A Nonholonomic Model of the Paul Trap

In this paper, equations of motion for the problem of a ball rolling without slipping on a rotating hyperbolic paraboloid are obtained. Integrals of motions and an invariant measure are found. A detailed linear stability analysis of the ball’s rotations at the saddle point of the hyperbolic paraboloid is made. A three-dimensional Poincaré map generated by the phase flow of the problem is numerically investigated and the existence of a region of bounded trajectories in a neighborhood of the saddle point of the paraboloid is demonstrated. It is shown that a similar problem of a ball rolling on a rotating paraboloid, considered within the framework of the rubber model, can be reduced to a Hamiltonian system which includes the Brower problem as a particular case.     

Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension

We consider two models for directed polymers in space‐time independent random media (the O'Connell‐Yor semidiscrete directed polymer and the continuum directed random polymer) at positive temperature and prove their KPZ universality via asymptotic analysis of exact Fredholm determinant formulas for the Laplace transform of their partition functions. In particular, we show that for large time τ, the probability distributions for the free energy fluctuations, when rescaled by τ^1/3, converges to the GUE Tracy‐Widom distribution. We also consider the effect of boundary perturbations to the quenched random media on the limiting free energy statistics. For the semidiscrete directed polymer, when the drifts of a finite number of the Brownian motions forming the quenched random media are critically tuned, the statistics are instead governed by the limiting Baik–Ben Arous–Péché distributions from spiked random matrix theory. For the continuum polymer, the boundary perturbations correspond to choosing the initial data for the stochastic heat equation from a particular class, and likewise for its logarithm—the Kardar‐Parisi‐Zhang equation. The Laplace transform formula we prove can be inverted to give the one‐point probability distribution of the solution to these stochastic PDEs for the class of initial data. © 2014 Wiley Periodicals, Inc.     

On the rank of incidence matrices in projective Hjelmslev spaces

Let \(R\) be a finite chain ring with \(|R|=q^m\) , \(R/{{\mathrm{Rad}}}R\cong \mathbb {F}_q\) , and let \(\Omega ={{\mathrm{PHG}}}({}_RR^n)\) . Let \(\tau =(\tau _1,\ldots ,\tau _n)\) be an integer sequence satisfying \(m=\tau _1\ge \tau _2\ge \cdots \ge \tau _n\ge 0\) . We consider the incidence matrix of all shape \(\varvec{m}^s=(\underbrace{m,\ldots ,m}_s)\) versus all shape \(\tau \) subspaces of \(\Omega \) with \(\varvec{m}^s\preceq \tau \preceq \varvec{m}^{n-s}\) . We prove that the rank of \(M_{\varvec{m}^s,\tau }(\Omega )\) over \(\mathbb {Q}\) is equal to the number of shape \(\varvec{m}^s\) subspaces. This is a partial analog of Kantor’s result about the rank of the incidence matrix of all \(s\) dimensional versus all \(t\) dimensional subspaces of \({{\mathrm{PG}}}(n,q)\) . We construct an example for shapes \(\sigma \) and \(\tau \) for which the rank of \(M_{\sigma ,\tau }(\Omega )\) is not maximal.     

Equality of Lifshitz and van Hove exponents on amenable Cayley graphs

We study the low energy asymptotics of periodic and random Laplace operators on Cayley graphs of amenable, finitely generated groups. For the periodic operator the asymptotics is characterised by the van Hove exponent or zeroth Novikov–Shubin invariant. The random model we consider is given in terms of an adjacency Laplacian on site or edge percolation subgraphs of the Cayley graph. The asymptotic behaviour of the spectral distribution is exponential, characterised by the Lifshitz exponent. We show that for the adjacency Laplacian the two invariants/exponents coincide. The result holds also for more general symmetric transition operators. For combinatorial Laplacians one has a different universal behaviour of the low energy asymptotics of the spectral distribution function, which can be actually established on quasi-transitive graphs without an amenability assumption. The latter result holds also for long range bond percolation models.     

Implantation of undifferentiated and pre-differentiated human neural stem cells in the R6/2 transgenic mouse model of Huntington’s disease

Background

The expression pattern and function of miRNAs in the rat model of temporal lobe epilepsy have not been well defined. Profiling miRNA expression in the rat model of temporal lobe epilepsy and investigating the function of specific miRNAs in epilepsy offers the prospect of a deeper understanding of the mechanisms of epilepsy.

Methods

The lithium-pilocarpine-induced status epilepticus model and the temporal lobe epilepsy model were established in Sprague?CDawley rats. Samples were analysed to detect deregulated miRNAs in the hippocampal temporal lobe, and several of these deregulated miRNAs were confirmed by qPCR. The expression of the pro-apoptotic miR-34a was detected at 1?day, 7?days and 2?weeks post-status epilepticus and at 2?months after temporal lobe epilepsy. The antagomir of miR-34a was then utilised. The expression of miR-34a after targeting and the expression change of activated caspase-3 protein were examined. The effects of altering the expression of miR-34a and activated caspase-3 protein on neuronal survival and neuronal death or apoptosis post-status epilepticus were assessed.

Results

The miRNA microarray detected 9 up-regulated miRNAs (miR-146a, -211, -203, -210, -152, -31, -23a, -34a, -27a) and 15 down-regulated miRNAs (miR-138*, -301a, -136, -153, -19a, -135b, -325-5p, -380, -190, -542-3p, -33, -144, -542-5p, -543, -296*). Some of the deregulated miRNAs (miR-146a, miR-210, miR-27a, miR-135b and miR-33) were confirmed using qPCR. Furthermore, an increase in expression of the pro-apoptotic miR-34a was demonstrated in the post-status epilepticus rat hippocampus. miR-34a was significantly up-regulated at 1?day, 7?days and 2?weeks post-status epilepticus and at 2?months after temporal lobe epilepsy. Experiments with the miR-34a antagomir revealed that targeting miR-34a led to an inhibition of activated caspase-3 protein expression, which may contribute to increased neuronal survival and reduced neuronal death or apoptosis.

Conclusions

Our study showed the expression profile of miRNAs in the hippocampus in a rat model of temporal lobe epilepsy and an increase in the expression of the pro-apoptotic miR-34a in post-status epilepticus rats. The results show that miR-34a is up-regulated during seizure-induced neuronal death or apoptosis, and targeting miR-34a is neuroprotective and is associated with an inhibition of an increase in activated caspase-3 protein.     

Phase behaviour,structural properties and intermolecular interactions of systems based on substituted thiacalix[4]arene and nonionic surfactants

Supramolecular organised materials were prepared from nonionic surfactants and the following macrocyclic ionic liquids: n-tert-butylthiacalix[4]arenes containing quaternary ammonium fragments with amino acid substituents. Tetraethylene glycol monododecyl ether and decadiethylene glycol monododecyl ether were used as nonionic surfactants. They form lamellar and hexagonal mesophases in aqueous media, respectively. Liquid crystal and structural properties of these systems were studied. Intermolecular interactions of system components leading to formation of lyomesophases were estimated. Molecular structure of thiacalixarene contributes to the formation of a hydrogen bonding with surfactants. This process, in turn, initiates formation of a denser packed hexagonal structure.     

Radical–anion coupling through reagent design: hydroxylation of aryl halides

The design and development of an oxime-based hydroxylation reagent, which can chemoselectively convert aryl halides (X = F, Cl, Br, I) into phenols under operationally simple, transition-metal-free conditions is described. Key to the success of this approach was the identification of a reducing oxime anion which can interact and couple with open-shell aryl radicals. Experimental and computational studies support the proposed radical-nucleophilic substitution chain mechanism.

The design and development of an oxime-based hydroxylation reagent, which can chemoselectively convert aryl halides (X = F, Cl, Br, I) into phenols under operationally simple, transition-metal-free conditions is described.     

Why density augmentation occurs in dilute supercritical solutions

The conventional explanation of the density augmentation in a supercritical solvent, observed spectroscopically when a small amount of a solute was added, involved the clustering of the solvent about individual solute molecules. Here it is suggested that the augmentation is not caused by the solute, but rather it is due to the preexisting near critical fluctuations in the pure solvent and the preference of the solute for the high density regions of the supercritical solvent. It is also shown that the local composition of the solute molecules about a solute molecules is enhanced compared to its bulk composition.     

Multiplex metal-detection based assay (MMDA) for COVID-19 diagnosis and identification of disease severity biomarkers

The ongoing COVID-19 pandemic caused by SARS-CoV-2 highlights the urgent need to develop sensitive methods for diagnosis and prognosis. To achieve this, multidimensional detection of SARS-CoV-2 related parameters including virus loads, immune response, and inflammation factors is crucial. Herein, by using metal-tagged antibodies as reporting probes, we developed a multiplex metal-detection based assay (MMDA) method as a general multiplex assay strategy for biofluids. This strategy provides extremely high multiplexing capability (theoretically over 100) compared with other reported biofluid assay methods. As a proof-of-concept, MMDA was used for serologic profiling of anti-SARS-CoV-2 antibodies. The MMDA exhibits significantly higher sensitivity and specificity than ELISA for the detection of anti-SARS-CoV-2 antibodies. By integrating the high dimensional data exploration/visualization tool (tSNE) and machine learning algorithms with in-depth analysis of multiplex data, we classified COVID-19 patients into different subgroups based on their distinct antibody landscape. We unbiasedly identified anti-SARS-CoV-2-nucleocapsid IgG and IgA as the most potently induced types of antibodies for COVID-19 diagnosis, and anti-SARS-CoV-2-spike IgA as a biomarker for disease severity stratification. MMDA represents a more accurate method for the diagnosis and disease severity stratification of the ongoing COVID-19 pandemic, as well as for biomarker discovery of other diseases.

A MMDA platform is developed by using metal-tagged antibodies as reporting probes combined with machine learning algorithms, as a general strategy for highly multiplexed biofluid assay.