Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops

In this sequel to arXiv:1711.11507 we classify the boundaries of amplituhedra relevant for determining the branch points of general two-loop amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills theory. We explain the connection to on-shell diagrams, which serves as a useful cross-check. We determine the branch points of all two-loop NMHV amplitudes by solving the Landau equations for the relevant configurations and are led thereby to a conjecture for the symbol alphabets of all such amplitudes.Comment: 42 pages, 6 figures, 8 tables; v2: minor corrections and improvement

All-Helicity Symbol Alphabets from Unwound Amplituhedra

We review an algorithm for determining the branch points of general amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills theory from amplituhedra. We demonstrate how to use the recent reformulation of amplituhedra in terms of `sign flips' in order to streamline the application of this algorithm to amplitudes of any helicity. In this way we recover the known branch points of all one-loop amplitudes, and we find an `emergent positivity' on boundaries of amplituhedra.Comment: 38 pages, 5 figures, 1 big table; v2: minor corrections and improvement

Evidence for a Nonplanar Amplituhedron

The scattering amplitudes of planar N = 4 super-Yang-Mills exhibit a number of remarkable analytic structures, including dual conformal symmetry and logarithmic singularities of integrands. The amplituhedron is a geometric construction of the integrand that incorporates these structures. This geometric construction further implies the amplitude is fully specified by constraining it to vanish on spurious residues. By writing the amplitude in a dlog basis, we provide nontrivial evidence that these analytic properties and “zero conditions” carry over into the nonplanar sector. This suggests that the concept of the amplituhedron can be extended to the nonplanar sector of N = 4 super-Yang-Mills theory

Computing Maximally Supersymmetric Scattering Amplitudes

This dissertation reviews work in computing N = 4 super-Yang–Mills (sYM) and N = 8maximally supersymmetric gravity (mSUGRA) scattering amplitudes in D = 4 spacetimedimensions in novel ways.After a brief introduction and overview in Ch. 1, the various techniques used to construct amplitudes in the remainder of the dissertation are discussed in Ch. 2. This includes several new concepts such as d log and pure integrand bases, as well as how to construct the amplitude using exactly one kinematic point where it vanishes. Also included in this chapter is an outline of the Mathematica package on shell diagrams and numerics.m (osdn) that was developed for the computations herein. The rest of the dissertation is devoted to explicit examples.In Ch. 3, the starting point is tree-level sYM amplitudes that have integral representations with residues that obey amplitude relations. These residues are shown to have corresponding residue numerators that allow a double copy prescription that results in mSUGRA residues. In Ch. 4, the two-loop four-point sYM amplitude is constructed in several ways, showcasing many of the techniques of Ch. 2; this includes an example of how to use osdn. The two-loop five-point amplitude is also presented in a pure integrand representation with comments on how it was constructed from one homogeneouscut of the amplitude. On-going work on the two-loop n-point amplitude is presented at the end of Ch. 4.In Ch. 5, the three-loop four-point amplitude is presented in the d log representation andin the pure integrand representation.In Ch. 6, there are several examples of four- through seven-loop planar diagrams that illustrate how considerations of the singularity structure of the amplitude underpin dual-conformal invariance. Taken with the previous examples, this is additional evidence that the structure known to exist in the planar sector extends to the full theory. At the end of this chapter is a proof that all mSUGRA amplitudes have a pole at infinity for (L ≥ 4)-loops. Finally in Ch. 7, the current status of ultraviolet divergences in the five-loop four-point mSUGRA amplitude is addressed. This includes a discussion of ongoing work aimed at resolving the mSUGRA finiteness question.The following Mathematica scripts are submitted with this dissertation:• on shell diagrams and numerics.m with dependencies:– all_trees *.m– external_kinematics_*_point.m– rational_external_*_point.mwhere “*” is a wild-card string of any set of characters of any length – either an integeror a number spelled out

Ethylene glycol ethers induce oxidative stress in the rat brain

Ethylene glycol ethers (EGEs) are components of many industrial and household products. Their hemolytic and gonadotoxic effects are relatively well known while their potential adverse effects on the central nervous system have not yet been clearly demonstrated. The aim of the present study was to examine the effects of 4-week administration of 2-buthoxyethanol (BE), 2-phenoxyethanol (PHE) and 2-ethoxyethanol (EE) on the total antioxidant capacity, activity of some antioxidant enzymes, such as the superoxide dismutase (SOD), catalase, glutathione peroxidase (GPX) and glutathione reductase and lipid peroxidation in the frontal cortex and hippocampus in the rat. These studies showed that BE and PHE decreased the total antioxidant activity, SOD and GPX activity, while increased lipid peroxidation in the frontal cortex. Like in the frontal cortex, also in the hippocampus BE and PHE attenuated the total antioxidant activity, however, lipid peroxidation was increased only in animals which received BE while reduction in GPX activity was present in rats administered PHE. The obtained data indicated that 4-week administration of BE and PHE, but not EE, reduced the total antioxidant activity and enhanced lipid peroxidation in the brain. In the frontal cortex, adverse effects of PHE and BE on lipid peroxidation probably depended on reduction in SOD and GPX activity, however, in the hippocampus the changes in the total antioxidant activity and lipid peroxidation were not connected with reduction of the investigated antioxidant enzyme activity

Application of metabolomics in toxicological analysis

The aim of this article was to present the most important aspects of the modern application of metabolomics in toxicology. The information contained herein comes from works that have appeared in recent years in specialist periodicals and publications devoted to the discussed issue. The first part of the work describes what metabolomics is, what is its main area of interest and why it stands out from other sciences ”omics”. Two strategies in metabolomics research were then described: targeted, which is characterized by the quantification and qualitative determination of a specific, selected pool of 50 to 500 metabolites, and non-targeted, which measures all metabolites present in the sample, which is referred to as the "metabolomic fingerprint". The course of a standard metabolome analysis is also presented, with an emphasis on the techniques of sample preparation and analyte determination, as well as the proper selection of the method for the tested material. The following part of the article discusses selected studies related to the use of metabolomics in the diagnosis of drug use and in the assessment of drug toxicity. Experiences related to new biomarkers, such as γ-hydroxy butyric acid (GHB) metabolites, which can extend the diagnostic window of this substance, and compounds whose absence in the urine indicates adulteration and manipulation of this material are discussed. The efforts of scientists in the development of a predictive model enabling the prediction of pharmacological profiles of new psychoactive substances (NPS), as well as research to deepen the knowledge of the metabolism and pathological effects of psychoactive substances, including cocaine and methamphetamine, were pointed out. The final part of the work is devoted to the use of thanatometabolomics in forensic post mortem toxicological analysis and the latest reports describing attempts to use metabolomics in computer-aided toxicological predictive analysis. This review highlights new application opportunities for metabolomics and its current struggles with practical application in the field

Logarithmic Singularities and Maximally Supersymmetric Amplitudes

The dual formulation of planar =4 super-Yang-Mills scattering amplitudes makes manifest that the integrand has only logarithmic singularities and no poles at infinity. Recently, Arkani-Hamed, Bourjaily, Cachazo and Trnka conjectured the same singularity properties hold to all loop orders in the nonplanar sector as well. Here we conjecture that to all loop orders these constraints give us the key integrand level analytic information contained in dual conformal symmetry. We also conjecture that to all loop orders, while N=8 supergravity has poles at infinity, at least at four points it has only logarithmic singularities at finite locations. We provide nontrivial evidence for these conjectures. For the three-loop four-point N=4 super-Yang-Mills amplitude, we explicitly construct a complete basis of diagram integrands that has only logarithmic singularities and no poles at infinity. We then express the complete amplitude in terms of the basis diagrams, with the coefficients determined by unitarity. We also give examples at three loops showing how to make the logarithmic singularity properties manifest via d log forms. We give additional evidence at four and five loops supporting the nonplanar logarithmic singularity conjecture. Furthermore, we present a variety of examples illustrating that these constraints are more restrictive than dual conformal symmetry. Our investigations show that the singularity structures of planar and nonplanar integrands in N=4 super-Yang-Mills are strikingly similar. While it is not clear how to extend either dual conformal symmetry or a dual formulation to the nonplanar sector, these results suggest that related concepts might exist and await discovery. Finally, we describe the singularity structure of N=8 supergravity at three loops and beyond