The Max-Flow Min-Cut Theorem for Countable Networks

We prove a strong version of the Max-Flow Min-Cut theorem for countable networks, namely that in every such network there exist a flow and a cut that are "orthogonal" to each other, in the sense that the flow saturates the cut and is zero on the reverse cut. If the network does not contain infinite trails then this flow can be chosen to be mundane, i.e. to be a sum of flows along finite paths. We show that in the presence of infinite trails there may be no orthogonal pair of a cut and a mundane flow. We finally show that for locally finite networks there is an orthogonal pair of a cut and a flow that satisfies Kirchhoff's first law also for ends.Comment: 19 pages, to be published in Journal of Combinatorial Theory, Series

Analysis of the Brinkman-Forchheimer equations with slip boundary conditions

In this work, we study the Brinkman-Forchheimer equations driven under slip boundary conditions of friction type. We prove the existence and uniqueness of weak solutions by means of regularization combined with the Faedo-Galerkin approach. Next we discuss the continuity of the solution with respect to Brinkman's and Forchheimer's coefficients. Finally, we show that the weak solution of the corresponding stationary problem is stable

Orbitofrontal Cortex and the Early Processing of Visual Novelty in Healthy Aging

Event-related potential (ERP) studies have previously found that scalp topographies of attention-related ERP components show frontal shifts with age, suggesting an increased need for compensatory frontal activity to assist with top-down facilitation of attention. However, the precise neural time course of top-down attentional control in aging is not clear. In this study, 20 young (mean: 22 years) and 14 older (mean: 64 years) adults completed a three-stimulus visual oddball task while high-density ERPs were acquired. Colorful, novel distracters were presented to engage early visual processing. Relative to young controls, older participants exhibited elevations in occipital early posterior positivity (EPP), approximately 100 ms after viewing colorful distracters. Neural source models for older adults implicated unique patterns of orbitofrontal cortex (BA 11) activity during early visual novelty processing (100 ms), which was positively correlated with subsequent activations in primary visual cortex (BA 17). Older adult EPP amplitudes and OFC activity were associated with performance on tests of complex attention and executive function. These findings are suggestive of age-related, compensatory neural changes that may driven by a combination of weaker cortical efficiency and increased need for top-down control over attention. Accordingly, enhanced early OFC activity during visual attention may serve as an important indicator of frontal lobe integrity in healthy aging

The topology of connections between rat prefrontal, motor and sensory cortices

The connections of prefrontal cortex (PFC) were investigated in the rat brain to determine the order and location of input and output connections to motor and somatosensory cortex. Retrograde (100 nl Fluoro-Gold) and anterograde (100 nl Biotinylated Dextran Amines, BDA; Fluorescein and Texas Red) neuronanatomical tracers were injected into the subdivisions of the PFC (prelimbic, ventral orbital, ventrolateral orbital, dorsolateral orbital) and their projections studied. We found clear evidence for organized input projections from the motor and somatosensory cortices to the PFC, with distinct areas of motor and cingulate cortex projecting in an ordered arrangement to the subdivisions of PFC. As injection location of retrograde tracer was moved from medial to lateral in PFC, we observed an ordered arrangement of projections occurring in sensory-motor cortex. There was a significant effect of retrograde injection location on the position of labelled cells occurring in sensory-motor cortex (dorsoventral, anterior-posterior and mediolateral axes p < 0.001). The arrangement of output projections from PFC also displayed a significant ordered projection to sensory-motor cortex (dorsoventral p < 0.001, anterior-posterior p = 0.002 and mediolateral axes p < 0.001)

Effect of angiotensin receptor blockade on insulin sensitivity and endothelial function in abdominally obese hypertensive patients with impaired fasting glucose

AngII (angiotensin II) may contribute to cardiovascular risk in obesity via adverse effects on insulin sensitivity and endothelial function. In the present study, we examined the effects of ARB (angiotensin receptor blocker) therapy (losartan, 100 mg/day) on insulin sensitivity and endothelial function in 53 subjects with stage I hypertension, abdominal obesity and impaired fasting glucose. The study design was a randomized double-blinded parallel design placebo-controlled multi-centre trial of 8 weeks duration. We used the hyperinsulinaemic-euglycaemic clamp technique to measure insulin sensitivity (expressed as the 'M/I' value) and RH-PAT (reactive hyperaemia-peripheral arterial tonometry) to measure endothelial function. Additional measures included HOMA (homoeostasis model assessment)-B, an index of pancreatic β-cell function, and markers of inflammation [e.g. CRP (C-reactive protein)] and oxidative stress (e.g. F2-isoprostanes). ARB therapy did not alter insulin sensitivity [5.2 (2.7) pre-treatment and 4.6 (1.6) post-treatment] compared with placebo therapy [6.1 (2.9) pre-treatment and 5.3 (2.7) post-treatment; P value not significant], but did improve the HOMA-B compared with placebo therapy (P=0.05). ARB therapy also did not change endothelial function [RH-PAT, 2.15 (0.7) pre-treatment and 2.11 (0.7) post-treatment] compared with placebo therapy [RH-PAT, 1.81 (0.5) pre-treatment and 1.76 (0.7) post-treatment; P value not significant]. Markers of inflammation and oxidative stress were not significantly changed by ARB therapy. In conclusion, ARB therapy did not alter peripheral insulin sensitivity or endothelial function in this cohort of patients with essential hypertension, abdominal obesity and impaired fasting glucose, but did improve pancreatic β-cell function

Corporate Responsibility for Reality Show Participants

The American Broadcasting Company’s (ABC) reality dating show “Bachelor in Paradise” made headlines when the show was suspended pending allegations of sexual misconduct by an anonymous producer. While those allegations were later concluded to be unfounded, the questions of responsibility over the actions by reality show contestants remain. Where is the line between show-related activities that may involve the company that produces the content, and individual activities, in which the company has no potential liability? This post was originally published on the Cardozo Arts & Entertainment Law Journal website on February 10, 2019. The original post can be accessed via the Archived Link button above

Tribute to John Pickering

One of my colleagues asked me soon after John died, How could someone live to be eighty-nine years old and yet there is no one who had a bad word to say about him? This is an intriguing question. It is not because John Pickering did not have strongly held views about things. Anyone who ever tangled with John in crafting a brief knew how tenacious he was. John was direct and candid and you knew where he stood on any matter. It is not because John was easygoing. When he saw something that he wanted changed, he did not take no for an answer. He was relentless and tireless. It is not because he was not demanding. Working for John was hard work. He set high standards for himself and he expected you to work at the same level