Among the most important models for long-range dependent time series is the class of ARFIMA$(p,d,q)$ (Autoregressive Fractionally Integrated Moving Average) models. Estimating the long-range dependence parameter $d$ in ARFIMA models is a well-studied problem, but the literature regarding the estimation of $d$ in the presence of missing data is very sparse. There are two basic approaches to dealing with the problem: missing data can be imputed using some plausible method, and then the estimation can proceed as if no data were missing, or we can use a specially tailored methodology to estimate $d$ in the presence of missing data. In this work, we review some of the methods available for both approaches and compare them through a Monte Carlo simulation study. We present a comparison among 35 different setups to estimate $d$, under tenths of different scenarios, considering percentages of missing data ranging from as few as 10\% up to 70\% and several levels of dependence.

In this study, the global scientific workforce is explored through large-scale, generational, cross-sectional, and longitudinal approaches. We examine 4.3 million nonoccasional scientists from 38 OECD countries publishing in 1990-2021. Our interest is in the changing distribution of young male and female scientists over time across 16 STEMM (science, technology, engineering, mathematics, medicine) disciplines. We unpack the details of the changing scientific workforce using age groups. Some disciplines are already numerically dominated by women, and the change is fast in some and slow in other disciplines. In one-third of disciplines, there are already more youngest female than male scientists. Across all disciplines combined, the majority of women are young women. And more than half of women scientists (55.02%) are located in medicine. The usefulness of global bibliometric data sources in analyzing the scientific workforce along gender, age, discipline, and time is tested. Traditional aggregated data about scientists in general hide a nuanced picture of the changing gender dynamics within and across disciplines and age groups. The limitations of bibliometric datasets are explored, and global studies are compared with national-level studies. The methodological choices and their implications are shown, and new opportunities for how to study scientists globally are discussed.

We propose a methodology to estimate the market value of pharmaceutical drugs. Our approach combines the event study method with a discounted cash flow model that infers drug values from stock market responses to drug development announcements. We estimate the average value of a drug developed by small firms (those below the 95th percentile of market capitalization) to be \$2.16 billion. At the preclinical stage, the risk-adjusted and present discounted average net value of drugs is \$50 million. Leveraging these estimates, we also determine the expected drug development cost at the start of the discovery stage to be \$38 million. We estimate values and costs for several therapeutic areas (e.g., neoplasm, infections) and explore applying these estimates to design policies that support drug development through drug buyouts and targeted preclinical interventions.

The task of identifying resolving sets has been extensively studied due to its wide relevance in fields such as chemistry, robot navigation, combinatorial optimization, pattern recognition, and image processing. These applications have helped motivate and establish the theoretical foundations of the subject. Notably, problems of this type are generally known to be NP-hard. This study introduces an alternative structural representation for the crystal cubic carbon \( CCC(n) \). Building on this model, we determine the minimum sizes of both a doubly resolving set and a strong resolving set for $CCC(n)$.

We study actual bidding behavior when a new auction format gets introduced into the marketplace. More specifically, we investigate this question using a novel dataset on internet display advertising auctions that exploits a staggered adoption by different publishers (sellers) of first-price auctions (FPAs), instead of the traditional second-price auctions (SPAs). We analyze the auction format change using difference-in-differences regressions and a synthetic difference-in-differences estimator, which better handles pre-trends. The results show that revenue per sold impression (price) jumps considerably for treated publishers relative to control publishers, with increases ranging from 25% to 75% of the pre-treatment price level of the treated group. Moreover, for later auction format changes, the increase in price levels under FPAs relative to those under SPAs tends to dissipate over time, reminiscent of the revenue equivalence theorem, although the extent of this reversion depends on the specification. We view these results as suggestive of initially insufficient bid shading following the format change, as opposed to an immediate transition to a new Bayesian Nash equilibrium, with prices tending to decline in several specifications in a manner consistent with gradual adjustment in bidding behavior as bidders learn to shade their bids. Our work constitutes one of the first field studies on bidders'responses to auction format changes, providing an important complement to theoretical model predictions. As such, it provides valuable information to auction designers when considering the implementation of different formats.

In this article we prove a necessary and a sufficient condition for a finite subset of the special linear group to be dominated. These conditions are purely geometric in nature, as they only involve the trace and the eigenvectors of the matrices, and can be computed explicitly. Our sufficient condition, in particular, provides a simple algorithm for constructing a dominated set with prescribed eigenvectors. The techniques involved in our proofs take advantage of the interaction between dominated sets and two-dimensional hyperbolic geometry.

We study distributional learning of context-free languages under a fixed recognizable congruence $\sim_h$ given as the kernel of an explicit finite monoid homomorphism $h:Σ^*\to M$. For this fixed-$h$ setting, we develop a finite typed reconstruction theory for context-free $\sim_h$-substitutable languages. Starting from a reduced context-free grammar, we introduce a typed refinement that records both yield types and outer context types, show that the relevant structure is concentrated in a finite typed reconstruction basis, and prove that this basis is exposed by a finite observation set. Occurrences of the same nonterminal symbol may therefore have to be separated when their outer $h$-contexts differ. We then prove exact reconstruction from positive data. From any finite sample $K\subseteqΣ^*$, we construct a canonical hypothesis grammar $\hat G(K)$, and we show that once $K$ contains the finite observation set associated with the target typed grammar, $\hat G(K)$ generates the target language exactly. Consequently, for every explicit finite monoid homomorphism $h$, the class $\mathcal C_h^{\mathrm{cf}}$ of context-free $\sim_h$-substitutable languages is identifiable in the limit from positive data, with polynomial-time hypothesis construction and update. For the linear subclass $\mathcal C_h^{\mathrm{lin}}$, we further prove polynomial upper bounds on characteristic-sample size and word length. Thus the same learner gives a full polynomial time-and-data result for the linear subclass.