Two-point Connection Research Articles

Topological Characteristics of the Pore Network in the Tight Sandstone Using Persistent Homology.

Tight sandstone reservoirs have become important areas for unconventional reservoir development, and their pore network is a key feature for identifying tight sandstone, which affects fluid migration path and reservoir development efficiency. However, the connectivity characteristics of the pore network at different scales have remained unclear owing to the numerous pores and uneven pore shape. Here, using pore size distributions from many hundreds of tight sandstone samples and subsequent topological data analysis, we construct the topological structure of the pore network in the Yanchang Formation tight sandstone of the Ordos Basin in China and visualize the topological characteristics of the pore network with distances. We show that there are three connected groups within the pore structure of the tight sandstone. The topology of the pore network resides on a trident ring manifold, suggesting that the pore network in the tight sandstone encompasses three obvious dominant connection paths. One prominent bar on the H0 dimension in the barcode indicates a two-point connection from nanoscale to microscale in the pore network. Three prominent bars with varying durations on the H1 dimension indicate the presence of three separate multipoint connections within a limited extent in the pore network. Connectivity of combined pores is good and controlled by the topological structure of the pore network. This demonstration of pore connections on a trident ring manifold provides a population-level visualization of the pore network in the tight sandstone.

On the CFT describing the spin clusters in 2d Potts model

We have considered clusters of like spins in the Q-Potts model, the spin Potts clusters (S clusters). Using Monte Carlo simulations, we studied these clusters on a square lattice with periodic boundary conditions for values of Q ∈ [1, 4]. We continue the work initiated by Delfino et al (2013 J. Stat. Mech. P11011) by measuring the universal finite size corrections of the two-point connectivity. The numerical data are perfectly compatible with the conformal field theory (CFT) prediction, thus supporting the existence of a consistent CFT, still unknown, describing the connectivity Potts spin clusters. We provided in particular new insights on the energy field of such theory. For Q = 2, we found a good agreement with the prediction that the Ising spin clusters behave as the Fortuin–Kasteleyn ones at the tri-critical point of the dilute one-Potts model. We show that the structure constants are likely to be given by the imaginary Liouville structure constants, consistently with the results by Delfino et al (2013 J. Stat. Mech. P11011); Ang and Sun (2021 arXiv:2107.01788). For Q ≠ 2 instead, the structure constants we measure do not correspond to any known bootstrap solutions. The validity of our analysis is backed up by the measures of the spin Potts cluster wrapping probability for Q = 3. We evaluate the main critical exponents and the correction to the scaling. A new exact and compact expression for the torus one-point of the Q-Potts energy field is also given.

Relationships between lognormal distributions of neural properties, activity, criticality, and connectivity.

Relationships between convergence of inputs onto neurons, divergence of outputs from them, synaptic strengths, nonlinear firing response properties, and randomness of axonal ranges are systematically explored by interrelating means and variances of synaptic strengths, firing rates, and soma voltages. When self-consistency is imposed, it is found that broad distributions of synaptic strength are a necessary concomitant of the known massive convergence of inputs to individual neurons, and observed widths of lognormal distributions of synaptic strength and firing rate are explained provided the brain is in a near-critical state, consistent with independent observations. The strongest individual synapses are shown to have an effect on soma voltage comparable to the effect of all others combined, which supports suggestions that they may have a key role in neural communication. Remarkably, inclusion of moderate randomness in characteristic axonal ranges is shown to account for the observed [Formula: see text]-fold variability in two-point connectivity at a given separation and [Formula: see text]-fold overall when the known mean exponential fall-off is included, consistent with observed near-lognormal distributions. Inferred axonal deviations from straight-line paths are also consistent with independent estimates.

Level Set Percolation in the Two-Dimensional Gaussian Free Field.

The nature of level set percolation in the two-dimensional Gaussian free field has been an elusive question. Using a loop-model mapping, we show that there is a nontrivial percolation transition and characterize the critical point. In particular, the correlation length diverges exponentially, and the critical clusters are "logarithmic fractals," whose area scales with the linear size as A∼L^{2}/sqrt[lnL]. The two-point connectivity also decays as the log of the distance. We corroborate our theory by numerical simulations. Possible conformal field theory interpretations are discussed.

Research on the three-dimensional detection system of the rail full profile

To solve the problem of slow speed, low precision and low efficiency of manual measurement in the current inspection of rail. Based on the non-contact laser profilers, a three-dimensional detection system of the full profile of rail is proposed by using the integrated combination of four laser profilers. The top straightness of the rail is detected by two-point connection method and the bottom distortion of the rail is detected by the common-plane method. After field testing, the machine measurement accuracy of the rail height, rail head width, rail bottom width and rail waist width in both rail head and tail are 0.039, 0.037, 0.029, 0.036mm and 0.047, 0.037, 0.039, 0.042mm respectively; The distortion are 0.035 and 0.039mm respectively. Experiments show that the system can complete the measurement of rail efficiently and steadily, and improve the speed, accuracy and efficiency of measurement.

Three- and four-point connectivities of two-dimensional critical Q-Potts random clusters on the torus

In a recent paper, we considered the effects of the torus lattice topology on the two-point connectivity of Q-Potts clusters. These effects are universal and probe non-trivial structure constants of the theory. We complete here this work by considering the torus corrections to the three- and four-point connectivities. These corrections, which depend on the scale invariant ratios of the triangle and quadrilateral formed by the three and four given points, test other non-trivial structure constants. We also present results of Monte Carlo simulations in good agreement with our predictions.

Two-point connectivity of two-dimensional critical Q-Potts random clusters on the torus

We consider the two dimensional Q-random-cluster Potts model on the torus and at the critical point. We study the probability for two points to be connected by a cluster for general values of . Using a conformal field theory (CFT) approach, we provide the leading topological corrections to the plane limit of this probability. These corrections have universal nature and include, as a special case, the universality class of two-dimensional critical percolation. We compare our predictions to Monte Carlo measurements. Finally, we take Monte Carlo measurements of the torus energy one-point function that we compare to CFT computations.

CSTAT+: A GPU-accelerated spatial pattern analysis algorithm for high-resolution 2D/3D hydrologic connectivity using array vectorization and convolutional neural network operators

Connectivity is a state-of-the-art concept that improves the current understanding of hydrological processes at multiple scales. Two-point connectivity statistics provide a promising approach to quantify hydrologic connectivity, which measures the probability of any two nodes in a hydrologically relevant pattern that are connected based on their separation distances. However, limited computational capacity has been the main constraint for implementations in large gridded patterns (>1 million nodes). Here, we propose a new algorithm based on array vectorization and convolutional neural network operators (convolution and pooling) that leverages parallel computational capacity of a GPU. Test results suggested that the new algorithm significantly increases the computational efficiency and is also sensitive to the variability of connectivity states and robust to complex topography. We envision that our algorithm can pave the way for investigating behaviors in large-scale (e.g., watershed) processes, based on quantifying the connectivity of gridded hydrological patterns and digital elevation models.

Experimental research for elastic modulus of cement paste at ultra-early age based on indentation technique

Based on the principle of indentation method, a testing method for ultra-early elastic modulus (EMod) of cement paste using micro-force testing machine is proposed in this study. The test results show that if the loading time is less than 2 min, the influence of cement paste viscosity can be neglected, and the ultra-early EMod of cement paste can be measured by this indentation method. Experiments prove that the EMod measured by the indentation method of conical indenter with semiangle of 45° are close to that obtained by the traditional stress-strain testing method. In order to verify the test method, different cement pastes in variety of water-binder (w/b) ratio and fly ash content are prepared, and the error between the indentation method and the traditional stress-strain method is less than 15%. The dynamic EMod is tested through using ultrasonic method, and the overall trend is consistent with the results of the indentation method. The experimental results show the relationship between the ultra-early EMod and time is linear function. Defining the EMod of initial setting time as the zero point, the EMod of the earliest measurable time through traditional stress-strain method as the end point, the ultra-early EMod of cement paste would be predicted by two-point connection. Compared with the indentation method, the error is less than 20%.

Characterization of silver nanoparticle-modified decellularized rat esophagus for esophageal tissue engineering: Structural properties and biocompatibility

Decellularized esophageal matrices are ideal scaffolds for esophageal tissue engineering. Unfortunately, in order to improve transplantation possibilities, they require modification to reduce their degradation rate and immunogenicity. To date, no modifying agent has been approved to overcome these limitations. The objective of this study was to evaluate the ability of silver nanoparticles (AgNPs) to improve the structural stability and biocompatibility of decellularized rat esophagi. AgNPs have the advantage over currently used agents in that they bind with collagen fibers in a highly ordered manner, via non-covalent binding mechanisms forming multiple binding sites, while other agents provide only two-point connections between collagen molecules. Rat esophagi were decellularized, loaded with 5μg/mL of AgNPs (100nm), and then treated with an immobilization-complex buffer composed of ethyl carbodiimide hydrochloride and N-hydroxysuccinimide (EDC/NHS). Then, they were evaluated in terms of ultra-structural morphology, water uptake, invitro resistance to enzymatic and thermal degradation, indentation strength, invitro anti-calcification, cytocompatibility with rat bone marrow derived stromal cells (rat-BMSCs), angiogenic properties, and invivo biocompatibility, and compared to scaffolds modified using glutaraldehyde and EDC/NHS complex buffer alone. AgNP-modified scaffolds showed an improved ultrastructure, good water uptake, and considerable resistance against invitro degradation and indentation, and a high resistance against invitro calcification. Moreover, they were cytocompatible for allogeneic rat-BMSCs. Additionally, AgNPs did not alter the angiogenic properties of the modified scaffolds and decreased host immune responses after their subcutaneous implantation. The structural properties and biocompatibility of decellularized esophageal matrices could be improved by conjugation with AgNPs.

Holographic Van der Waals phase transition of the higher-dimensional electrically charged hairy black hole

With motivation by holography, employing black hole entropy, two-point connection function and entanglement entropy, we show that, for the higher-dimensional Anti-de Sitter charged hairy black hole in the fixed charged ensemble, a Van der Waals-like phase transition can be observed. Furthermore, based on the Maxwell equal-area construction, we check numerically the equal-area law for a first order phase transition in order to further characterize the Van der Waals-like phase transition.

Linear and nonlinear dielectric theory for a slab: The connections between the phenomenological coefficients and the susceptibilities.

The response of dielectric media to electromagnetic fields can be described by using either the response to a Maxwell field E or to an externally produced field E. The former response is measured by phenomenological (dielectric) coefficients and the latter by susceptibilities. With the purpose of clarifying some recent proposals, the connections between the linear (two-point) and first non-vanishing nonlinear (four-point) dielectric coefficients and the susceptibilities for media confined to a slab are examined using a general procedure developed sometime ago. Unlike the relations found for correlations between a local polarization density and the integrated polarization densities (total polarizations), the point-point connections give rise to non-vanishing cross correlations between polarization densities which are parallel and perpendicular to the slab surfaces. The cross correlations in the two-point connections vanish when one polarization density is integrated to form the correlations between a local polarization density and the total polarization thereby losing angular information. The integrated parallel and perpendicular correlations remain different. When the four-point connections are similarly integrated most, but not all, cross correlations vanish. The angular correlations induced by the slab surfaces render the use of point-point correlations that are valid for isotropic media invalid for use in the integrated slab densities. In addition, the nonlinear fluctuations in the perpendicular components are drastically reduced relative to those in the parallel components or in isotropic media.

Specific energy contributions associated with competing hydrogen bond motifs

The semi-classical density sums (SCDS-Pixel) method [1] was used to study the intermolecular interaction energies in six polymorphs of phenobarbital, a model system for the barbiturate class of compounds.[2] Barbiturates display a rigid pyrimidinetrione ring whose two N–H and three C=O functions can be employed in H-bonding. The ensuing intermolecular N–H···O=C interactions result in a small set of standard H-bonded chain, layer and framework motifs.[3] Even though the average number of N–H···O=C bonds per molecule is always two, the standard barbiturate H-bond motifs differ in the number of intermolecular two-point and one-point N–H···O=C connections per molecule, i.e. (1; 0), (½; 1), (0; 2). For each polymorph (I, II, III, V, VI, X), cumulated Pixel energies, E(n), were calculated for the first n (n = 1, 2, 3, ...) interactions associated with the highest individual contributions to the lattice energy. The obtained sets of E(n) values were compared to one another to establish the differences associated with the formation of the alternate N–H···O=C motifs. Those polymorphs whose N–H···O bonded structures are dominated by two-point connections have superior E(n) values for small clusters of molecules (low n). However, this advantage diminishes gradually if larger clusters of molecules are considered and is completely compensated at n = 8. This indicates that crystal packing on the basis of one-point connection N–H···O=C motifs is viable only because the latter enable the formation of more advantageous weaker interactions which are dominated by dispersion forces. This case illustrates that an assessment of competing H-bond motifs cannot be restricted to just those molecules that are directly involved in H-bond interactions. Rather, the complete crystal packing has to be taken into account. [Figure: Evolution of the difference between E(n) (form V; one-point connections) and E(n)' (form III; two-point connections) with n].

Aromatic-proline interactions: electronically tunable CH/π interactions.

Proline residues have unique roles in protein folding, structure, and function. Proline and the aromatic amino acids comprise the encoded cyclic protein residues. Aromatic protein side chains are defined by their negatively charged π faces, while the faces of the proline ring are partially positively charged. This polarity results from their two-point connection of the side chain to the electron-withdrawing protein backbone, and the lower electronegativity of hydrogen compared to carbon, nitrogen, and oxygen. The hydrogens adjacent to the carbonyl and amide nitrogen, Hα and Hδ, respectively, are the most partially positive. Proline's side chain is also conformationally restricted, allowing for interaction with aromatic residues with minimal entropic or steric penalty. Proline and aromatic residues can interact favorably with each other, due to both the hydrophobic effect and the interaction between the π aromatic face and the polarized C-H bonds, called a CH/π interaction. Aromatic-proline interactions can occur locally, for example, to stabilize cis-amide bonds, and over larger distances, in the tertiary structures of proteins, and intermolecularly in protein-protein interactions. In peptides and proteins, aromatic-proline sequences more readily adopt cis-prolyl amide bonds, where the aromatic ring interacts with the proline ring in the cis conformation. In aromatic-proline sequences, Trp and Tyr are more likely to induce cis-amide bonds than Phe, suggesting an aromatic electronic effect. This result would be expected for a CH/π interaction, in which a more electron-rich aromatic would have a stronger (more cis-stabilizing) interaction with partial positive charges on prolyl hydrogens. In this Account, we describe our investigations into the nature of local aromatic-proline interactions, using peptide models. We synthesized a series of 26 peptides, TXPN, varying X from electron-rich to electron poor aromatic amino acids, and found that the population of cis-amide bond (Ktrans/cis) is tunable by aromatic electronics. With 4-substituted phenylalanines, we observed a Hammett correlation between aromatic electronics and Ktrans/cis, with cis-trans isomerism electronically controllable by 1.0 kcal/mol. All aromatic residues exhibit a higher cis population than Ala or cyclohexylalanine, with Trp showing the strongest aromatic-proline interaction. In addition, proline stereoelectronic effects can modulate cis-trans isomerism by an additional 1.0 kcal/mol. The aromatic-proline interaction is enthalpic, consistent with its description as a CH/π interaction. Proline-aromatic sequences can also promote cis-prolyl bonds, either through interactions of the aromatic ring with the preceding cis-proline or with the Hα prior to cis-proline. Within proline-rich peptides, sequences commonly found in natively disordered proteins, aromatic residues promote multiple cis-amide bonds due to multiple favorable aromatic-proline interactions. Collectively, we found aromatic-proline interactions to be significantly CH/π in nature, tunable by aromatic electronics. We discuss these data in the context of aromatic-proline and aromatic-glycine interactions in local structure, in tertiary structure, in protein-protein interactions, and in protein assemblies.

Neural field dynamics under variation of local and global connectivity and finite transmission speed

Spatially continuous networks with heterogeneous connections are ubiquitous in biological systems, in particular neural systems. To understand the mutual effects of locally homogeneous and globally heterogeneous connectivity, we investigate the stability of the steady state activity of a neural field as a function of its connectivity. The variation of the connectivity is implemented through manipulation of a heterogeneous two-point connection embedded into the otherwise homogeneous connectivity matrix and by variation of the connectivity strength and transmission speed. Detailed examples including the Ginzburg–Landau equation and various other local architectures are discussed. Our analysis shows that developmental changes such as the myelination of the cortical large-scale fiber system generally result in the stabilization of steady state activity independent of the local connectivity. Non-oscillatory instabilities are shown to be independent of any influences of time delay.

Two-point heterogeneous connections in a continuum neural field model

We examine a novel heterogeneous connection scheme in a 1D continuum neural field model. Multiple two-point connections are added to a local connection function in order to model the "patchy" connections seen in, for example visual cortex. We use a numerical approach to solve the equations, choosing the locations of the two-point connections stochastically. We observe self-sustained persistent fluctuations of activity which can be classified into two types (one of which is similar to that seen in network models of discrete excitable neurons, the other being particular to this model). We study the effect of parameters such as system size and the range, number and strength of connections, on the probability that a particular realisation of the connections is able to exhibit persistent fluctuations.

Neural field dynamics with local and global connectivity and time delay

Spatially continuous networks with heterogeneous connections are ubiquitous in biological systems, in particular neural systems. To understand the mutual effects of locally homogeneous and globally heterogeneous connectivity, we investigate the stability of the rest-state activity of a neural field as a function of its connectivity. The variation of the connectivity is operationalized through manipulation of a heterogeneous two-point connection embedded into the otherwise homogeneous connectivity matrix, as well as by variation of connectivity strength and a finite transmission speed. The latter results in a time delay of communication among individual brain areas. We demonstrate that the local connectivity generates the well-known power-law behaviour of the electroencephalographic power spectrum with an exponent close to -2, whereas the global connections generate a more characteristic line spectrum. These spectral characteristics are routinely observed in large-scale topographies of the human brain.

On honeycomb representation and SIGMOID material assignment in optimal topology synthesis of compliant mechanisms

This paper introduces a new honeycomb based domain representation and SIGMOID material function to model continuum topology optimization domains with fixed grids. The two-point connectivity ensured with hexagonal cells is shown to circumvent singularities related to checkerboard patterns and point flexures that are typically observed with one-point connected rectangular cells. The novel SIGMOID function is developed to assign the ‘solid’ material for very low values of design variables (probabilities) and ‘void’ material for those further lower than the threshold, thus encouraging the binary material assignment. The performance of the SIGMOID function is compared with the previously proposed SIMP and PEAK material assignment functions. It is shown that both SIMP and PEAK functions can be over-restrictive in that the material is assigned only for probabilities close to one. The proposed modeling is suitable for topology optimization objectives wherein the number of constraints is large and gradient-based algorithms are chosen. Numerous examples on material layout determination for compliant mechanisms are solved with flexibility-stiffness and flexibility-strength multi-criteria formulations to illustrate the essence of this paper.

Single polymer dynamics in elongational flow and the confluent Heun equation

We investigate the non-equilibrium dynamics of an isolated polymer in a stationary elongational flow. We compute the relaxation time to the steady-state configuration as a function of the Weissenberg number. A strong increase of the relaxation time is found around the coil-stretch transition, which is attributed to the large number of polymer configurations. The relaxation dynamics of the polymer is solved analytically in terms of a central two-point connection problem for the singly confluent Heun equation.

The central two-point connection problem for the reduced confluent Heun equation

Integral symmetry of the confluent Heun equation reduces the central two-point connection problem for the reduced confluent Heun equation to the asymptotical problem. Some heuristic formulae for the transition matrix are obtained and compared with results of the computational calculations.