Traditionally, studies in experimental physiology have been conducted in small groups of human participants, animal models or cell lines. Identifying optimal study designs that achieve sufficient power for drawing proper statistical inferences to detect group level effects with small sample sizes has been challenging. Moreover, average effects derived from traditional group-level inference do not necessarily apply to individual participants. Here, we introduce N-of-1 trials as an innovative study design that can be used to draw valid statistical inference about the effects of interventions on individual participants and can be aggregated across multiple study participants to provide population-level inferences more efficiently than standard group randomized trials. N-of-1 trials have been used in healthcare settings since the late 1980s, but without large-scale adoption and with few applications in experimental physiology research settings. In this manuscript, we introduce the key components and design features of N-of-1 trials, describe statistical analysis and interpretations of the results, and describe some available digital tools to facilitate their use using examples from experimental physiology.

Lightweight, single-use explosion containment structures provide an effective solution for neutralizing rogue explosives, combining affordability with ease of transport. This paper introduces a three-stage simulation framework that captures the distinct physical processes and time scales involved in detonation, shock propagation, and large, plastic structural deformations. The hypothesis is that as the structure becomes lighter and more flexible, its dynamic interaction with the gaseous explosion products becomes increasingly significant. Unlike previous studies that rely on empirical models to approximate pressure loads, this framework employs a partitioned procedure to couple a finite volume compressible fluid dynamics solver with a finite element structural dynamics solver. The level set and embedded boundary methods are utilized to track the fluid-fluid and fluid-structure interfaces. The interfacial mass, momentum, and energy fluxes are computed by locally constructing and solving one-dimensional bi-material Riemann problems. A case study is presented involving a thin-walled steel chamber subjected to an internal explosion of $250~\text{g}$ TNT. The result shows a $30\%$ increase in the chamber volume due to plastic deformation, with its strains remaining below the fracture limit. Although the incident shock pulse carries the highest pressure, the subsequent pulses from wave reflections also contribute significantly to structural deformation. The high energy and compressibility of the explosion products lead to highly nonlinear fluid dynamics, with shock speeds varying across both space and time. Comparisons with simpler simulation methods reveal that decoupling the fluid and structural dynamics overestimates the plastic strain by $43.75\%$, while modeling the fluid dynamics as a transient pressure load fitted to the first shock pulse underestimates the plastic strain by $31.25\%$.

This paper re-examines the limit theorems of Abadie and Imbens for nearest-neighbor matching estimators of average treatment effects with a fixed number of matches. We establish, for the first time, a non-normalized central limit theorem (CLT) with an explicitly calculated limiting variance. The key ingredients are to prove the convergence of the normalizing statistic appearing in the CLT of Abadie and Imbens to its mean, and to calculate the closed form of the limit of this mean. The former closes a gap in the argument of an unpublished work (Abadie and Imbens, 2002), while the latter resolves a question raised in Abadie and Imbens (2006).

We survey the role of Lie algebras in the study of unstable homotopy groups.

This paper develops an adaptive generic proximal bundle method, shows its complexity, and presents numerical experiments comparing this method with two bundle methods on a set of optimization problems.

We analyse a model that describes the propagation of many pathogens within and between many species. A branching process approximation is used to compute the probability of disease outbreaks. Special cases of aquatic environments with two host species and one or two pathogens are considered both analytically and computationally.

Using correct design metrics and understanding the limitations of the underlying technology is critical to developing effective scheduling algorithms. Unfortunately, existing scheduling techniques used \emph{incorrect} metrics and had \emph{unrealistic} assumptions for fair scheduling of multi-tenant FPGAs where each tenant is aimed to share approximately the same number of resources both spatially and temporally. This paper introduces an enhanced fair scheduling algorithm for multi-tenant FPGA use, addressing previous metric and assumption issues, with three specific improvements claimed First, our method ensures spatiotemporal fairness by considering both spatial and temporal aspects, addressing the limitation of prior work that assumed uniform task latency. Second, we incorporate energy considerations into fairness by adjusting scheduling intervals and accounting for energy overhead, thereby balancing energy efficiency with fairness. Third, we acknowledge overlooked aspects of FPGA multi-tenancy, including heterogeneous regions and the constraints on dynamically merging/splitting partially reconfigurable regions. We develop and evaluate our improved fair scheduling algorithm with these three enhancements. Inspired by the Greek goddess of law and personification of justice, we name our fair scheduling solution THEMIS: \underline{T}ime, \underline{H}eterogeneity, and \underline{E}nergy \underline{Mi}nded \underline{S}cheduling. We used the Xilinx Zedboard XC7Z020 to quantify our approach's savings. Compared to previous algorithms, our improved scheduling algorithm enhances fairness between 24.2--98.4\% and allows a trade-off between 55.3$\times$ in energy vs. 69.3$\times$ in fairness. The paper thus informs cloud providers about future scheduling optimizations for fairness with related challenges and opportunities.

In this study, we unveil an eccentric superradiance phenomenon in molecular aggregates coupled to surface plasmon polaritons. Through the quantization of electromagnetic fields in media, we demonstrate that superradiance can be significantly enhanced by polaritons and its behavior distinguishably surpasses the Dick's $N$ scaling law. To understand the mechanism of this anomalous phenomenon, we derive an analytical expression of the superradiance rate, which is general for molecular aggregates in arbitrary dispersive and absorbing media. Furthermore, we show the importance of intermolecular distance for this extraordinary superradiance.

Cavity quantum electrodynamics (CQED) and its extensions are widely used for the description of exciton-polariton systems. However, the exciton-polariton models based on CQED vary greatly within different contexts. One of the most significant discrepancies among these CQED models is whether one should include direct intermolecular interactions in the CQED Hamiltonian. To answer this question, in this article, we derive an effective dissipative CQED model including free-space dipole-dipole interactions (CQED-DDI) from a microscopic Hamiltonian based on macroscopic quantum electrodynamics. Dissipative CQED-DDI successfully captures the nature of vacuum fluctuations in dielectric media and separates it into the free-space effects and the dielectric-induced effects. The former include spontaneous emissions, dephasings and dipole-dipole interactions in free space; the latter include exciton-polariton interactions and photonic losses due to dielectric media. We apply dissipative CQED-DDI to investigate the exciton-polariton dynamics (the population dynamics of molecules above a plasmonic surface) and compare the results with those based on the methods proposed by several previous studies. We find that direct intermolecular interactions are a crucial element when employing CQED-like models to study exciton-polariton systems involving multiple molecules.

We propose an approach to estimate how individuals' expectations influence their responses to a counterfactual change. The approach relies on average partial effects, which recover counterfactual impacts under conditions that we specify. We propose a three-step estimation method that relies on panel data on subjective expectations. We illustrate our approach in a model of consumption and saving, focusing on the impact of an income tax that not only changes current income but also affects beliefs about future income. Applying our approach to Italian survey data, we find that individuals' beliefs matter for evaluating the impact of tax policies on consumption decisions.

We study the structure of the higher genus Gromov-Witten theory of the total space $K\mathbb{P}^{n-1}$ of the canonical bundle of the projective space $\mathbb{P}^{n-1}$. We prove the finite generation property for the Gromov-Witten potential of $K\mathbb{P}^{n-1}$ by working out the details of its cohomological field theory (CohFT). More precisely, we prove that the Gromov-Witten potential of $K\mathbb{P}^{n-1}$ lies in an explicit polynomial ring using the Givental-Teleman classification of the semisimple CohFTs. In arXiv:2301.08389, we carried out a parallel study for $[\mathbb{C}^n/\mathbb{Z}_n]$ and proved that the Gromov-Witten potential of $[\mathbb{C}^n/\mathbb{Z}_n]$ lies in a similar polynomial ring. The main result of this paper is a crepant resolution correspondence for higher genus Gromov-Witten theories of $K\mathbb{P}^{n-1}$ and $[\mathbb{C}^n/\mathbb{Z}_n]$, which is proved by establishing an isomorphism between the polynomial rings associated to $K\mathbb{P}^{n-1}$ and $[\mathbb{C}^n/\mathbb{Z}_n]$. This paper generalizes the works of Lho-Pandharipande arXiv:1804.03168 for the case of $[\mathbb{C}^3/\mathbb{Z}_3]$ and Lho arXiv:2211.15878 for the case $[\mathbb{C}^5/\mathbb{Z}_5]$ to arbitrary $n\geq 3$.

We prove holomorphic anomaly equations for $\mathbb{C}^5/\mathbb{Z}_5$.

We present a unified framework, with quantitative estimates, for deterministic interacting particle systems whose pairwise interactions may depend on heterogeneous labels. Heterogeneity is kept at every level by adding a frozen label variable $x\inΩ$ to the state. Within this framework we compare several limiting procedures: the direct continuum / graph limit, the mean field limit yielding a Vlasov equation on the extended space of labels and states, the Liouville lift of the particle system together with propagation of chaos through marginals of arbitrary order, and the hydrodynamic moment closures. We give a common language for these limits and identify precisely where the various passages commute and where they do not; in particular, we separate the continuum / graph limit equation from the classical hydrodynamic Euler equations and characterize when the former arises as a moment closure of the latter (linearity in $(ξ,ξ')$ or monokinetic ansatz). Along the way, we prove quantitative convergence estimates for the graph limit and for the passages from particles or Liouville to Vlasov, and we discuss the limitations of the framework, in particular concerning singular kernels and stochastic dynamics. The paper is written as a survey with original contributions, with an emphasis on estimates, examples, and a clear delineation of scope.

In the Labourie-Loftin parametrization of the Hitchin component of surface group representations into SL(3,R), we prove an asymptotic formula for holonomy along rays in terms of local invariants of the holomorphic differential defining that ray. Globally, we show that the corresponding family of equivariant harmonic maps to a symmetric space converge to a harmonic map into the asymptotic cone of that space. The geometry of the image may also be described by that differential: it is weakly convex and a (one-third) translation surface. We define a compactification of the Hitchin component in this setting for triangle groups that respects the parametrization by Hitchin differentials.

We construct solutions of Schrödinger equations which are asymptotically self-similar solutions as time goes to infinity. Also included are situations with two bubbles. These solutions are global, with non-zero $L^2$ norms, and are stable. As such they are not of the standard asymptotic decomposition of linear waves and localized waves. Such weakly localized solutions were expected in view of previous works \cite{Liu-Sof1,Liu-Sof2} on the large time behavior of general dispersive equations. It is shown that one can associate a \emph{scattering channel} to such solutions, with the dilation operator as the asymptotic ``Hamiltonian''.

We examine cosmological inflation in a broad family of scalar-tensor models characterized by scalar-dependent non minimal kinetic couplings and Gauss-Bonnet terms. Using a slow roll-approximation, we compute in detail theoretical expectations of observables as spectral indexes, scalar-to-tensor ratio, their running and their running of the running in terms of the parameters which characterize the scalar-tensor model. Hierarchies of consistency equations relating scalar and tensor pertubations and higher order running parameters are presented and examined at the slow roll approximation for the kind of models of interest in this work. From We find detailed expressions for constraints among these parameters. For a specific model, we analyse such quantities and make contact with latest Planck observational data .

In this paper, we present a relative proof for Goldbach's strong conjecture. To this end, we first present a heuristic model for representing even numbers called Semi-continuous Model for Even Numbers or briefly S.C.E Model, and then by using this model we categorize all even numbers into 75 distinct typical structures. Also in this direction, we employ this model along with the following inequality to obtain the relative proof \begin{equation} \frac{x}{\ln x} \leq_{x \geq 17} π(x) \leq_{x>1} 1.2251 \frac{x}{\ln x} \end{equation} where $π(x)$ denotes the number of all primes smaller than and equal to $x$. This inequality is presented by Pierre Dusart in his paper [P. Dusart, Explicit estimates of some functions over primes, Ramanujan J. 45 (2016), No. 1, 227-251]. In fact, by relative proof we mean that 74 typical structures out of 75 ones satisfy Goldbach's strong conjecture. Also, since the last typical structure is the dominant structure over all even numbers, we come up with three unproven inequalities for elements of S.C.E model using each of which, we can prove Goldbach's strong conjecture for this structure too. It is necessary to say that, we guess theses three inequalities can be proved the same as to Dusart's inequality.

Scattering diagrams arose in the context of mirror symmetry, but a special class of scattering diagrams (the cluster scattering diagrams) were recently developed to prove key structural results on cluster algebras. We use the connection to cluster algebras to calculate the function attached to the limiting wall of a rank-2 cluster scattering diagram of affine type. In the skew-symmetric rank-2 affine case, this recovers a formula due to Reineke. In the same case, we show that the generating function for signed Narayana numbers appears in a role analogous to a cluster variable. In acyclic finite type, we construct cluster scattering diagrams of acyclic finite type from Cambrian fans and sortable elements, with a simple direct proof.