Combinatorics of BB-orbits and Bruhat--Chevalley order on involutions

Let $B$ be the group of invertible upper-triangular complex $n\times n$ matrices, $\mathfrak{u}$ the space of upper-triangular complex matrices with zeroes on the diagonal and $\mathfrak{u}^*$ its dual space. The group $B$ acts on $\mathfrak{u}^*$ by $(g.f)(x)=f(gxg^{-1})$, $g\in B$, $f\in\mathfrak{u}^*$, $x\in\mathfrak{u}$. To each involution $\sigma$ in $S_n$, the symmetric group on $n$ letters, one can assign the $B$-orbit $\Omega_{\sigma}\in\mathfrak{u}^*$. We present a combinatorial description of the partial order on the set of involutions induced by the orbit closures. The answer is given in terms of rook placements and is dual to A. Melnikov's results on $B$-orbits on $\mathfrak{u}$. Using results of F. Incitti, we also prove that this partial order coincides with the restriction of the Bruhat--Chevalley order to the set of involutions.Comment: 27 page

Quiet SDS Josephson Junctions for Quantum Computing

Unconventional superconductors exhibit an order parameter symmetry lower than the symmetry of the underlying crystal lattice. Recent phase sensitive experiments on YBCO single crystals have established the d-wave nature of the cuprate materials, thus identifying unambiguously the first unconventional superconductor. The sign change in the order parameter can be exploited to construct a new type of s-wave - d-wave - s-wave Josephson junction exhibiting a degenerate ground state and a double-periodic current-phase characteristic. Here we discuss how to make use of these special junction characteristics in the construction of a quantum computer. Combining such junctions together with a usual s-wave link into a SQUID loop we obtain what we call a `quiet' qubit --- a solid state implementation of a quantum bit which remains optimally isolated from its environment.Comment: 4 pages, 2 ps-figure

Limit theorems for von Mises statistics of a measure preserving transformation

For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1<n,...,i_d<n} f(T^{i_1}x,...,T^{i_d}x),\, n=1,2,...,$$ where $f$ (called the \emph{kernel}) is a function from $X^d$ to $\R$ and $C_1, C_2,...$ are appropriate normalizing constants. We observe that the above random variables are well defined and belong to $L_r(\mu)$ provided that the kernel is chosen from the projective tensor product $$L_p(X_1,\mathcal F_1, \mu_1) \otimes_{\pi}...\otimes_{\pi} L_p(X_d,\mathcal F_d, \mu_d)\subset L_p(\mu^d)$$ with $p=d\,r,\, r\ \in [1, \infty).$ We establish a form of the individual ergodic theorem for such sequences. Next, we give a martingale approximation argument to derive a central limit theorem in the non-degenerate case (in the sense of the classical Hoeffding's decomposition). Furthermore, for $d=2$ and a wide class of canonical kernels $f$ we also show that the convergence holds in distribution towards a quadratic form $\sum_{m=1}^{\infty} \lambda_m\eta^2_m$ in independent standard Gaussian variables $\eta_1, \eta_2,...$. Our results on the distributional convergence use a $T$--\,invariant filtration as a prerequisite and are derived from uni- and multivariate martingale approximations

Neuronal Variability during Handwriting: Lognormal Distribution

We examined time-dependent statistical properties of electromyographic (EMG) signals recorded from intrinsic hand muscles during handwriting. Our analysis showed that trial-to-trial neuronal variability of EMG signals is well described by the lognormal distribution clearly distinguished from the Gaussian (normal) distribution. This finding indicates that EMG formation cannot be described by a conventional model where the signal is normally distributed because it is composed by summation of many random sources. We found that the variability of temporal parameters of handwriting - handwriting duration and response time - is also well described by a lognormal distribution. Although, the exact mechanism of lognormal statistics remains an open question, the results obtained should significantly impact experimental research, theoretical modeling and bioengineering applications of motor networks. In particular, our results suggest that accounting for lognormal distribution of EMGs can improve biomimetic systems that strive to reproduce EMG signals in artificial actuators

Conservative treatment of a left atrial intramural hematoma after left atrial thrombus resection and concomitant mitral valve replacement - case report

Left atrial intramural hematoma is a seldom cause of left atrial mass. It has been described to occur spontaneously, after interventional procedures, after blunt chest trauma, or after aortocoronary bypass surgery. We present a case of mitral valve replacement together with the removal of a large intraatrial space-occupying lesion. Intraoperative transesophageal echocardiography confirmed a successful resection of this mass. Surprisingly, upon admission to ICU, transesophageal and transthoracic echocardiography revealed a recurrence of an intramural lesion, closest matching a hematoma, which was confirmed by contrast-enhanced computed tomography. Surgical intervention was thoroughly discussed but a conservative management was favoured. 3 months after surgery, a reassessed transthoracic echocardiography and computed tomography demonstrated an almost complete resolution of the pre-existing hematoma

Topology by Design in Magnetic nano-Materials: Artificial Spin Ice

Artificial Spin Ices are two dimensional arrays of magnetic, interacting nano-structures whose geometry can be chosen at will, and whose elementary degrees of freedom can be characterized directly. They were introduced at first to study frustration in a controllable setting, to mimic the behavior of spin ice rare earth pyrochlores, but at more useful temperature and field ranges and with direct characterization, and to provide practical implementation to celebrated, exactly solvable models of statistical mechanics previously devised to gain an understanding of degenerate ensembles with residual entropy. With the evolution of nano--fabrication and of experimental protocols it is now possible to characterize the material in real-time, real-space, and to realize virtually any geometry, for direct control over the collective dynamics. This has recently opened a path toward the deliberate design of novel, exotic states, not found in natural materials, and often characterized by topological properties. Without any pretense of exhaustiveness, we will provide an introduction to the material, the early works, and then, by reporting on more recent results, we will proceed to describe the new direction, which includes the design of desired topological states and their implications to kinetics.Comment: 29 pages, 13 figures, 116 references, Book Chapte

Blind trials of computer-assisted structure elucidation software

<p>Abstract</p> <p>Background</p> <p>One of the largest challenges in chemistry today remains that of efficiently mining through vast amounts of data in order to elucidate the chemical structure for an unknown compound. The elucidated candidate compound must be fully consistent with the data and any other competing candidates efficiently eliminated without doubt by using additional data if necessary. It has become increasingly necessary to incorporate an <it>in silico </it>structure generation and verification tool to facilitate this elucidation process. An effective structure elucidation software technology aims to mimic the skills of a human in interpreting the complex nature of spectral data while producing a solution within a reasonable amount of time. This type of software is known as computer-assisted structure elucidation or CASE software. A systematic trial of the ACD/Structure Elucidator CASE software was conducted over an extended period of time by analysing a set of single and double-blind trials submitted by a global audience of scientists. The purpose of the blind trials was to reduce subjective bias. Double-blind trials comprised of data where the candidate compound was unknown to both the submitting scientist and the analyst. The level of expertise of the submitting scientist ranged from novice to expert structure elucidation specialists with experience in pharmaceutical, industrial, government and academic environments.</p> <p>Results</p> <p>Beginning in 2003, and for the following nine years, the algorithms and software technology contained within ACD/Structure Elucidator have been tested against 112 data sets; many of these were unique challenges. Of these challenges 9% were double-blind trials. The results of eighteen of the single-blind trials were investigated in detail and included problems of a diverse nature with many of the specific challenges associated with algorithmic structure elucidation such as deficiency in protons, structure symmetry, a large number of heteroatoms and poor quality spectral data.</p> <p>Conclusion</p> <p>When applied to a complex set of blind trials, ACD/Structure Elucidator was shown to be a very useful tool in advancing the computer's contribution to elucidating a candidate structure from a set of spectral data (NMR and MS) for an unknown. The synergistic interaction between humans and computers can be highly beneficial in terms of less biased approaches to elucidation as well as dramatic improvements in speed and throughput. In those cases where multiple candidate structures exist, ACD/Structure Elucidator is equipped to validate the correct structure and eliminate inconsistent candidates. Full elucidation can generally be performed in less than two hours; this includes the average spectral data processing time and data input.</p

Stochastic Competition between Mechanistically Independent Slippage and Death Pathways Determines Cell Fate during Mitotic Arrest

Variability in cell-to-cell behavior within clonal populations can be attributed to the inherent stochasticity of biochemical reactions. Most single-cell studies have examined variation in behavior due to randomness in gene transcription. Here we investigate the mechanism of cell fate choice and the origin of cell-to-cell variation during mitotic arrest, when transcription is silenced. Prolonged mitotic arrest is commonly observed in cells treated with anti-mitotic drugs. Cell fate during mitotic arrest is determined by two alternative pathways, one promoting cell death, the other promoting cyclin B1 degradation, which leads to mitotic slippage and survival. It has been unclear whether these pathways are mechanistically coupled or independent. In this study we experimentally uncoupled these two pathways using zVAD-fmk to block cell death or Cdc20 knockdown to block slippage. We then used time-lapse imaging to score the kinetics of single cells adopting the remaining fate. We also used kinetic simulation to test whether the behaviors of death versus slippage in cell populations where both pathways are active can be quantitatively recapitulated by a model that assumes stochastic competition between the pathways. Our data are well fit by a model where the two pathways are mechanistically independent, and cell fate is determined by a stochastic kinetic competition between them that results in cell-to-cell variation

Genotyping of Capreolus pygargus Fossil DNA from Denisova Cave Reveals Phylogenetic Relationships between Ancient and Modern Populations

BACKGROUND: The extant roe deer (Capreolus Gray, 1821) includes two species: the European roe deer (C. capreolus) and the Siberian roe deer (C. pygargus) that are distinguished by morphological and karyotypical differences. The Siberian roe deer occupies a vast area of Asia and is considerably less studied than the European roe deer. Modern systematics of the Siberian roe deer remain controversial with 4 morphological subspecies. Roe deer fossilized bones are quite abundant in Denisova cave (Altai Mountains, South Siberia), where dozens of both extant and extinct mammalian species from modern Holocene to Middle Pleistocene have been retrieved. METHODOLOGY/PRINCIPAL FINDINGS: We analyzed a 629 bp fragment of the mitochondrial control region from ancient bones of 10 Holocene and four Pleistocene Siberian roe deer from Denisova cave as well as 37 modern specimen belonging to populations from Altai, Tian Shan (Kyrgyzstan), Yakutia, Novosibirsk region and the Russian Far East. Genealogical reconstructions indicated that most Holocene haplotypes were probably ancestral for modern roe deer populations of Western Siberia and Tian Shan. One of the Pleistocene haplotypes was possibly ancestral for modern Yakutian populations, and two extinct Pleistocene haplotypes were close to modern roe deer from Tian Shan and Yakutia. Most modern geographical populations (except for West Siberian Plains) are heterogeneous and there is some tentative evidence for structure. However, we did not find any distinct phylogenetic signal characterizing particular subspecies in either modern or ancient samples. CONCLUSION/SIGNIFICANCE: Analysis of mitochondrial DNA from both ancient and modern samples of Siberian roe deer shed new light on understanding the evolutionary history of roe deer. Our data indicate that during the last 50,000 years multiple replacements of populations of the Siberian roe deer took place in the Altai Mountains correlating with climatic changes. The Siberian roe deer represent a complex and heterogeneous species with high migration rates and without evident subspecies structure. Low genetic diversity of the West Siberian Plain population indicates a recent bottleneck or founder effect

Repressive Effects of Resveratrol on Androgen Receptor Transcriptional Activity

The chemopreventive effects of resveratrol (RSV) on prostate cancer have been well established; the androgen receptor (AR) plays pivotal roles in prostatic tumorigenesis. However, the exact underlying molecular mechanisms about the effects of RSV on AR have not been fully elucidated. A model system is needed to determine whether and how RSV represses AR transcriptional activity.The AR cDNA was first cloned into the retroviral vector pOZ-N and then integrated into the genome of AR-negative HeLa cells to generate the AR(+) cells. The constitutively expressed AR was characterized by monitoring hormone-stimulated nuclear translocation, DNA binding, and transcriptional activation, with the AR(-) cells serving as controls. AR(+) cells were treated with RSV, and both AR protein levels and AR transcriptional activity were measured simultaneously. Chromatin immunoprecipitation (ChIP) assays were used to detect the effects of RSV on the recruitment of AR to its cognate element (ARE).AR in the AR (+) stable cell line functions in a manner similar to that of endogenously expressed AR. Using this model system we clearly demonstrated that RSV represses AR transcriptional activity independently of any effects on AR protein levels. However, neither the hormone-mediated nucleus translocation nor the AR/ARE interaction was affected by RSV treatment.We demonstrated unambiguously that RSV regulates AR target gene expression, at least in part, by repressing AR transcriptional activity. Repressive effects of RSV on AR activity result from mechanisms other than the affects of AR nuclear translocation or DNA binding