Potential reconstruction from general power spectrum in single-field inflation

We suggest a new method to reconstruct, within canonical single-field inflation, the inflaton potential directly from the primordial power spectrum which may deviate significantly from near scale-invariance. Our approach relies on a more generalized slow-roll approximation than the standard one, and can probe the properties of the inflaton potential reliably. We give a few examples for reconstructing potential and discuss the validity of our method.

Analysing intra-party power: Swedish selection committees over five decades

Unlike political parties in many other countries, Swedish ones have not adopted more inclusive methods for choosing their election candidates and party leaders. While the party congress formally selects important party offices, the process is managed, prior to the formal vote, by a selection committee vested with the task of filtering the pool of potential leaders and proposing one of them as the new leader. In this article, we survey the composition of these selection committees over time to investigate the extent to which change has taken place. Specifically, we investigate whether the composition of these powerful committees, which decide who joins the ranks of the country’s political leaders, has developed over time in relation to what prominent theories of intra-party power might lead us to expect. We derive testable expectations from prominent conceptualisations of intra-party power and apply these empirically. Specifically, we study the composition of party selection committees in Sweden over 50 years, 1969–2019. In total, this includes 40 different selection committees and almost 400 individuals. Contrary to conventional wisdom on intra-party power relations, the empirical analysis reveals a surprising degree of stability, raising questions about common claims of general power shifts within parties.

A Note on a Fourier Sine Transform

This is a compilation of definite integrals of the product of the hyperbolic cosecant function and polynomial raised to a general power. In this work, we used our contour integral method to derive a Fourier sine transform in terms of the Lerch function. Almost all Lerch functions have an asymmetrical zero-distribution. A summary table of the results are produced for easy reading. A vast majority of the results are new.

Identifying Communication Topologies on Twitter

Social networks are known for their decentralization and democracy. Each individual has a chance to participate and influence any discussion. Even with all the freedom, people’s behavior falls under patterns that are observed in numerous situations. In this paper, we propose a methodology that defines and searches for common communication patterns in topical networks on Twitter. We analyze clusters according to four traits: number of nodes the cluster has, their degree and betweenness centrality values, number of node types, and whether the cluster is open or closed. We find that cluster structures can be defined as (a) fixed, meaning that they are repeated across datasets/topics following uniform rules, or (b) variable if they follow an underlying rule regardless of their size. This approach allows us to classify 90% of all conversation clusters, with the number varying by topic. An increase in cluster size often results in difficulties finding topological shape rules; however, these types of clusters tend to exhibit rules regarding their node relationships in the form of centralization. Most individuals do not enter large-scale discussions on Twitter, meaning that the simplicity of communication clusters implies repetition. In general, power laws apply for the influencer connection distribution (degree centrality) even in topical networks.

The thermal feedback effects on the temperature evolution during reheating

The time dependence of the temperature during the reheating process is studied. We consider the thermal feedback effects of the produced particles on the effective dissipation rate of the inflaton field, which can lead to enhanced production of particles. We parameterize the temperature dependence of the dissipation rate in terms of a Taylor expansion containing the vacuum decay rate and the thermal terms. By solving the Boltzmann equations for the energy densities of the inflaton and radiation, we provide analytic estimates for a general power-law dependence on the temperature. In this way, we describe the entire reheating process. The maximum temperature of the reheating process and its dependence on model parameters are studied in different cases. The impact of the thermal feedback effects on the expansion history of the universe and the cosmic microwave background (CMB) is discussed. We also discuss the range of validity of our approach.

Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal Graphs

In this work, we introduce a new topological index called a general power sum-connectivity index and we discuss this graph invariant for some classes of extremal graphs. This index is defined by Y α G = ∑ u v ∈ E G d u d u + d v d v α , where d u and d v represent the degree of vertices u and v , respectively, and α ≥ 1 . A connected graph G is called a k -generalized quasi-tree if there exists a subset V k ⊂ V G of cardinality k such that the graph G − V k is a tree but for any subset V k − 1 ⊂ V G of cardinality k − 1 , the graph G − V k − 1 is not a tree. In this work, we find a sharp lower and some sharp upper bounds for this new sum-connectivity index.

Multi-spin soft bootstrap and scalar-vector Galileon

We use the amplitude soft bootstrap method to explore the space of effective field theories (EFT) of massless vectors and scalars. It is known that demanding vanishing soft limits fixes uniquely a special class of EFTs: non-linear sigma model, scalar Galileon and Born-Infeld theories. Based on the amplitudes analysis, we conjecture no-go theorems for higher-derivative vector theories and theories with coupled vectors and scalars. We then allow for more general soft theorems where the non-trivial part of the soft limit of the (n+1)-pt amplitude is equal to a linear combination of n-pt amplitudes. We derive the form of these soft theorems for general power-counting and spins of particles and use it as an input into the soft bootstrap method in the case of Galileon power-counting and coupled scalar-vector theories. We show that this unifies the description of existing Galileon theories and leads us to the discovery of a new exceptional theory: Special scalar-vector Galileon.

Reduction of one-loop integrals with higher poles by unitarity cut method

Unitarity cut method has been proved to be very useful in the computation of one-loop integrals. In this paper, we generalize the method to the situation where the powers of propagators in the denominator are larger than one in general. We show how to use the trick of differentiation over masses to translate the problem to the integrals where all powers are just one. Then by using the unitarity cut method, we can find the wanted reduction coefficients of all basis except the tadpole. Using this method, we calculate the reduction of scalar bubble, scalar triangle, scalar box and scalar pentagon with general power of propagators.

Introducing pre-impact air-cushioning effects into the Wagner model of impact theory

In this analysis, we consider the effects of non-quiescent initial conditions driven by pre-impact air–water interactions on the classical Wagner model of impact theory. We consider the problem of a rigid, solid impactor moving vertically towards a liquid pool. Prior to impact, viscous forces in the air act to deform the liquid free surface, inducing a flow in the pool. These interactions are then incorporated as initial conditions in the post-impact analysis. We derive expressions for the size of the effective contact set, the leading-order pressure and force on the impactor, and the speed and thickness of the jet at its base. In all cases, we show that the effect of the pre-impact behaviour is to cushion the impactor, reducing the size of the effective contact set and, hence, the force on the impactor. Small- and large-time asymptotic solutions are derived for general power-law impactors, and we show that the effects of the air die away as the impact progresses, so that we approach the classical Wagner solution.