Distinguished Subset Research Articles

Small nuclear ribonucleoprotein particle assembly in vivo: Demonstration of a 6S RNA-free core precursor and posttranslational modification

The in vivo synthesis and assembly of human small nuclear ribonucleoproteins (snRNPs) have been studied using pulse/chase analysis. Antibodies derived from patients with systemic lupus erythematosus (SLE) and mixed connective tissue disease (MCTD) recognize distinguishable subsets of pulse-labeled snRNP peptides. These antibodies were used to immunoprecipitate sucrose gradient fractionated pulse-labeled and pulse/chased snRNP proteins. The results indicate that assembly of the U RNA-containing snRNPs is a multistep process involving prior assembly of an RNA-free 6S core particle. This precursor contains snRNP peptides D, E, F, and G, which are common to all the different U RNA-containing particles. Furthermore, a posttranslational modification of one of the U1 snRNP-specific peptides has been observed, and the kinetics of this process indicates that the modification occurs after particle assembly. Functional and structural implications of a protein core for snRNP particles are discussed.

単調縮少写像の下で閉じた動的計画法のクラスについて

This paper considers a class of general dynamic programs which satisfies the mono tonicity and con- traction assumption, and in which the sets of cost functions and policies are closed under the monotone contraction operators. This class of dynamic programs includes, piecewise linear, affine dynamic programs, partially observable Markov decision processes, and many sequential decision processes under uncertainty such as machine maintenance control models and search problems with incomplete infOImation. An algorithm based on generalized policy improvement has the property that it only generates cost functions and policies belonging to subsets of cost functions and policies, respectively. as special cases. This paper considers a class of dynamic programs, called closed, with the property that the generalized policy improvement algorithm stays within a certain subset of cost functions and policies. In other words, the sets of cost functions and policies generated by the algo­ rithm are closed under the monotone contraction operators. Furthermore, it is possible to keep such sets within distinguished small subsets of the sets of all bounded cost functions and all stationary policies, respectively. This property is very important to dynamic programming from a computational aspect. The class of closed dynamic programs includes piecewise linear dynamic progralnming (16), affine dynamic programming (5), (6), partially ob­ servable Markov decision processes (7), (IS), (17) and many sequential decision processes with imperfect information such as machine maintenance models (17) and search models. The approximation of dynamic programs is

Serologic cross-reactions among rabbit secretory IgA molecules: Evidence for multiple subclasses of secretory IgA-f molecules

Serologie cross-reactions among allotypes of rabbit secretory IgA (sIgA) of the f-subclass were examined by quantitative radiobinding assays with various allo-anti-alpha chain reagents. Numerous cross-reactions were observed which demonstrated the complexity of the C αf allotypes. One of the reagents used in these studies reacted not only with all sIgA molecules of the immunogen C αf allotype but also with all sIgA molecules of the other C αf allotypes. Aliquots of the antiserum were each adsorbed with IgA molecules of these C αf allotypes and then used in radiobinding studies with sIgA-f molecules of the various C αf allotypes. The adsorbed reagents reacted with some but not all sIgA-f molecules, thus indicating that the C αf allotypes each comprise more than one serologically distinguishable subset. Results from these radiobinding experiments were used to develop a model in which each of the five IgA-f allotypes comprises at least two serologically distinguishable subsets. Each of these subsets expresses a unique pattern of C α determinants. These C α determinants appear to be protein in nature rather than carbohydrate as periodate oxidation of the sIgA-f glycoproteins does not affect the reactions of the molecules with the cross-reactive alloreagents. IgA molecules of the serologically distinguishable subsets presumably differ in amino acid sequence in the constant region and, thus, would be products of distinct C α genes. Therefore, it is probable that the cross-reactions of these molecules, which were previously thought to comprise a single subclass, sIgA-f, may reflect the presence of more than one subclass of sIgA-f molecules, i.e., a third subclass of rabbit sIgA.

On the lattice theory of function semi‐norms

We consider the lattice of function semi‐norms over a measure space, as well as certain distinguished subsets. We determine which subsets are sublattices and, in turn, which of these are Dedekind complete. We also investigate the extent to which the distributive and DeMorgan Laws are valid in this setting.

Cell surface antigens of human astrocytoma defined by mouse monoclonal antibodies: identification of astrocytoma subsets.

The surface antigens of cultured human malignant astrocytomas were analyzed by using mouse monoclonal antibodies. BALB/c mice were immunized repeatedly with either SK-MG-1 [a glial fibrillary acidic protein (GFA)-negative astrocytoma line] or SK-AO2 (a GFA-positive astrocytoma line). After fusion with NS/1 mouse myeloma cells, 12 antibody-producing clones were selected for detailed study. Serological analysis permitted the identification of nine distinct antigenic systems. Four monoclonal antibodies (Ab AJ225, Ab AO10, Ab AJ8, and Ab AO122) identified cell surface antigens preferentially expressed on tumors of neuroectodermal origin, and these antibodies subdivided the astrocytoma panel into distinguishable subsets. The determinant detected by Ab AO10 and Ab AJ8 showed mutually exclusive expression on the astrocytoma lines. The AO10 and AJ8 phenotypes appeared to reflect the differentiation state of the cultured cells; 4/7 AO10-positive astrocytomas expressed GFA, an intracellular astrocyte differentiation antigen, whereas all AJ8-positive astrocytoma (9/9) were GFA-negative. Five antibodies (Ab AJ10, Ab AJ9, Ab AJ17, Ab AJ425, and Ab AJ2) recognized determinants widely distributed on normal and malignant cells. Four antibodies defined in this study precipitated proteins from reduced preparations of radioisotope-labeled SK-MG-1 and SK-AO2 cells: Ab AJ225 (Mr 145,000); Ab AO122 (Mr265,000); Ab AJ10 (Mrs 195,000 and 165,000); and Ab AJ2 (Mrs 170,000, 140,000, 140,000, and 28,000).

Production of monoclonal antibodies to human IFN-alpha and their use for analysis of the antigenic composition of various natural interferons.

We have established three hybridoma cell lines (designated EBI-1, -2, and -3) secreting immunoglobulin G (IgG) antibodies specific for human alpha-interferon (HuIFN-alpha) by fusing P3X63Ag8.6.5.3 myeloma cells with spleen cells of mice immunized with human "lymphoblastoid" (NC-37) interferon (IFN). The antibodies were used to study the antigenic diversity of a number of IFNs derived from blood leukocytes and lymphoid cell lines. When incubated with 10 U of IFN, EBI-1 antibodies completely neutralized the antiviral activity of HuIFN-alpha rA produced in E coli as well as of IFN produced spontaneously in several lymphoblastoid cell lines. In contrast, only 60-70% of alpha-interferon (IFN-alpha) induced in leukocytes, lymphoma, or lymphoblastoid cell lines by Sendai virus or poly (I):(C) could be neutralized by the antibody; furthermore, IFN-alpha produced spontaneously in bromodeoxyuridine-treated lymphoma cells was also only partially neutralized. EBI-2 and EBI-3 antibodies were tested against a smaller set of samples and found to react similarly. Our results indicate that human IFN-alpha subtypes can be grouped into at least two antigenically distinguishable subsets, one of which being represented by IFN-alpha A, and that these subsets can be expressed differently under different conditions in a given cell type.

Wide-field neurons in somatosensory thalamus of domestic cats under barbiturate anesthesia

A sample of 392 somatosensory thalamic neurons from barbiturate-anesthetized cats, all responsive to stimulation of the contralateral forepaw (CFP), was compared with a previously described sample from chloralose-anesthetized animals with respect to (i) the functional properties of CFP-responsive neurons isolated within nucleus ventralis posterolateralis (VPL), (ii) the spatial distributions of distinguishable neuronal subsets within VPL, and (iii) the distribution of CFP-evoked single-unit discharge along the mediolateral dimension of the nucleus and over time. Eighty-two percent of the barbiturate neurons were responsive only to CFP; their receptive fields were small, usually confined to one or two digits or an area on the paw dorsum. Members of this sa subset were predominantly excited by light touch or deflection of hairs. The other 18% responded to stimulation of at least one “off-focus” limb in addition to CFP. These ∼ sa neurons possessed larger receptive fields (though not as large as those observed under chloralose), which were bilaterally disposed in 32% of this subset. Fifty-eight percent of the ∼ sa neurons were excited by light touch or hair deflection. The proportion of the barbiturate sample subject to corticofugal influences (62%) was smaller than that under chloralose (74%), with inhibitory influences predominating on both sa and ∼ sa neurons in contrast to an excitatory effect on ∼ sa neurons under chloralose. Compared with chloralose data, impulse discharge reached peak intensity earlier and overall duration of response was reduced for all subsets. Although the spike density distribution for ∼ sa neurons was particularly abbreviated, this subset was well represented among VPL neurons responding to stimulation of the forepaw. As they are seen in barbiturate preparations also, wide-field somatosensory thalamic neurons are not an artifact of chloralose anesthesia.

Decomposition of graph functions

The V-functions of Tutte [1] are generalized to U-functions on graphs with a distinguished subset of vertices. The class of U-functions of two variables generalize dichromatic polynomials as well as the W-functions defined by Tutte [2]. The values of U-functions on a graph G are characterized in terms of spanning subgraphs of G and also in terms of collections of simple graphs constructed from G. Decompositions of dichromatic polynomials as well as dichromatic U-functions are obtained in terms of decompositions of G.

Some Finite Point Geometries

Finite sets with distinguished subsets called lines give examples of the theory of balanced incomplete block designs.

Average boundary conditions in Cauchy problems

We consider the general Cauchy problem with initial data in a Hilbert space and with a formal dissipative linear generator. A complete parametrization is known of the (abstract) boundary conditions which make this problem well set. We exhibit a distinguished subset B E of the set B of boundary conditions and demonstrate explicitly that the evolution associated with each B in B can be represented as a (time independent) average over the evolutions associated with B′ in B E . Applications are discussed to Schrödinger equations in bounded regions or with singular potentials.

On linear spaces in which every plane is either projective or affine

A linear space is a set S whose elements are called points, provided with certain distinguished subsets called lines such that any two points are contained in one and only one line and every line contains at least two points. The line passing through two points x and y will be denoted by xy. A subspace of a linear space S is a subset V of S such that any line having at least two points in V is contained in IF. The subspace generated by a subset X of S will be the intersection of all subspaces containing .V and will be denoted by (X>. A plane of a linear space S is a subspace generated by a triangle, that is by three non-coUinear points of S. An affine plane is a linear space A containing at least three non-collinear points and such that for every line L of A and any point p ~L, there is one and only one line L' such that p~U and LnL' =0. In an affine plane A, we shall say that a line L is parallel to a line L' (and write L//L') if LnL' =0 or L =L'. A projective plane is a linear space P containing at least four points, no three of which are collinear, and such that any two lines of P have a point in common. It is well-known that in a projective or an affine plane all lines have the same cardinality. The purpose of this paper is to prove the following theorem:

Difference sets and planar polarities

A block design is a finite set p of elements called points, where |p| = v, together with certain distinguished subsets of p called blocks, such that(i) each block contains k points,(ii) each point is contained in r blocks, and(iii) two distinct points are contained in precisely λ blocks.

Kernels of compound games with simple components

The kernel is a solution concept for a cooperative game. It reflects symmetry properties of the characteristic function and desirability relations over the set of the players. Given m games over disjoint sets of players and an m-person game,one defines a compound game over the union of the m disjoint sets. These m games are the components and the above rnperson game is called the quotient. The quotient may be treated as a game played by representatives of the component games. The kernel of the compound game is characterized fully. The compound kernel is, in fact, a composition of the components' kernels by means of a distinguished subset of the imputation space of the quotient game. This subset depends also on the number of veto players in each component. An effective formula for the compound kernel is given for compound simple games. This formula enables short cuts in the computations leading to the kernel of a decomposable game. The results are applied to compound majority games and a complete description of their kernels is given.

Tensor compositions and lists of combinatorial structures

By a list B we mean a finite linearly ordered set. Let be a sublist and let V denote a vector space isomorphic to the free vector space generated by B over a field F of characteristic zero. Assume the isomorphism is explicitly given by a function Let S be a distinguished subset of V and let Q be a finite set. A function will be called an S-composition of L if . Various compositions of a list provide alternative ways of generating, storing, and manipulating the list in machine computation. In this paper we study some of the properties of such compositions in the case where B = RD is a finite function spaceV is an algebra of tensors, and S certain distinguished subsets of V such as the homogeneous tensors. The problem of generating compositions of lists of orbit classes of L under group actions is also considered.

Incidence axioms for affine geometry

In terms of incidence alone it is possible to define an affine plane, as Artin does [I], by calling lines parallel if they do not intersect, and basing the definition on the Euclidean axiom that there is a unique parallel to a line through a point not on the line. In higher dimensions we can define afine geometry by deleting the points and lines of a hyperplane from a projective geometry, using the axioms of Veblen and Young [4]. It is an easy exercise to show that the Artin approach and that of Veblen and Young agree in the definition of an afIine plane. Sut in higher dimensions it is not clear how an afline geometry can be defined directly so that it can be shown to arise from a projective geometry by deleting the points and lines of a hyperplane. This paper gives a set of axioms which have this property. We must define parallelism in such a way that nonintersecting lines in a plane are parallel. But the real surprise is that this is not enough. In Section 5 an example is given of a geometry in which every plane is an afhne plane, but the geometry as a whole is not an afline geometry. If we think of the embedding of an affine geometry into a projective geometry, lines are parallel if and only if they pass through the same projective point at infinity. In particular, the abstract property of parallelism between lines must be transitive, and three parallel lines need not lie in a plane. Thus the axiom of transitivity of parallelism (Axiom A4 in Section 2) is a three-dimensional axiom. The axioms are given in Section 2. Affine planes are defined in Section 3, and their main properties are developed there. The issue as to whether or not the plane is Desarguesian does not arise. In Section 4, the ideal (infinite) points and lines are defined and adjoined to the affine geometry. It is shown that the resulting geometry is a projective geometry. From the treatment here, it follows that if we have an incidence geometry, consisting of points and certain distinguished subsets of points which we call

Some types of error in a choice response task.

Errors from a serial response task involving single-finger responses to alphabetic stimuli are analysed and discussed in relation to findings which have been reported from tasks with more compatible stimulus-response relationships. Errors are divided into three distinguishable subsets and in each case found to have longer latencies than correct responses. Those which result from mirroring the required response about the centre of the hand are found to resist elimination during practice and their frequency seems to depend on the type of code used. In all cases error correction times are faster than the times to make a correct response but mirror errors and errors involving a finger adjacent to the correct response are corrected faster than other errors. The findings are discussed in relation to the theory of choice reaction time and error correction.

Choice Functions and Revealed Preference

(1) Much of revealed preference theory has been concerned with choices restricted to certain distinguished subsets of alternatives, in particular to a class of convex polyhedra (e.g., budget triangles in the two commodity case). This restriction may have some rationale for analyzing the preferences of competitive consumers, but it makes the results unusable for other types of choices, e.g., of government bureaucracies, of voters, of consumers in an imperfect market. If the restriction is removed, the axiomatic structure of revealed preference theory changes radically. This axiomatic structure is studied in Sections 2-5. In Section 6 the rationale of restricting the domain of choice functions and that of rationality conditions is critically examined.

An Axiomatic Line Geometry

In their classic treatment (5) Veblen and Young build n-dimensional projective geometry from points and lines. Naturally, each line becomes identified with the set of points with which it is incident, and many treatments build from points alone, postulating the existence of certain distinguished subsets of the set of points. From either point of view, some labour is required, even in the two-dimensional case, to establish duality; hence a considerable interest attaches to self-dual systems of axioms; cf. (2; 3).

A Topological Approach to Geometry

The purpose of this paper is to summarize a method by which at least certain topological spaces can be characterized up to homeomorphism class. The method employs the notion of a geometry defined on a set by means of distinguished subsets called k-flats which are generalizations of k-dimensional subspaces. The set theoretic axioms defining a geometry are intended to embody the essence of anything that mathematicians have ever called a geometry. If the set on which a geometry has been defined is also a topological space, then the topology and geometry may be axiomatically related in such a manner that the topology can be completely characterized. We shall concern ourselves in this paper primarily with characterizing Rm as a topological space using the properties generalized from the Euclidean geometry on Rm. In Rm, the usual Euclidean geometry, the standard metric, and the algebraic structure of Rn as a vector space are tightly bound together. In our initial abstraction we do away with coordinatization, metrics, and the algebraic structure of geometries derived from linear manifolds. A geometry is defined as follows: Let X be a set. An element of X is called a point. We define G = { F-1, FO, ... , Fn } to be a geometry on X if the following axioms are satisfied: 1) Fi consists of subsets of X, I <i ?n. An element of Fi is called an i-flat, or merely a flat. 2) The only 1-flat is the empty set, i.e. F-1'{ 0}. 3) Fi consists of proper subsets of X, -1 i <n. 4) Every set of i+1 points not all contained in some k-flat, k<i, is contained in a unique i-flat, -1 i <s?n. 5) The intersection of any two flats is again a flat. 6) If k <i, then no i-flat is contained in any k-flat. n is called the length of G and we write 1(G) = n. i is called the dimension of Fi, as well as the dimension of any flat f in Ft; we write dim f=i. By G* we denote { J1, * * *, Fn, F'n+l }, where F'n+l = { X }. X is then considered to be an n+1-flat. The axioms defining a geometry are independent. The most trivial example of a geometry on a set X is where the i-flats of X are subsets of X of cardinality i+1. Clearly the usual Euclidean geometry on Rm is a geometry in our sense of length m -1. The great circle geometry on the 2-sphere S2 is also a geometry on the set of points of S2. If we let F-1 = { 0 }, FO { { x, y } I x is antipodal to y }, and Fl = { C| C is a great circle }, then G = { PF, FO, Fl } is a geometry of length 1. The length of any geometry is assumed to be finite throughout this paper, although this is not required for many results. Suppose now, and for the remainder of this paper, that X is a topological space on which a geometry of length m -1 _ 0 has been defined. We need a concept which will act as a link between geometry and topology, and for this purpose we use a generalized notion of convexity.

The representations of S5

According to McKinsey and Tarski [3], who introduced the notion, a closure algebra Γ = (K, ∪, ∩, –, C) is a Boolean algebra (K, ∪, ∩, –) with an additional unary operator C, closed in K, such that, for every x, y ϵ K, x ⊆ Cx, CCx = Cx, C(x∪y) = Cx∪Cy, CΛ = Λ. McKinsey [2] has proved that a matrix Γ = (K, D, ∪, ∩, –, C) is a representation (normal matrix) of S4, if and only if (1) (K, ∪, ∩, –, C) is a closure algebra, (2) D is an additive ideal of K, (3) if – Cx ϵ D then x = Λ, D being the distinguished proper subset of K and ∪, ∩, –, C having been made to correspond to ∨, ·, ∼, ◊, respectively. Following McKinsey, one proves immediatelyTheorem 1. A matrix Γ is a representation of S5, if and only if it is a closure algebra and(α) for every x ϵ K, –C–Cx = Cx, and(β) D is an additive ideal of K such that, for every x ϵ D, Cx = V.This raises the question of alternative characterizations of S5. Because of (β), one may without substantial loss of generality put D = {V}. The question then becomes one for conditions that are in closure algebras equivalent to (α). One such characterization has been given by McKinsey and Tarski [4]. Defining x∸y = C(x∩–y) and ¬x = V∸x, these authors have shown that the closed elements K* of a closure algebra Γ form a Brouwerian algebra Γ* = (K*, ∪, ∩, ∸), and furthermore that Γ* is a Boolean algebra under ∪, ∩, ¬, if and only if, for every x ϵ K*,