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Journal articles on the topic 'Minimal subset'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Fomin, Fedor V., Pinar Heggernes, Dieter Kratsch, Charis Papadopoulos, and Yngve Villanger. "Enumerating Minimal Subset Feedback Vertex Sets." Algorithmica 69, no. 1 (December 15, 2012): 216–31. http://dx.doi.org/10.1007/s00453-012-9731-6.

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2

SHAH, I. "DIRECT ALGORITHMS FOR FINDING MINIMAL UNSATISFIABLE SUBSETS IN OVER-CONSTRAINED CSPs." International Journal on Artificial Intelligence Tools 20, no. 01 (February 2011): 53–91. http://dx.doi.org/10.1142/s0218213011000036.

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In many situations, an explanation of the reasons behind inconsistency in an overconstrained CSP is required. This explanation can be given in terms of minimal unsatisfiable subsets (MUSes) of constraints. This paper presents algorithms for finding minimal unsatisfiable subsets (MUSes) of constraints in overconstrained CSPs with finite domains and binary constraints. The approach followed is to generate subsets in the subset space, test them for consistency and record the inconsistent subsets found. We present three algorithms as variations of this basic approach. Each algorithm generates subsets in the subset space in a different order and curtails search by employing various search pruning mechanisms. The proposed algorithms are anytime algorithms: a time limit can be set on an algorithm's search and the algorithm can be made to find a subset of MUSes. Experimental evaluation of the proposed algorithms demonstrates that they perform two to three orders of magnitude better than the existing indirect algorithms. Furthermore, the algorithms are able to find MUSes in large CSP benchmarks.

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3

Legut, Jerzy, and Maciej Wilczyński. "How to Obtain Maximal and Minimal Subranges of Two-Dimensional Vector Measures." Tatra Mountains Mathematical Publications 74, no. 1 (December 1, 2019): 85–90. http://dx.doi.org/10.2478/tmmp-2019-0022.

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Abstract Let (X, ℱ) be a measurable space with a nonatomic vector measure µ =(µ1, µ2). Denote by R(Y) the subrange R(Y)= {µ(Z): Z ∈ ℱ, Z ⊆ Y }. For a given p ∈ µ(ℱ) consider a family of measurable subsets ℱp = {Z ∈ ℱ : µ(Z)= p}. Dai and Feinberg proved the existence of a maximal subset Z* ∈ Fp having the maximal subrange R(Z*) and also a minimal subset M* ∈ ℱp with the minimal subrange R(M*). We present a method of obtaining the maximal and the minimal subsets. Hence, we get simple proofs of the results of Dai and Feinberg.

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4

JOHNSON, WILL. "INTERPRETABLE SETS IN DENSE O-MINIMAL STRUCTURES." Journal of Symbolic Logic 83, no. 04 (December 2018): 1477–500. http://dx.doi.org/10.1017/jsl.2018.50.

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AbstractWe give an example of a dense o-minimal structure in which there is a definable quotient that cannot be eliminated, even after naming parameters. Equivalently, there is an interpretable set which cannot be put in parametrically definable bijection with any definable set. This gives a negative answer to a question of Eleftheriou, Peterzil, and Ramakrishnan. Additionally, we show that interpretable sets in dense o-minimal structures admit definable topologies which are “tame” in several ways: (a) they are Hausdorff, (b) every point has a neighborhood which is definably homeomorphic to a definable set, (c) definable functions are piecewise continuous, (d) definable subsets have finitely many definably connected components, and (e) the frontier of a definable subset has lower dimension than the subset itself.

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5

Miao, Maoxuan, Jinran Wu, Fengjing Cai, and You-Gan Wang. "A Modified Memetic Algorithm with an Application to Gene Selection in a Sheep Body Weight Study." Animals 12, no. 2 (January 15, 2022): 201. http://dx.doi.org/10.3390/ani12020201.

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Selecting the minimal best subset out of a huge number of factors for influencing the response is a fundamental and very challenging NP-hard problem because the presence of many redundant genes results in over-fitting easily while missing an important gene can more detrimental impact on predictions, and computation is prohibitive for exhaust search. We propose a modified memetic algorithm (MA) based on an improved splicing method to overcome the problems in the traditional genetic algorithm exploitation capability and dimension reduction in the predictor variables. The new algorithm accelerates the search in identifying the minimal best subset of genes by incorporating it into the new local search operator and hence improving the splicing method. The improvement is also due to another two novel aspects: (a) updating subsets of genes iteratively until the no more reduction in the loss function by splicing and increasing the probability of selecting the true subsets of genes; and (b) introducing add and del operators based on backward sacrifice into the splicing method to limit the size of gene subsets. Additionally, according to the experimental results, our proposed optimizer can obtain a better minimal subset of genes with a few iterations, compared with all considered algorithms. Moreover, the mutation operator is replaced by it to enhance exploitation capability and initial individuals are improved by it to enhance efficiency of search. A dataset of the body weight of Hu sheep was used to evaluate the superiority of the modified MA against the genetic algorithm. According to our experimental results, our proposed optimizer can obtain a better minimal subset of genes with a few iterations, compared with all considered algorithms including the most advanced adaptive best-subset selection algorithm.

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6

HE, QING, XIU-RONG ZHAO, and ZHONG-ZHI SHI. "MINIMAL CONSISTENT SUBSET FOR HYPER SURFACE CLASSIFICATION METHOD." International Journal of Pattern Recognition and Artificial Intelligence 22, no. 01 (February 2008): 95–108. http://dx.doi.org/10.1142/s0218001408006132.

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Hyper Surface Classification (HSC), which is based on Jordan Curve Theorem in Topology, has proven to be a simple and effective method for classifying a larger database in our previous work. To select a representative subset from the original sample set, the Minimal Consistent Subset (MCS) of HSC is studied in this paper. For HSC method, one of the most important features of MCS is that it has the same classification model as the entire sample dataset, and can totally reflect its classification ability. From this point of view, MCS is the best way of sampling from the original dataset for HSC. Furthermore, because of the minimum property of MCS, every single deletion or multiple deletions from it will lead to a reduction in generalization ability, which can be exactly predicted by the proposed formula in this paper.

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7

Le, Dung, and Anthony J. Macula. "On the probability that subset sequences are minimal." Discrete Mathematics 207, no. 1-3 (September 1999): 285–89. http://dx.doi.org/10.1016/s0012-365x(99)00112-0.

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8

Fredriksson, Kimmo. "On building minimal automaton for subset matching queries." Information Processing Letters 110, no. 24 (November 2010): 1093–98. http://dx.doi.org/10.1016/j.ipl.2010.09.014.

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9

Zhao, Xiangfu, Dantong Ouyang, and Liming Zhang. "Computing all minimal hitting sets by subset recombination." Applied Intelligence 48, no. 2 (June 30, 2017): 257–70. http://dx.doi.org/10.1007/s10489-017-0971-7.

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10

Ikeda, Koichiro. "Minimal but not strongly minimal structures with arbitrary finite dimensions." Journal of Symbolic Logic 66, no. 1 (March 2001): 117–26. http://dx.doi.org/10.2307/2694913.

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AbstractAn infinite structure is said to be minimal if each of its definable subset is finite or cofinite. Modifying Hrushovski's method we construct minimal, non strongly minimal structures with arbitrary finite dimensions. This answers negatively to a problem posed by B. I Zilber.

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11

Sun, Cui-Fang, and Tian-Tian Tao. "On g-adic minimal asymptotic bases of order h." International Journal of Number Theory 15, no. 02 (March 2019): 389–406. http://dx.doi.org/10.1142/s1793042119500209.

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Let [Formula: see text] be the set of all nonnegative integers. Let [Formula: see text] be a subset of [Formula: see text] and [Formula: see text] be a nonempty subset of [Formula: see text]. Denote by [Formula: see text] the set of all finite, nonempty subsets of [Formula: see text]. For integer [Formula: see text], let [Formula: see text] be the set of all numbers of the form [Formula: see text], where [Formula: see text] and [Formula: see text]. Let [Formula: see text] be any integer. For [Formula: see text], let [Formula: see text]. In this paper, we show that for any [Formula: see text], the set [Formula: see text] is a minimal asymptotic basis of order [Formula: see text]. We also prove that for any [Formula: see text] and [Formula: see text], the set [Formula: see text] is a minimal asymptotic basis of order [Formula: see text].

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12

Moors, W. B., and J. R. Giles. "Generic continuity of minimal set-valued mappings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 63, no. 2 (October 1997): 238–62. http://dx.doi.org/10.1017/s1446788700000677.

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AbstractWe study classes of Banach spaces where every set-valued mapping from a complete metric space into subsets of the Banach space which satisfies certain minimal properties, is single-valued and norm upper semi-continuous at the points of a dense Gδ subset of its domain. Characterisations of these classes are developed and permanence properties are established. Sufficiency conditions for membership of these classes are defined in terms of fragmentability and σ-fragmentability of the weak topology. A characterisation of non membership is used to show that l∞ (N) is not a member of our classe of generic continuity spaces.

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13

Alawneh, Tahani Nawaf, and Mehmet Ali Tut. "Using Rough Set Theory to Find Minimal Log with Rule Generation." Symmetry 13, no. 10 (October 10, 2021): 1906. http://dx.doi.org/10.3390/sym13101906.

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Data pre-processing is a major difficulty in the knowledge discovery process, especially feature selection on a large amount of data. In literature, various approaches have been suggested to overcome this difficulty. Unlike most approaches, Rough Set Theory (RST) can discover data de-pendency and reduce the attributes without the need for further information. In RST, the discernibility matrix is the mathematical foundation for computing such reducts. Although it proved its efficiency in feature selection, unfortunately it is computationally expensive on high dimensional data. Algorithm complexity is related to the search of the minimal subset of attributes, which requires computing an exponential number of possible subsets. To overcome this limitation, many RST enhancements have been proposed. Contrary to recent methods, this paper implements RST concepts in an iterated manner using R language. First, the dataset was partitioned into a smaller number of subsets and each subset processed independently to generate its own minimal attribute set. Within the iterations, only minimal elements in the discernibility matrix were considered. Finally, the iterated outputs were compared, and those common among all reducts formed the minimal one (Core attributes). A comparison with another novel proposed algorithm using three benchmark datasets was performed. The proposed approach showed its efficiency in calculating the same minimal attribute sets with less execution time.

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14

Tennakoon, Ruwan B., Alireza Bab-Hadiashar, Zhenwei Cao, Reza Hoseinnezhad, and David Suter. "Robust Model Fitting Using Higher Than Minimal Subset Sampling." IEEE Transactions on Pattern Analysis and Machine Intelligence 38, no. 2 (February 1, 2016): 350–62. http://dx.doi.org/10.1109/tpami.2015.2448103.

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15

BENIERE, J. C., and G. MEIGNIEZ. "Flows without minimal set." Ergodic Theory and Dynamical Systems 19, no. 1 (February 1999): 21–30. http://dx.doi.org/10.1017/s0143385799126567.

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In this paper we prove, using explicit constructions, that every non-compact manifold (except, of course, surfaces of finite genus) can be endowed with a non-singular flow without minimal subset, that is to say: a flow such that each orbit closure contains a smaller one.

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16

Tanovic, Predrag. "Some questions concerning minimal structures." Publications de l'Institut Math?matique (Belgrade), no. 96 (2007): 79–83. http://dx.doi.org/10.2298/pim0796079t.

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An infinite first-order structure is minimal if its each definable subset is either finite or co-finite. We formulate three questions concerning order properties of minimal structures which are motivated by Pillay?s Conjecture (stating that a countable first-order structure must have infinitely many countable, pairwise non-isomorphic elementary extensions).

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17

Lee, Jiwon, Seunghwa Lee, Jihye Kim, and Hyunok Oh. "Combinatorial Subset Difference—IoT-Friendly Subset Representation and Broadcast Encryption." Sensors 20, no. 11 (June 2, 2020): 3140. http://dx.doi.org/10.3390/s20113140.

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In the Internet of Things (IoT) systems, it is often required to deliver a secure message to a group of devices. The public key broadcast encryption is an efficient primitive to handle IoT broadcasts, by allowing a user (or a device) to broadcast encrypted messages to a group of legitimate devices. This paper proposes an IoT-friendly subset representation called Combinatorial Subset Difference (CSD), which generalizes the existing subset difference (SD) method by allowing wildcards (*) in any position of the bitstring. Based on the CSD representation, we first propose an algorithm to construct the CSD subset, and a CSD-based public key broadcast encryption scheme. By providing the most general subset representation, the proposed CSD-based construction achieves a minimal header size among the existing broadcast encryption. The experimental result shows that our CSD saves the header size by 17% on average and more than 1000 times when assuming a specific IoT example of IP address with 20 wildcards and 2 20 total users, compared to the SD-based broadcast encryption. We prove the semantic security of CSD-based broadcast encryption under the standard l-BDHE assumption, and extend the construction to a chosen-ciphertext-attack (CCA)-secure version.

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18

Nakaoka, Fumie, and Nobuyuki Oda. "Some applications of minimal open sets." International Journal of Mathematics and Mathematical Sciences 27, no. 8 (2001): 471–76. http://dx.doi.org/10.1155/s0161171201006482.

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We characterize minimal open sets in topological spaces. We show that any nonempty subset of a minimal open set is pre-open. As an application of a theory of minimal open sets, we obtain a sufficient condition for a locally finite space to be a pre-Hausdorff space.

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19

LING, DENGRONG, and MIN TANG. "ON MINIMAL ASYMPTOTIC -ADIC BASES." Bulletin of the Australian Mathematical Society 92, no. 3 (August 5, 2015): 374–79. http://dx.doi.org/10.1017/s0004972715000805.

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Let $g\geq 2$ be a fixed integer. Let $\mathbb{N}$ denote the set of all nonnegative integers and let $A$ be a subset of $\mathbb{N}$. Write $r_{2}(A,n)=\sharp \{(a_{1},a_{2})\in A^{2}:a_{1}+a_{2}=n\}.$ We construct a thin, strongly minimal, asymptotic $g$-adic basis $A$ of order two such that the set of $n$ with $r_{2}(A,n)=2$ has density one.

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20

Drexler, Dominik, Jendrik Seipp, and David Speck. "Subset-Saturated Transition Cost Partitioning." Proceedings of the International Conference on Automated Planning and Scheduling 31 (May 17, 2021): 131–39. http://dx.doi.org/10.1609/icaps.v31i1.15955.

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Cost partitioning admissibly combines the information from multiple heuristics for optimal state-space search. One of the strongest cost partitioning algorithms is saturated cost partitioning. It considers the heuristics in sequence and assigns to each heuristic the minimal fraction of the remaining costs that are needed for preserving all heuristic estimates. Saturated cost partitioning has recently been generalized in two directions: first, by allowing to use different costs for the transitions induced by the same operator, and second, by preserving the heuristic estimates for only a subset of states. In this work, we unify these two generalizations and show that the resulting subset-saturated transition cost partitioning algorithm usually yields stronger heuristics than the two generalizations by themselves.

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21

Lamalem, Yasser, Khalid Housni, and Samir Mbarki. "Enumeration of the minimal node cutsets based on necessary minimal paths." IAES International Journal of Artificial Intelligence (IJ-AI) 9, no. 2 (June 1, 2020): 175. http://dx.doi.org/10.11591/ijai.v9.i2.pp175-182.

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<p>Reliability evaluation is an important research field for a complex network. The most popular methods for such evaluation often use Minimal Cuts (MC) or Minimal paths (MP). Nonetheless, few algorithms address the issue of the enumeration of all minimal cut sets from the source node s to the terminal node t when only the nodes of the network are subject to random failures. This paper presents an effective algorithm which enumerates all minimal node cuts sets of a network. The proposed algorithm runs in two steps: The first one is used to generate a subset of paths, called necessary minimal paths, instead of all minimal paths. Whereas, the second step stands to build all minimal cutsets from the necessary minimal paths.</p>

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22

Alimohammady, M., and M. Roohi. "Fixed Point in Minimal Spaces." Nonlinear Analysis: Modelling and Control 10, no. 4 (October 25, 2005): 305–14. http://dx.doi.org/10.15388/na.2005.10.4.15111.

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This paper deals with fixed point theory and fixed point property in minimal spaces. We will prove that under some conditions f : (X,M) → (X,M) has a fixed point if and only if for each m-open cover {Bα} for X there is at least one x ∈ X such that both x and f(x) belong to a common Bα. Further, it is shown that if (X,M) has the fixed point property, then its minimal retract subset enjoys this property.

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23

Flores-Lagunes, Alfonso, William C. Horrace, and Kurt E. Schnier. "Identifying technically efficient fishing vessels: a non-empty, minimal subset approach." Journal of Applied Econometrics 22, no. 4 (2007): 729–45. http://dx.doi.org/10.1002/jae.942.

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24

Deng, Guixin, and Xiangneng Zeng. "Long minimal zero-sum sequences over a finite subset of Z." European Journal of Combinatorics 67 (January 2018): 78–86. http://dx.doi.org/10.1016/j.ejc.2017.07.004.

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25

Sommers, Eric N. "B-Stable Ideals in the Nilradical of a Borel Subalgebra." Canadian Mathematical Bulletin 48, no. 3 (September 1, 2005): 460–72. http://dx.doi.org/10.4153/cmb-2005-043-4.

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AbstractWe count the number of strictly positive B-stable ideals in the nilradical of a Borel subalgebra and prove that the minimal roots of any B-stable ideal are conjugate by an element of the Weyl group to a subset of the simple roots. We also count the number of ideals whose minimal roots are conjugate to a fixed subset of simple roots.

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26

HUANG, WEN, SONG SHAO, and XIANGDONG YE. "An answer to Furstenberg’s problem on topological disjointness." Ergodic Theory and Dynamical Systems 40, no. 9 (April 10, 2019): 2467–81. http://dx.doi.org/10.1017/etds.2019.23.

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In this paper we give an answer to Furstenberg’s problem on topological disjointness. Namely, we show that a transitive system $(X,T)$ is disjoint from all minimal systems if and only if $(X,T)$ is weakly mixing and there is some countable dense subset $D$ of $X$ such that for any minimal system $(Y,S)$, any point $y\in Y$ and any open neighbourhood $V$ of $y$, and for any non-empty open subset $U\subset X$, there is $x\in D\cap U$ such that $\{n\in \mathbb{Z}_{+}:T^{n}x\in U,S^{n}y\in V\}$ is syndetic. Some characterization for the general case is also given. By way of application we show that if a transitive system $(X,T)$ is disjoint from all minimal systems, then so are $(X^{n},T^{(n)})$ and $(X,T^{n})$ for any $n\in \mathbb{N}$. It turns out that a transitive system $(X,T)$ is disjoint from all minimal systems if and only if the hyperspace system $(K(X),T_{K})$ is disjoint from all minimal systems.

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27

Maříková, Jana. "Type-definable and invariant groups in o-minimal structures." Journal of Symbolic Logic 72, no. 1 (March 2007): 67–80. http://dx.doi.org/10.2178/jsl/1174668384.

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AbstractLet M be a big o-minimal structure and G a type-definable group in Mn. We show that G is a type-definable subset of a definable manifold in Mn that induces on G a group topology. If M is an o-minimal expansion of a real closed field, then G with this group topology is even definably isomorphic to a type-definable group in some Mk with the topology induced by Mk. Part of this result holds for the wider class of so-called invariant groups: each invariant group G in Mn has a unique topology making it a topological group and inducing the same topology on a large invariant subset of the group as Mn.

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28

Wencel, Roman. "Topological properties of sets definable in weakly o-minimal structures." Journal of Symbolic Logic 75, no. 3 (September 2010): 841–67. http://dx.doi.org/10.2178/jsl/1278682203.

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AbstractThe paper is aimed at studying the topological dimension for sets definable in weakly o-minimal structures in order to prepare background for further investigation of groups, group actions and fields definable in the weakly o-minimal context. We prove that the topological dimension of a set definable in a weakly o-minimal structure is invariant under definable injective maps, strengthening an analogous result from [2] for sets and functions definable in models of weakly o-minimal theories. We pay special attention to large subsets of Cartesian products of definable sets, showing that if X, Y and S are non-empty definable sets and S is a large subset of X × Y. then for a large set of tuples , where k = dim(Y), the union of fibers is large in Y. Finally, given a weakly o-minimal structure , we find various conditions equivalent to the fact that the topological dimension in enjoys the addition property.

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29

ONSHUUS, ALF, and CHARLES STEINHORN. "ON LINEARLY ORDERED STRUCTURES OF FINITE RANK." Journal of Mathematical Logic 09, no. 02 (December 2009): 201–39. http://dx.doi.org/10.1142/s0219061309000896.

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O-minimal structures have long been thought to occupy the base of a hierarchy of ordered structures, in analogy with the role that strongly minimal structures play with respect to stable theories. This is the first in an anticipated series of papers whose aim is the development of model theory for ordered structures of rank greater than one. A class of ordered structures to which a notion of finite rank can be assigned, the decomposable structures, is introduced here. These include all ordered structures definable (as subsets of n-tuples of the universe) in o-minimal structures. The principal result in this paper, Theorem 5.1, asserts roughly that a decomposable structure [Formula: see text] can be partitioned into finitely many definable subsets such that on each set the restriction of < is a "twisted lexicographic" order. As a consequence (Corollary 5.1), for all n and linear orders ≺ definable on a subset X ⊆ Mn in an o-minimal structure [Formula: see text], there is a definable partition of X such that the restriction of ≺ to each set in the partition is "lexicographic".

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30

Eiter, Thomas, and Antonius Weinzierl. "Preference-Based Inconsistency Management in Multi-Context Systems." Journal of Artificial Intelligence Research 60 (October 30, 2017): 347–424. http://dx.doi.org/10.1613/jair.5416.

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Multi-Context Systems (MCS) are a powerful framework for interlinking possibly heterogeneous, autonomous knowledge bases, where information can be exchanged among knowledge bases by designated bridge rules with negation as failure. An acknowledged issue with MCS is inconsistency that arises due to the information exchange. To remedy this problem, inconsistency removal has been proposed in terms of repairs, which modify bridge rules based on suitable notions for diagnosis of inconsistency. In general, multiple diagnoses and repairs do exist; this leaves the user, who arguably may oversee the inconsistency removal, with the task of selecting some repair among all possible ones. To aid in this regard, we extend the MCS framework with preference information for diagnoses, such that undesired diagnoses are filtered out and diagnoses that are most preferred according to a preference ordering are selected. We consider preference information at a generic level and develop meta-reasoning techniques on diagnoses in MCS that can be exploited to reduce preference-based selection of diagnoses to computing ordinary subset-minimal diagnoses in an extended MCS. We describe two meta-reasoning encodings for preference orders: the first is conceptually simple but may incur an exponential blowup. The second is increasing only linearly in size and based on duplicating the original MCS. The latter requires nondeterministic guessing if a subset-minimal among all most preferred diagnoses should be computed. However, a complexity analysis of diagnoses shows that this is worst-case optimal, and that in general, preferred diagnoses have the same complexity as subset-minimal ordinary diagnoses. Furthermore, (subset-minimal) filtered diagnoses and (subset-minimal) ordinary diagnoses also have the same complexity.

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31

KOVACSICS, PABLO CUBIDES, LUCK DARNIÈRE, and EVA LEENKNEGT. "TOPOLOGICAL CELL DECOMPOSITION AND DIMENSION THEORY IN P-MINIMAL FIELDS." Journal of Symbolic Logic 82, no. 1 (March 2017): 347–58. http://dx.doi.org/10.1017/jsl.2016.45.

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AbstractThis paper addresses some questions about dimension theory for P-minimal structures. We show that, for any definable set A, the dimension of $\bar A\backslash A$ is strictly smaller than the dimension of A itself, and that A has a decomposition into definable, pure-dimensional components. This is then used to show that the intersection of finitely many definable dense subsets of A is still dense in A. As an application, we obtain that any definable function $f:D \subseteq {K^m} \to {K^n}$ is continuous on a dense, relatively open subset of its domain D, thereby answering a question that was originally posed by Haskell and Macpherson.In order to obtain these results, we show that P-minimal structures admit a type of cell decomposition, using a topological notion of cells inspired by real algebraic geometry.

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32

Bell, John L. "Finite sets and frege structures." Journal of Symbolic Logic 64, no. 4 (December 1999): 1552–56. http://dx.doi.org/10.2307/2586795.

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Call a family of subsets of a set E inductive if and is closed under unions with disjoint singletons, that is, ifA Frege structure is a pair (E, ν) with ν a map to E whose domain dom(ν) is an inductive family of subsets of E such thatIn [2] it is shown in a constructive setting that each Frege structure determines a subset which is the domain of a model of Peano's axioms. In this note we establish, within the same constructive setting, three facts. First, we show that the least inductive family of subsets of a set E is precisely the family of decidable Kuratowski finite subsets of E. Secondly, we establish that the procedure presented in [2] can be reversed, that is, any set containing the domain of a model of Peano's axioms determines a map which turns the set into a minimal Frege structure: here by a minimal Frege structure is meant one in which dom(ν) is the least inductive family of subsets of E. And finally, we show that the procedures leading from minimal Frege structures to models of Peano's axioms and vice-versa are mutually inverse. It follows that the postulation of a (minimal) Frege structure is constructively equivalent to the postulation of a model of Peano's axioms.All arguments will be formulated within constructive (intuitionistic) set theory.

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33

Komkov, Stepan A. "Continuality of classes of functions in multivalued logic with minimal logarithmic growth rate." Discrete Mathematics and Applications 32, no. 2 (April 1, 2022): 97–103. http://dx.doi.org/10.1515/dma-2022-0009.

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Abstract We show that in multivalued logic there exist a continual family of pairwise incomparable closed sets with minimal logarithmic growth rate and a continual chain of nested closed sets with minimal logarithmic growth rate. As a corollary we prove that any subset-preserving class in multivalued logic contains a continual chain of nested closed sets and a continual family of pairwise incomparable closed sets such that none of the sets is a subset of any other precomplete class.

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34

Novotný, Jiři, and Miroslav Novotný. "On Dependence in Wille’s Contexts." Fundamenta Informaticae 19, no. 3-4 (October 1, 1993): 343–53. http://dx.doi.org/10.3233/fi-1993-193-406.

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A concept in Wille’s context can be generated starting with a set of features. The problem of finding a minimal subset of the given set of features that generates the same concept as the given one is solved using a suitable dependence space and constructing reducts of one of its subsets. This result can be applied to information systems where it enables to cancel superfluous values of attributes.

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Alsaafin, Areej, and Ashraf Elnagar. "A Minimal Subset of Features Using Feature Selection for Handwritten Digit Recognition." Journal of Intelligent Learning Systems and Applications 09, no. 04 (2017): 55–68. http://dx.doi.org/10.4236/jilsa.2017.94006.

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Urfat, Nuriyev, and Ordin Burak †. "Computing near-optimal solutions for the dominating subset with minimal weight problem." International Journal of Computer Mathematics 81, no. 11 (November 2004): 1309–18. http://dx.doi.org/10.1080/03057920412331272126.

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Sun, Fuming, E. Xu, and Hongyu Ma. "Design and comparison of minimal symmetric model-subset for maneuvering target tracking." Journal of Systems Engineering and Electronics 21, no. 2 (April 2010): 268–72. http://dx.doi.org/10.3969/j.issn.1004-4132.2010.02.016.

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Gosztolya, Gábor, András Beke, Tilda Neuberger, and László Tóth. "Laughter Classification Using Deep Rectifier Neural Networks with a Minimal Feature Subset." Archives of Acoustics 41, no. 4 (December 1, 2016): 669–82. http://dx.doi.org/10.1515/aoa-2016-0064.

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Abstract Laughter is one of the most important paralinguistic events, and it has specific roles in human conversation. The automatic detection of laughter occurrences in human speech can aid automatic speech recognition systems as well as some paralinguistic tasks such as emotion detection. In this study we apply Deep Neural Networks (DNN) for laughter detection, as this technology is nowadays considered state-of-the-art in similar tasks like phoneme identification. We carry out our experiments using two corpora containing spontaneous speech in two languages (Hungarian and English). Also, as we find it reasonable that not all frequency regions are required for efficient laughter detection, we will perform feature selection to find the sufficient feature subset.

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Alzohairi, Mohammad. "Triangle-free graphs which are minimal for some nonstable 4-vertex subset." Arab Journal of Mathematical Sciences 21, no. 2 (July 2015): 159–69. http://dx.doi.org/10.1016/j.ajmsc.2015.02.003.

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40

Tseng, Frank S. C., Arbee L. P. Chen, and Wei-Pang Yang. "Searching a minimal semantically-equivalent subset of a set of partial values." VLDB Journal 2, no. 4 (October 1993): 489–512. http://dx.doi.org/10.1007/bf01263049.

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Ballas, Z. K., and W. Rasmussen. "Lymphokine-activated killer (LAK) cells. IV. Characterization of murine LAK effector subpopulations." Journal of Immunology 144, no. 1 (January 1, 1990): 386–95. http://dx.doi.org/10.4049/jimmunol.144.1.386.

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Abstract The precursors of murine lymphokine-activated killers (LAK) can be divided into two major subsets: NK-like (CD8-, NK1.1+, asialo GM1+) and T-like (CD8+, NK1.1-, asialo GM1+). LAK effectors have generally been characterized as being either CD8+ or NK1.1+. In this study, we divided each of these effector subsets further by virtue of their expression of B220 (as defined by the mAb 6B2) and Ly-24 (Pgp-1). Freshly obtained CD8+ and NK1.1+ cells were found, by fluorescence analysis, to be B220-. Lytically active LAK effector subsets were either CD8+ B220+ Ly-24+ or NK1.1+ B220+ Ly-24+. Most interestingly, a distinct NK1.1+ B220- Ly-24+ subset existed but had minimal lytic activity, suggesting that only a subset of NK cells is capable of acquiring the broad lytic activity of LAK. The acquisition of the B220 marker by the CD8+ subset closely paralleled its expression of lytic activity. However, classical MHC-restricted CD8+ CTL were Ly-24+ but remained B220- suggesting that the acquisition of the B220 marker, as defined by the 6B2 mAb, is not merely the result of cellular differentiation but may serve as a marker of MHC-nonrestricted killers. Three "classes" of target cells were examined for their susceptibility to lysis by the LAK effector subsets: YAC-1 (NK sensitive), CL27A (NK resistant), and autologous lymphoblasts that have been modified with 2, 4, 6-trinitrobenzene sulfonic acid. YAC-1 was lysed exclusively by the NK1.1+ B220+ Ly-24+ subset, 2,4,6-trinitrobenzene sulfonic acid-self was lysed exclusively by the CD8+ B220+ Ly-24+ subset whereas CL27A was lysed by both subsets. This pattern of lysis was confirmed by the in vivo depletion of NK1.1+ cells. It, therefore, appears that LAK effector subsets may be more selective in their lytic repertoire than previously thought.

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Verona, Andrei, and Maria Elena Verona. "A Note on Minimal Usco Maps." Canadian Mathematical Bulletin 34, no. 3 (September 1, 1991): 412–16. http://dx.doi.org/10.4153/cmb-1991-066-8.

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AbstractWe prove that the composition of a minimal usco map, defined on a Baire space, with a lower semicontinuous function is single valued and usco at each point of a dense G$ subset of its domain. This extends earlier results of Kenderov and Fitzpatrick. As a first consequence, we prove that a Banach space, with the property that there exists a strictly convex, weak* lower semicontinuous function on its dual, is a weak Asplund space. As a second consequence, we present a short proof of the fact that a Banach space with separable dual is an Asplund space.

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Carling, D. E., S. Kuninaga, and K. A. Brainard. "Hyphal Anastomosis Reactions, rDNA-Internal Transcribed Spacer Sequences, and Virulence Levels Among Subsets of Rhizoctonia solani Anastomosis Group-2 (AG-2) and AG-BI." Phytopathology® 92, no. 1 (January 2002): 43–50. http://dx.doi.org/10.1094/phyto.2002.92.1.43.

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Hyphal anastomosis reactions, rDNA-internal transcribed spacer (ITS) sequences, and virulence of isolates representing Rhizoctonia solani AG-BI and six subsets of anastomosis group (AG)-2 (-2-1, -2-2 IIIB, -2-2 IV, -2-2 LP, -2-3, and -2-4) were compared. AG-2-4 is a subset described for the first time in this report. Anastomosis reactions within AG-BI and the listed subsets of AG-2 were generally strong but, between subsets, ranged from strong to a very weak “bridging” -type reaction. Anastomosis reaction alone generally did not provide adequate evidence for placement of an isolate into a subset of AG-2. Anastomosis reactions between AG-BI and the original subsets of AG-2 (-2-1 and -2-2) are very strong; for this reason, we propose that it be included as a subset of AG-2 (designation AG-2 BI). Subsets -2-3 and -2-4 show very weak bridging-type anastomosis reactions with all other subsets of AG-2 and thus may be candidates for independent AG status. Grouping within AG-2 based on rDNA-ITS sequences was consistent with the abovementioned subsets. However, grouping based on virulence as measured herein does not conform to established grouping patterns within AG-2 and does not seem useful as a group-defining criterion. A broad range of damage was observed among members of the most virulent subsets (-2-1, -2-2 IIIB, -2-2 IV, and -2-4), whereas other subsets (-2 BI, -2-2 LP, and -2-3) were similar to one another in causing a minimal level of damage. Group-specific primer pairs for each of the seven subsets of AG-2 were designed based on the abovementioned rDNA-ITS sequences. Primer pairs proved dependable and subset specific in polymerase chain reaction amplifications of purified genomic DNA from 109 isolates of R. solani and two isolates of binucleate Rhizoctonia. These primers will provide a simple and useful method for subset-specific characterization within AG-2 if further critical evaluations confirm their specificity.

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Etesami, Jalal, Negar Kiyavash, and Todd Coleman. "Learning Minimal Latent Directed Information Polytrees." Neural Computation 28, no. 9 (September 2016): 1723–68. http://dx.doi.org/10.1162/neco_a_00874.

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We propose an approach for learning latent directed polytrees as long as there exists an appropriately defined discrepancy measure between the observed nodes. Specifically, we use our approach for learning directed information polytrees where samples are available from only a subset of processes. Directed information trees are a new type of probabilistic graphical models that represent the causal dynamics among a set of random processes in a stochastic system. We prove that the approach is consistent for learning minimal latent directed trees. We analyze the sample complexity of the learning task when the empirical estimator of mutual information is used as the discrepancy measure.

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Desoteux, Matthis, Corentin Louis, Kevin Bévant, Denise Glaise, and Cédric Coulouarn. "A Minimal Subset of Seven Genes Associated with Tumor Hepatocyte Differentiation Predicts a Poor Prognosis in Human Hepatocellular Carcinoma." Cancers 13, no. 22 (November 10, 2021): 5624. http://dx.doi.org/10.3390/cancers13225624.

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Hepatocellular carcinoma (HCC) is a deadly cancer worldwide as a result of a frequent late diagnosis which limits the therapeutic options. Tumor progression in HCC is closely correlated with the dedifferentiation of hepatocytes, the main parenchymal cells in the liver. Here, we hypothesized that the expression level of genes reflecting the differentiation status of tumor hepatocytes could be clinically relevant in defining subsets of patients with different clinical outcomes. To test this hypothesis, an integrative transcriptomics approach was used to stratify a cohort of 139 HCC patients based on a gene expression signature established in vitro in the HepaRG cell line using well-controlled culture conditions recapitulating tumor hepatocyte differentiation. The HepaRG model was first validated by identifying a robust gene expression signature associated with hepatocyte differentiation and liver metabolism. In addition, the signature was able to distinguish specific developmental stages in mice. More importantly, the signature identified a subset of human HCC associated with a poor prognosis and cancer stem cell features. By using an independent HCC dataset (TCGA consortium), a minimal subset of seven differentiation-related genes was shown to predict a reduced overall survival, not only in patients with HCC but also in other types of cancers (e.g., kidney, pancreas, skin). In conclusion, the study identified a minimal subset of seven genes reflecting the differentiation status of tumor hepatocytes and clinically relevant for predicting the prognosis of HCC patients.

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Godfrey, D. I., J. Kennedy, T. Suda, and A. Zlotnik. "A developmental pathway involving four phenotypically and functionally distinct subsets of CD3-CD4-CD8- triple-negative adult mouse thymocytes defined by CD44 and CD25 expression." Journal of Immunology 150, no. 10 (May 15, 1993): 4244–52. http://dx.doi.org/10.4049/jimmunol.150.10.4244.

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Abstract We have subdivided mouse CD4-CD8-CD3- triple-negative (TN) thymocytes into four subsets based upon expression of CD44 and CD25, including CD44+CD25-, CD44+CD25+, CD44-CD25+ and CD44-CD25-. Characterization of these cells revealed several features distinct to each subset, in particular the expression of high levels of c-kit (the receptor for stem cell factor) by CD44+CD25-TN and CD44+CD25+TN but not by CD44-CD25+TN and CD44-CD25-TN. The CD44+CD25+TN subset also included the IL-7 and stem cell factor-responsive cells, whereas only minimal responsiveness was observed by the CD44- populations. These subsets also showed differential cytokine production potential (CD44+CD25- > CD44+CD25+ > CD44-CD25+ > CD44-CD25-) after stimulation with calcium ionophore, PMA and IL-1. The repopulation potential of these subsets in 2-deoxyguanosine-treated fetal thymic lobes supports the following maturation sequence: CD44+CD25- -->CD44+CD25+ -->CD44-CD25+ -->CD44-CD25-. Furthermore, the sequence of progression from CD44+CD25+ to CD44-CD25+ cells was confirmed by their TCR beta-chain gene configuration. The former population exhibits germ-line TCR beta-chain configuration, whereas the latter subset shows a rearranged pattern.

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Apraiz, J. "Observability Inequalities for Parabolic Equations over Measurable Sets and Some Applications Related to the Bang-Bang Property for Control Problems." Applied Mathematics and Nonlinear Sciences 2, no. 2 (December 15, 2017): 543–58. http://dx.doi.org/10.21042/amns.2017.2.00045.

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AbstractThis article presents two observability inequalities for the heat equation over Ω× (0,T). In the first one, the observation is from a subset of positive measure in Ω× (0,T), while in the second, the observation is from a subset of positive surface measure on ∂Ω× (0,T). We will provide some applications for the above-mentioned observability inequalities, the bang-bang property for the minimal time, time optimal and minimal norm control problems, and also establish new open problems related to observability inequalities and the aforementioned applications.

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Fang, Hongqing, Pei Tang, and Hao Si. "Feature Selections Using Minimal Redundancy Maximal Relevance Algorithm for Human Activity Recognition in Smart Home Environments." Journal of Healthcare Engineering 2020 (November 27, 2020): 1–13. http://dx.doi.org/10.1155/2020/8876782.

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In this paper, maximal relevance measure and minimal redundancy maximal relevance (mRMR) algorithm (under D-R and D/R criteria) have been applied to select features and to compose different features subsets based on observed motion sensor events for human activity recognition in smart home environments. And then, the selected features subsets have been evaluated and the activity recognition accuracy rates have been compared with two probabilistic algorithms: naïve Bayes (NB) classifier and hidden Markov model (HMM). The experimental results show that not all features are beneficial to human activity recognition and different features subsets yield different human activity recognition accuracy rates. Furthermore, even the same features subset has different effect on human activity recognition accuracy rate for different activity classifiers. It is significant for researchers performing human activity recognition to consider both relevance between features and activities and redundancy among features. Generally, both maximal relevance measure and mRMR algorithm are feasible for feature selection and positive to activity recognition.

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Igusa, Gregory. "Nonexistence of minimal pairs for generic computability." Journal of Symbolic Logic 78, no. 2 (June 2013): 511–22. http://dx.doi.org/10.2178/jsl.7802090.

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AbstractA generic computation of a subset A of ℕ consists of a computation that correctly computes most of the bits of A, and never incorrectly computes any bits of A, but which does not necessarily give an answer for every input. The motivation for this concept comes from group theory and complexity theory, but the purely recursion theoretic analysis proves to be interesting, and often counterintuitive. The primary result of this paper is that there are no minimal pairs for generic computability, answering a question of Jockusch and Schupp.

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Baizhanov, Bektur Sembiuly. "Expansion of a model of a weakly o-minimal theory by a family of unary predicates." Journal of Symbolic Logic 66, no. 3 (September 2001): 1382–414. http://dx.doi.org/10.2307/2695114.

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AbstractA subset A ⊆ M of a totally ordered structure M is said to be convex, if for any a, b ∈ A: [a < b → ∀t (a < tb → t ∈ A)]. A complete theory of first order is weakly o-minimal (M. Dickmann [D]) if any model M is totally ordered by some ∅-definable formula and any subset of M which is definable with parameters from M is a finite union of convex sets. We prove here that for any model M of a weakly o-minimal theory T. any expansion M+ of M by a family of unary predicates has a weakly o-minimal theory iff the set of all realizations of each predicate is a union of a finite number of convex sets (Theorem 63). that solves the Problem of Cherlin-Macpherson-Marker-Steinhorn [MMS] for the class of weakly o-minimal theories.

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