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Conway’s real closed field No of surreal numbers is a sweeping generalization of the real numbers and the ordinals to which a number of elementary functions such as log and exponentiation have been shown to extend. The problems of identifying significant classes of functions that can be so extended and of defining integration for them have proven to be formidable. In this paper we address this and related unresolved issues by showing that extensions to No, and thereby integrals, exist for most functions arising in practical applications. In particular, we show they exist for a large subclass of the resurgent functions, a subclass that contains the functions that at ∞ are semi-algebraic, semi-analytic, analytic, meromorphic, and Borel summable as well as solutions to nonresonant linear and nonlinear meromorphic systems of ODEs or of difference equations. By suitable changes of variables we deal with arbitrarily located singular points. We further establish a sufficient condition for the theory to carry over to ordered exponential subfields of No more generally and illustrate the result with structures familiar from the surreal literature. The extensions of functions and integrals that concern us are constructive in nature, which permits us to work in NBG less the Axiom of Choice (for both sets and proper classes). Following the completion of the positive portion of the paper, it is shown that the existence of such constructive extensions and integrals of substantially more general types of functions (e.g. 

We call a pair of vertex-disjoint, induced subtrees of a rooted tree twins if they have the same counts of vertices by out-degrees. The likely maximum size of twins in a uniformly random, rooted Cayley tree of size n → ∞ is studied. It is shown that the expected number of twins of √ size (2 + δ) log n · log log n approaches zero, while the expected number √ of twins of size (2 − δ) log n · log log n approaches infinity. 

Reactis® is a suite of tools produced by Reactive Systems, Inc. (RSI), for automated test generation from, and verification of, sys- tems given in either the modeling languages MATLAB® / Simulink® / Stateflow® of The MathWorks, Inc., or ANSI C. RSI was founded by three of the authors of this paper in 1999, with the first release of Reactis coming in 2002; the tools are used in the testing and validation of embed- ded control systems in a variety of industries, including automotive and aerospace / defense. This paper traces the development of the Reactis tool suite from earlier research on model-checking tools undertaken by the authors and others, highlighting the importance of both the foun- dational basis of Reactis and the essential adaptations and extensions needed for a commercially successful product. 

We analyze non-perturbatively the one-dimensional Schrödinger equation describing the emission of electrons from a model metal surface by a classical oscillating electric field. Placing the metal in the half-space x 0, the Schrödinger equation of the system is i∂t ψ = − 2 1 ∂x 2 ψ + (x)(U − E x cos ωt)ψ, t > 0, x ∈ R, where (x) is the Heaviside function and U > 0 is the effective confining potential (we choose units so that m = e = = 1). The amplitude E of the external electric field and the frequency ω are arbitrary. We prove existence and uniqueness of classical solutions of the Schrödinger equation for general initial conditions ψ(x, 0) = f (x), x ∈ R. When 2the initial condition is in L the evolution is unitary and the wave function goes to zero at any fixed x as t → ∞. To show this we prove a RAGE type theorem and show that the discrete spectrum of the quasienergy operator is empty. To obtain positive electron current we consider non-L 2 initial conditions containing an incoming beam from the left. The beam is partially reflected and partially transmitted for all t > 0. For these initial conditions we show that the solution approaches in the large t limit a periodic state that satisfies an infinite set of equations formally derived, under the assumption that the solution is periodic by Faisal et al. (Phys Rev A 72:023412, 2005). Due to a number of pathological features of the Hamiltonian (among which unboundedness in the physical as well as the spatial Fourier domain) the existing methods to prove such results do not apply, and we introduce new, more general ones. The actual solution exhibits a very complex behavior, as seen both analytically and numerically. It shows a steep increase in the current as the frequency passes a threshold value ω = ωc , with ωc depending on the strength of the electric field. For small E, ωc represents the threshold in the classical photoelectric effect, as described by Einstein’s theory. 

In this work we study the problem of minimizing the round complexity for securely evaluating multiparty functionalities while making black-box use of polynomial time assumptions. In Eurocrypt 2016, Garg et al. showed that assuming all parties have access to a broadcast channel, then at least four rounds of communication are required to securely realize non-trivial functionalities in the plain model. A sequence of works follow-up the result of Garg et al. matching this lower bound under a variety of assumptions. Unfortunately, none of these works make black-box use of the underlying cryptographic primitives. In Crypto 2021, Ishai, Khurana, Sahai, and Srinivasan came closer to matching the four-round lower bound, obtaining a five-round protocol that makes black-box use of oblivious transfer and PKE with pseudorandom public keys. In this work, we show how to realize any input-less functionality (e.g., coin-tossing, generation of key-pairs, and so on) in four rounds while making black-box use of two-round oblivious transfer. As an additional result, we construct the first four-round MPC protocol for generic functionalities that makes black-box use of the underlying primitives, achieving security against non-aborting adversaries. Our protocols are based on a new primitive called list two-party computation. This primitive offers relaxed security compared to the standard notion of secure two-party computation. Despite this relaxation, we argue that this tool suffices for our applications. List two-party computation is of independent interest, as we argue it can also be used for the generation of setups, like oblivious transfer correlated randomness, in three rounds. Prior to our work, generating such a setup required at least four rounds of interactions or a trusted third party. 

Methyl salicylate is an important inter- and intra-plant signaling molecule, but is deemed undesirable by humans when it accumulates to high levels in ripe fruits. Balancing the tradeoff between consumer satisfaction and overall plant health is challenging as the mechanisms regulating volatile levels have not yet been fully elucidated. In this study, we investigated the accumulation of methyl salicylate in ripe fruits of tomatoes that belong to the red-fruited clade. We determine the genetic diversity and the interaction of four known loci controlling methyl salicylate levels in ripe fruits. In addition to Non-Smoky Glucosyl Transferase 1 (NSGT1), we uncovered extensive genome structural variation (SV) at the Methylesterase (MES) locus. This locus contains four tandemly duplicated Methylesterase genes and genome sequence investigations at the locus identified nine distinct haplotypes. Based on gene expression and results from biparental crosses, functional and non-functional haplotypes for MES were identified. The combination of the non-functional MES haplotype 2 and the non-functional NSGT1 haplotype IV or V in a GWAS panel showed high methyl salicylate levels in ripe fruits, particularly in accessions from Ecuador, demonstrating a strong interaction between these two loci and suggesting an ecological advantage. The genetic variation at the other two known loci, Salicylic Acid Methyl Transferase 1 (SAMT1) and tomato UDP Glycosyl Transferase 5 (SlUGT5), did not explain volatile variation in the red-fruited tomato germplasm, suggesting a minor role in methyl salicylate production in red-fruited tomato. Lastly, we found that most heirloom and modern tomato accessions carried a functional MES and a non-functional NSGT1 haplotype, ensuring acceptable levels of methyl salicylate in fruits. Yet, future selection of the functional NSGT1 allele could potentially improve flavor in the modern germplasm. 

Abstract Despite the increasing feasibility of sequencing whole genomes from diverse taxa, a persistent problem in phylogenomics is the selection of appropriate genetic markers or loci for a given taxonomic group or research question. In this review, we aim to streamline the decision-making process when selecting specific markers to use in phylogenomic studies by introducing commonly used types of genomic markers, their evolutionary characteristics, and their associated uses in phylogenomics. Specifically, we review the utilities of ultraconserved elements (including flanking regions), anchored hybrid enrichment loci, conserved nonexonic elements, untranslated regions, introns, exons, mitochondrial DNA, single nucleotide polymorphisms, and anonymous regions (nonspecific regions that are evenly or randomly distributed across the genome). These various genomic elements and regions differ in their substitution rates, likelihood of neutrality or of being strongly linked to loci under selection, and mode of inheritance, each of which are important considerations in phylogenomic reconstruction. These features may give each type of marker important advantages and disadvantages depending on the biological question, number of taxa sampled, evolutionary timescale, cost effectiveness, and analytical methods used. We provide a concise outline as a resource to efficiently consider key aspects of each type of genetic marker. There are many factors to consider when designing phylogenomic studies, and this review may serve as a primer when weighing options between multiple potential phylogenomic markers. 

Abstract College science programs exhibit high rates of student attrition, especially among Students of Color, women, members of the LGBTQ+ community, and those with disabilities. Many of the reasons students choose to leave or feel pushed out of science can be mitigated through participation in faculty-mentored research. However, faculty resources are limited, and not every student has access to faculty mentoring due to systemic or structural barriers. By bringing authentic scientific research into the classroom context, course-based undergraduate research experiences (CUREs) expand the number of students who participate in research and provide benefits similar to faculty-mentored research. Instructors also benefit from teaching CUREs. Using a systematic review of 14 manuscripts concerning the Malate Dehydrogenase CUREs Community (MCC) and malate dehydrogenase (MDH) CUREs, we demonstrate that CUREs can be implemented flexibly, are authentic research experiences, generate new scientific discoveries, and improve student outcomes. Additionally, CURE communities offer substantial advantages to faculty wishing to implement CUREs. 

This review discusses the intriguing yet controversial concept of metabolons, focusing on the malate dehydrogenase-citrate synthase (MDH-CISY) metabolon as a model. Metabolons are multienzyme complexes composed of enzymes that catalyze sequential reactions in metabolic pathways. Metabolons have been proposed to enhance metabolic pathway efficiency by facilitating substrate channeling. However, there is skepticism about the presence of metabolons and their functionality in physiological conditions in vivo. We address the skepticism by reviewing compelling evidence supporting the existence of the MDH-CISY metabolon and highlighting its potential functions in cellular metabolism. The electrostatic interaction between MDH and CISY and the intermediate oxaloacetate, channeled within the metabolon, has been demonstrated using various experimental techniques, including protein–protein interaction assays, isotope dilution studies, and enzyme coupling assays. Regardless of the wealth of in vitro evidence, further validation is required to elucidate the functionality of MDH-CISY metabolons in living systems using advanced structural and spatial analysis techniques.