (F-S) transition and relaxation processes occur in numerous supercooled liquids upon cooling toward the glass transition temperature. The key question is whether and how these two dynamic processes are correlated. Here, we show a direct link between the two processes for both metallic glass-forming liquids (MGFLs) with different fragilities and also for nonmetallic glass-forming liquids. By comparing the F-S transition extent parameter f with the parameter r that characterizes the competition between the α and the slow β relaxations, we have discovered a negative exponential connection between the two parameters of supercooled liquids. The finding indicates that the slow β relaxation plays a dominant role in the F-S transition. This work provides new insight into the microscopic mechanism of the F-S transition and creates a strong basis for predicting whether and to what extent the F-S transition occurs in supercooled liquids.

Flow properties of components for dry compound feed

Animal feed often consists of different components and is normally stored in tower silos as a mixture. The components differ in terms of their flow properties, which determine the flow out process. In this study a series of key components like crushed grain and crushed meals of native and imported oils and legumes were examined. To characterize the flow properties, shear strength measurements with the Jenike shear cell were carried out and the flowability ff c and the outlet diameter were calculated. The tensile strength was measured with a device according to Ashton. The results show the known tendency between the flowability ff c and the amount of fine components. Because of the different bulk materials the coefficient of determination is low. The flowability based on own investigations is lower than the flowability of Jenike. The evaluation of the results did not demonstrate any influence of the ingredients on the flow properties of the components examined. Fig. 2. Flowability for grains and dry compound feed (presented in the second table) as a function of the fine component. Grain material: wheat bran, rye bran, wheat meal, rye meal, barley meal, oat meal and maize meal. No grain material: dried grass, rapeseed meal, cotton meal, linseed meal, sunflower meal, tapioca meal, fodder yeast and soya bean meal. ► Components of animal feed differ in terms of shear strength and flowability. ► Bulk goods with a lower share of fines have better flow properties. ► An exponential connection is shown between flowability and fine share. ► The particle form seems to influence the flow properties. ► The flow properties are not influenced by the investigated ingredients.

REMARKS ON THE STATISTICAL ORIGIN OF THE GEOMETRICAL FORMULATION OF QUANTUM MECHANICS

A quantum system can be entirely described by the Kähler structure of the projective space [Formula: see text] associated to the Hilbert space [Formula: see text] of possible states; this is the so-called geometrical formulation of quantum mechanics. In this paper, we give an explicit link between the geometrical formulation (of finite dimensional quantum systems) and statistics through the natural geometry of the space [Formula: see text] of non-vanishing probabilities [Formula: see text] defined on a finite set En: = {x1, …, xn}. More precisely, we use the Fisher metric gF and the exponential connection ∇(1) (both being natural statistical objects living on [Formula: see text]) to construct, via the Dombrowski splitting theorem, a Kähler structure on [Formula: see text] which has the property that it induces the natural Kähler structure of a suitably chosen open dense subset of ℙ(ℂn). As a direct physical consequence, a significant part of the quantum mechanical formalism (in finite dimension) is encoded in the triple [Formula: see text].

Arsenic for the fool: An exponential connection

Anthropogenic arsenic is insidiously building up together with natural arsenic to a level unprecedented in the history of mankind. Arsenopyrite (FeAsS) is the principal ore of arsenic and gold in hard rock mines; it is formed by a coupled substitution of sulphur by arsenic in the structure of pyrite (FeS2) — nicknamed “fool's gold”. Other important sources of anthropogenic arsenic are fossil fuels such as coal and oil. Here I report on the first indication that the environmental concentration of total arsenic in topsoils – in the 7–18ppm range – is exponentially related to the prevalence and mortality of Alzheimer's disease and other dementias in European countries. This evidence defies the imputed absence of verified cases of human morbidity or mortality resulting from exposure to low-level arsenic in topsoils.

Exponential families admitting almost complex structures

We discuss exponential families admitting almost complex structures which are parallel relative to an exponential connection (e–connection) or mixture connection (m–connection). The multinomial distribution, negative multinomial distribution and multivariate normal distribution are important examples of the exponential family. We give almost complex structures which are parallel relative to the exponential or mixture connection for these exponential families. Also, we prove spaces of the multinomial distribution and negative multinomial distribution are of constant curvature with respect to the α–connection.

Connections on Non-Parametric Statistical Manifolds by Orlicz Space Geometry

The non-parametric version of Information Geometry has been developed in recent years. The first basic result was the construction of the manifold structure on ℳμ, the maximal statistical models associated to an arbitrary measure μ (see Ref. 48). Using this construction we first show in this paper that the pretangent and the tangent bundles on ℳμ are the natural domains for the mixture connection and for its dual, the exponential connection. Second we show how to define a generalized Amari embedding AΦ:ℳμ→SΦ from the Exponential Statistical Manifold (ESM) ℳμ to the unit sphere SΦ of an arbitrary Orlicz space LΦ. Finally we show that, in the non-parametric case, the α-connections ∇α(α∈(-1,1)) must be defined on a suitable α-bundle ℱα over ℳμ and that the bundle-connection pair (ℱα, ∇α) is simply (isomorphic to) the pull-back of the Amari embedding Aα: ℳμ→S2/1-α were the unit sphere S2/1-αcL2/1-α is equipped with the natural connection.

Diagnostic Measures for Model Criticism

Abstract We discuss the problem of model criticism, with emphasis on developing summary diagnostic measures. We approach model criticism by identifying possible troublesome features of the currently entertained model, embedding the model in an elaborated model, and measuring the value of elaborating. This requires three elements: a model elaboration, a prior distribution, and a utility function. Each triplet generates a different diagnostic measure. We focus primarily on the measure given by a Kullback—Leibler divergence between the marginal prior and posterior distributions on the elaboration parameter. We also develop a linearized version of this diagnostic and use it to show that our procedure is related to other tools commonly used for model diagnostics, such as Bayes factors and the score function. One attraction of this approach is that it allows model criticism to be performed jointly with parameter inference and prediction. Also, this diagnostic approach aims at maintaining an exploratory nature to the criticism process, while affording feasibility of implementation. In this article we present the general outlook and discuss general families of elaborations for use in practice; the exponential connection elaboration plays a key role. We then describe model elaborations for use in diagnosing: departures from normality, goodness of fit in generalized linear models, and variable selection in regression and outlier detection. We illustrate our approach with two applications.

Propagation of spindle waves in a thalamic slice model

1. We study the propagation and dynamics of spindle waves in thalamic slices by developing and analyzing a model of reciprocally coupled populations of excitatory thalamocortical (TC) neurons and inhibitory thalamic reticular (RE) neurons. 2. Each TC neuron has three intrinsic ionic currents: a low-threshold T-type Ca+2 current (ICa-T), a hyperpolarization-activated cation ("sag") current (Ih) and a leak current. Each RE cell also has three currents: ICa-T, a leak current, and a calcium-activated potassium current (IAHP). Isolated TC cells are at rest, can burst when released or depolarized from a hyperpolarized level, and burst rhythmically under moderate constant hyperpolarizing current. Isolated RE cells are at a hyperpolarized resting membrane potential and can burst when depolarized. 3. TC cells excite RE cells with fast alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) synapses, and RE cells inhibit TC cells with fast gamma-aminobutyric acid-A (GABAA) and slow GABAB synapses and inhibit each other with GABAA synapses only. GABAB postsynaptic conductances operate far from saturation, and the slow inhibitory postsynaptic potentials (IPSPs) increase with the width of the presynaptic burst. The model network is a one-dimensional cellular array with localized coupling. The synaptic coupling strength decays with the distance between the pre- and postsynaptic cells, either exponentially or as a step function. 4. The "intact" network can oscillate with partial synchrony and a population frequency of approximately 10 Hz. RE cells emit bursts almost at every oscillation cycle, whereas TC cells do so almost at every other cycle. Block of GABAB receptors hardly changes the network behavior. Block of GABAA receptors leads the network to a slowed oscillatory state, where the population frequency is approximately 4 Hz and both RE and TC cells fire unusually long bursts at every cycle and in full synchrony. These results are consistent with the experimental observations of von Krosigk, Bal, and McCormick. We obtain such consistency only when the above assumptions regarding the synaptic dynamics, particularly nonsaturating GABAB synapses, are fulfilled. 5. The slice model has a stable rest state with no neural activity. By initially depolarizing a few neurons at one end of the slice while all the other cells are at rest, a recruitment process may be initiated, and a wavefront of oscillatory activity propagates across the slice. Ahead of the wavefront, neurons are quiescent; neurons behind it oscillate. We find that the wave progresses forward in a lurching manner. TC cells that have just become inhibited must be hyperpolarized for a long enough time before they can fire rebound bursts and recruit RE cells. This step limits the wavefront velocity and may involve a substantial part of the cycle when no cells at the front are depolarized. 6. The wavefront velocity increases linearly with the characteristic spatial length of the connectivity (the footprint length). It increases only gradually with the synaptic strength, logarithmically in the case of an exponential connection function and only slightly for a step connection function. It also decreases gradually with a potassium leak conductance that hyperpolarizes RE cells. 7. To reproduce the experimentally measured wavefront velocity of approximately 1 mm/s, together with other in vitro observations, both the RE-to-TC and the TC-to-RE projections in the model should be spatially localized. The sum of the RE-to-TC and the TC-to-RE synaptic footprint lengths should be on the order of 100 microns. (ABSTRACT TRUNCATED AT 250 WORDS)