Intuitive Formula Research Articles

Prediction of Thermal Postbuckling Behavior Of Uniform Shear Flexible Column Undergoing Large Lateral Deflections Through An Intuitive Formulation

This paper presents a simple intuitive formulation to predict the thermal postbuckling behavior of uniform shear flexible columns, subjected a uniform temperature rise from its stress free condition, undergoing large lateral deflections. The two ends of the columns are restrained to move axially, so that a mechanical equivalent of the constant compressive load is developed, due to the increase in temperature. The proposed formulation is based on the use of nonlinearities existing in both the axial displacement and lateral deflection, which differs from the von-Karman type nonlinearity due to the moderately large lateral deflections only. In this paper, a simple analytical formula is developed to predict the thermal post buckling behavior of columns, considering both the nonlinearities. The numerical results obtained from the developed intuitive formulas match very well, for the slender columns. Since, there are no results available in the literature, to compare the current results with the case of the shear flexible columns, the authors are of the opinion that the trends of these results, given in this paper, show that there is a reasonable probability that the present results are reliable.

Intuitive analytical solution for the uniformly loaded elastica using elliptic integrals

In this work, an approximate analytical solution was given for the large deformation of a cantilever beam subjected to a uniformly distributed load using elliptic integrals and Jacobi elliptic functions. The formulation is based on reducing the differential equation of the problem to the same one that describes the classical, force-loaded elastica by introducing a modified arc length parameter. A new, intuitive formula was given for the relation between the deflection angle and the non-dimensional load. The results were validated by the nonlinear shooting method with the Matlab program. The method can be used only in the case of one inflection point, but gives accurate results even for extremely large deflections.

Proxying credit curves via Wasserstein distances

Credit risk plays a key role in financial modeling, and financial institutions are required to incorporate it in their pricing, as well as in capital requirement calculations. A common manner to extract credit worthiness information for existing and potential counterparties is based on the Credit Default Swap (CDS) market. Nonetheless, not all counterparties of a financial institution have (liquid) CDSs traded in the market. In this case, financial institutions shall employ a proxy methodology to estimate the default probabilities of these counterparties. Starting from the intersection methodology for credit curves, in this article we investigate whether it is possible to construct proxy credit curves from CDS quotes by means of (weighted) Wasserstein barycenters. We show how, under simple and common assumptions, this revised methodology leads to elementary and intuitive formulae to calculate distances between CDS-implied default probability distributions. Further, we illustrate how to use this information to construct proxy CDS quotes.

Accumulation of Particles and Formation of a Dissipative Structure in a Nonequilibrium Bath.

The standard textbooks contain good explanations of how and why equilibrium thermodynamics emerges in a reservoir with particles that are subjected to Gaussian noise. However, in systems that convert or transport energy, the noise is often not Gaussian. Instead, displacements exhibit an -stable distribution. Such noise is commonly called Lévy noise. With such noise, we see a thermodynamics that deviates from what traditional equilibrium theory stipulates. In addition, with particles that can propel themselves, so-called active particles, we find that the rules of equilibrium thermodynamics no longer apply. No general nonequilibrium thermodynamic theory is available and understanding is often ad hoc. We study a system with overdamped particles that are subjected to Lévy noise. We pick a system with a geometry that leads to concise formulae to describe the accumulation of particles in a cavity. The nonhomogeneous distribution of particles can be seen as a dissipative structure, i.e., a lower-entropy steady state that allows for throughput of energy and concurrent production of entropy. After the mechanism that maintains nonequilibrium is switched off, the relaxation back to homogeneity represents an increase in entropy and a decrease of free energy. For our setup we can analytically connect the nonequilibrium noise and active particle behavior to entropy decrease and energy buildup with simple and intuitive formulae.

Two Applications of Coset Cardinality Spectrum of Distributed Arithmetic Coding

Distributed Arithmetic Coding (DAC) is a practical realization of Slepian-Wolf coding that partitions source space into cosets. Coset Cardinality Spectrum (CCS) is an important property of DAC that was defined in our previous work. In this paper, we give two applications of CCS. First, we find that DAC bitstream is not compact. The rate loss of DAC bitstream is caused by two factors: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unequal coset partitioning</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bit indivisibility</i> . It is proved that as code length goes to infinity, the expected value of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bit-indivisibility</i> rate loss will tend to 0.5 for any irrational Rate Change Step (RCS), where the RCS refers to the rate change when one source bit is flipped. With the help of CCS, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bit-indivisibility</i> rate loss can be compensated to some extend. Especially, for any irrational RCS, as code length goes to infinity, the expected value of the remaining <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bit-indivisibility</i> rate loss after compensation will tend to about 0.47. The second application of CCS is DAC decoder design. We derive the formula of path metric and find that in the original paper on DAC, the intuitive formula of path metric is not correct. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">backward-replacing</i> algorithm is proposed to make full use of memory. Experimental results confirm the correctness of theoretical analyses.

Displacement prediction and optimization of a non-circular planetary gear hydraulic motor

The non-circular planetary gear hydraulic motor is a low-speed and high-torque hydraulic motor with excellent performance. It has the characteristics of a wide speed range, low weight and is widely used in various fields. Aiming to solve the problem of there being no intuitive formula for calculating the displacement of the non-circular planetary gear hydraulic motor at present, based on the analysis of the effects of structural parameters on the displacement of the motor, this paper proposes a formula for calculating the displacement of a non-circular planetary gear hydraulic motor when the pitch curve of the sun wheel is a high-order ellipse. The formula allows the direct calculation and prediction of the displacement of the motor. To improve the unit volume displacement of the hydraulic motor (which determines the power density of the motor), based on the analysis of the unit volume displacement constraints, an optimization equation is proposed by adding an optimization factor to the original equation of the pitch curve of the sun wheel. It is seen that the addition of the new optimization factor eliminates the self-interlacing of the pitch curve of inner ring gear. This elimination increases the unit volume displacement of the motor.

Formula for the estimation of urine osmolality in healthy cats

A simple and intuitive formula for the estimation of urine osmolality (Uosm) using the measured concentrations of major active urine osmolytes over a wide range of urine dilutions was proposed in healthy cats. Sixty-three urine samples were retrieved using ultrasound-guided cystocentesis from sixteen healthy cats under 5 years of age receiving intravenous infusion over a period of 24 h. Samples were collected at baseline (T0), T2, T6, T12, and T24. Urine osmolality was measured using a freezing-point osmometer, and the concentrations of osmolytes (urea, sodium, glucose, and potassium) were evaluated. A simple linear regression model for a clinical use was selected, and the agreement between the calculated and actual urine osmolalities was assessed. Urinary concentrations of urea, sodium and glucose were the three variables included in the model with the lowest AICC. Urine osmolality can be predicted accurately and precisely using urine urea, sodium and glucose with the following equation: Uosm = 1.25 × urea (mmol/l) or 20.87 × urea (g/l) + 1.1 × sodium (mmol/l) + 67 × glucose (mmol/l) or 3.72 × glucose (mg/dl). The concordance correlation coefficient for repeated measures between the actual and the calculated urine osmolality was extremely close to 1, which supported a high agreement: 0.996 (CI 95%: [0.993; 0.998]). In a population of healthy cats, urine osmolality can be predicted accurately and precisely using urinary urea, sodium and glucose concentrations. Similar formulae could potentially be established to help the clinician in pathological situations.

Bayesian information criterion approximations to Bayes factors for univariate and multivariate logistic regression models.

Schwarz's criterion, also known as the Bayesian Information Criterion or BIC, is commonly used for model selection in logistic regression due to its simple intuitive formula. For tests of nested hypotheses in independent and identically distributed data as well as in Normal linear regression, previous results have motivated use of Schwarz's criterion by its consistent approximation to the Bayes factor (BF), defined as the ratio of posterior to prior model odds. Furthermore, under construction of an intuitive unit-information prior for the parameters of interest to test for inclusion in the nested models, previous results have shown that Schwarz's criterion approximates the BF to higher order in the neighborhood of the simpler nested model. This paper extends these results to univariate and multivariate logistic regression, providing approximations to the BF for arbitrary prior distributions and definitions of the unit-information prior corresponding to Schwarz's approximation. Simulations show accuracies of the approximations for small samples sizes as well as comparisons to conclusions from frequentist testing. We present an application in prostate cancer, the motivating setting for our work, which illustrates the approximation for large data sets in a practical example.

A note about ‘on replenishment schedule for deteriorating items with time-proportional demand’

In the Economic Order Quantity (EOQ) model for exponentially deteriorating items, the inventory deterioration rate is proportional to the inventory level, which leads to an exponentially decreasing inventory level over time. Due to polynomial and exponential terms in the total cost function, an exact closed form solution is not possible. Previously, an approximation for the total cost function and a closed form optimal solution for the order interval have been proposed for this problem. However, the proposed closed form formula is complicated and it is not intuitive. It is also assumed without justification that the average inventory level is equal to half of the order quantity. We justify this assumption and show that the same approximation yields a much more intuitive formula when it is used to determine the optimal order quantity instead of the order interval. Our intuitive optimal order quantity formula is more likely to be adopted in practice.

Modelling and predicting the competitive effects of vertical mergers: The bargaining leverage over rivals effect

AbstractA new competitive effect of vertical mergers, based on the Nash bargaining model, has begun to play an important role in antitrust authorities’ evaluations of vertical mergers in the United States, Canada and abroad. The key idea is that a vertical merger will increase the bargaining leverage of the merged firm over its downstream rivals. Its bargaining leverage increases because it now takes into account the additional profit that its own downstream division will earn if it withholds inputs from downstream rivals, which changes its threat point in the bargaining game with downstream rivals. Consequently, the merged firm can increase the price that it charges rival downstream firms for inputs. One strong appeal of this theory is that it provides a simple and very intuitive formula to measure the upward pricing pressure caused by a vertical merger due to changes in bargaining leverage, based on variables whose values can generally be estimated using available data. This article describes this new competitive effect, which will be called the bargaining leverage over rivals (BLR) effect, and derives the upward pricing pressure formula. It also explains why this new competitive effect is distinct from the older raising rivals’ costs (RRC) effect that has been widely discussed in the economics literature, and discusses the relationship between the two different effects.

A Practical Approach to Quantitative Model Risk Assessment

Model-based decisions are highly sensitive to model risk that arises from the inadequacy of the adopted model. This paper reviews the existing literature on model risk assessment and shows how to use the theoretical results to develop a corresponding best practice. Specifically, we develop tools to assess the contribution to model risk of each of the assumptions that underpin the adopted model. Furthermore, we introduce new model risk measures and propose an intuitive formula for computing model risk capital. Some numerical examples and a case study illustrate our results.

An Introduction to Bayesian Multilevel Models Using brms: A Case Study of Gender Effects on Vowel Variability in Standard Indonesian.

Purpose Bayesian multilevel models are increasingly used to overcome the limitations of frequentist approaches in the analysis of complex structured data. This tutorial introduces Bayesian multilevel modeling for the specific analysis of speech data, using the brms package developed in R. Method In this tutorial, we provide a practical introduction to Bayesian multilevel modeling by reanalyzing a phonetic data set containing formant (F1 and F2) values for 5 vowels of standard Indonesian (ISO 639-3:ind), as spoken by 8 speakers (4 females and 4 males), with several repetitions of each vowel. Results We first give an introductory overview of the Bayesian framework and multilevel modeling. We then show how Bayesian multilevel models can be fitted using the probabilistic programming language Stan and the R package brms, which provides an intuitive formula syntax. Conclusions Through this tutorial, we demonstrate some of the advantages of the Bayesian framework for statistical modeling and provide a detailed case study, with complete source code for full reproducibility of the analyses ( https://osf.io/dpzcb /). Supplemental Material https://doi.org/10.23641/asha.7973822.

Absorber Model: the Halo-like model for the Lyman-α forest

We present a semi-analytic model for the Lyman-α forest that is inspired by the Halo Model. This model is built on the absorption line decomposition of the forest. Flux correlations are decomposed into those within each absorption line (the 1-absorber term) and those between separate lines (the 2-absorber term), treating the lines as biased tracers of the underlying matter fluctuations. While the nonlinear exponential mapping between optical depth and flux requires an infinite series of moments to calculate any statistic, we show that this series can be re-summed (truncating at the desired order in the linear matter overdensity). We focus on the z=2–3 line-of-sight power spectrum. Our model finds that 1-absorber term dominates the power on all scales, with most of its contribution coming from H I columns of 1014–1015 cm−2, while the smaller 2-absorber contribution comes from lower columns that trace overdensities of a few. The prominence of the 1-absorber correlations indicates that the line-of-sight power spectrum is shaped principally by the lines' number densities and their absorption profiles, with correlations between lines contributing to a lesser extent. We present intuitive formulae for the effective optical depth as well as the large-scale limits of 1-absorber and 2-absorber terms, which simplify to integrals over the H I column density distribution with different equivalent-width weightings. With minimalist models for the bias of absorption systems and their peculiar velocity broadening, our model predicts values for the density bias and velocity gradient bias that are consistent with those found in simulations.

Late-Arriving Signals Contribute Less to Cell-Fate Decisions

Gene regulatory networks are largely responsible for cellular decision-making. These networks sense diverse external signals and respond by adjusting gene expression, enabling cells to reach environment-dependent decisions crucial for their survival or reproduction. However, information-carrying signals may arrive at variable times. Besides the intrinsic strength of these signals, their arrival time (timing) may also carry information about the environment and can influence cellular decision-making in ways that are poorly understood. For example, it is unclear how the timing of individual phage infections affects the lysis-lysogeny decision of bacteriophage λ despite variable infection times being likely in the wild and even in laboratory conditions. In this work, we combine mathematical modeling with experimentation to address this question. We develop an experimentally testable theory, which reveals that late-infecting phages contribute less to cellular decision-making. This implies that infection delays lower the probability of lysogeny compared to simultaneous infections. Furthermore, we show that infection delays reduce lysogenization by providing insufficient CII for threshold crossing during the critical decision-making period. We find evidence for a cutoff time after which subsequent infections cannot influence the cellular decision. We derive an intuitive formula that approximates the probability of lysogeny for variable infection times by a time-weighted average of probabilities for simultaneous infections. We validate these theoretical predictions experimentally. Similar concepts and simplifying modeling approaches may help elucidate the mechanisms underlying other cellular decisions.

Structural vulnerability and resilience to currency crisis: Foreign currency debt versus export

Is there any factor that is not analyzed in the literature but is important for preventing currency crises? I argue that exports are an important factor to prevent currency crises that has not been frequently analyzed in the existing theoretical literature. Using the third generation model of currency crises, I derive a simple and intuitive formula that captures an economy’s structural vulnerability characterized by the elasticity of exports and repayments for foreign currency denominated debt. I graphically show that the possibility of currency crisis equilibrium depends on this structural vulnerability and also analyze how this vulnerability impacts the effectiveness of monetary policy response.

Foreclosure loss severity and distressed home mortgage refinance

PurposeThe problem in alleviating homeowner mortgage distress through refinance is how to achieve meaningful alleviation without prospectively harming the financier. The problem revolves around two parameters from real estate finance – the probability that the distress leads to foreclosure and resulting foreclosure loss severity for the financier if foreclosure does occur. Previous analysis focuses on reducing the probability that homeowner distress leads to foreclosure. By contrast, the purpose of this paper is to focus on reducing foreclosure loss severity.Design/methodology/approachThe study develops a new intuitive formula for foreclosure loss severity to quantify its dependence on transaction costs. The study shows that foreclosure loss severity reduction is feasible by introducing a new refinancing instrument that lowers foreclosure transaction costs and applying property law to derive the structure of the refinancing instrument.FindingsForeclosure loss severity reduction can subsidize concessions on scheduled payments for homeowners with arbitrarily poor credit without prospective harm to the financier.Research limitations/implicationsQuantification of mortgage distress relief is limited to distressed mortgages described by representative parameter values from various government studies.Practical implicationsFor most distressed homeowners, payment and principal reductions could exceed those available from the recent government programs.Social implicationsImplementation should significantly enlarge the pool of homeowners eligible for mortgage distress relief.Originality/valueThe mortgage refinance is qualitatively different from that available under existing government refinance programs because it is based on an arms-length exchange of property rights that makes market sense regardless of whether the refinancing results in subsequent homeowner default.

Local distinguishability of Dicke states in quantum secret sharing

We comprehensively investigate the local distinguishability of orthogonal Dicke states under local operations and classical communication (LOCC) from both qualitative and quantitative aspects. Based on our work, defects in the LOCC-quantum secret sharing (QSS) scheme can be complemented, and the information leakage can be quantified. For (k1,k2,k,n)-threshold LOCC-QSS scheme, more intuitive formulas for unambiguous probability and guessing probability were established, which can be used for determining the parameter k1 and k2 directly.

Matrix description of differential relations of moment functions in structural reliability sensitivity analysis

In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessary. Based on that, the structural system reliability is analyzed with a fourth-order moment method. The reliability sensitivity is required to conduct the differential operation of the numerical characteristic functions. A reliability sensitivity analysis formula is then derived in combination with the relation of the differential operation. Based on the matrix theory and Kronecker algebra, this paper systematically derives a matrix expression of the first four moments of the state functions, and establishes the matrix relation between the first four moments of the state functions and those of the basic random variables. On this basis, a differential operation formula of the first four moments of the state functions is further derived against the first four moments of the basic random variables. The vector relation between the state functions and the multidimensional basic random variables is described by means of the matrix operation to extend the operation method. Finally, a concise and intuitive formula is obtained to explore the inherent essential relation between the numerical characteristics of the state functions and those of the basic random variables, leading to a universal equation for the two kinds of numerical characteristics.

An Accurate Pricing Formula for Vanilla Options in a Cash Dividend Framework with Linear Algorithmic Complexity

The aim of this article is to provide a fast and efficient formula to price vanilla options in presence of cash dividends. Bos & Vandermark have provided a simple and intuitive formula but not really accurate for long maturities or for strikes far from the money. Many authors have proposed some accurate formula but with a polynomial (quadratic for Henry-Labordere) algorithmic complexity in the number of dividends. In this article we derive a formula whose accuracy is equivalent to that of Henry-Labordere but with a linear algorithmic complexity, preserving the call-put parity and the continuity of the vanilla price at each ex-dividend dates.

The Sharpe ratio of estimated efficient portfolios

Investors often adopt mean–variance efficient portfolios for achieving superior risk-adjusted returns. However, such portfolios are sensitive to estimation errors, which affect portfolio performance. To understand the impact of estimation errors, I develop simple and intuitive formulas of the squared Sharpe ratio that investors should expect from estimated efficient portfolios. The new formulas show that the expected squared Sharpe ratio is a function of the length of the available data, the number of assets and the maximum attainable Sharpe ratio. My results enable the portfolio manager to assess the value of efficient portfolios as investment vehicles, given the investment environment.