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Our study commemorates this event by presenting a retrospective of the publications related to the use of mathematical tools for the analysis of economic, ecological, and environmental phenomena. We analyzed 1257 scientific publications using bibliometric techniques to examine the most productive and influential authors and their contributions in the economic, ecological, and environmental fields. Co-authorship among the top authors and countries, co-occurrence of the keywords, bibliographic coupling of the documents and authors, and author co-citation were analyzed by applying network analysis techniques using VOSviewer software, identifying the intellectual structure of the research and the collaborative networks in the fields. The results show that mathematics has grown impressively in terms of publication and citation. The contributions come from all over the world, but the majority are from the People's Republic of China and Spain. The results also show themes and trends in the economic, environmental, and ecological fields and a predominant use of mathematical tools in optimization processes in order to rigorously substantiate the decisions of investors and policymakers. Thus, our study offers support for any researcher to understand the current state of the art and develop a comprehensive understanding of journal publications. [ABSTRACT FROM AUTHOR]

New oscillatory properties for the oscillation of unbounded solutions to a class of thirdorder neutral differential equations with several deviating arguments are established. Several oscillation results are established by using generalized Riccati transformation and a integral average technique under the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems. [ABSTRACT FROM AUTHOR]

The article presents information related to the periodical that focuses on mathematics. Topics discussed include declaration on equal opportunities, diversity and scientific collaboration; new trends in algorithmic randomness and computable analysis; nonlocal conservation laws; mathematical models; and mathematical analysis and quantum systems.

The notions of "mathematicalness" and "mathematicability" of nature appear in the context of attempts at explaining the effectiveness of mathematics in the description of the world. Mathematicalness of nature means that structures of the world are mathematical. But is this true? Is nature mathematical? In the paper some reasons for mathematicalness of nature are considered. Mathematical analysis is widely used in physics. Its application requires continuity of time and space. There are also different kinds of infinity in the mathematical theories used in physics. This raises the issue: whether the material world is continuous or we "impose" on nature certain properties in order to use convenient mathematical tools. Is mathematics a useful tool, or does it reflect nature? So, is nature mathematical or only mathematicable? The article shows that mathematicalness of nature is only a metaphysical hypothesis. [ABSTRACT FROM AUTHOR]

The paper presents some interesting aspects related to the biography and works of Romanian mathematician Caius Iacob (1912--1992). He was famous for his works in the fields of mathematical analysis, fluid mechanics, classical hydrodynamics and compressible-flow theory. At the age of 19, he graduated from the Mathematics Faculty in Bucharest, and then he went to Paris to continue his studies at the Faculty of Sciences, where he worked on a PhD thesis under the advice of famous French mathematician Henri Villat. On 24 June 1935, Caius Iacob successfully presented to the Sorbonne committee his PhD thesis about "Determination of conjugated harmonic functions with some limit conditions, and their applications in hydrodynamics". Returning to Romania, Caius Iacob had a long and successful career teaching mathematics and mechanics at the universities of Timişoara, Cluj and Bucharest. His most important work is considered the "Mathematical introduction to the mechanics of fluids". This book, providing original ways to work with classical hydrodynamics and compressibleflow theory, was published in Romanian in 1952 and in French in 1959. In 1955, he was elected a Corresponding Member of the Romanian Academy, becoming a titular Member in 1963. He was also President of the Mathematics Section of the Romanian Academy from 1980 until the end of his life, in 1992. In 1991, he initiated the foundation of the "Romanian Academy Institute of Applied Mathematics". In 2001 the institute merged with the "Centre for Mathematical Statistics", which had been created in 1964 by mathematician Gheorghe Mihoc, thus creating the "Gheorghe Mihoc -- Caius Iacob Institute of Mathematical Statistics and Applied Mathematics" of the Romanian Academy. [ABSTRACT FROM AUTHOR]

Dopaminergic neurons (DAs) of the rodent substantia nigra pars compacta (SNc) display varied electrophysiological properties in vitro. Despite this, projection patterns and functional inputs from DAs to other structures are conserved, so in vivo delivery of consistent, well-timed dopamine modulation to downstream circuits must be coordinated. Here we show robust coordination by linear parameter controllers, discovered through powerful mathematical analyses of data and models, and from which consistent control of DA subthreshold oscillations (STOs) and spontaneous firing emerges. These units of control represent coordinated intracellular variables, sufficient to regulate complex cellular properties with radical simplicity. Using an evolutionary algorithm and dimensionality reduction, we discovered metaparameters, which when regressed against STO features, revealed a 2-dimensional control plane for the neuron’s 22-dimensional parameter space that fully maps the natural range of DA subthreshold electrophysiology. This plane provided a basis for spiking currents to reproduce a large range of the naturally occurring spontaneous firing characteristics of SNc DAs. From it we easily produced a unique population of models, derived using unbiased parameter search, that show good generalization to channel blockade and compensatory intracellular mechanisms. From this population of models, we then discovered low-dimensional controllers for regulating spontaneous firing properties, and gain insight into how currents active in different voltage regimes interact to produce the emergent activity of SNc DAs. Our methods therefore reveal simple regulators of neuronal function lurking in the complexity of combined ion channel dynamics. [ABSTRACT FROM AUTHOR]

Modern logistics processes and systems can feature extremely complicated dynamics. Agent Based Modeling is emerging as a powerful modeling tool for design, analysis and control of such logistics systems. However, the complexity of the model itself can be overwhelming and mathematical meta-modeling tools are needed that aggregate information and enable fast and accurate decision making and control system design. Here we present Koopman Mode Analysis (KMA) as such a tool. KMA uncovers exponentially growing, decaying or oscillating collective patterns in dynamical data. We apply the methodology to two problems, both of which exhibit a bifurcation in dynamical behavior, but feature very different dynamics: Medical Treatment Facility (MTF) logistics and ship fueling (SF) logistics. The MTF problem features a transition between efficient operation at low casualty rates and inefficient operation beyond a critical casualty rate, while the SF problem features a transition between short mission life at low initial fuel levels and sustained mission beyond a critical initial fuel level. Both bifurcations are detected by analyzing the spectrum of the associated Koopman operator. Mathematical analysis is provided justifying the use of the Dynamic Mode Decomposition algorithm in punctuated linear decay dynamics that is featured in the SF problem. [ABSTRACT FROM AUTHOR]

This paper presents the theoretical and methodological conceptions of designing teaching tasks to promote the contextualization of lessons in Mathematical Analysis in educational Mathematics. It is aimed at conceiving teaching tasks, by adopting a pedagogical professional approach, to promote this contextualization. Theoretical (historical-logical, analytic-synthetic, and inductive-deductive) methods of research were used. Students, graduates, and experienced professors were interviewed in order to collect data on professors' performance in promoting the contextualization of lessons in Mathematical Analysis in educational Mathematics. Additionally, such documents as syllabuses, regulations, scientific papers, doctoral and master's theses were analyzed. This paper contributes to the contextualization of lessons in Mathematical Analysis in educational Mathematics through the pedagogical professional approach. [ABSTRACT FROM AUTHOR]

Neurons in different layers of sensory cortex generally have different functional properties. But what determines firing rates and tuning properties of neurons in different layers? Orientation selectivity in primary visual cortex (V1) is an interesting case to study these questions. Thalamic projections essentially determine the preferred orientation of neurons that receive direct input. But how is this tuning propagated though layers, and how can selective responses emerge in layers that do not have direct access to the thalamus? Here we combine numerical simulations with mathematical analyses to address this problem. We find that a large-scale network, which just accounts for experimentally measured layer and cell-type specific connection probabilities, yields firing rates and orientation selectivities matching electrophysiological recordings in rodent V1 surprisingly well. Further analysis, however, is complicated by the fact that neuronal responses emerge in a dynamic fashion and cannot be directly inferred from static neuroanatomy, as some connections tend to have unintuitive effects due to recurrent interactions and strong feedback loops. These emergent phenomena can be understood by linearizing and coarse-graining. In fact, we were able to derive a low-dimensional linear dynamical system effectively describing stimulus-driven activity layer by layer. This low-dimensional system explains layer-specific firing rates and orientation tuning by accounting for the different gain factors of the aggregate system. Our theory can also be used to design novel optogenetic stimulation experiments, thus facilitating further exploration of the interplay between connectivity and function. [ABSTRACT FROM AUTHOR]

Grey wolf optimization (GWO) algorithm is a new emerging algorithm that is based on the social hierarchy of grey wolves as well as their hunting and cooperation strategies. Introduced in 2014, this algorithm has been used by a large number of researchers and designers, such that the number of citations to the original paper exceeded many other algorithms. In a recent study by Niu et al., one of the main drawbacks of this algorithm for optimizing real‐world problems was introduced. In summary, they showed that GWO's performance degrades as the optimal solution of the problem diverges from 0. In this paper, by introducing a straightforward modification to the original GWO algorithm, that is, neglecting its social hierarchy, the authors were able to largely eliminate this defect and open a new perspective for future use of this algorithm. The efficiency of the proposed method was validated by applying it to benchmark and real‐world engineering problems. [ABSTRACT FROM AUTHOR]

The article discusses a series of events in Bonn Mathematics "Tea Time with Women in Mathematics" that offers female students and researchers the opportunity to become part of a network to exchange experiences in mathematics. Topics discussed include analysis of partial differential equations; declaration on equal opportunities, diversity and scientific collaboration; new trends in algorithmic randomness and computable analysis; mathematical models; and mathematical analysis.

Abstract Let E be an elliptic curve over the rational field Q. Let K be a quadratic extension of Q. We show that (under mild conditions on E) for every r > 0 , there are infinitely many quadratic twists E d / Q of E / Q such that Image 1. [ABSTRACT FROM AUTHOR]

The qPCR method provides an inexpensive, rapid method for estimating relative telomere length across a set of biological samples. Like all laboratory methods, it involves some degree of measurement error. The estimation of relative telomere length is done subjecting the actual measurements made (the Cq values for telomere and a control gene) to non-linear transformations and combining them into a ratio (the TS ratio). Here, we use computer simulations, supported by mathematical analysis, to explore how errors in measurement affect qPCR estimates of relative telomere length, both in cross-sectional and longitudinal data. We show that errors introduced at the level of Cq values are magnified when the TS ratio is calculated. If the errors at the Cq level are normally distributed and independent of true telomere length, those in the TS ratio are positively skewed and proportional to true telomere length. The repeatability of the TS ratio declines sharply with increasing error in measurement of the Cq values for telomere and/or control gene. In simulated longitudinal data, measurement error alone can produce a pattern of low correlation between successive measures of relative telomere length, coupled with a strong negative dependency of the rate of change on initial relative telomere length. Our results illustrate the importance of reducing measurement error: a small increase in error in Cq values can have large consequences for the power and interpretability of qPCR estimates of relative telomere length. The findings also illustrate the importance of characterising the measurement error in each dataset—coefficients of variation are generally unhelpful, and researchers should report standard deviations of Cq values and/or repeatabilities of TS ratios—and allowing for the known effects of measurement error when interpreting patterns of TS ratio change over time. [ABSTRACT FROM AUTHOR]

Abstract The Suslin hypothesis states that there are no nonseparable complete dense linear orderings without endpoints which have the countable chain condition. ZF + A D + + V = L (P (R)) proves the Suslin hypothesis. In particular, if L (R) ⊨ AD , then L (R) satisfies the Suslin hypothesis, which answers a question of Foreman. [ABSTRACT FROM AUTHOR]

Abstract Some cases of the LFED Conjecture, proposed by the second author [15] , for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the field of fractions k (x) of the polynomial algebra k [ x ] , the formal power series algebra k [ [ x ] ] and the Laurent formal power series algebra k [ [ x ] ] [ x − 1 ] , where x = (x 1 , x 2 , ... , x n) denotes n commutative free variables and k a field of characteristic zero. Furthermore, the relation between the LFED Conjecture and the Duistermaat–van der Kallen Theorem [3] is also discussed and emphasized. [ABSTRACT FROM AUTHOR]

Abstract We study the differential identities of the algebra U T 2 of 2 × 2 upper triangular matrices over a field of characteristic zero. We let the Lie algebra L = Der (U T 2) of derivations of U T 2 (and its universal enveloping algebra) act on it. We study the space of multilinear differential identities in n variables as a module for the symmetric group S n and we determine the decomposition of the corresponding character into irreducibles. If V is the variety of differential algebras generated by U T 2 , we prove that unlike the other cases (ordinary identities, group graded identities) V does not have almost polynomial growth. Nevertheless we exhibit a subvariety U of V having almost polynomial growth. [ABSTRACT FROM AUTHOR]

Abstract Given a finite group G , we say that G has property P n if for every prime integer p , G has at most n − 1 irreducible characters whose degrees are multiples of p. In this paper, we classify all finite groups that have property P 4. We show that the groups satisfying property P 4 are exactly the finite groups with at most three nonlinear irreducible characters, one solvable group of order 168, SL 2 (3) , A 5 , S 5 , PSL 2 (7) and A 6. [ABSTRACT FROM AUTHOR]

Abstract Let R ⊆ Q be rings such that the inclusion φ : R → Q is an epimorphism in the category of rings and Q is flat both as a right and as a left R -module. Assume that F. dim (Q Q ) = 0 , that is, that every left Q -module has projective dimension 0 or ∞. We prove that the following conditions are equivalent: (i) Flat left R -modules are strongly flat. (ii) Matlis-cotorsion left R -modules are Enochs-cotorsion. (i i i) h -divisible left R -modules are weak-injective. (iv) Homomorphic images of weak-injective left R -modules are weak-injective. (v) Homomorphic images of injective left R -modules are weak-injective. (vi) Left R -modules of weak dimension ≤1 are of projective dimension ≤1. (vii) The cotorsion pairs (P 1 , H D) and (F 1 , W I) coincide. Moreover, if R is a right and left Ore ring, S is its set of regular elements and Q = R [ S − 1 ] = [ S − 1 ] R is the classical ring of quotients of R , then the seven conditions above are also equivalent to: (v i i i) Divisible left R -modules are weak-injective. This extends a result by Fuchs and Salce (2018) [10] for modules over a commutative ring R. [ABSTRACT FROM AUTHOR]

We introduce a general class of codes which includes several well-known classes of deletion/insertion correcting codes as special cases. For example, the Helberg code, the Levenshtein code, the Varshamov–Tenengolts code, and most variants of these codes including most of those which have been recently used in studying DNA-based data storage systems are all special cases of our code. Then, using a number theoretic method, we give an explicit formula for the weight enumerator of our code which in turn gives explicit formulas for the weight enumerators and for the sizes of all the aforementioned codes. We also obtain the size of the shifted Varshamov–Tenengolts code. Another application which automatically follows from our result is an explicit formula for the number of binary solutions of an arbitrary linear congruence which, to the best of our knowledge, is the first result of its kind in the literature and might be also of independent interest. Our general result might have more applications/implications in information theory, computer science, and mathematics. [ABSTRACT FROM AUTHOR]

Abstract Let g E H be the Eguchi–Hanson metric on the blow-up of ℂ 2 at the origin. In this paper we show that m g E H is not balanced for any positive integer m. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study the representation theory of the Fuss–Catalan algebras, FC n (a , b). We prove that this algebra is cellular with a cellular basis and forms a tower of recollement, as defined by Cox, Martin, Parker, and Xi [7] , and hence, it is quasi-hereditary algebra if a , b are non-zero complex numbers. [ABSTRACT FROM AUTHOR]

Abstract Let F / Q p be a finite extension. We explore the universal supersingular mod p representations of GL 2 (F) by computing a basis for their spaces of invariants under the pro- p Iwahori subgroup. This generalizes works of Breuil and Schein (from Q p and the totally ramified cases to an arbitrary extension F / Q p). Using these results we then construct, for an unramified F / Q p , quotients of the universal supersingular modules which have as quotients all the supersingular representations of GL 2 (F) with a GL 2 (O F) -socle that is expected to appear in the mod p local Langlands correspondence. A construction in the case of an extension of Q p with inertia degree 2 and suitable ramification index is also presented. [ABSTRACT FROM AUTHOR]

tudies on high ability in mathematics rarely take a teacher's perspective. The purpose of our study is to add such a perspective, which we will do by using positioning theory to analyze elementary teachers' discussions on mathematical tasks, aiming to challenge all pupils, including the highly able. The study is conducted in the context of a two-year long teacher professional development program on high ability. Teachers expressed both their teaching and the mathematical tasks as helpful in orchestrating teaching suitable for highly able pupils. They highlight the opportunities given by some tasks as well as the importance of guiding highly able pupils to go further in such tasks. However, they expressed their own limited mathematical knowledge and time needed for pupils with learning difficulties as obstacles to orchestrate teaching for the highly able. The results show that it is important to, in close cooperation with teachers, further explore how to orchestrate teaching that challenges highly able pupils. [ABSTRACT FROM AUTHOR]

Abstract An interval matrix is a matrix whose entries are intervals in R. Let p , q ∈ N ∖ { 0 } and let α = ([ α _ i , j , α ‾ i , j ]) i , j be a p × q interval matrix; given a p × q matrix A with entries in R , we say that A ∈ α if a i , j ∈ [ α _ i , j , α ‾ i , j ] for any i , j. We establish a criterion to say if an interval matrix contains a matrix of rank 1. Moreover we determine the maximum rank of the matrices contained in a given interval matrix. Finally, for any interval matrix α with no more than 3 columns, we describe a way to find the range of the ranks of the matrices contained in α . [ABSTRACT FROM AUTHOR]

In this paper, we use Schauder and Banach fixed point theorems to study the existence, uniqueness and stability of bounded nonhomogeneous iterative functional differential equations of the form x' (t) = λ1x(t) + λ2x[2](t)+...+λnx[n](t)+f(t). [ABSTRACT FROM AUTHOR]

Existence results of infinitely many solutions for a fourth-order differential equation are established. This equation depends on two real parameters. The approach is based on an infinitely many critical points theorem. [ABSTRACT FROM AUTHOR]

We introduce a new order on rough sets inspired by the notion of accuracy measure. Rough sets ordered by this accuracy-type order form a complete lattice, which is isomorphic to the lattice where rough sets are ordered traditionally by the inclusion relation. Although the lattices are order-isomorphic, the elements can be totally differently located in them. The isomorphy of the lattices is verified by introducing the so-called boundary representation of rough sets. Some basic properties of the introduced order are also presented and an illustrative example demonstrates the relationship between the different structures. [ABSTRACT FROM AUTHOR]

In this paper we study the probability that the commutator of a randomly chosen pair of elements, one from a subring of a finite ring and other from the ring itself is equal to a given element of the ring. [ABSTRACT FROM AUTHOR]

In this study, we firstly give some properties the family F and F-convex function which are defined by B. Samet. Then, we obtain some midpoint inequalities for differentiable function. Moreover, we establish some midpoint and trapezoid type inequalities for function whose second derivatives in absolute value are F-convex. [ABSTRACT FROM AUTHOR]

Abstract Let P be a poset of size 2 k that has a greatest and a least element. We prove that, for sufficiently large n , the Boolean lattice 2 [ n ] can be partitioned into copies of P. This resolves a conjecture of Lonc. [ABSTRACT FROM AUTHOR]

Background: Expressing anthropometric parameters (height, weight, BMI) as z-score is a key principle in the clinical assessment of children and adolescents. The Centre for Disease Control and Prevention (CDC) growth charts and the CDC-LMS method for z-score calculation are widely used to assess growth and nutritional status, though they can be imprecise in some percentiles. Objective: To improve the accuracy of z-score calculation by revising the statistical method using the original data used to develop current z-score calculators. Design: A Gaussian Process Regressions (GPR) was designed and internally validated. Z-scores for weight-for-age (WFA), height-for-age (HFA) and BMI-for-age (BMIFA) were compared with WHO and CDC-LMS methods in 1) standard z-score cut-off points, 2) simulated population of 3000 children and 3) real observations 212 children aged 2 to 18 yo. Results: GPR yielded more accurate calculation of z-scores for standard cut-off points (p<<0.001) with respect to CDC-LMS and WHO approaches. WFA, HFA and BMIFA z-score calculations based on the 3 different methods using simulated and real patients, showed a large variation irrespective of gender and age. Z-scores around 0 +/- 1 showed larger variation than the values above and below +/- 2. Conclusion: The revised z-score calculation method was more accurate than CDC-LMS and WHO methods for standard cut-off points. On simulated and real data, GPR based calculation provides more accurate z-score determinations, and thus, a better classification of patients below and above cut-off points. Statisticians and clinicians should consider the potential benefits of updating their calculation method for an accurate z-score determination. [ABSTRACT FROM AUTHOR]

Analytical similarity assessment of critical quality attributes (CQAs) serves as a foundation for the development of biosimilar products and facilitates an abbreviated subsequent clinical evaluation. In this study, we establish a statistical evaluation roadmap with statistical approaches for some selected CQAs from Tier 1, because they are most relevant to clinical outcomes and require the most rigorous statistical methods. In the roadmap, we incorporate 3 methods—ranking and tier assignment of quality attributes, the equivalence test, and the Mann–Whitney test for equivalence—that are important to determine analytical similarity between the reference and biosimilar products. For the equivalence test, we develop a power calculation formula based on the two one-sided tests procedure. Exact sample sizes can be numerically calculated. Then, we propose a flexible idea for selecting the number of reference lots (nR) and the number of biosimilar lots (nT) to adjust for serious unbalanced sample sizes. From results of extensive simulations under various parameter settings, we obtain a workable strategy to determine the optimum sample size combination (nT, nR) for the equivalence test of CQAs from Tier 1. R codes are provided to facilitate implementation of the roadmap and corresponding methods in practice. [ABSTRACT FROM AUTHOR]

Algebraic topology studies topological spaces with the help of tools from abstract algebra. The main focus of this paper is to show that many concepts from algebraic topology can be conveniently expressed in terms of (normal) factor graphs. As an application, we give an alternative proof of a classical duality result of Kramers and Wannier, which expresses the partition function of the 2-D Ising model at a low temperature in terms of the partition function of the 2-D Ising model at a high temperature. Moreover, we discuss analogous results for the 3-D Ising model and the Potts model. [ABSTRACT FROM AUTHOR]

In analysis of multi-component complex systems, such as neural systems, identifying groups of units that share similar functionality will aid understanding of the underlying structures of the system. To find such a grouping, it is useful to evaluate to what extent the units of the system are separable. Separability or inseparability can be evaluated by quantifying how much information would be lost if the system were partitioned into subsystems, and the interactions between the subsystems were hypothetically removed. A system of two independent subsystems are completely separable without any loss of information while a system of strongly interacted subsystems cannot be separated without a large loss of information. Among all the possible partitions of a system, the partition that minimizes the loss of information, called the Minimum Information Partition (MIP), can be considered as the optimal partition for characterizing the underlying structures of the system. Although the MIP would reveal novel characteristics of the neural system, an exhaustive search for the MIP is numerically intractable due to the combinatorial explosion of possible partitions. Here, we propose a computationally efficient search to precisely identify the MIP among all possible partitions by exploiting the submodularity of the measure of information loss, when the measure of information loss is submodular. Submodularity is a mathematical property of set functions which is analogous to convexity in continuous functions. Mutual information is one such submodular information loss function, and is a natural choice for measuring the degree of statistical dependence between paired sets of random variables. By using mutual information as a loss function, we show that the search for MIP can be performed in a practical order of computational time for a reasonably large system (N = 100 ∼ 1000). We also demonstrate that MIP search allows for the detection of underlying global structures in a network of nonlinear oscillators. [ABSTRACT FROM AUTHOR]

Sufficient conditions for the compactness in generalized Morrey spaces of the composition of a convolution operator and the operator of multiplication by an essentially bounded function are obtained. Very weak conditions on the function are also obtained under which the commutator of the operator of multiplication by such a function and a convolution operator is compact. The compactness of convolution operators in domains of cone type is investigated. [ABSTRACT FROM AUTHOR]

Vectorization is a technique that replaces a set-valued optimization problem with a vector optimization problem. In this work, by using an extension of the Gerstewitz function, a vectorizing function is defined to replace a given set-valued optimization problem with respect to the set less order relation. Some properties of this function are studied. Moreover, relationships between a set-valued optimization problem and a vector optimization problem, derived via vectorization of this set-valued optimization problem, are examined. Furthermore, necessary and sufficient optimality conditions are presented without any convexity assumption. [ABSTRACT FROM AUTHOR]

We exhibit a method to use continued fractions in function fields to find new families of hyperelliptic curves over the rationals with given torsion order in their Jacobians. To show the utility of the method, we exhibit a new infinite family of curves over Q with genus two whose Jacobians have torsion order eleven. [ABSTRACT FROM AUTHOR]

Bayesian network classifiers (BNCs) have demonstrated competitive classification performance in a variety of real-world applications. A highly scalable BNC with high expressivity is extremely desirable. This paper proposes Redundant Dependence Elimination (RDE) for improving the classification performance and expressivity of k-dependence Bayesian classifier (KDB). To demonstrate the unique characteristics of each case, RDE identifies redundant conditional dependencies and then substitute/remove them. The learned personalized k-dependence Bayesian Classifier (PKDB) can achieve high-confidence conditional probabilities, and graphically interpret the dependency relationships between attributes. Two thyroid cancer datasets and four other cancer datasets from the UCI machine learning repository are selected for our experimental study. The experimental results prove the effectiveness of the proposed algorithm in terms of zero-one loss, bias, variance and AUC. [ABSTRACT FROM AUTHOR]

Countries, research institutions, and scholars are interested in identifying and promoting high-impact and transformative scientific research. This paper presents a novel set of text- and citation-based metrics that can be used to identify high-impact and transformative works. The 11 metrics can be grouped into seven types: Radical-Generative, Radical-Destructive, Risky, Multidisciplinary, Wide Impact, Growing Impact, and Impact (overall). The metrics are exemplified, validated, and compared using a set of 10,778,696 MEDLINE articles matched to the Science Citation Index ExpandedTM. Articles are grouped into six 5-year periods (spanning 1983–2012) using publication year and into 6,159 fields constructed using comparable MeSH terms, with which each article is tagged. The analysis is conducted at the level of a field-period pair, of which 15,051 have articles and are used in this study. A factor analysis shows that transformativeness and impact are positively related (ρ = .402), but represent distinct phenomena. Looking at the subcomponents of transformativeness, there is no evidence that transformative work is adopted slowly or that the generation of important new concepts coincides with the obsolescence of existing concepts. We also find that the generation of important new concepts and highly cited work is more risky. Finally, supporting the validity of our metrics, we show that work that draws on a wider range of research fields is used more widely. [ABSTRACT FROM AUTHOR]

Linear feedback shift registers (LFSRs) play a significant role in communications security and we investigate design of a selected class of word-based LFSRs known as σ -LFSRs. Both the search algorithm and the construction algorithm generate efficient primitive σ -LFSRs. The search algorithm first constructs the σ -polynomial and then checks the primitiveness of the σ -polynomial, whereas the construction algorithm for the σ -LFSR, first finds a primitive polynomial f ( x ) and then constructs the primitive σ -LFSR from f ( x ) . In this paper, we present some novel results pertaining to the search algorithm for primitive σ -LFSR along with the exhaustive search space complexity of the search algorithm for σ -LFSRs. Then we investigate and compare the performance of the construction algorithm with the search algorithm for the primitive σ -LFSR. Finally, the number of σ -LFSRs similar to the σ -LFSRs generated by the construction algorithm is provided. [ABSTRACT FROM AUTHOR]

We study the distribution of strategies in a large game that models how agents choose among different double auction markets. We classify the possible mean field Nash equilibria, which include potentially segregated states where an agent population can split into subpopulations adopting different strategies. As the game is aggregative, the actual equilibrium strategy distributions remain undetermined, however. We therefore compare with the results of a reinforcement learning dynamics inspired by Experience-Weighted Attraction (EWA) learning, which at long times leads to Nash equilibria in the appropriate limits of large intensity of choice, low noise (long agent memory) and perfect imputation of missing scores (fictitious play). The learning dynamics breaks the indeterminacy of the Nash equilibria. Non-trivially, depending on how the relevant limits are taken, more than one type of equilibrium can be selected. These include the standard homogeneous mixed and heterogeneous pure states, but also heterogeneous mixed states where different agents play different strategies that are not all pure. The analysis of the reinforcement learning involves Fokker-Planck modeling combined with large deviation methods. The theoretical results are confirmed by multi-agent simulations. [ABSTRACT FROM AUTHOR]

Inversive distance circle packing metric was introduced by P Bowers and K Stephenson [7] as a generalization of Thurston's circle packing metric [34] . They conjectured that the inversive distance circle packings are rigid. For nonnegative inversive distance, Guo [22] proved the infinitesimal rigidity and then Luo [27] proved the global rigidity. In this paper, based on an observation of Zhou [37] , we prove this conjecture for inversive distance in ( − 1 , + ∞ ) by variational principles. We also study the global rigidity of a combinatorial curvature introduced in [14,16,19] with respect to the inversive distance circle packing metrics where the inversive distance is in ( − 1 , + ∞ ) . [ABSTRACT FROM AUTHOR]

In this article, a notion of neutrosophic triplet (NT) normed ring space is given and properties of NT normed ring spaces are studied. We demonstrate that NT normed ring is different from the classical one. Also, we show that a neutrosophic triplet normed ring can be a neutrosophic triplet norm when certain conditions are met. [ABSTRACT FROM AUTHOR]

We discuss the behavior of the spark of a matrix under multiplication by invertible matrices. We also give a necessary and sufficient condition for an NSP constant of a matrix to be finite. [ABSTRACT FROM AUTHOR]

We investigate the connection between conditional local limit theorems and the local time of integer-valued stationary processes. We show that a conditional local limit theorem (at 0) implies the convergence of local times to Mittag-Leffler distributions, both in the weak topology of distributions and a.s. in the space of distributions. [ABSTRACT FROM AUTHOR]

We prove a conjecture by Tu, Zeng, Li, and Helleseth concerning trinomials f α , β ( x ) = x + α x q ( q − 1 ) + 1 + β x 2 ( q − 1 ) + 1 ∈ F q 2 [ x ] , α β ≠ 0 , q even, characterizing all the pairs ( α , β ) ∈ F q 2 2 for which f α , β ( x ) is a permutation of F q 2 . [ABSTRACT FROM AUTHOR]

We study 3-dimensional digital nets over F 2 generated by matrices ( I , B , B 2 ) where I is the identity matrix and B is a square matrix. We give a characterization of B for which the t -value of the digital net is 0. As a corollary, we prove that such B satisfies B 3 = I . [ABSTRACT FROM AUTHOR]

Solving a well-known problem of Maharam, Talagrand [18] constructed an exhaustive non uniformly exhaustive submeasure, thus also providing the first example of a Maharam algebra that is not a measure algebra. To each exhaustive submeasure one can canonically assign a certain countable ordinal, its exhaustivity rank. In this paper, we use carefully constructed Schreier families and norms derived from them to provide examples of exhaustive submeasures of arbitrary high exhaustivity rank. This gives rise to uncountably many non isomorphic separable atomless Maharam algebras. [ABSTRACT FROM AUTHOR]