Let (X,Y ) be a random point in R with a (joint) cumulative distribution function (c.d.f.) F and continuous marginal c.d.f.’s FX and FY , so that F (x, y) = P(X 6 x, Y 6 y), FX(x) = P(X 6 x), and FY (y) = P(Y 6 y) for all real x and y. Then F is continuous as well, since |F (x2, y2)−F (x1, y1)| 6 |FX(x2)−FX(x1)|+|FY (y2)−FY (y1)| for all x1, y1, x2, y2 in R. Vice versa, if F (x, y) is continuou...

In this article we present several logical schemes. The scheme FinRecExD2 deals with a non empty set A, an element B of A, a natural number C, and a ternary predicate P, and states that: There exists a finite sequence p of elements of A such that len p = C but p1 = B or C = 0 but for every natural number n such that 1 ¬ n and n < C holds P[n, pn, pn+1] provided the parameters meet the following...

The following propositions are true: (1) For all natural numbers n, m such that n 6= 0 and m 6= 0 holds (n ·m− n − m) + 1 ­ 0. (2) For all real numbers x, y such that y > 0 holds min(x,y) max(x,y) ¬ 1. (3) For all real numbers x, y such that for every real number c such that c > 0 and c < 1 holds c · x ­ y holds y ¬ 0. (4) Let p be a finite sequence of elements of R. Suppose that for every natu...

1. Determine the supremum and the infimum of (x− 1)x−1xx (x− (1/2))2x−1 for x > 1. 2. Let n and k be integers with n ≥ 0 and k ≥ 1. Let x0, x1, · · ·, xn be n+1 distinct points in R and let y0, y1, · · ·, yn be n + 1 real numbers (not necessarily distinct). Prove that there exists a polynomial p of degree at most n in the coordinates of x with respect to the standard basis for which p(xi) = yi ...

Let y1 and y2 be principal and nonprincipal solutions of the nonoscillatory differential equation (r(t)y′)′ + f(t)y = 0. In an earlier paper we showed that if ∫∞(f − g)y1y2 dt converges (perhaps conditionally), and a related improper integral converges absolutely and sufficently rapidly, then the differential equation (r(t)x′)′ + g(t)x = 0 has solutions x1 and x2 that behave asymptotically like...

1. Proof for Theorems Now we will do discriminative learning with the presence of hidden variables. Our step is similar to standard EM[3] while the primary difference is that we are given labels Y = {y1, . . . , yn} in addition to observations X = {x1, . . . , xn}, and we want to estimate the model θ that minimizes the negative log-likelihood function L(θ;Y,X) = − log Pr(Y |X; θ). We proceed by...

PURPOSE Malignant epithelial ovarian cancer effusions are important in disease dissemination and clinical outcome. The identification of biochemical events active in effusions may improve our identification and application of targeted therapeutics. EXPERIMENTAL DESIGN Archival effusion samples for which outcome information was known were studied. Clinical variables were comparable between the...

BACKGROUND Malignant B-cell clones are affected by both acquired genetic alterations and by inherited genetic variations changing the inflammatory tumour microenvironment. METHODS We investigated 50 inflammatory response gene polymorphisms in 355 B-cell non-Hodgkin's lymphoma (B-NHL) samples encompassing 216 diffuse large B cell lymphoma (DLBCL) and 139 follicular lymphoma (FL) and 307 contro...

A clinician’s attention is normally drawn to a system only when it malfunctions. The HLA system is no exception in this regard, but in contrast to other systems, it also arouses interest when it functions well — too well, in fact. The most dramatic malfunction of the HLA system occurs when its genes falter in their expression, resulting in HLA class I or class II deficiencies (the bare lymphocy...