We explore three results related to hardness of counting. Interestingly, at their core each of these results relies on a simple — yet powerful — technique due to Valiant and Vazirani. Does SAT become any easier if we are guaranteed that the formula we are given has at most one solution? Alternately, if we are guaranteed that a given boolean formula has a unique solution does it become any easie...

background and objective: determination of hormone receptor status in the management of breast cancer is well-established. the aim of this study was to evaluate the frequency of androgen receptor (ar) expression in invasive ductal carcinoma of breast. materials and methods: for this purpose, 55 cases of invasive ductal breast carcinoma were examined using a monoclonal antibody against ar on for...

In standard treatments of probability, Pr(A|B) is defined as the ratio of Pr(A intersectionB) to Pr(B), provided that Pr(B)>0. This account of conditional probability suggests a psychological question, namely, whether estimates of Pr(A|B) arise in the mind via implicit calculation of Pr(A intersectionB)/Pr(B). We tested this hypothesis (Experiment 1) by presenting brief visual scenes composed o...

This paper presents aspects of the coordination chemistry of mono- and divalent manganese complexes supported by the anionic tris(phosphino)borate ligand, [PhBP(i)(Pr)3] (where [PhBP(i)(Pr)3] = [PhB(CH(2)P(i)Pr2)3]-). The Mn(II) halide complexes, [PhBP(i)(Pr)3]MnCl (1) and [PhBP(i)(Pr)3]MnI (2), have been characterized by X-ray diffraction, SQUID magnetometry, and EPR spectroscopy. Compound 2 s...

One of the basic principles behind conditioning is that “conditioning on a high-probability event keeps things reasonably unchanged; however, if we condition on a low-probability event, then all bets could be off”. More precisely, suppose we wish to estimate Pr[A | B]. Note, in general, that this could be less than, equal to, or greater than Pr[A]. We now prove that if Pr[B] is “high”, then Pr[...

The progesterone receptor (PR), a ligand-activated transcription factor, recruits the primary coactivator steroid receptor coactivator-1 (SRC-1) gene promoters. It is known that PR transcriptional activity is paradoxically coupled to its ligand-dependent down-regulation. However, despite its importance in PR function, the regulation of SRC-1 expression level during hormonal exposure is poorly u...

Laboratory-adapted (LA) macrophage-tropic (M-tropic) human immunodeficiency virus type 1 (HIV-1) isolates (e.g., HIV-1(Ba-L)) and low-passage primary (PR) isolates differed markedly in tropism for syngeneic neonatal monocytes, monocyte-derived macrophages (MDMs), and placental macrophages (PMs). Newly adherent neonatal monocytes and cultured PMs were highly refractory to infection with PR HIV-1...

PR proteins play key roles in various aspects of cell differentiation and organismal development, and, when dysregulated, are involved in carcinogenesis.1–6 The defining feature of PR proteins is a conserved sequence termed the PR (PRDI-BF1 and RIZ1 homology) domain,7 which is almost always accompanied by an array of C2H2-like zinc fingers. Other sequences that are present in PR proteins show l...