Topological Criteria Research Articles

Nonliquid cellular states: Gluing gauge-higher-symmetry-breaking versus gauge-higher-symmetry-extension interfacial defects

The existence of quantum nonliquid states and fracton orders, both gapped and gapless states, challenges our understanding of phases of entangled matter. We generalize the cellular topological states to liquid or nonliquid cellular states. We propose a mechanism to construct more general non-Abelian states by gluing gauge-symmetry-breaking versus gauge-symmetry-extension interfaces as extended defects in a cellular network, including defects of higher symmetries, in any dimension. Our approach also naturally incorporates the anyonic particle/string condensations and composite string (related to particle-string or p-string)/membrane condensations. This approach shows gluing the familiar extended topological quantum field theory or conformal field theory data via topology, geometry, and renormalization consistency criteria (via certain modified group cohomology or cobordism theory data) in a tensor network can still guide us to analyze the nonliquid states. (Part of the Abelian construction can be understood from the $K$-matrix Chern-Simons theory approach and the coupled-layer-by-junction constructions.) This approach may also lead us toward a unifying framework for quantum systems of both higher symmetries and subsystem/subdimensional symmetries.

Systems pharmacology, proteomics and in vivo studies identification of mechanisms of cerebral ischemia injury amelioration by Huanglian Jiedu Decoction

Ethnopharmacological relevanceHuanglian Jiedu Decoction (HLJDD) has the effect of clearing heat and detoxifying, and has been considered as an effective prescription for cerebral ischemia (CI) for thousands of years in traditional Chinese medicine (TCM). It can improve the quality of life of patients with ischemic stroke, but its pharmacological mechanism remains unclear. Aim of the studyThe study aimed to explore the pharmacological action and potential mechanism of HLJDD against CI by systems pharmacology, proteomics and in vivo experiments. Materials and methodsIn this study, databases such as TCMIP V2.0 and Genecards were used to predict compounds, targets and CI related targets, and network topology criteria of protein-protein interaction (PPI) network was used to screen core targets. The Database for Annotation, Visualization and Integrated Discovery database (DAVID) was used to discover biological processes and pathways. In addition, molecular docking was performed between the screened core biological active compounds and targets to verify the binding activity. Finally, proteomics and Western blot were performed on cerebral cortex tissues of middle cerebral artery occlusion (MCAO) model rats with HLJDD intervention to further verify the predicted results. Results77 compounds and 308 targets of HLJDD were identified, 54 of which were predicted to be associated with cerebral ischemia. PPI network and enrichment results showed that 8 targets, including AKT1, PTGS2 and TLR4, were core targets of HLJDD in CI. And 19 signaling pathways, including Rap1 signaling pathway, cAMP signaling pathway and arachidonic acid metabolism, were identified as key pathways to the therapeutic activity of HLJDD in CI. Combined with proteomics studies, we identified that Rap1 signaling pathway and upstream and downstream targets were the key mechanisms. Molecular biology experiments showed that RAP1A and AKT expression levels were significantly up-regulated in middle cerebral artery occlusion (MCAO) rats treated with HLJDD (P < 0.0001), GRIN1 expression level was significantly down-regulated (P < 0.0001). However, ACTB expression level was slightly down-regulated (P > 0.05), which may be related to the biological function. ConclusionThis study confirms the pharmacological effect of HLJDD on cerebral ischemia. These results indicate that HLJDD mediates various pathways such as inhibition of apoptosis, regulation of oxygen balance, inhibition of excitatory toxicity and maintenance of basic cell functions to improve CI by regulating Rap1 signaling pathway.

Topological Superconductivity in an Extended s -Wave Superconductor and Its Implication to Iron-Based Superconductors

In the presence of both space and time reversal symmetries, an s-wave A1g superconducting state is usually topologically trivial. Here we demonstrate that an exception can take place in a type of nonsymmorphic lattice structures. We specify the demonstration in a system with a centrosymmetric space group P4/nmm, the symmetry group that governs iron-based superconductors, by showing the existence of a second-order topological state protected by a mirror symmetry. The topological superconductivity is featured by 2Z degenerate Dirac cones on the (1,0) edge, and Z pairs of Majorana modes at the intersection between the (1,1) and (1,-1) edges. The topological invariance and Fermi surface criterion for the topological state are provided. Moreover, we point out that the previously proposed s-wave state in iron-based superconductors, which features a sign-changed superconducting order parameter between two electron pockets, is such a topological state. Thus, these results not only open a new route to pursue topological superconductivity, but also establish a measurable quantity to settle one long-lasting debate on the pairing nature of iron-based superconductors.

Microstructural characteristics of 3-d networks

AbstractThe structural characteristics of three-dimensional (3-d) irregular networks, such as random polycrystals, are described using scaling arguments based on the properties of Average N-hedra (ANH’s). ANH’s comprise a special set of highly symmetric polyhedral cells that satisfy topological and geometrical criteria demanded in 3-d space-filling networks. All the geometrical properties of ANH’s may be obtained from exact analytical expressions already derived in [1]. The utility and ease of use of these formulas have been carefully checked against accurate simulations of the excess free energy and evolution kinetics of foams and polycrystals. The vertex-to-vertex distance is chosen in this paper as the consistent gauge to estimate an important microstructure feature set presented here for irregular 3-d networks. In the case of annealed polycrystals this includes the total grain boundary area and its associated stored energy per unit volume, the triple line length per unit volume, and the number density of triple lines and quadra-junctions – all of which may be expressed in terms of the polycrystal's grain number density.

Measurements using a prototype array of plastic scintillator bars for reactor based electron anti-neutrino detection

We report measurement of reactor based electron anti-neutrinos from a prototype array of plastic scintillator bars (mini-ISMRAN) located inside Dhruva research reactor hall, BARC. The detector setup took data for 128 days for reactor on (RON) and 51 days for reactor off (ROFF) condition. A detailed analysis procedure is developed to select the anti-neutrino candidate events based on the energy deposition, number of bars hit as well as topological event selection criteria in position and time. Each of these selection criteria are compared with Monte Carlo based simulations and further an embedding technique is used to estimate the efficiencies from a data driven background study. The obtained anti-neutrino like events in RON condition are 218 ± 50 (stat) ± 37 (sys) after background subtraction. The obtained results are compared with theoretical estimation which yields 214 ± 32 (sys) anti-neutrino events for the RON condition.

Functional Complex Networks Based on Operational Architectonics: Application on EEG-based Brain–computer Interface for Imagined Speech

A new method for analyzing brain complex dynamics and states is presented. This method constructs functional brain graphs and is comprised of two pylons: (a) Operational architectonics (OA) concept of brain and mind functioning. (b) Network neuroscience. In particular, the algorithm utilizes OA framework for a non-parametric segmentation of EEG signals, which leads to the identification of change points, namely abrupt jumps in EEG amplitude, called Rapid Transition Processes (RTPs). Subsequently, the time coordinates of RTPs are used for the generation of undirected weighted complex networks fulfilling a scale-free topology criterion, from which various network metrics of brain connectivity are estimated. These metrics form feature vectors, which can be used in machine learning algorithms for classification and/or prediction. The method is tested in classification problems on an EEG-based BCI data set, acquired from individuals during imagery pronunciation tasks of various words/vowels. The classification results, based on a Naïve Bayes classifier, show that the overall accuracies were found to be above chance level in all tested cases. This method was also compared with other state-of-the-art computational approaches commonly used for functional network generation, exhibiting competitive performance. The method can be useful to neuroscientists wishing to enhance their repository of brain research algorithms.

Generalized adaptive refinement for grid-based hexahedral meshing

Due to their nice numerical properties, conforming hexahedral meshes are considered a prominent computational domain for simulation tasks. However, the automatic decomposition of a general 3D volume into a small number of hexahedral elements is very challenging. Methods that create an adaptive Cartesian grid and convert it into a conforming mesh offer superior robustness and are the only ones concretely used in the industry. Topological schemes that permit this conversion can be applied only if precise compatibility conditions among grid elements are observed. Some of these conditions are local, hence easy to formulate; others are not and are much harder to satisfy. State-of-the-art approaches fulfill these conditions by prescribing additional refinement based on special building rules for octrees. These methods operate in a restricted space of solutions and are prone to severely over-refine the input grids, creating a bottleneck in the simulation pipeline. In this article, we introduce a novel approach to transform a general adaptive grid into a new grid meeting hexmeshing criteria, without resorting to tree rules. Our key insight is that we can formulate all compatibility conditions as linear constraints in an integer programming problem by choosing the proper set of unknowns. Since we operate in a broader solution space, we are able to meet topological hexmeshing criteria at a much coarser scale than methods using octrees, also supporting generalized grids of any shape or topology. We demonstrate the superiority of our approach for both traditional grid-based hexmeshing and adaptive polycube-based hexmeshing. In all our experiments, our method never prescribed more refinement than the prior art and, in the average case, it introduced close to half the number of extra cells.

Local topology and bifurcation hot-spots in proteins with SARS-CoV-2 spike protein as an example.

Novel topological methods are introduced to protein research. The aim is to identify hot-spot sites where a bifurcation can alter the local topology of the protein backbone. Since the shape of a protein is intimately related to its biological function, a substitution that causes a bifurcation should have an enhanced capacity to change the protein’s function. The methodology applies to any protein but it is developed with the SARS-CoV-2 spike protein as a timely example. First, topological criteria are introduced to identify and classify potential bifurcation hot-spot sites along the protein backbone. Then, the expected outcome of asubstitution, if it occurs, is estimated for a general class of hot-spots, using a comparative analysis of the surrounding backbone segments. The analysis combines the statistics of structurally commensurate amino acid fragments in the Protein Data Bank with general stereochemical considerations. It is observed that the notorious D614G substitution of the spike protein is a good example of a bifurcation hot-spot. A number of topologically similar examples are then analyzed in detail, some of them are even better candidates for a bifurcation hot-spot than D614G. The local topology of the more recently observed N501Y substitution is also inspected, and it is found that this site is proximal to a different kind of local topology changing bifurcation.

Multi criteria decision analysis to determine the suitability of agricultural crops for land consolidation areas

Crop selection for sustainable and effective agricultural land management has to take into accounts several issues such as chemical, physical, environmental, economic and social conditions. Especially after land consolidation projects, sustainable agricultural crop management should be investigated for each crop which are suitable for the project area to benefit from the land consolidation contributions such as irrigation, roads, modified parcel boundaries and surfaces. Thus, Geographical Information Systems (GIS) aided suitability analysis techniques are required to determine the suitable crops for the consolidated areas. In this study, Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) multi-criteria decision techniques are integrated with GIS to determine most suitable crops for parcels. The suitability maps of wheat, clover, sugar beet and corn crops are generated for the projected area using 63 Land Mapping Units (LMU) with considering pH, lime, texture, salinity, organic matter, electrical conductivity, permeability, slope, aspect and the distance to settlements and roads within chemical, physical, topological and socio-economic criteria.

The rank two p-curvature conjecture on generic curves

We prove the p-curvature conjecture for rank two vector bundles with connection on generic curves. Our ingredients include new deformation techniques for vector bundles with vanishing p-curvatures on families of varieties, as well as topological criteria for finiteness of surface group representations in terms of simple loops and pairs of pants.

Poisson Dixmier-Moeglin equivalence from a topological point of view

A complex affine Poisson algebra A is said to satisfy the Poisson Dixmier-Moeglin equivalence if the Poisson cores of maximal ideals of A are precisely those Poisson prime ideals that are locally closed in the Poisson prime spectrum P.spec A and if, moreover, these Poisson prime ideals are precisely those whose extended Poisson centers are exactly the complex numbers. In this paper, we provide some topological criteria for the Poisson Dixmier-Moeglin equivalence for A in terms of the poset (P.spec A, ⊆) and the symplectic leaf or core stratification on its maximal spectrum. In particular, we prove that the Zariski topology of the Poisson prime spectrum and of each symplectic leaf or core can detect the Poisson Dixmier-Moeglin equivalence for any complex affine Poisson algebra. Moreover, we generalize the weaker version of the Poisson Dixmier-Moeglin equivalence for a complex affine Poisson algebra proved in [J. Bell, S. Launois, O. L. Sanchez and B. Moosa, Poisson algebras via model theory and differential-algebraic geometry, J. Eur. Math. Soc. (JEMS) 19 (2017), 2019–2049] to the general context of a commutative differential algebra.

Topological and geometric hyperbolicity criteria for polynomial automorphisms of

AbstractWe prove that uniform hyperbolicity is invariant under topological conjugacy for dissipative polynomial automorphisms of $\mathbb {C}^2$ . Along the way we also show that a sufficient condition for hyperbolicity is that local stable and unstable manifolds of saddle points have uniform geometry.

Interfacial Influence of Strontium Niobium Engulfed Reduced Graphene Oxide Composite for Sulfamethazine Detection: Employing an Electrochemical Route in Real Samples

Sulfonamides are a broad assortment of drugs utilized in treating bacterial diseases in veterinary and human existence as anti-infection agents. The escalating usage of such medications requires explicit recognition. This work describes the electrochemical detection of sulfamethazine (SMZ) (a subgroup of sulfonamides) using strontium niobium combined with reduced graphene oxide (SN/rGO) as composite material. The structural and topological criteria illustrate the surface immaculateness and elemental presence of the crystalline material SN/rGO with XRD and FE-SEM analysis. Additional examinations of chemical states and the functional group were identified with XPS and FT-IR measurements. The feasibility of the sensor was inspected in the record of electrochemical studies. Electrochemical impedance spectroscopy (EIS) and cyclic voltammetry (CV) studies have demonstrated the effective implementation of the fabricated sensor with facilitating higher electroactive sites and enhanced conductance with SN/rGO. The amalgamation of SN and rGO has substantial influence with a lower limit of detection 6 nM with linearity from 0.009 μM to 128 μM. The limit of quantification was about 0.0224 μM. The specific detection acquired over anti-interference studies and real-world actualize over milk, honey, and human blood serum tests mirror SN/rGO modified platform’s viable capability. The construction of SN/rGO is envisioned as a promising dais for improved SMZ sensing in real samples.

Implementation of Typology Criteria for Design Knowledge Reflecting Design Diversification

As the design-related knowledge base grows to remain abreast of technological and scientific advancements, ‘Design Knowledge’ has emerged as a new genre of pragmatic design. Criteria need to be determined to establish a typology as a knowledge-based system supporting education, literature, and industrial organizations. To this end, this study establishes criteria for design knowledge typology while considering design diversification by applying existing topological criteria to the classification of books, industries, and academic disciplines along with new views of design theorists. A matrix analysis was conducted to test the applicability of the design knowledge language data by checking them against extracted and defined criteria. We found it impossible to consistently typify contemporary design concepts with single-attribute criteria; the multiple-criteria classification method is much more effective. Further, contemporary design language has evolved from object-based to concept-based terms. Our study lays the groundwork for a useful typology for a design study schema.

Subgraphs of Interest Social Networks for Diffusion Dynamics Prediction.

Finding the building blocks of real-world networks contributes to the understanding of their formation process and related dynamical processes, which is related to prediction and control tasks. We explore different types of social networks, demonstrating high structural variability, and aim to extract and see their minimal building blocks, which are able to reproduce supergraph structural and dynamical properties, so as to be appropriate for diffusion prediction for the whole graph on the base of its small subgraph. For this purpose, we determine topological and functional formal criteria and explore sampling techniques. Using the method that provides the best correspondence to both criteria, we explore the building blocks of interest networks. The best sampling method allows one to extract subgraphs of optimal 30 nodes, which reproduce path lengths, clustering, and degree particularities of an initial graph. The extracted subgraphs are different for the considered interest networks, and provide interesting material for the global dynamics exploration on the mesoscale base.

A hybrid topological and shape-matching approach for structure analysis.

Properties of crystalline and amorphous materials are characterized by the underlying long-range and local crystalline order. Deformations and defects are structural hallmarks of plasticity, ice formation, and crystal growth mechanisms. Partitioning topological networks into constituent crystal building blocks, which is the basis of topological identification criteria, is an intuitive approach for classification in both bulk and confinement. However, techniques reliant on the convex hull for assigning orientations of component units fail for non-convex blocks. Here, we propose a new framework, called Topological Unit Matching (TUM), which exploits information from topological criteria for an efficient shape-matching procedure. TUM is a general family of algorithms, capable of quantifying deformations and unambiguously determining grains of bulk and confined ice polymorphs. We show that TUM significantly improves the identification of quasi-one-dimensional ice by including deformed prism blocks. We demonstrate the efficacy of TUM by analyzing supercooled water nanoparticles, amorphous ice, and phase transitions in an ice nanotube. We also illustrate the superiority of TUM in resolving topological defect structures with minimal parameterization.

Welded extensions and ribbon restrictions of diagrammatical moves

In this paper, we consider local moves on classical and welded diagrams of string links, and the notion of welded extension of a classical move. Such extensions being non-unique in general, the idea is to find a topological criterion which could isolate one extension from the others. To that end, we turn to the relation between welded string links and knotted surfaces in [Formula: see text], and the ribbon subclass of these surfaces. This provides a topological interpretation of classical local moves as surgeries on surfaces, and of virtual local moves as surgeries on ribbon surfaces. Comparing these surgeries leads to the notion of ribbon residue of a classical local move, and we show that up to some broad conditions there can be at most one welded extension which is a ribbon residue. We provide three examples of ribbon residues, for the self-crossing change, the Delta and the band-pass moves. However, for the latter, we note that the given residue is actually not an extension of the band-pass move, showing that a classical move may have a ribbon residue and a welded extension, but no ribbon residue which is an extension.

Formation of a Ni- and Be-free Zr-based glassy alloy in centimeter scale

A Ni- and Be- free Zr-Al-Cu-Y glassy alloy in centimeter scale has been developed and understood via clusters in this letter. Glass-formers in Zr-Al-Cu system was understood and constructed by Zr-Al and Zr-Cu clusters proportionately. Clusters Cu-Cu7Zr5 and Al-Al2Zr8, which conform to the topological packing compact criterion, were chosen and used. The ratio between clusters is determined by electrons per atom ratio. Alloy with highest GFA located at Zr48.65Cu43.24Al8.11 which could be regarded as 0.5Al-Al2Zr8 + Cu-Cu7Zr5. Its critical diameter is 6 mm, superior than Zr50Cu40Al10 of which critical diameter is about 3 mm at the same laboratory environment. Furthermore, 2 at.% Y alloying greatly enhances GFA leading to centimeter scale. Its reason was also discussed from the aspect of clusters. The results in this letter might provide a way of designing good glass-formers, understanding microalloying and expand the application range of amorphous alloys.

A Topological Approach of Principal Component Analysis

Large datasets are increasingly widespread in many disciplines. The exponential growth of data requires the development of more data analysis methods in order to process information more efficiently. In order to better visualize the data, many methods such as Principal Component Analysis (PCA) and MultiDimensional Scaling (MDS) allow to extract a low-dimensional structure from high-dimensional data set. The proposed approach, called Topological Principal Component Analysis (TPCA), is a multidimensional descriptive method witch studies a homogeneous set of continuous variables defined on the same set of individuals. It is a topological method of data analysis that consists of comparing and classifying proximity measures from among some of the most widely used proximity measures for continuous data. Proximity measures play an important role in many areas of data analysis, the results strongly depend on the proximity measure chosen. So, among the many existing measures, which one is most useful? Are they all equivalent? How to identify the one that is most appropriate to analyze the correlation structure of a set of quantitative variables. TPCA proposes an appropriate adjacency matrix associated to an unknown proximity measure according to the data under consideration, then analyzes and visualizes, with graphic representations, the relationship structure of the variables relating to, the well known PCA problem. Its uses the concept of neighborhood graphs and compares a set of proximity measures for continuous data which can be more-or-less equivalent a topological equivalence criterion between two proximity measures is defined and statistically tested according to the topological correlation between the variables considered. An example on real data illustrates the proposed approach.

Systems theoretic properties of linear RLC circuits

We consider the differential-algebraic systems obtained by modified nodal analysis of linear RLC circuits from a systems theoretic viewpoint. We derive expressions for the set of consistent initial values and show that the properties of controllability at infinity and impulse controllability do not depend on parameter values but rather on the interconnection structure of the circuit. We further present circuit topological criteria for behavioral stabilizability.