Extremal Subsets Research Articles

A unique proteomic profile on surface IgM ligation in unmutated chronic lymphocytic leukemia

AbstractChronic lymphocytic leukemia (CLL) is characterized by a highly variable clinical course with 2 extreme subsets: indolent, ZAP70− and mutated immunoglobulin heavy chain gene (M-CLL); and aggressive, ZAP70+ and unmutated immunoglobulin heavy chain (UM-CLL). Given the long-term suspicion of antigenic stimulation as a primum movens in the disease, the role of the B-cell receptor has been extensively studied in various experimental settings; albeit scarcely in a comparative dynamic proteomic approach. Here we use a quantitative 2-dimensional fluorescence difference gel electrophoresis technology to compare 48 proteomic profiles of the 2 CLL subsets before and after anti-IgM ligation. Differentially expressed proteins were subsequently identified by mass spectrometry. We show that unstimulated M- and UM-CLL cells display distinct proteomic profiles. Furthermore, anti-IgM stimulation induces a specific proteomic response, more pronounced in the more aggressive CLL. Statistical analyses demonstrate several significant protein variations according to stimulation conditions. Finally, we identify an intermediate form of M-CLL cells, with an indolent profile (ZAP70−) but sharing aggressive proteomic profiles alike UM-CLL cells. Collectively, this first quantitative and dynamic proteome analysis of CLL further dissects the complex molecular pathway after B-cell receptor stimulation and depicts distinct proteomic profiles, which could lead to novel molecular stratification of the disease.

Minimum Degree Orderings

It is known that, given an edge-weighted graph, a maximum adjacency ordering (MA ordering) of vertices can find a special pair of vertices, called a pendent pair, and that a minimum cut in a graph can be found by repeatedly contracting a pendent pair, yielding one of the fastest and simplest minimum cut algorithms. In this paper, we provide another ordering of vertices, called a minimum degree ordering (MD ordering) as a new fundamental tool to analyze the structure of graphs. We prove that an MD ordering finds a different type of special pair of vertices, called a flat pair, which actually can be obtained as the last two vertices after repeatedly removing a vertex with the minimum degree. By contracting flat pairs, we can find not only a minimum cut but also all extreme subsets of a given graph. These results can be extended to the problem of finding extreme subsets in symmetric submodular set functions.

Language and the Modulation of Impulsive Aggression

Language and the Modulation of Impulsive Aggression

Extremal Subsets of $\{1,...,n\}$ Avoiding Solutions to Linear Equations in Three Variables

We refine previous results to provide examples, and in some cases precise classifications, of extremal subsets of $\{1,...,n\}$ containing no solutions to a wide class of non-invariant, homogeneous linear equations in three variables, i.e.: equations of the form $ax+by=cz$ with $a+b \neq c$.

Polarization and variations of Blazar

Blazar is an extreme subset of AGNs，constituting less than a few percent of the known AGN population. While Blazar have some properties in common with other AGNs，they have some characteristics that set them apart. The observation properties are probably the cause of strong beaming effect，and these properties would be mutually correlated. The relationship between the polarization and the magnitude variation in brightness，as well as the core-dominance parameter are derived and used statistically to compare with the observational data of Blazar smaples. The result suggests that the polarization, variation and the core-dominance parameters are possible indications of the beaming effect.

An infinite-dimensional generalization of the Jung theorem

A complete characterization of the extremal subsets of Hilbert spaces, which is an infinite-dimensional generalization of the classical Jung theorem, is given. The behavior of the set of points near the Chebyshev sphere of such a subset with respect to the Kuratowski and Hausdorff measures of noncompactness is investigated.

Differentiation in metric spaces

1.1. The Aim. This paper is devoted to the study of the first order geometry of metric spaces. Our study was mainly motivated by the observation that whereas the advanced features of the theories of Alexandrov spaces with upper and lower curvature bounds are quite different, the beginnings are almost identical, at least as far as only first order derivatives are concerned (for example tangent spaces and the first variation formula). One is naturally led to the question on which spaces the first order geometry can be established. As it turns out the same first order geometry exists in many other spaces that we call geometric. The class of geometric spaces contains all Holder continuous Riemannian manifolds, sufficiently convex and smooth Finsler manifolds ([LY]), a big class of subsets of Riemannian manifolds (for example sets of positive reach, see [Fed59] and [Lyta]), surfaces with an integral curvature bound ([Res93]) and extremal subsets of Alexandrov spaces with lower curvature bound ([PP94a]). The last case was discussed in [Pet94] and the proof of the first variation formula was a major step towards proving the deep gluing theorem ([Pet94]). Moreover the class of geometric spaces is stable under metric operations, even under such a difficult one as taking quotients. Finally the existence of the first order geometry is a good assumption for studying features of higher order, such as gradient flows of semi-concave functions ([PP94b] and [Lytc]). One of the main issues of this paper is the establishing of natural, easily verifiable axioms, that describe this first order geometry and their consequences.

Phase-space overlap measures. I. Fail-safe bias detection in free energies calculated by molecular simulation

We consider ways to quantify the overlap of the parts of phase space important to two systems, labeled A and B. Of interest is how much of the A-important phase space lies in that important to B, and how much of B lies in A. Two measures are proposed. The first considers four total-energy distributions, formed from all combinations made by tabulating either the A-system or the B-system energy when sampling either the A or B system. Measures for A in B and B in A are given by two overlap integrals defined on pairs of these distributions. The second measure is based on information theory, and defines two relative entropies which are conveniently expressed in terms of the dissipated work for free-energy perturbation (FEP) calculations in the A-->B and B-->A directions, respectively. Phase-space overlap is an important consideration in the performance of free-energy calculations. To demonstrate this connection, we examine bias in FEP calculations applied to a system of independent particles in a harmonic potential. Systems are selected to represent a range of overlap situations, including extreme subset, subset, partial overlap, and nonoverlap. The magnitude and symmetry of the bias (A-->B vs B-->A) are shown to correlate well with the overlap, and consequently with the overlap measures. The relative entropies are used to scale the amount of sampling to obtain a universal bias curve. This result leads to develop a simple heuristic that can be applied to determine whether a work-based free-energy measurement is free of bias. The heuristic is based in part on the measured free energy, but we argue that it is fail-safe inasmuch as any bias in the measurement will not promote a false indication of accuracy.

Equilibrium analysis in financial markets with countably many securities

An F-cone is a pointed and generating convex cone of a real vector space that is the union of a countable family of finite dimensional polyhedral convex cones such that each of which is an extremal subset of the subsequent one. In this paper, we study securities markets with countably many securities and arbitrary finite portfolio holdings. Moreover, we assume that each investor is constrained to have a non-negative end-of-period wealth. If, under the portfolio dominance order, the positive cone of the portfolio space is an F-cone, then Edgeworth allocations and non-trivial quasi-equilibria exist. This result extends the case where, as in Aliprantis et al. [J. Math. Econom. 30 (1998a) 347], the positive cone is a Yudin cone.

Genotype by environment interaction for milk yield in Sarda dairy sheep

Genotype by environment interaction (GEI) for milk yield (ME) wasinvestigated by analyzing 40 140 first lactation records performed in 538 flocks. Flock–year effects from national genetic evaluation were used to define low (L), medium (M) and high (H) yielding environments. Differences observed between adjacent subsets were approximately 20% of the trait overall mean. Sire variance components estimated using multitrait analysis were 58, 82 and 149% of the estimate from the complete dataset (L, M and H, respectively) and genetic correlation coefficient between extreme subsets was 0.66, lower than genetic correlations obtained from randomly sampled subsets. Rank correlation coefficients between estimated transmitting abilities (ETA), obtained independently within L, M and H subsets for 71 AI rams having at least 10 daughters per subset, were lower than one (ranging from 0.42 to 0.56). These results strongly supported the existence of GEI for milk yield in Sarda sheep flocks. The influence of GEI on phenotypic responses in flocks differing in yield level could be due to a reduced expression of genes under conditions of restricted environmental opportunity. Splitting the selection scheme according to farming conditions does not seem a suitable solution for the Sarda breeding program. Thus, to provide farmers with genotypes suitable to exhibit a good phenotypic expression in different conditions, the selection across all environments, in which the descendants are expected to perform, still seems the best option.

A lower and upper bounds version of a variational inequality

Introducing the concept of extremal subset to solve one open problem raised in [1]: find the conditions for a lower and upper bounds version of a variational inequality. A few applications are given.

Best Approximation from the Intersection of a Closed Convex Set and a Polyhedron in Hilbert Space, Weak Slater Conditions, and the Strong Conical Hull Intersection Property

Let X be a (real) Hilbert space, C be a closed convex subset, and $H_i =\{x\in X\mid \la x, h_i\ra \le b_i\} \quad (i=1,2,..., m)$ be a finite collection of half-spaces. Under the assumption that $K:=C\cap (\cap_1^mH_i)$ is not empty, the problem of characterizing the best approximation from K to any $x\in X$ is considered. The "strong conical hull intersection property" (strong CHIP), which was introduced by us in 1997, is shown to be both necessary and sufficient for the following "perturbation property" to hold: for each $x\in X$, an element $x_0\in K$ satisfies $x_0=P_K(x)$ if and only if $x_0=P_C(x-\sum_1^m\lambda_ih_i)$ for some scalars $\lambda_i\ge 0$ with $\lambda_i[\la x_0, h_i\ra -b_i]=0$ for each i. Here $P_D(z)$ denotes the unique best approximation from D to z. In other words, determining the best approximation from the set K to any point is equivalent to the (generally easier) problem of determining the best approximation from the set C to a perturbation of that point. Moreover, even when the strong CHIP does not hold, the perturbation property still holds, except now C must be replaced by a certain convex extremal subset of C. We also show that the strong CHIP is weaker than any of the weak Slater conditions that one can naturally impose on the sets in question. These results generalize the main results of our 1997 paper [J. Approx. Theory, 90, pp. 385--444] and hence those of several other papers as well.

Repeatability of different stability parameters for grain yield in chickpea

AbstractThe presence of genotype × environment (GE) interactions in plant breeding experiments has led to the development of several stability parameters in the past few decades. The present study investigated the repeatability of these parameters for 16 chickpea (Cicer arietinum L.) genotypes by correlating their estimates obtained from extreme subsets of environments within a year and also over years. Based on the estimates of response and stability parameters within each trial, the ranking of genotypes in the low‐yielding subset differed from that in the high‐yielding subset. This indicates poor repeatability for response and stability parameters over the extreme environmental subsets. The estimates of mean yield and stability parameters represented by ecovalence, W2i, were consistent over years, whereas those of response parameters (bi, and S2i) showed poor repeatability. Our results suggest that single‐year results for yield and stability can be used effectively for selecting cultivars with stable grain yield if tested in a wider range of environments.

Maximal Spacing Configurations in Graphs

Let G=(V, E) be a simple connected graph of order [mid ]V[mid ]=n[ges ]2 and minimum degree δ, and let 2[les ]s[les ]n. We define two parameters, the s-average distance μs(G) and the s-average nearest neighbour distance Λs(G), with respect to each of which V contains an extremal subset X of order s with vertices ‘as spread out as possible’ in G. We compute the exact values of both parameters when G is the cycle Cn, and show how to obtain the corresponding optimal arrangements of X. Sharp upper and lower bounds are then established for Λs(G), as functions of s, n and δ, and the extremal graphs described.

Younger and Brighter - New Distances to Globular Clusters Based on HIPPARCOS Parallax Measurements of Local Subdwarfs

view Abstract Citations (239) References (67) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Younger and Brighter - New Distances to Globular Clusters Based on HIPPARCOS Parallax Measurements of Local Subdwarfs Reid, I. Neill Abstract We have used new parallax measurements, obtained by the Hipparcos satellite, of fifteen nearby, metal-poor stars to re-define the subdwarf main-sequence. All of these stars have parallaxes determined to an accuracy of at least 12%. Comparing these measurements against previous ground-based data for nine stars reveals a systematic offset of 5%, in the sense that the Hipparcos parallaxes are smaller (i.e., the inferred distances are larger). The availability of the Hipparcos observations expands the local subdwarf sample to the extent that we can separate the stars by abundance into intermediate ([Fe/H]∼-1.4) and extreme ([Fe/H] ∼-2) subsets. Main-sequence fitting techniques are then used to match stars of the appropriate abundance range to the color-magnitude diagrams of the seven globular clusters: M5, NGC 6752, M13, M13, M92, M30, and M68. We derive respective distance moduli of 14.45, 13.17, 14.48, 15.38, 14.93, 14.95, and 15.29 magnitudes, with formal uncertainties of ±0.1 mag. The metal-poor systems M68, M15, and M30 have moderate foreground reddening, and varying by ±0.02 mag can change the derived distances by up to ±7%. With the exception of NGC 6752, however, our derived distances exceed previous estimates, particularly in the case of the four [Fe/H]∼-2.1 globulars, where our distance moduli are 0.3 mag higher than the current standard values. We discuss briefly how these findings affect the RR Lyrae distance scale, isochrone-based estimates of the age of globular clusters and our picture of the early stages of star formation in the Galaxy. We note that our results go some way towards reconciling the apparent contradiction between the cluster ages and recent determinations of the Hubble constant. Publication: The Astronomical Journal Pub Date: July 1997 DOI: 10.1086/118462 arXiv: arXiv:astro-ph/9704078 Bibcode: 1997AJ....114..161R Keywords: GALAXIES: DISTANCES AND REDSHIFTS; GLOBULAR CLUSTERS: GENERAL; Astrophysics E-Print: to appear in AJ full text sources arXiv | ADS | data products SIMBAD (54) NED (1)

On weak convergence implying strong convergence under extremal conditions

It is well known that under suitable extreme point conditions for the limit function, weak convergence in an L 1-space can imply strong convergence. T. Rzez̆uchowski [ Bull. Austral. Math. Soc. 39 (1989), 201–214] has shown that a similar phenomenon can occur under an extremal subset condition. We generalize his result in several respects by means of the associated Young measures, similar to the analysis given in [E. J. Balder, Bull. Austral. Math. Soc. 33 (1986), 363–368].

Extreme subsets of operator intervals

Extreme subsets of operator intervals

POSITIVE FUNCTIONALS ON ℒ(Rn)

Let ℒ(E) be a space of operators on a finite dimensional Hilbert space E, and let ℒ(E)* be its dual. In this paper the positive part P is considered for the unit ball of ℒ(E)*. We investigate the structure of extremal subsets of P. In particular it is given a characterization of extreme positive functionals on ℒ(E).

The p-body rank of an n-electron state

Extreme subsets of the set Pnp of all p-body matrices are discussed. The concept of p-body rank of an n-electron wavefunction is defined and its physical meaning is investigated.

Topologies and continuous functions on extreme points and pure states

There are various ways of using the affine geometry of a compact convex set K to topologize its extreme boundary ∂eK (see [2, 7, 10] and the references quoted therein). The best-known method is to take as closed sets the traces on ∂eK of the closed split faces of K. This topology is known as the facial topology [1, 2, 4], and is significant because the facially continuous functions correspond to the order-bounded linear operators on A(K) and to the multipliers in A(K) [1, 3, 20]. Typically, split faces are scarce, so that the facial topology is coarse. The Choquet topology [7, 15, 18], whose closed sets are the traces of compact extremal subsets of K, is finer, but is usually less easily recognized. The Bishop–de Leeuw theorem was extended in [5] by showing that a maximal measure on K induces a measure on a σ-algebra on ∂eK containing the Choquet closed sets as well as the traces of the Baire subsets of K. The maximal topology is finer even than the Choquet topology, and the Bishop-de Leeuw theorem was further extended in [18] to a σ-algebra including the maximally closed sets. Although the definition of the maximal topology in [18] made use of integral representation theory, a geometrical description of it will be given in Proposition 2·1 below. The Choquet and maximally continuous functions on ∂eK were characterized in [18] in terms of the geometry and integral representation theory of K, respectively. It will be shown in Theorem 2·4 that the Choquet and maximally continuous functions coincide if is a union of faces of K, even though the topologies may differ.