Proof of the Formula of Cachazo, He and Yuan for Yang-Mills Tree Amplitudes in Arbitrary Dimension

A proof is given of the formula, recently proposed by Cachazo, He and Yuan (CHY) for gluon tree amplitudes in pure Yang-Mills theory in arbitrary dimension. The approach is to first establish the corresponding result for massless $\phi^3$ theory using the BCFW recurrence relation and then to extend this to the gauge theory case. Additionally, it is shown that the scattering equations introduced by CHY can be generalized to massive particles, enabling the description of tree amplitudes for massive $\phi^3$ theory.Comment: 27 p

General Solution of the Scattering Equations

The scattering equations, originally introduced by Fairlie and Roberts in 1972 and more recently shown by Cachazo, He and Yuan to provide a kinematic basis for describing tree amplitudes for massless particles in arbitrary space-time dimension, have been reformulated in polynomial form. The scattering equations for N particles are equivalent to N-3 polynomial equations h_m=0, m=1,...,N-3, in N-3 variables, where h_m has degree m and is linear in the individual variables. Facilitated by this linearity, elimination theory is used to construct a single variable polynomial equation of degree (N-3)! determining the solutions. \Delta_N is the sparse resultant of the system of polynomial scattering equations and it can be identified as the hyperdeterminant of a multidimensional matrix of border format within the terminology of Gel'fand, Kapranov and Zelevinsky. Macaulay's Unmixedness Theorem is used to show that the polynomials of the scattering equations constitute a regular sequence, enabling the Hilbert series of the variety determined by the scattering equations to be calculated, independently showing that they have (N-3)! solutions.Comment: v2 completes the proof that the construction yields \Delta_N for all N, identifies it as the hyperdeterminant of a multidimensional matrix, and proves that the polynomial scattering equations constitute a regular sequence, enabling the Hilbert series of the associated variety to be calculated, 26 page

The Polynomial Form of the Scattering Equations

The scattering equations, recently proposed by Cachazo, He and Yuan as providing a kinematic basis for describing tree amplitudes for massless particles in arbitrary space-time dimension (including scalars, gauge bosons and gravitons), are reformulated in polynomial form. The scattering equations for $N$ particles are shown to be equivalent to a Moebius invariant system of $N-3$ equations, $\tilde h_m=0$, $2 \leq m \leq N-2$, in $N$ variables, where $\tilde h_m$ is a homogeneous polynomial of degree m, with the exceptional property of being linear in each variable taken separately. Fixing the Moebius invariance appropriately, yields polynomial equations $h_m=0$, $1 \leq m \leq N-3$, in $N-3$ variables, where $h_m$ has degree $m$. The linearity of the equations in the individual variables facilitates computation, e.g the elimination of variables to obtain single variable equations determining the solutions. Expressions are given for the tree amplitudes in terms of the $\tilde h_m$ and $h_m$. The extension to the massive case for scalar particles is described and the special case of four dimensional space-time is discussed.Comment: 24 page

A Behavioral and Neural Evaluation of Prospective Decision-Making under Risk

Making the best choice when faced with a chain of decisions requires a person to judge both anticipated outcomes and future actions. Although economic decision-making models account for both risk and reward in single-choice contexts, there is a dearth of similar knowledge about sequential choice. Classical utility-based models assume that decision-makers select and follow an optimal predetermined strategy, regardless of the particular order in which options are presented. An alternative model involves continuously reevaluating decision utilities, without prescribing a specific future set of choices. Here, using behavioral and functional magnetic resonance imaging (fMRI) data, we studied human subjects in a sequential choice task and use these data to compare alternative decision models of valuation and strategy selection. We provide evidence that subjects adopt a model of reevaluating decision utilities, in which available strategies are continuously updated and combined in assessing action values. We validate this model by using simultaneously acquired fMRI data to show that sequential choice evokes a pattern of neural response consistent with a tracking of anticipated distribution of future reward, as expected in such a model. Thus, brain activity evoked at each decision point reflects the expected mean, variance, and skewness of possible payoffs, consistent with the idea that sequential choice evokes a prospective evaluation of both available strategies and possible outcomes

Impact of European Water Framework Directive Article 7 on Drinking Water Directive compliance for pesticides: challenges of a prevention-led approach

Article 7 of the European Water Framework Directive (WFD) promotes a prevention-led approach to European Drinking Water Directive (DWD) compliance for those parameters that derive from anthropogenic influences on raw water quality. However, the efficacy of pollution prevention interventions is currently uncertain and likely to be variable, which makes absolute compliance with the drinking water standard a significant challenge. Member State governments, the WFD competent authority, the DWD competent authority, water suppliers and agriculture are all affected by and have a different perspective on the nature of this challenge. This paper presents a discussion of these perspectives applicable to stakeholders in all European Member States; the analysis is supported with examples from England and Wales. Improved understanding of the challenges faced by each group is needed if these groups are to achieve the shared goals of WFD Article 7 compliance and DWD compliance without a disproportionately negative impact on agricultural productivity. In addition, the European Commission needs to be aware of and address a potential incompatibility between WFD Article 7 and the DWD. With this in mind, targeted recommendations for action are presented for each stakeholder group

Transcription Through the Eye of a Needle: Daily and Annual Cyclic Gene Expression Variation in Douglas-Fir Needles

Background: Perennial growth in plants is the product of interdependent cycles of daily and annual stimuli that induce cycles of growth and dormancy. In conifers, needles are the key perennial organ that integrates daily and seasonal signals from light, temperature, and water availability. To understand the relationship between seasonal cycles and seasonal gene expression responses in conifers, we examined diurnal and circannual needle mRNA accumulation in Douglas-fir (Pseudotsuga menziesii) needles at diurnal and circannual scales. Using mRNA sequencing, we sampled 6.1 × 109 reads from 19 trees and constructed a de novo pan-transcriptome reference that includes 173,882 tree-derived transcripts. Using this reference, we mapped RNA-Seq reads from 179 samples that capture daily and annual variation. Results: We identified 12,042 diurnally-cyclic transcripts, 9299 of which showed homology to annotated genes from other plant genomes, including angiosperm core clock genes. Annual analysis revealed 21,225 circannual transcripts, 17,335 of which showed homology to annotated genes from other plant genomes. The timing of maximum gene expression is associated with light intensity at diurnal scales and photoperiod at annual scales, with approximately half of transcripts reaching maximum expression +/− 2 h from sunrise and sunset, and +/− 20 days from winter and summer solstices. Comparisons with published studies from other conifers shows congruent behavior in clock genes with Japanese cedar (Cryptomeria), and a significant preservation of gene expression patterns for 2278 putative orthologs from Douglas-fir during the summer growing season, and 760 putative orthologs from spruce (Picea) during the transition from fall to winter. Conclusions: Our study highlight the extensive diurnal and circannual transcriptome variability demonstrated in conifer needles. At these temporal scales, 29% of expressed transcripts show a significant diurnal cycle, and 58.7% show a significant circannual cycle. Remarkably, thousands of genes reach their annual peak activity during winter dormancy. Our study establishes the fine-scale timing of daily and annual maximum gene expression for diverse needle genes in Douglas-fir, and it highlights the potential for using this information for evaluating hypotheses concerning the daily or seasonal timing of gene activity in temperate-zone conifers, and for identifying cyclic transcriptome components in other conifer species

The Future Possibility of Consumer-Grade Quantum Computers

Quantum computers are rapidly evolving and are on the edge of becoming useful for the first time. The theoretical limit of computational speed for quantum computers would put even small-scale quantum computers well ahead of any classical computer. With more researchers attempting to build their own, it has become a race to see who can create the first truly useful quantum computer. Once such computers become both useful and prevalent, massive advancements in many fields of science can be achieved, leading to a scientific revolution. Advances in quantum computing lead some researchers and consumers to question whether the technology can ever be adapted for a wide commercial market. Based on press releases, news sources, and recent research papers, this review surveys the possibility that the average consumer will able to use quantum computers for the first time. Information about upcoming projects, along with some conjecture, suggests that through cloud technology the average consumer may be able to use a quantum computer by 2030

An Uneasy Union: Same-Sex Marriage and Religious Exemption in Washington State

Same-sex marriage promises to be one of the defining issues of the twenty-first century. While supporters of same-sex marriage have welcomed a shift in the public’s perception and increasing acceptance of same-sex marriage in the last decade, controversy remains over how to balance the competing rights between marriage equality and religious freedom. While most same-sex marriage statutes around the country include religious exemptions for religious officials, it is unclear how, or whether, these protections should extend to wedding service providers who have a religious objection to same-sex marriage. Conflicts between same-sex couples seeking wedding services and wedding service providers who have religious objections to same-sex marriage are inevitable, and despite the relatively recent legalization of same-sex marriage in Washington, such conflicts have already occurred and will undoubtedly continue to take place in the future. In order to balance these competing rights, this Comment argues that the Washington Legislature should adopt a “refuse and refer” method that allows wedding service providers with a religious objection to same-sex marriage, in limited circumstances, to decline to provide wedding services to same-sex couples. Such a solution would safeguard the dignitary interests of same-sex couples while also protecting wedding service providers with deep-seated religious objections to same-sex marriage from litigation for refusing to provide wedding services to same-sex couples

Current Algebra on the Torus

We derive the N-point one-loop correlation functions for the currents of an arbitrary affine Kac-Moody algebra. The one-loop amplitudes, which are elliptic functions defined on the torus Riemann surface, are specified by group invariant tensors and certain constant taudependent functions. We compute the elliptic functions via a generating function, and explicitly construct the invariant tensor functions recursively in terms of Young tableaux. The lowest tensors are related to the character formula of the representation of the affine algebra. These general current algebra loop amplitudes provide a building block for open twistor string theory, among other applications