Study On Some Matrix Equations Involving The Weighted Geometric Mean and Their Application

In this paper we consider two matrix equations that involve the weighted geometric mean. We use the fixed point theorem in the cone of positive definite matrices to prove the existence of a unique positive definite solution. In addition, we study the multi-step stationary iterative method for those equations and prove the corresponding convergence. A fidelity measure for quantum states based on the matrix geometric mean is introduced as an application of matrix equation.

Conditional generative models for sampling and phase transition indication in spin systems

In this work, we study generative adversarial networks (GANs) as a tool to learn the distribution of spin configurations and to generate samples, conditioned on external tuning parameters or other quantities associated with individual configurations. For concreteness, we focus on two examples of conditional variables---the temperature of the system and the energy of the samples. We show that temperature-conditioned models can not only be used to generate samples across thermal phase transitions, but also be employed as unsupervised indicators of transitions. To this end, we introduce a GAN-fidelity measure that captures the model’s susceptibility to external changes of parameters. The proposed energy-conditioned models are integrated with Monte Carlo simulations to perform over-relaxation steps, which break the Markov chain and reduce auto-correlations. We propose ways of efficiently representing the physical states in our network architectures, e.g., by exploiting symmetries, and to minimize the correlations between generated samples. A detailed evaluation, using the two-dimensional XY model as an example, shows that these incorporations bring in considerable improvements over standard machine-learning approaches. We further study the performance of our architectures when no training data is provided near the critical region.

Non-Gaussianity of Four-Photon Superpositions of Fock States

We study two families of four-photon superpositions of the Fock states: even vacuum squeezed states (EVSS) and orthogonal-even coherent states (OECS). These families are distinguished due to several properties: for certain values of parameters, they give the fourth-order uncertainty products close to the known minimal value (which is lower than for the Gaussian states); they have equal dimensionless values of the second- and fouth-order moments of the coordinate and momentum for all values of parameters; they possess zero covariances for all values of parameters. Since these states are obviously non-Gaussian, we consider them as good candidates to compare several different measures of non-Gaussianity proposed by different authors for the past fifteen years. The reference Gaussian states in all examples are thermal states dependent on a single parameter (an effective temperature or the coordinate variance). We analyze the measures based on the normalized Hilbert–Schmidt distance and the relative entropy (introduced by Genoni–Paris–Banaszek), the fidelity measure (Ghiu–Marian–Marian) and its logarithmic analog (Baek–Nha), as well as the Mandilara–Karpov–Cerf “Gaussianity parameter”. These measures are compared with the kurtosis of the coordinate probability density and with the non-Gaussian behavior of the Wigner function.

Fidelity Assessment Checklist Development for Community Nursing Research in Early Childhood

Nurses play an important role in promoting positive childhood development via early interventions intended to support parenting. Despite recognizing the need to deliver vital parenting programs, monitoring fidelity has largely been ignored. Fidelity refers to the degree to which healthcare programs follow a well-defined set of criteria specifically designed for a particular program model. With increasing demands for early intervention programs to be delivered by non-specialists, rigorous yet pragmatic strategies for maintaining fidelity are needed. This paper describes the step-by-step development and evaluation of a program fidelity measure, using the Attachment and Child Health (ATTACH™) parenting program as an exemplar. The overall quality index for program delivery varied between “very good” to “excellent,” with a mean of 4.3/5. Development of checklists like the ATTACH™ fidelity assessment checklist enables the systematic evaluation of program delivery and identification of therapeutic components that enable targeted efforts at improvement. In future, research should examine links between program fidelity and targeted outcomes to ascertain if increased fidelity scores yield more favorable effects of parenting programs.

Classification of tall-forb vegetation in the Pamir-Alai and western Tian Shan Mountains (Tajikistan and Kyrgyzstan, Middle Asia)

Aims: To complete the syntaxonomic scheme for tall-forb vegetation of the montane and alpine belts in the Pamir-Alai and western Tian Shan Mountains in Tajikistan and Kyrgyzstan with some remarks on its environmental predictors. Study area: Middle Asia: Tajikistan and Kyrgyzstan. Methods: A total of 244 relevés were sampled in 2013–2019 using the seven-degree cover-abundance scale of the Braun-Blanquet approach. These were classified with a modified TWINSPAN algorithm with pseudospecies cut-levels 0%, 5% and 25%, and total inertia as a measure of cluster heterogeneity. Diagnostic species were identified using the phi coefficient as a fidelity measure. NMDS was used to explore the relationships between the distinguished groups. Results: Our classification revealed 19 clusters of tall-forb vegetation in Middle Asia. Among others we found forb communities typical for Tian Shan, western Pamir-Alai, forb-scree vegetation of Pamir-Alai, dry tall-forbs and typical forbs of the alpine belt. A total of eight new tall-forb associations and five communities were distinguished. The forb vegetation of Middle Asia has been assigned to the class Prangetea ulopterae Klein. The main factors differentiating the species composition of the researched vegetation are elevation, mean annual temperature, sum of annual precipitation and inclination of the slope. Conclusions: The paper presents the first insight into the comprehensive classification of the alpine forb vegetation in Middle Asia and fosters progress in explaining the relationship of boreo-temperate and Mediterranean-like (Irano-Turanian) vegetation in western Asian and central Asian subregions of the Irano-Turanian phytogeographical region. Taxonomic references: The nomenclature of the vascular plants follows generally Cherepanov (1995) and for Bromus spp. The Plant List (2020) Version 1.1. http://www.theplantlist.org/. Syntaxonomic references: The names of syntaxa are used in accordance with Ermakov (2012), Gadghiev et al. (2002) and Nowak et al. (2018). Abbreviation: NMDS = Non-metric Multidimensional Scaling.

Source Coding with a Causal Helper

A multi-terminal network, in which an encoder is assisted by a side-information-aided helper, describes a memoryless identically distributed source to a receiver, is considered. The encoder provides a non-causal one-shot description of the source to both the helper and the receiver. The helper, which has access to causal side-information, describes the source to the receiver sequentially by sending a sequence of causal descriptions depending on the message conveyed by the encoder and the side-information subsequence it has observed so far. The receiver reconstructs the source causally by producing on each time unit an estimate of the current source symbol based on what it has received so far. Given a reconstruction fidelity measure and a maximal allowed distortion, we derive the rates-distortion region for this setting and express it in terms of an auxiliary random variable. When the source and side-information are drawn from an independent identically distributed Gaussian law and the fidelity measure is the squared-error distortion we show that for the evaluation of the rates-distortion region it suffices to choose the auxiliary random variable to be jointly Gaussian with the source and side-information pair.