ALTHOUGH graft-versus-host disease (GVHD) has been a major concern after small-bowel transplantation (SBTX), the lack of suitable experimental model has allowed only limited study of GVHD after solid-organ transplantation. l We recently developed a clinically relevant experimental animal model of GVHD of fully allogeneic SBTX. This study describes histopathological evolution of the disease. cyt...

Introduction The vast majority of scientific community believes that P!=NP, with countless supporting arguments. The number of people who believe otherwise probably amounts to as few as those opposing the 2 Law of Thermodynamics. But isn’t nature elegant enough, not to resource to brute-force search? In this article, a novel concept of dimensionality is presented, which may lead to a more effic...

We initiate the rigorous study of classification in semimetric spaces, which are point sets with a distance function that is non-negative and symmetric, but need not satisfy the triangle inequality. We define the density dimension dens and discover that it plays a central role in the statistical and algorithmic feasibility of learning in semimetric spaces. We compute this quantity for several w...

(1 + ) [1396]. (2) [1898]. (H,C,K) [901]. (p) [1898]. (t, n) [194]. (Z3; +) [1010]. + [1614]. 0− 1 [1281]. 0.863 [503]. 0/1 [269]. 1 [1484, 499, 729, 993]. 1.5 [1003]. 2 [499, 1853, 918, 1141, 993, 426, 1493]. 3 [456, 2504, 458, 906, 1456, 2557, 334, 703, 2618, 920, 811, 504, 2494, 808, 1289, 845, 355, 2547, 348, 835, 740, 1182]. 3/2 [499]. 3 [196]. 4 [1731, 920]. 6 [1731]. 3 [742]. K [2293]. ◦...

We review Andr\'e Luiz Barbosa's paper"P != NP Proof,"in which the classes P and NP are generalized and claimed to be proven separate. We highlight inherent ambiguities in Barbosa's definitions, and show that attempts to resolve this ambiguity lead to flaws in the proof of his main result.

This note is a commentary on, and critique of, André Luiz Barbosa’s paper entitled “P != NP Proof.” Despite its provocative title, what the paper is seeking to do is not to prove P 6= NP in the standard sense in which that notation is used in the literature. Rather, Barbosa is (and is aware that he is) arguing that a different meaning should be associated with the notation P 6= NP, and he claim...

This paper reports on three recent research directions that begin to explore the subject of fully multivariate algorithmics, meaning by this the largely uncharted theoretical landscape that lies beyond parameterized complexity and algorithmics — itself a natural two-dimensional generalization of the familiar one-dimensional framework of P versus NP .

The size of an arithmetical formula is the number of symbols (+,×) which it contains. The complexity of a polynomial defined over a field k is the minimum size of formulas defining it (see [10]). Using this notion of complexity, Valiant gave algebraic analogs to algorithmic complexity problems such as P = NP (see [10, 11, 12]). In this context, we would like to find lower bounds to the complexi...

An artificially designed Turing Machine algorithm Mo generates the instances of the satisfiability problem, and check their satisfiability. Under the assumption P = NP , we show that Mo has a certain property, which, without the assumption, Mo does not have. This leads to P 6= NP by

In [1], the claim is put forth that P=NP; the form of this claim is an algorithm which purportedly can solve the 3SAT problem in O(n) time. The 3SAT problem (or “3-SAT problem,” as it is refered to in [1]) is to determine if the formula d1 ∧ d2 ∧ · · · ∧ dm (1) is satisfiable, where each clause dk with 1 ≤ k ≤ m is a disjunction of at most three variables or their negations from the set B = {b1...