On randomized estimators of the Hafnian of a nonnegative matrix

Gaussian Boson Samplers aim to demonstrate quantum advantage by performing a sampling task believed to be classically hard. The probabilities of individual outcomes in the sampling experiment are determined by the Hafnian of an appropriately constructed symmetric matrix. For nonnegative matrices, there is a family of randomized estimators of the Hafnian based on generating a particular random matrix and calculating its determinant. While these estimators are unbiased (the mean of the determinant is equal to the Hafnian of interest), their variance may be so high as to prevent an efficient estimation. Here we investigate the performance of two such estimators, which we call the Barvinok and Godsil-Gutman estimators. We find that in general both estimators perform well for adjacency matrices of random graphs, demonstrating a slow growth of variance with the size of the problem. Nonetheless, there are simple examples where both estimators show high variance, requiring an exponential number of samples. In addition, we calculate the asymptotic behavior of the variance for the complete graph. Finally, we simulate the Gaussian Boson Sampling using the Godsil-Gutman estimator and show that this technique can successfully reproduce low-order correlation functions.Comment: 11 pages, 7 figure

Проблеми та перспективи розвитку птахівництва в Україні

The article stipulates that the modern poultry farming in Ukraine is the most dynamic sector of productive livestock and able to produce in large quantities and in a short time. As one of the most automated and mechanized agricultural sectors it contains significant potential to meet the needs of the country's food resources. Poultry production has several advantages compared to pigs and cattle, namely for maturation compared to other animal products, half the consumption power in 3-5 times lower in feed use of protein. Despite the fact that the domestic industrial poultry farming is gradually emerging in the general stabilization but significant rise is observed. A number of major theoretical and practical issues of commercial poultry and problems to improve its efficiency are not studied enough or need to be reviewed from the standpoint of modernity, particularly in the context of Ukraine's accession to the WTO. The authors reviewed the scientific and practical principles and current status of poultry and efficiency cost of its products in agricultural enterprises. It is necessary to investigate the problems and prospects of functioning of the industry. The analysis of poultry production by categories of farms in Ukraine was made. The basic directions and practical principles enhance the economic efficiency of poultry farming in Ukraine.В статье рассмотрены научно-теоретические основы и современное состояние развития птицеводства и экономическую эффективность производства его продукции в сельскохозяйственных предприятиях. Исследованы проблемы и перспективы функционирования отрасли. Проведен анализ динамики поголовья птицы, производства продукции птицеводства по категориям хозяйств в Украине. Обоснованы основные направления и практические основы по повышению уровня экономической эффективности птицеводства в Украине.У статті розглянуто науково-теоретичні засади та сучасний стан розвитку птахівництва і економічну ефективність виробництва його продукції в сільськогосподарських підприємствах. Досліджено проблеми та перспективи функціонування галузі. Проведено аналіз динаміки поголів’я птиці, виробництва продукції птахівництва за категоріями господарств в Україні. Обґрунтовано основні напрямки та практичні засади щодо підвищення рівня економічної ефективності птахівництва в Україні

Проблеми та перспективи розвитку птахівництва в Україні

The article stipulates that the modern poultry farming in Ukraine is the most dynamic sector of productive livestock and able to produce in large quantities and in a short time. As one of the most automated and mechanized agricultural sectors it contains significant potential to meet the needs of the country's food resources. Poultry production has several advantages compared to pigs and cattle, namely for maturation compared to other animal products, half the consumption power in 3-5 times lower in feed use of protein. Despite the fact that the domestic industrial poultry farming is gradually emerging in the general stabilization but significant rise is observed. A number of major theoretical and practical issues of commercial poultry and problems to improve its efficiency are not studied enough or need to be reviewed from the standpoint of modernity, particularly in the context of Ukraine's accession to the WTO. The authors reviewed the scientific and practical principles and current status of poultry and efficiency cost of its products in agricultural enterprises. It is necessary to investigate the problems and prospects of functioning of the industry. The analysis of poultry production by categories of farms in Ukraine was made. The basic directions and practical principles enhance the economic efficiency of poultry farming in Ukraine.В статье рассмотрены научно-теоретические основы и современное состояние развития птицеводства и экономическую эффективность производства его продукции в сельскохозяйственных предприятиях. Исследованы проблемы и перспективы функционирования отрасли. Проведен анализ динамики поголовья птицы, производства продукции птицеводства по категориям хозяйств в Украине. Обоснованы основные направления и практические основы по повышению уровня экономической эффективности птицеводства в Украине.У статті розглянуто науково-теоретичні засади та сучасний стан розвитку птахівництва і економічну ефективність виробництва його продукції в сільськогосподарських підприємствах. Досліджено проблеми та перспективи функціонування галузі. Проведено аналіз динаміки поголів’я птиці, виробництва продукції птахівництва за категоріями господарств в Україні. Обґрунтовано основні напрямки та практичні засади щодо підвищення рівня економічної ефективності птахівництва в Україні

Accurate formation energies of charged defects in solids: a systematic approach

Defects on surfaces of semiconductors have a strong effect on their reactivity and catalytic properties. The concentration of different charge states of defects is determined by their formation energies. First-principles calculations are an important tool for computing defect formation energies and for studying the microscopic environment of the defect. The main problem associated with the widely used supercell method in these calculations is the error in the electrostatic energy, which is especially pronounced in calculations that involve surface slabs and 2D materials. We present an internally consistent approach for calculating defect formation energies in inhomogeneous and anisotropic dielectric environments, and demonstrate its applicability to the cases of the positively charged Cl vacancy on the NaCl (100) surface and the negatively charged S vacancy in monolayer MoS2

Insights into reactivity and defect properties of semiconductor surfaces from first-principles computations

We use first-principles computations based on Ehrenfest dynamics and density functional theory to study water and methanol photo-oxidation on a model photo-catalytic material – the (110) surface of rutile titanium dioxide. We simulate photo-excitation in titania and the subsequent excited-state reaction trajectories. Analysis of the coupled dynamics of the electronic and ionic subsystems allows us to establish a novel reaction mechanism, for which we propose the name “photo-induced C-H acidity.” We provide a detailed and intuitive interpretation of the mechanism in terms of Lewis structures, identify the driving forces of the process, and propose general design principles for efficient photo-catalytic systems. Another important factor in the reactivity of semiconductor catalysts is the presence of defects in surface and subsurface regions. Knowledge of the formation energies of defects and impurities in different charge states is required in order to obtain insight into their concentration and stability. We develop an internally consistent method for calculating formation energies of charged defects based on density functional theory, which is applicable to both surface regions of semiconducting materials and two-dimensional materials. We discuss the implementation and usage details of the method and provide an example of its usage for studying sulfur vacancy formation in MoS2 monolayer.Chemical Physic

Establishing the limits of efficiency of perovskite solar cells from first principles modeling

The recent surge in research on metal-halide-perovskite solar cells has led to a seven-fold increase of efficiency, from similar to 3% in early devices to over 22% in research prototypes. Oft-cited reasons for this increase are: (i) a carrier diffusion length reaching hundreds of microns; (ii) a low exciton binding energy; and (iii) a high optical absorption coefficient. These hybrid organic-inorganic materials span a large chemical space with the perovskite structure. Here, using first-principles calculations and thermodynamic modelling, we establish that, given the range of band-gaps of the metal-halide-perovskites, the theoretical maximum efficiency limit is in the range of similar to 25-27%. Our conclusions are based on the effect of level alignment between the perovskite absorber layer and carrier-transporting materials on the performance of the solar cell as a whole. Our results provide a useful framework for experimental searches toward more efficient devices

Health Is not always written in bone: using a modern comorbidity index to assess disease load in paleopathology

Paleopathology has revealed much about disease in the past but is usually limited to conditions with osteological manifestations; this often excludes acute soft tissue infections and causes of death for most individuals in the past and present. Our understanding of the evolution of disease is essential for contextualizing and predicting the epidemiological shifts that are happening in modern society, as high rates of infectious disease coexist alongside high rates of chronic disease in rates unlike those observed previously in human history. Moreover, many physiological states not previously classified as “disease” (obesity) have become pathologized, influencing our conception of disease and what defines health. By using the Galler Collection, a pre-antibiotic and pre-chemotherapeutic osteological series with modern autopsy records, our research quantifies disease burden of the past using the Charlson Index (CI), a modern comorbidity index of disease severity. Galler Collection remains and autopsy records were scored with the Charlson Index to correlate bone findings with soft tissue findings, and statistical analysis was performed for cumulative scores and absolute diagnosis counts, with patients stratified by sex and cause of death (pneumonia or cancer). Osteological diagnosis counts were more predictive of soft-tissue autopsy disease counts than were associated cumulative CI scores. Diagnosis counts and CI scores for osteological data were more closely related to associated soft tissue data for cancer patients than for pneumonia patients. This research indicates how interdisciplinary paleopathological analysis assists in making more reliable assessments of health and mortality in the past, with implications for trending and predicting future epidemiological shifts

Strain effects on the behavior of isolated and paired sulfur vacancy defects in monolayer MoS2

We investigate the behavior of sulfur vacancy defects, the most abundant type of intrinsic defect in monolayer MoS2, using first-principles calculations based on density functional theory. We consider the dependence of the isolated defect formation energy on the charge state and on uniaxial tensile and compressive strain up to 5%. We also consider the possibility of defect clustering by examining the formation energies of pairs of vacancies at various relative positions, and their dependence on charge state and strain. We find that there is no driving force for vacancy clustering, independent of strain in the material. The barrier for diffusion of S vacancies is larger than 1.9 eV in both charged and neutral states regardless of the presence of other nearby vacancies. We conclude that the formation of extended defects from S vacancies in planar monolayer MoS2 is hindered both thermodynamically and kinetically