wanyu/IteraTeR_full_sent huggingface dataset:
Original:  2 ) five quantitative  attributes indicating the degree of intensity of the valence or sentiment (from extremely negative to extremely positive), and the degree of intensity of fear, of anger, of sadness and of joy emotions (from extremely low intensity to extremely high intensity), and 3 ) two qualitative attributes indicating the sentiment category and the dominant emotion category , respectively .
Revised:  2 ) five quantitative attributes indicating the degree of intensity of the valence or sentiment (from extremely negative to extremely positive), and the degree of intensity of fear, of anger, of sadness and of joy emotions (from extremely low intensity to extremely high intensity), and 3 ) two qualitative attributes indicating the sentiment category and the dominant emotion category the tweet is mainly expressing .
Edit intent: clarity
Original:  In this paper we study the intrinsic tradeoff between the space complexity of the sketch and its estimation error in the Random Oracle model.
Revised: Estimating the cardinality (number of distinct elements) of a large multiset is a classic problem in streaming and sketching, dating back to Flajolet and Martin's classic Probabilistic Counting (PCSA) algorithm from 1983. In this paper we study the intrinsic tradeoff between the space complexity of the sketch and its estimation error in the Random Oracle model.
Edit intent: meaning-changed
Original:  It captures the tension between the limiting Shannon entropy (H) of the sketch and its normalized Fisher information (I), which characterizes (asymptotically) the variance of a statistically efficient estimator.
Revised:  It captures the tension between the limiting Shannon entropy (H) of the sketch and its normalized Fisher information (I), which characterizes (asymptotically) the variance of a statistically efficient , asymptotically unbiased estimator. Our results are as follows.
Edit intent: meaning-changed
Original:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but  tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Revised:  We prove that all base-q variants of Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Edit intent: clarity
Original:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but  tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Revised:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin 's PCSA sketch have Fish-number H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Edit intent: clarity
Original:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but  tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Revised:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 \approx 1.98016 and that every base-q generalizations of (\textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Edit intent: meaning-changed
Original:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but  tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Revised:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q \textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Edit intent: clarity
Original:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but  tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Revised:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{ )\textsf{LogLog are strictly worse than H_0/I_0, but tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Edit intent: meaning-changed
Original:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but  tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Revised:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper \textsf{LogLog are strictly worse than H_0/I_0, but tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Edit intent: fluency
Original:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but  tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Revised:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{ are strictly worse than H_0/I_0, but tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Edit intent: meaning-changed
Original:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but  tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Revised:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{LogLog variant of (Hyper)LogLog has Fish-number worse than H_0/I_0, but tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Edit intent: meaning-changed
Original:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but  tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Revised:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but that they tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty.
Edit intent: clarity
Original:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but  tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% \infty. All other known sketches have even worse \mathsf{Fish-numbers.
Revised:  We prove that many variants of the \mathsf{PCSA Flajolet and Martin have \mathsf{Fish H_0/I_0 , where H_0,I_0 are two precisely-defined constants, and that all base-q generalizations of (\textsf{Hyper )\textsf{LogLog are strictly worse than H_0/I_0, but tend to H_0/I_0 in the limit as q %DIFDELCMD < \to%%% -numbers.
Edit intent: meaning-changed
Original:  We introduce a new sketch called \mathsf{Fishmonger} }  that is based on a smoothed, compressed version of \mathsf{PCSA with a different estimation function.
Revised:  We introduce a new sketch called \mathsf{Fishmonger} } \rightarrow \infty. Here H_0,I_0 are precisely defined constants. We describe a sketch called Fishmonger that is based on a smoothed, compressed version of \mathsf{PCSA with a different estimation function.
Edit intent: meaning-changed
Original:  We introduce a new sketch called \mathsf{Fishmonger} }  that is based on a smoothed, compressed version of \mathsf{PCSA with a different estimation function. \mathsf{Fishmonger has \mathsf{Fish} number H_0/I_0 \approx 1.98.
Revised:  We introduce a new sketch called \mathsf{Fishmonger} } that is based on a smoothed, compressed version of \mathsf{PCSA with a different has \mathsf{Fish} number H_0/I_0 \approx 1.98.
Edit intent: clarity
Original:  It stores }  ]  O(\log^2\log U) + (  H_0/I_0)b \approx 1.98b bits , and estimates cardinalities of multisets of U%DIFDELCMD < ] %%% with a standard error of ( 1 +o(1)) /\sqrt{b}.
Revised:  It stores } estimator function. It is proved that with high probability, Fishmonger processes a multiset of ] O(\log^2\log U) + ( H_0/I_0)b \approx 1.98b bits , and estimates cardinalities of multisets of U%DIFDELCMD < ] %%% with a standard error of ( 1 +o(1)) /\sqrt{b}.
Edit intent: meaning-changed
Original:  It stores }  ]  O(\log^2\log U) + (  H_0/I_0)b \approx 1.98b bits , and estimates cardinalities of multisets of U%DIFDELCMD < ] %%% with a standard error of ( 1 +o(1)) /\sqrt{b}.
Revised:  It stores } U] O(\log^2\log U) + ( H_0/I_0)b \approx 1.98b bits , and estimates cardinalities of multisets of U%DIFDELCMD < ] %%% with a standard error of ( 1 +o(1)) /\sqrt{b}.
Edit intent: meaning-changed
Original:  It stores }  ]  O(\log^2\log U) + (  H_0/I_0)b \approx 1.98b bits , and estimates cardinalities of multisets of U%DIFDELCMD < ] %%% with a standard error of ( 1 +o(1)) /\sqrt{b}.
Revised:  It stores } ] such that at all times, its space is O(\log^2\log U) + ( H_0/I_0)b \approx 1.98b bits , and estimates cardinalities of multisets of U%DIFDELCMD < ] %%% with a standard error of ( 1 +o(1)) /\sqrt{b}.
Edit intent: meaning-changed
Original:  It stores }  ]  O(\log^2\log U) + (  H_0/I_0)b \approx 1.98b bits , and estimates cardinalities of multisets of U%DIFDELCMD < ] %%% with a standard error of ( 1 +o(1)) /\sqrt{b}.
Revised:  It stores } ] O(\log^2\log U) + ( 1+o(1))( H_0/I_0)b \approx 1.98b bits , and estimates cardinalities of multisets of U%DIFDELCMD < ] %%% with a standard error of ( 1 +o(1)) /\sqrt{b}.
Edit intent: fluency
Original:  It stores }  ]  O(\log^2\log U) + (  H_0/I_0)b \approx 1.98b bits , and estimates cardinalities of multisets of U%DIFDELCMD < ] %%% with a standard error of ( 1 +o(1)) /\sqrt{b}.
Revised:  It stores } ] O(\log^2\log U) + ( H_0/I_0)b \approx 1.98b bits U%DIFDELCMD < ] %%% with a standard error of ( 1 +o(1)) /\sqrt{b}.
Edit intent: coherence
Original:  It stores }  ]  O(\log^2\log U) + (  H_0/I_0)b \approx 1.98b bits , and estimates cardinalities of multisets of U%DIFDELCMD < ] %%% with a standard error of ( 1 +o(1)) /\sqrt{b}.
Revised:  It stores } ] O(\log^2\log U) + ( H_0/I_0)b \approx 1.98b bits , and estimates cardinalities of multisets of %DIFDELCMD < ] %%% with a standard error of ( 1 +o(1)) /\sqrt{b}.
Edit intent: meaning-changed
Original:  It stores }  ]  O(\log^2\log U) + (  H_0/I_0)b \approx 1.98b bits , and estimates cardinalities of multisets of U%DIFDELCMD < ] %%% with a standard error of ( 1 +o(1)) /\sqrt{b}.
Revised:  It stores } ] O(\log^2\log U) + ( H_0/I_0)b \approx 1.98b bits , and estimates cardinalities of multisets of U%DIFDELCMD < ] %%% and its standard error is 1 +o(1)) /\sqrt{b}.
Edit intent: coherence
Original:  It stores }  ]  O(\log^2\log U) + (  H_0/I_0)b \approx 1.98b bits , and estimates cardinalities of multisets of U%DIFDELCMD < ] %%% with a standard error of ( 1 +o(1)) /\sqrt{b}.
Revised:  It stores } ] O(\log^2\log U) + ( H_0/I_0)b \approx 1.98b bits , and estimates cardinalities of multisets of U%DIFDELCMD < ] %%% with a standard error of ( 1 /\sqrt{b}.
Edit intent: meaning-changed
Original:  \mathsf{Fishmonger's space-error tradeoff improves on state-of-the-art sketches like }\textsf{HyperLogLog , or even compressed representations of it.
Revised:  's space-error tradeoff improves on state-of-the-art sketches like }\textsf{HyperLogLog , or even compressed representations of it.
Edit intent: coherence
Original:  \mathsf{Fishmonger's space-error tradeoff improves on state-of-the-art sketches like }\textsf{HyperLogLog , or even compressed representations of it.
Revised:  \mathsf{Fishmonger's space-error tradeoff improves on state-of-the-art sketches like }\textsf{ , or even compressed representations of it.
Edit intent: meaning-changed
Original:  \mathsf{Fishmonger's space-error tradeoff improves on state-of-the-art sketches like }\textsf{HyperLogLog , or even compressed representations of it. \mathsf{Fishmonger can be used in a distributed environment (where substreams are sketched separately and composed later).
Revised:  \mathsf{Fishmonger's space-error tradeoff improves on state-of-the-art sketches like }\textsf{HyperLogLog can be used in a distributed environment (where substreams are sketched separately and composed later).
Edit intent: coherence
Original:  We conjecture that the \mathsf{Fish}-number }  H_0/I_0 is a universal lower bound for any such composable sketch .
Revised:  We conjecture that the \mathsf{Fish}-number } We give circumstantial evidence that H_0/I_0 is the optimum Fish-number of mergeable sketches for Cardinality Estimation. We define a class of linearizable sketches and prove that no member of this class can beat H_0/I_0 is a universal lower bound for any such composable sketch .
Edit intent: meaning-changed
Original:  In this paper, we primarily study thetolerant versions of the classicuniformity andidentity testing problems, providing improved query complexity bounds in the conditional sampling model. In this paper , we prove that tolerant uniformity testing in the conditional sampling model can be solved using O(\varepsilon^{-2}) queries, which is known to be optimal and improves upon the O(\varepsilon^{-20})-query algorithm of  [CRS15].
Revised:  In this paper, we primarily study thetolerant versions of the classicuniformity andidentity testing problems, providing improved query complexity bounds for several classic distribution testing problems in this model. First , we prove that tolerant uniformity testing in the conditional sampling model can be solved using O(\varepsilon^{-2}) queries, which is known to be optimal and improves upon the O(\varepsilon^{-20})-query algorithm of [CRS15].
Edit intent: meaning-changed
Original:  In this paper , we prove that tolerant uniformity testing in the conditional sampling model can be solved using O(\varepsilon^{-2}) queries, which is known to be optimal and improves upon the O(\varepsilon^{-20})-query algorithm of  [CRS15].
Revised:  In this paper , we prove that tolerant uniformity testing in the conditional sampling model can be solved using O(\varepsilon^{-2}) queries, which is optimal and improves upon the O(\varepsilon^{-20})-query algorithm of [CRS15].
Edit intent: coherence
Original:  In this paper , we prove that tolerant uniformity testing in the conditional sampling model can be solved using O(\varepsilon^{-2}) queries, which is known to be optimal and improves upon the O(\varepsilon^{-20})-query algorithm of  [CRS15].
Revised:  In this paper , we prove that tolerant uniformity testing in the conditional sampling model can be solved using O(\varepsilon^{-2}) queries, which is known to be optimal and improves upon the O(\varepsilon^{-20})-query algorithm of Canonne et al. [CRS15].
Edit intent: meaning-changed
Original:  Our bound even holds under the Pair Conditional Sampling model, a restricted version of the conditional sampling model where every queried subset S either must have exactly 2 elements, or must be the entire domain of the distribution.
Revised:  This bound even holds under the Pair Conditional Sampling model, a restricted version of the conditional sampling model where every queried subset S either must have exactly 2 elements, or must be the entire domain of the distribution.
Edit intent: fluency
Original:  Our bound even holds under the Pair Conditional Sampling model, a restricted version of the conditional sampling model where every queried subset S either must have exactly 2 elements, or must be the entire domain of the distribution. We also prove that tolerant identity testing in the conditional sampling model can be solved in \tilde{O}(\varepsilon^{-4}) queries, which is the first known bound independent of the support size of the distribution for this problem.
Revised:  Our bound even holds under the Pair Conditional Sampling model, a restricted version of the conditional sampling model called the Pair Conditional Sampling model. Next, we prove that tolerant identity testing in the conditional sampling model can be solved in \tilde{O}(\varepsilon^{-4}) queries, which is the first known bound independent of the support size of the distribution for this problem.
Edit intent: clarity
Original:  \tilde{O})-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O} ] Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log n \cdot \varepsilon^{-2}) for the query complexity, improving upon both the known upper and lower bounds in [CRS15].
Revised:  Next, we use our algorithm for tolerant uniformity testing to get an\tilde{O})-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O} ] Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log n \cdot \varepsilon^{-2}) for the query complexity, improving upon both the known upper and lower bounds in [CRS15].
Edit intent: meaning-changed
Original:  \tilde{O})-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O} ] Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log n \cdot \varepsilon^{-2}) for the query complexity, improving upon both the known upper and lower bounds in [CRS15].
Revised:  \tilde{O}(\varepsilon^{-4)-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O} ] Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log n \cdot \varepsilon^{-2}) for the query complexity, improving upon both the known upper and lower bounds in [CRS15].
Edit intent: meaning-changed
Original:  \tilde{O})-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O} ] Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log n \cdot \varepsilon^{-2}) for the query complexity, improving upon both the known upper and lower bounds in [CRS15].
Revised:  \tilde{O})-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O}(\varepsilon^{-22 ] Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log n \cdot \varepsilon^{-2}) for the query complexity, improving upon both the known upper and lower bounds in [CRS15].
Edit intent: clarity
Original:  \tilde{O})-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O} ] Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log n \cdot \varepsilon^{-2}) for the query complexity, improving upon both the known upper and lower bounds in [CRS15].
Revised:  \tilde{O})-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O} Can15] Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log n \cdot \varepsilon^{-2}) for the query complexity, improving upon both the known upper and lower bounds in [CRS15].
Edit intent: clarity
Original:  \tilde{O})-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O} ] Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log n \cdot \varepsilon^{-2}) for the query complexity, improving upon both the known upper and lower bounds in [CRS15].
Revised:  \tilde{O})-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O} ]. Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log n \cdot \varepsilon^{-2}) for the query complexity, improving upon both the known upper and lower bounds in [CRS15].
Edit intent: fluency
Original:  \tilde{O})-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O} ] Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log n \cdot \varepsilon^{-2}) for the query complexity, improving upon both the known upper and lower bounds in [CRS15].
Revised:  \tilde{O})-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O} ] Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log N \cdot \varepsilon^{-2}) for the query complexity, improving upon both the known upper and lower bounds in [CRS15].
Edit intent: fluency
Original:  \tilde{O})-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O} ] Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log n \cdot \varepsilon^{-2}) for the query complexity, improving upon both the known upper and lower bounds in [CRS15].
Revised:  \tilde{O})-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O} ] Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log n \cdot \varepsilon^{-2}) for the query complexity, where the domain of the distribution has size N. This improves upon both the known upper and lower bounds in [CRS15].
Edit intent: meaning-changed
Original: We establish a novel characterization of totally positive matrices via a sign non-reversal property.
Revised: A matrix A is totally positive (or non-negative) of order k, denoted TP_k (or TN_k), if all minors of size \leq k are positive (or non-negative). It is well-known that such matrices are characterized by the variation diminishing property together with the sign non-reversal property.
Edit intent: meaning-changed