Riemann-Hilbert analysis for Jacobi polynomials orthogonal on a single contour

Classical Jacobi polynomials $P_{n}^{(\alpha,\beta)}$, with $\alpha, \beta>-1$, have a number of well-known properties, in particular the location of their zeros in the open interval $(-1,1)$. This property is no longer valid for other values of the parameters; in general, zeros are complex. In this paper we study the strong asymptotics of Jacobi polynomials where the real parameters $\alpha_n,\beta_n$ depend on $n$ in such a way that $$\lim_{n\to\infty}\frac{\alpha_{n}}{n}=A, \quad \lim_{n\to\infty}\frac{\beta_{n}}{n}=B,$$ with $A,B \in \mathbb{R}$. We restrict our attention to the case where the limits $A,B$ are not both positive and take values outside of the triangle bounded by the straight lines A=0, B=0 and $A+B+2=0$. As a corollary, we show that in the limit the zeros distribute along certain curves that constitute trajectories of a quadratic differential. The non-hermitian orthogonality relations for Jacobi polynomials with varying parameters lie in the core of our approach; in the cases we consider, these relations hold on a single contour of the complex plane. The asymptotic analysis is performed using the Deift-Zhou steepest descent method based on the Riemann-Hilbert reformulation of Jacobi polynomials.Comment: 37 pages, 10 figure

Readout from iconic memory involves similar neural processes as selective spatial attention

Iconic memory and spatial attention are often considered as distinct topics, but may have functional similarities. Here we provide fMRI evidence for some common underlying neural effects. Participants judged three visual stimuli in one hemifield of a bilateral array comprising six stimuli. The relevant hemifield for partial report was indicated by an auditory cue, administered either before the visual array (pre-cues, spatial attention) or shortly after (post-cues, iconic memory). Pre- and post-cues led to similar activity modulations in lateral occipital cortex, contralateral to the cued side, indicating that readout from iconic memory can have similar neural effects to spatial attention. We also found common bilateral activation of a fronto-parietal network for post-cue and pre-cue trials. These neuroimaging data suggest that some common neural mechanisms underlie selective spatial attention and readout from iconic memory. Some differences were also found, with post-cues leading to higher activity in right middle frontal gyrus

The Contribution of Late-type/Irregulars to the Faint Galaxy Counts from HST Medium Deep Survey Images

We present a complete morphologically classified sample of 144 faint field galaxies from the HST Medium Deep Survey with 20.0 < I <22.0 mag. We compare the global properties of the ellipticals, early and late-type spirals, and find a non-negligible fraction (13/144) of compact blue [(V-I) < 1.0 mag] systems with $r^{1/4}$-profiles. We give the differential galaxy number counts for ellipticals and early-type spirals independently, and find that the data are consistent with no-evolution predictions based on conventional flat Schechter luminosity functions (LF's) and a standard cosmology. Conversely, late-type/Irregulars show a steeply rising differential number count with slope $(\frac{\delta log N}{\delta m}) = 0.64\pm 0.1$. No-evolution models based on the Loveday et al. (1992) and Marzke et al. (1994b) {\it local} luminosity functions under-predict the late-type/Irregular counts by 1.0 and 0.5 dex, respectively, at I = 21.75 mag. Examination of the Irregulars alone shows that $\sim 50$% appear inert and the remainder have multiple cores. If the inert galaxies represent a non-evolving late-type population, then a Loveday-like LF ($\alpha\simeq -1.0$) is ruled out for these types, and a LF with a steep faint-end ($\alpha\simeq -1.5$) is suggested. If multiple core structure indicates recent star-formation, then the observed excess of faint blue field galaxies is likely due to {\it evolutionary} processes acting on a {\it steep} field LF for late-type/Irregulars. The evolutionary mechanism is unclear, but 60% of the multiple-core Irregulars show close companions. To reconcile a Marzke-like LF with the faint redshift surveys, this evolution must be preferentially occurring in the brightest late-type galaxies with z > 0.5 at I = 21.75 mag.Comment: 29 pages, 1 catalog and 10 figures. The figures and catalog can be found at http://www.phys.unsw.edu.au/~spd/bib.htm

U.S. Society and the Evolving Needs of the Baby Boomer Generation as it Relates to Alzheimer\u27s Disease

The Baby Boomer generation, those born between the years 1946-1964, are beginning to reach the age of when symptoms of initial onset of Alzheimer’s Disease become prevalent. This causes a concern for society in the United States due to the high number of persons that make up this generation that are likely to significantly increase the already high number of Alzheimer’s Disease cases in the United States. Causes for concern include the high number of people within this generation reaching age of initial onset of Alzheimer’s disease, the impact the disease as a whole on individuals, as well as their families, caregivers, and society. While there is no cure for the progression of Alzheimer’s disease currently, research into the development of a cure has been deemed a priority. There are growing concerns of the level of care available to the elderly population and the lack of diagnosis in the early stages of the disease. Research presents resolutions for society, that when implemented, can alleviate some of these concerns. Further research into the alleviation of the current and future concerns that the Baby Boomer Generation generates for United States’ society is discussed

A Consideration of the More Extended Use of the Special Verdict

This discussion will cover only subdivision (a) of Rule 49 of the Federal Rules of Civil Procedure, but I feel that I should briefly distinguish it from subdivision (b), the other subdivision of the rule, since the cases reveal a surprising amount of confusion regarding them. Subdivision (a) provides that the court may require the jury to return only a special verdict in the form of special findings on each issue of fact formulated by the pleadings and the evidence. The special verdict may be in the form of either written findings or written questions, susceptible of categorical or other brief answer, covering the factual issues. In any case, it is purely a fact verdict. The jury finds the basic facts and the court then arrives at appropriate conclusions of law and enters judgment accordingly. No general verdict is submitted to the jury with a special verdict

Proposed Improvements in Veteran Administration Mental Health and Substance Abuse Treatment Services

The U.S. government provides many health care benefits to veterans, both during and after they serve. Unfortunately, the benefits become a necessity for many veterans who return home because of the mental and physical trauma that they sustain during their time being active duty. The U.S. Department of Veterans Affairs has created a healthcare system specifically for veterans that provides medical centers and outpatient clinics with a variety of services throughout the country. The trauma that veterans experience often requires them to have care that is specialized for them in areas like substance abuse and mental health. While they can receive care at VA locations, it is often not a choice for a veteran to travel the distance to that location or wait weeks or months for an appointment and are forced to get care in the civilian sector. Because of this, the VA has started to allow veterans to receive care at non-VA facilities and as a result, quality of care and specialization for veterans is very important. The services that are provided at those locations are reviewed for both availability and range of services for veterans. This thesis analyzes existing data on substance abuse treatment services and mental health services for both veterans and civilians in order to assess trends for services available and treatment options. Overall, treatment type availability has not changed since the Opioid Safety Initiative. VA facilities are not increasing their availability of alternative therapies, but telemedicine therapy has become more available nationwide. Veteran specific programs are slightly decreasing in non-VA mental health facilities unlike non-VA substance abuse facilities where the program availability is increasing. Increased access to alternative treatments can help medical institutions provide more diverse and better-quality treatment plans for veterans

Attentional load and sensory competition in human vision: Modulation of fMRI responses by load fixation during task-irrelevant stimulation in the peripheral visual field.

Perceptual suppression of distractors may depend on both endogenous and exogenous factors, such as attentional load of the current task and sensory competition among simultaneous stimuli, respectively. We used functional magnetic resonance imaging (fMRI) to compare these two types of attentional effects and examine how they may interact in the human brain. We varied the attentional load of a visual monitoring task performed on a rapid stream at central fixation without altering the central stimuli themselves, while measuring the impact on fMRI responses to task-irrelevant peripheral checkerboards presented either unilaterally or bilaterally. Activations in visual cortex for irrelevant peripheral stimulation decreased with increasing attentional load at fixation. This relative decrease was present even in V1, but became larger for successive visual areas through to V4. Decreases in activation for contralateral peripheral checkerboards due to higher central load were more pronounced within retinotopic cortex corresponding to 'inner' peripheral locations relatively near the central targets than for more eccentric 'outer' locations, demonstrating a predominant suppression of nearby surround rather than strict 'tunnel vision' during higher task load at central fixation. Contralateral activations for peripheral stimulation in one hemifield were reduced by competition with concurrent stimulation in the other hemifield only in inferior parietal cortex, not in retinotopic areas of occipital visual cortex. In addition, central attentional load interacted with competition due to bilateral versus unilateral peripheral stimuli specifically in posterior parietal and fusiform regions. These results reveal that task-dependent attentional load, and interhemifield stimulus-competition, can produce distinct influences on the neural responses to peripheral visual stimuli within the human visual system. These distinct mechanisms in selective visual processing may be integrated within posterior parietal areas, rather than earlier occipital cortex