Note on islands in path-length sequences of binary trees

An earlier characterization of topologically ordered (lexicographic) path-length sequences of binary trees is reformulated in terms of an integrality condition on a scaled Kraft sum of certain subsequences (full segments, or islands). The scaled Kraft sum is seen to count the set of ancestors at a certain level of a set of topologically consecutive leaves is a binary tree.Comment: 4 page

On instantaneous codes

Maximal instantaneous codes are characterized by the property that they allow unique parsing of every infinite string. The sequence of codeword lengths of a maximal instantaneous code, sequenced in lexicographic order of the codewords, completely determines the code itself. Any increasing, decreasing or unimodal reordering of such a sequence again corresponds to a maximal instantaneous code. Lexicographic length sequences are characterized by a family of Kraft-type equalities

Speaking and cognitive distractions during EEG-based brain control of a virtual neuroprosthesis-arm

BACKGROUND: Brain-computer interface (BCI) systems have been developed to provide paralyzed individuals the ability to command the movements of an assistive device using only their brain activity. BCI systems are typically tested in a controlled laboratory environment were the user is focused solely on the brain-control task. However, for practical use in everyday life people must be able to use their brain-controlled device while mentally engaged with the cognitive responsibilities of daily activities and while compensating for any inherent dynamics of the device itself. BCIs that use electroencephalography (EEG) for movement control are often assumed to require significant mental effort, thus preventing users from thinking about anything else while using their BCI. This study tested the impact of cognitive load as well as speaking on the ability to use an EEG-based BCI. FINDINGS: Six participants controlled the two-dimensional (2D) movements of a simulated neuroprosthesis-arm under three different levels of cognitive distraction. The two higher cognitive load conditions also required simultaneously speaking during BCI use. On average, movement performance declined during higher levels of cognitive distraction, but only by a limited amount. Movement completion time increased by 7.2%, the percentage of targets successfully acquired declined by 11%, and path efficiency declined by 8.6%. Only the decline in percentage of targets acquired and path efficiency were statistically significant (p < 0.05). CONCLUSION: People who have relatively good movement control of an EEG-based BCI may be able to speak and perform other cognitively engaging activities with only a minor drop in BCI-control performance

Osteoporosis in young adults: pathophysiology, diagnosis, and management

Postmenopausal osteoporosis is mainly caused by increased bone remodeling resulting from estrogen deficiency. Indications for treatment are based on low areal bone mineral density (aBMD, T-score ≤ −2.5), typical fragility fractures (spine or hip), and more recently, an elevated 10-year fracture probability (by FRAX®). In contrast, there is no clear definition of osteoporosis nor intervention thresholds in younger individuals. Low aBMD in a young adult may reflect a physiologically low peak bone mass, such as in lean but otherwise healthy persons, whereas fractures commonly occur with high-impact trauma, i.e., without bone fragility. Furthermore, low aBMD associated with vitamin D deficiency may be highly prevalent in some regions of the world. Nevertheless, true osteoporosis in the young can occur, which we define as a T-score below −2.5 at spine or hip in association with a chronic disease known to affect bone metabolism. In the absence of secondary causes, the presence of fragility fractures, such as in vertebrae, may point towards genetic or idiopathic osteoporosis. In turn, treatment of the underlying condition may improve bone mass as well. In rare cases, a bone-specific treatment may be indicated, although evidence is scarce for a true benefit on fracture risk. The International Osteoporosis Foundation (IOF) convened a working group to review pathophysiology, diagnosis, and management of osteoporosis in the young, excluding children and adolescents, and provide a screening strategy including laboratory exams for a systematic approach of this conditio

Antichain cutsets of strongly connected posets

Rival and Zaguia showed that the antichain cutsets of a finite Boolean lattice are exactly the level sets. We show that a similar characterization of antichain cutsets holds for any strongly connected poset of locally finite height. As a corollary, we get such a characterization for semimodular lattices, supersolvable lattices, Bruhat orders, locally shellable lattices, and many more. We also consider a generalization to strongly connected hypergraphs having finite edges.Comment: 12 pages; v2 contains minor fixes for publicatio

Signaling via PI3K/FOXO1A pathway modulates formation and survival of human embryonic stem cell-derived endothelial cells

Vascular derivatives of human embryonic stem cells (hESC) are being developed as sources of tissue-specific cells for organ regeneration. However, identity of developmental pathways that modulate the specification of endothelial cells is not known yet. We studied phosphatidylinositol 3-kinase (PI3K)-Forkhead box O transcription factor 1A (FOXO1A) pathways during differentiation of hESC toward endothelial lineage and on proliferation, maturation, and cell death of hESC-derived endothelial cells (hESC-EC). During differentiation of hESC, expression of FOXO1A transcription factor was linked to the expression of a cluster of angiogenesis- and vascular remodeling-related genes. PI3K inhibitor LY294002 activated FOXO1A and induced formation of CD31(+) hESC-EC. In contrast, differentiating hESC with silenced FOXO1A by small interfering RNA (siRNA) showed lower mRNA levels of CD31 and angiopoietin2. LY294002 decreased proliferative activity of purified hESC-EC, while FOXO1A siRNA increased their proliferation. LY294002 inhibits migration and tube formation of hESC-EC; in contrast, FOXO1A siRNA increased in vitro tube formation activity of hESC-EC. After in vivo conditioning of cells in athymic nude rats, cells retain their low FOXO1A expression levels. PI3K/FOXO1A pathway is important for function and survival of hESC-EC and in the regulation of endothelial cell fate. Understanding these properties of hESC-EC may help in future applications for treatment of injured organs