Opposite Boundary Research Articles

RNA structure in splicing: An evolutionary perspective

ABSTRACTPre-mRNA splicing is a key post-transcriptional regulation process in which introns are excised and exons are ligated together. A novel class of structured intron was recently discovered in fish. Simple expansions of complementary AC and GT dimers at opposite boundaries of an intron were found to form a bridging structure, thereby enforcing correct splice site pairing across the intron. In some fish introns, the RNA structures are strong enough to bypass the need of regulatory protein factors for splicing. Here, we discuss the prevalence and potential functions of highly structured introns. In humans, structured introns usually arise through the co-occurrence of C and G-rich repeats at intron boundaries. We explore the potentially instructive example of the HLA receptor genes. In HLA pre-mRNA, structured introns flank the exons that encode the highly polymorphic β sheet cleft, making the processing of the transcript robust to variants that disrupt splicing factor binding. While selective forces that have shaped HLA receptor are fairly atypical, numerous other highly polymorphic genes that encode receptors contain structured introns. Finally, we discuss how the elevated mutation rate associated with the simple repeats that often compose structured intron can make structured introns themselves rapidly evolving elements.

Boudinage and folding as an energy instability in ductile deformation

AbstractWe present a theory for the onset of localization in layered rate‐ and temperature‐sensitive rocks, in which energy‐related mechanical bifurcations lead to localized dissipation patterns in the transient deformation regime. The implementation of the coupled thermomechanical 2‐D finite element model comprises an elastic and rate‐dependent von Mises plastic rheology. The underlying system of equations is solved in a three‐layer pure shear box, for constant velocity and isothermal boundary conditions. To examine the transition from stable to localized creep, we study how material instabilities are related to energy bifurcations, which arise independently of the sign of the stress conditions imposed on opposite boundaries, whether in compression or extension. The onset of localization is controlled by a critical amount of dissipation, termed Gruntfest number, when dissipative work by temperature‐sensitive creep translated into heat overcomes the diffusive capacity of the layer. Through an additional mathematical bifurcation analysis using constant stress boundary conditions, we verify that boudinage and folding develop at the same critical Gruntfest number. Since the critical material parameters and boundary conditions for both structures to develop are found to coincide, the initiation of localized deformation in strong layered media within a weaker matrix can be captured by a unified theory for localization in ductile materials. In this energy framework, neither intrinsic nor extrinsic material weaknesses are required, because the nucleation process of strain localization arises out of steady state conditions. This finding allows us to describe boudinage and folding structures as the same energy attractor of ductile deformation.

Selection of head and whisker coordination strategies during goal-oriented active touch.

In the rodent whisker system, a key model for neural processing and behavioral choices during active sensing, whisker motion is increasingly recognized as only part of a broader motor repertoire employed by rodents during active touch. In particular, recent studies suggest whisker and head motions are tightly coordinated. However, conditions governing the selection and temporal organization of such coordinated sensing strategies remain poorly understood. We videographically reconstructed head and whisker motions of freely moving mice searching for a randomly located rewarded aperture, focusing on trials in which animals appeared to rapidly "correct" their trajectory under tactile guidance. Mice orienting after unilateral contact repositioned their whiskers similarly to previously reported head-turning asymmetry. However, whisker repositioning preceded head turn onsets and was not bilaterally symmetric. Moreover, mice selectively employed a strategy we term contact maintenance, with whisking modulated to counteract head motion and facilitate repeated contacts on subsequent whisks. Significantly, contact maintenance was not observed following initial contact with an aperture boundary, when the mouse needed to make a large corrective head motion to the front of the aperture, but only following contact by the same whisker field with the opposite aperture boundary, when the mouse needed to precisely align its head with the reward spout. Together these results suggest that mice can select from a diverse range of sensing strategies incorporating both knowledge of the task and whisk-by-whisk sensory information and, moreover, suggest the existence of high level control (not solely reflexive) of sensing motions coordinated between multiple body parts.

Semi-analytic Conjugate Gradient Method applied to a simple Inverse Heat Conduction Problem

Considering heat transfers in a one-dimensional domain, an academic identification problem is solved by the implementation of a conjugate gradient method (CGM). While temperature measurements are available on a domain boundary, inverse heat conduction problem (IHCP) is solved in order to estimate heat flux on the opposite boundary. Such problem has been widely investigated and the main novelty of our approach will be seen in the explicit formulation of CGM solution which is given into an approximation space split into a polynomial part and an exponential part. Then, a filtering property of the CGM is exhibited.

Disturbance Rejection in n + 1 Coupled 1-D Linear Hyperbolic PDEs Using Collocated Sensing and Control

We derive a full state feedback law and a state observer for a class of disturbance rejection problems for n+1 linear coupled partial differential equations (PDEs). The disturbance enters the system at one boundary, while the actuation and sensing are limited to the opposite boundary. We solve this by separately designing a state feedback controller and an observer, and show that they can be combined into an output feedback control law that rejects the effect of the disturbance with exponential decay. The performance of output feedback controller is demonstrated in a simulation.

RNA structure replaces the need for U2AF2 in splicing.

RNA secondary structure plays an integral role in catalytic, ribosomal, small nuclear, micro, and transfer RNAs. Discovering a prevalent role for secondary structure in pre-mRNAs has proven more elusive. By utilizing a variety of computational and biochemical approaches, we present evidence for a class of nuclear introns that relies upon secondary structure for correct splicing. These introns are defined by simple repeat expansions of complementary AC and GT dimers that co-occur at opposite boundaries of an intron to form a bridging structure that enforces correct splice site pairing. Remarkably, this class of introns does not require U2AF2, a core component of the spliceosome, for its processing. Phylogenetic analysis suggests that this mechanism was present in the ancestral vertebrate lineage prior to the divergence of tetrapods from teleosts. While largely lost from land dwelling vertebrates, this class of introns is found in 10% of all zebrafish genes.

Lozenge Tilings with Free Boundaries

We study lozenge tilings of a domain with partially free boundary. In particular, we consider a trapezoidal domain (half-hexagon), s.t. the horizontal lozenges on the long side can intersect it anywhere to protrude halfway across. We show that the positions of the horizontal lozenges near the opposite flat vertical boundary have the same joint distribution as the eigenvalues from a Gaussian Unitary Ensemble (the GUE-corners/minors process). We also prove the existence of a limit shape of the height function, which is also a vertically symmetric plane partition. Both behaviors are shown to coincide with those of the corresponding doubled fixed boundary hexagonal domain. We also consider domains where the different sides converge to $${\infty}$$ at different rates and recover again the GUE-corners process near the boundary.

Loneliness and its opposite: sex, disability, and the ethics of engagement

Few people these days would oppose making the public realm of space, social services and jobs accessible to women and men with disabilities. But what about access to the private realm of desire and sexuality? How can one also facilitate access to that, in ways that respect the integrity of disabled adults, and also of those people who work with and care for them? Loneliness and Its Opposite documents how two countries generally imagined to be progressive engage with these questions in very different ways. Denmark and Sweden are both liberal welfare states, but they diverge dramatically when it comes to sexuality and disability. In Denmark, the erotic lives of people with disabilities are acknowledged and facilitated. In Sweden, they are denied and blocked. Why do these differences exist, and how do both facilitation and hindrance play out in practice? Loneliness and Its Opposite charts complex boundaries between private and public, love and sex, work and intimacy, and affection and abuse. It shows how providing disabled adults with access to sexual lives is not just crucial for a life with dignity. It is an issue of fundamental social justice with far reaching consequences for everyone.

Delineation of connectivity structures in 2‐D heterogeneous hydraulic conductivity fields

AbstractConnectivity is a critical aquifer property controlling anomalous transport behavior at large scales. But connectivity cannot be easily defined in a continuous field based on information of the hydraulic conductivity alone. We conceptualize it as a connecting structure—a connected subset of a continuous hydraulic conductivity field that consists of paths of least hydraulic resistance. We develop a simple and robust numerical method to delineate the connectivity structure using information of the hydraulic conductivity field only. First, the topology of the connectivity structure is determined by finding the path(s) of least resistance between two opposite boundaries. And second, a series of connectivity structures are created by inflating and shrinking the individual channels. Finally, we apply this methodology to different heterogeneous fields. We show that our method captures the main flow channels as well as the pathways of early time solute arrivals. We find our method informative to study connectivity in 2‐D heterogeneous hydraulic conductivity fields.

Onset of convection in a two–phase binary mixture with the Soret effect in weightlessness

The linear stability of mechanical equilibrium in a two–layer system formed by different phases of the same binary mixture is investigated. The temperature difference is applied to the layers by heating and cooling the opposite rigid boundaries. In the state of mechanical equilibrium, the applied temperature gradient induces concentration gradients due to the Soret effect. The conservation of mass for the mixture components leads to the dependence of layer thicknesses on the applied temperature difference. In weightlessness, the main mechanisms of instability in the considered system are related to phase change and Marangoni effect. The calculations are performed for cyclohexane–methanol binary mixture, which has a liquid–liquid miscibility gap. The analytical solution of amplitude equations for monotonic perturbations is found and expression for the critical temperature difference is derived. It is shown that the phase change instability is long–wave and favoured when the difference between interfacial concentrations in the basic state decreases. When the Marangoni effect is taken into account, additional monotonic and oscillatory modes appear. They result from the interplay between thermocapillarity and phase change with latent heat release/absorption. The most unstable monotonic and oscillatory modes are identified depending on the heating regime and relative thickness of the layers.

Fractional order control of the two-dimensional wave equation

Control of systems governed by the two-dimensional linear wave equation in finite spatial domain is considered and presented through vibrating rectangular membranes. The membranes are modeled by modal decomposition in one spatial axis and infinite dimensional transfer functions in the other. The transfer functions are built of fractional order exponents, regarded as non-pure delays, which are shown to represent traveling waves whose shape changes during motion. The membranes are controlled in closed loop to achieve position profile tracking and attenuation of disturbances. The actuation is along two opposite boundaries, which controls the entire wave motion between them. The control algorithm stops the wave propagation in the control axis by creating active non-reflecting boundaries. In addition, it compensates the remaining non-pure delay by extending the classical dead time compensation principle. As a result, despite the infinite dimension of the system and its fractional order transfer functions, the closed loop transfer function is given by a rational first order lag with a pure time delay. The resulting controllers are also of fractional order and their implementation is obtained by dedicated approximations. The system stability with the approximated controllers is investigated formally using robustness tools. The control algorithm is demonstrated by means of several examples.

Hysteresis Loop and Scanning Curves for Argon Adsorbed in Mesopore Arrays Composed of Two Cavities and Three Necks

Hysteresis loops and scanning curves for argon adsorbed in sequential mesopore arrays consisting of two cavities and three necks have been studied using Grand Canonical Monte Carlo simulation. We examined four different pore configurations and find that there are two patterns for scanning: (i) Type S1, the scanning curve crosses the hysteresis loop from one boundary to the opposite boundary with the possibility that condensation/evaporation occurs within the hysteresis loop; and (ii) Type S2, the scanning curve leaves one boundary and then returns to the same boundary. The first array has three necks with sizes that are smaller than the critical width (which demarcates cavitation from pore blocking as the mechanism for evaporation from a cavity). The second, third, and fourth arrays are the same as the first with the exception that one neck is larger than the critical width. This large neck connects the large cavity to the gas surroundings in array 2, connects the two cavities in array 3, and connects the small cavity to the gas surroundings in array 4. The mechanism of evaporation from the arrays 1 and 3 is found to be cavitation, they have the same type of hysteresis loop (H2a), but their descending scanning curves (DSC) are different. The DSC of array1 scans across the hysteresis loop (Type S1), while that of array 3 is of Type S2. In arrays 2 and 4, the evaporation follows a sequence of pore blocking and cavitation from the two cavities; a double loop of Type H2a. Although these two arrays have the same type of hysteresis loop, their scanning curves are different. Array 2 has Type S1 scanning with a subloop within the primary hysteresis loop, while array 4 has Type S2 scanning curve with a subloop.

Interacting topological insulator and emergent grand unified theory

Motivated by the Pati-Salam Grand Unified Theory, we study $(4+1)d$ topological insulators with $SU(4) \times SU(2)_1 \times SU(2)_2$ symmetry, whose $(3+1)d$ boundary has 16 flavors of left-chiral fermions, which form representations $(\mathbf{4}, \mathbf{2}, \mathbf{1})$ and $(\bar{\mathbf{4}}, \mathbf{1}, \mathbf{2})$. The key result we obtain is that, without any interaction, this topological insulator has a $\mathbb{Z}$ classification, namely any quadratic fermion mass operator at the $(3+1)d $ boundary is prohibited by the symmetries listed above; while under interaction this system becomes trivial, namely its $(3+1)d$ boundary can be gapped out by a properly designed short range interaction without generating nonzero vacuum expectation value of any fermion bilinear mass, or in other words, its $(3+1)d$ boundary can be driven into a "strongly coupled symmetric gapped (SCSG) phase". Based on this observation, we propose that after coupling the system to a dynamical $SU(4) \times SU(2)_1 \times SU(2)_2$ lattice gauge field, the Pati-Salam GUT can be fully regularized as the boundary states of a $(4+1)d$ topological insulator with a {\it thin} fourth spatial dimension, the thin fourth dimension makes the entire system generically a $(3+1)d$ system. The mirror sector on the opposite boundary will {\it not} interfere with the desired GUT, because the mirror sector is driven to the SCSG phase by a carefully designed interaction and is hence decoupled from the GUT.

Polyaxial stress-induced variable aperture model for persistent 3D fracture networks

This paper presents a stress-induced variable aperture model to characterise the effect of polyaxial stress conditions on the fluid flow in three-dimensional (3D) persistent fracture networks. Geomechanical modelling of the fractured rock is achieved by the finite-discrete element method (FEMDEM), which can capture deformability of matrix blocks, heterogeneity of stress fields as well as sliding and opening of pre-existing fractures. Propagation of new cracks is not required for this study of persistent fracture systems. The deformed fracture network topologies include details of dilation, opening and closing of fracture apertures, from which the local variations in hydraulic apertures are derived. Stress-controlled distribution of fracture apertures is modelled with both fracture-scale and network-scale effects considered. Under a geomechanical condition with low differential stress ratio, fracture porosity is dominated by the fracture-scale roughness. However, with the increase of stress ratio, some favourably oriented fractures are reactivated for shearing, and matrix blocks are promoted to rotate and generate large openings along their boundaries, which tend to be the key contributors to the aperture field in such persistent systems. The flow behaviour is then considered for these stressed but static solid skeletons and is investigated using a finite element solution to the Laplace problem of single-phase fluid flow. The equivalent permeability tensor of each cube-shaped rock mass is computed based on a series of flow simulations under a macroscopic pressure differential applied at opposite model boundaries with no-flow conditions on the remaining boundaries. Components of the permeability tensor are found to vary more than three orders of magnitude with respect to the change of stress ratio. Large aperture channels formed under a critical stress state accommodate significant localisation features in the flow structure of the network. The results of this study have important implications for upscaling permeability to grid block properties for reservoir flow simulation.

On the energy conservation during the active deformation in molecular dynamics simulations

In this paper, we examined the energy conservation for the current schemes of applying active deformation in molecular dynamics (MD) simulations. Specifically, two methods are examined. One is scaling the dimension of the simulation box and the atom positions via an affine transformation, suitable for the periodic system. The other is moving the rigid walls that interact with the atoms in the system, suitable for the non-periodic system. Based on the calculation of the external work and the internal energy change, we present that the atom velocities also need to be updated in the first deformation method; otherwise the energy conservation cannot be satisfied. The classic updating scheme is examined, in which any atom crossing the periodic boundary experiences a velocity delta that is equal to the velocity difference between the opposite boundaries. In addition, a new scheme which scales the velocities of all the atoms according to the strain increment is proposed, which is more efficient and realistic than the classic scheme. It is also demonstrated that the Virial stress instead of its interaction part is the correct stress definition that corresponds to Cauchy stress in the continuum mechanics.

A new benchmark with high accurate solution for hot–cold fluids mixing

A new benchmark is proposed for the verification of buoyancy-driven flow codes. The benchmark deals with mixing hot and cold fluids from the opposite boundaries of an open channel. A high accurate solution is developed using the Fourier–Galerkin (FG) method and compared to the results of an advanced finite element (FE) model. An excellent agreement is observed between the FG and FE solutions for different Reynolds numbers which demonstrates the viability of the solutions in benchmarking buoyancy-driven flow numerical codes.

Compressive behavior of nanocrystalline nickel at various temperatures and strain rates

In this paper, compressive behavior of electrodeposited nano-crystalline (nc) Ni at various temperatures and strain rates is studied using a low temperature mechanic test system. Plastic deformation mechanisms of nc Ni caused by compression are characterized by the strain rate sensitivity index, the activation volume, and examined by scanning electron microscopy and high resolution transmission electron microscopic analysis. Results show that at low temperatures, the plastic deformation of nc Ni is mainly dominated by grain boundary accommodated dislocations. In other words, during plastic deformation of nc Ni at low temperatures, the intrinsic dislocation at the grain boundary bends up and expands without obstacles to the opposite grain boundary in the inner grain dislocation-free zone, until the occurrence of similar cutting forest-dislocation behavior appearing at opposite grain boundary. Moreover, the residual dislocations in the grain boundary bending out during plastic deformation could increase the strain compatibility and decrease the stress concentration. At room temperature, the plastic deformation mechanism of nc Ni is controlled by the deformation of grain boundary accommodated dislocations and grain slipping/rotating. Based on the above analyses, differences in compressive behavior of nc Ni at various temperatures and strain rates can be revealed by the correlation of deformation mechanisms of grain boundary accommodated dislocations and residual dislocation movement, temperature and defects in nc Ni.

New algorithm to test percolation conditions within the Newman–Ziff algorithm

A new algorithm to test percolation conditions for the solution of percolation problems on a lattice and continuum percolation for spaces of an arbitrary dimension has been proposed within the Newman–Ziff algorithm. The algorithm is based on the use of bitwise operators and does not reduce the efficiency of the operation of the Newman–Ziff algorithm as a whole. This algorithm makes it possible to verify the existence of both clusters touching boundaries at an arbitrary point and single-loop clusters continuously connecting the opposite boundaries in a percolating system with periodic boundary conditions. The existence of a cluster touching the boundaries of the system at an arbitrary point for each direction, the formation of a one-loop cluster, and the formation of a cluster with an arbitrary number of loops on a torus can be identified in one calculation by combining the proposed algorithm with the known approaches for the identification of the existence of a percolation cluster. The operation time of the proposed algorithm is linear in the number of objects in the system.

Spatial periodicity in bed form‐scale solute and thermal transport models of the hyporheic zone

AbstractSpatially periodic solute boundaries force symmetry across a model domain by ensuring that concentrations and concentration gradients are identical at the same location on opposite boundaries. They have been used in multiple publications on a hyporheic zone model of a single ripple or dune style bed form, including variable density flow and reactive transport variants. We evaluate simulations of multibed form models without imposing spatially periodic transport to demonstrate that nonphysical solute distributions arise from the periodic solute transport assumption. That is, the flow field within the single bed form model leads to a transport scenario that violates the forced symmetry of periodic solute boundary conditions, culminating in a physically unrealistic solute distribution. Our results show that lack of symmetry between boundaries is a function of the vertical concentration gradient and two‐dimensionless parameters characterizing the hyporheic and underflow flow regimes, and the solute exchange between them. We assess the error associated with the spatially periodic assumption based on an analysis of solute fluxes across the lateral bed form model boundaries. While the focus is on steady state concentration distributions, the implications for transient solute transport models are also discussed. We conclude that periodic solute transport boundary conditions should be applied only to bed form models that have minimal vertical dispersive and diffusive solute transfer. This includes gaining systems and tracers such as temperature, for which a temporally periodic flux reversal occurs across the top boundary.

Continuity Transition with a Single Regular Curved-Knot Spline Surface

We propose a specialized form of the curved-knot B-spline surface of Hayes [1982] that we call regular curved-knot spline surface . Unlike the original formulation where the knots of the first parametric coordinate can evolve arbitrarily with respect to the second coordinate, our formulation designs the knot functions as special curves that guarantee a monotonic blending of the knots corresponding to opposite surface boundaries. Furthermore, we demonstrate that local derivatives on the boundary can be described as an ordinary B-spline surface. The latter property allows for constructing smooth transitions between B-spline boundaries with different knot vectors.