Partial Isometries of a Sub-Riemannian Manifold

In this paper, we obtain the following generalisation of isometric $C^1$-immersion theorem of Nash and Kuiper. Let $M$ be a smooth manifold of dimension $m$ and $H$ a rank $k$ subbundle of the tangent bundle $TM$ with a Riemannian metric $g_H$. Then the pair $(H,g_H)$ defines a sub-Riemannian structure on $M$. We call a $C^1$-map $f:(M,H,g_H)\to (N,h)$ into a Riemannian manifold $(N,h)$ a {\em partial isometry} if the derivative map $df$ restricted to $H$ is isometric; in other words, $f^*h|_H=g_H$. The main result states that if $\dim N>k$ then a smooth $H$-immersion $f_0:M\to N$ satisfying $f^*h|_H<g_H$ can be homotoped to a partial isometry $f:(M,g_H)\to (N,h)$ which is $C^0$-close to $f_0$. In particular we prove that every sub-Riemannian manifold $(M,H,g_H)$ admits a partial isometry in $\R^n$ provided $n\geq m+k$.Comment: 13 pages. This is a revised version of an earlier submission (minor revision

Scaling of load in communications networks

We show that the load at each node in a preferential attachment network scales as a power of the degree of the node. For a network whose degree distribution is p(k) ~ k^(-gamma), we show that the load is l(k) ~ k^eta with eta = gamma - 1, implying that the probability distribution for the load is p(l) ~ 1/l^2 independent of gamma. The results are obtained through scaling arguments supported by finite size scaling studies. They contradict earlier claims, but are in agreement with the exact solution for the special case of tree graphs. Results are also presented for real communications networks at the IP layer, using the latest available data. Our analysis of the data shows relatively poor power-law degree distributions as compared to the scaling of the load versus degree. This emphasizes the importance of the load in network analysis.Comment: 4 pages, 5 figure

Resting EEG Microstates and Autonomic Heart Rate Variability Do Not Return to Baseline One Hour After a Submaximal Exercise.

Recent findings suggest that an acute physical exercise modulates the temporal features of the EEG resting microstates, especially the microstate map C duration and relative time coverage. Microstate map C has been associated with the salience resting state network, which is mainly structured around the insula and cingulate, two brain nodes that mediate cardiovascular arousal and interoceptive awareness. Heart rate variability (HRV) is dependent on the autonomic balance; specifically, an increase in the sympathetic (or decrease in the parasympathetic) tone will decrease variability while a decrease in the sympathetic (or increase in the parasympathetic) tone will increase variability. Relying on the functional interaction between the autonomic cardiovascular activity and the salience network, this study aims to investigate the effect of exercise on the resting microstate and the possible interplay with this autonomic cardiovascular recovery after a single bout of endurance exercise. Thirty-eight young adults performed a 25-min constant-load cycling exercise at an intensity that was subjectively perceived as "hard." The microstate temporal features and conventional time and frequency domain HRV parameters were obtained at rest for 5 min before exercise and at 5, 15, 30, 45, and 60 min after exercise. Compared to the baseline, all HRV parameters were changed 5 min after exercise cessation. The mean durations of microstate B and C, and the frequency of occurrence of microstate D were also changed immediately after exercise. A long-lasting effect was found for almost all HRV parameters and for the duration of microstate C during the hour following exercise, indicating an uncompleted recovery of the autonomic cardiovascular system and the resting microstate. The implication of an exercise-induced afferent neural traffic is discussed as a potential modulator of both the autonomic regulation of heart rate and the resting EEG microstate

A computational framework for identifying design guidelines to increase the penetration of targeted nanoparticles into tumors

Targeted nanoparticles are increasingly being engineered for the treatment of cancer. By design, they can passively accumulate in tumors, selectively bind to targets in their environment, and deliver localized treatments. However, the penetration of targeted nanoparticles deep into tissue can be hindered by their slow diffusion and a high binding affinity. As a result, they often localize to areas around the vessels from which they extravasate, never reaching the deep-seeded tumor cells, thereby limiting their efficacy. To increase tissue penetration and cellular accumulation, we propose generalizable guidelines for nanoparticle design and validate them using two different computer models that capture the potency, motion, binding kinetics, and cellular internalization of targeted nanoparticles in a section of tumor tissue. One strategy that emerged from the models was delaying nanoparticle binding until after the nanoparticles have had time to diffuse deep into the tissue. Results show that nanoparticles that are designed according to these guidelines do not require fine-tuning of their kinetics or size and can be administered in lower doses than classical targeted nanoparticles for a desired tissue penetration in a large variety of tumor scenarios. In the future, similar models could serve as a testbed to explore engineered tissue-distributions that arise when large numbers of nanoparticles interact in a tumor environment.Human Frontier Science Program (Strasbourg, France)David H. Koch Institute for Integrative Cancer Research at MIT (Marie D. and Pierre Casimir-Lambert Fund)National Institutes of Health (U.S.) (Grant U54 CA151884)National Cancer Institute (U.S.) (Koch Institute Support (Core) Grant P30-CA14051

Unusual DNA Structure and DNA Damage Recognition: Structure and Dynamic Markers

Nucleic acids play a central role in many biological processes, including information storage, gene expression, serving as messengers or structural components and even catalysis. Their diverse roles have made them targets of interest to diagnose and treat an array of human disorders such as infections, degenerative diseases and cancer. Nature has evolved proteins and ligands that recognize specific nucleic acid sequences or structures and control their function, demonstrating that this can be efficiently accomplished. This has led to the development of wide variety of synthetic molecules that selectively bind to nucleic acids. In turn, this has precipitated numerous studies which showed that nucleic acid structures and their dynamic properties must be understood in order to efficiently target specific sequences or structures

Movement-Related Cortical Potential Amplitude Reduction after Cycling Exercise Relates to the Extent of Neuromuscular Fatigue.

Exercise-induced fatigue affects the motor control and the ability to generate a given force or power. Surface electroencephalography allows researchers to investigate movement-related cortical potentials (MRCP), which reflect preparatory brain activity 1.5 s before movement onset. Although the MRCP amplitude appears to increase after repetitive single-joint contractions, the effects of large-muscle group dynamic exercise on such pre-motor potential remain to be described. Sixteen volunteers exercised 30 min at 60% of the maximal aerobic power on a cycle ergometer, followed by a 10-km all-out time trial. Before and after each of these tasks, knee extensor neuromuscular function was investigated using maximal voluntary contractions (MVC) combined with electrical stimulations of the femoral nerve. MRCP was recorded during 60 knee extensions after each neuromuscular sequence. The exercise resulted in a significant decrease in the knee extensor MVC force after the 30-min exercise (-10 ± 8%) and the time trial (-21 ± 9%). The voluntary activation level (VAL; -6 ± 8 and -12 ± 10%), peak twitch (Pt; -21 ± 16 and -32 ± 17%), and paired stimuli (P100 Hz; -7 ± 11 and -12 ± 13%) were also significantly reduced after the 30-min exercise and the time trial. The first exercise was followed by a decrease in the MRCP, mainly above the mean activity measured at electrodes FC1-FC2, whereas the reduction observed after the time trial was related to the FC1-FC2 and C2 electrodes. After both exercises, the reduction in the late MRCP component above FC1-FC2 was significantly correlated with the reduction in P100 Hz (r = 0.61), and the reduction in the same component above C2 was significantly correlated with the reduction in VAL (r = 0.64). In conclusion, large-muscle group exercise induced a reduction in pre-motor potential, which was related to muscle alterations and resulted in the inability to produce a maximal voluntary contraction

The Large Scale Curvature of Networks

Understanding key structural properties of large scale networks are crucial for analyzing and optimizing their performance, and improving their reliability and security. Here we show that these networks possess a previously unnoticed feature, global curvature, which we argue has a major impact on core congestion: the load at the core of a network with N nodes scales as N^2 as compared to N^1.5 for a flat network. We substantiate this claim through analysis of a collection of real data networks across the globe as measured and documented by previous researchers.Comment: 4 pages, 5 figure

Micro RNA Expression after Ingestion of Fucoidan; A Clinical Study

Fucoidans are a class of fucose‐rich sulfated polysaccharides derived from brownmacroalgae that exert a range of biological activities in vitro and in vivo. To generate an unbiasedassessment of pathways and processes affected by fucoidan, a placebo‐controlled double‐blind pilotstudy was performed in healthy volunteers. Blood samples were taken immediately before and 24h after ingestion of a single dose of 1 g of Undaria pinnatifida fucoidan (UPF) or placebo. Levels ofisolated miRNAs were analyzed using Taqman Open Array Human MicroRNA panels. Out of 754miRNAs screened, UPF affected a total of 53 miRNAs. Pathway analysis using the TALOS dataanalysis tool predicted 29 different pathways and processes that were largely grouped into cellsurface receptor signaling, cancer‐related pathways, the majority of which were previouslyassociated with fucoidans. However, this analysis also identified nine pathways and processes thathave not been associated with fucoidans before. Overall, this study illustrates that even a single doseof fucoidans has the potential to affect the expression of genes related to fundamental cellularprocesses. Moreover, it confirms previous data that fucoidans influence immunity, cancer cells,inflammation, and neurological function

Partially Saturated Bicyclic Heteroaromatics as an sp³-Enriched Fragment Collection.

Fragment-based lead generation has proven to be an effective means of identifying high-quality lead compounds for drug discovery programs. However, the fragment screening sets often used are principally comprised of sp²-rich aromatic compounds, which limits the structural (and hence biological) diversity of the library. Herein, we describe strategies for the synthesis of a series of partially saturated bicyclic heteroaromatic scaffolds with enhanced sp³ character. Subsequent derivatization led to a fragment collection featuring regio- and stereo-controlled introduction of substituents on the saturated ring system, often with formation of new stereocenters.EPSRC BBSRC MRC Wellcome Trust D.G.T. thanks AstraZeneca for funding. S.L.M. thanks BASF for funding.