The Cardinality of an Oracle in Blum-Shub-Smale Computation

We examine the relation of BSS-reducibility on subsets of the real numbers. The question was asked recently (and anonymously) whether it is possible for the halting problem H in BSS-computation to be BSS-reducible to a countable set. Intuitively, it seems that a countable set ought not to contain enough information to decide membership in a reasonably complex (uncountable) set such as H. We confirm this intuition, and prove a more general theorem linking the cardinality of the oracle set to the cardinality, in a local sense, of the set which it computes. We also mention other recent results on BSS-computation and algebraic real numbers

Noncomputable functions in the Blum-Shub-Smale model

Working in the Blum-Shub-Smale model of computation on the real numbers, we answer several questions of Meer and Ziegler. First, we show that, for each natural number d, an oracle for the set of algebraic real numbers of degree at most d is insufficient to allow an oracle BSS-machine to decide membership in the set of algebraic numbers of degree d + 1. We add a number of further results on relative computability of these sets and their unions. Then we show that the halting problem for BSS-computation is not decidable below any countable oracle set, and give a more specific condition, related to the cardinalities of the sets, necessary for relative BSS-computability. Most of our results involve the technique of using as input a tuple of real numbers which is algebraically independent over both the parameters and the oracle of the machine

Noncomputable Functions in the Blub-Shub-Smale Model

Working in the Blum-Shub-Smale model of computation on the real numbers, we answer several questions of Meer and Ziegler. First, we show that, for each natural number d, an oracle for the set of algebraic real numbers of degree at most d is insufficient to allow an oracle BSS-machine to decide membership in the set of algebraic numbers of degree d + 1. We add a number of further results on relative computability of these sets and their unions. Then we show that the halting problem for BSS-computation is not decidable below any countable oracle set, and give a more specific condition, related to the cardinalities of the sets, necessary for relative BSS-computability. Most of our results involve the technique of using as input a tuple of real numbers which is algebraically independent over both the parameters and the oracle of the machine

Third-Generation W(CNAr)₆ Photoreductants (CNAr = Fused-Ring and Alkynyl-Bridged Arylisocyanides)

Homoleptic tungsten(0) arylisocyanides possess photophysical and photochemical properties that rival those of archetypal ruthenium(II) and iridium(III) polypyridine complexes. Previous studies established that extending the π-system of 2,6-diisopropylphenylisocyanide (CNDipp) by coupling aryl substituents para to the isocyanide functionality results in W(CNDippAr)₆ oligoarylisocyanide complexes with greatly enhanced metal-to-ligand charge transfer (MLCT) excited-state properties relative to those of W(CNDipp)₆. Extending electronic modifications to delineate additional design principles for this class of photosensitizers, herein we report a series of W(CNAr)₆ compounds with naphthalene-based fused-ring (CN-1-(2-ⁱPr)-Naph) and CNDipp-based alkynyl-bridged (CNDipp^(CC)Ar) arylisocyanide ligands. Systematic variation of the secondary aromatic system in the CNDippCCAr platform provides a straightforward method to modulate the photophysical properties of W(CNDipp^(CC)Ar)₆ complexes, allowing access to an extended range of absorption/luminescence profiles and highly reducing excited states, while maintaining the high molar absorptivity MLCT absorption bands, high photoluminescence quantum yields, and long excited-state lifetimes of previous W(CNAr)₆ complexes. Notably, W(CN-1-(2-iPr)-Naph)₆ exhibits the longest excited-state lifetime of all W(CNAr)₆ complexes explored thus far, highlighting the potential benefits of utilizing fused-ring arylisocyanide ligands in the construction of tungsten(0) photoreductants

Third-Generation W(CNAr)₆ Photoreductants (CNAr = Fused-Ring and Alkynyl-Bridged Arylisocyanides)

Homoleptic tungsten(0) arylisocyanides possess photophysical and photochemical properties that rival those of archetypal ruthenium(II) and iridium(III) polypyridine complexes. Previous studies established that extending the π-system of 2,6-diisopropylphenylisocyanide (CNDipp) by coupling aryl substituents para to the isocyanide functionality results in W(CNDippAr)₆ oligoarylisocyanide complexes with greatly enhanced metal-to-ligand charge transfer (MLCT) excited-state properties relative to those of W(CNDipp)₆. Extending electronic modifications to delineate additional design principles for this class of photosensitizers, herein we report a series of W(CNAr)₆ compounds with naphthalene-based fused-ring (CN-1-(2-ⁱPr)-Naph) and CNDipp-based alkynyl-bridged (CNDipp^(CC)Ar) arylisocyanide ligands. Systematic variation of the secondary aromatic system in the CNDippCCAr platform provides a straightforward method to modulate the photophysical properties of W(CNDipp^(CC)Ar)₆ complexes, allowing access to an extended range of absorption/luminescence profiles and highly reducing excited states, while maintaining the high molar absorptivity MLCT absorption bands, high photoluminescence quantum yields, and long excited-state lifetimes of previous W(CNAr)₆ complexes. Notably, W(CN-1-(2-iPr)-Naph)₆ exhibits the longest excited-state lifetime of all W(CNAr)₆ complexes explored thus far, highlighting the potential benefits of utilizing fused-ring arylisocyanide ligands in the construction of tungsten(0) photoreductants

Bioactive growth hormone in humans: Controversies, complexities and concepts

Objective: To revisit a finding, first described in 1978, which documented existence of a pituitary growth factor that escaped detection by immunoassay, but which was active in the established rat tibia GH bioassay. Methods: We present a narrative review of the evolution of growth hormone complexity, and its bio-detectability, from a historical perspective. Results: In humans under the age of 60, physical training (i.e. aerobic endurance and resistance training) are stressors which preferentially stimulate release of bioactive GH (bGH) into the blood. Neuroanatomical studies indicate a) that nerve fibers directly innervate the human anterior pituitary and b) that hind limb muscle afferents, in both humans and rats, also modulate plasma bGH. In the pituitary gland itself, molecular variants of GH, somatotroph heterogeneity and cell plasticity all appear to play a role in regulation of this growth factor. Conclusion: This review considers more recent findings on this often forgotten/neglected subject. Comparison testing of a) human plasma samples, b) sub-populations of separated rat pituitary somatotrophs or c) purified human pituitary peptides by GH bioassay vs immunoassay consistently yield conflicting results

Bostonia: The Boston University Alumni Magazine. Volume 11

Founded in 1900, Bostonia magazine is Boston University's main alumni publication, which covers alumni and student life, as well as university activities, events, and programs

Circumvention of Mcl-1-Dependent Drug Resistance by Simultaneous Chk1 and MEK1/2 Inhibition in Human Multiple Myeloma Cells

The anti-apoptotic protein Mcl-1 plays a major role in multiple myeloma (MM) cell survival as well as bortezomib- and microenvironmental forms of drug resistance in this disease. Consequently, there is a critical need for strategies capable of targeting Mcl-1-dependent drug resistance in MM. The present results indicate that a regimen combining Chk1 with MEK1/2 inhibitors effectively kills cells displaying multiple forms of drug resistance stemming from Mcl-1 up-regulation in association with direct transcriptional Mcl-1 down-regulation and indirect disabling of Mcl-1 anti-apoptotic function through Bim up-regulation and increased Bim/Mcl-1 binding. These actions release Bak from Mcl-1, accompanied by Bak/Bax activation. Analogous events were observed in both drug-naïve and acquired bortezomib-resistant MM cells displaying increased Mcl-1 but diminished Bim expression, or cells ectopically expressing Mcl-1. Moreover, concomitant Chk1 and MEK1/2 inhibition blocked Mcl-1 up-regulation induced by IL-6/IGF-1 or co-culture with stromal cells, effectively overcoming microenvironment-related drug resistance. Finally, this regimen down-regulated Mcl-1 and robustly killed primary CD138+MM cells, but not normal hematopoietic cells. Together, these findings provide novel evidence that this targeted combination strategy could be effective in the setting of multiple forms of Mcl-1-related drug resistance in MM

Structure, Spectroscopy, and Electrochemistry of Manganese(I) and Rhenium(I) Quinoline Oximes

Reactions of α- and β-diimine quinoline aldoximes with Mn(I) and Re(I) tricarbonyl halides afford quinoline oxime complexes. Both Mn(I) and Re(I) complexes experience severe geometric strain due to ligand steric interactions: 6-membered metallocycles exhibit more pronounced distortions than 5-membered ones, consistent with density functional theory structural analyses. Such distortions likely also affect reactivity patterns, as evidenced by Re(I)-induced deoximation of a quinoline variant containing a CF_3-ketoxime

Structure, Spectroscopy, and Electrochemistry of Manganese(I) and Rhenium(I) Quinoline Oximes

Reactions of α- and β-diimine quinoline aldoximes with Mn(I) and Re(I) tricarbonyl halides afford quinoline oxime complexes. Both Mn(I) and Re(I) complexes experience severe geometric strain due to ligand steric interactions: 6-membered metallocycles exhibit more pronounced distortions than 5-membered ones, consistent with density functional theory structural analyses. Such distortions likely also affect reactivity patterns, as evidenced by Re(I)-induced deoximation of a quinoline variant containing a CF_3-ketoxime