Cubic interaction vertices in higher spin theories

Based purely on symmetry considerations, we derive the following result: in momentum space, the coefficient of the cubic interaction vertex for a spin $\lambda$ field is equal to the corresponding Yang-Mills (spin 1) coefficient, raised to the power $\lambda$. This result is valid for all $\lambda$ for Lagrangians that contain a cubic interaction vertex of the form $\lambda$-$\lambda$-$\lambda$, in four-dimensional flat spacetime. For $\lambda=3$, we present an additional derivation of this result.Comment: 6 pages, published versio

Oxidizing SuperYang-Mills from (N=4,d=4) to (N=1,d=10)

We introduce superspace generalizations of the transverse derivatives to rewrite the four-dimensional N=4 Yang-Mills theory into the fully ten-dimensional N=1 Yang-Mills in light-cone form. The explicit SuperPoincare algebra is constructed and invariance of the ten-dimensional action is proved.Comment: 15 page

Eleven-Dimensional Supergravity in Light-Cone Superspace

We show that Supergravity in eleven dimensions can be described in terms of a constrained superfield on the light-cone, without the use of auxiliary fields. We build its action to first order in the gravitational coupling constant \kappa, by "oxidizing" (N=8,d=4) Supergravity. This is simply achieved, as for N=4 Yang-Mills, by extending the transverse derivatives into superspace. The eleven-dimensional SuperPoincare algebra is constructed and a fourth order interaction is conjectured.Comment: 18 page

Automated Screening for Three Inborn Metabolic Disorders: A Pilot Study

Background: Inborn metabolic disorders (IMDs) form a large group of rare, but often serious, metabolic disorders. Aims: Our objective was to construct a decision tree, based on classification algorithm for the data on three metabolic disorders, enabling us to take decisions on the screening and clinical diagnosis of a patient. Settings and Design: A non-incremental concept learning classification algorithm was applied to a set of patient data and the procedure followed to obtain a decision on a patient’s disorder. Materials and Methods: Initially a training set containing 13 cases was investigated for three inborn errors of metabolism. Results: A total of thirty test cases were investigated for the three inborn errors of metabolism. The program identified 10 cases with galactosemia, another 10 cases with fructosemia and the remaining 10 with propionic acidemia. The program successfully identified all the 30 cases. Conclusions: This kind of decision support systems can help the healthcare delivery personnel immensely for early screening of IMDs

Efficient Investment in Children

Many would say that children are society's most precious resource. So, how should we invest in them? To gain insight into this question, a dynamic general equilibrium model is developed where children differ by ability. Parents invest time and money in their offspring, depending on their altruism. This allows their children to grow up as more productive adults. First, the efficient allocation is characterized. Next, this is compared with the outcome that arises when financial markets are incomplete. The situation where child-care markets are also lacking is then examined. Additionally, the consequences of impure altruism are analyzed.Investment in children; efficiency; imperfect financial markets; impure altruism; lack of child-care markets.

Efficient investment in children

Many would say that children are society’s most precious resource. So, how should it invest in them? To gain insight into this question, a dynamic general equilibrium model is developed where children differ by ability. Parents invest time and money in their offspring, depending on their altruism. This allows their children to grow up as more productive adults. First, the efficient allocation for the framework is characterized. Next, this is compared with the case of incomplete financial markets. Then, the situation where childcare markets are also lacking is examined. Additionally, the effects of impure altruism are analyzed.Econometric models

Kernel solutions of the Kostant operator on eight-dimensional quotient spaces

After introducing the generators and irreducible representations of the ${\rm su}(5)$ and ${\rm so}(6)$ Lie algebras in terms of the Schwinger's scillators, the general kernel solutions of the Kostant operators on eight-dimensional quotient spaces ${\rm su}(5)/{\rm su}(4)\times {\rm u}(1)$ and ${\rm so}(6)/{\rm so}(4)\times {\rm so}(2)$ are derived in terms of the diagonal subalgebras ${\rm su}(4)\times {\rm u}(1)$ and ${\rm so}(4)\times {\rm so}(2)$, respectively.Comment: 13 pages. Typos correcte

Validating and Implementing Modified Filinov Phase Filtration in Semiclassical Dynamics

The Mixed Quantum-Classical Initial Value Representation (MQC-IVR) is a recently introduced approximate semiclassical (SC) method for the calculation of real-time quantum correlation functions. MQC-IVR employs a modified Filinov filtration (MFF) scheme to control the overall phase of the SC integrand, extending the applicability of SC methods to complex systems while retaining their ability to accurately describe quantum coherence effects. Here, we address questions regarding the effectiveness of the MFF scheme in combination with SC dynamics. Previous work showed that this filtering scheme is of limited utility in the context of semiclassical wavepacket propagation, but we find the MFF is extraordinarily powerful in the context of correlation functions. By examining trajectory phase and amplitude contributions to the real-time SC correlation function in a model system, we clearly demonstrate that the MFF serves to reduce noise by damping amplitude only in regions of highly oscillatory phase leading to a reduction in computational effort while retaining accuracy. Further, we introduce a novel and efficient MQC-IVR formulation that allows for linear scaling in computational cost with the total simulation length, a significant improvement over the more-than quadratic scaling exhibited by the original method.Comment: 8 pages, 3 figure