dataesr/scientific-paragraphs-categorization huggingface dataset:
This follows from the fact that every query q expressible in RA + {∩, ∪} is monotonic, that is, q(D) ⊆ q(D ′ ) for all databases D and D ′ such that D ⊆ D ′. However, in RA + {-}, one can express queries that are not monotonic. Indeed, consider e = R -S We conclude this section by showing that adding duplicate elimination to a fragment that does not already have it increases its expressive power. Proposition 5. L ⊊ L{ε} for every fragment L of RA without duplicate elimination.
Corollary k ∩ = #(ā, e ∩ , D) = #(ā, e ′ 1 , D) ´(#(ā, e ′ 1 , D) ´#(ā, e ′ 2 , D) ) = m ´(m ´n) k ∪ = #(ā, e ∪ , D) = #(ā, e ′ 1 , D) + ( #(ā, e ′ 2 , D) ´#(ā, e ′ 1 , D) ) = m + (n ´m) If m ≥ n, we have that 0 ≤ m ´n = m -n ≤ m and n ´m = 0, therefore k ∩ = m -(m -n) = n and k ∪ = m. Otherwise, when n > m, we have that m ´n = 0 and n ´m = n -m, so k ∩ = m ´0 = m and k ∪ = m + n -m = n. Thus, k ∩ = min(m, n) and k ∪ = max(m, n). Now, since e ′ 1 ≡ The proof of Proposition 5 is based on the fact that, on databases with relations of even size, every RA + {-} expression can only yield a relation of even size, as the following lemma shows. Lemma 5. Let L be a fragment of bag relational algebra without duplicate elimination, let e be an RA + {-} expression, and let D be a database such that, for every relation name R, the number of occurrences of every tuple in R D is even.
Certain and possible answers under bag semantics Dealing with incomplete information is a recurring topic in many different areas of logic and computer science. In database theory, the main way to deal with the lack of information is via incomplete databases. Intuitively, an incomplete database D is a compact representation of a possibly infinite collection D of complete databases, which define the semantics of D. In this paper, we use incomplete databases with marked (or labeled) nulls. This model of incompleteness is very common in the database literature  [17, 18]  and naturally occurs in many different scenarios, e. g. , in data exchange and integration (cf. [24] [25] [26] ). In this model databases are populated by constants and nulls, coming from two disjoint and countably infinite sets denoted by ( c, R v(D) ) = ∑ ā:v(ā)=c # ( ā, R D ).
The set D is defined as D = {v(D) | v is a valuation}. When relations are sets, the standard way to answer a query q on an incomplete database D is to compute certain answers, i. e. , tuples that are in q(D ′ ) for every D ′ ∈ D , and possible answers, i. e. , tuples that are in q(D ′ ) for some D ′ ∈ D. When relations are bags, however, one must also take multiplicities into account. In what follows, this is done by computing the minimum and maximum number of occurrences of a tuple in the answers across all databases in D (cf. [21] ). Let D be a database, let q be a relational algebra expression of arity n, and let ā ∈ Const(D) n be a tuple of constants, we define min(ā, q, D) and max(ā, q, D) as follows: min(ā, q, D) = min D ′ ∈ D # ( ā, q(D ′ ) ) ; (1a) max(ā, q, D) = max D ′ ∈ D # ( ā, q(D ′ ) ).
(1b) Intuitively, min(ā, q, D) and max(ā, q, D) are extensions of certain and possible answers to bag databases. Indeed, min(ā, q, D) ≥ 1 if and only if ā is in q(D ′ ) for every D ′ ∈ D (and thus it is a certain answer), and max(ā, q, D) ≥ 1 if ā is in q(D ′ ) for some D ′ ∈ D (and thus it is a possible answer). Thus, from now on we assume min(ā, q, D) and max(ā, q, D) as our standard notion of query answers and study their complexity. More specifically, we will focus on data complexity, that is, computing min(ā, q, D) and max(ā, q, D) for a fixed query q. Depending on the type of comparison we use, several decision problems arise from the computation of min and max. These decision problems are defined as follows.
Inputs: an incomplete database D, a tuple ā ∈ Const(D) n , a non-negative integer k. Question: is max(ā, q, D) θ k? Whether the number k is represented in unary or binary form does not matter: the results will be the same regardless. All tractability results are shown assuming binary representation, and all matching hardness results will be proved for the case when k is represented in unary. The choice of inequalities, i. e. , < vs ≤ or > vs ≥, is not important: since k is an integer, ≤ k is the same condition as < k + 1. As for the case of certain and possible answers, the complexity of the above problems depends on the fragment of RA in which the query q is expressed. While for some of these fragments the problems can be proved to be intractable, there are fragments of RA for which computing min(ā, q, D) is tractable and can actually be done via naive evaluation.
The naive evaluation of a query q of arity n on a bag database D is defined as the bag obtained by assuming that each null value in Null(D) is a distinct constant and evaluating q directly over D. In what follows, we will denote by naive(ā, q, D) the number of occurrences of a tuple ā ∈ Const(D) n in the result of the naive evaluation of an RA query q on an incomplete database D. It is well known that naive(ā, q, D) can be computed in DLogSpace in data complexity  [5, 6]. Example 2. On a database with relations R = {a, ⊥ 1 , ⊥ 1 } and S = {⊥ 1 , ⊥ 2 }, the naive evaluation of σ 1=2 (R × S), ε(R) and R ∩ S gives {(⊥ 1 , ⊥ 1 ), (⊥ 1 , ⊥ 1 )}, {a, ⊥ 1 } and {⊥ 1 }, respectively.
Complexity of certain and possible answers We now turn our attention to the complexity of evaluating bag relational algebra expressions on incomplete databases, that is, solving the problems MIN θ [q] and MAX θ [q] for queries in various fragments of RA. As already explained, these problems are natural bag analogs of the notions of certainty and possibility over set databases. In Section 5. 1, we first provide upper and lower bounds for full RA. When the relation θ is < or >, the results are easily derivable from the results for the set case in  [19] ; we complement them with the exact complexity for equality. After introducing our technical framework in Section 5. 2, we then focus -in Section 5. 3 -on the problem MIN θ [q], proving the exact tractability boundary shown in Fig. 1. We start by showing that in all fragments up to RA + {∩}, the value of min can be computed by naive evaluation of queries, which extends a result in  [21].
We then show that beyond this fragment the problem becomes intractable: NP-complete for <, coNP-complete for >, and DP-complete for =. In particular, we show that the problem is intractable for all fragments containing SPC{∪}, and all fragments containing SPC{ε}. Next, in Section 5. 4, we look at MAX θ [q]. It was shown in  [21]  that for > the problem is NP-complete, even for very simple queries. Here, we complete the picture and settle the case for =, even when q is a query that simply returns a relation from the database. Finally, in Section 5. 5, we discuss what happens with more complex selection conditions in queries.
Upper and lower bounds for full RA Before delving into the complexity of the different fragments of RA, we briefly look at the complexity of evaluating general expressions. First, observe that RA queries are generic, i. e. , invariant under permutations of the domain. In the bag case, this is stated as follows. Proposition 6. Let D and D ′ be complete databases, let ρ be a bijection between adom(D) and adom(D ′ ) such that D ′ = ρ(D), and let q ∈ RA be a query of arity n. Then, #(ā, q, D) = #(ρ ā, q, D ′ ) for every tuple ā ∈ adom(D) n. Proof. By induction on the structure of q.
□ Intuitively, the above tells us that we need to take into account only finitely many valuations in order to compute the values in (1a) and (1b). Upper bounds of NP, coNP, and DP follow straightforwardly. Proposition 7. Let q be an expression in RA. Then: • MIN < [q] and MAX > [q] are in NP; • MIN > [q] and MAX < [q] are in coNP; • MIN = [q] and MAX = [q] are in DP. Proof. Let D be an incomplete bag database, let ā be a tuple in adom n (D), and let k be a positive integer. Assume a set C ⊆ Const such that C is disjoint with adom(D) and the cardinality of C is the same as the cardinality of Null(D). Let V be the set of valuations for Null(D) defined as follows: V = {v | range(v) ⊆ (C∪Const(D))}. Clearly, for each D ′ ∈ D there exists a valuation v ∈ V and a bijection ρ from adom(vD) to adom(D ′ ) such that ρ is the identity over Const(D) and ρ(vD) = D ′.
Finally, to solve MIN = [q], one can simply solve an instance of MIN < [q] with input D, a, and k + 1, and an instance of MIN > [q] with input D, a, and k -1. The same technique can be used to solve MAX = [q]. To prove the claim, we observe the following. For a given valuation v, checking whether #(v ā, q, vD)θk can be done in DLogSpace in the size of D for q ∈ RA and θ ∈ {<, >}. Moreover, valuations for Null(D) can be guessed using a number of bits that is polynomial in the size of D. □ For general RA expressions, all of these problems are complete in their respective classes. Proposition 8. Let q be an expression in RA. Then: • MIN < [q] and MAX > [q] are NP-hard; • MIN > [q] and MAX < [q] are coNP-hard; • MIN = [q] and MAX = [q] are DP-hard. Proof. The results for < and > follow directly from the fact that set databases can be simulated by bag databases.
Theorem 1. Let q be an RA + {∩} expression of arity n, let D be a database, and let ā ∈ Const(D) n. Then, min(ā, q, D) = naive(ā, q, D). Proof. This is an immediate consequence of a more general result that we shall see later on (Proposition 9). □ From the fact that bag relational algebra queries are in DLogSpace with respect to data complexity  [5, 6] , we then immediately get the following: Corollary 5. For expressions q in RA + {∩}, the problems MIN < [q], MIN > [q] and MIN = [q] are all in DLogSpace. □ As a matter of fact, RA + {∩} is the best fragment for which we can compute certain answers efficiently under bag semantics. To show this, from the diagram in Fig. 1 , it suffices to prove that the problem is intractable for SPC{∪}, as well as for all fragments with duplicate elimination.
This is what we do next; in particular, we shall see that in all of these fragments the intractable complexity is exactly the same, namely NP-complete, coNP-complete, and DP-complete, when θ is <, >, and =, respectively. Hardness for SPC{∪}. We first study the max-union operator ∪. Recall that, in the set case, adding union is harmless and preserves the property that certain answers can be found by naive evaluation. But under bag semantics, adding ∪ to SPC gives rise to a substantial increase in the complexity of computing min. Theorem 2. There exists an SPC{∪} query q for which MIN < [q] is NP-hard, MIN > [q] is coNP-hard, and MIN = [q] is DP-hard. Proof. Let ϕ be a k-CNF formula, and define dbenc(ϕ) as the database with relations R and T , where R is the encoding R ϕ of ϕ, and T consists of precisely |ϕ| occurrences of (0, 1) k.
Proposition 9. Let q be an RA + {∩} query of arity n, where selection conditions are positive Boolean combinations of equalities; then, MIN < [q] and MIN > [q] can be solved in DLogSpace. More precisely, for every database D and for every n-tuple ā of constants, min(ā, q, D) = naive(ā, q, D). Proof. For every valuation v, we have v(ā) = ā and naive(ā, q, D) ≤ ∑ ā′ :v(ā ′ )=ā naive(ā ′ , q, D) ≤ # ( ā, q, v(D) ) , (8) where the rightmost inequality is by Lemma 9, which is given in Appendix. Let us now define a valuation ṽ whose restriction to Null(D) is injective and such that the image of Null(D) under it is disjoint with Const(D). In other words, each null in D is mapped to a distinct constant that does not appear in D. From the definition of naive evaluation, it then follows that # ( ā, q, ṽ(D) ) = naive(ā, q, D).
Proposition 10. In the extension of SPC that allows arbitrary Boolean combinations of equalities as selection conditions, there is a query q for which MIN < [q] is NP-complete, MIN > [q] is coNPcomplete, and MIN = [q] is DP-complete. Proof. Let ϕ be a k-CNF formula, and define dbenc(ϕ) as the database D ϕ with relations R and T , where R is the encoding R ϕ of ϕ and T consists of a single occurrence of (0, 1) k. Consider the query q = π () ( σ γ (R × T ) ) , where γ is the disjunction of all inequalities i ̸ = j for every i ∈ {1,. , 2 k } and j = 2 k + 1. We will show that dbenc and q satisfy the properties of Lemma 8. For a valuation v, the answer to q on v(D ϕ ) consists of as many occurrences of () as there are tuples different from (0, 1) k in R ϕ. More precisely, # ( (), q, v(D ϕ ) ) = ∑ ā̸ =(0,1) k # ( ā, v(R ϕ ) ) = |v(R ϕ )| -# ( (0, 1) k , v(R ϕ ) ).
and, • for any given database D, we have that each x i = |e ′ i (D)| and each y j = |e ′′ j (D)|. □ The proofs of the next two lemmas can be found in Appendix. Let D be a database over a schema with a nullary relation symbol R, and let e be an RA + {∪} expression that mentions only R. Then, |e(D)| ≥ |R D |. Let D be a database over a schema consisting of two nullary relation symbols R and S, and let e be an RA + {∪} expression that mentions both R and S. Then, |e(D)| ≥ |R D | and |e(D)| ≥ |S D |.
Const and Null, respectively. More formally, a k-ary relation is a finite bag of k-ary tuples over Const ∪ Null. A database D then maps each k-ary relation symbol R in the schema to a k-ary bag relation R D. Given a database D = {R D 1 ,. , R D n }, we write Const(D) and Null(D) for the set of constants and nulls occurring in the R D i s, respectively. The active domain of D is the set Const(D) ∪ Null(D), denoted by adom(D). We say that D is complete if Null(D) = ∅. The semantics D of a database D is defined by means of valuations. A valuation v is a map v: Null(D) → Const, and the result of applying v to D is the complete database v(D) obtained by replacing each null ⊥ ∈ Null(D) with v(⊥). Observe that applying v to each relation R D in D preserves multiplicities, i. e. , for each relation name R in the schema and each tuple c ∈ R v(D) the following equality holds: #.
3. L{∪} and L{∩} are incomparable, for L ∈ {SPC, RA + }. Let e ∈ RA + {∩, ∪}; by induction on the structure of e we will show that there exists an expression e ′ ∈ RA + {-} that is equivalent to e. The base case is when e ∈ RA + , which is trivially also in RA + {-}. For the inductive step, let e = e 1 ⋆e 2 , with e 1 , e 2 ∈ RA + {∩, ∪} and ⋆ ∈ {∩, ∪}. By the induction hypothesis, there exist e ′ 1 , e ′ 2 ∈ RA + {-} such that e ′ i ≡ e i for i = 1, 2. Consider ⋆ ≡ e 1 ⋆ e 2 for ⋆ ∈ {∩, ∪}. To this end, let D be a database and let ā be a tuple; moreover, let m = #(ā, e ′ 1 , D) and n = #(ā, e ′.
e = e 1 -e 2. Then, k = m ´n where m = #(ā, e 1 , D) and n = #(ā, e 2 , D). As k > 0, we have that m > n; in turn, m is positive and, by the induction hypothesis, even. If n = 0, then k = m is even; otherwise, n is even as well by the induction hypothesis, so k = mn is obviously even. Let L be a fragment of bag relational algebra without duplicate elimination. Clearly, L{ε} is at least as expressive as L, so we only need to show that there exists a query that is expressible in the former but not in latter. To this end, consider a schema consisting of a nullary relation name R, and take any database D such that |R D | is a positive even number. Then, for every L expression over R, we have that |e(D)| is even by Lemma 5. Hence, the L{ε} expression.
Lemma 3. Lemma 4. 34 and, • for any given database D, we have that each x i = |e ′ i (D)| and each y j = |e ′′ j (D)|. □ The proofs of the next two lemmas can be found in Appendix. Let D be a database over a schema with a nullary relation symbol R, and let e be an RA + {∪} expression that mentions only R. Then, |e(D)| ≥ |R D |. Let D be a database over a schema consisting of two nullary relation symbols R and S, and let e be an RA + {∪} expression that mentions both R and S. Then, |e(D)| ≥ |R D | and |e(D)| ≥ |S D |.
3. L{∪} and L{∩} are incomparable, for L ∈ {SPC, RA + }. Let e ∈ RA + {∩, ∪}; by induction on the structure of e we will show that there exists an expression e ′ ∈ RA + {-} that is equivalent to e. The base case is when e ∈ RA + , which is trivially also in RA + {-}. For the inductive step, let e = e 1 ⋆e 2 , with e 1 , e 2 ∈ RA + {∩, ∪} and ⋆ ∈ {∩, ∪}. By the induction hypothesis, there exist e ′ 1 , e ′ 2 ∈ RA + {-} such that e ′ i ≡ e i for i = 1, 2. Consider ⋆ ≡ e 1 ⋆ e 2 for ⋆ ∈ {∩, ∪}. To this end, let D be a database and let ā be a tuple; moreover, let m = #(ā, e ′ 1 , D) and n = #(ā, e ′ the RA + {-} expressions e ∩ = e ′ 1 -(e ′ 1 -e ′ 2 ) and e ∪ = e ′ 1 ⊎(e ′ 2 -e ′ 1 ); we will show that e Finally, we show that with additive union and difference one can express both intersection and max-union, therefore RA + {-} is the most expressive fragment of RA without duplicate elimination.
e = e 1 -e 2. Then, k = m ´n where m = #(ā, e 1 , D) and n = #(ā, e 2 , D). As k > 0, we have that m > n; in turn, m is positive and, by the induction hypothesis, even. If n = 0, then k = m is even; otherwise, n is even as well by the induction hypothesis, so k = mn is obviously even. Let L be a fragment of bag relational algebra without duplicate elimination. Clearly, L{ε} is at least as expressive as L, so we only need to show that there exists a query that is expressible in the former but not in latter. To this end, consider a schema consisting of a nullary relation name R, and take any database D such that |R D | is a positive even number. Then, for every L expression over R, we have that |e(D)| is even by Lemma 5. Hence, the L{ε} expression □Proof of Proposition 5.
By the same token, we can expect doctors to be more willing to use digital tools if patients demand them. Consequently, patient buy-in is needed to make this system work, and that will only be possible if digital health developers and companies consider their expectations and concerns  [80]. These can range from user interface and user experience  [81]  considerations to confidentiality and privacy issues  [82] [83] [84]. Portugal has no direct equivalent to prescription apps or the German Ministry of Health's DiGA program. The Portuguese reimbursement scheme for pharmaceuticals is centrally negotiated and decided by the Regulatory Authority for Medicines and Medical Devices (INFARMED). Medical devices in the European Union market are subject to a conformity assessment  [38] , being the definition of medical devices already extended, in law, to software and software apps.
Limitations, both ex-ante and ex-post data collection, will be documented in the paper. The study will start with a cross-sectional, web-based survey delivered through the University of Porto's dynamic email function. The web-based survey will be based on the survey questionnaire made available in Borghouts paper. This questionnaire will be translated into Portuguese using a licensed translator. Afterward, it will be circulated between an equal number of students and teachers (estimated to be 5 each) affiliated with the Faculty of Medicine of the University of Porto for input. Received input will concentrate on how to adjust it to (1) include important questions to ask regarding the usage of digital health tools with a focus on MH and (2) adapt to a Portuguese MH context. Obtained feedback will be incorporated to produce a final web-based survey questionnaire for this study.
We will also ask the University of Porto's website management team to divulge the survey, providing a link to access it and following all privacy-related issues. To preserve privacy, respondents will not be asked to provide any identifiable information. Additionally, invited participants will not be tracked for having started or completed the survey, increasing privacy but limiting the possibility of reminders. High comparability with the Borghouts et al  [89]  study is expected due to the nature of the questions in the Borghouts et al  [89]  survey instrument and their relevance in a Portuguese population, leading us to believe that few questions will be dropped or significantly altered. Gathered data will be assessed according to the same pattern as that offered in the Borghouts et al  [89]  paper to allow for maximum comparability between results.
Collection of Antibiotic Exposure The way in which antibiotic exposure was collected was not specified in 13% (6/47) of studies. More than half of the studies (27/47) assessed antibiotic exposure through medical records. This may induce a bias as the exposure to antibiotics is not systematically and homogeneously collected and traced in medical records. Patient interviews, which are subject to recall bias, were used in 13% (6/47) of studies. The assessment of delivered antibiotics in pharmacy databases was conducted in 9% (4/47) of studies. Because data reported by community pharmacies often relate to the dispensing of antibiotics, they may not reflect the actual consumption by patients.
MATERIALS AND METHODS The study design was based on a review of the current literature searched on PubMed database using different combinations of keywords, with a special focus on the period 2017-2022 (Figure  1 ). In order to provide an update of the main recent findings on EMT driving parameters, the keyword "EMT cancer" was crossed with those of the signaling pathways, tumor microenvironment components and other specific EMT drivers (Figure  2 ). All relevant articles published in English were considered, with a special focus on reviews or works providing important breakthroughs in the field (covered in chapter 3). In a second step the keywords "curcumin cancer" or "curcuminoids cancer" were crossed with "EMT cancer" and all recent reports highlighting important findings were included (chapters 4-5).
, 2018). Moreover,  Kinoshita et al. (2020)  also reported that the combined secretion of TGF-β1and interleukin 6 (IL-6) by cancer cells induced a heterogeneity of T regs and/or interleukin 17 (IL-17)producing T helper 17 cells, favoring the progression of biliary tract cancer cells. Monocytes and monocytic-MDSCs are recruited from blood to the tumor by several cytokines, including CCL2, CCL5 and CSF1, which differentiate into TAMs  (Taki et al. , 2021). Recent investigations on TAMs have revealed they induce EMT in osteosarcoma cells by activating the COX-2/STAT3 axis  (Han et al. , 2019). Subsequently, a pan-cancer EMT analysis of 22 cancer types in TCGA datasets highlighted that the first distinctive feature of the EMT-high (mesenchymal) tumors was the enrichment in TAMs  (Tiwari et al.
NON-CODING RNAS AS NEW TARGETS OF CURCUMINOIDS The ability of curcuminoids to target multiple signaling pathways involved in EMT in cancer has led researchers to investigate its action on ncRNAs  (Toden et al. , 2015) , a rapidly growing research field as a 5-times increase was observed in the number of relevant articles between 2008-2016 and 2017-2022 on the PubMed database. Moreover, a special focus on EMT was observed during the two last years. Together with DNA methylation changes induced by curcumin, the first functional genomic studies allowed to profile several miRNAs of interest  (Huminiecki et al. , 2017). The list was recently updated, identifying  miR-7, miR-17-5p, miR-20a, miR-21, miR-22, miR-27a, miR-29b, miR-33b, miR-34a, miR-34c, miR-49, miR-101, miR-141, miR-185, miR-200a, miR-200b, miR-200c , and miR-429as potential targets  (Ashrafizadeh et al.
They have also filled validated questionnaires, performed neuropsychological tests Since 5HTT has been associated with impulsivity, stroop task total error count was used to measure it. Patient distribution according to allele status has been established. Follow-up data were obtained in order to see eventual reasons for death. Results: 334 patients had SS phenotype (19. 8%), 855 patients had SL phenotype (50. 7%), and finally 499 patients had LL phenotype (29. 6%). People with SS genotype were more impulsive than those with SL and LL as measured by Stroop total error task (p¼0. 039). This is in line with previous studies, that showed SS phenotype to be associated with impulsivity and suicidal attempts. Next, available data for clear deaths has been analysed. In the follow up 12 deaths were registered.