dataesr/scientific-paragraphs-categorization huggingface dataset:
To confirm the accuracy of our 'diffuse + point + extended' model description, an initial binned likelihood analysis was performed over the entire dataset. Firstly, a likelihood analysis was performed with the normalisation of all sources within 15 • being left free to vary. Thereafter, a second likelihood fit was performed with all point sources with a test statistic 1 , TS, greater than 25 able to vary spectrally. Finally, all sources with T S < 1 were removed from our model, and all sources with a 3FGL T S var > 72. 44 were fitted again with the normalisation and spectral shape left free to vary. The Fermi science tool gttsmap was then used in conjunction with the final best-fit model from the three-step initial analysis, to construct a 17 • × 17 • TS map centred on Cen A. This TS map was used to identify additional sources of γ-rays that were not accounted for in our best-fit model.
As can be seen in Figure  1 , there are three > 5σ excesses in the TS map indicating three new point sources of γrays have been found in our dataset. These new point sources were accounted for by a power-law fixed at the (α J2000 ,β J2000 ) of the peak excess, and a final likelihood fit was performed with the normalisation and spectral index of the new point sources free to vary. Interestingly, we note that two of these point sources are located on the boundary of Cen A's lobes. Once the dataset was modelled correctly, a summedlikelihood analysis was used to study the spectrum of Cen A's core. The data were binned into ten logarithmically 1 The test statistic, TS, is defined as twice the difference between the log-likelihood of two different models, 2[logL -logL 0 ], where L and L 0 are defined as the likelihoods of individual model fits  [28].
Here we examine whether this prompt emission is sufficient to explain the anomalous spectral component between 2. 6 GeV and ∼ 5 TeV. Throughout this work, we have assumed the existence of a spike in the distribution of the DM-induced by the adiabatic growth of a supermassive black hole at the centre of the galaxy-with a power-law index of γ sp = 7/3. Such a spiky profile has been suggested in Ref. [21] , although it is very debated. Indeed, a plethora of astro- FIG. 4. A combined spectrum of our LAT analysis, shown with black circles, and the H. E. S. S. spectrum above Eγ = 250 GeV, taken from  [7] , shown in red. The broken power-law model, shown in blue, is preferred over the power law model, shown in red, with a significance > 5σ. The grey histogram, with the right hand y-axis, shows the TS value for each spectral bin for the LAT data points.
The bin with a TS< 25, is replaced with an upper limit at 95% confidence level. Note that the last upper limit is not shown since it overlaps in energy with the H. E. S. S. data points. The broken power law fit allows for a smooth transition with the γ-ray spectrum reported here and the H. E. S. S. spectrum. physical phenomena could lead to a much shallower profile, such as non-adiabatic BH growth (as expected if the BH seed was brought in by a merger)  [20, 42]  or an offcenter position of the central BH, while others may have the opposite effect of making the formation or survival of spikes more likely, such as for instance enhanced accretion of DM to counteract the depopulation of chaotic orbits in a triaxial DM halo  [29]. It is also important to remember that even if a spike could form, the process of dynamical relaxation by DM scattering off stars could smooth down the spike and lead to a DM halo profile of the form ρ ∝ r -3/2 instead  [20, 29].
CLINICAL RESEARCH Other Data Collection Trained staff administered standardized questionnaires and performed clinical examinations at baseline. Sociodemographic data, smoking status, and history of cardiovascular diseases (CVD) (coronary heart disease, myocardial infarction, heart failure, stroke, peripheral artery disease, artery surgery, or angioplasty) were recorded. Body mass index (BMI) was calculated and categorized (<25, 25À30, $30 kg/m 2 ). We used the World Health Organization's Anatomical Therapeutic chemical classification system to code drugs. All three centers collected blood at baseline. Hypercholesterolemia was defined as use of statins or fasting serum cholesterol of $6. 2 mmol/l. Diabetes was defined as the current use of antidiabetic drugs and/or fasting serum glucose of $7.
Of note, we used the MDRD equation with which eGFR was normally distributed, in contrast to the CKD-EPI equation in this elderly population. Previous analyses showed that both equations provided similar prevalence estimates of CKD  8  and similar hazard ratios of all-cause and cardiovascular mortality associated with CKD. 30  Our study also has limitations. First, we included only elderly participants, precluding extrapolation to other age groups. Second, as treatment adherence and ambulatory BP data were not available, true treatmentresistant hypertension may have been misclassified with pseudo-resistance in a number of cases. Third, albuminuria was not available at baseline and therefore could not be adjusted for in the multivariable analyses or used in the definition of CKD. Fourth, we may have lacked statistical power in some of the associations studied, particularly for stroke events.
ACKNOWLEDGMENTS The  Three-City Study  is conducted under a partnership agreement between the  Institut National de la Santé and la Recherche Médicale (INSERM) , the  Victor Segalen Bordeaux II University, and Sanofi-Aventis. The  Fondation pour la Recherche Médicale  funded the preparation and initiation of the study. The  Fondation Plan Alzheimer  partly funded the follow-up of the study. The 3C Study is also supported by the  Caisse Nationale Maladie des Travailleurs Salariés ,  Direction Générale de la Santé ,  MGEN, Institut de la Longévité, Conseils Régionaux of Aquitaine and Bourgogne ,  Fondation de France , and  Ministry of Research-INSERM Programme "Cohortes et collections de données biologiques ". The study also received a grant from the  Agence Nationale de la Recherche (ANR). The CKD ancillary study at the 4-year follow-up was funded by the  French-speaking Society of Nephrology.
Whereas purest strategic games such as Go and Chess seem timeless, the lifetime of a video game is short, influenced by popular culture, trends, boredom and technological innovations. Even the important budget and developments allocated by editors cannot guarantee a timeless success. Instead, novelties and corrections are proposed to extend an inevitably bounded lifetime. Novelties can unexpectedly break the balance of a game, as players can discover unbalanced strategies that developers did not take into account. In the new context of electronic sports, an important challenge is to be able to detect game balance issues. In this article, we consider real time strategy games (RTS) and present an efficient pattern mining algorithm as a basic tool for game balance designers that enables one to search for unbalanced strategies in historical data through a Knowledge Discovery in Databases process (KDD).
In the first case, we show how existing pattern mining methods enable with slight modifications to discover frequent strategies and compute a balance measure. In the second case, the most general, existing approaches fail: we propose an original algorithm, BALANCESPAN. • (ii) We show through experiments that BALANCESPAN is scalable and able to discover patterns of interest in a large StarCraft II dataset that can help detecting balance issues. For that matter, we anchor our algorithm in a Knowledge Discovery in Databases process  [8]. Pattern mining is one of the many steps of this interactive and iterative process guided by an expert of the data domain who selects and interprets the patterns  [9] ,  [10]. The paper is organized as follows. Section II recalls the basics of sequential pattern mining before the introduction of our mining problem in Section III.
II. PRELIMINARIES We recall the basic definitions of frequent sequential patterns  [11]  and emerging patterns  [12]  useful in the sequel. Let I be a finite set of items. Any non-empty subset X ✓ I is called an itemset. A sequence s = hX 1 ,. , X l i is an ordered list of l > 0 itemsets. l is the length of the sequence, whereas P l i=1 |X i | is its size. Considering I as a set of events (or actions), an itemset denotes simultaneous events while the order between two itemsets indicates a strict preceding relation. A sequence database D is a set of |D| sequences over I. Sequences may have different lengths and sizes and are uniquely identified, see Table  I  (omitting the third column).
Definition (subsequence). A sequence s = hX 1 ,. , X ls i is a subsequence of a sequence s 0 = hX 0 1 ,. , X 0 l 0 s i, denoted s v s 0 , if there exists 1  j 1 < j 2 <. < j ls  l 0 s such that X 1 ✓ X 0 j1 , X 2 ✓ X 0 j2 ,. , X ls ✓ X 0 j ls. Definition (Support and frequency) The support of a sequence s in a database D is sup(s, D) = {s 0 2 D | s v s 0 }. Its frequency is freq(s, D) = |sup(s, D)|/|D|. Problem (Frequent sequential pattern mining). Given a minimal frequency threshold 0 <  1, the problem is to find all sequences s such as freq(s, D). In some cases, each sequence of D is associated to a class label. Let class : D ! {+, } a mapping that associates to each sequence a positive or negative label (hence two classes). D is accordingly partitioned into two databases, with the positive (resp.
negative) sequences D + (resp. D ) and D = D + [ D , D + \ D = ;. The growth-rate characterizes the discriminating power of a pattern for one class  [12] ,  [13]. Definition (Growth-rate). Given a sequence database D = D + [ D , the growth-rate of a sequential pattern from D x to D y (x 6 = y and x, y 2 {+, }), is given by  c, d, e, f , g} be the sequence database given in Table  I. For brevity, we drop commas and braces for singletons. For a given sequence s = habci, we have growth rate(s, D x , D y ) = |sup(s, D x )| |D x | ⇥ |D y | |sup(s, D y )| Example. Let D = {s 1 , s 2 , s 3 , s 4 } with I = {a, b, s v s 1 , s v s 4 , s 6 v s 2 , s 6 v s 3. With = 3 4 , hacci is frequent, ha{bc}ai is not. We have growth rate(hcbi, D , D + ) = 2 2 ⇥ 2 1 = 2, i. e. , hcbi is twice more present in class than in class +.
III. THE PROBLEM OF STRATEGY ELICITATION A zero-sum game, or competitive interaction, can be modeled as a sequence of actions performed by two players where exactly one player wins (no ties). Such a sequential game can be represented as a sequence of sets of actions, each action performed by one of the two players. When both players play in real-time, one can describe these interactions as sequences of itemsets. An itemset is then a set of simultaneous actions, or within an insignificant interval of time. Definition (Interaction (sequence) database). Given a set of players P layers and a set of actions Actions, a sequence database R is called an interaction database. Each sequence denotes one single game, i. e. , an interaction between two players, and is defined over the set of items I = Actions ⇥ P layers.
A mapping class : R ! P layers gives the winner of each interaction. Example. In Table  II , s 1 can be interpreted as: "Player p 1 did action a, then he did b and c while player p 2 did c, and finally p 1 did d while p 2 did a. At the end, the player p 1 wins". Given an interaction database, the problem is to find sequences of actions of both interacting players (supposing that those actions are mutually dependent) as generalizations that appear frequently and to be able to characterize their discriminating ability for a win or loss through a so-called balance measure. In the current sequential pattern mining settings, the goal is to find frequent sub-sequences of actions (i. e. , strategies) and their balance (a growth-rate like measure). However, the notion of class has to be revisited to be able to handle winner and loser class labels, instead of the winning player.
Indeed, intuitively, mining emerging patterns from an interaction database with the winning players as classes (as given in Table  II ) does not fulfill our objectives: we wish to discriminate victories and not victorious players themselves. As such, existing emerging sequential pattern mining methods and algorithms cannot be used to answer our problem. We propose to differentiate two cases of interaction databases: (i) non-mirror interaction databases where both players have different (non-intersecting) sets of available actions; (ii) mirror interaction databases where both players can perform the same actions. We show that in the first case, emerging patterns as introduced in the literature (Section II) are able to answer the problem by slightly modifying the interaction database representation.
In the second case, the most general one, we need new settings, and we propose to embed the class (positive or negative) in the definition of the items of a sequence, see Table  IV. This is formalized in the two next sections, and it enables the design of efficient pattern mining algorithms in Section VI. s 1 h(p 1 , a){(p 1 , b)(p 1 , c)(p 2 , c)}{(p 2 , a)(p 1 , d)}i p 1 s 2 h(p 3 , a){(p 3 , b)(p 3 , c)(p 3 , d)}{(p 1 , b)(p 1 , c)}i p 3 IV. BALANCED PATTERNS IN NON-MIRROR DATABASES In this section, we consider an interaction database, called a non-mirror database, where the set of actions is different for each of the players in a single interaction. It means that we only have two types of players in each sequence and in the whole database (e. g. , Protoss and Zerg factions in the RTS game StarCraft II), and these types are determined by the actions they can do.
As such, the type can also be used as a winning class label. To characterize balanced patterns in such databases, we consider a simple transformation of the original interaction database R by dropping the player associated to each action, and labeling each sequence by the type of the winner. This enables to express a balance measure as a growthrate measure in this new data representation. The transformed database is then formally defined as follows. Definition (Transformed interaction database). A sequence database T defined over the set of items (actions) I 1 [ I 2 such as I 1 \ I 2 = ; and class : T ! {I 1 , I 2 } is called a transformed interaction database. Consider an interaction s 2 T where the winner is characterized by the actions I 1 : we have class(s) = I 1 that gives the winner of the interaction.
This brings back the problem of finding frequent balanced interaction patterns to well-known the emerging patterns settings. Indeed, consider an arbitrary pattern s over I 1 [ I 2 : its support in the whole database sup(s,T ) tells us its frequency, while sup(s,T I1 ) and sup(s,T I2 ) enable to define a balance measure as a growth-rate. Problem (Mining balanced patterns from non-mirrors interactions). Let T be a transformed database obtained from a non-mirror interaction database R. T is defined over I 1 [I 2 where I k represents the type k of player (k 2 {1, 2}) and class : T ! {I 1 , I 2 } assigns to any sequence its winner type. is a minimum frequency threshold. The problem is to extract the set of so-called frequent balanced patterns F t such as for any s 2 F t , freq(s,T I1 ) and freq(s,T I2 ) (implying freq(s,T ) ) and the balance measure is computed and given by: balance(s, T k ) = |sup(s, T k )| |sup(s, T 1 )| + |sup(s, T 2 )| Remark.
The balance measure is a normalized version of the growth rate given in previous section such that balance(. ) 2 ]0, 1] and balance(s, T 1 ) + balance(s, T 2 ) = 1 which entails a zero-sum game property. Example. Table  III  gives a transformed interaction database T , obtained from a non-mirror interaction database R, with I 1 = {a, b} and I 2 = {c} being the sets of actions of each player type. With = 0. 2, s = h{ab}{c}i is a frequent balanced pattern since freq(s, T I1 ) = 2  3 and freq(s, T I2 ) = 1 2. Moreover, balance(s, T I1 ) = 2  3 and balance(s, T I2 ) = 1 3. It means that s wins two times more for the type 1 of player than for the type 2. s 1 h{ab}{c}i I 1 s 2 h{ab}{a}{c}i I 1 s 3 h{abc}{c}i I 2 s 4 h{ac}{a}{c}i I 1 s 5 h{c}{b}{ac}i I 2 TABLE IV A SIGNED INTERACTION DATABASE. id s 2 S s 1 ha + {b + c }i s 2 ha + {b + c }c + i s 3 hd + {b + c + }d i s 4 ha {b + c + }i V.
Definition (Signed interaction database). Recall that Actions is a finite set of actions shared by both players. We introduce I s = Actions ⇥ {+, } denoting actions associated either to a positive or negative class. A signed database S is built from an interaction database R as follows: Each action of an interaction sequence is signed + if it is performed by the winner and signed if performed by the loser (both players and class labels are dropped). Definition (Dual of an item, itemset and sequence). Let I s = Actions ⇥ {+, } be the set of signed items, or actions. For any (a, c) 2 I s , also written a c , we define its dual as dual(a, c) = dual(a c ) = (a, {+, }\c) = a {+, }\c Informally, it means that the dual of a signed action is the same action where the class c has changed. This definition is simply propagated for itemsets and sequences of itemsets, for any X ✓ I s and any s = hX 1 , X 2 ,.
i a sequence over I s : dual(X) = {dual(x), 8x 2 X} dual(s) = hdual(X 1 ), dual(X 2 ),. i Example. In Table  IV , we have I s = {a, b, c, d} ⇥ {+, }, dual(a + ) = a and dual(s 1 ) = ha {b c + }i. These definitions enable now to naturally introduce a balance measure that would, for a sequential pattern s give the proportion of its support among the support of both itself and its dual. Definition (Balance measure). Let s be a frequent sequential pattern in a database S. The balance measure of s is balance (s) = |sup(s, S)| |sup(s, S)| + |sup(dual(s), S)| (1) This intuitive definition however does not hold. Since actions are shared by the two players, both a sub-sequence and its dual may occur in a single sequence s 2 S. Consider the following example: S = {h{a + b }{a b + }i, h{a b + }i} with = 1 2.
Problem (Mining balanced patterns from signed interactions). Let S be a signed interaction database defined over I s generated from an interaction database R, and a minimum frequency threshold. The problem is to extract the set of socalled frequent balanced patterns F s such as for s 2 F s , freq(s, S) , freq(dual(s), S) and the balance measure is computed and given by (2). Furthermore, the fact that both s and dual(s) have to be frequent leads to redundant information: it is enough to keep s along with its support, balance measure and intersection of support common(s) = |sup(s, S) \ sup(dual(s, S))| to know the measures of its dual. As such, the problem is also to compute a non redundant collection of patterns F s where, if s 2 F s then dual(s) 6 2 F s. Example. Table  IV  gives a signed interaction database S obtained from an arbitrary R.
VI. ALGORITHMS We present several algorithms to extract frequent balanced patterns from interaction databases. We introduce first a wellknown framework for mining frequent sequential patterns, called PATTERN-GROWTH and its associated algorithm PRE-FIXSPAN  [11]. A. The PREFIXSPAN algorithm Given a sequence database D over items I and a minimum frequency threshold , PREFIXSPAN outputs all frequent sequential patterns and only them  [11]. Firstly, the database D is scanned once to find all the frequent items from I, called size-1 sequential patterns. Secondly, each of these prefixes is used to divide the search space: for one prefix, say hai (and a 2 I), one retains only sequences of D containing a and only keeps for each of these sequences the longest suffix starting by a. The set of the prefixes sequences of the remaining sequences is called a projected database w.
r. t. to prefix hai, written D |hai. Thirdly, this projected database is scanned to generate the size-2 sequential patterns having hai as prefix. The process is recursively applied leading to a tree structure where each node represents a frequent sequential pattern (associated with a projected database of a least d ⇥|D|e sequences) and an edge to an extension: the item added to a size-k sequential pattern to generate a size-(k +1) sequential pattern. For a prefix s and an item a, two kinds of extensions are considered: appending a as a new suffix itemset of s, noted s s a, and appending a within the last itemset of s, written s i a ( denotes an extension in general). At the end, the pattern tree structure is explored and each node outputs a pattern. Example. We briefly illustrate PREFIXSPAN on the toy example of the Table I with = 0.
5. A larger example is available in the original publication of PREFIXSPAN  [11] (|sup(haai, D |hai )| = 2), habi (|sup(habi, D |hai )| = 4), h(ab)i (|sup(h(ab)i, D |hai )| = 2), haci (|sup(haci, D |hai )| = 4), hadi (|sup(hadi, D |hai )| = 2) and haf i (|sup(haf i, D |hai )| = 2). Then for each of these sequential patterns of size 2 PREFIXSPAN creates the projected databases and extracts frequent patterns of size 3, and so on.
B. Mining Balanced Patterns with EMERGSPAN Given a sequential database over an arbitrary I, where each sequence is labeled by a class (among two classes) and a minimum frequency threshold, the general problem here is to find all frequent patterns, each one provided with its growth-rate. In our settings, this involves mining a non-mirror interaction database R as a transformed database T where sequences are composed of actions of both players and the class label gives the winner's type. The balance measure is then exactly the growth rate as defined in the general settings and can be computed in negligible time as a post-processing  [14]. Based on PREFIXSPAN, EMERGSPAN works as follows. For each sequence of the database T , its class is appended as a new itemset at its end. It ensures that frequent patterns containing a class label are leaves of the pattern tree, and that two sequential patterns that differ only by their classes have the same direct parent, allowing a direct computation of the balance measure.
Example. To illustrate how EMERGSPAN works, let us consider the previous example on the transformed interaction database T of Table  III. Remind that this database is obtained from a non-mirror interaction database R, with I 1 = {a, b} and I 2 = {c} being the sets of actions of each player type. Thus, we transformed each of these sequences by appending the item I 1 (resp. I 2 ) at the end if the player with actions in I 1 (resp. I 2 ) won. For example, s 2 becomes h{ab}acI 1 i. The exploration of EMERGSPAN works the same way as PREFIXS-PAN excepted that it only keeps patterns that end up with either I 1 or I 2. Thus, computing balance of pattern hX 1. X l I j i only requires to backtrack to the parent (i. e. , hX 1. X l i) to get its support to evaluate the balance. So, when EMERGSPAN deals with the sequential pattern s = h{ab}cI 1 i, since the last item of s is I 1 , it will output this pattern, and to compute its balance measure, it uses the support of its parent node s 0 = h{ab}ci: balance(s) = |sup(s,T )| |sup(s 0 ,T )| = 0.
67. C. Mining Balanced Patterns with PREFIXSPANNAIVE Now we consider a signed interaction database S over I s and a minimal frequency threshold. The problem is to extract the set of frequent sequential patterns and compute their balanced measure. We first use the original PREFIXSPAN algorithm to build the frequent pattern tree structure. We need for each pattern to (i) compute its balance, and (ii) to ensure that for a pattern and its dual only one of them is outputted. We then propose to store for each node (equivalently sequential pattern) a pointer to its dual pattern. At the first level of the tree, a node represents a single frequent item, and there is a pointer towards its dual (if both are frequent). Recursively, when an item is used to expand a sequential pattern p to obtain a pattern q, we compute the pointer towards dual(q) by searching among the children of dual(p).