Open Problems Related to Quantum Query Complexity

I offer a case that quantum query complexity still has loads of enticing and fundamental open problems—from relativized QMA versus QCMA and BQP versus IP , to time/space tradeoffs for collision and element distinctness, to polynomial degree versus quantum query complexity for partial functions, to the Unitary Synthesis Problem and more.

Crossworld Predication in Natural Language

Некоторые предложения естественного языка, такие как «Джон мог быть выше, чем Мэри, как она есть», не допускают адекватного анализа в терминах стандартной семантики возможных миров, поскольку содержат кросс-мировую предикацию, которая в стандартной семантике не отображается. Для логического анализа такого рода предложений автором была разработана (и представлена в других публикациях) логика для кросс-мировой предикации (СРL). В статье приведен ряд примеров, демонстрирующих широкую распространенность феномена кросс-мировой предикации в естественном языке и описаны главные особенности семантики СРL (кросс-мировая интерпретация предикатов и использование частичных функций от переменных к возможным мирам в истинностной оценке формул), а также охарактеризована специфика синтаксиса СРL и онтологии, лежащей в ее основе. Some sentences of natural language cannot be adequately analyzed in terms of standard possible world semantics because they involve cross-world predication that cannot be reflected by means of standard semantics. An instance is ‘John might be taller than Mary is’. In some other papers the author proposed a logic for cross-word predication (CPL) that can be used to logically analyze sentences of this sort. In this paper, some examples are adduced that show that cross-world predication is highly widespread in natural language. The main features of the semantics of CPL are described, namely cross-world interpretation of predicates, and using partial functions from variables to possible worlds in the evaluation of formulas. Finally, the specificity of the syntax of CPL, and the ontology behind the semantics of CPL is characterized.

INCLUSIVE DIAGNOSTICS AND STIMULATION OF SOCIALLY DISADVANTAGED CHILDREN OF A PRE-SCHOOL AGE: EXPERIMENTAL VERIFICATION

The research focuses on the diagnostics and stimulation of socially disadvantaged children of a pre-school age, which is a crucial component of inclusive education. The aim of the research was to experimentally verify through input and output orientation diagnostics the effectiveness of the stimulation program for 5 to 6 year old socially disadvantaged children in kindergartens. The results of the input and output orientation screening of 5 to 6 year old children from the experimental and control groups were analysed. Furthermore, the effectiveness of the stimulation program intended for the training of areas of deficits of partial functions and symptoms in the experimental group was verified, and conclusions and recommendations for pedagogical theory and practice in the area of inclusive approaches at the pre-primary stage of the school system were formulated. The research demonstrated that the experimental group of children achieved statistically significantly better results in the post-test, focused on the area of symptoms measured by the t-test, than the control group. It was also confirmed that both groups of socially disadvantaged children (control and experimental) achieved statistically significantly better results in the post-test, focused on the area of deficits of partial functions, than in the pre-test. Keywords: inclusive diagnostics, inclusive education, pre-school age, socially disadvantaged children

Functional Partial Fuzzy Relations

We study fuzzy relations that satisfy the functionality property and that their membership functions can be partial functions. Such fuzzy relations are called partial fuzzy relations, and the variable-domain fuzzy set theory is a framework that provides powerful tools for handling these objects. There, the special operations based on connectives and quantifiers of a partial fuzzy logic are in use. The undefined degrees of membership are carried via those special operations. Furthermore, we show that a suitable combination of these operations leads to a meaningful definition of the functionality property, and we investigate its basic characteristics.

Definitional schemes for primitive recursive and computable functions

The unary primitive recursive functions can be defined in terms of a finite set of initial functions together with a finite set of unary and binary operations that are primitive recursive in their inputs. We reduce arity considerations, by show that two fixed unary operations suffice, and a single initial function can be chosen arbitrarily. The method works for many other classes of functions, including the unary partial computable functions. For this class of partial functions we also show that a single unary operation (together with any finite set of initial functions) will never suffice.

Maize catalases localized in peroxisomes support the replication of maize chlorotic mottle virus

Co-infection of maize chlorotic mottle virus (MCMV) with a virus in the Potyviridae family, such as sugarcane mosaic virus, usually leads to maize lethal necrosis (MLN). Over the past decade, MCMV/MLN has emerged in many countries/regions of the world and resulted in serious yield loss in maize production. Although partial functions of some MCMV-encoded proteins have been identified, the host factors related to MCMV replication are poorly understood. Here, we show that maize peroxisomes can form aggregated bodies in MCMV-infected leaf cells. The dsRNA binding-dependent fluorescence complementation assay indicated that the aggregated peroxisomes in maize served as the major replication site of MCMV. In addition, our results revealed that all the three maize catalases were present mostly in peroxisomes in the presence or absence of MCMV. Furthermore, we determined that inhibition of catalase activity or induction of reactive oxygen species (ROS) in maize protoplasts significantly reduced the accumulation of MCMV RNA. In summary, this research reveals the replication site of MCMV and an important role of maize catalases in supporting virus replication. Our results are conducive to understanding the pathogenesis of MCMV and identifying targets for resistance breeding or gene regulation strategies.

ML-based group method of data handling: an improvement on the conventional GMDH

Machine learning (ML) has been recognized as a feasible and reliable technique for the modeling of multi-parametric datasets. In real applications, there are different relationships with various complexities between sets of inputs and their corresponding outputs. As a result, various models have been developed with different levels of complexity in the input–output relationships. The group method of data handling (GMDH) employs a family of inductive algorithms for computer-based mathematical modeling grounded on a combination of quadratic and higher neurons in a certain number of variable layers. In this method, a vector of input features is mapped to the expected response by creating a multistage nonlinear pattern. Usually, each neuron of the GMDH is considered a quadratic partial function. In this paper, the basic structure of the GMDH technique is adapted by changing the partial functions to enhance the complexity modeling ability. To accomplish this, popular ML models that have shown reasonable function approximation performance, such as support vector regression and random forest, are used, and the basic polynomial functions in the GMDH are replaced by these ML models. The regression feasibility and validity of the ML-based GMDH models are confirmed by computer simulation.

DESIGN OF AND WITH SENSING MACHINE ELEMENTS - USING THE EXAMPLE OF A SENSING ROLLING BEARING

In this paper the development process of a sensing rolling bearing is presented, from which finally design rules for sensing machine elements are derived. In the first step, the requirements of the users are determined. It turns out user of sensing machine elements want to continue to use the advantage of the standardized machine elements and costs should not be incurred by redesign or complex assembly. With these requirements the development of the sensing rolling bearing is started, in which the different presented technologies are reviewed for their suitability regarding the requirements. With the selected technology measuring the electric rolling bearing impedance to estimate rolling bearing loads, a first prototype is developed by creating a functional structure of the product and focusing on the partial solution of the most relevant partial functions. This prototype is then tested with regard to its functionality. Finally, generalizable design rules for sensing machine elements are derived from the development.

Thermodynamic study of the thallium-thulium tellurides by EMF method

In this study the phase equilibria in the Tl2Te–Tl2Te3–TlTmTe2compositions area of the Tl–Tm–Te ternary system were studied by powder X-ray diffraction (PXRD) analysis. Based on PXRD data, the solid-phase equi-libria diagram was plotted. The thermodynamic functions of the Tl9TmTe6and TlTmTe2ternary compounds were calculated by the electromotive forces method. The electrochemical cells of the following type (−) TmТе (s.) | glycerol + KCl + TmCl3 | (Tm in alloys of Tl–Tm–Te system) (s.) (+) were assembled and their EMF were measured in the 300-450 Ktemperature range. Based on obtained EMF data for the Tl2Te3–TlTe–TlTmTe2and TlTe–TlTmTe2–Tl9TmTe6three-phase regions, the relative partial thermodynamic functions of TmTe in alloys were calculated. The combination of these functions with the partial molar functions of thulium in TmTe allowed calculating the corresponding partial functions of thulium in the above phase regions. The potential-forming reactions responsible for the indicated partial molar values were obtained based on con-structed solid-phase equilibria diagram. Using indicated potential-forming reactions, for the first time, the standard thermodynamic functions of formation and standard entropies of the Tl9TmTe6and TlTmTe2 compounds were calculated.