Group Equations Research Articles

Binding Curve Viewer: Visualizing the Equilibrium and Kinetics of Protein-Ligand Binding and Competitive Binding.

Understanding the thermodynamics and kinetics of the protein-ligand interaction is essential for biologists and pharmacologists. To visualize the equilibrium and kinetics of the binding reaction with 1:1 stoichiometry and no cooperativity, we obtained the exact relationship of the concentration of the protein-ligand complex and the time in the second-order binding process and numerically simulated the process of competitive binding. First, two common concerns in measuring protein-ligand interactions were focused on how to avoid the titration regime and how to establish the appropriate incubation time. Then, we gave examples of how the commonly used experimental conditions of [L]0 ≫ [P]0 and [I]0 ≫ [P]0 affected the estimation of the kinetic and thermodynamic properties. Theoretical inhibition curves were calculated, and the apparent IC50 and IC50 were estimated accordingly under predefined conditions. Using the estimated apparent IC50, we compared the apparent Ki and Ki calculated by using the Cheng-Prusoff equation, Lin-Riggs equation, and Wang's group equation. We also applied our tools to simulate high-throughput screening and compare the results of real experiments. The visualization tool for simulating the saturation experiment, kinetic experiments of binding and competitive binding, and inhibition curve, "Binding Curve Viewer," is available at www.eplatton.net/binding-curve-viewer.

Semi-inclusive jet functions and jet substructure in JET(I) and JET(II) algorithms

Within the framework of Soft Collinear Effective Theory, we present calculations of semi-inclusive jet functions and fragmenting jet functions at next-to-leading order (NLO) for both quark- and gluon-initiated jets, for jet algorithms of $J_{E_T}^{(I)}$ and $J_{E_T}^{(II)}$ where one maximizes a suitable jet function. We demonstrate the consistency of the obtained results with the standard perturbative QCD calculations for $J_{E_T}^{(I)}$ algorithm, while the results for fragmenting jet functions with the $J_{E_T}^{(II)}$ algorithm are new. The renormalization group (RG) equation for both semi-inclusive jet functions and fragmenting jet functions are derived and shown to follow the time-like DGLAP evolution equations, independent of specific jet algorithms. The RG equation can be used to resum single logarithms of the jet size parameter $\beta$ for highly collimated jets in these algorithms where $\beta \gg 1$.

Sparsification of SAT and CSP Problems via Tractable Extensions

Unlike polynomial kernelization in general, for which many non-trivial results and methods exist, only few non-trival algorithms are known for polynomial-time sparsification. Furthermore, excepting problems on restricted inputs (such as graph problems on planar graphs), most such results rely upon encoding the instance as a system of bounded-degree polynomial equations. In particular, for satisfiability (SAT) problems with a fixed constraint language Γ, every previously known result is captured by this approach; for several such problems, this is known to be tight. In this work, we investigate the limits of this approach—in particular, does it really cover all cases of non-trivial polynomial-time sparsification? We generalize the method using tools from the algebraic approach to constraint satisfaction problems (CSP). Every constraint that can be modelled via a system of linear equations, over some finite field F, also admits a finite domain extension to a tractable CSP with a Maltsev polymorphism; using known algorithms for Maltsev languages, we can show that every problem of the latter type admits a “basis” of O ( n ) constraints, which implies a linear sparsification for the original problem. This generalization appears to be strict; other special cases include constraints modelled via group equations over some finite group G . For sparsifications of polynomial but super-linear size, we consider two extensions of this. Most directly, we can capture systems of bounded-degree polynomial equations in a “lift-and-project” manner, by finding Maltsev extensions for constraints over c -tuples of variables, for a basis with O ( n c ) constraints. Additionally, we may use extensions with k -edge polymorphisms instead of requiring a Maltsev polymorphism. We also investigate characterizations of when such extensions exist. We give an infinite sequence of partial polymorphisms φ 1 , φ 2 , …which characterizes whether a language Γ has a Maltsev extension (of possibly infinite domain). In the complementary direction of proving lower bounds on kernelizability, we prove that for any language not preserved by φ 1 , the corresponding SAT problem does not admit a kernel of size O ( n 2−ε ) for any ε > 0 unless the polynomial hierarchy collapses.

A Study of Interaction Effects and Quantum Berezinskii- Kosterlitz-Thouless Transition in the Kitaev Chain

The physics of the topological state of matter is the second revolution in quantum mechanics. We study the effect of interactions on the topological quantum phase transition and the quantum Berezinskii-Kosterlitz-Thouless (QBKT) transition in topological state of a quantum many-body condensed matter system. We predict a topological quantum phase transition from topological superconducting phase to an insulating phase for the interacting Kitaev chain. We observe interesting behaviour from the results of renormalization group study on the topological superconducting phase. We derive the renormalization group (RG) equation for QBKT through different routes with a few exact solutions along with the physical explanations, wherein we find the existence of two new important emergent phases apart from the two conventional phases of this model Hamiltonian. We also present results of a length-scale dependent study to predict asymptotic freedom like behaviour of the system. We do rigorous quantum field theoretical renormalization group calculations to solve this problem.

The Wiener Measure on the Heisenberg Group and Parabolic Equations

In this paper, we study questions related to the theory of stochastic processes on Lie nilpotent groups. In particular, we consider the stochastic process on the Heisenberg group H3(ℝ) whose trajectories satisfy the horizontal conditions in the stochastic sense relative to the standard contact structure on H3 (ℝ). It is shown that this process is a homogeneous Markov process relative to the Heisenberg group operation. There was found a representation in the form of a Wiener integral for a one-parameter linear semigroup of operators for which the Heisenberg sublaplacian generated by basis vector fields of the corresponding Lie algebra L(H3) is producing. The main method of solving the problem in this paper is using the path integrals technique, which indicates the common direction of further development of the results.

Cosmological Constant in SUGRA Models with Degenerate Vacua

The extrapolation of couplings up to the Planck scale within the standard model (SM) indicates that the Higgs effective potential can have two almost degenerate vacua, which were predicted by the multiple point principle (MPP). The application of the MPP to ( N = 1 ) supergravity (SUGRA) implies that the SUGRA scalar potential of the hidden sector possesses at least two exactly degenerate minima. The first minimum is associated with the physical phase in which we live. In the second supersymmetric (SUSY) Minkowski vacuum, the local SUSY may be broken dynamically, inducing a tiny vacuum energy density. In this paper, we consider the no-scale-inspired SUGRA model in which the MPP conditions are fulfilled without any extra fine-tuning at the tree-level. Assuming that at high energies, the couplings in both phases are identical, one can estimate the dark energy density in these vacua. Using the two-loop renormalization group (RG) equations, we find that the measured value of the cosmological constant can be reproduced if the SUSY breaking scale M S in the physical phase is of the order of 100 TeV. The scenario with the Planck scale SUSY breaking is also discussed.

New matter phases at high temperature and density

It is widely accepted that a new phase structure will emerge in nuclear matter at high temperature and density. In this article the QCD (quantum chromodynamic) phase transitions are briefly reviewed from both theoretical and experimental aspects. Basing on the general principle of QCD and modern phase transition theory, we analyze potential phases in the strong interacting nuclear matter. The phase structure could be understood intuitively through the breaking and restoration of fundamental symmetries of QCD. In the space spanned by the temperature, baryon and isospin chemical potential there are different phases corresponding to three important symmetries, i.e. the color, chiral and isospin. At low temperature and density, the color and isospin symmetries are preserved, while the chiral one is spontaneously broken. At high temperature or density, the color or isospin or both of them would be broken as the chiral restoration. In order to explore the detailed structure of the phase diagram various theoretical approaches of studying the transitions are introduced, such as lattice QCD, mean field calculation basing on effective models, functional renormalization group and Dyson-Schwinger equation. In experiments there are two kinds of physics systems to realize conditions of QCD phase transitions: the relativistic heavy ion collisions and compact stars. Nuclear collision is the only way to approach hot QCD in laboratories on the earth. We focus on some robust probes to the quark gluon plasma formed in the early stage of the collisions. There are generally two types of the traditional signals which are focusing on the profile of the fire ball and the internal interaction of it respectively. For the first case we introduce collective flows as observables for the shape of fire ball. While for the second we review the jet quenching and the heavy flavor suppression. In the hot fire ball the classical transport theory should be modified by including quantum effects induced by the chiral restoration. This novel transport phenomenon of QCD at high temperature is named by the chiral anomalous transport. On the phase transitions at high density, we review the recent progress on color superconductivity and pion superfluidity. Color superconductivity is formed at high baryon chemical potential when quarks pair with each other into diquarks and condense. While pion superfluidity would emerge at high isospin chemical potential with pion condensate. Model studies suggest these states are able to exist in the core of compact star. By modifying the structure of them, such as the mass-radius relation, these states are expected to be identified by astronomical observation at higher precision. Currently dense systems are difficult to produce at main facilities of the world, such as RHIC (relativistic heavy ion collider) and LHC (large hadron collider) because of the designed high energy scale of the accelerators. Therefore it is a critical need for the facilities which could cover the low and medium energy region where the potential critical point and various phase structures would locate. Considering the running and constructing heavy ion facilities, the CSR (cooler-storage-ring) in Lanzhou and the high intensity HIAF (heavy-ion accelerator facility) in Huizhou, the properties of the new QCD phases and their realizations in nuclear collisions will be the new frontier of nuclear physics in China.

Investigation on maneuverability of a twin-screw ship driven by one screw

It is possible for a twin-screw ship that one screw failure occurs during navigation, and the maneuverability in this case should be noticed by ship designers and operators. It is of great significance to evaluate the related risk. Firstly, a mathematical model for the twin-screw ship maneuvering motion with one failed screw is developed based on the maneuvering model group (MMG) equations, and verified by the model test results. Secondly, the maneuvering motions of a twin-screw liquefied natural gas (LNG) ship with one free rotating failure screw or with one locked failure screw are simulated and compared by using the mathematical model. It is shown that the numerical modeling results are in agreement with the model test results. Compared with those of normal navigation, the port turning ability of the ship with one failed port screw is better, but the starboard turning ability and yaw checking ability become worse. The maneuverability of the ship with locked failure screw is better than that with free failure screw, although the ship speed drops obviously.

Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations

Computational kinematics is a fundamental tool for the design, simulation, control, optimization and dynamic analysis of multibody systems. The analysis of complex multibody systems and the need for real time solutions requires the development of kinematic and dynamic formulations that reduces computational cost, the selection and efficient use of the most appropriated solvers and the exploiting of all the computer resources using parallel computing techniques. The topological approach based on group equations and natural coordinates reduces the computation time in comparison with well-known global formulations and enables the use of parallelism techniques which can be applied at different levels: simultaneous solution of equations, use of multithreading routines, or a combination of both. This paper studies and compares these topological formulation and parallel techniques to ascertain which combination performs better in two applications. The first application uses dedicated systems for the real time control of small multibody systems, defined by a few number of equations and small linear systems, so shared-memory parallelism in combination with linear algebra routines is analyzed in a small multicore and in Raspberry Pi. The control of a Stewart platform is used as a case study. The second application studies large multibody systems in which the kinematic analysis must be performed several times during the design of multibody systems. A simulator which allows us to control the formulation, the solver, the parallel techniques and size of the problem has been developed and tested in more powerful computational systems with larger multicores and GPU.

Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization

An approach to QCD vacuum as a medium describable in terms of statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields is reviewed. These fields play the role of the confining medium for color charged fields as well as underline the mechanism of realization of chiral $SU_{\mathrm L}(N_f)\times SU_{\mathrm R}(N_f)$ and $U_{\mathrm A}(1)$ symmetries. Hadronization formalism based on this ensemble leads to manifestly defined quantum effective meson action. Strong, electromagnetic and weak interactions of mesons are represented in the action in terms of nonlocal $n$-point interaction vertices given by the quark-gluon loops averaged over the background ensemble. Systematic results for the mass spectrum and decay constants of radially excited light, heavy-light mesons and heavy quarkonia are presented. Relationship of this approach to the results of functional renormalization group and Dyson-Schwinger equations, and the picture of harmonic confinement is briefly outlined.

The Quantum Group and Harper Equation on a Honeycomb Lattice

The tight-binding model of quantum particle on a honeycomb lattice is investigated in the presence of homogeneous magnetic field. The one-particle Hamiltonian is expressed in terms of the generators of the quantum group Uq(sl2). The corresponding Harper equation is rewritten as a system of two coupled functional equations in the complex plane. The system is shown to exhibit certain symmetry that allows one to resolve the entanglement, and the basic single equation determining the eigenvalues and eigenstates is obtained. Equations specifying the roots of eigenstates in the complex plane are found.

Revisiting the vacuum energy scenario from the renormalization group method of the QFT theory

In this paper the vacuum energy scenario (or time-dependent cosmological constant) from the renormalization group (RG) equation is studied. By considering the renormalization group scale described by the Hubble parameter, we apply the current observational data to constrain this RG dark energy model. Concretely, the different combinations of cosmic observational data, including the kinematical and the dynamical part, are investigated to constrain the RG model. For comparison we also consider the cosmic constraints on the dark model by taking the Ricci scalar as the renormalization group scale. In addition, we compare these two RG dark energy models with the cosmological constant.

Solution of the two dimensional diffusion and transport equations in a rectangular lattice with an elliptical fuel element using Fourier transform methods: One and two group cases

A method for solving the diffusion and transport equations in a rectangular lattice cell with an elliptical fuel element has been developed using a Fourier expansion of the neutron flux. The method is applied to a one group model with a source in the moderator. The cell flux is obtained and also the associated disadvantage factor. In addition to the one speed case, we also consider the two group equations in the cell which now become an eigenvalue problem for the lattice multiplication factor. The method of solution relies upon an efficient procedure to solve a large set of simultaneous linear equations and for this we use the IMSL library routines. Our method is compared with the results from a finite element code. The main drawback of the problem arises from the very large number of terms required in the Fourier series which taxes the storage and speed of the computer. Nevertheless, useful solutions are obtained in geometries that would normally require the use of finite element or analogous methods, for this reason the Fourier method is useful for comparison with that type of numerical approach. Extension of the method to more intricate fuel shapes, such as stars and cruciforms as well as superpositions of these, is possible.

Lateral Response of Pile Group

The main objective for this study is to determine the relationship between pile spacing and p-multipliers (fm - pile-to-pile modulus multiplier) for a laterally loaded pile-group. In addition, the appropriate p-multipliers for a 3-pile group configuration at 2D, 4D, 6D and 8D pile spacing is also determined. Therefore, a three-dimensional finite element approach was used to assess the lateral pile and pile group response subjected to pure lateral load. Results of the influence of load intensities, group configuration, pile spacing are discussed in terms of response of load vs. lateral displacement, load vs. soil resistance and corresponding p-y curves. The improved plots can be used for laterally loaded pile design and also to produce the group action design p-multiplier curves and equations. As a result, design curves were developed and applied on the actual case studies and similar expected cases for assessment of pile group behavior using improved p-multiplier. A design equation was derived from predicted design curves to be used in the evaluation of the lateral pile group action. It was found that the group interaction effect led to reduced lateral resistance for the pile in the group relative to that for the single pile.

Model-Based Verifying and Design of Autonomous Airship

Based on the Kirchhoff equations, Newton-Euler laws, boundary layer theory and mass definition, the six degrees of freedom dynamic model of airship complete with aerodynamic forces, wind effect is presented. Then, the nonlinear dynamic model is divided into three group equations by restricting airship motion in different planes respectively. The motion characteristics of airship, including stability, the effect of ballast position and rotational damping, are studied using linearized model. The results of simulation verify the correctness of the theoretical analysis and airship design.

단일 3축 가속도센서를 사용한 보행 시 대사에너지 예측

The purpose of this study was to compare metabolic energy expenditure with the computed kinetic energy for different speeds of walking and running over the treadmill and to find the relevance for individual and group equation by performing a statistical analysis, Bland-Altman plot. Seven male subjects participated, and they were required to walk and run on the treadmill with the gas analyzer and triaxial accelerometer. Walking speeds were 3.0, 4.0, 5.0 and 6.0 km/h and running speeds were 7.0, 8.0 and 9.0 km/h respectively. Kinetic energy was calculated by the integration of acceleration data and compared with the metabolic energy measured by a gas analyzer. Correlation coefficients showed relatively good between the measured metabolic energy and the calculated kinetic energy. In addition, a dramatic increase in kinetic energy was also observed at the transition speed of walking and running, and two standard deviations in Bland-Altman plot, derived from the difference between measured and predicted values, were 1.14, 2.53, 2.93, 1.80, 2.80, 0.60 and 2.48 respectively. It was showed that there is no difference for methods of how to predict the kinetic energy expenditure for individual and group even though people had each different physical characteristic.

A group-theoretical approach to study atomic motion in a laser field

A group-theoretical approach is applied to study the behavior of lossless two-level atoms in a standing-wave laser field. Due to the recoil effect, the internal and external atomic degrees of freedom become coupled. The internal dynamics is described quantum mechanically in terms of the SU(2) group parameters. The evolution operator is found in an explicit way after solving a single ODE for one of the group parameters. The translational motion in a standing wave is governed by the classical Hamilton equations which are coupled to the SU(2) group equations. It is shown that the full set of equations may be chaotic in some ranges of the control parameters and initial conditions. It means physically that there are regimes of motion with chaotic center-of-mass motion and irregular internal dynamics. It is established that the chaotic regime is specified by the character of oscillations of the group parameter characterizing the mean interaction energy between the atom and the laser field. It is shown that the effect of chaotic walking can be observed in a real experiment with cold atoms crossing a standing-wave laser field.

트레드밀 보행 시 단일 3축 가속도센서를 사용한 대사에너지 소모량 예측

The purpose of this study was to investigate the relevance of the prediction equations derived from the relationship between metabolic energy expenditure and kinetic energy, for different speeds of walking and running over the treadmill. Seven male subjects participated in this study. A tri-axial accelerometer was attached on between the left and right posterior superior iliac spines. Kinetic energy was calculated by the integration of acceleration data and compared with the metabolic energy measured by a gas analyzer. Correlation coefficients were determined to find a relationship between the kinetic energy and the metabolic energy expenditure. Also, the difference between measured and predicted values was used to find the relevance for individual and group equations. Results showed a relatively good correlation between the measured metabolic energy and the calculated kinetic energy. In addition, a dramatic increase in kinetic energy was observed at the transition speed of walking and running (6 km/h). There was no difference in how to predict the kinetic energy expenditure for individual and group even though people have different physical characteristics. This study would be useful to predict metabolic energy expenditures by the regression analysis with acceleration data.

A new method to estimate energy expenditure from abdominal and rib cage distances

The aim of this paper is to validate a new method of energy expenditure (EE) estimation stemming solely from the measurement of rib cage, abdominal and chest wall distances. We set out to prove that the variations of these distances, measured by two pairs of electromagnetic coils, lead to the estimation of the ventilation (VE) and the EE. Eleven subjects were recruited to take part in this study (27.6 ± 5.4 years; 73.7 ± 9.7 kg). Each subject participated in two tests. The objective of Test 1 was to determine the individual and group equations between the VE and EE during light to moderate activities while Test 2 compared the two pairs of electromagnetic coils with the indirect calorimetry so as to estimate EE in upright sitting and standing positions and during walking exercises. During Test 2, we compared EE measured by indirect calorimetry (EE(IC-Val-REF)) with EE estimated by the two pairs of electromagnetic coils through the application of: (1) the individual equation (EE(mag-Val-INDIV)) and (2) the group equation (EE(mag-val-GROUP)). The results show that there is no significant difference between EE(IC-Val-REF) and EE(mag-Val-INDIV) and between EE(IC-Val-REF) and EE(mag-val-GROUP) for each activity. Furthermore, the mean difference seems to show that the estimation of EE is better with the group equation. In conclusion, on the proven basis of this study we are able to validate this new method which permits the estimation of EE from abdominal and rib cage distances. This study also highlights the advantage of using a group equation to the estimate EE.

Conductance through a potential barrier embedded in a Luttinger liquid: Nonuniversal scaling at strong coupling

We calculate the linear response conductance of electrons in a Luttinger liquid with arbitrary interaction ${g}_{2}$, and subject to a potential barrier of arbitrary strength, as a function of temperature. We map the Hamiltonian in the basis of scattering states into an effective low energy Hamiltonian in current algebra form. First the renormalization group (RG) equation for weak interaction is derived in the current operator language both using the operator product expansion and the equation of motion method. To access the strong coupling regime, two methods of deducing the RG equation from perturbation theory, based on the scaling hypothesis and on the Callan-Symanzik formulation, are discussed. The important role of scale-independent terms is emphasized. The latter depend on the regularization scheme used (length versus temperature cutoff). Analyzing the perturbation theory in the fermionic representation, the diagrams contributing to the renormalization group $\ensuremath{\beta}$-function are identified. A universal part of the $\ensuremath{\beta}$-function is given by a ladder series and summed to all orders in ${g}_{2}$. First nonuniversal corrections beyond the ladder series are discussed and are shown to differ from the exact solutions obtained within conformal field theory which use a different regularization scheme. The RG equation for the temperature-dependent conductance is solved analytically. Our result agrees with known limiting cases.