§3.3. H p spaces again §3.4. #°°(ID>) as a multiplier algebra §3.5. Inner functions 45 §3.6. Historical notes Chapter 4. P 2 (/_i) 49 §4.1. Other spaces with H°°(TD>) as the multiplier algebra 49 §4.2. Vector-valued-P 2 (/u) spaces Chapter 5. Pick Redux §5.1. Necessity of positivity of the Pick matrix §5.2. The Szego kernel has the Pick property §5.3. The Caratheodory problem §5.4. Uniqueness of the Szego kernel §5.5. Historical notes Chapter 6. Qualitative Properties of the Solution of the Pick Problem in H°°(B) §6.1. A formula for the solution §6.2. The realization formula for H°°(B) §6.3. Another formula for the solution §6.4. The Nevanlinna problem Chapter 7. Characterizing Kernels with the Complete Pick Property §7.1. Characterization of the complete Pick property §7.2. Another characterization of the complete Pick property §7.3. Holomorphic spaces with the complete Pick property §7.4. The Sobolev space §7.5. The M sxt Pick property §7.6. Historical notes Contents xi Chapter 8. The Universal Pick Kernel §8.1. The universal kernel 97 §8.2. The realization formula for the universal kernel §8.3. Qualitative properties of solutions of the Pick problem for complete Pick kernels §8.4. The Toeplitz-corona theorem §8.5. Beurling theorems §8.6. Holomorphic complete Pick spaces §8.7. The Nevanlinna problem §8.8. Uniqueness of kernels with the Pick property §8.9. Historical notes Chapter 9.

Measurement of correlations between brain regions (functional connectivity) using blood oxygen level dependent (BOLD) fMRI has proven to be a powerful tool for studying the functional organization of the brain. Recently, dynamic functional connectivity has emerged as a major topic in the resting-state BOLD fMRI literature. Here, using simulations and multiple sets of empirical observations, we confirm that imposed task states can alter the correlation structure of BOLD activity. However, we find that observations of "dynamic" BOLD correlations during the resting state are largely explained by sampling variability. Beyond sampling variability, the largest part of observed "dynamics" during rest is attributable to head motion. An additional component of dynamic variability during rest is attributable to fluctuating sleep state. Thus, aside from the preceding explanatory factors, a single correlation structure-as opposed to a sequence of distinct correlation structures-may adequately describe the resting state as measured by BOLD fMRI. These results suggest that resting-state BOLD correlations do not primarily reflect moment-to-moment changes in cognitive content. Rather, resting-state BOLD correlations may predominantly reflect processes concerned with the maintenance of the long-term stability of the brain's functional organization.

Alzheimer's disease (AD) is characterized by two molecular pathologies: cerebral β-amyloidosis in the form of β-amyloid (Aβ) plaques and tauopathy in the form of neurofibrillary tangles, neuritic plaques, and neuropil threads. Until recently, only Aβ could be studied in humans using positron emission tomography (PET) imaging owing to a lack of tau PET imaging agents. Clinical pathological studies have linked tau pathology closely to the onset and progression of cognitive symptoms in patients with AD. We report PET imaging of tau and Aβ in a cohort of cognitively normal older adults and those with mild AD. Multivariate analyses identified unique disease-related stereotypical spatial patterns (topographies) for deposition of tau and Aβ. These PET imaging tau and Aβ topographies were spatially distinct but correlated with disease progression. Cerebrospinal fluid measures of tau, often used to stage preclinical AD, correlated with tau deposition in the temporal lobe. Tau deposition in the temporal lobe more closely tracked dementia status and was a better predictor of cognitive performance than Ab deposition in any region of the brain. These data support models of AD where tau pathology closely tracks changes in brain function that are responsible for the onset of early symptoms in AD.

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IntroductionIn this paper, we shall be looking at a special class of bordered (algebraic) varieties that are contained in the bidisk D 2 in C 2. Condition (0.2) means that the variety exits the bidisk through the distinguished boundary of the bidisk, the torus. We shall use OV to denote the set given by (0.2): topologically, it is the boundary of V within Zp, the zero set of p, rather than in all of C 2. We shall always assume that p is chosen to be minimal, i.e. so that no irreducible component of Zp is disjoint from D 2 and so that p has no repeated irreducible factors.Why should one single out distinguished varieties from other bordered varieties?One of the most important results in operator theory is T. Andb's inequality