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This paper investigates experimentally the relationship between inequality in endowment and deception. Our basic design is adopted from Gneezy (2005): two players interact in a deception game. It is common knowledge that player 1 has private information about the payoffs for both players of two alternative actions. Player 1 sends a message to player 2, indicating which alternative putatively will end up in a higher payoff for player 2. The message, which can either be true or false, does not affect the payoffs of the players. Player 2 has no information about the payoffs. However, player 2 selects one of the two alternatives A or B, which is payoff-relevant for both players. Our paper adds value to the literature by extending Gneezy (2005) in two ways. First, we systematically vary the initial endowment of players 1 and 2 (common knowledge to both of them). Second, we do not limit ourselves to the standard population of university students but also recruit chess players that are not enrolled in any degree program. Doing so, we want to find out if our results remain robust over a non-standard subject population which is known to be experienced to some extent in strategic interactions. Our main findings are: (i) non-students behave more honestly than students, (ii) students are more likely to trust the opponent’s message, and (iii) students and non-students behave differently to variation in initial endowment.

The paper explains the fundamentals of Harmony in Gradation, a formula and the concept that we found on April 28, 2018, which we originally called as Haryadi Index, which we are promoting to be "the Formula for Everything". In detail, the paper explains the background of the findings, formulas, reasons, and methods of using Harmony in Gradation in all branches of science.

This paper is devoted to establish a computational approach to predict the processes with almost cyclostationary structure. The main idea is based on the estimating of the support of spectra and using the discrete Fourier transform and periodogram of almost cyclostationary processes. The simulated and real datasets are applied to study the performance of the introduced approach. The results confirm that the presented method acts efficiently for simulated and real datasets.

The paper interprets the concept “operator in the separable complex Hilbert space” (particalry, “Hermitian operator” as “quantity” is defined in the “classical” quantum mechanics) by that of “quantum information”. As far as wave function is the characteristic function of the probability (density) distribution for all possible values of a certain quantity to be measured, the definition of quantity in quantum mechanics means any unitary change of the probability (density) distribution. It can be represented as a particular case of “unitary” qubits. The converse interpretation of any qubits as referring to a certain physical quantity implies its generalization to non-Hermitian operators, thus neither unitary, nor conserving energy. Their physical sense, speaking loosely, consists in exchanging temporal moments therefore being implemented out of the space-time “screen”. “Dark matter” and “dark energy” can be explained by the same generalization of “quantity” to non-Hermitian operators only secondarily projected on the pseudo-Riemannian space-time “screen” of general relativity according to Einstein's “Mach’s principle” and his field equation.

*Exploratory graph analysis* (EGA) is used to estimate the structural organization of variables, uncovering latent dimensions as clusters of nodes. EGA first estimates a weighted network then uses the Walktrap algorithm to detect clusters of nodes. The Walktrap algorithm uses random walks to estimate the topography of a graph. The number of random walks taken (*t*) is typically set statically. However, the impact of *t* and the properties determining its optimization have yet to be fully researched. The present study proposes and tests a new approach optimizing *t* by iteratively varying *t* and employ *total entropy fit index* as a fit index to identify the number of steps that best fit the data using a Monte-Carlo simulation varying data structure characteristics. Results indicate that the proposed method is most effective for a higher number of variables per factor and when variables are polytomous. Varying *t* is important as spurious connections are introduced between communities. An empirical example using the Developmental Coordination Disorder Questionnaire is shown demonstrating improved measure interpretation by optimizing the Walktrap algorithm. The paper finishes with a discussion about the relevance of the findings and future directions for research.

The standard framework for analyzing games with incomplete information models players as if they form beliefs about their opponents' beliefs about their opponents' beliefs and so on, that is, as if players have an infinite depth of reasoning. This strong assumption has nontrivial implications, as is well-known. This paper therefore generalizes the type spaces of Harsanyi (1967-1968) to model that players can have a finite depth of reasoning. The innovation is that players can have a coarse perception of the higher-order beliefs of other players, thus formalizing the small-world idea of Savage (1954) in a type-space context. Unlike the case in other models of finite-order reasoning, players with a finite depth of reasoning can have nontrivial higher-order beliefs about certain events. Intuitively, some higher-order events are generated by events of lower orders, making it possible for players to reason about them, even if they have a finite depth of reasoning.

The multibridge R package allows a Bayesian evaluation of informed hypotheses H_r applied to frequency data from an independent binomial or multinomial distribution. multibridge uses bridge sampling to efficiently compute Bayes factors for the following hypotheses concerning the latent category proportions theta: (a) hypotheses that postulate equality constraints (e.g., theta_1 = theta_2 = theta_3); (b) hypotheses that postulate inequality constraints (e.g., theta_1 < theta_2 < theta_3) or (theta_1 > theta_2 > theta_3); (c) hypotheses that postulate combinations of inequality constraints and equality constraints (e.g., theta_1 < theta_2 = theta_3); and (d) hypotheses that postulate combinations of (a)--(c) (e.g., theta_1 < theta_2 = theta_3, theta_4). Any informed hypothesis H_r may be compared against the encompassing hypothesis H_e that all category proportions vary freely, or against the null hypothesis H_0 that all category proportions are equal. multibridge facilitates the fast and accurate comparison of large models with many constraints and models for which relatively little posterior mass falls in the restricted parameter space. This paper describes the underlying methodology and illustrates the use of multibridge through fully reproducible examples.

A lockdown implies a shift from the public to the private sphere, and from market to non-market production, thereby increasing the volume of unpaid work. Already before the pandemic, unpaid work was disproportionately borne by women. This paper studies the effect of working from home for pay (WFH), due to a lockdown, on the change in the division of housework and childcare within couple households. While previous studies on the effect of WFH on the reconciliation of work and family life and the division of labour within the household suffered from selection bias, we are able to identify this effect by drawing upon the shock of the first COVID-19 lockdown in Austria. The corresponding legal measures left little choice over WFH. In any case, WFH is exogenous, conditional on a small set of individual and household characteristics we control for. We employ data from a survey on the gendered aspects of the lockdown. The dataset includes detailed information on time use during the lockdown and on the quality and experience of WFH. Uniquely, this survey data also includes information on the division, and not only magnitude, of unpaid work within households. Austria is an interesting case in this respect as it is characterized by very conservative gender norms. The results reveal that the probability of men taking on a larger share of housework increases if men are WFH alone or together with their female partner. By contrast, the involvement of men in childcare increased only in the event that the female partner was not able to WFH. Overall, the burden of childcare, and particularly homeschooling, was disproportionately borne by women.

In this paper, we propose a model-based method to study conditional dependence be- tween response accuracy and response time (RT) with the diffusion IRT model. To this end, we extend the previously proposed model by introducing variability across persons and items in cognitive capacity and in the initial bias of the response processes. We show that the extended model can explain the behavioral patterns of conditional dependency found in the previous studies in psychometrics. The first variability component in cognitive capacity can predict positive and negative conditional dependency and their interaction with the item difficulty. The second variability in the initial bias can account for the early changes in the response accuracy as a function of RTs given the person and item effects, producing the curvilinear conditional accuracy functions. We also provide a simulation study to validate the parameter recovery of the proposed model and two empirical applications to describe how to implement the model to study conditional dependency underlying data response accuracy and RTs.

Let $F_2$ be the prime field of two elements and let $GL_s:= GL(s, F_2)$ be the general linear group of rank $s.$ Denote by $\mathscr A$ the Steenrod algebra over $F_2.$ The (mod-2) Lambda algebra, $\Lambda,$ is one of the tools to describe those mysterious "Ext-groups". In addition, the $s$-th algebraic transfer of William Singer \cite{Singer} is also expected to be a useful tool in the study of them. This transfer is a homomorphism $Tr_s: F_2 \otimes_{GL_s}P_{\mathscr A}(H_{*}(B\mathbb V_s, F_2))\to {\rm Ext}_{\mathscr {A}}^{s,s+*}(F_2, F_2),$ where $\mathbb V_s$ denotes the elementary abelian $2$-group of rank $s$, and $H_*(B\mathbb V_s)$ is the homology group of the classifying space of $\mathbb V_s,$ while $P_{\mathscr A}(H_{*}(B\mathbb V_s, F_2))$ means the primitive part of $H_{*}(B\mathbb V_s, F_2)$ under the action of $\mathscr A.$ It has been shown that $Tr_s$ is highly non-trivial and, more precisely, that $Tr_s$ is an isomorphism for $s\leq 3.$ In addition, Singer proved that $Tr_4$ is an isomorphism in some internal degrees. He was also investigated the image of the fifth transfer by using invariant theory. In this note, we use another method to study the image of $Tr_5.$ More precisely, by direct computations using a representation of $Tr_5$ over the algebra $\Lambda,$ we show that $Tr_5$ detects the non-zero elements $h_0d_0\in {\rm Ext}_{\mathscr A}^{5, 5+14}(F_2, F_2),\ h_2e_0\in {\rm Ext}_{\mathscr A}^{5, 5+20}(F_2, F_2)$ and $h_1h_4c_0\in {\rm Ext}_{\mathscr A}^{5, 5+24}(F_2, F_2).$ The same argument can be used for homological degrees $s\geq 6$ under certain conditions., Comment: 10 pages. This article is to update some references and to correct some minor errors in a paper with the same title published in Advances in Mathematics: Scientific Journal

Let $P_s:= \mathbb F_2[x_1,x_2,\ldots ,x_s]$ be the graded polynomial algebra over the prime field of two elements, $\mathbb F_2$, in $s$ variables $x_1, x_2, \ldots , x_s$, each of degree one. This algebra is considered as a graded module over the mod-2 Steenrod algebra, $\mathscr {A}$. We are interested in the "hit" problem of finding a minimal set of generators for $\mathscr A$-module $P_s.$ This problem is unresolved for every $s\geqslant 5.$ In this paper, we study the hit problem of five variables in a generic degree, from which we investigate Singer's conjecture [Math. Z. 202 (1989), 493-523] for the transfer homomorphism of rank $5$ in degrees given. This gives an efficient method to study the algebraic transfer and it is different from the ones of Singer., Comment: 29 pages. Comments very welcome!

This paper lays down key issues in ordinality, summarizing the points of those who argue for and against using standard linear models in analyzing Likert type items/scales. It also presents a proposed broad-sketch approach to data simulation for answering when Likert type data can be considered interval rather than ordinal

Equal parameter estimates across subgroups is a substantial requirement of statistical tests. Ignoring subgroup differences poses a threat to study replicability, model specification, and theory development. One powerful statistical method that allows testing for parameter invariance is structural change tests. A core element of those tests is the empirical fluctuation process. In the case of parameter invariance, the fluctuation process asymptotically follows a Brownian bridge. This asymptotic assumption further provides the basis for inference. However, in this paper, we show that the empirical fluctuation process does not follow a Brownian bridge in small samples. Thus, methods of obtaining the sampling distribution are incorrect, and the p-value misspecified. Therefore, we implement an alternative solution to obtaining the sampling distribution - permutation approaches. Permutation approaches obtain the sampling distribution through resampling of the dataset, avoiding unmet distributional assumptions. We show that the permutation approach solves the issue of the misspecified sampling distribution and increases power, therefore serves as a superior method to standard asymptotic approximations of the sampling distribution.

SIR model is one of the simplest methods used in prediction of endemic/pandemic outbreaks. We examined SIRD model for development of COVID-19 in Kuwait which was started on 24 February 2020 by 5 patients in Kuwait. This paper investigates sensitivity of SIRD model for development of COVID-19 in Kuwait based on duration of progressed days of data. For Kuwait, we have fitted SIRD model to COVID-19 data for 20, 40, 60, 80, 100, and 116 days of data and assessed sensitivity of the model with number of days of data. The parameters of SIRD model are obtained using an optimization algorithm (lsqcurvefit) in MATLAB. The total population of 50,000 is equally applied for all Kuwait time intervals. Results of SIRD model indicates that after 40 days the peak infectious day can be adequately predicted; althogh, error percentage from sensetivity analysis indicates that different exposed population sizes are not correctly predicted. SIRD type models are too simple to robustly capture all features of COVID-19 and more precise methods are needed to tackle nonlinear dynamics of a pandemic.

Attention Schema Theory (AST) is a recent proposal to provide a scientific explanation for the basis of subjective awareness. In AST, the brain constructs a representation of attention taking place in its own (and others') mind (`the attention schema'). Moreover, this representation is incomplete for efficiency reasons. This inherent incompleteness of the attention schema results in the inability of humans to understand how their own subjective awareness arises (related to the so-called `hard problem' of consciousness). Given this theory, the present paper asks whether a mind (either human or machine-based) that incorporates attention, and that contains a representation of its own attention, can ever have a complete representation. Using a simple yet general model and a mathematical argument based on classical topology, we show that a complete representation of attention is not possible, since it cannot faithfully represent streams of attention. In this way, the study supports one of the core aspects of AST, that the brain's representation of its own attention is necessarily incomplete., 13 pages, 1 figure, (version 5 is a slightly revised version of version 4, which was a moderately revised version of 3 (which was identical to versions 1 and 2, except that the figure was reduced in size to allow easier downloads)

In the paper, by convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein's theorem for completely monotonic functions, and other analytic techniques, the authors (1) verify decreasing monotonicity of a ratio between three derivatives of a function involving trigamma function; (2) find necessary and sufficient conditions for a function defined by three derivatives of a function involving trigamma function to be completely monotonic. These results confirm previous guesses posed by the first author and generalize corresponding known conclusions.

In the paper, by virtue of convolution theorem for the Laplace transforms, logarithmic convexity of the gamma function, Bernstein's theorem for completely monotonic functions, and other techniques, the author finds necessary and sufficient conditions for a difference defined by four derivatives of a function containing trigamma function to be completely monotonic. Moreover, by virtue of Cebysev integral inequality, the author presents logarithmic convexity of the sequence of polygamma functions.

In the paper, by convolution theorem for the Laplace transforms, some properties of a function involving exponential function, and other analytic techniques, the author finds necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic.

In the paper, by convolution theorem of the Laplace transforms, Bernstein's theorem for completely monotonic functions, and logarithmic concavity of a function involving exponential functions, the author(1) finds necessary and sufficient conditions for a ratio involving trigamma and tetragamma functions to be monotonic on the right real semi-axis; and(2) presents alternative proofs of necessary and sufficient conditions for a function and its negativity involving trigamma and tetragamma functions to be completely monotonic on the positive semi-axis.These results generalizes known conclusions recently obtained by the author.

In 1859, Bernhard Riemann, a German mathematician, published a paper to the Berlin Academy that would change mathematics forever. The mystery of prime numbers was the focus. At the core of the presentation was indeed a concept that had not yet been proven by Riemann, one that to this day baffles mathematicians. The way we do business could have been changed if the Riemann hypothesis holds true, which is because prime numbers are the key element for banking and e-commerce security. It will also have a significant influence, impacting quantum mechanics, chaos theory, and the future of computation, on the cutting edge of science. In this article, we look at some well-known results of Riemann Zeta function in a different light. We explore the proofs of Zeta integral Representation, Analytic continuity and the first functional equation. Initially, we observe omitting a logical undefined term in the integral representation of Zeta function by the means of Gamma function. For that we propound some modifications in order to reasonably justify the location of the non-trivial zeros on the critical line: s= 1/2 by assuming that ζ(s) and ζ(1-s) simultaneously equal zero. Consequently, we conditionally prove Riemann Hypothesis.

The random variate m is, in combinatorics, a basis for comparing permutations, as well as the solution to a centuries-old riddle involving the mishandling of hats. In statistics, m is the test statistic for a disused null hypothesis statistical test (NHST) of association, the matching method. In this paper, I show that the matching method has an absolute and relatively low limit on its statistical power. I do so first by reinterpreting Rae’s theorem (1987), which describes the joint distributions of m with several rank correlation statistics under a true null. I then derive this property solely from m’s unconditional sampling distribution, on which basis I develop the concept of a deficient statistic—a statistic that is insufficient and inconsistent and inefficient with respect to its parameter. Finally, I demonstrate an application for m that makes use of its deficiency to qualify the sampling error in a jointly estimated sample correlation.

The Numworks/TI-84 python calculator, which encapsulates, functionality ranging from a python shell, to built in and customisable support for statistics, functions, regression, sequences and data mining, is directly amenable to a functionality as a math and code gym towards mental arithmetic and several number theory based therapies, such as prime number therapy. Similar functionality is achieved on the slack channel, with the Wolfram Alpha API.In this paper we describe the use of python scripts towards primality detection exercises, of both small primes and arbitrary sized numbers and several other exercises including sequence prediction, inspired by branch prediction architectures, plotting functions and exercises in data mining, in spotting patterns and forming a basket of associations.Keywords: Numworks, Math and code gym, primality detection, data mining, basket of associations, sequences, branch prediction, plotting graphs.

The popularity of deep reinforcement learning (DRL) applications in economics has increased exponentially. DRL, through a wide range of capabilities from reinforcement learning (RL) to deep learning (DL), offers vast opportunities for handling sophisticated dynamic economics systems. DRL is characterized by scalability with the potential to be applied to high-dimensional problems in conjunction with noisy and nonlinear patterns of economic data. In this paper, we initially consider a brief review of DL, RL, and deep RL methods in diverse applications in economics, providing an in-depth insight into the state-of-the-art. Furthermore, the architecture of DRL applied to economic applications is investigated in order to highlight the complexity, robustness, accuracy, performance, computational tasks, risk constraints, and profitability. The survey results indicate that DRL can provide better performance and higher efficiency as compared to the traditional algorithms while facing real economic problems in the presence of risk parameters and the ever-increasing uncertainties.

Increasing attention is being given to assessing treatment effect heterogeneity from individuals belonging to qualitatively different latent subgroups. Inference routinely proceeds by first separating the individuals into mutually-exclusive subgroups, then estimating the average treatment effects among individuals in the same subgroup. Because the subgroups are only latently associated with the observed variables, the true individual subgroup memberships are rarely known with certainty in practice and often have to be imputed. Ignoring the uncertainty in the imputed memberships precludes misclassification, which can potentially lead to biased results and incorrect conclusions. In this paper, we propose a strategy for assessing the sensitivity of inference to classification uncertainty when using such classify-analyze approaches for subgroup effect analyses. We exploit each individual's (typically nonzero) predictive or posterior subgroup membership probabilities to gauge the stability of the resultant subgroup-specific average causal effects estimates over different, carefully-selected subsets of the individuals. Because the membership probabilities are subject to sampling variability, we propose Monte Carlo confidence intervals that explicitly acknowledge the imprecision in the estimated subgroup memberships via perturbations using a parametric bootstrap. Using two different publicly available datasets, we illustrate how the proposed strategy supplements existing subgroup effect analyses to shed light on the potential impact of classification uncertainty on inference.

For decades, it has been suggested organizations utilize mechanical decisions. Unfortunately, organizations continue to rely on holistic judgments. Perhaps part of the reasons organizations continue to rely on judgment when mak- ing decisions is because the reported statistics associated with mechanical judgments (e.g., R2) are not intuitive to stakeholders. For example, it is unclear in terms of turnover whether an R2 change from 0.23 under the old (holistic) system to an R2 of 0.27 under the (mechanical) system is enough of an improvement to justify the cost of changing selection methods. In this paper, we argue that researchers instead report changes in criteria of interest (e.g., absenteeism rate before versus after utilizing a mechanical selection sys- tem). This can be accomplished by utilizing a multiple imputation algorithm that simulates optimal selection decisions. Additionally, we provide both an R-package, as well as a point-and-click Shiny app that allows researchers to easily estimate intuitive statistics (e.g., improvement in turnover, proportion of applicants for which an optimal and holistic system agree).

In the paper, with the aid of the Fa\`a di Bruno formula, some properties of the Bell polynomials of the second kind, and a general derivative formula for a ratio of two differentiable functions, the authors establish several closed and determinantal forms for convolved Fibonacci numbers.

A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. A comparison to Mach’s doctrine is used to be revealed the fundamental and philosophical reductionism of Husserl’s phenomenology leading to a kind of Pythagoreanism in the final analysis. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Godel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Godel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. Thus the problem which of the two mathematics is more relevant to our being (rather than reality for reality is external only to Godel mathematics) is discussed. An information interpretation of the Schrodinger equation is involved to illustrate the above problem.

Objective The Self-Importance of Moral Identity Scale (SMIS) was developed by Aquino and Reeds with the purpose of measuring how people evaluate their private (Internalization subscale) and public (Symbolization subscale) moral identity. SMIS has become commonly and broadly used in many studies. The aim of this paper is to validate the Polish version of SMIS by analyzing its structure and relation to similar measures (such as The Moral Self-Concept Scale developed by Stake and The Moral Self-Image Scale created by Jordan, Leliveld and Tenbrunsel), declared past prosocial behaviors and readiness to donate money. Methods The translation-back-translation procedure was used to maintain semantic, idiomatic, and conceptual equivalence of the original scale. Throughout four separate studies the psychometric properties of the Polish version of the scale were assessed: Study 1 (N = 529) was carried out to derive the factor structure using the exploratory factor analysis (EFA) and cross-validate it; Study 2 (N = 602) and Study 3 (N = 899) were performed to confirm and replicate the structure with the confirmatory factor analysis (CFA); gender-balanced Study 4 (N = 862) was conducted to assess measurement invariance over gender using multigroup CFA, and to normalize the scale. Validity of the scale was assessed based on each study. Results A stable two-factor structure using 10 items was replicated in four different samples. The results showed that reliability (α) was between 0.71 and 0.81 for Internalization, and 0.76 and 0.81 for Symbolization. Validity was confirmed in terms of the expected pattern of correlations with morality measures and factorial structure. Metric invariance across gender was confirmed with possible exception of factor loadings on two items regarding communication of values. Polish normalization for men and women was constructed. Conclusions Polish validation of SMIS proved to be a structurally consistent and valid measure.

This paper presents an electrostatic situation in which the circulation of an electrostatic field around a closed path is non-zero. This fact contradicts the theorem that the circulation of an electrostatic field around any closed path is zero.

This article describes kmr, a Stata command to estimate a micro compliance function using group’s nonresponse rates (2007, Journal of Econometrics 136: 213-235), which can be used to correct survey weights for unit nonresponse. We illustrate the use of kmr with an empirical example using the Current Population Survey and state-level nonresponse rates. (Stone Center on Socio-Economic Inequality Working Paper)

Humans expect downwards moving objects to accelerate and upwards moving objects to decelerate. These results have been interpreted as humans maintaining an internal model of gravity. We have previously suggested an interpretation of these results within a Bayesian framework of perception: earth gravity could be represented as a Strong Prior that overrules noisy sensory information (Likelihood) and therefore attracts the final percept (Posterior) very strongly. Based on this framework, we use published data from a timing task involving gravitational motion to determine the mean and the standard deviation of the Strong Earth Gravity Prior. To get its mean, we refine a model of mean timing errors we proposed in a previous paper (Björn Jörges & López-Moliner, 2019), while expands the range of conditions under which it yields adequate predictions of performance. This underscores our previous conclusion that the gravity prior is likely to be very close to 9.81 m/s². To obtain the standard deviation, we identify different sources of sensory and motor variability reflected in timing errors. We then model timing responses based on quantitative assumptions about these sensory and motor errors for a range of standard deviations of the earth gravity prior, and find that a standard deviation of around 2 m/s² makes for the best fit. This value is likely to represent an upper bound, as there are strong theoretical reasons along with support empirical evidence for the standard deviation of the earth gravity being lower than this value.

Number theory is one of the core branches of pure mathematics. It has played an important role in the study of natural numbers. In this paper, we are presenting a theorem on the numbers of form 10^x , where x ∊ Z+ . The proposed theorem have a major application in computer science. It can be used to predict ‘n’ bits which will always represent more than 10^x total numbers. We proved that the nature of the ‘n’ bits is always one of the forms 10i, 10i + 4, or 10i + 7, where i ∊ W .

This paper develops a new representational model of similarity data that combines continuous dimensions with discrete features. An algorithm capable of learning these representations is described, and a Bayesian model selection approach for choosing the appropriate number of dimensions and features is developed. The approach is demonstrated on a classic data set that considers the similarities between the numbers 0 through 9.

The binding problem refers to the puzzle of how the brain combines objects’ properties such as motion, color, shape, location, sound, etc., from diverse regions of the brain and forms a unified subjective experience. Holographic physical systems, recently discovered darlings of theoretical physics, began with research into black holes but have since evolved into the study of condensed matter systems in the laboratory like superfluids and superconductors. A primary example is the AdS/CFT correspondence. A recent conjecture of this correspondence suggests that holographic systems combine information from across a boundary surface, sort out the simplest description of said information, and, in turn, use it to determine the geometry of spacetime itself in the interior - a kind of geometric hologram. Although we would never tend to think of these two processes as related, in this paper we point out ten similarities between the two and show that holographic systems are the only physical systems that match the subjective and computational characteristics of the binding problem.

In order to investigate the stances of high school students and researchers toward STEM subjects, we introduce the methodology of forma mentis networks -- free association networks enriched with affective attributes that represent how people conceptually perceive and structure their stance toward a given topic. In this paper, we constructed separate forma mentis networks for ($N_s=159$) Italian high school students and ($N_r=59$) interdisciplinary professionals and researchers in order to investigate how these groups differed in their mental associations and emotional perceptions of STEM subjects. At the global scale, STEM concepts occupied central positions in students' forma mentis network, suggesting that students understood the general importance of such topics in science. At a microscopic scale, although the concept of "science'' was positively perceived in both the students' and professionals' forma mentis networks, students not only perceived STEM concepts such as "physics'' and "mathematics'' as negative but also associated them with other negative STEM-related concepts. This aura of negative emotional associations towards quantitative STEM subjects was absent in professionals. Cross-validation with external datasets suggested that the negative emotional aura in the forma mentis network of students might be attributed to science anxiety. Further consideration of the semantic associates of maths and physics indicated that their negative aura may originate from a negative, dry perception of the technical methodology and quantitative tools frequently taught in these subjects (e.g., "function'', "integral'').Whereas students associated mathematics and physics with quantitative tools, professionals linked the same disciplines to more general and creative aspects of science and displayed a positive stance towards these concepts. Overall, our results underline the crucial importance of emphasising nontechnical and applied aspects in the teaching of quantitative disciplines, highlighting the necessity of establishing interdisciplinary links between science, the complexity of the real-world and creativity in order to enhance the impact of STEM education and outreach activities.

Since the use of finite element (FE) simulations for the dynamic analysis of railway beams on frictionally damped foundations are (i) very time consuming, and (ii) require advanced know-how and software that go beyond the available resources of typical civil engineering firms, this paper aims to demonstrate the potential of Artificial Neural Networks (ANN) to effectively predict the maximum displacements and the critical velocity in railway beams under moving loads. Four ANN-based models are proposed, one per load velocity range ([50, 175] ∪ [250, 300] m/s; ]175, 250[ m/s) and per displacement type (upward or downward). Each model is function of two independent variables, a frictional parameter and the load velocity. Among all models and the 663 data points used, a maximum error of 5.4 % was obtained when comparing the ANN- and FE-based solutions. Whereas the latter involves an average computing time per data point of thousands of seconds, the former does not even need a millisecond. This study was an important step towards the development of more versatile (i.e., including other types of input variables) ANN-based models for the same type of problem.

Despite the prevalence of real-world and laboratory tasks where people select among many options, cognitive models have traditionally focused on choices among small sets of alternatives. This has resulted in theoretical and empirical gaps in understanding the decision processes that go into selections among many alternatives or responses that fall along a continuum. This paper addresses these issues by modeling decisions in a perceptual study where participants produce continuous orientation judgments. The experiments showed that manipulations of stimulus difficulty and time pressure have parallel effects to binary choice, with greater stimulus difficulty yielding slower and less accurate responses and time pressure resulting in faster responses at the expense of accuracy. These effects were well accounted for by the circular diffusion model developed by Smith (2016), with drift magnitude parameters shifting with difficulty and threshold parameters shifting with time pressure. However, a manipulation of bias using a predecision cue resulted in bimodal distributions of responses that cannot be explained by the model in its original formulation. To account for this result, I developed a theory of bias based on split attention and racing 2D diffusion processes. This model suggests that responses are determined by both cue-driven and stimulus-driven evidence accumulation processes, such that the winning process determines responses and response times (RTs). As a result, it predicts critical features of responses and response times in the conditions with predecision cues, including bimodal distributions of responses and the longer RTs observed when there was a discrepancy between cue and stimulus orientations. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Motivated by the recent replication and reproducibility crisis, Gelman and Carlin (2014, Perspect. Psychol. Sci., 9, 641) advocated focusing on controlling for Type S/M errors, instead of the classic Type I/II errors, when conducting hypothesis testing. In this paper, we aim to fill several theoretical gaps in the methodology proposed by Gelman and Carlin (2014, Perspect. Psychol. Sci., 9, 641). In particular, we derive the closed-form expression for the expected Type M error, and study the mathematical properties of the probability of Type S error as well as the expected Type M error, such as monotonicity. We demonstrate the advantages of our results through numerical and empirical examples.

The present paper discussed a simple but specific case of scheduling tollbooth collectors in a toll section part of Jakarta toll road network. A number of requirements asked by toll road management were considered alongside with goal preferences in order to provide an efficient timetable for tollbooth collectors. A non-preemptive goal programming approach were employed to simultaneously minimized the shortage of workdays from its ideal level and the number of off-on-off scheduling patterns.

In this paper, we studied inclusion problem with polynomials data in $R^3.$ We provided a Theorem that guaranted the solution of this problem. Moreover, by using standard potential theory, we approached the solution by using Green's Theorem.

In some recent papers a few approximations to the implicit Nikuradse–Prandtl–Karman equation were shown. The Nikuradse–Prandtl–Karman equation for calculation of the hydraulic friction factor is valid for the hydraulically smooth regime of turbulence. Accuracy of these approximations for the friction factor in so called smooth pipes is checked and related problems from the hydraulics are analyzed in the spotlight of the recently developed equations. It can be concluded that pipes can be treated as smooth below certain value of the Reynolds number but after that even new polished pipes with a minor roughness follow the transitional and subsequently the rough law of flow at a higher values of the Reynolds number.

This paper presents evolutionary optimization of explicit approximations of the empirical Colebrook’s equation that is used for the calculation of the turbulent friction factor (λ), i.e., for the calculation of turbulent hydraulic resistance in hydraulically smooth and rough pipes including the transient zone between them. The empirical Colebrook’s equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of the inner pipe surface (ε/D). It is implicit in the unknown friction factor (λ). The implicit Colebrook’s equation cannot be rearranged to derive the friction factor (λ) directly, and therefore, it can be solved only iteratively [λ = f(λ, R, ε/D)] or using its explicit approximations [λ≈f(R, ε/D)], which introduce certain error compared with the iterative solution. The optimization of explicit approximations of Colebrook’s equation is performed with the aim to improve their accuracy, and the proposed optimization strategy is demonstrated on a large number of explicit approximations published up to date where numerical values of the parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After that improvement, the computational burden stays unchanged while the accuracy of approximations increases in some of the cases very significantly.

In this paper I extend the concept of observer effect to the realm of secondary data analysis. When analyzing what appear to be the same secondary data utilizing the same methods, macro-comparative researchers arrive at different results. I argue that this is a product of idiosyncratic variation directly or indirectly produced by the researcher. Even when this bias produces only small perturbations in interpretation or results, the consequences may be large for small-N analyses. Using an influential study by Brooks and Manza I analyze this secondary observer effect. Two replications of the practice of compiling seemingly identical secondary datasets produced variation. Reanalysis of the divergent values in these datasets and a second look at the original tables produces similar but not identical results. A rough calculation of the size of the secondary observer effect suggests that about a 0.32 standardized standard deviations across variable scores. Simulations of this size of secondary observer effect show that significant changes in findings occur.

In the last years, there has been a considerable increase of research into the neuroimaging correlates of inter-individual temperament and character variability-an endeavour for which the term 'personality neuroscience' was coined. Among other neuroimaging modalities and approaches, substantial work focuses on functional connectivity in resting state (rs-FC) functional magnetic resonance imaging data. In the current paper, we set out to independently query the questions asked in a highly cited study that reported a range of functional connectivity correlates of personality dimensions assessed by the widely used 'Big Five' Personality Inventory. Using a larger sample (84 subjects) and an equivalent data analysis pipeline, we obtained widely disagreeing results compared to the original study. Overall, the results were in line with the hypotheses of no relation between functional connectivity and personality, when more precise permutation-based multiple testing procedures were applied. The results demonstrate that as with other neuroimaging studies, great caution should be applied when interpreting the findings, among other reasons due to multiple testing problem involved at several levels in many neuroimaging studies. Of course, the current study results can not ultimately disprove the existence of some link between personality and brain's intrinsic functional architecture, but clearly shows that its form is very likely different and much more subtle and elusive than was previously reported.

All exact algorithms for solving subset sum problem (SUBSET\_SUM) are exponential (brute force, branch and bound search, dynamic programming which is pseudo-polynomial). To find the approximate solutions both a classical greedy algorithm and its improved variety, and different approximation schemes are used.This paper is an attempt to build another greedy algorithm by transferring representation of analytic geometry to such an object of discrete structure as a set. Set of size $n$ is identified with $n$-dimensional space with Euclidean metric, the subset-sum is identified with (hyper)plane.