254 research outputs found
Universality of a mesenchymal transition signature in invasive solid cancers
No full textIn this brief communication, additional computational validation is provided consistent with the unifying hypothesis that a shared biological mechanism of mesenchymal transition, reflected by a precise gene expression signature, may be present in all types of solid cancers when they reach a particular stage of invasiveness
A subset of co-expressed genes in Slug-based cancer mesenchymal transition signature remains coexpressed in normal samples in a tissue-specific manner
No full textA recently identified gene expression signature of EMT markers containing the transcription factor Slug was found present in samples from many publicly available cancer gene expression datasets of multiple cancer types except leukemia. We also found many of these genes co-expressed in human cancer xenografted cells, but not in mouse stroma cells, suggesting that the signature is largely produced by cancer cells undergoing some type of EMT. Here we report that a partial signature consisting of a subset of the co-expressed genes of the full signature, including at least Slug (SNAI2), collagens COL1A1, COL1A2, COL3A1, COL6A3 and genes DCN and LUM, is also present in leukemia, in which case it is also strongly associated with the chemokine CXCL12 (aka SDF1). The same subset of co-expressed genes is also strongly present even in normal samples in a tissue-specific manner, with lowest expression in brain tissues and highest expression in reproductive system tissues. The full signature, with prominent presence of COL11A1, THBS2 and INHBA appears to be triggered in solid cancers particularly when cancer cells encounter adipocytes
On a discrete Korovkin theorem
No full textAbstractIn [G. A. Anastassiou, A discrete Korovkin theorem, J. Approx. Theory 45 (1985), pp. 383–388, Theorem 3], a discrete Korovkin theorem was given. We restate the theorem here and its proof, correcting a mistake in the above reference
Quantitative Self Adjoint Operator Other Direct Approximations
No full textHere we give a series of self adjoint operator positive linear operators general results. Then we present specific similar results related to neural networks. This is a quantitative treatment to determine the degree of self adjoint operator uniform approximation with rates, of sequences of self adjoint positive linear operators in general, and in particular of self adjoint specific neural network operators. The approach is direct relying on Gelfand’s isometry. It follows [4] (Anastassiou, J. Nonlinear Sci. Appl. (2016))
Approximation by Positive Sublinear Operators
No full textHere we study the approximation of functions by positive sublinear operators under differentiability. We produce general Jackson type inequalities under initial conditions. We apply these to a series of well-known Max-product operators. So our approach is quantitative by producing inequalities with their right hand sides involving the modulus of continuity of a high order derivative of the function under approximation. It follows Anastassiou, Coroianu, Gal (J. Comput. Anal. Appl. 12(2):396–406, 2010, [3])
Some Shift-Invariant Integral Operators, Univariate Case, Revisited
No full textIn recent articles the first author and H. Gonska [e.g., see G. Anastassiou, C. Cottin, and H. Gonska, Global smoothness of approximating functions, Analysis, 11, 43-57 (1991); G. Anastassiou and H. Gonska, On some shift-invariant integral operators, univariate case, Ann. Pol. Math. LXI.3, 225-243 (1995)] studied global smoothness preservation by some univariate and multivariate linear operators over compact domains and ℝn, n ≥ 1. In particular, they studied a very general positive linear integral type operator [e.g., see G. Anastassiou and H. Gonska, On some shift-invariant integral operators, univariate case, Ann. Pol. Math. LXI.3, 225-243 (1995)] over ℝn that was introduced through a convolution-like integration of another general positive linear operator with a scaling-type function. In this article the authors, among others, extend and generalize [G. Anastassiou and H. Gonska, On some shift-invariant integral operators, univariate case, Ann. Pol. Math. LXI.3, 225-243 (1995)]. Also certain new similar but more general integral operators are introduced and studied. These operators arise in a natural way, and for all these sufficient conditions are given for shift invariance, preservation of higher-order global smoothness and sharpness of the related inequalities, convergence to the unit using the first modulus of continuity, shape preservation, and preservation of continuous probabilistic distribution functions. Several examples of very general specialized operators, old and new, are given that satisfy all the above properties
Multivariate fractional Ostrowski type inequalities
No full textAbstractOptimal upper bounds are given for the deviation of a value of a multivariate function of a fractional space from its average, over convex and compact subsets of RN,N≥2. In particular we work over rectangles, balls and spherical shells. These bounds involve the supremum and L∞ norms of related multivariate fractional derivatives of the function involved. The inequalities produced are sharp, namely they are attained. This work has been motivated by the works of Ostrowski [A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funcktion von ihrem Integralmittelwert, Commentarii Mathematici Helvetici 10 (1938) 226–227], 1938, and of the author [G.A. Anastassiou, Fractional Ostrowski type inequalities, Communications in Applied Analysis 7 (2) (2003) 203–208], 2003
General Weighted Opial Inequalities for Linear Differential Operators
No full textAbstractA complete set of Lr (r≠0) form very general Opial type weighted inequalities is given for a general linear differential operator L. These involve its related initial value problem solution y, Ly, the associated Green's function H, and initial conditions point x0∈R. This work is inspired by work of R. P. Agarwal and P. Y. H. Pang (1995, “Opial Inequalities with Applications in Differential and Difference Equations,” Kluwer Academic, Dordrecht) and G. A. Anastassiou (1998, Math. Inequalities Appl.1, No. 2, 193–200) and generalizes their related results. An application to proving uniqueness in solutions of initial value problems is given at the end
Private equity funds and hedge funds: a primer
No full textPrivate equity funds and hedge funds are both alternative asset classes that are continuously growing in importance. Although they have different focuses, they share some characteristics. First of all, both have or allegedly have a significant impact on the economy as well as the financial system they operate in. Therefore, the question of a potential regulation of both asset classes arises. Due to the lack of sophisticated knowledge about the differences of these asset classes, market players fear that attempts to regulate hedge funds will adversely affect private equity funds. Besides the regulatory issue, there are several other links between these two asset classes that have to be looked at. The relationship between those two asset classes is therefore of general importance. Last months' developments in the hedge fund industry (e.g. rumors about turbulences as well as hedge funds forcing the dismissal of the CEO of Deutsche Börse) have now even led to a broad public debate about private equity and hedge funds. At least in Germany the debate has been partly fueled by the fact that both types of funds are highly funded by institutional investors from abroad. Due to this the debate widened and included criticism on Anglo-Saxon style capitalism as well. In the light of the last German elections, hedge funds and private equity funds have even been compared to locusts, notorious for exhausting whole countries. However, the distinction between hedge funds and private equity funds remains very vague in this discussion, so that deep mistrust is spread among the public opinion against these new, mostly unknown and misunderstood types of investors. For this reason it is important to * discuss the arguments for or against regulation, * look at the major links between the two asset classes, * look at the major differences that exist between the asset classes, and * conceive a set of criteria to clearly distinguish between both types of funds. The purpose of this paper is to comment on possible solutions to the above mentioned tasks. It outlines preliminary thoughts and findings. Further, it comments on the steps that we think should be taken to further enhance perception of private equity funds as opposed to hedge funds from a public as well as a regulatory perspective. --Private Equity Funds,Hedge Funds
Ostrowski type inequalities on H-type groups
No full textAbstractThe main aim of this paper is to establish an Ostrowski type inequality on H-type groups using the L∞ norm of the horizontal gradient. The work has been motivated by the work of Anastassiou and Goldstein in [G.A. Anastassiou, J.A. Goldstein, Higher order Ostrowski type inequalities over Euclidean domains, J. Math. Anal. Appl. 337 (2008) 962–968]
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