Single Sum Research Articles

A complete solution classification and unified algorithmic treatment for the one- and two-step asymmetric S-transverse mass M ˜ T 2 $$ {\tilde{M}}_{\mathrm{T}2} $$ event scale statistic

The MT2 or "s-transverse mass" statistic was developed to associate a parent mass scale to a missing transverse energy signature, given that escaping particles are generally expected in pairs, while collider experiments are sensitive to just a single transverse momentum vector sum. This document focuses on the generalized extension of that statistic to asymmetric one- and two-step decay chains, with arbitrary child particle masses and upstream missing transverse momentum. It provides a unified theoretical formulation, complete solution classification, taxonomy of critical points, and technical algorithmic prescription for treatment of the MT2 event scale. An implementation of the described algorithm is available for download, and is also a deployable component of the author's selection cut software package AEACuS (Algorithmic Event Arbiter and Cut Selector). Appendices address combinatoric event assembly, algorithm validation, and a complete pseudocode.

Superconformal sum rules and the spectral density flow of the composite dilaton (ADD) multiplet in N $$ \mathcal{N} $$ =1 theories

We discuss the signature of the anomalous breaking of the superconformal symmetry in $\mathcal{N}=1$ super Yang Mills theory, mediated by the Ferrara-Zumino hypercurrent ($\mathcal{J}$) with two vector ($\mathcal V$) supercurrents $(\mathcal{JVV})$ and its manifestation in the anomaly action, in the form of anomaly poles. This allows to investigate in a unified way both conformal and chiral anomalies. The analysis is performed in parallel to the Standard Model, for comparison. We investigate, in particular, massive deformations of the $\mathcal{N}=1$ theory and the spectral densities of the anomaly form factors which are extracted from the components of this correlator. In this extended framework it is shown that all the anomaly form factors are characterized by spectral densities which flow with the mass deformation. In particular, the continuum contributions from the two-particle cuts of the intermediate states turn into into poles in the zero mass limit, with a single sum rule satisfied by each component. Non anomalous form factors, instead, in the same anomalous correlators, are characterized by non-integrable spectral densities. These tend to uniform distributions as one moves towards the conformal point, with a clear dual behaviour. As in a previous analysis of the dilaton pole of the Standard Model, also in this case the poles can be interpreted as signaling the exchange of a composite dilaton/axion/dilatino (ADD) multiplet in the effective Lagrangian.[...]

On the summability of bivariate rational functions

We present criteria for deciding whether a bivariate rational function in two variables can be written as a sum of two (q-)differences of bivariate rational functions. Using these criteria, we show how certain double sums can be evaluated, first, in terms of single sums and, finally, in terms of values of special functions.

Tuning nuclearity of clusters by positional change of functional group: Synthesis of polynuclear clusters, crystal structures and magnetic properties

Four neutral polynuclear magnetic clusters, [MnIII6MnII2NaI2(N3)8(μ4-O)2(L1)6(CH3OH)2] (1), [MnIII6NaI2(N3)4(μ4-O)2(L2)4(CH3COO)4] (2), [NiII5(N3)4(HL1)4(HCOO)2(CH3OH)2(H2O)2]·2CH3OH (3) and [NiII4NaI2(N3)4(HL2)6]·2CH3OH (4) have been synthesized using tetradentate ligands H2L1-2 along with azide as a co-ligand. H2L1-2 are the products formed in situ upon condensation of 2-hydroxy-3-methoxybenzaldehyde with 1-aminopropan-2-ol and 1-aminopropan-3-ol, respectively. Single crystal X-ray diffraction and bond valence sum calculation showed that complex 1 is composed of both MnIII and MnII. Complex 3 contains coordinated formate, which was formed upon in situ oxidation of methanol. The magnetic study over a wide range of temperatures of all the complexes (1–4) showed that 1 and 2 are antiferromagnetic whereas other two (3–4) are predominantly ferromagnetic. The estimated ground states of the complexes are S≈3(1), S=4(2), S=5(3) and S≈4(4), respectively.

Exact high temperature expansion of the one-loop thermodynamic potential with complex chemical potential

We present a derivation of an exact high temperature expansion for a one-loop thermodynamic potential $\Omega(\tilde{\mu})$ with complex chemical potential $\tilde{\mu}$. The result is given in terms of a single sum the coefficients of which are analytical functions of $\tilde{\mu}$ consisting of polynomials and polygamma functions, decoupled from the physical expansion parameter $\beta m$. The analytic structure of the coefficients permits us to explicitly calculate the thermodynamic potential for the imaginary chemical potential and analytically continue the domain to the complex $\tilde{\mu}$ plane. Furthermore, our representation of $\Omega(\tilde{\mu})$ is particularly well suited for the Landau--Ginzburg-type of phase transition analysis. This fact, along with the possibility of interpreting the imaginary chemical potential as an effective generalized-statistics phase, allows us to investigate the singular origin of the $m^3$ term appearing only in the bosonic thermodynamic potential.

Sum rules and spectral density flow in QCD and in superconformal theories

We discuss the signature of the anomalous breaking of the superconformal symmetry in $\mathcal{N}=1$ super Yang Mills theory and its manifestation in the form of anomaly poles. Moreover, we describe the massive deformations of the $\mathcal{N}=1$ theory and the spectral densities of the corresponding anomaly form factors. These are characterized by spectral densities which flow with the mass deformation and turn the continuum contributions from the two-particle cuts of the intermediate states into poles, with a single sum rule satisfied by each component. The poles can be interpreted as signaling the exchange of a composite axion/dilaton/dilatino (ADD) multiplet in the effective Lagrangian. We conclude that global anomalous currents characterized by a single flow in the perturbative picture always predict the existence of composite interpolating fields.

Pyrrolizidine Alkaloids in the Food Chain: Development, Validation, and Application of a New HPLC-ESI-MS/MS Sum Parameter Method

Contamination of food and feed with pyrrolizidine alkaloids is currently discussed as a potential health risk. Here, we report the development of a new HPLC-ESI-MS/MS sum parameter method to quantitate the pyrrolizidine alkaloid content in complex food matrices. The procedure was validated for honey and culinary herbs. Isotopically labeled 7-O-9-O-dibutyroyl-[9,9-(2)H2]-retronecine was synthesized and utilized as an internal standard for validation and quantitation. The total pyrrolizidine alkaloid content of a sample is expressed as a single sum parameter: retronecine equivalents (RE). Ld/Lq for honey was 0.1 μg RE/kg/0.3 μg RE/kg. For culinary herbs, 1.0 μg RE/kg/3.0 μg RE/kg (dry weight, dw) and 0.1 μg RE/kg/0.3 μg RE/kg (fresh weight, fw) were determined, respectively. The new method was applied to analyze 21 herbal convenience products. Fifteen products (71%) were pyrrolizidine alkaloid positive showing pyrrolizidine alkaloid concentrations ranging from 0.9 to 74 μg RE/kg fw.

So the kids are busy, what now? Teacher perceptions of the use of hand-held game consoles in West Australian primary classrooms

<p>Games technology in the form of hand-held game consoles (HGCs) when focussed on specific academic skill development has the capacity to engage students in learning and in turn produce positive academic results. This current research explores teacher perceptions of the implementation of HGCs to enhance the development of mental maths skills (namely the recall of single digit addition, subtraction and multiplication sums) in nine Year 4 classrooms and, through a series of structured interviews and observations, categorises these educators in terms of their role in the classroom. It was hypothesised that the teaching style would impact on the student's motivation and engagement when using the HGCs, however, it became evident that by maintaining set classroom structures the HGCs appeared to have the capacity to engage and motivate students, regardless of the approach of the teacher.</p><p> </p>

Multidimensional structure of the Groningen Frailty Indicator in community-dwelling older people

BackgroundDue to the rapidly increasing number of older people worldwide, the prevalence of frailty among older adults is expected to escalate in coming decades. It is crucial to recognize early onset symptoms to initiate specific preventive care. Therefore, early detection of frailty with appropriate screening instruments is needed. The aim of this study was to evaluate the underlying dimensionality of the Groningen Frailty Indicator (GFI), a widely used self-report screening instrument for identifying frail older adults. In addition, criterion validity of GFI subscales was examined and composition of GFI scores was evaluated.MethodsA cross-sectional study design was used to evaluate the structural validity, internal consistency and criterion validity of the GFI questionnaire in older adults aged 65 years and older. All subjects completed the GFI questionnaire (n = 1508). To assess criterion validity, a smaller sample of 119 older adults completed additional questionnaires: De Jong Gierveld Loneliness Scale, Hospital Anxiety Depression Scale, RAND-36 physical functioning, and perceived general health item of the EuroQol-5D. Exploratory factor analysis and Mokken scale analysis were used to evaluate the structural validity of the GFI. A Venn diagram was constructed to show the composition of GFI subscale scores for frail subjects.ResultsThe factor structure of the GFI supported a three-dimensional structure of the scale. The subscales Daily Activities and Psychosocial Functioning showed good internal consistency, scalability, and criterion validity (Daily Activities: Cronbach’s α = 0.81, Hs = .84, r = −.62; Psychosocial Functioning: Cronbach’s α = 0.80, Hs = .35, r = −.48). The subscale Health Problems showed less strong internal consistency but acceptable scalability and criterion validity (Cronbach’s α = .57, Hs = .35, r = −.48). The present data suggest that 90% of the frail older adults experience problems in the Psychosocial Functioning domain.ConclusionsThe present findings support a three-dimensional factor structure of the GFI, suggesting that a multidimensional assessment of frailty with the GFI is possible. These GFI subscale scores produce a richer assessment of frailty than with a single overall sum GFI score, and likely their use will contribute to more directed and customized care for older adults.

Determination of Deoxynivalenol and Nivalenol in Wheat by Ultra-Performance Liquid Chromatography/Photodiode-Array Detector and Immunoaffinity Column Cleanup

An ultra-performance liquid chromatography (UPLC®) method has been developed for the simultaneous determination of deoxynivalenol (DON) and nivalenol (NIV) in wheat. Ground sample was extracted with water and the filtered extract was cleaned up through an immunoaffinity column containing a monoclonal antibody specific for DON and NIV. Toxins were separated and quantified by UPLC® with photodiode-array detector (λ = 220 nm) in less than 3 min. Mean recoveries from blank wheat samples spiked with DON and NIV at levels of 100–2,000 μg/kg (each toxin) ranged from 85 to 95 % for DON and from 81 to 88 % for NIV, with relative standard deviations less than 7 %. Similar recoveries were observed from spiked samples when methanol/water (80:20, v/v) was used as extraction solvent. However, by using a wheat sample naturally contaminated with DON and NIV, the one-way analysis of variance (Student–Newman–Keuls test) between different extraction solvents and modes showed that water extraction provided a significant increase (P < 0.001) in toxin concentrations (mean values of six replicate analyses) with respect to methanol/water (80:20, v/v). No significant difference was observed between shaking (60 min) and blending (3 min). The limit of detection (LOD) of the method was 30 μg/kg for DON and 20 μg/kg for NIV (signal-to-noise ratio 3:1). The immunoaffinity columns showed saturation of DON/NIV binding sites at levels higher than 2,000 ng in blank wheat extracts spiked with the corresponding amount of mycotoxin, as single mycotoxin or sum of DON and NIV. The range of applicability of the method was from LOD to 4,000 μg/kg, as single mycotoxin or sum of DON and NIV in wheat. The analyses of 20 naturally contaminated wheat samples showed DON contamination in all analyzed samples at level ranging from 30 to 2,700 μg/kg. NIV was detected in two samples at negligible toxin levels (up to 46 μg/kg). This is the first UPLC® method using immunoaffinity column cleanup for the simultaneous and sensitive determination of DON and NIV in wheat.

Ray convergence in a flux-like propagation formulation

The energy flux formulation of waveguide propagation is closely related to the incoherent mode sum, and its simplicity has led to development of efficient computational algorithms for reverberation and target echo strength, but it lacks the effects of convergence or modal interference. By starting with the coherent mode sum and rejecting the most rapid interference but retaining beats on a scale of a ray cycle distance it is shown that convergence can be included in a hybrid formulation requiring minimal extra computation. Three solutions are offered by evaluating the modal intensity cross terms using Taylor expansions. In the most efficient approach the double summation of the cross terms is reduced to a single numerical sum by solving the other summation analytically. The other two solutions are a local range average and a local depth average. Favorable comparisons are made between these three solutions and the wave model Orca with, and without, spatial averaging in an upward refracting duct. As a by-product, it is shown that the running range average is very close to the mode solution excluding its fringes, given a relation between averaging window size and effective number of modes which, in turn, is related to the waveguide invariant.

Two-point derivative dispersion relations

A new derivation is given for the representation, under certain conditions, of the integral dispersion relations of scattering theory through local forms. The resulting expressions have been obtained through an independent procedure to construct the real part and consist of new mathematical structures of double infinite summations of derivatives. In this new form the derivatives are calculated at the generic value of the energy E and separately at the reference point E = m that is the lower limit of the integration. This new form may be more interesting in certain circumstances and directly shows the origin of the difficulties in convergence that were present in the old truncated forms called standard-derivative dispersion relations (DDR). For all cases in which the reductions of the double to single sums were obtained in our previous work, leading to explicit demonstration of convergence, these new expressions are seen to be identical to the previous ones. We present, as a glossary, the most simplified explicit results for the DDR’s in the cases of imaginary amplitudes of forms (E/m)λ[ln (E/m)]n that cover the cases of practical interest in particle physics phenomenology at high energies. We explicitly study the expressions for the cases with λ negative odd integers, that require identification of cancelation of singularities, and provide the corresponding final results.

A Polynomial Time Algorithm for Rayleigh Ratio on Discrete Variables: Replacing Spectral Techniques for Expander Ratio, Normalized Cut, and Cheeger Constant

A general form of minimizing the Rayleigh ratio on discrete variables is shown here, for the first time, to be polynomial time solvable. This is significant because major problems in clustering, partitioning, and imaging can be presented as the Rayleigh ratio minimization on discrete variables and an orthogonality constraint. These challenging problems are modeled as the normalized cut problem, the graph expander ratio problem, the Cheeger constant problem, or the conductance problem, all of which are NP-hard. These problems have traditionally been solved, heuristically, using the “spectral technique.” A unified framework is provided here whereby all these problems are formulated as a constrained minimization form of a quadratic ratio, referred to here as the Rayleigh ratio. The quadratic ratio is to be minimized on discrete variables and a single sum constraint that we call the balance or orthogonality constraint. When the discreteness constraints on the variables are disregarded, the resulting continuous relaxation is solved by the spectral method. It is shown here that the Rayleigh ratio minimization subject to the discreteness constraints requiring each variable to assume one of two values in {−b,1} is solvable in strongly polynomial time, equivalent to a single minimum s,t cut algorithm on a graph of same size as the input graph, for any nonnegative value of b. This discrete form for the Rayleigh ratio problem was often assumed to be NP-hard. Not only is it shown here that the discrete Rayleigh ratio problem is polynomial time solvable, but also the algorithm is more efficient than the spectral algorithm. Furthermore, an experimental study demonstrates that the new algorithm provides in practice an improvement, often dramatic, on the quality of the results of the spectral method, both in terms of approximating the true optimum of the Rayleigh ratio problem on both the discrete variables and the balance constraint, and in terms of the subjective partition quality. A further contribution here is the introduction of a problem, the quantity-normalized cut, generalizing all the Rayleigh ratio problems. The discrete version of that problem is also solved with the efficient algorithm presented. This problem is shown, in a companion paper, to enable the modeling of features essential to clustering that are valuable in practical applications.

Structural Solutions for Additively Coupled Sum Constrained Games

We propose and analyze a new family of games played by resource-constrained players. In particular, each strategic user has a single sum resource constraint over its action space and its own action impacts its own payoff through additive combinations of the other users' actions. We investigate convergence properties of various solutions for these games with and without real-time information exchange. First, when users cannot exchange messages with each other, but desire to maximize their individual utilities, we derive sufficient conditions under which best response dynamics converges to a globally asymptotically stable Nash equilibrium. Second, when users can exchange price signals in real-time to achieve coordination, we also establish the convergence properties of two action update mechanisms, including gradient play and Jacobi update. The investigated game model and our proposed solutions are readily applicable to various multi-user interaction, including communication networking applications, such as power control and flow control.

Expansions for bivariate extreme value distributions

Expressions for moment properties have not been known even for the simplest of the bivariate extreme value distributions. Here, simple expansions are derived for various properties of any given bivariate extreme value distribution. Each expansion is a single infinite sum. The properties considered include product moments, conditional moments, joint moment generating function and others. Computational efficiencies of these expansions are established with respect to standard approaches for computing moment properties.

Securitizing Structured Settlement Payment Streams: A Primer

The term “structured settlement” refers to a broad category of financial resolutions between an aggrieved party and a party deemed to be responsible (or their insurer). In a structured settlement, often used to settle wrongful death and personal injury cases, the plaintiff is paid money over time, rather than in a single lump sum. This article provides an introduction to structured settlements, including how they benefit plaintiffs and insurers, how they are underwritten, how their transactions function, how they are securitized, how they have performed in the asset-backed securities marketplace, and how their risks are uncorrelated to the risks to which many other asset classes are exposed. <b>TOPICS:</b>Legal and regulatory issues for structured finance, legal/regulatory/public policy

Estimating the Leaf Area of Irvingia Gabonensis (Aubry-Lecomte Ex O’ Rorke) Baill from Linear Measurement

Leaf area measurements are of great value in physiological and agronomic studies. Leaf area is important for plant light interception, growth analysis, photosynthesis, leaf area index estimation among others. This study focused on estimating the leaf of Irvingia gabonensis using a linear (non-destructive) measurement. A total of 90 leaves were selected randomly from nursery and field which represented different leaf sizes ranging from small (3 cm width), medium (5 cm width) and large (7 cm width). The lamina length (L) and lamina width (W) were measured with a ruler, while the leaf area (LA) were measured using a software model WinRHizo PRO2005, installed on computer system with an attached scanning machine. The best fit model was selected based on F test and coefficient of determination R2. Correlation of all parameters is significant at 1% level. Product of square length and width [(LW)2] correlated best with leaf area having a correlation coefficient (r) of 0.99. Quadratic and linear regression of the data produced thirteen leaf area models. The best five models were derived from single dimensional measurement product and sum of length and width of either lamina length or width. The five top models were recommended for leaf area estimation of Irvingia gabonensis but for ease of application, model 13 (Y = 0.2309x2- 2.5694x + 67.268: R2 = 99%) was preferred for its simplicity. The models developed and recommended in this study can be adopted for rapid and accurate estimation of adaxial leaf area of I. gabonensis under field conditions.

An explicit formula for the linearization coefficients of Bessel polynomials

We prove a single sum formula for the linearization coefficients of the Bessel polynomials. In two special cases we show that our formula reduces indeed to Berg and Vignat's formulas in their proof of the positivity results about these coefficients (Constructive Approximation, 27(2008), 15-32). As a bonus we also obtain a generalization of an integral formula of Boros and Moll (J. Comput. Appl. Math. 106 (1999), 361-368).

Investigating reinforcer magnitude and reinforcer delay: A contingency management analog study.

The influence of reinforcer magnitude and reinforcer delay on smoking abstinence was studied using an analog model of contingency management. Participants (N = 103, 74% men) visited our laboratory 3 times daily for 5 days and received money for providing a breath sample that indicated smoking abstinence (carbon monoxide level ≤6 parts per million). Using a factorial design, we assigned participants randomly to 1 of 4 groups that could earn a total of either $207.50 (high-magnitude condition) or $70.00 (low-magnitude condition), and received earnings either at each visit (no-delay condition) or in a single lump sum 1 week following the study (delay condition). High-magnitude reinforcement, regardless of delay, was associated with higher rates of abstinence than was low-magnitude reinforcement. High magnitude of reinforcement provided immediately but in incremental amounts was associated with longer intervals to relapse during treatment in comparison with high-magnitude reinforcement provided in a single lump sum after a delay. Low rates of responding in the low-magnitude conditions made interpretation of the impact of delay in those conditions difficult. These findings further demonstrate that high magnitude of reinforcement results in better outcomes than does low magnitude of reinforcement, and that a delay to reinforcement can be detrimental-even when a high magnitude of reinforcement is provided.

Actuarial assessment of damages in personal injury litigation: how precise are we?

In personal injury litigation, claimants may seek their compensation for future losses or expenses as a lump sum that is determined by the product of a multiplicand and a multiplier. The multiplicand represents the annual loss in earnings and other benefits, as assessed at the trial date, while the multiplier discounts future pecuniary values into a single present-day lump sum amount. At present, multipliers in the UK are calculated using actuarial methods and based on assumed mortality and interest rates. However, it is entirely possible that these assumptions are incorrect, and if they are, then all claimants who rely on the same set of actuarial multipliers will be affected. In this article, we investigate how the uncertainty surrounding mortality and interest rate assumptions affects the precision of actuarial multipliers. With the aid of stochastic models, we estimate the possible range of values that an actuarial multiplier can take. Language: en