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In analyzing finite-state Markov chains knowing the exact eigenvalues of the transition probability matrix P P is important information for predicting the explicit transient behavior of the system. Once the eigenvalues of P P are known, linear algebra and duality theory are used to find P k P^{k} where k = 2 , 3 , 4 , … k= 2,3,4,\ldots . This article is about finding explicit eigenvalue formulas, that scale up with the dimension of P P for various Markov chains. Eigenvalue formulas and expressions of P k P^{k} are first presented when P P is tridiagonal and Toeplitz. These results are generalized to tridiagonal matrices with alternating birth-death probabilities. More general eigenvalue formulas and expression of P k P^{k} are obtained for non-tridiagonal transition matrices P P that have both catastrophe-like and birth-death transitions. Similar results for circulant matrices are also explored. Applications include finding probabilities of sample paths restricted to a strip and generalized ballot box problems. These results generalize to Markov processes with P k P^{k} being replaced by e Q t e^{Qt} where Q Q is a transition rate matrix.

The goal of this work was to determine which standard particle size metric derived from optical analysis most closely approximates the sieved weight percent of irregularly shaped powder intended to be used for directed energy deposition. In this investigation, equivalent circle diameter, maximum diameter, minimum diameter, and perimeter were used as metrics to “virtually sieve” the particles in samples of irregularly shaped powder into the following particle size bins: 150 µm. The percentage in the 45 µm – 150 µm bin were then compared to the weight percent of the powder mechanically sieved into this size range. The absolute difference between the virtually sieved percentage and the mechanically sieved percentage was assessed for 81 samples of mechanically-generated stainless steel 316L powder, all produced under different processing conditions in an oscillation ball mill. This difference was found to be on average, the least with the minimum diameter assessed as an area percentage, followed by the equivalent diameter assessed as an area percentage, and then the maximum diameter assessed as a percentage of the total number of particles ranked third. These findings and the methodology used to obtain them may be used by powder production process engineers and quality assurance personnel to assist in process control as more diverse additive manufacturing feedstocks become utilized.

The objective of this work is to study the feasibility of mechanically-generated feedstock for use in directed energy deposition (DED) processing. Mechanically-generated powder was created by machining 316L stainless steel bar stock followed by comminution of the resulting chips through oscillation ball milling. This methodology's production yield and processing time for the specifications of a commercially available DED system are presented along with resulting powder morphology. Performance of the mechanically-generated feedstock was compared to gas-atomized powder and evaluated based on the following figures of merit: flowability, printed part height, printed part density, and chemical compositional stability throughout processing. Mechanically-generated feedstock was created to meet deposition system requirements. Compared with gas-atomized powder, mechanically-generated powder did not flow as well through the powder-delivery system. Parts printed from mechanically-generated feedstock were generally taller than their counterparts from gas-atomized feedstock, but their densities were less predictable. Chemical composition of prints using both feedstocks was within standard nominal compositions for 316L stainless steel.

Statement of problem Composite resin and amalgam restorations are indicated for the restoration of posterior teeth. With increased esthetic demands, long-term clinical studies are required to evaluate the restorative success and reasons for failure of these materials. Purpose The purpose of this retrospective study was to determine the survival and reasons for failure of directly placed 2-surface composite resin restorations and directly placed 2-surface amalgam restorations on premolars placed by Canadian dental students. Material and methods Using The University of Manitoba's dental management software and paper charts, all 2-surface composite resin and 2-surface amalgam restorations placed on premolars between January 1, 2002, and May 30, 2014, were included. Short-term failure (within 2 years), long-term failure, and reasons for failure were collected. A Kaplan-Meier survival estimate with an associated P value comparing composite resin to amalgam restoration curves was performed using SPSS statistical software. Results Over 12 years, 1695 composite resin and 1125 amalgam 2-surface premolar restorations were placed. Of these restorations, 134 composite resins (7.9%) and 66 amalgams (5.9%) failed. Short-term failures (2 years or less) consisted of 57 composite resin (4%) and 23 amalgam (2.3%) restorations. Long-term failures (greater than 2 years) consisted of 77 composite resin (4.5%) and 43 amalgam (3.8%) restorations. After 12 years of service, the survival probability of composite resin restorations was 86% and that of amalgam restorations 91.5%. The differences in composite resin and amalgam survival curves were also found to be statistically significant ( P =.009 for Log-rank test). The main reasons for failure were recurrent caries and fracture of the tooth being restored. Conclusions Within the limitations of this study, both composite resin and amalgam restorations had acceptable success rates and similar failure modes. Recurrent caries was still the most common reason for failure.

Our prior work demonstrated the involvement of the caudal granular subregion of the insular cortex in a rat model of nicotine self-administration. Recent studies in various animal models of addiction for nicotine and other drugs have identified a role for the rostral agranular subregion (RAIC). The current research was undertaken to examine the involvement of the RAIC in a rat model of nicotine self-administration. We investigated the inactivating effects of local infusions of a γ-aminobutyric acid agonist mixture (baclofen/muscimol) into the RAIC on nicotine self-administration under a fixed-ratio 5 (FR-5) schedule and on reinstatement of nicotine seeking induced by nicotine-associated cues in rats. We also evaluated the effects of RAIC inactivation on food self-administration under an FR5 schedule as a control. Inactivation of the RAIC decreased nicotine, but not food, self-administration. RAIC inactivation also prevented the reinstatement, after extinction, of nicotine seeking induced by nicotine-associated cues. Our study indicates that the RAIC is involved in nicotine-taking and nicotine-seeking in rats. Modulating insular cortex function appears to be a promising approach for nicotine dependence treatment.

Substance-related and addictive disorders, in particular gambling disorder, are known to be associated with risky decision-making behavior. Several neuroimaging studies have identified the involvement of the insular cortex in decision-making under risk. However, the extent of this involvement remains unclear and the specific contributions of two distinct insular subregions, the rostral agranular (RAIC) and the caudal granular (CGIC), have yet to be examined. Animals were trained to perform a rat gambling task (rGT), in which subjects chose between four options that differed in the magnitude and probability of rewards and penalties. In order to address the roles of the RAIC and CGIC in established choice behavior, pharmacological inactivations of these two subregions via local infusions of GABA receptor agonists were performed following 30 rGT training sessions. The contribution made by the RAIC or CGIC to the acquisition of choice behavior was also determined by lesioning these areas before behavioral training. Inactivation of the RAIC, but not of the CGIC, shifted rats' preference toward options with greater reward frequency and lower punishment. Before rGT acquisition, lesions of the RAIC, but not the CGIC, likewise resulted in a higher preference for options with greater reward frequency and lower punishment, and this persisted throughout the 30 training sessions. Our results provide confirmation of the involvement of the RAIC in rGT choice behavior and suggest that the RAIC may mediate detrimental risky decision-making behavior, such as that associated with addiction and gambling disorder.

Dopamine, a neurotransmitter with 5 receptor subtypes, is critical to the dependence-forming properties of drugs of abuse. The role of the dopamine D4 receptor subtype in substance use disorders has remained somewhat elusive but the recent development of selective ligands holds promise for future investigations of this receptor subtype in substance use disorders, including alcohol use disorder. The purpose of the present study was to further elucidate the effects of a selective antagonist (L-745,870) and agonist (PD 168,077) on alcohol self-administration and reinstatement induced either by cues or stress. It was found that the D4 antagonist, but not agonist, reduced alcohol intake at the highest doses. Further, the D4 antagonist reduced stress-induced reinstatement, with no effects on cue-induced reinstatement; the agonist was without effect on either form of reinstatement. The dopamine D4 receptor antagonist was without effect on food reinforcement. This work deepens existing lines of evidence that the dopamine D4 receptor is involved in substance use disorders and suggests that dopamine D4 receptor blockade diminishes motivation for alcohol-taking without influencing natural food rewards. Furthermore, there appears to be a plausible effect of dopamine D4 receptor blockade interfering with stress- but not cue-induced alcohol-seeking.

We reinvestigate the classic portfolio optimization problem where the notion of portfolio risk is captured by the 'Foster–Hart risk'—a new, bankruptcy-proof, reserve based measure of risk, extremely sensitive to left tail events (Foster and Hart, 2009). To include financial market frictions induced by market microstructure, we employ a general, ex-ante transaction cost function with fixed, linear and quadratic penalty terms in the objective function. We represent the US equity market by the Dow Jones Industrial Average (DJIA) index and study the performance of the Foster–Hart optimal DJIA portfolio. In order to capture the skewed and leptokurtotic nature of real life stock returns, we model the returns of the DJIA constituents as an ARMA–GARCH process with multivariate 'normal tempered stable' innovations. We demonstrate that the Foster–Hart optimal portfolio’s performance is superior to those obtained under several techniques currently in use in academia and industry. Science Foundation Ireland

The dopamine D3 receptor (DRD3) has been proposed as a target for drug development for the treatment of addictive disorders. Recently, the anxiolytic buspirone has been shown to have affinity for DRD3 and DRD4, and interest in repurposing it for addictive disorders has grown. Binding of [3H]-(+)-PHNO in the rat cerebellum and striatum was used to measure occupancy by buspirone of DRD3 or DRD2, respectively. Effects of buspirone in the rat gambling task (rGT) and the five-choice serial reaction time task (5-CSRTT) were examined. Buspirone occupied both the DRD2 and DRD3 at high doses and the DRD3, but not the DRD2, in the narrow dose range of 3 mg/kg. At 10 mg/kg, a disruption of performance on rGT was observed. All measures of performance on the rGT, except for perseverations, were affected at 3 mg/kg. On the 5-CSRTT, omissions were increased. Impairments in the rGT were not mimicked by the effects induced by satiation. Further, buspirone did not impair food-maintained responding under a progressive ratio schedule of reinforcement at any dose, suggesting that the effects of buspirone on the rGT cannot be explained by non-selective actions. Although buspirone had effects on the rGT at the dose that selectively occupied the DRD3, the effects found do not parallel those found in previous studies of the effects of selective DRD3 antagonists on the rGT. Thus, buspirone may impair performance on the rGT through actions at multiple receptor sites.

From canyons to glaciers, from geology to astrobiology, the amount of exciting surface science awaiting us at Mars greatly outstrips available mission opportunities. Based on the thrice-flown Aerospace Corporation Earth Reentry Breakup Recorder (REBR), we present a method for accurate landing of small instrument payloads on Mars, utilizing excess cruise-stage mass on larger missions. One to a few such microlanders might add 1-5% to the cost of a primary mission with inconsequential risk. Using the REBR and JPL Deep Space 2 starting points for a passively stable entry vehicle provides a low mass and low ballistic coefficient, enabling subsonic deployment of a steerable parawing glider, capable of 10+ km of guided flight at a 3:1 glide ratio. Originally developed for the Gemini human space program, the parawing is attractive for a volume-limited microprobe, minimizing descent velocity, and providing sufficient remaining volume for a useful scientific payload. The ability to steer the parawing during descent offers unique opportunities, including terrain-relative navigation for landing within tens of meters of one of several specified targets within a given uncertainty ellipse. In addition to scientific value, some Mars human exploration Strategic Knowledge Gaps could be addressed with deployment of focused instruments at multiple locations.