On the Fundamental Property of the Linear Group of Transformation in the Plane

1895 ◽  
Vol 10 (1/6) ◽  
pp. 3
Author(s):  
Arnold Emch
Keyword(s):  
Linear Group ◽  
Fundamental Property ◽  
Group Of Transformation

On generic complexity of the subset sum problem in monoids and groups of integer matrix of order two

2020 ◽  
Vol 25 (4) ◽  
pp. 10-15
Author(s):  
Alexander Nikolaevich Rybalov
Keyword(s):  
Linear Group ◽  
Modular Group ◽  
Special Linear Group ◽  
Second Order ◽  
Integer Matrix ◽  
Subset Sum ◽  
Algorithmic Problems ◽  
Almost All ◽  
Subset Sum Problems ◽  
Generic Complexity

Generic-case approach to algorithmic problems was suggested by A. Miasnikov, I. Kapovich, P. Schupp and V. Shpilrain in 2003. This approach studies behavior of an algo-rithm on typical (almost all) inputs and ignores the rest of inputs. In this paper, we prove that the subset sum problems for the monoid of integer positive unimodular matrices of the second order, the special linear group of the second order, and the modular group are generically solvable in polynomial time.

Surfactant Impurities Can Explain the Jones-Ray Effect

2018 ◽  
Author(s):  
Timothy Duignan ◽  
Marcel Baer ◽  
Christopher Mundy
Keyword(s):  
Surface Tension ◽  
Electrostatic Potential ◽  
Driving Forces ◽  
Salt Water ◽  
Fundamental Property ◽  
Apparent Contradiction ◽  
Low Salt ◽  
Air Water Interface ◽  
Added Salt ◽  
Effect Of Surface

<div> <p> </p><div> <div> <div> <p>The surface tension of dilute salt water is a fundamental property that is crucial to understanding the complexity of many aqueous phase processes. Small ions are known to be repelled from the air-water surface leading to an increase in the surface tension in accordance with the Gibbs adsorption isotherm. The Jones-Ray effect refers to the observation that at extremely low salt concentration the surface tension decreases in apparent contradiction with thermodynamics. Determining the mechanism that is responsible for this Jones-Ray effect is important for theoretically predicting the distribution of ions near surfaces. Here we show that this surface tension decrease can be explained by surfactant impurities in water that create a substantial negative electrostatic potential at the air-water interface. This potential strongly attracts positive cations in water to the interface lowering the surface tension and thus explaining the signature of the Jones-Ray effect. At higher salt concentrations, this electrostatic potential is screened by the added salt reducing the magnitude of this effect. The effect of surface curvature on this behavior is also examined and the implications for unexplained bubble phenomena is discussed. This work suggests that the purity standards for water may be inadequate and that the interactions between ions with background impurities are important to incorporate into our understanding of the driving forces that give rise to the speciation of ions at interfaces. </p> </div> </div> </div> </div>

On the Measurement of Cooperativity and the Physico-Chemical Meaning of the Hill Coefficient

2019 ◽  
Vol 20 (9) ◽  
pp. 861-872 ◽  
Author(s):  
Andrea Bellelli ◽  
Emanuele Caglioti
Keyword(s):  
Ligand Binding ◽  
Hormone Receptors ◽  
Fundamental Property ◽  
Statistical Correlation ◽  
Hill Coefficient ◽  
Biological Macromolecules ◽  
Physico Chemical ◽  
Physiological Relevance ◽  
Minimum Estimate ◽  
The Hill

Cooperative ligand binding is a fundamental property of many biological macromolecules, notably transport proteins, hormone receptors, and enzymes. Positive homotropic cooperativity, the form of cooperativity that has greatest physiological relevance, causes the ligand affinity to increase as ligation proceeds, thus increasing the steepness of the ligand-binding isotherm. The measurement of the extent of cooperativity has proven difficult, and the most commonly employed marker of cooperativity, the Hill coefficient, originates from a structural hypothesis that has long been disproved. However, a wealth of relevant biochemical data has been interpreted using the Hill coefficient and is being used in studies on evolution and comparative physiology. Even a cursory analysis of the pertinent literature shows that several authors tried to derive more sound biochemical information from the Hill coefficient, often unaware of each other. As a result, a perplexing array of equations interpreting the Hill coefficient is available in the literature, each responding to specific simplifications or assumptions. In this work, we summarize and try to order these attempts, and demonstrate that the Hill coefficient (i) provides a minimum estimate of the free energy of interaction, the other parameter used to measure cooperativity, and (ii) bears a robust statistical correlation to the population of incompletely saturated ligation intermediates. Our aim is to critically evaluate the different analyses that have been advanced to provide a physical meaning to the Hill coefficient, and possibly to select the most reliable ones to be used in comparative studies that may make use of the extensive but elusive information available in the literature.

scholarly journals Order Conditions for Sampling the Invariant Measure of Ergodic Stochastic Differential Equations on Manifolds

2021 ◽  
Author(s):  
Adrien Laurent ◽  
Gilles Vilmart
Keyword(s):  
Invariant Measure ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Linear Group ◽  
Langevin Equation ◽  
Numerical Experiments ◽  
Special Linear Group ◽  
Order Conditions ◽  
High Order ◽  
Differential Equations On Manifolds

AbstractWe derive a new methodology for the construction of high-order integrators for sampling the invariant measure of ergodic stochastic differential equations with dynamics constrained on a manifold. We obtain the order conditions for sampling the invariant measure for a class of Runge–Kutta methods applied to the constrained overdamped Langevin equation. The analysis is valid for arbitrarily high order and relies on an extension of the exotic aromatic Butcher-series formalism. To illustrate the methodology, a method of order two is introduced, and numerical experiments on the sphere, the torus and the special linear group confirm the theoretical findings.

Representations induced from the Zelevinsky segment and discrete series in the half-integral case

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ivan Matić
Keyword(s):  
Linear Group ◽  
Local Field ◽  
General Linear Group ◽  
Discrete Series ◽  
Series Representation ◽  
General Linear ◽  
Composition Series ◽  
Induced Representations ◽  
Discrete Series Representation

AbstractLet {G_{n}} denote either the group {\mathrm{SO}(2n+1,F)} or {\mathrm{Sp}(2n,F)} over a non-archimedean local field of characteristic different than two. We study parabolically induced representations of the form {\langle\Delta\rangle\rtimes\sigma}, where {\langle\Delta\rangle} denotes the Zelevinsky segment representation of the general linear group attached to the segment Δ, and σ denotes a discrete series representation of {G_{n}}. We determine the composition series of {\langle\Delta\rangle\rtimes\sigma} in the case when {\Delta=[\nu^{a}\rho,\nu^{b}\rho]} where a is half-integral.

TOPOLOGICAL QUANTIZATION OF THE MAGNETIC FLUX

2000 ◽  
Vol 15 (24) ◽  
pp. 1491-1495 ◽  
Author(s):  
DANIEL WISNIVESKY
Keyword(s):  
Quantum Theory ◽  
Charged Particle ◽  
Magnetic Flux ◽  
Linear Group ◽  
Connected Region ◽  
Magnetic Tube ◽  
Dirac Monopole ◽  
Multiply Connected ◽  
Quantum Problem ◽  
Multiply Connected Region

We discuss the quantum problem of a charged particle in a multiply connected region encircling a magnetic tube, using a theory in which space and internal coordinates are derived from the parameters of a linear group of transformations (group space quantum theory). Based only on symmetry considerations, we show that, the magnetic flux in the tube must be quantized in multiples of the Dirac monopole charge.

scholarly journals Antigen receptor repertoires of one of the smallest known vertebrates

2021 ◽  
Vol 7 (1) ◽  
pp. eabd8180
Author(s):  
Orlando B. Giorgetti ◽  
Prashant Shingate ◽  
Connor P. O’Meara ◽  
Vydianathan Ravi ◽  
Nisha E. Pillai ◽  
...  
Keyword(s):  
Immune Responses ◽  
Antigen Receptor ◽  
Fundamental Property ◽  
Cell Receptor ◽  
Immune Reactivity ◽  
Self Similarity ◽  
Frequency Distributions ◽  
Scale Free ◽  
Scale Free Networks ◽  
Incomplete Sampling

The rules underlying the structure of antigen receptor repertoires are not yet fully defined, despite their enormous importance for the understanding of adaptive immunity. With current technology, the large antigen receptor repertoires of mice and humans cannot be comprehensively studied. To circumvent the problems associated with incomplete sampling, we have studied the immunogenetic features of one of the smallest known vertebrates, the cyprinid fish Paedocypris sp. “Singkep” (“minifish”). Despite its small size, minifish has the key genetic facilities characterizing the principal vertebrate lymphocyte lineages. As described for mammals, the frequency distributions of immunoglobulin and T cell receptor clonotypes exhibit the features of fractal systems, demonstrating that self-similarity is a fundamental property of antigen receptor repertoires of vertebrates, irrespective of body size. Hence, minifish achieve immunocompetence via a few thousand lymphocytes organized in robust scale-free networks, thereby ensuring immune reactivity even when cells are lost or clone sizes fluctuate during immune responses.

scholarly journals The log-linear group-lasso estimator and its asymptotic properties

Bernoulli ◽  
2012 ◽  
Vol 18 (3) ◽  
pp. 945-974 ◽  
Author(s):  
Yuval Nardi ◽  
Alessandro Rinaldo
Keyword(s):  
Linear Group ◽  
Asymptotic Properties ◽  
Group Lasso ◽  
Log Linear ◽  
Lasso Estimator
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