This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The complexity classes range from AC0 for the weakest theory up to the polynomial hierarchy. Each bounded theorem in a theory translates into a family of (quantified) propositional tautologies with polynomial size proofs in the corresponding proof system. The theory proves the soundness of the associated proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P.

We present a detailed study of the nuclear star clusters (NSCs) and massive black holes (BHs) of four of the nearest low-mass early-type galaxies: M32, NGC 205, NGC 5102, and NGC 5206. We measure dynamical masses of both the BHs and NSCs in these galaxies using Gemini/NIFS or VLT/SINFONI stellar kinematics, Hubble Space Telescope (HST ) imaging, and Jeans Anisotropic Models. We detect massive BHs in M32, NGC 5102, and NGC 5206, while in NGC 205, we find only an upper limit. These BH mass estimates are consistent with previous measurements in M32 and NGC 205, while those in NGC 5102 & NGC 5206 are estimated for the first time, and both found to be <10 6 M . This adds to just a handful of galaxies with dynamically measured sub-million M central BHs. Combining these BH detections with our recent work on NGC 404's BH, we find that 80% (4/5) of nearby, low-mass (10 9 − 10 10 M ; σ ∼ 20 − 70 km s −1 ) early-type galaxies host BHs. Such a high occupation fraction suggests the BH seeds formed in the early epoch of cosmic assembly likely resulted in abundant seeds, favoring a low-mass seed mechanism of the remnants, most likely from the first generation of massive stars. We find dynamical masses of the NSCs ranging from 2 − 73 × 10 6 M and compare these masses to scaling relations for NSCs based primarily on photometric mass estimates. Color gradients suggest younger stellar populations lie at the centers of the NSCs in three of the four galaxies (NGC 205, NGC 5102, and NGC 5206), while the morphology of two are complex and are best-fit with multiple morphological components (NGC 5102 and NGC 5206). The NSC kinematics show they are rotating, especially in M32 and NGC 5102 (V /σ ∼ 0.7).

Coronary artery disease (CAD) remains the leading cause of mortality among cardiovascular diseases, responsible for 16% of the world’s total deaths. According to a statistical report published in 2020, the global prevalence of CAD was estimated at 1655 per 100,000 people and is predicted to exceed 1845 by 2030. Annually, in the United States, CAD accounts for approximately 610,000 deaths and costs more than 200 billion dollars for healthcare services. Most patients with CAD need to be treated over long periods with a combination of drugs. Therefore, the inappropriate use of drugs, or drug-related problems (DRPs), can lead to many consequences that affect these patients’ health, including decreased quality of life, increased hospitalization rates, prolonged hospital stays, increased overall health care costs, and even increased risk of morbidity and mortality. DRPs are common in CAD patients, with a prevalence of over 60%. DRPs must therefore be noticed and recognized by healthcare professionals. This chapter describes common types and determinants of DRPs in CAD patients and recommends interventions to limit their prevalence.

We improve the dynamical black hole (BH) mass estimates in three nearby low-mass early-type galaxies-NGC 205, NGC 5102, and NGC 5206. We use new HST /STIS spectroscopy to fit the star formation histories of the nuclei in these galaxies, and use these measurements to create local colormass-to-light ratio (M/L) relations. We then create new mass models from HST imaging and combined with adaptive optics kinematics, we use Jeans dynamical models to constrain their BH masses. The masses of the central BHs in NGC 5102 and NGC 5206 are both below one million solar masses and are consistent with our previous estimates, 9.12 +1.84 −1.53 × 10 5 M and 6.31 +1.06 −2.74 × 10 5 M (3σ errors), respectively. However, for NGC 205, the improved models suggests the presence of a BH for the first time, with a best-fit mass of 6.8 +95.6 −6.7 × 10 3 M (3σ errors). This is the least massive central BH mass in a galaxy detected using any method. We discuss the possible systematic errors of this measurement in detail. Using this BH mass, the existing upper limits of both X-ray, and radio emissions in the nucleus of NGC 205 suggest an accretion rate 10 −5 of the Eddington rate. We also discuss the color-M/L eff relations in our nuclei and find that the slopes of these vary significantly between nuclei. Nuclei with significant young stellar populations have steeper color-M/L eff relations than some previously published galaxy color-M/L eff relations.

The electrostatic layer-by-layer (LbL) assembly approach offers large potential in the area of drug delivery from thin films; however, because the processing technique is aqueous-based, there have been few strategies proposed to incorporate hydrophobic molecules into these films. Here we create an LbL film that is capable of incorporating hydrophobic drug at high loadings via encapsulation with lineardendritic block copolymer micelles and demonstrate for the first time release times of a hydrophobic antibacterial agent over a period of several weekssa significant improvement over reports of other micelleencapsulated thin films with release times of several minutes. The amphiphilic linear-dendritic block copolymer is composed of poly(propylene oxide) (PPO), which forms the hydrophobic core creating the compartment for hydrophobic drug encapsulation, and poly(amidoamine) (PAMAM), which forms the outer corona of the micelle. The PAMAM is polycationic, enabling LbL deposition with negatively charged poly(acrylic acid) (PAA). The stable PPO-PAMAM micelles incorporated into the LbL films encapsulated a hydrophobic bactericide, triclosan, which have loading capacities as high as 80-90%. Film thickness and UV-vis measurements confirm the formation of the LbL film and incorporation of triclosan into the film. Fluorescence measurements of PPO-PAMAM/PAA films with pyrene indicated the presence of hydrophobic domains in the film. GISAXS revealed regular spacing of approximately 10.5 nm in the direction parallel to the film substrate, which is approximately the same size as the PPO-PAMAM micelles in aqueous solution. Volume fraction measurements based on elemental analysis and TGA confirm the GISAXS data. An in vitro release study revealed long release times of triclosan on the order of weeks, and a Kirby Bauer test was performed on Staphylococcus aureus, demonstrating that the drug released was still active to inhibit the growth of bacteria.