Local Formula Research Articles

Evaluating the Catastrophic Rainfall of 14 July 2016 in the Catchment Basin of the Urbanized Strzyza Stream in Gdańsk, Poland

We analyzed the causes, the course, and consequences of the extreme precipitation events that occurred 14 July 2016 in the watershed of Strzyza Creek in Gdansk, Poland. Automated rain gauges located in Strzyza catchment registered a total precipitation lasting about 16 hours – from 129 to 160 mm of rain depth. More in-depth analysis based on rain data collected by Gdansk University of Technology (GUT) rain station was done. The course of rainfall was compared with existing rain models on the national range and also with local rain formula. The results showed that, according to the Chomicz classification, the rainfall can be qualified as torrential. Its course far exceeded the theoretical values calculated for the probability of occurrence 1% (return time: 100 years). Although the analyzed rain episode was characterized by extremely high instantaneous rainfall intensities, the duration of the most intensive middle stage of about eight hours caused the highest daily rain sum registered in Gdansk in the history of meteorological measurements. As a result, the rainfall caused two fatalities in the lower part of the Strzyza watershed. It was noted that this type of rain qualified as an extraordinary event at the turn of the XX and XXI centuries in areas located in the Mediterranean region. Rainfalls that currently occurr in this part of Europe are also characterized by proportionally higher parameters that should be considered as an indisputable effect of climate change on a global scale.

Surface operators, chiral rings and localization in mathcal{N} =2 gauge theories

We study half-BPS surface operators in supersymmetric gauge theories in four and five dimensions following two different approaches. In the first approach we analyze the chiral ring equations for certain quiver theories in two and three dimensions, coupled respectively to four- and five-dimensional gauge theories. The chiral ring equations, which arise from extremizing a twisted chiral superpotential, are solved as power series in the infrared scales of the quiver theories. In the second approach we use equivariant localization and obtain the twisted chiral superpotential as a function of the Coulomb moduli of the four- and five-dimensional gauge theories, and find a perfect match with the results obtained from the chiral ring equations. In the five-dimensional case this match is achieved after solving a number of subtleties in the localization formulas which amounts to choosing a particular residue prescription in the integrals that yield the Nekrasov-like partition functions for ramified instantons. We also comment on the necessity of including Chern-Simons terms in order to match the superpotentials obtained from dual quiver descriptions of a given surface operator.

Challenges and Choices: A Multidistrict Analysis of Statewide Mandated Democratic Engagement

This article seeks to deepen our understanding of the nature and quality of democratic participation in educational reform by examining the first-year implementation of California’s Local Control Funding Formula (LCFF) mandating civic engagement in district decision-making. Drawing on democratic theory, empirical literature, and data from 10 districts, we find that even when district leaders committed to involving stakeholders in decision-making, achieving this vision was often constrained by power imbalances, deeply engrained institutional habits, and limited capacity. We also find that climates of trust, support from external organizations, and homogeneity appeared to provide the foundation for deeper, broader democratic engagement in a few cases. The article concludes with implications for policy, practice, and future research.

Localization of Chern–Simons type invariants of Riemannian foliations

We prove an Atiyah–Bott–Berline–Vergne type localization formula for Killing foliations in the context of equivariant basic cohomology. As an application, we localize some Chern–Simons type invariants, for example the volume of Sasakian manifolds and secondary characteristic classes of Riemannian foliations, to the union of closed leaves. Various examples are given to illustrate our method.

A symbol calculus for foliations

The classical Getzler rescaling theorem of [15] is extended to the transverse geometry of foliations. More precisely, a Getzler rescaling calculus, [15], as well as a Block–Fox calculus of asymptotic pseudodifferential operators (A‰ \Psi DOs), [10], is constructed for all transversely spin foliations. This calculus applies to operators of degree m globally times degree \ell in the leaf directions, and is thus an appropriate tool for a better understanding of the index theory of transversely elliptic operators on foliations [13]. The main result is that the composition of A‰ \Psi DOs is again an A \Psi ‰DO, and includes a formula for the leading symbol. Our formula is more complicated due to its wide generality but its form is essentially the same, and it simplifies notably for Riemannian foliations. In short, we construct an asymptotic pseudodifferential calculus for the “leaf space” of any foliation. Applications will be derived in [5,6] where we give a Getzler-like proof of a local topological formula for the Connes–Chern character of the Connes–Moscovici spectral triple of [20], as well as the (semi-finite) spectral triple given in [5], yielding an extension of the seminal Atiyah–Singer L^2 covering index theorem, [2], to coverings of “leaf spaces” of foliations.

Bicovariograms and Euler characteristic of regular sets

AbstractWe establish an expression of the Euler characteristic of ar‐regular planar set in function of some variographic quantities. The usualframework is relaxed to aregularity assumption, generalising existing local formulas for the Euler characteristic. We give also general bounds on the number of connected components of a measurable set ofin terms of local quantities. These results are then combined to yield a new expression of the mean Euler characteristic of a random regular set, depending solely on the third order marginals for arbitrarily close arguments. We derive results for level sets of some moving average processes and for the boolean model with non‐connected polyrectangular grains in. Applications to excursions of smooth bivariate random fields are derived in the companion paper, and applied for instance toGaussian fields, generalising standard results.

A local relative trace formula for PGL(2)

Following a scheme inspired by B. Feigon, we describe the spectral side of a local relative trace formula for $G:= PGL(2,\rm E)$ relative to the symmetric subgroup $H:=PGL(2,\rm F)$ where $\rm E/\rm F$ is an unramified quadratic extension of local non archimedean fields of characteristic $0$. This spectral side is given in terms of regularized normalized periods and normalized $C$-functions of Harish-Chandra. Using the geometric side obtained in a more general setting by P. Delorme, P. Harinck and S. Souaifi , we deduce a local relative trace formula for $G$ relative to $H$. We apply our result to invert some orbital integrals.

Scalar curvature in conformal geometry of Connes–Landi noncommutative manifolds

We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on noncommutative two tori, the quantum part of the curvature consists of actions of the modular derivation through two local curvature functions. Explicit expressions for those functions are obtained for all even dimensions (greater than two). In dimension four, the one variable function shows striking similarity to the analytic functions of the characteristic classes appeared in the Atiyah-Singer local index formula, namely, it is roughly a product of the $j$-function (which defines the $\hat A$-class of a manifold) and an exponential function (which defines the Chern character of a bundle). By performing two different computations for the variation of the Einstein-Hilbert action, we obtain a deep internal relations between two local curvature functions. Straightforward verification for those relations gives a strong conceptual confirmation for the whole computational machinery we have developed so far, especially the Mathematica code hidden behind the paper.

Teacher perceptions of gifted and talented certification practices in a Southern California school district: A replication study

ABSTRACTThis study focused on a partial replication of a mixed-methods study of teachers regarding certification practices in Gifted and Talented Education (GATE). Data sources included Likert survey questions as well as openended questions with current teachers at seven schools within a Southern California school district. Since completion of the original study in 2006, there have been changes in new local control funding formulas that affect Gifted Education. In light of these changes, a partial replication study measuring current teacher perceptions of GATE certification practices compared findings with previous perceptions in the district. The survey sample (N = 93) included faculty from the originally sampled k-12 schools. Results indicate that perceptions of gifted identification and characteristics vary according to GATE certification status of the teacher, but not according to grade level taught. Teacher perceptions of the necessity for GATE certification and/or training have changed since the original study was conducted. Teachers indicated that training is valuable, but not necessary for all teachers. When compared to the previous study, findings indicate positive growth in teachers’ perceptual knowledge regarding gifted student characteristics and the value of teacher training.

Distributed Intermittent Connectivity Control of Mobile Robot Networks

In this paper we develop an intermittent communication framework for teams of mobile robots. Robots move along the edges of a mobility graph and communicate only when they meet at the vertices of this graph, giving rise to a dynamic communication network. We design distributed controllers for the robots that determine meeting times at the nodes of the mobility graph so that connectivity of the communication network is ensured over time, infinitely often. We show that this requirement can be captured by a global Linear Temporal Logic (LTL) formula that forces robots to meet infinitely often at the meeting points. To generate motion plans that satisfy the LTL expression, we propose a novel technique that approximately decomposes the global LTL formula into local LTL formulas and assigns them to the robots. Since the approximate decomposition of the LTL formula can result in conflicting robot behaviors, we develop a distributed conflict resolution scheme that generates conflict-free motion plans that satisfy the global LTL expression. By appropriately introducing delays in the execution of the generated motion plans we show that the proposed controllers can be executed asynchronously.

Towards the Irving-Kirkwood limit of the mechanical stress tensor.

The probability density functions (PDFs) of the local measure of pressure as a function of the sampling volume are computed for a model Lennard-Jones (LJ) fluid using the Method of Planes (MOP) and Volume Averaging (VA) techniques. This builds on the study of Heyes, Dini, and Smith [J. Chem. Phys. 145, 104504 (2016)] which only considered the VA method for larger subvolumes. The focus here is typically on much smaller subvolumes than considered previously, which tend to the Irving-Kirkwood limit where the pressure tensor is defined at a point. The PDFs from the MOP and VA routes are compared for cubic subvolumes, . Using very high grid-resolution and box-counting analysis, we also show that any measurement of pressure in a molecular system will fail to exactly capture the molecular configuration. This suggests that it is impossible to obtain the pressure in the Irving-Kirkwood limit using the commonly employed grid based averaging techniques. More importantly, below in LJ reduced units, the PDFs depart from Gaussian statistics, and for , a double peaked PDF is observed in the MOP but not VA pressure distributions. This departure from a Gaussian shape means that the average pressure is not the most representative or common value to arise. In addition to contributing to our understanding of local pressure formulas, this work shows a clear lower limit on the validity of simply taking the average value when coarse graining pressure from molecular (and colloidal) systems.

Albumin adjustment of total calcium does not improve the estimation of calcium status

Background: There is a longstanding controversy as to whether plasma measurements of total calcium should be adjusted for albumin concentration, and if so which formulas are the most appropriate.Methods: Ionised calcium, total calcium and albumin results, analysed at the same time at Uppsala University Hospital Laboratory between February 2005 and June 2013, were retrieved from a laboratory information system. The dataset included results from 20,003 patients. Total calcium was albumin-modified by a locally derived formula, based on 3106 patients from the dataset, and formulas from the literature. The agreement between the reference method ionised calcium and unadjusted total calcium and the seven different albumin-modifying calcium formulas, respectively, were compared with intra-class correlation coefficients (ICC).Results: Total calcium showed substantial agreement to ionised calcium, ICC 0.85 (95% CI 0.84–0.86) for the whole validation cohort. Albumin-modified calcium by different formulas showed significantly less or equal agreement, however the locally determined formula performed better than formulas taken from the literature. Also, total calcium classified the patient as hypo-normo- or hypercalcemic right in 82% of the patients. The albumin-modified calcium did not classify patients significantly better except in the subgroup hypoalbuminemia (<30 g/L) where the local formula classified the patients slightly better than total calcium.Conclusions: Albumin modification of total calcium determinations is unlikely to add valuable information, and this practice should be abandoned. Ionised calcium should be used more frequently when aberrant results for total calcium are followed up, or in patients with known hypoalbuminemia.

Elliptic genera of 2d (0,2) gauge theories from brane brick models

We compute the elliptic genus of abelian 2d (0,2) gauge theories corresponding to brane brick models. These theories are worldvolume theories on a single D1-brane probing a toric Calabi-Yau 4-fold singularity. We identify a match with the elliptic genus of the non-linear sigma model on the same Calabi-Yau background, which is computed using a new localization formula. The matching implies that the quantum effects do not drastically alter the correspondence between the geometry and the 2d (0,2) gauge theory. In theories whose matter sector suffers from abelian gauge anomaly, we propose an ansatz for an anomaly cancelling term in the integral formula for the elliptic genus. We provide an example in which two brane brick models related to each other by Gadde-Gukov-Putrov triality give the same elliptic genus.

Accuracy Graphs of Spectrum-Based Fault Localization Formulas

The effectiveness of spectrum-based fault localization techniques primarily relies on the accuracy of their fault localization formulas. Theoretical studies prove the relative accuracy orders of selected formulas under certain assumptions, forming a graph of their theoretical accuracy relations. However, it is unclear whether in such a graph the relative positions of these formulas may change when some assumptions are relaxed. On the other hand, empirical studies can measure the actual accuracy of any formula in controlled settings that more closely approximate practical scenarios but in less general contexts. In this paper, we propose an empirical framework of accuracy graphs and their construction that reveal the relative accuracy of formulas. Our work not only evaluates the association between certain assumptions and the theoretical relations among formulas, but also expands our knowledge to reveal new potential accuracy relationships of other formulas which have not been discovered by theoretical analysis. Using our proposed framework, we identified a list of formula pairs in which a formula is consistently statistically more accurate than or similar in accuracy to another, enlightening directions for further theoretical analysis.

On Local Combinatorial Formulas for Chern Classes of a Triangulated Circle Bundle

A principal circle bundle over a PL polyhedron can be triangulated and thus obtains combinatorics. The triangulation is assembled from triangulated circle bundles over simplices. To every triangulated circle bundle over a simplex we associate a necklace (in the combinatorial sense). We express rational local formulas for all powers of the first Chern class in terms of expectations of the parities of the associated necklaces. This rational parity is a combinatorial isomorphism invariant of a triangulated circle bundle over a simplex, measuring the mixing by the triangulation of the circular graphs over vertices of the simplex. The goal of this note is to sketch the logic of deducing these formulas from Kontsevitch’s cyclic invariant connection form on metric polygons.

Novel local buckling formulae for cold-formed C-section columns considering end condition effect

It is well accepted that, for a long column, the effect of end conditions on the local buckling load can be ignored due to its less impact. However, such an assumption may be inappropriate for a stub column. According to the available literature, the research dealt with such a problem was found to be quite rare. In this scenario, this paper aims to derive novel local buckling formulae for cold-formed C-section column, which takes both the effects of cross-section plate element interactions and end conditions into account. Initially, an equivalent simplified web local buckling model was proposed, in which the cross-section plate element interaction of the flanges and the lips on the web were modeled by rotational springs and the loaded edges were assumed to be uniformly compressed and to be simply supported or fixed. Subsequently, based on the energy method and the theory of Bleich, explicit expressions for the local buckling load of the column were derived. Further, simplifications to the rigorous formulae were made to allow them to be easily used by the engineers. Finally, in order to verify the accuracy of the derived formulae, the results obtained from the derived formulae were compared with the numerical results obtained from the computer software CUFSM. The comparison results show that the formulae proposed in this paper can be used successfully in estimating the local buckling loads for pin-ended or fix-ended C-section columns with a practical length.

Coign of vantage and action: Considering California’s local accountability and school finance plans for English learners

Local control has been a bedrock principle of public schooling in America since its inception. In 2013, the California Legislature codified a new local accountability approach for school finance. An important component of the new California Local Control Funding Formula (LCFF) approach is a focus on English learners (ELs). The law mandates that every school district produce a Local Control Accountability Plan (LCAP) to engage the local community in defining outcomes and determining funding for ELs. Based on an exploratory analysis of a representative sample of LCAPs, we show that, although California’s new approach offered an opportunity to support locally-defined priorities and alternatives to top-down accountability, few if any districts had yet taken full advantage of the opportunity. That is, the school districts in our sample had not yet engaged with the local community to facilitate significant changes to accountability or redistribution of funding and resources to support educational equity for ELs.

Continuous solutions of nonlinear Cauchy-Riemann equations and pseudoholomorphic curves in normal coordinates

We establish elliptic regularity for nonlinear, inhomogeneous Cauchy-Riemann equations under weak assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the solution set can be explicitly calculated. The methods also give local parametric formulas for pseudoholomorphic curves with respect to some continuous almost complex structures.

Localization of gestational age reference table and its application in prenatal screening

Objective: To establish a fetal biparietal diameter (BPD)-gestational age formula based on the data of pregnant women from Xiaoshan District of Hangzhou, and to evaluate its application in prenatal screening. Methods: Data of 3500 pregnant women with gestational age between 15 weeks and 19 weeks+6 receiving prenatal screening in Xiaoshan Hospital during May 2014 and May 2015 were collected. BPDs were used to establish a localized BPD-gestational age formula. The localized formula was used to evaluate the prenatal screening risks in 1759 pregnant women with irregular menstrual cycles or uncertain last menstrual period (LMP) in Xiaoshan District, and the results were compared with those calculated using formula in LifeCycle 4.0. Results: With localized formula, the total positive rate of Down syndrome, trisomy 18 syndrome and deformity of neural tube was decreased from 6.96% to 5.85% ( P<0.05), in which the positive rate of Down syndrome decreased ( P<0.05), that of deformity of neural tube increased ( P<0.05), and that of trisomy 18 syndrome remained the same ( P>0.05). The median MoMs of free-hCG β and α-fetoprotein calculated using localized formula were significantly different from those calculated using the formula in LifeCycle 4.0 (all P<0.05), and the former ones were more closer to 1. For women of fetus diagnosed with the above diseases, the positive rate calculated using localized formula was almost the same as that calculated using the formula in LifeCycle 4.0. Conclusion: BPD-gestational age formula should be localized based on the statistical analysis of the local population, which will help to reduce the false positive rate, and make the results more accurate and reliable in prenatal screening.

Approximation of Durrmeyer Type Operators Depending on Certain Parameters

Motivated by a number of recent investigations, we consider a new analogue of Bernstein-Durrmeyer operators based on certain variants. We derive some approximation properties of these operators. We also compute local approximation and Voronovskaja type asymptotic formula. We illustrate the convergence of aforementioned operators by making use of the software MATLAB which we stated in the paper.