Existence Of Subset Research Articles

Does the period table appear doubled? Two variants of division of elements into two subsets. Internal and secondary periodicity

Demarcation of elements for two subsets appears to be the most fundamental approach to their classification. If one draws a vertical straight line through the middle of each block of elements in the Periodic table, all the elements are divided into two subsets: “early” and “later”. For example, in the d-block, the early ones are Sc–Mn, and the late ones, respectively, are Fe–Zn. Later elements partially repeat the properties of the early ones, and this is defined as the internal periodicity. Another criterion for dividing the elements into two subsets is the evenness and oddness of the sum of n + l, where n is the principal quantum number, and l is the orbital quantum number for the outer electron subshells. Properties of the odd elements (for example, B–Ne, Ga–Kr, Tl–Rn in the p-block) are closer to each other than to properties of even elements (Al–Ar, In–Xe), and vice versa. This regularity is manifested as the secondary periodicity. The history of concepts, which considered the existence of subsets as well as of inner and secondary periodicities, is discussed. The features of the electronic structure, which underlie the existence of subsets, are considered. The existence of subsets was depicted earlier by dividing the periodic table into two tables or by applying a mirror-symmetric table. Small changes are proposed in the conventional Periodic table, allowing to reflect the existence of the considered subsets.

An application of DEA in efficiency evaluation of universities

In order to demonstrate the helpfulness of data envelopment analysis (DEA) modelling to conduct decision making units (DMUs), here a case study has been developed to efficiency evaluation of departments of a university. The slack-based measure (SBM) model has been used in order for efficiency assessment and also benefiting from the advantages of non-radial models. This model has been developed in presence of trade-off technology. Also, some modifications are made in this model due to the existence of subset of input and (or) outputs which can only take integer values. Among the chosen input and output factors, there exist explanatory factors thus we use the theory of fuzzy DEA in order to deal with these factors. Finally, the acquired results show the necessary alterations for the inefficient units and generate guidance for using resources and plans effective strategy.

The Composition of the B Cell Receptor Repertoire In 7428 Cases of Chronic Lymphocytic Leukemia: One Third Stereotyped, Two Thirds Heterogeneous - What Does This Mean?

AbstractAbstract 43Chronic lymphocytic leukemia (CLL) is characterized by the existence of subsets (clusters) of cases with restricted, “stereotyped” immunoglobulin (IG) variable heavy complementarity-determining region 3 (VH CDR3) sequences within their B cell receptors (BcR), suggesting selection by common epitopes or classes of structurally similar epitopes. Emerging evidence indicates that the grouping of CLL cases into distinct clusters with “stereotyped” BcR is functionally and prognostically relevant. Further than that, several issues remain open: (i) the refinement of criteria for identification of BcR stereotypy and cluster assignment; (ii) the true frequency of BcR stereotypy; (iii) the total number of clusters and relative size of each; and, (iv) the identification of “CLL-biased” features in BcR stereotypes. To address these issues, we systematically examined VH CDR3 stereotypy in 7596 IGHV-D-J sequences from 7428 patients with CLL (168 cases, 2.2%, with two productive sequences), three times the size of the largest published series. Recent studies in both normal B cells and other (non-CLL) B cell malignancies along with accumulated experience in our group led to an advanced clustering bioinformatics algorithm applying more stringent criteria than before. A novel parameter was also included; the usage of IGHV genes, which takes into account the role of the germline-encoded specificities in (super)antigen recognition. The algorithm assigns sequences in a cluster only if exhibiting >50% amino acid identity and >70% amino acid VH CDR3 similarity and also carrying IGHV genes that share common ancestry and, thus, belong to the same IGHV phylogenetic clan. To increase the likelihood that cluster assignment reflects actual structural relatedness, we also required that each cluster consisted only of sequences with identical VH CDR3 length and identical offsets of common patterns. Following this new approach, 2308/7596 (30.4%) CLL sequences were assigned to 952 different ground-level clusters with shared patterns and unique characteristics, each containing 2 to 56 cases. Different types of VH CDR3 patterns were identified, independent of mutational status, as “mainly germline”, i.e. deriving from restricted associations of specific IGHD and IGHJ genes, and “junctional+germline”, i.e. extending over V-D and/or D-J junctions as well. In several clusters of mutated sequences, the cluster-defining features were ubiquitous junctional residues. Common sequences among ground-level clusters enabled grouping into clearly delineated, higher-order (HO) clusters that were considerably larger in size and displayed ‘CLL-biased’ features with regard to: IGHV gene usage, somatic hypermutation (for clusters with mutated sequences) and VH CDR3 pattern composition. As an example, the largest HO cluster, including 213 sequences (2.8% of the cohort), utilized the IGHV3-21 gene with an acidic residue at VH CDR3 position 107 (3 of 9), while the second-ranking HO cluster, including 184 sequences (2.1% of the cohort), utilized different IGHV genes of Clan I (e.g. IGHV1-2, 1–3, 1–8, 1–18, 5-a, 7-4-1) with a QWL motif at VH CDR3 positions 108–110 (4-6 of 13). Based on random set simulations (using the actual sequences) and starting from a critical mass of 2000 cases, each increase of the total set by a 1000 random cases resulted in an increase in the percentage of stereotypy to ∼2% (i.e. from 21% in 2000 cases to 25% in 3000 cases to 30% in 7000), though not proportional to the increase of the cohort. Perhaps most important, however, was the finding that the percentage of sequences in known major clusters was remarkably stable compared to previous studies on smaller series. These results strongly indicate that not all CLL belong to stereotyped subsets even if the cohort size is increased significantly, corroborating our previous hypothesis that CLL consists of two distinct categories, one with stereotyped and the other with heterogeneous BcR, likely of different ontogenetic origin. Furthermore, they demonstrate that the major clusters collectively represent a sizeable proportion of the cohort. Consequently, this deeper, more robust, compartmentalized examination of BcR structures in association with other biological and clinical information may eventually pave the way for the introduction of specialized treatment protocols applicable to a significant number of patients assigned to the same cluster. Disclosures:No relevant conflicts of interest to declare.

Understanding human myeloid dendritic cell subsets for the rational design of novel vaccines

Dendritic cells (DCs) orchestrate a repertoire of immune responses that endows resistance to infection and tolerance to self. Understanding the principles by which DCs control immunity and tolerance has provided a rich basis for studying and improving clinical outcome of human disease treatment. Several features contribute to the complexity of the DC system. Among these, plasticity and existence of subsets are prominent determinants to the quality of the elicited immune responses. Indeed, different DC subsets are distributed in peripheral tissues and the blood and display different microbial receptors, surface molecules and cytokine expression, all of which influence the immunologic outcome. The biologic raison d'être for separate DC subsets has been the focus of many studies including our own and is being reviewed with an emphasis on human skin DCs.

Gene expression identifies heterogeneity of soft tissue sarcomas

9574 Background: Soft tissue sarcomas (STS) exhibit heterogeneity in their clinical behavior, even within histological subtypes. Histological appearance is determined by gene expression. However, metastatic propensity, tumor growth, and response to chemotherapy may be determined by gene expression patterns that do not correlate well with morphology. One approach to identify heterogeneity is to search for markers that correlate with differences in tumor behavior. Alternatively, subsets may be identified based on gene expression patterns independent of knowledge of clinical outcome. We have reported gene expression patterns that distinguish two broad classes of clear cell renal carcinoma (ccRCC) independent of histological appearance, and other patterns that can distinguish heterogeneity of serous ovarian carcinoma (OVCA). Methods: In this study, gene expression in 41 samples of STS (including malignant fibrous histiocytoma (MFH), leiomyosarcoma, liposarcoma, and synovial sarcoma), 12 samples of fibromatosis, and 17 normal tissues was determined at Gene Logic Inc. (Gaithersburg, MD) using Affymetrix GeneChip U_133 arrays containing approximately 40,000 genes/ESTs. Gene expression analysis was performed with the Gene Logic Genesis Enterprise System Software. Results: Hierarchical clustering using two gene sets, one that distinguished two subsets of ccRCC, and a second set that distinguished two subsets of OVCA, both generated subgroups within the STS that for some, but not all, subtypes correlated with histology, and also suggested the existence of subsets of MFH. Both gene sets also identified the same two subsets of the fibromatosis samples. In addition, genes expressed uniquely in MFH, leiomyosarcomas, and liposarcomas among these and 512 samples from 17 other normal tissue types were identified. Conclusions: The ability to sub-classify histological subtypes of STS, including identifying possible subsets of MFH, using gene sets derived from studies of two different carcinomas suggests that these subgroups may have biological significance. Some of the genes identified as over-expressed in particular subsets of STS compared with a variety of normal tissues may reflect possible targets to which anti-tumor therapy could be directed, and may also be useful for sub-classification of STS. No significant financial relationships to disclose.

Immunoglobulin light chain repertoire in chronic lymphocytic leukemia

AbstractImmunoglobulin kappa (IGK) and immunoglobulin lambda (IGL) light chain repertoire was analyzed in 276 chronic lymphocytic leukemia (CLL) cases and compared with the relevant repertoires from normal, autoreactive, and neoplastic cells. Twenty-one functional IGKV genes were used in IGKV-J rearrangements of 179 kappa-CLL cases; the most frequent genes were IGKV3-20(A27), IGKV1-39/1D-39(O2/O12), IGKV1-5(L12), IGKV4-1(B3), and IGKV2-30(A17); 90 (50.3%) of 179 IGK sequences were mutated (similarity < 98%). Twenty functional IGLV genes were used in IGLV-J rearrangements of 97 lambda-CLL cases; the most frequent genes were IGLV3-21(VL2-14), IGLV2-8(VL1-2), and IGLV2-14(VL1-4); 44 of 97 IGL sequences (45.4%) were mutated. Subsets with “CLL-biased” homologous complementarity-determining region 3 (CDR3) were identified: (1) IGKV2-30-IGKJ2, 7 sequences with homologous kappa CDR3 (KCDR3), 5 of 7 associated with homologous IGHV4-34 heavy chains; (2) IGKV1-39/1D-39-IGKJ1/4, 4 unmutated sequences with homologous KCDR3, 2 of 4 associated with homologous IGHV4-39 heavy chains; (3) IGKV1-5-IGKJ1/3, 4 sequences with homologous KCDR3, 2 of 4 associated with unmutated nonhomologous IGHV4-39 heavy chains; (4) IGLV1-44-IGLJ2/3, 2 sequences with homologous lambda CDR3 (LCDR3), associated with homologous IGHV4-b heavy chains; and (5) IGLV3-21-IGLJ2/3, 9 sequences with homologous LCDR3, 3 of 9 associated with homologous IGHV3-21 heavy chains. The existence of subsets that comprise given IGKV-J/IGLV-J domains associated with IGHV-D-J domains that display homologous CDR3 provides further evidence for the role of antigen in CLL pathogenesis.

Endothelial cells in the bone marrow of patients with multiple myeloma

AbstractEndothelial cells (EC) were extracted through a lectin-based method from bone marrow of 57 patients with active multiple myeloma (MM) and compared with their healthy quiescent counterpart, human umbilical vein EC (HUVEC). MMECs exhibit specific antigens that indicate ongoing angiogenesis and embryo vasculogenesis; solid intercellular connections, hence stability of MM neovessels; and frequent interactions with plasma cells, hence tumor dissemination. They show heterogeneous antigen expression, hence existence of subsets. Their main genetic markers are indicative of a vascular phase. They show intrinsic angiogenic ability, because they rapidly form a capillary network in vitro, and extrinsic ability, because they generate numerous new vessels in vivo. They vividly secrete growth and invasive factors for plasma cells. They signal through kinases mandatory for development of neovascularization. Ultrastructurally, they are abnormal and show metabolic activation, like tumor ECs. Thalidomide heavily interferes with their functions. Vasculogenesis and angiogenesis might contribute to the MM vascular tree and progression, in the form of growth, invasion, and dissemination. In view of the heterogeneity of the antigenic phenotype of MMECs, a mixture (or a sequence) of antiangiogenic agents coupled with thalidomide would seem plausible for the biologic management of MM.

Complexity of choosing subsets from color sets

We raise and investigate the algorithmic complexity of the following problem. Given a graph G = ( V, E) and p-element sets L( v) for its vertices v ∈ V such that | L( u) ∪ L( v)| ⩾ p + r for all edges uv ∈ E, do there exist q-element subsets C( v) ⊆ L( v) with C( u) ∩ C( v) = 0 for all uv ∈ E? Here p, q, r are positive integers, p ⩾ q and p + r ⩾ 2 q. We characterize precisely which triples ( p, q, r) admit a polynomial solution, and for which ones the problem is NP-complete. Moreover, it is shown that for some restricted ranges of p and r with respect to q, the existence of subsets C( v) ⊂ L( v) for every collection { L( v)| v ∈ V{, is closely related to Turán's problem on uniform hypergraphs.

Universally Nonmeasurable Subgroups of &amp;#8477

Simple proofs (by use of the axion of choice in one form or another) of the existence of subsets of the real line R that are not measurable with respect to the Lebesgue outer measure A can be found in almost any textbook that discusses measure theory. Some of these examples are actually subgroups of the additive group R. Indeed, no subgroup H of DR for which R/H is countably infinite can be A-measurable and such subgroups can be obtained by use of a Hamel basis (see [3]). A particularly illuminating discussion of A-nonmeasurability is given in [5]. In this note we modify a transfinite induction argument given by F. Bernstein

ALGEBRAIC CONNECTIVITY

Let [Formula: see text] be a type of algebra in the sense of universal algebra. By defining singular simplices in algebras and emulating singular [co] homology, we introduce for each variety, pseudo-variety, and divisional class V of type [Formula: see text], a homology and cohomology theory which measure the V-connectivity of type-[Formula: see text] algebras. Intuitively, if we were to think of an algebra as a space and subalgebras which lie in V as simplices, then V-connectivity describes the failure of subalgebras to lie in V, i.e., it describes the "holes" in this space. These [co]homologies are functorial on the class of type-[Formula: see text] algebras and are characterized by a natural topological interpretation. All these notions extend to subsets of algebras. One obtains for this algebraic connectivity, the long exact sequences, relative [co]homologies, and the analogues of the usual [co]homological notions of the algebraic topologists. In fact, we show that the [co]homologies are actually the same as the simplicial [co]homology of simplicial complexes that depend functorially on the algebras. Thus the connectivities in question have a natural geometric meaning. This allows the wholesale import into algebra of the concepts, results, and techniques of algebraic topology. In particular, functoriality implies that the [co]homology of a pair of algebras A ⊆ B is an invariant of the position of A in B. When one V contains another, we obtain relationships between the [co] homology theories in the form of long exact sequences. Furthermore for finite algebras, V-[co]homology is effectively computable if membership in V is. We obtain an analogue of the Poincaré lemma (stating that subsets of an algebra in V are V-homologically trivial), extremely general guarantees of the existence of subsets with non-trivial V-homology for algebras not in V, long exact V-homotopy sequences, as well as analogues of the powerful Eilenberg-Zilber theorems and Kunneth theorems in the setting of V-connectivity for V a variety or pseudo-variety. Also in the more general case of any divisionally closed V, we construct the long exact Mayer-Vietoris sequences for V-homology. Results for homomorphisms include an algebraic version of contiguity for homomorphisms (which implies they are V-homotopic) and a proof that V-surmorphisms are V-homotopy equivalences. If we allow the divisional classes to vary, then algebraic connectivity may be viewed as a functor from the category of pairs W ⊆ V of divisional classes of [Formula: see text]-algebras with inclusions as morphisms' to the category of functors from pairs of [Formula: see text]-algebras to pairs of simplicial complexes. Examples show the non-triviality of this theory (e.g. "associativity tori"), and two preliminary applications to semigroups are given: 1) a proof that the group connectivity of a torsion semigroup S is homotopy equivalent to a space whose points are the maximal subgroups of S, and 2) an aperiodic connectivity analogue of the fundamental lemma of complexity.

Bellini, carpaccio, and receptors in the central nervous system

With the convergence of science from the fields of neurobiology and immunology, many exciting and challenging surprises have emerged regarding cytokines, neuroendocrine hormones, neuropeptides, excitatory amino acids, and their receptors. For some time neurobiologists have known that subsets of neural cells had different receptors for the same ligand. Those subsets of cells could be as different as neurons and astrocytes and as closely related as astrocytes from different lineages or anatomical areas. The neurobiological puzzle has been to determine the functional meaning of these differences. Immunologists in contrast have long understood the clear cut differences between T and B lymphocytes or T helper/inducer and T cytotoxic/suppressor cells and their response to cytokines. However, it is only very recently that they have discovered preferential use by these cells of different receptors for an identical cytokine ligand. Indeed, identical cytokines in the central nervous system and immune response may induce their pleiotropic responses by utilizing different receptors in these two systems. Immunologic paradigms may help neurobiologists predict the existence of subsets of neural cells and their function. Likewise, neurobiology may enable immunologists to predict roles for receptors in gene families as well as the existence of as yet unidentified receptors.

Countable dense homogeneous spaces under Martin’s axiom

We show that Martin’s axiom for countable partial orders implies the existence of a countable dense homogeneous Bernstein subset of the reals. Using Martin’s axiom we derive a characterization of the countable dense homogeneous spaces among the separable metric spaces of cardinality less thanc. Also, we show that Martin’s axiom implies the existence of a subset of the Cantor set which isλ-dense homogeneous for everyλ <c.

Dirichlet Series and Convolution Equations

In this paper we wish to propose a totally new approach to the theory of Dirichlet series, with the hope that our method will be able to shed new light on some old problems in the area. Our viewpoint is to consider Dirichlet series as a very particular case of solutions of homogeneous convolution equations, and to consider these objects in the framework of a general theory of Fourier analysis on non-algebraic varieties. In view of the character of this paper (which has to be considered preliminary, even though a relatively large number of results is obtained), we would like to briefly describe the philosophy which underlies our approach. From a historical point of view, the theory of Fourier integrals has been devised to be able to represent an arbitrary function as a linear combination of exponentials. Thus, functions on R (or Rn) which are sufficiently small at infinity, were given such representations with the use of exponentials with real frequencies. When larger growths at infinity had to be handled, it became necessary to allow the use of exponentials with complex frequencies and, as an immediate consequence, the Fourier integral representations became essentially non-unique, as every exponential exp(jc-z), z^C, has many integral representations (via the Cauchy formula) as a limit of linear combinations of exponentials. In the sixties, these natural considerations led L. Ehrenpreis to consider Fourier integral representations of (for example) C°° functions, with the specific purpose of finding out the existence of subsets S of C (which Ehrenpreis called sufficient sets) such that integral representations could exist with frequencies in S. Ehrenpreis developed a quite powerful theory (the so called theory of ^4t/-spaces [7]) with the idea of studying integral representations with exponentials whose frequencies were restricted to belong to some algebraic variety in C (or Cn). This study, in particular, provided a wealth of results on solutions of systems of linear constant coefficients partial differential equations (in which case S is the

Leukemic cell differentiation in childhood leukemias. Analysis by enzyme markers.

Enzyme marker analysis has become a valuable tool in leukemia research, especially as a part of the so-called multiple marker analysis which combines several disciplines for characterization of leukemia cells. In this study the qualitative activities of three enzyme markers were determined in leukemic cells from pediatric patients with acute leukemias: acid phosphatase (E.C. 3.1.3.2), carboxylic esterase (E.C. 3.1.1.1) and hexosaminidase (E.C. 3.2.1.30). The leukemia subtypes displayed different types of isoenzyme patterns. No additional isoenzyme was found that was not observed in normal blood cells, nor a single isoenzyme specific for a leukemia subtype. The biochemical profiles illustrated the existence of subsets in cALL, T-ALL and AML. The enzymologic polymorphism and the immunologic heterogeneity seen in leukemia subclasses have led together to an extended classification scheme of leukemias as well as to model schemes of normal hematopoietic cell differentiation. Despite former and constantly published assumptions there are still no specific markers of leukemia cells.

Typological factor analysis: A new classification method applied to geology

The purpose of typological factor analysis is to detect, within a multidimensional sample, the existence of subsets characterized by different maximal elongation directions. The method which has been successfully applied in the field of pattern recognition can be considered from two points of view: (1) an automatic classification or “dynamic clustering” technique: and (2) a form of factor analysis. Using this form of analysis nuclei of affine varieties (points, axes, planes, etc) are identified. Different case studies were analyzed in order to establish the advantages of the method compared to other methods. Geochemical analyses of rock samples; that is, rhyolites, mafic, and intermediate rocks of the Normetal (Abitibi) area were subjected to typological factor analysis for the purpose of classification of geological deposits and detection of geochemical anomalies. The method was also applied to the classification of sediments from the Barataria Bay area in Louisiana.

Current Concepts of the Antibody Response: Heterogeneity of Lymphoid Cells, Interactions, and Factors

Evidence is described for T-T interactions, for the existence of subsets of T cells with defined functions, for subcellular factors as mediators of these interactions, and for the heterogeneity of lymphocyte receptors for antigen. The following topics are discussed: cell interactions in the induction of helper cells; interactions in the induction of suppressor T cells; heterogeneity of T cells; cell cooperation in immune induction; and speculations on T-cell receptors. (HLW)

Heterogeneity of B cells: direct evidence of selective triggering of distinct subpopulations by polyclonal activators.

This investigation was undertaken to assess directly the previous postulate that distinct subsets of B cells in the adult mouse spleen are selectivity triggered by different polyclonal B-cell activators (PBA). Several strains of mice and lipopolysaccharide (LPS), purified protein derivative of tuberculin (PPD), and dextran sulphate (DS) were used in this study. Two experimental approaches were used: stimulation after addition of two PBAs simultaneously to cell cultures and eliminating the responding population to one PBA, by a hot pulse of radioactive thymidine, on a later response to another PBA. The results of these experiments indicated that DS stimulated a cell population completely different from that stimulated by the LPS- and PPD-sensitive cells. When LPS and PPD stimulations were compared, it was found that the cells responding to these PBAs were largely distinct, although some cells were sensitive to both these PBAs. The extension of the overlaps in these subsets (the number of cells that could be activated by either PBA) was found to vary from one strain to another. These experiments gave direct evidence of the existence of subsets that can be activated by different PBAs. The present results also provided indications of the functional performance of distinct subsets of B cells on activation.