Motivated by the classical Eulerian triangle and triangular arrays from staircase tableaux and tree-like tableaux, we study a generalized Eulerian array Tn,kn,k≥0, which satisfies the recurrence ...relation:Tn,k=λ(a1k+a2)Tn−1,k+(b1−da1)n−(b1−2da1)k+b2−d(a1−a2)Tn−1,k−1+d(b1−da1)λ(n−k+1)Tn−1,k−2, where T0,0=1 and Tn,k=0 unless 0≤k≤n. We derive some properties of Tn,kn,k≥0, including the explicit formulae of Tn,k and the exponential generating function of the generalized Eulerian polynomial Tn(q), and the ordinary generating function of Tn(q) in terms of the Jacobi continued fraction expansion, and real rootedness and log-concavity of Tn(q), stability of the iterated Turán-type polynomial Tn+1(q)Tn−1(q)−Tn2(q). Furthermore, we also prove the q-Stieltjes moment property and 3-q-log-convexity of Tn(q) and that the triangular convolution preserves Stieltjes moment property of sequences. In addition, we also give a criterion for γ-positivity in terms of the Jacobi continued fraction expansion. In consequence, we get γ-positivity of a generalized Narayana polynomial, which implies that of Narayana polynomials of types A and B in a unified manner. We also derive γ-positivity for a symmetric sub-array of Tn,kn,k≥0, which in particular gives a unified proof of γ-positivity of Eulerian polynomials of types A and B.
Our results not only can immediately apply to Eulerian triangles of two kinds and arrays from staircase tableaux and tree-like tableaux, but also to segmented permutations and flag excedance numbers in colored permutations groups in a unified approach. In particular, we also confirm a conjecture of Nunge about the unimodality from segmented permutations.
Finnish perceptions of log and log architecture Lakkala, Matti; Luusua, Aale; Pihlajaniemi, Janne
Scandinavian journal of forest research,
08/2020, Letnik:
35, Številka:
5-6
Journal Article
Recenzirano
Odprti dostop
The use of log construction is increasing in Finland. This development is desirable for ecological and economic reasons. However, due to changes related to the technical properties of logs and their ...overall popularity, introduction of novel building typologies and urbanization in general, it is unclear how the public currently experience logs as a construction material and technique. Thus, in this paper our aim is to examine logs and log building holistically as a phenomenon in the Finnish context, and to explore what kind of perceptions of the log as an architectural material there currently are among Finnish laypersons. To do so, we analyse interviews conducted among 18 Finnish laypersons. The study method utilized a semi-structured interview combined with a walk-along interview in a log construct built by our research team. Results are discussed through the lens of relevant wood research and the Finnish history of logs. Results suggest that logs are currently perceived as a topical and trendy material because of their naturalness, warmth and healthiness. Stereotypes related to logs, such as ruralness or traditionality, are changing or begin to appear differently. The visibility of log structures was found to be meaningful to the study participants in various ways.
Cancer immunotherapy trials have two special features: a delayed treatment effect and a cure rate. Both features violate the proportional hazard model assumption and ignoring either one of the two ...features in an immunotherapy trial design will result in substantial loss of statistical power. To properly design immunotherapy trials, we proposed a piecewise proportional hazard cure rate model to incorporate both delayed treatment effect and cure rate into the trial design consideration. A sample size formula is derived for a weighted log‐rank test under a fixed alternative hypothesis. The accuracy of sample size calculation using the new formula is assessed and compared with the existing methods via simulation studies. A real immunotherapy trial is used to illustrate the study design along with practical consideration of balance between sample size and follow‐up time.
It is a classical result of Ginibre that the normalized bulk k-point correlation functions of a complex n × n Gaussian matrix with independent entries of mean zero and unit variance are ...asymptotically given by the determinantal point process on ℂ with kernel $K_{\infty }(z, w) := \frac{1}{\pi }e^{-|z|^{2}/2-|w|^{2}/2+z\bar{w}}$ in the limit n → ∞. In this paper, we show that this asymptotic law is universal among all random n × n matrices Mn whose entries are jointly independent, exponentially decaying, have independent real and imaginary parts and whose moments match that of the complex Gaussian ensemble to fourth order. Analogous results at the edge of the spectrum are also obtained. As an application, we extend a central limit theorem for the number of eigenvalues of complex Gaussian matrices in a small disk to these more general ensembles. These results are non-Hermitian analogues of some recent universality results for Hermitian Wigner matrices. However, a key new difficulty arises in the non-Hermitian case, due to the instability of the spectrum for such matrices. To resolve this issue, we the need to work with the log-determinants log | det(Mn − z0)| rather than with the Stieltjes transform 1/ntr(Mn − z0)−1, in order to exploit Girko's Hermitization method. Our main tools are a four moment theorem for these log-determinants, together with a strong concentration result for the log-determinants in the Gaussian case. The latter is established by studying the solutions of a certain nonlinear stochastic difference equation. With some extra consideration, we can extend our arguments to the real case, proving universality for correlation functions of real matrices which match the real Gaussian ensemble to the fourth order. As an application, we show that a real n × n matrix whose entries are jointly independent, exponentially decaying and whose moments match the real Gaussian ensemble to fourth order has $\sqrt{\frac{2n}{\pi}}+o(\sqrt{n})$ real eigenvalues asymptotically almost surely.
Epidemiologic studies often quantify exposure using biomarkers, which commonly have statistically skewed distributions. Although normality assumption is not required if the biomarker is used as an ...independent variable in linear regression, it has become common practice to log-transform the biomarker concentrations. This transformation can be motivated by concerns for nonlinear dose-response relationship or outliers; however, such transformation may not always reduce bias. In this study, we evaluated the validity of motivations underlying the decision to log-transform an independent variable using simulations, considering eight scenarios that can give rise to skewed X and normal Y. Our simulation study demonstrates that (1) if the skewness of exposure did not arise from a biasing factor (e.g., measurement error), the analytic approach with the best overall model fit best reflected the underlying outcome generating methods and was least biased, regardless of the skewness of X and (2) all estimates were biased if the skewness of exposure was a consequence of a biasing factor. We additionally illustrate a process to determine whether the transformation of an independent variable is needed using NHANES. Our study and suggestion to divorce the shape of the exposure distribution from the decision to log-transform it may aid researchers in planning for analysis using biomarkers or other skewed independent variables.
Lipophilicity is a crucial parameter for drug discovery, usually determined by the logarithmic partition coefficient (Log P) between octanol and water. However, the available detection methods have ...restricted the widespread use of the partition coefficient in inorganic medicinal chemistry, and recent investigations have shifted towards chromatographic lipophilicity parameters, frequently without a conversion to derive Log P. As high-performance liquid chromatography (HPLC) instruments are readily available to research groups, a HPLC-based method is presented and validated to derive the partition coefficient of a set of 19 structurally diverse and cytotoxic platinum(IV) complexes exhibiting a dynamic range of at least four orders of magnitude. The chromatographic lipophilicity parameters φ0 and Log kw were experimentally determined for the same set of compounds, and a correlation was obtained that allows interconversion between the two lipophilicity scales, which was applied to an additional set of 34 platinum(IV) drug candidates. Thereby, a φ0 = 58 corresponds to Log P = 0. The same approaches were successfully evaluated to determine the distribution coefficient (Log D) of five ionisable platinum(IV) compounds to sample pH-dependent effects on the lipophilicity. This study provides straight-forward HPLC-based methods to determine the lipophilicity of cytotoxic platinum(IV) complexes in the form of Log P and φ0 that can be interconverted and easily expanded to other metal-based compound classes.
A growing number of studies have tried to assess the effects of social media on adolescents, who are among the most avid social media users. To establish the effects of social media use, we need ...accurate and valid instruments to measure adolescents’ time spent with these media. The aim of this preregistered study was to examine the accuracy and convergent validity of retrospective surveys and experience sampling method (ESM) surveys, by comparing adolescents’ responses to these self-report measures with their digital trace data. The sample consisted of 125 adolescents (48% girls; Mage = 14.1) with Android smartphones. In both retrospective surveys and ESM, adolescents overestimated their time spent on social media. They more accurately estimated their time spent on platforms that are used in a less fragmented way (Instagram) than on platforms that are used in a more fragmented way (Snapchat). The between-person convergent validity of adolescents’ time estimates according to retrospective surveys and ESM reached the threshold for minimum acceptable convergent validity (r ranged from .55 to .65). The within-person convergent validity of adolescents’ ESM estimates of their time spent on social media was unacceptable (r = .32). The between- and within-person convergent validity of ESM estimates decreased over time (i.e., fatigue effect).
It is well-known that measures whose density is the form e−V where V is a uniformly convex potential on Rn attain strong concentration properties. In search of a notion of log-concavity on the ...discrete hypercube, we consider measures on {−1,1}n whose multi-linear extension f satisfies log∇2f(x)⪯βIn, for β≥0, which we refer to as β-semi-log-concave. We prove that these measures satisfy a nontrivial concentration bound, namely, any Hamming Lipchitz test function φ satisfies Varνφ≤n2−Cβ for Cβ>0. As a corollary, we prove a concentration bound for measures which exhibit the so-called Rayleigh property. Namely, we show that for measures such that under any external field (or exponential tilt), the correlation between any two coordinates is non-positive, Hamming-Lipschitz functions admit nontrivial concentration.
Customer retention is important in the financial services industry. Machine learning has been incorporated into customer data analytics to predict client churn risks. Despite its success, existing ...approaches primarily use only structured data, e.g., demographics and account history. Data mining with unstructured data, e.g., customer interaction, can reveal more insights, which has not been adequately leveraged. In this research, we propose a customer churn prediction model utilizing the unstructured data, which is the spoken contents in phone communication. We collected a large-scale call center dataset with two million calls from more than two hundred thousand customers and conducted extensive experiments. The results show that our model can accurately predict the client churn risks and generate meaningful insights using interpretable machine learning with personality traits and customer segments. We discuss how these insights can help managers develop retention strategies customized for different customer segments.
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