There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

We describe Hi-C, a method that probes the three-dimensional architecture of whole genomes by coupling proximity-based ligation with massively parallel sequencing. We constructed spatial proximity maps of the human genome with Hi-C at a resolution of 1 megabase. These maps confirm the presence of chromosome territories and the spatial proximity of small, gene-rich chromosomes. We identified an additional level of genome organization that is characterized by the spatial segregation of open and closed chromatin to form two genome-wide compartments. At the megabase scale, the chromatin conformation is consistent with a fractal globule, a knot-free, polymer conformation that enables maximally dense packing while preserving the ability to easily fold and unfold any genomic locus. The fractal globule is distinct from the more commonly used globular equilibrium model. Our results demonstrate the power of Hi-C to map the dynamic conformations of whole genomes.

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Comprehensive mapping of long-range interactions reveals folding principles of the human genome.

A number of recently discovered protein structures incorporate a rather unexpected structural feature: a knot in the polypeptide backbone. These knots are extremely rare, but their occurrence is likely connected to protein function in as yet unexplored fashion. Our analysis of the complete Protein Data Bank reveals several new knots which, along with previously discovered ones, can shed light on such connections. In particular, we identify the most complex knot discovered to date in human ubiquitin hydrolase, and suggest that its entangled topology protects it against unfolding and degradation by the proteasome. Knots in proteins are typically preserved across species and sometimes even across kingdoms. However, we also identify a knot which only appears in some transcarbamylases while being absent in homologous proteins of similar structure. The emergence of the knot is accompanied by a shift in the enzymatic function of the protein. We suggest that the simple insertion of a short DNA fragment into the gene may suffice to turn an unknotted into a knotted structure in this protein.

Intricate Knots in Proteins: Function and Evolution

We consider the passage of long polymers of length N through a hole in a membrane. If the process is slow, it is in principle possible to focus on the dynamics of the number of monomers s on one side of the membrane, assuming that the two segments are in equilibrium. The dynamics of $s(t)$ in such a limit would be diffusive, with a mean translocation time scaling as ${N}^{2}$ in the absence of a force, and proportional to N when a force is applied. We demonstrate that the assumption of equilibrium must break down for sufficiently long polymers (more easily when forced), and provide lower bounds for the translocation time by comparison to unimpeded motion of the polymer. These lower bounds exceed the time scales calculated on the basis of equilibrium, and point to anomalous (subdiffusive) character of translocation dynamics. This is explicitly verified by numerical simulations of the unforced translocation of a self-avoiding polymer. Forced translocation times are shown to strongly depend on the method by which the force is applied. In particular, pulling the polymer by the end leads to much longer times than when a chemical potential difference is applied across the membrane. The bounds in these cases grow as ${N}^{2}$ and ${N}^{1+\ensuremath{\nu}},$ respectively, where $\ensuremath{\nu}$ is the exponent that relates the scaling of the radius of gyration to N. Our simulations demonstrate that the actual translocation times scale in the same manner as the bounds, although influenced by strong finite size effects which persist even for the longest polymers that we considered $(N=512).$

/pdf/anomalous-dynamics-of-forced-translocation-l0he6le85d.pdf

Anomalous dynamics of forced translocation

Motivated by recent studies of Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)], we study self-organized criticality in models of ``running'' sandpiles. Our analysis reveals rich temporal structures in the flow of sand: at very short time scales, the flow is dominated by single avalanches. These avalanches overlap at intermediate time scales; their interactions lead to 1/f noise in the flow. We show that scaling in this region is a consequence of conservation laws and is exhibited in many examples of driven-diffusion equations for transport. At very long time scales, the sandpiles exhibit system-wide discharge events. These events also obey scaling and are found to be anticorrelated. We derive the ${\mathit{f}}^{1/2}$ mean-field power spectrum for these events and show that a threshold instability of the model, coupled with some stochasticity, is the underlying origin of the long-time anticorrelation.

Avalanches, hydrodynamics, and discharge events in models of sandpiles

We study the statistical mechanics of two-dimensional surfaces of fixed connectivity embedded in $d$ dimensions, as exemplified by hard spheres tethered together by strings into a triangular net. Without self-avoidance, entropy generates elastic interactions at large distances, and the radius of gyration ${R}_{G}$ increases as ${(\mathrm{ln}L)}^{\frac{1}{2}}$, where $L$ is the linear size of the uncrumpled surface. With self-avoidance ${R}_{G}$ grows as ${L}^{\ensuremath{\nu}}$, with $\ensuremath{\nu}=\frac{4}{(d+2)}$ as obtained from a Flory theory and in good agreement with our Monte Carlo results for $d=3$.

Statistical mechanics of tethered surfaces.

/pdf/anomalous-dynamics-of-translocation-1zkmn8es7i.pdf

Mehran Kardar

Papers

Intricate Knots in Proteins: Function and Evolution

Anomalous dynamics of forced translocation

Avalanches, hydrodynamics, and discharge events in models of sandpiles

Statistical mechanics of tethered surfaces.

Anomalous dynamics of translocation