Distribution of the time at which the deviation of a Brownian motion is maximum before its first-passage time

We calculate analytically the probability density $P(t_m)$ of the time $t_m$ at which a continuous-time Brownian motion (with and without drift) attains its maximum before passing through the origin for the first time. We also compute the joint probability density $P(M,t_m)$ of the maximum $M$ and $t_m$. In the driftless case, we find that $P(t_m)$ has power-law tails: $P(t_m)\sim t_m^{-3/2}$ for large $t_m$ and $P(t_m)\sim t_m^{-1/2}$ for small $t_m$. In presence of a drift towards the origin, $P(t_m)$ decays exponentially for large $t_m$. The results from numerical simulations are in excellent agreement with our analytical predictions.Comment: 13 pages, 5 figures. Published in Journal of Statistical Mechanics: Theory and Experiment (J. Stat. Mech. (2007) P10008, doi:10.1088/1742-5468/2007/10/P10008

Random Convex Hulls and Extreme Value Statistics

In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of $n$ independent random walks. In the continuum time limit this reduces to $n$ independent planar Brownian trajectories for which we compute exactly, for all $n$, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].Comment: 61 pages (pedagogical review); invited contribution to the special issue of J. Stat. Phys. celebrating the 50 years of Yeshiba/Rutgers meeting

Comprehensive transcriptome-wide analysis of spliceopathy correction of myotonic dystrophy using CRISPR-Cas9 in iPSCs-derived cardiomyocytes

CTG repeat expansion (CTGexp) is associated with aberrant alternate splicing that contributes to cardiac dysfunction in myotonic dystrophy type 1 (DM1). Excision of this CTGexp repeat using CRISPR-Cas resulted in the disappearance of punctate ribonuclear foci in cardiomyocyte-like cells derived from DM1-induced pluripotent stem cells (iPSCs). This was associated with correction of the underlying spliceopathy as determined by RNA sequencing and alternate splicing analysis. Certain genes were of particular interest due to their role in cardiac development, maturation, and function (TPM4, CYP2J2, DMD, MBNL3, CACNA1H, ROCK2, ACTB) or their association with splicing (SMN2, GCFC2, MBNL3). Moreover, while comparing isogenic CRISPR-Cas9-corrected versus non-corrected DM1 cardiomyocytes, a prominent difference in the splicing pattern for a number of candidate genes was apparent pertaining to genes that are associated with cardiac function (TNNT, TNNT2, TTN, TPM1, SYNE1, CACNA1A, MTMR1, NEBL, TPM1), cellular signaling (NCOR2, CLIP1, LRRFIP2, CLASP1, CAMK2G), and other DM1-related genes (i.e., NUMA1, MBNL2, LDB3) in addition to the disease-causing DMPK gene itself. Subsequent validation using a selected gene subset, including MBNL1, MBNL2, INSR, ADD3, and CRTC2, further confirmed correction of the spliceopathy following CTGexp repeat excision. To our knowledge, the present study provides the first comprehensive unbiased transcriptome- wide analysis of the differential splicing landscape in DM1 patient-derived cardiac cells after excision of the CTGexp repeat using CRISPR-Cas9, showing reversal of the abnormal cardiac spliceopathy in DM1

Peptide-conjugated oligonucleotides evoke long-lasting myotonic dystrophy correction in patient-derived cells and mice

Antisense oligonucleotides (ASOs) targeting pathologic RNAs have shown promising therapeutic corrections for many genetic diseases including myotonic dystrophy (DM1). Thus, ASO strategies for DM1 can abolish the toxic RNA gain-of-function mechanism caused by nuclear-retained mutant transcripts containing CUG expansions (CUGexp). However, systemic use of ASOs for this muscular disease remains challenging due to poor drug distribution to skeletal muscle. To overcome this limitation, we test an arginine-rich Pip6a cell-penetrating peptide and show that Pip6a-conjugated morpholino phosphorodiamidate oligomer (PMO) dramatically enhanced ASO delivery into striated muscles of DM1 mice following systemic administration in comparison with unconjugated PMO and other ASO strategies. Thus, low-dose treatment of Pip6a-PMO-CAG targeting pathologic expansions is sufficient to reverse both splicing defects and myotonia in DM1 mice and normalizes the overall disease transcriptome. Moreover, treated DM1 patient-derived muscle cells showed that Pip6a-PMO-CAG specifically targets mutant CUGexp-DMPK transcripts to abrogate the detrimental sequestration of MBNL1 splicing factor by nuclear RNA foci and consequently MBNL1 functional loss, responsible for splicing defects and muscle dysfunction. Our results demonstrate that Pip6a-PMO-CAG induces high efficacy and long-lasting correction of DM1-associated phenotypes at both molecular and functional levels, and strongly support the use of advanced peptide-conjugates for systemic corrective therapy in DM1

Formation of laser plasma channels in a stationary gas

The formation of plasma channels with nonuniformity of about +- 3.5% has been demonstrated. The channels had a density of 1.2x10^19 cm-3 with a radius of 15 um and with length >= 2.5 mm. The channels were formed by 0.3 J, 100 ps laser pulses in a nonflowing gas, contained in a cylindrical chamber. The laser beam passed through the chamber along its axis via pinholes in the chamber walls. A plasma channel with an electron density on the order of 10^18 - 10^19 cm-3 was formed in pure He, N2, Ar, and Xe. A uniform channel forms at proper time delays and in optimal pressure ranges, which depend on the sort of gas. The influence of the interaction of the laser beam with the gas leaking out of the chamber through the pinholes was found insignificant. However, the formation of an ablative plasma on the walls of the pinholes by the wings of the radial profile of the laser beam plays an important role in the plasma channel formation and its uniformity. A low current glow discharge initiated in the chamber slightly improves the uniformity of the plasma channel, while a high current arc discharge leads to the formation of overdense plasma near the front pinhole and further refraction of the laser beam. The obtained results show the feasibility of creating uniform plasma channels in non-flowing gas targets.Comment: 15 pages, 7 figures, submitted to Physics of Plasma

Animal Interactions and the Emergence of Territoriality

Inferring the role of interactions in territorial animals relies upon accurate recordings of the behaviour of neighbouring individuals. Such accurate recordings are rarely available from field studies. As a result, quantification of the interaction mechanisms has often relied upon theoretical approaches, which hitherto have been limited to comparisons of macroscopic population-level predictions from un-tested interaction models. Here we present a quantitative framework that possesses a microscopic testable hypothesis on the mechanism of conspecific avoidance mediated by olfactory signals in the form of scent marks. We find that the key parameters controlling territoriality are two: the average territory size, i.e. the inverse of the population density, and the time span during which animal scent marks remain active. Since permanent monitoring of a territorial border is not possible, scent marks need to function in the temporary absence of the resident. As chemical signals carried by the scent only last a finite amount of time, each animal needs to revisit territorial boundaries frequently and refresh its own scent marks in order to deter possible intruders. The size of the territory an animal can maintain is thus proportional to the time necessary for an animal to move between its own territorial boundaries. By using an agent-based model to take into account the possible spatio-temporal movement trajectories of individual animals, we show that the emerging territories are the result of a form of collective animal movement where, different to shoaling, flocking or herding, interactions are highly heterogeneous in space and time. The applicability of our hypothesis has been tested with a prototypical territorial animal, the red fox (Vulpes vulpes)