Partial Description Research Articles

Finite type invariants of knots in homology 3–spheres with respect to null LP–surgeries

We study a theory of finite type invariants for null-homologous knots in rational homology 3-spheres with respect to null Lagrangian-preserving surgeries. It is an analogue in the setting of the rational homology of the Goussarov-Rozansky theory for knots in integral homology 3-spheres. We give a partial combinatorial description of the graded space associated with our theory and determine some cases when this description is complete. For null-homologous knots in rational homology 3-spheres with a trivial Alexander polynomial, we show that the Kricker lift of the Kontsevich integral and the Lescop equivariant invariant built from integrals in configuration spaces are universal finite type invariants for this theory; in particular it implies that they are equivalent for such knots.

Projective duals to algebraic and tropical hypersurfaces

We study a tropical analogue of the projective dual variety of a hypersurface. When $X$ is a curve in $\mathbb{P}^2$ or a surface in $\mathbb{P}^3$, we provide an explicit description of $\text{Trop}(X^*)$ in terms of $\text{Trop}(X)$, as long as $\text{Trop}(X)$ is smooth and satisfies a mild genericity condition. As a consequence, when $X$ is a curve we describe the transformation of Newton polygons under projective duality, and recover classical formulas for the degree of a dual plane curve. For higher dimensional hypersurfaces $X$, we give a partial description of $\text{Trop}(X^*)$.

Weak Values and Quantum Properties

We investigate in this work the meaning of weak values through the prism of property ascription in quantum systems. Indeed, the weak measurements framework contains only ingredients of the standard quantum formalism, and as such weak measurements are from a technical point of view uncontroversial. However attempting to describe properties of quantum systems through weak values -- the output of weak measurements -- goes beyond the usual interpretation of quantum mechanics, that relies on eigenvalues. We first recall the usual form of property ascription, based on the eigenstate-eigenvalue link and the existence of "elements of reality". We then describe against this backdrop the different meanings that have been given to weak values. We finally argue that weak values can be related to a specific form of property ascription, weaker than the eigenvalues case but still relevant to a partial description of a quantum system.

Separation of conditions as a prerequisite for quantum theory

We introduce the notion of “separation of conditions” meaning that a description of statistical data obtained from experiments, performed under a set of different conditions, allows for a decomposition such that each partial description depends on mutually exclusive subsets of these conditions. Descriptions that allow a separation of conditions are shown to entail the basic mathematical framework of quantum theory. The Stern–Gerlach and the Einstein–Podolsky–Rosen–Bohm experiment with three, respectively nine possible outcomes are used to illustrate how the separation of conditions can be used to construct their quantum theoretical descriptions. It is shown that the mathematical structure of separated descriptions implies that, under certain restrictions, the time evolution of the data can be described by the von Neumann/Schrödinger equation.

Probabilistic Modeling of Microbial Metabolic Networks for Integrating Partial Quantitative Knowledge Within the Nitrogen Cycle.

Understanding the interactions between microbial communities and their environment sufficiently to predict diversity on the basis of physicochemical parameters is a fundamental pursuit of microbial ecology that still eludes us. However, modeling microbial communities is problematic, because (i) communities are complex, (ii) most descriptions are qualitative, and (iii) quantitative understanding of the way communities interact with their surroundings remains incomplete. One approach to overcoming such complications is the integration of partial qualitative and quantitative descriptions into more complex networks. Here we outline the development of a probabilistic framework, based on Event Transition Graph (ETG) theory, to predict microbial community structure across observed chemical data. Using reverse engineering, we derive probabilities from the ETG that accurately represent observations from experiments and predict putative constraints on communities within dynamic environments. These predictions can feedback into the future development of field experiments by emphasizing the most important functional reactions, and associated microbial strains, required to characterize microbial ecosystems.

An updated and annotated checklist of the Tylenchulidae (Nematoda: Criconematoidea) of Iran.

The list of plant parasitic nematodes of the family Tylenchulidae, collected from Iran, is updated. Forty-one species belonging to five genera and three subfamilies are included in the list. Data for seven species of Paratylenchus are added, of which two species-P. perminimus and P. salubris-are new records for the Iranian nematofauna. The list of species, further information on their morphometrics, references to full or partial descriptions, associated plants, geographical distribution and some taxonomic remarks are provided. More detailed studies on some doubtful populations are added. Information on the taxonomic position of species in different classification schemes, as well as the preferences of some species for certain climatic conditions or ecological niches is provided.

Existence of a stable blow-up profile for the nonlinear heat equation with a critical power nonlinear gradient term

We consider a nonlinear heat equation with a double source: | u | p − 1 u |u|^{p-1}u and | ∇ u | q |\nabla u|^q . This equation has a double interest: in ecology, it was used by Souplet (1996) as a population dynamics model; in mathematics, it was introduced by Chipot and Weissler (1989) as an intermediate equation between the semilinear heat equation and the Hamilton-Jacobi equation. Further interest in this equation comes from its lack of variational structure. In this paper, we intend to see whether the standard blow-up dynamics known for the standard semilinear heat equation (with | u | p − 1 u |u|^{p-1}u as the only source) can be modified by the addition of the second source ( | ∇ u | q |\nabla u|^q ). Here arises a nice critical phenomenon at blow-up: - when q > 2 p / ( p + 1 ) q>2p/(p+1) , the second source is subcritical in size with respect to the first, and we recover the classicial blow-up profile known for the standard semilinear case; - when q = 2 p / ( p + 1 ) q=2p/(p+1) , both terms have the same size, and only partial blow-up descriptions are available. In this paper, we focus on this case, and start from scratch to: - first, formally justify the occurrence of a new blow-up profile, which is different from the standard semilinear case; - second, to rigorously justify the existence of a solution obeying that profile, thanks to the constructive method introduced by Bricmont and Kupiainen together with Merle and Zaag. Note that our method yields the stability of the constructed solution. Moreover, our method is far from being a straightforward adaptation of earlier literature and should be considered as a source of novel ideas whose application goes beyond the particular equation we are considering, as we explain in the introduction.

Multiple description image compression based on multiwavelets

Multiple description coding (MDC) is one of the source coding techniques to alleviate the problems of packet loss in the network. The decoder estimates the lost signals from received ones, based on the certain statistical correlation between descriptions. However, this correlation also leads to compression redundancy at the same time. Therefore, how to make efficient use of the introduced correlation has great importance in practical MDC approaches. In this paper, we propose a multiple description image coding scenario based on balanced multiwavelets. Two simple and effective methods to reconstruct the original image from partial descriptions are suggested. Furthermore, optimization criterion corresponding to this multiwavelet based system is provided. According to this criterion, we can choose appropriate multifilter banks to satisfy different demands. Experimental results show that the optimized multifilter banks in a simulated transform coding environment perform very well.

Reasons for disrupting detente on the Korean Peninsula

The article is devoted to the causes of the breakdown of detente on the Korean Peninsula. The author reveals the economic, social and political prerequisites for curtailing the dialogue between the DPRK and South Korea in the first half of the 1970s XX century. It also notes the role of the UN in resolving such key issues as the withdrawal of foreign troops from the territory of the Republic of Korea, as well as the dual membership of the North and the South in the UN. The author also considers the issue of unrealized opportunities for economic integration of the DPRK and South Korea. The material is supplemented with information about the ideological struggle between the countries, which was a significant reason for the growth of mutual distrust. The article reveals the features of the transformation of international relations, paying attention to the complexity of the forms and objectives of interstate cooperation. A special place is given to the study of the military aspect. The author characterizes the reasons why it was not possible to reduce the military tension on the Peninsula: the high level of the culture of militarism in the DPRK and the desire of South Korea to use joint us-Korean military exercises to strengthen its own political status. On the example of the situation described, the author gives a partial description of the particular detente, as a specific period of the Cold War. This material is useful not only for understanding the essence of detente, but also for assessing the prospects for the development of inter-Korean dialogue in our days.

Wire electrical discharge machining (EDM) setup parameters influence in functional surface roughness

Electrical discharge machining (EDM) is an important manufacturing process with broad use in hard-to-machine alloys and to achieve complex geometries. The ordinary attention in setup has been focused on the classical one-dimensional Ra frequently specified in mechanical parts. The EDM process has 2D patterns (wire) or 3D (electrode) and many functional requirements of engineering surfaces are evaluated through functional roughness parameters that have a scarce treatment in literature on EDM setup. This paper presents a systematic search study of the influence of setup parameters of wire EDM for two quite different metal alloys: aluminum A6082 and high speed steel (HSS) AISI M42. The experimental methodology includes the analysis by design of experiments under Taguchi approach, correlation, analysis of variance (ANOVA) and multivariate regression. The results show the complexity of the surface topography, its partial description based on standardized roughness parameters and the quantification of the EDM main control factor influences.

Polynomial parameter estimation of exponential power distribution data

The paper proposes an original approach to obtain the results of multiple measurements at random errors, which are described by the exponential power (generalized Gaussian) distribution model. The approach is based on the polynomial maximization method (PMM), which is based on Kunchchenko’s mathematical apparatus using stochastic polynomials and a partial description of random variables of high-order statistics (moments or cumulants). The theoretical foundations of PMM are presented in relation to finding the estimates of the informative parameter from an equally distributed random variables sample. There are analytical expressions for finding polynomial estimations. It is shown that r \leqslant 2, then polynomial estimates degenerate in linear arithmetic mean estimates . If the polynomial degree r = 3 then the relative accuracy of polynomial estimations increases. The features of numerical procedures (Newton-Raphson method) for finding the stochastic equation roots are considered. Obtained analytical that describe the dispersion of the PMM estimates for an asymptotic case (for n → ∞). It is shown that the theoretical value of reduction coefficient variance of PMM estimates (in comparison with the linear mean estimates) depends on the magnitude of the random error cumulative coefficients of the 4th and 6th order. Through multiple statistical tests (Monte Carlo method) carried out a comparative accuracy analysis of polynomial estimates with known non-parametric estimates (median, mid-range and mean). It is shown that with increasing size of sample the difference between theoretical and experimental data decreases. The efficiency areas for each method are constructed, depending on the exponential power distribution parameter and sample size. It is shown that the accuracy of the proposed approach can significantly (more than twofold) exceed the classical nonparametric estimation.

A branch-and-cut algorithm for the maximum [formula omitted]-balanced subgraph of a signed graph

We are interested in the solution of the maximumk-balanced subgraph problem. Let G=(V,E,s) be a signed graph and k a positive scalar. A signed graph is k-balanced if V can be partitioned into at most k sets in such a way that positive edges are found only within the sets and negative edges go between sets. The maximum k-balanced subgraph problem is the problem of finding a subgraph of G that is k-balanced and maximum according to the number of vertices. This problem has applications in clustering problems appearing in collaborative vs conflicting environments. The particular case k=2 yields the problem of finding a maximum balanced subgraph in a signed graph and its exact solution has been addressed before in the literature. In this paper, we provide a representatives formulation for the general problem and present a partial description of the associated polytope, including the introduction of strengthening families of valid inequalities. A branch-and-cut algorithm is described for finding an optimal solution to the problem. An ILS metaheuristic is implemented for providing primal bounds for this exact method and a branching rule strategy is proposed for the representatives formulation. Computational experiments, carried out over a set of random instances and on a set of instances from an application, show the effectiveness of the valid inequalities and strategies adopted in this work.

A free boundary model of epithelial dynamics

In this work we analyse a one-dimensional, cell-based model of an epithelial sheet. In the model, cells interact with their nearest neighbouring cells and move deterministically. Cells also proliferate stochastically, with the rate of proliferation specified as a function of the cell length. This mechanical model of cell dynamics gives rise to a free boundary problem. We construct a corresponding continuum-limit description where the variables in the continuum limit description are expanded in powers of the small parameter 1/N, where N is the number of cells in the population. By carefully constructing the continuum limit description we obtain a free boundary partial differential equation description governing the density of the cells within the evolving domain, as well as a free boundary condition that governs the evolution of the domain. We show that care must be taken to arrive at a free boundary condition that conserves mass. By comparing averaged realisations of the cell-based model with the numerical solution of the free boundary partial differential equation, we show that the new mass-conserving boundary condition enables the coarse-grained partial differential equation model to provide very accurate predictions of the behaviour of the cell-based model, including both evolution of the cell density, and the position of the free boundary, across a range of interaction potentials and proliferation functions in the cell based model.

МОДЕЛЮВАННЯ ПОСЛІДОВНОГО ОЦІНЮВАННЯ ПАРАМЕТРА ЗСУВУ АСИМЕТРИЧНО-РОЗПОДІЛЕНИХ ВИПАДКОВИХ ВЕЛИЧИН МЕТОДОМ МАКСИМІЗАЦІЇ ПОЛІНОМА

An original approach to finding sequential estimates of the parameter of bias of non-Gaussian asymmetric-distributed random variables is investigated in the paper. The polynomial maximization method (PlMM), which is based on the mathematical apparatus of stochastic Kunchchenko polynomials and a partial description of random variables by higher order statistics (moments or cumulants) is the basis of this approach. The classic approach to solving a posed problem, which is based on simple linear recurrent statistics, that does not take into account the peculiarities of probabilistic data distribution and is optimal only for Gaussian model, is analyzed. Analytical expressions for finding the estimates by polynomial maximization method at the second degree polynomial are obtained. A comparative analysis of the efficiency on the basis of the criterion of the magnitude of asymptotic dispersion of the estimates of various methods parameters is performed. It is shown that theoretical value of the coefficient of the reduction of PlMM-estimates dispersion (in comparison with linear estimates) depends on the magnitude of cumulative coefficients of asymmetry and excess of statistical data. On the basis of the received results, in MATLAB software environment a set of m-functions that realize statistical modeling by Monte-Carlo method of linear and polynomial sequential grading algorithms for the parameter of bias of non-Gaussian random variables with different types of distributions (ex-ponential, gamma, lognormal, Weibull, double-Gaussian ones) is developed. The combination of the obtained results shows that the application of the proposed approach can provide a significant reduc-tion in the time to make decisions when diagnosing the state of technical systems and technological processes.

The global dimension of the algebra of the monoid of all partial functions on an n-set as the algebra of the EI-category of epimorphisms between subsets

We prove that the global dimension of the complex algebra of the monoid of all partial functions on an n-set is n−1 for all n≥1. This is also the global dimension of the complex algebra of the category of all epimorphisms between subsets of an n-set. In our proof we use standard homological methods as well as combinatorial techniques associated to the representation theory of the symmetric group. As part of the proof, we obtain a partial description of the Cartan matrix of these algebras.

Frölicher–Nijenhuis cohomology on G2- and Spin(7)-manifolds

In this paper, we show that a parallel differential form [Formula: see text] of even degree on a Riemannian manifold allows to define a natural differential both on [Formula: see text] and [Formula: see text], defined via the Frölicher–Nijenhuis bracket. For instance, on a Kähler manifold, these operators are the complex differential and the Dolbeault differential, respectively. We investigate this construction when taking the differential with respect to the canonical parallel [Formula: see text]-form on a [Formula: see text]- and [Formula: see text]-manifold, respectively. We calculate the cohomology groups of [Formula: see text] and give a partial description of the cohomology of [Formula: see text].

Susceptibility of placental mitochondria to oxidative stress.

Two different mitochondrial fractions (MFs) have been characterized in the human placenta: the "light" and "heavy" fractions (LMF and HMF). Although these organelles are the main source of reactive oxygen species, an imbalance between their production and the rate of detoxification represents a serious threat to mitochondrial homeostasis and, in the case of the placenta, also to the fetus. The aim of this study was to evaluate the antioxidant capacity and susceptibility to oxidative stress in both types of MFs. Human MFs were isolated from healthy donors (n = 11) and either incubated or not with H2 O2 . Catalase (CAT) activity, and reduced glutathione (GSH), lipid peroxidation (LP), and protein carbonylation (PC) levels were determined. H2 O2 treatment increased LP and PC levels and decreased CAT activity. GSH levels were similar in control and treated MFs. H2 O2 caused oxidative damage in both LMF and HMF and the antioxidant system measured in these two MFs responded similarly. To the best of our knowledge, this is the first partial description of the antioxidant defense in placental HMF and LMF performed in a cell-free assay. The small number of antioxidant system parameters measured did not allow detecting differences between HMF and LMF.

Estimating stock closing indices using a GA-weighted condensed polynomial neural network

Accurate forecasting of changes in stock market indices can provide financial managers and individual investors with strategically valuable information. However, predicting the closing prices of stock indices remains a challenging task because stock price movements are characterized by high volatility and nonlinearity. This paper proposes a novel condensed polynomial neural network (CPNN) for the task of forecasting stock closing price indices. We developed a model that uses partial descriptions (PDs) and is limited to only two layers for the PNN architecture. The outputs of these PDs along with the original features are fed to a single output neuron, and the synaptic weight values and biases of the CPNN are optimized by a genetic algorithm. The proposed model was evaluated by predicting the next day’s closing price of five fast-growing stock indices: the BSE, DJIA, NASDAQ, FTSE, and TAIEX. In comparative testing, the proposed model proved its ability to provide closing price predictions with superior accuracy. Further, the Deibold-Mariano test justified the statistical significance of the model, establishing that this approach can be adopted as a competent financial forecasting tool.

A scalable new mechanism to store, query and serve the ATLAS detector description through a REST web API

Until now, geometry information for the detector description of the ATLAS experiment was only defined in C++ code, stored in online relational databases integrated into the experiment’s frameworks or described in files with text-based markup languages. In all cases, to build and use the complete detector geometry, a full software stack was needed. In this paper, we present a new and scalable mechanism to store the geometry data and to query and serve the detector description data through a web interface and a REST API. This new approach decouples the geometry information from the experiment’s framework. Moreover, it provides new functionalities to users, who can now search for specific volumes and get partial detector description, or filter geometry data based on custom criteria. We present two approaches to build a REST API to serve geometry data, based on two different technologies used in other fields and communities: The graph database Neo4j and the search engine ElasticSearch. We describe their characteristics, and we compare them in a HEP context.

Landscapes and Throughscapes in Italian Forest Worlds: Thinking Dramatically about the Anthropocene

Phenomenological descriptions of landscapes, trees, and terraces, combined with oral history and historical ecology, find traces of industrialization, plant disease, and forest fires in central Italian forests. Plant form, landscape form, and forest structure can be described through drawings that give resolutely partial descriptions of more-than-human encounters. This kind of knowledge of the landscape is potentially unstable and remade by the details that it contains. By using multiple methods for attending to more-than-human landscapes, we can learn to notice multiple throughscapes, landscape patterns that overlap and lie through each other, but which are linked to different histories. Multiplying histories means that rather than being seen as a single era, the Anthropocene can be understood as having many beginnings and coexisting histories that give rise to multiple futures.