dataesr/scientific-paragraphs-categorization huggingface dataset:
| DATA AND METHODOLOGY In order to track the collaborations between co-inventor physicians and firms in the medical device industry, and to assess their quality, we focus on publicly traded medical device companies operating in the United States and collect their innovation and financial data from 2005-5 years before the approval of the Sunshine Act, and about 10 years before its implementation-through 2018. Using the Compustat Global database, we first select publicly traded companies that have R&D expenditure data for at least two continuous years. We include multinational firms that manufacture or sell medical devices in the American market, even though they are not based in the United States. 7  There are several reasons why we only focus on publicly traded companies. First, although some non-listed firms (especially small start-ups) have made nontrivial contributions to medical device innovation, publicly-traded firms still dominate the market in terms of employment and assets.
Gravelle and Lowry (2016)  show that 82% of assets are owned by 1% of firms in this industry. Second, by selecting publicly traded firms, we can easily collect data on a range of firm-level variables. In particular, we can easily gather firm financial data such as annual R&D expenditure, revenues, number of employees, and market value from the Compustat dataset. All data have been adjusted for inflation using the GDP deflator for the country in which the firm was based. We use market exchange rates to convert financial data reported by multinationals in a foreign currency into US dollars. We measure collaborations between firms and physicians related to medical device technologies using patent data, collected from the Patent Examination Research Dataset (PatEx). The PatEx dataset contains all published patent applications filed at USPTO, along with their initial US patent classes.
The omission of patent applications awaiting grant decisions will lead to an underestimate of patent counts in the final years, which is avoided by using patent applications. To match the publicly traded companies with patent assignees, we first use the crosswalk file provided by Bessen (2009), which links assignee identification from the NBER patent data set with the gvkey number, the unique firm identifier from Compustat. This crosswalk file reflects ownership changes via mergers, acquisitions, or spin-offs. However, Bessen's list is not updated to 2018, the end year of our observation. For the rest of the unidentified medical device patents, we collect information on assignees from USPTO PatentView data and manually match them with a list of firm names which is obtained by standardizing the Compustat firm names and adding ownership changes using LexisNexis Corporate Affiliations.
This yields 49,288 medical device patent applications filed by 275 publicly traded firms to USPTO from 2005 to 2018. We match the inventors named in patents with a comprehensive physician list provided by the National Plan and Provider Enumeration System (NPPES) dataset in order to identify patents co-invented by firms and independent healthcare professionals. The NPPES data, available after 2004, provide full names, practice locations, medical specialties, and license number(s) for any physician with a National Provider Identifier, a unique identification number for licensed physicians in the United States. Compared with other databases used to identify physicians, the NPPES data covers more types of licensed healthcare providers, such as dentists and nurse practitioners, who are also important users of medical devices  (DesRoches et al.
Physicians with no or few academic publications have less to lose from these questions or concerns. In any given year, we measure physicians' reputations based on the cumulative number of publications (weighted by the impact factors of the journal in which the article was published) from 1990 until that year. There might be a relationship between collaborations with industry (affected by the Sunshine Act) and publications, as several studies are financed by private firms. Hence, to alleviate any endogeneity concern, after 2010 (including) our measure of reputation is time-invariant. We categorize physicians into two disjoint groups: "type-R physicians" are those with at least one publication, whereas "type-N physicians" are those who do not have any publications. 9  Publication data are retrieved from PubMed, which is a publicly available database maintained by the US National Library of Medicine, containing over 14 million articles from almost 5000 journals published in the United States and more than 70 other countries from 1950 to the present.
We gathered these data using PubHarvester, an open-source software tool  (Azoulay et al. , 2017). To assess the effect of the Sunshine Act on sellers and buyers, we use two datasets. The first dataset is a balanced panel of 3712 physicians with data on their basic demography and copatenting from 2005 to 2018. We use this dataset for testing the prediction states that the effect of an improvement in the information environment on the number of collaborations undertaken by type-R versus type-N physicians. Panel A of Table  1  shows the summary statistics of our major dependent variables. The second dataset comprises 3050 observations at the firmpatent type (co-invented vs. in-house)-year level. We utilize this dataset to assess the connection between advancements in the information environment and alterations in the overall quantity and quality of research collaboration output.
This might be due to some sort of anticipation effect, related to the timing of the Sunshine Act discussion and enactment. This Act was first proposed in 2007 by two US senators Charles Grassley, a Republican Senator from Iowa, and Herb Kohl, a democratic senator from Wisconsin. The act was "so named because it aims to shine a much-needed ray of sunlight on a situation that contributes to the exorbitant cost of health care," according to cosponsor Senator Charles Schumer"  (Campbell, 2007). Although an anticipation effect cannot be completely ruled out, our findings support our theory that it is primarily after the passage of the Sunshine Act in 2010 that type-R physicians begin to withdraw from collaborations. This behavior may be attributed to their desire to avoid damaging their reputation if their identity and compensation are disclosed in the federal database.
ACKNOWLEDGMENTS We thank the Editor,  Brian Silverman , and two anonymous reviewers for their precious help and guidance. We also thank participants at the Strategic Management Society annual conference (Toronto, 2021), AOM annual conferences (2021, 2022), Wharton Technology and Innovation Conference 2021, and seminar at the  HKUST  for comments on earlier drafts. Raffaele Conti  acknowledges financial support from  CY Initiative. Huiyan Zhang  acknowledges the generous financial support from  Fundação para a Ciência e a Tecnologia  ( SFRH/BD/127987/2016 ,  COVID/BD/151593/2021 ) and  Nagin Fellowship  of the year 2022.
Our framework is parameterized, allowing for different behaviors depending on the specific use case. We provide a broader scope of application to the methods encompassed by our approach, augmenting them with a larger theoretical and algorithmic structure. We establish an axiomatic study to better understand each method within our framework and present an algorithmic approach that includes exact methods, partitioning algorithms, and heuristics. Finally, we demonstrate the practical relevance of our approach through an empirical study on both real and synthetic datasets. Notably, the synthetic datasets are generated based on devised real-world scenarios, highlighting the context-dependent applicability of different Kemeny-based rank aggregation methods within our framework.
Introduction The problem of rank aggregation, where multiple rankings are aggregated into one consensus ranking, is studied and applied in various communities: in social choice theory  [1, 2] , within computer science as in algorithmics  [3] , databases  [4] [5] [6] , artificial intelligence  [7, 8] , but also in application domains such as physics  [9]  and biology  [10] [11] [12]. A substantial part of literature has focused on the aggregation of complete rankings without ties (i. e. , linear orderings, a. k. a permutations)  [13, 14, 3, 15, 7, [16] [17] [18] [19] [20]. In this context, the Kemeny rule consists in computing a Kemeny consensus, i. e. , a ranking that is as "close" as possible to the input rankings using the Kendall-τ distance. This problem is NP-hard in most cases  [21, 22, 18].
Rather than introducing yet another rank aggregation function, our aim is to establish a context-flexible framework capable of aggregating incomplete rankings with ties within a Kemeny paradigm. More precisely, our contributions are the following ones: • a unifying framework for aggregation of incomplete rankings with ties subsuming a variety of generalizations of the Kemeny score and enabling the conception of new methods on demand; Our framework is parameterized to allow different kinds of behaviors depending on the use cases (signification of non-ranked elements, etc. ) • a formal analysis of the framework, establishing links with the social choice theory, and between the parameters of the framework and some qualitative features of the datasets; • an algorithmic setting composed of an efficient Integer Linear Programming (ILP) exact algorithm, a set of partitioning properties and several heuristics; • a series of experiments to assess the practical applicability and effectiveness of the framework on both real and synthetic datasets with the latter being generated based on real-world use case scenarios.
The remainder of this paper is organized as follows. Section 2 focuses on related work. Section 3 provides the definitions of the major concepts underlying rank aggregation. Section 4 introduces a new unifying framework to handle incomplete rankings with ties. Section 5 performs a formal study of this framework. Section 6 introduces the algorithmic setting. Section 7 evaluates our framework on a very large number of datasets. Section 8 further discusses these results, establishes a user guide for rank aggregation of incomplete rankings with ties and outlines perspectives for future work. The complete version of the exact algorithm and the technical proofs of our results are given in the appendices.
for complete rankings with ties  [34]. The generalized induced Kendall-τ distance with penalty parameter p and the extended Kendall-τ distance do not penalize non-ranked elements whereas the pseudometric with penalty parameter p penalizes non-ranked elements towards ranked elements in a given ranking. Difference between methods to aggregate incomplete rankings. Table  1  highlights the differences between the methods of this group. More precisely, the penalty for placing A before H , H before A, B before C , F before H in the consensus ranking regarding the input ranking r 1 of Example 1 is given for each method. Table  1  highlights the huge variety of penalties from a method to another. More importantly, there is a lack of solutions provided when dealing with the large majority of real datasets which are incomplete.
For example, it makes sense to extend Borda to fit with the generalization of Kemeny presented in  [21]  by associating to each element its mean position on the rankings where it is ranked (in  [21] , non-ranked elements are not penalized). The elements are then sorted by increasing score. MedRank can also be extended to handle  [21]. The framework presented in Section 4 and the algorithms presented in this section, including the exact algorithm, have been implemented within a Python packaged named corankco available at https://pypi. org /project /corankco/.
Experiments We present three series of experiments in this section. First, we provide an evaluation of the scalability of our exact algorithm and the benefits of Proposition 2 and Theorem 4 to reduce the computation time of the exact algorithm (Subsection 7. 2). Second, we highlight links between the values of the penalty vectors of our model and the ability to partition the initial problem into smaller independent sub-problems using Theorem 4 (Subsection 7. 3). Finally, in Subsection 7. 4, we present experiments which underline the importance of correctly setting parameters to interpret non-ranked elements. We consider two datasets where non-ranked elements should be interpreted as either irrelevant or not fairly comparable to ranked elements. Without loss of generality (cf. subsection 5.
Setting and datasets Setting. Experiments were conducted on a four dual-core processor Intel Core 2. 9 GHz with 32 GB memory desktop using python 3. 8. The source code for the experiments is hosted in a separate project, distinct from the main Corankco Python package. This project can be accessed at https://github. com /pierreandrieu /experiments -corankco. It includes the datasets, a Dockerfile, and a readme file for reproducing the experiments. Datasets. Two datasets have been used for these experiments. The biological dataset consists of disease names and for each disease name, a tuple of rankings of genes obtained by querying the database Gene  [54]  using different formulations (synonyms) of the disease name. Based of the work of  [55] , we considered a total of 1,968 diseases (that is, 1,968 tuples of rankings).
The rankings are (naturally) incomplete and without ties. The number of rankings in each tuple of rankings varies from 3 to 63 with a mean of 10. 9 rankings, and the number of elements (genes) in each tuple of rankings varies from 30 to 1,121 with a mean of 215. 3 genes. (See Table  5. ) The student dataset is a generated dataset inspired by a real use case involving Master students. We consider here 100 groups of 300 students. A list of 17 teaching units are proposed to each group of students. Depending on the track they are registered on, they should validate a number of units: 280 students registered to track A have to validate 14 units (out of 17) while 20 students registered to track B have to validate 9 units (out of the same list of 17 units). Students registration to units have been uniformly generated and grades have been obtained following two normal laws N (μ, σ 2 ) (one for each track) described here-after: (i) N  (10, 25)  for the 280 students of track A; (ii) N  (16, 16)  for the 20 students of track B.
Grades higher than 20 (resp. smaller than 0) are set to 20 (resp. 0). By ranking the students according to their grade in each unit, this dataset can be seen as 100 tuples of 17 rankings over the 300 students. The rankings are incomplete as all the students are not involved in all the units and the rankings contain ties as students who have the same grade for a unit (rounded to one digit after the point) are considered as tied.
Scalability of the exact algorithm In this subsection, we focus on the number of elements to rank since it is the parameter which induces the exponential complexity in the Kemeny framework. Classically, exact algorithms can barely handle datasets containing more than a few dozens of elements to rank  [23, 45]. Interestingly, an ILP and a Branch and Bound algorithm have been recently introduced  [20]  allowing to rank until one hundred of elements, but only for complete rankings without ties. Our implementation  employs the well-regarded optimization solver, IBM ILOG CPLEX Optimization Studio (v. 20. 10)  [56] , recognized for its performance in optimization problems. This can potentially provide us with a competitive edge in achieving superior results compared to other studies, such as the matrix-based approach outlined in  [57].
While this latter method is constrained, capable of handling only up to 17 elements within an hour, it nonetheless has the benefit of being self-contained. We evaluate the scalability of our exact algorithm by considering the exact algorithm without optimization (EA) presented in Subsection 6. 1, the optimization offered by Proposition 2 (we call the corresponding algorithm EA-optim1) and by Theorem 4 (EA-optim2). We use a subset of the biological dataset: we consider the diseases for which the total number of genes in rankings range from 30 to 119. We compute a consensus ranking for each disease name and its synonyms, using the four generalizations of the Kemeny score in the literature able to handle incomplete rankings, namely UKSP, GPDP, EKS, IGKS (see Table  3  p. 8). We ignored IKS as IGKS is a generalization of IKS for rankings with ties.
We set p = 1 (see Table  3 ) to avoid creating artificial ties in the consensus (as there are no ties in the biological dataset). Results. Fig. 1  shows that the penalty vectors have no effect on the computation time of EA (without optimization). Moreover, Proposition 2 (EA-optim1) allows to reduce by half the computation time of EA in a very regular way for the first three KCFs and has almost no effect on average on the fourth KCF. We can see that optim1-optim2 (the combination of Proposition 2 and Theorem 4) is strongly efficient on the first three KCFs since it divides the computation time of the EA by approximately 100 on the smallest datasets  (30-49 elements)  and by approximately 20 on the larger datasets (50-119). Finally, optim1-optim2 is also quite efficient on the fourth KCF as it reduces the computation time in a regular way by 1.
5. Note that even if Proposition 2 appears less efficient than Theorem 4, both are useful as several datasets can only benefit from Proposition 2 (they have only one strongly connected components in the sense of Theorem 4). We now consider a second experiment where we measure the computation time of EA in its fully optimized version on the biological dataset (that is, we consider EA-optim1-optim2) with the four same KCFs, considering the diseases for which the total number of genes in the rankings is more than 130. For each dozen of number of elements (130-139, etc. ) if all the corresponding disease have a computation time < 600 s, we try the following range, otherwise we stop the experiment for this KCF. 3  p. 8).
Impact of penalty vector T. As discussed around Proposition 8, having low values for T compared to B reduces the chance to get many sub-problem. Here, for a given tuple of rankings and a given KCF, we focus when T decreases on the size of the largest SCC (strongly connected component) i. e. the size of the biggest sub-problem to resolve. The lower this number, the easiest the computation of a median. We fix B = (0, 1, 1, 0, 1, 0) as in GPDP and make T i vary from 0 to 1 by steps of 0. 25 for all i (except T 3 whose value is set to 0, as required by our model). We split the 1,968 biological datasets into four groups based on their size: less than 60 elements (gr 1 ), between 60 and 99 elements (gr 2 ) between 100 and 299 elements (gr 3 ) and 300 elements or more (gr 4 ). For each value of T and each group, we compute the average size of the biggest SCC.
Results. Table Impact of B 6 -T 6. We now investigate the influence of B 6 -T 6 on the ability to partition. This value is especially important as it is related to the unification process very commonly used in the literature  [44, 15, 36]  to transform real (incomplete) datasets into complete(d) datasets by appending at the end of each incomplete ranking the non-ranked elements in a unifying bucket. Recall that B 6 (resp. T 6 ) is the penalty for placing x before y (resp. tying x and y) in a consensus for each input ranking such that x and y are both non-ranked. The value of B 6 -T 6 indicates how much the tied elements in the unifying bucket should really be considered as "strongly" tied. Note that B 6 is the only penalty that differs between GPDP, the KCF with the most efficient EA-optim1-optim2, and UKSP, the KCF with the least efficient EA-optim1-optim2 (see Table  3  and Figs.
Experiment 5: When non-ranked elements are less relevant than ranked ones in a given ranking For this experiment, we use the biological dataset. Recall that for each disease name, a consensus ranking of genes is computed based on several rankings of genes obtained by different formulations of queries on the database Gene  [54]. Here, we use a goldstandard (GS) where for each disease, a set of genes known to be involved with this disease are provided. Such a GS is given by the database Orphanet  [58]  and available for 125 diseases. We make B 5 vary from 0 to 2. For each obtained KCF and for k varying between 10 and 100, we evaluate the consensus ranking obtained on the 125 datasets by counting the number of genes from the GS retrieved in the top-k elements of the consensus. The sum of the size of the GS over the 125 diseases is 515 (occurrences of genes).
In particular, we have provided an exact algorithm able to manage big real dataset. Our framework has two vectors B and T of six real positive coefficients as parameters (see Table  2  p. 7) so that it can be well fitted to different use cases. We summarize below some restrictions and guidelines for the choice of parameter values. First of all, three restrictions have to be considered to stay within a Kemeny framework: B 1 = T 3 = 0, T 1 = T 2 and T 4 = T 5. We now discuss the suitable values for the parameters regarding four major questions: • Do we need to prevent ties (ex aequo elements) in the consensus provided? • How should we manage the ties? Are elements tied because they are indifferently before/after one another or rather because they are intrinsically linked to one another, and it would make no sense to dissociate them? • How should we manage non-ranked elements? Are non-ranked elements interpreted as data less relevant than ranked elements or rather data that are unknown/incomparable with ranked data? • Do we want to generate a consensus that respects 3 classical axioms related to the social choice? (namely, Majority-like axiom, Condorcet-like axiom, Smith-like axiom, see Theorem 3).
Our framework allows to make an informed choice of the method to aggregate real rankings according to the context, and to have available an exact algorithm (with optimization) and heuristics. Empirical results with real and synthetic datasets demonstrate that the framework is effective. Future work. Future works will be both theoretical and experimental. We aim to investigate further the complexity of the rank aggregation problem when consensus rankings may have ties, which remains an open problem since 2004 with the work of Fagin et al. We also plan to extend works about generation of complete rankings without ties to generate synthetic datasets of incomplete rankings with ties while controlling several parameters such as similarity and proportion of nonranked elements. Such datasets will be helpful to highlight correlations between these parameters and the importance of the parameters of our framework with respect to the consensus rankings.
Hardware / Software Configurations and Test Instances For this computational experiment, we use a subset of the set of symmetric instances for the TSP from TSPLIB  [19]. This subset includes 20 instances -gr24, fri26, bayg29, swiss42, att48, gr48, hk48, eil51, berlin52, brazil58, st70, eil76, pr76, rat99, kroA100, kroB100, kroC100, kroD100, kroE100 and rd100 -with the number of nodes ranging from 24 to 100. The instances whose names are bold have their edge weight functions modified to the euclidean distance (without rounding to integer values). All tests were run on a computer with an Intel ® Core TM i7-4790 CPU, 8GB of DDR3-1600 RAM running Windows 10 Pro, version 21H2, within which CPLEX 20. 1. 0 Concert Technology for C++ was used. All CPLEX parameters are set to their default values, with the exception of the time limit, which is set to one hour -if an instance is not solved within the time limit, an optimal value is not obtained.